Geometric Dimensioning and Tolerancing (GD&T) Reference Book
Version 2.0 written by:
Due to increased complexity of products, and based on new function and process technologies, enhanced sensitivity is required at the dimensional management work for costeffective implementation of qualitative specifics in parts and systems. The company’s specific orientation to methods like “Best Practice” and “Lessons Learned” in respect of required values will not only prevent losses but also avoid increases on costs on account of unnecessary additional alignment work in the manufacturing process. Target conflicts arising from the well-known cross-effects between a wish and its feasibility and cost-efficiency can be changed by this.
Resume: ⇒ Tolerances play a critical role in the part and assembly group manufacturing and assembling as they bear on both function and costs.
Recommendation for implementation at Johnson Controls
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Table of Contents 1
Introduction: Tolerances ............................................................................. 13 1.1
What is Tolerance? ...............................................................................................13
1.1.1
Dimensional Tolerance .......................................................................................15
1.1.1.1 1.1.2
Form and Position (Geometric) Tolerances.........................................................16
1.1.3
Design Deviations ...............................................................................................17
1.1.4
Tolerance Zones .................................................................................................18
1.2
Why Do We Need Tolerances? .............................................................................19
1.3
What Types of Tolerance Deviations Do Exist?.....................................................20
1.4
What is “Right” Tolerance?....................................................................................21
2
Geometric Dimensioning and Tolerancing (GD&T) .................................. 22 2.1
Historical Background ...........................................................................................22
2.2
Norms and Standards ...........................................................................................24
2.2.1
What is a Norm/Standard? ..................................................................................24
2.2.2
Organizations .....................................................................................................25
2.2.3
Summary of Relevant DIN Standards .................................................................26
2.2.4
General Manufacturing Tolerances .....................................................................27
2.2.5
Legislative Framework for Standards ..................................................................28
2.2.6
OEM related overview for GD&T Standards........................................................28
2.3
3
Benefits of GD&T ..................................................................................................29
Types of Tolerances .................................................................................... 30 3.1
Tolerances of Form ...............................................................................................30
3.2
Tolerances of Profile .............................................................................................31
3.3
Tolerances of Orientation ......................................................................................32
3.4
Tolerances of Location ..........................................................................................33
3.5
Runout Tolerances ................................................................................................34
4
3
Different dimension groups ......................................................................16
Representation of Tolerances..................................................................... 36 4.1
Summary: Standard Drawing Layout .....................................................................36
4.2
Baseline Dimensioning ..........................................................................................37
4.2.1
Tolerance/Datum Arrow ......................................................................................37
4.2.2
Ideal/Theoretically Precise Dimension ................................................................39
4.2.3
Controlled Dimension..........................................................................................40
4.2.4
Datums ...............................................................................................................40
4.3
Feature Control Frame ..........................................................................................41
4.3.1
Controlled Properties ..........................................................................................43
4.3.2
Diameter .............................................................................................................45
4.3.3
Tolerance Values ................................................................................................45
4.3.4
Material Conditions .............................................................................................46
4.3.5
Datums ...............................................................................................................46
4.3.6
Additional Textual Data .......................................................................................47
4.3.7
Single and Combined Feature Control Frames ...................................................48
4.3.7.1
Single Feature Control Frame ..................................................................48
4.3.7.2
Combined Feature Control Frame ............................................................48
4.3.7.3
Example: Position Tolerance ....................................................................49
4.3.7.3.1 Single Feature Position Control Frame ................................................49 4.3.7.3.2 Combined Feature Position Control Frame ..........................................50 4.3.7.4
Example: Profile Tolerance ......................................................................50
4.3.7.4.1 Single Feature Profile Control Frame ...................................................51 4.3.7.4.2 Combined Feature Tolerance Frame with Directional Limit ..................51 4.3.7.4.3 Combined Feature Control Frame with Form Variation Ratio ...............52 4.3.7.5
Composite Feature Control Frame ...........................................................53
4.3.7.5.1 Example: Composite Position Tolerance..............................................53 4.4
Additional Symbols ...............................................................................................54
4.5
General Table of Tolerances .................................................................................55
5
Datums .......................................................................................................... 56 5.1
What are Datums good for? ..................................................................................57
5.2
Datum References in Drawings .............................................................................58
5.2.1
Datum Triangle ...................................................................................................58
5.2.2
Datum Locations / Datum Features.....................................................................58
5.2.3
Sequential Order of Datum Indications According to MBN 11011 .......................61
5.2.4
Axis / Plane as Datum.........................................................................................62
5.2.5
Coplanar Surface as Datum ................................................................................64
5.2.6
Unfolded State as Datum ....................................................................................64
5.2.7
Difference Between Datum Plane and Datum Location.......................................65
5.2.8
Sequence of Datums related to Datum Reference Frame ...................................66
5.3
4
Datum System ......................................................................................................68
5.3.1
6 Degrees of Freedom ........................................................................................68
5.3.2
The 3-2-1 Rule ....................................................................................................69
5.3.3
Determination of Datum System .........................................................................75
5.3.4
Datum System Requirements .............................................................................76
5.3.5
Datum System Arrangement ...............................................................................76
5.3.6
Determination of Datum/Locating Distance (Effective Distance) .........................77
5.3.7
Determination of Unilateral Surface Tolerances ..................................................79
5.3.8
Definition of Datums through Coordinate Data ....................................................81
5.4
Locator Selection Strategy ....................................................................................82
5.4.1
Hole/Oblong Hole Principle .................................................................................82
5.4.2
Opening ..............................................................................................................83
5.4.3
Distance between Locators .................................................................................84
5.4.4
Low Strain Arrangement with Locators ...............................................................84
5.4.5
Curvilinear Surfaces as Locator ..........................................................................85
5.4.6
Pressing Tools and Locators...............................................................................85
5.4.7
Locators on Vertical Surfaces .............................................................................85
5.4.8
Locator Block and Pin Layout .............................................................................86
5.4.9
Locator Pins on Plastic Parts ..............................................................................86
6
Material Conditions...................................................................................... 87 6.1
Regardless of Feature Size (RFS) Material Conditions .........................................87
6.2
Maximum Material Condition (MMC) .....................................................................87
6.3
Least Material Condition (LMC) .............................................................................88
6.4
Bonus Tolerance ...................................................................................................88
6.5
Comparison between MMC and RFS ....................................................................89
6.6
Comparison of MMC and LMC ..............................................................................91
6.7
Hole-Piston Interplay .............................................................................................92
6.7.1 6.8
Effective Condition ................................................................................................93
6.8.1
7
Example of MMC ................................................................................................92
Example: Effective condition ...............................................................................94
Tolerance Principles .................................................................................... 96 7.1
Tolerance Principle ...............................................................................................97
7.1.1
Basics of Envelope Principle ...............................................................................97
7.1.2
Tolerance by Envelope Principle .........................................................................98
7.1.3
Basics of Independence Principle .....................................................................100
7.1.4
Tolerance by Independence Principle ...............................................................100
8
Differences between ASME and ISO Standard ........................................ 104
9
Specifics of Use of MBN 11011 ................................................................. 112
5
9.1
Surface Lines as Datums ....................................................................................112
9.2
Angular Measure Tolerances (± Tolerances).......................................................112
9.3
Stepped Measures ..............................................................................................113
9.4
Surface Profile Outline Symbols ..........................................................................113
9.5
Concentricity / Coaxiality, Symmetry ...................................................................114
9.6
Combined Feature Control Frame for Position and Surface Tolerances ..............114
10
Best Business Practice (Simplified GD&T) .............................................. 116
10.1
Position vs. Concentricity ....................................................................................116
10.2
PROFILE VS. PERPENDICULARITY .................................................................117
10.3
PROFILE VS. PARALLELISM.............................................................................118
10.4
PROFILE VS. ANGULARITY ..............................................................................119
10.5
PROFILE VS. POSITION ....................................................................................120
11
Measurement Uncertainty and Tolerances .............................................. 121
11.1
Measuring and Manufacturing Process Capability ...............................................122
11.2
Determination of Measurement Uncertainty ........................................................123
11.3
Measurement Uncertainty Considerations...........................................................125
11.4
Measurement Uncertainty Implications................................................................126
12
Tolerancing Processes and Concepts ..................................................... 127
12.1
Product Definition ................................................................................................127
12.2
Illustration of Tolerancing Process by Means of General Car Development Process 127
12.3
Tolerance Assessment in FMEA .........................................................................131
12.3.1 12.4
Process Prerequisites for Functional Dimensioning Concept ..............................133
12.4.1 12.5
13
Required Data and Information .....................................................................133 VDA Standardized Tolerancing Process Draft .....................................................136
Tolerance Analysis and Tolerance Simulation ........................................ 137
13.1
What Is Tolerance Analysis? ...............................................................................137
13.2
What Do We Need Tolerance Analysis for? ........................................................137
13.3
Prerequisites for Effective Tolerance Analysis.....................................................138
13.3.1 13.4
Requirements Placed on Drawings ...............................................................139 Tolerance Simulation ..........................................................................................140
13.4.1
6
Example for Assignment of FMEA Ratings to Characteristic Classes ............132
One-dimensional Simulation / Calculation .....................................................142
13.4.1.1
Example of One-dimensional Simulation / Calculation............................143
13.4.1.2
Excel Spreadsheet for One-dimensional Simulation / Calculation ..........143
13.4.2
3D Analysis Process .....................................................................................144
13.4.2.1
Monte Carlo Simulation and Sensitivity Analysis ( HLM Analysis) ..........146
13.4.2.1.1 Monte Carlo Simulation....................................................................148 13.4.2.1.2 Sensitivity Analysis (HLM Analysis) .................................................149 13.4.3
13.4.3.1
Tolerance and Manufacturability Calculation ..........................................152
13.4.3.2
Examples of Manufacturability for cp and cpk ........................................152
13.5
14
Example: 3D / 1D Method Workflow for Interiors .................................................153
Tolerance Management at JC: Dimensional Management ..................... 154
14.1
Dimensional Management Objectives .................................................................154
14.2
General Tolerance Analysis Process at JC .........................................................157
14.2.1
Relevant GD&T Reports According to PLUS Action Plan ..............................158
14.2.2
Support Options for Individual PLUS Stages .................................................159
14.2.3
Tolerancing Communication Platform: Workgroup on Tolerancing ................160
14.3
15
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Characteristic Values of Process Capabilities Cp and Cpk ............................150
Quality Objectives at Johnson Controls ...............................................................161
Annex .......................................................................................................... 162
15.1
Guidance for Practice..........................................................................................162
15.2
Wikipedia Page on Dimensional Management ....................................................164
Table of Figures Figure 1:Comparison of a geometrically ideal shape, tolerance zone and true profile ...........14 Figure 2:Dimensional tolerance ............................................................................................15 Figure 3:dimension groups ...................................................................................................16 Figure 4: Zones of tolerance .................................................................................................18 Figure 5:Qualitative characteristics .......................................................................................19 Figure 6: Hole series alignment precision .............................................................................19 Figure 7: Gap & Flush focus .................................................................................................19 Figure 8: Possible errors if tolerance specifications are absent ............................................20 Figure 9: Deviation ratios......................................................................................................21 Figure 10: Representation of a standard drawing layout .......................................................36 Figure 11: Representation of a tolerated feature...................................................................37 Figure 12: Representation of a tolerated feature (2) .............................................................38 Figure 13: Representation of a tolerance arrow (datum arrow) .............................................38 Figure 14: Representation of a tolerance arrow (datum arrow) (2) ........................................38 Figure 15: Representation of a tolerance arrow (datum arrow) (3) ........................................39 Figure 16: Representation of the ideal/theoretically precise dimension.................................39 Figure 17: Representation of a controlled dimension ............................................................40 Figure 18: Representation of datums....................................................................................40 Figure 19: Representation of a feature control frame ............................................................42 Figure 20: Representation of descriptions in a feature control frame ....................................42 Figure 21: Representation of symbols of controlled properties .............................................43 Figure 22: Diameter symbol..................................................................................................45 Figure 23: Indication of tolerance values ..............................................................................45 Figure 24: Datum reference letter indications in a feature control frame ...............................46 Figure 25: Datum indication according to coordinates ..........................................................46 Figure 26: XYZ coordinate system........................................................................................47 Figure 27: Additional textual data .........................................................................................47 Figure 28: Additional textual data (2) ....................................................................................47 Figure 29: Example – additional textual data ........................................................................48 Figure 30: Single feature control frame .................................................................................48 Figure 31: Combined feature control frame ..........................................................................48 Figure 32: Single/combined feature control frame with a position tolerance example ...........49 Figure 33: Single feature position control frame....................................................................49 Figure 34: Combined feature position control frame .............................................................50 Figure 35: Single/combined feature control frame with a profile tolerance example ..............50 Figure 36: Single feature control frame .................................................................................51 Figure 37: Combined feature profile tolerance frame with a directional limit .........................51 Figure 38: Combined feature control frame with a form deviation ratio .................................52 Figure 39: Composite feature control frame..........................................................................53 Figure 40: Composite position tolerance ..............................................................................53 Figure 41: Datum feature......................................................................................................56 Figure 42: Datum – datum feature relationship .....................................................................56 Figure 43: Sequential order of datums..................................................................................57 Figure 44: Representation options for datum triangles relating to different datum features ...58 Figure 45: Types of datum features/datum locations ............................................................59
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Figure 46: Surface datum locations ......................................................................................59 Figure 47: Line datum locations............................................................................................60 Figure 48: Point datum locations ..........................................................................................60 Figure 49: Off-frame indication of a datum............................................................................61 Figure 50: Datum referencing sequence ...............................................................................61 Figure 51: Sequential order of datums..................................................................................62 Figure 52: Central plane of outer datum features..................................................................62 Figure 53:Central plane of an inner datum feature................................................................62 Figure 54: A datum axis of an outer dimensioned feature (shaft) ..........................................63 Figure 55: Datum axis of an inner dimensioned feature (hole) ..............................................63 Figure 56: A datum plane with a flatness tolerance ..............................................................63 Figure 57: Coplanar plane as datum.....................................................................................64 Figure 58: Unfolded state as datum ......................................................................................64 Figure 59: Difference between a datum plane and a datum location.....................................65 Figure 60: Effects related to different datum sequences .......................................................67 Figure 61: 6 degrees of freedom .........................................................................................68 Figure 62: 6 degrees of freedom (2) .....................................................................................68 Figure 63: 3-2-1 rule .............................................................................................................69 Figure 64: 3-2-1 rule (2).......................................................................................................70 Figure 65: Example 1 for the 3-2-1 rule (1) ...........................................................................70 Figure 66: Example 1 for the 3-2-1 rule(2) ............................................................................71 Figure 67: Example 2 for the 3-2-1 rule ................................................................................71 Figure 68: Example2 for the 3-2-1 rule (2) ............................................................................72 Figure 69: Example 3 for the 3-2-1 rule ................................................................................72 Figure 70: Example 4 for the 3-2-1 rule ................................................................................73 Figure 71: Example 4 for the 3-2-1 rule (2) ...........................................................................73 Figure 72: Example 5 for the 3-2-1 rule ................................................................................74 Figure 73: Determination of a datum system ........................................................................75 Figure 74: Determination of a datum system influencing measurement results ....................75 Figure 75: Datum system arrangement – part defect ............................................................76 Figure 76: A part with a defined tolerance in different systems .............................................77 Figure 77.Determination of an effective/locating distance .....................................................77 Figure 78. Determination of the datum/locating distance (2) .................................................78 Figure 79. Determination of the datum (locating) distance (critical area) ..............................78 Figure 80. Determination of unilateral surface tolerances .....................................................79 Figure 81: Determination of unilateral surface tolerances (Example 1) .................................79 Figure 82: Determination of unilateral surface tolerances (Example 2) .................................80 Figure 83: Determination of unilateral surface tolerances (Example 3) .................................80 Figure 84: Definition of datums through coordinate data.......................................................81 Figure 85: The hole/oblong hole principle .............................................................................82 Figure 86: The hole/oblong hole principle (2)........................................................................83 Figure 87: Locator selection strategy ....................................................................................83 Figure 88: Distance between locators...................................................................................84 Figure 89: Locator pins on plastic parts ................................................................................86 Figure 90: Representation of bonus tolerances ....................................................................88 Figure 91: Representation of tolerance array........................................................................89 Figure 92:Example of MMC ..................................................................................................92
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Figure 93:Comparison between MMC and LMC for an outer feature ....................................93 Figure 94: Tolerance principles ............................................................................................96 Figure 95: Tolerance principles (2) .......................................................................................97 Figure 96: Examples of applications where the envelope principle cannot be used ..............99 Figure 97: DIN 7167 Tolerance ............................................................................................99 Figure 98: DIN 7167 Tolerance (2) .....................................................................................100 Figure 99: ISO 8015 Tolerancing ........................................................................................101 Figure 100: Taylor testing principle .....................................................................................102 Figure 101: Taylor testing principle (2) ...............................................................................103 Figure 102: Drawing representations ..................................................................................105 Figure 103: Geometric tolerance notations .........................................................................106 Figure 104: Fig. 104: Special tolerancing............................................................................107 Figure 105: Special location tolerances ..............................................................................108 Figure 106: Special feature control frames .........................................................................109 Figure 107: Profile tolerancing ............................................................................................110 Figure 108: Boundary control .............................................................................................111 Figure 109: Surface line as datum ......................................................................................112 Figure 110: Angular measure tolerances ............................................................................112 Figure 111: Stepped measures ..........................................................................................113 Figure 112: Surface profile outline symbols ........................................................................113 Figure 113: Concentricity / coaxiality and symmetry ...........................................................114 Figure 114: Combined feature control frame for position and surface tolerances................114 Figure 115: Best Practice: Positon vs. Concentricity ...........................................................116 Figure 116: Not preferred: Position vs. Concentricity ..........................................................116 Figure 117: Best Practice: Profile vs Perpendicularity.........................................................117 Figure 118: Not preferred: Position vs. Perpendicularity .....................................................117 Figure 119: Best Practice: Profile vs. Parallelism................................................................118 Figure 120: Non-Preferred: Profile. vs Parallelism ..............................................................118 Figure 121: Best Pracice: Profile vs. Angularity ..................................................................119 Figure 122: Non-Preferred: Profile vs. Angularity...............................................................119 Figure 123: Best Practice: Profile vs. Position ....................................................................120 Figure 124: Non-Preferred: Profile vs. Position ...................................................................120 Figure 125: Measurement result and measurement uncertainty .........................................121 Figure 126: Overlay of manufacturing process and measuring process variances..............122 Figure 127: Effect of %GRR on the characteristic quality process capability variable Cp....123 Figure 128: extended area on uncertainty, area of conformity, area of nonconformity ........125 Figure 129: Areaof tolerance (USG – OSG) .......................................................................126 Figure 130: System boundaries of a complete vehicle ........................................................128 Figure 131: A part and a component in a complete vehicle ................................................129 Figure 132: Dimensional quality implementation process ...................................................133 Figure 133: Concept stage ................................................................................................134 Figure 134: Development ...................................................................................................135 Figure 135 Representation of results (quality- and function-related customer requirements) ...........................................................................................................................................137 Figure 136: Product requirements for the tolerance analysis ..............................................138 Figure 137: : Requirements placed on drawings .................................................................139 Figure 138: Requirements placed on drawings (2) .............................................................139
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Figure 139: 1D and 3D simulation ......................................................................................140 Figure 140: Execution of 1D Studies ..................................................................................143 Figure 141: 1D Excel spreadsheet......................................................................................143 Figure 142: 3D analysis overview .......................................................................................144 Figure 143: Development process assessment ..................................................................145 Figure 144: Comparison between the Monte Carlo simulation and the sensitivity analysis .147 Figure 145: Monte Carlo simulation procedure ...................................................................148 Figure 146: Normal distribution...........................................................................................148 Figure 147: Sensitivity analysis procedure..........................................................................149 Figure 148: HLM Report .....................................................................................................149 Figure 149: Six Sigma region in a HLM Report ...................................................................150 Figure 150: Tolerance and manufacturability calculation ....................................................152 Figure 151: Example of a garage for cp and Cpk................................................................152 Figure 152: Example of 1D and 3D workflow for interiors ...................................................153 Figure 153: Costs needed for manufacturability..................................................................155 Figure 154: Cost reduction through preventive action by DM..............................................156 Figure 155: General tolerance analysis process at JC ........................................................157 Figure 156: GD&T reports in the PLUS plan .......................................................................158 Figure 157: Support options in the PLUS plan ....................................................................159 Figure 158: Workgroup on tolerancing ................................................................................160 Figure 159: Quality objectives at JC ...................................................................................161
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Table Overview Table 1: Design deviations ...................................................................................................17 Table 2: Summary of relevant DIN standards .......................................................................26 Table 3: General manufacturing tolerances ..........................................................................27 Table 4: OEM related GD&T Standard .................................................................................28 Table 5: Tolerances of form ..................................................................................................30 Table 6: Tolerances of profile ...............................................................................................31 Table 7: Tolerances of orientation ........................................................................................32 Table 8: Tolerances of location (position) .............................................................................33 Table 9: Runout tolerances ..................................................................................................35 Table 10: Symbols for form tolerance indications .................................................................43 Table 11: Symbols for profile tolerance indications ...............................................................44 Table 12: Symbols for orientation tolerance indications ........................................................44 Table 13: Symbols for location tolerance indications ............................................................44 Table 14: Symbols for runout tolerance indications ..............................................................45 Table 15: Material conditions ................................................................................................46 Table 16: Additional symbols ................................................................................................54 Table 17: General table of tolerances ...................................................................................55 Table 18: Comparison between MMC and RFS....................................................................90 Table 19: Comparison between MMC and LMC ...................................................................91 Table 20: Comparison between MMC and LMC for an inner feature: ...................................92 Table 21: Comparison between MMC and LMC for an outer feature ...................................93 Table 22: Effective condition with an inner feature ( MMC) ...................................................94 Table 23: Effective condition table of an outer feature (MMC) ..............................................94 Table 24: Effective condition table of an inner feature (LMC)................................................95 Table 25: Effective condition table of an outer feature ( LMC) ..............................................95 Table 26: Form deviations and envelopes of simple geometric features ............................102 Table 27:Use of unilateral surface tolerances .....................................................................115 Table 28: Overview of uncertainty components ..................................................................124 Table 29: Measurement uncertainty considerations for limit values (tolerance zone boundaries) ........................................................................................................................125 Table 30: Assignment of FMEA ratings to characteristic classes ........................................132
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1 Introduction: Tolerances 1.1 What is Tolerance? A part basically comprises individual geometric-shape features. Though a design engineer indicates the geometrically ideal shape of a product in its drawing, due to manufacturing inaccuracies and measurement uncertainties real values vary to some extent around the desired ideal value. The maximum permissible deviation of actual values from the desired value is set by the engineer by means of tolerance data. In addition to functionality of a part, the aim behind such tolerance data definition is the fundamental interchangeability principle. Independently manufactured parts should be matchable within predefined limits without selection or modification, and able of performing the required function. ‘Tolerance’ refers to the entire range over which a specific dimension may vary; the following types of tolerances are distinguished: •
dimensional tolerance
•
form tolerance
•
position tolerance
Dimensional tolerance refers to the dimension range within which a dimension may vary with regard to its geometrically ideal measure (e.g. a hole may not be smaller than a minimum measure).
Form tolerance refers to the dimension range within which a geometric feature may vary with regard to its geometrically ideal shape (e.g. the hole jacket surface must not be excessively curved).
Position tolerance refers to the dimension range within which a geometric feature may vary with regard to its geometrically ideal position relative to other geometric features. Two tolerances are distinguished here: orientation tolerance (e.g. a hole must not be excessively skewed) and location tolerance (e.g. a hole must not be positioned in a wrong location).
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The following are representations of the difference between a geometrically ideal shape, tolerance zone and the true profile for a line profile.
required geometrically ideal shape
The engineer has assigned a geometrically ideal shape to the part. tolerance
tolerance zone
The part has been assigned a tolerance of 0.04 mm. Such value may be dragged as a kind of “frame” around the geometrically ideal shape, which is then referred to as ‘tolerance zone’.
True profile
The true profile is the resulting feature of the real part and it shows whether the tolerance has been respected. Figure 1:Comparison of a geometrically ideal shape, tolerance zone and true profile
14
1.1.1 Dimensional Tolerance The standards system of ISO (International Standards Organization) lays down that a dimensional tolerance demarcates, using only two-point measurement, the established actual local dimension of a geometric feature. A dimensional tolerance is defined by means limit dimensions or tolerance symbols, without setting any limitations as to shape or position.
The figure shows the required outline of a hole.
The dimensional tolerance defines the hole diameter.
Where only a dimensional tolerance is stated, different hole alternatives are possible and all of them will comply with the dimensional tolerance set. The figure illustrates, however, how the actual outline may deviate from that desired.
Figure 2:Dimensional tolerance
15
1.1.1.1 Different dimension groups
Related to distance dimensions we distinguish between four dimension groups.
Figure 3:dimension groups
a) Outer dimension (e.g. bolt diameter or sheet-metal thickness) b) Inner dimension (e.g. hole diameter or groove width): This two groups connect alternate surfaces or elements of the same surface (at lateral area) c) Fan dimension (e.g. step length or groove depth): They are used between equal orientated surfaces. A fan dimension can only measured with a auxiliary tool. (e.g. with a docked ruler.) This kind of dimension should be defined with a clear drawing enrollment. d) Distance dimension (e.g. Hole center distance or pitch dimension): They have a extraordinary status, because it is no real dimensional tolerance, but rather a position tolerance.
1.1.2
Form and Position (Geometric) Tolerances
As described earlier in this section, every workpiece deviates to some extent from the geometrically ideal appearance. However, the critical factors affecting functionality of a mechanically manufactured workpiece are shape and position parameters. In line with that, shape and position parameters are indicated in a drawing only if they are necessary for operability and/or production cost-efficiency of the workpiece. The procedure for determining shape and position tolerances relies on the tolerance zone definition principle, meaning that a zone within which the element concerned (plane, axis or central plane) must fall needs to be defined.
16
1.1.3 Design Deviations Design deviations
True deviation
Geometrically ideal (required)
Nominal design
nominal design
Dimensional deviation
Shape deviation
Position deviations
Dimensional deviation
Shape deviation
Location deviation
Orientation deviation
Surface
Surface deviation
Table 1: Design deviations
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1.1.4 Tolerance Zones Geometric features with indicated tolerances must be always within the tolerance zone. Basically, tolerance zones can be defined using either of the following methods: -
as area between two equidistant lines or two parallel straight lines
-
as space between two parallel planes
-
as space within a cylinder
-
as space within a rectangular prism or a sphere
-
as circle area
-
as area between two concentric circles
-
as space between two coaxial cylinders
Area between two
Space between two
Space inside
parallel straight lines
parallel planes
a cylinder
Space inside
Area between two
Space between two
a rectangular prism
concentrically circles
coaxial cylinders
Figure 4: Zones of tolerance
A tolerance zone is demarcated by means of two border lines or border planes or border circles that correspond to the ideal shape of the geometric feature. The tolerated feature may have any direction within the tolerance zone, unless other limiting data are provided.
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1.2 Why Do We Need Tolerances? Tolerances Principally, a product is subject to certain quality requirements that must be met to ensure the required quality characteristics – qualitative requirements placed on the product
function-oriented
customer-oriented Figure 5:Qualitative characteristics
function of the part/assembly group. group For example, hole series alignment precision requires a function-oriented focus.
Figure 6: Hole series alignment precision
A customer-oriented oriented focus, in turn, is driven by optical requirements. Good ood gap & flush with design-oriented oriented consideration is required here. Flush Gap
Figure 7: Gap & Flush focus
19
Q1P = D + M Quality product = design engineering activities + manufacturing activities
The definition of a tolerance related to geometry should cause the effect, that the geometry part deviates from the notional ideal shape only within this tolerance zone. In practice, for example, a sheet-metal edge serving as endstop must be sufficiently flat; or a rolling-element bearing seat must have sufficient cylindricity.
Smart engineering concepts using geometric tolerancing will ensure that specified quality targets of the final product be met.
Where no tolerances are defined, the following consequences may emerge:
The pin wouldn’t enter the hole (shape error)
The pin’s position in the hole would be skewed (position error)
Figure 8: Possible errors if tolerance specifications are absent
Conclusion: Form and position tolerances are required to ensure trouble-free interchangeability of parts and assembly groups!
1.3 What Types of Tolerance Deviations Do Exist? Basically, three different tolerance deviations are distinguished: -
part/material-specific deviations
-
process deviations
-
individual part deviations
The following figure shows the ratios of the three deviation types:
20
part/material-specific deviations
process deviations
individual part deviations Figure 9: Deviation ratios
Process deviations result from the part assembling sequence, assembly clearances, directional orientation of parts and the tool design.
1.4
What is “Right” Tolerance?
The following points should be considered at the use of tolerances:
if a specified tolerance is two narrow, manufacturing problems arise and the product costs excessively increases
if a specified tolerance is to broad, process problems are encountered and the attainment of quality (functionality) objectives becomes more difficult.
A “right” tolerance is as large as possible and as small as necessary!
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2 Geometric Dimensioning and Tolerancing (GD&T) GD&T (Geometric Dimensioning and Tolerancing) is an international symbol-based language that is used on engineering drawings to accurately describe or determine the function of a part or a certain assembly and the intrinsic objective of the drawing. It complements the traditional “plus-minus” or coordinate methods. The main purpose of GD&T is to describe part/assembly geometric requirements so as to ensure that the part/assembly will have the required shape, alignment precision and function. The GD&T symbol language defines the: •
size
•
shape
•
orientation/direction
•
component position/location
The strictly defined, symbol-based GD&T language aims at preventing erroneous interpretations of comments and/or notes. The symbols clarify how a certain feature should be made and controlled as GD&T precisely defines the part testing principle (gage check or measurement).
2.1 Historical Background The first use of technical drawings with tolerances dates back to the turn of the 19th and 20th centuries. Before that, only small or dimension-less specifications were used, thus leaving a large room for decision-making and manufacturing deliberations. Along with growing requirements on products and the emergence of measurement methods with increasingly improved efficiency, the number and types of tolerance specifications have increased. The following types of tolerances have been defined: •
form tolerances
•
profile tolerances
•
orientation tolerances
•
position tolerances
•
runout tolerances
The GD&T theory was developed by Stanley Parker at the Torpedo royal factory in Alexandria (Scotland) in the late 1930’s, and it was first accepted as British “standard” by the
22
British Navy. Different publications on tolerances of both British and US origins triggered interest also on the part of the International Standards Organization (ISO). The major contributors to the development of the GD&T system were the aviation and military industries. During the World War II, the exchange of arms between the USA and Great Britain revealed the need for universal interchangeability of different product parts. 1920: The first GD&T applications in the USA were measuring systems using specialist measurement requirement terms as opposed to formal tolerance systems. Earl Buckingham’s work can be considered as an example of the new system. 1940: One example of industrial standards comes from Chevrolet Division of General Motors Corporation 1945: The first army-related work was published, entitled “The U.S. Army Ordnance Manual on Dimensioning and Tolerancing“. The G.A Gladmann’s “Drawing Office Practice in Relation to Interchangeable Components” was presented at an annual meeting of SAE military engineers in Detroit and led to an extensive discussion. 1949: MIL-STD-8 was the first standard to find its firm place in all military sectors. Though no dimensioning symbols were used in it, it contained basic dimensioning specifications as well as definitions for datums (or RPS/MLP points), as well as tolerance descriptions comparable to the today’s Y14.5 standards. 1953: MIL-STD-8A was the first US concept to determine the future development, containing the first examples of geometric symbols for datum (reference) points, flatness, straightness, perpendicularity, parallelism, concentricity and proper positioning. 1959: MIL-STD-8B is a follow-up to MIL-STD-8A, adding to it right-angle tolerance zones, perfect shapes with the maximum material condition, M- and S-adjustments and zero tolerances with the M-adjustment. 1963: MIL-STD-8C was another follow-up to the preceding standards, though featuring a greater focus placed on the illustration of different terms. Moreover, projected tolerances were incorporated. 1973: ANSI Y14.5 standard contains the diameter symbol, composite position tolerances, datum references, projected tolerance symbols and dual dimensioning systems. 1982: 1982 ANSI Y14.5 standard provides more in-depth details as compared to its predecessor of 1973. Some further symbols were added and dimensioning attributes further elaborated. 1994: 1984 ANSI Y14.5 standard contains positioning of 2 individual parts, profile assembling, controlled radius and some new symbols. The dual dimensioning system was deleted.
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2.2 Norms and Standards The purpose of standardization is reproducibility of production outputs and comparable quality standards through application of operation-specific norms.
2.2.1 What is a Norm/Standard? Standard is a document that has been proposed, upon agreement with the stakeholders involved, for a particular process or a service. Stakeholders may include manufacturers, sellers, buyers, consumers and production certification bodies. Such a document contains technical marks or other specific criteria to ensure its uniform application in form of rules, guidelines or definitions. The application of standards guarantees to all operators an unambiguous reference in terms of technical marking, quality, feasibility and safety. Products and services should be designed with a focus on the objective and be both comparable and compatible. Standards present a summary of best practices. They represent the outcome derived from experience and knowledge of all stakeholders and have been developed with a view to satisfying the demand from the society and the technology.
Special standard means: ● a generally accepted standard determined by certain processes ● a recognized engineering rule that has been developed during a standardization process and exists in a paper form as standard sheet
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2.2.2
Organizations
DIN means “Deutsches Institut für Normung” – German Standardization Institution, which is the national standardization organization of the Federal Republic of Germany. It pursues the role of the German member of European and international standardization organizations for relevant tasks. The “International Standardization Organization” (ISO) is an international association of standardization organizations. It prepares international standards and planned standardization procedures and activities for development and implementation of rules to unify tangible and intangible objects. DIN-ISO then refers to German unmodified transposition of an ISO standard. EN is the acronym of “European Norm”, referring to rules that have been ratified by one of the three European Standardization Committees. DIN EN ISO: standards developed under the auspices of ISO or the “European Committee for Standardization” that are then published by both organizations.
ASME (“American Society of Mechanical Engineers”) is a professional association of mechanical engineers in the USA. One of principal functions of the Association is development of technical guidelines and standards. ASME Standards are applied worldwide. In the dimension, geometry and surface standardization sector, it applies to those German businesses that are manufacturing in the USA, or in Germany according to US drawings. The current US standard applying to the entire Dimensioning and Tolerancing complex is ASME Y14.5M – 1994. Dimensioning and Tolerancing The structure and scope of the ASME standard differs to some extent from its DIN-ISO counterparts, and there are also some differences in the content in certain points.
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2.2.3 Summary of Relevant DIN Standards Standard
Title
DIN 7167
Relationship between tolerances of size, form, and parallelism; envelope requirement without individual indication on a drawing
DIN 7185
Statistical tolerancing: terms, application guidelines and drawing data
DIN 16901
Plastic moldings - Tolerances and acceptance conditions for linear dimensions
DIN ISO 286 - Part 1
ISO system of limits and fits - Bases of tolerances, deviations and fits
DIN ISO 286 - Part 2
ISO system of limits and fits- Tables of standard tolerance grades and limit deviations for holes and shafts
DIN ISO 1101
Technical drawings - Tolerancing of form, orientation, location and run-out Generalities, definitions, symbols, indications on drawings
DIN ISO 1660
Technical drawings - Dimensioning and tolerancing of profiles
DIN ISO 2692
Geometrical product specifications - Geometrical tolerancing - Maximum material condition
DIN ISO 2768 - Part 1
General tolerances - Tolerances for linear and angular dimensions without individual tolerance indications
DIN ISO 2768 - Part 2
General tolerances - Geometrical tolerances for features without individual tolerance indications
DIN ISO 3040
Technical drawings - Dimensioning and tolerancing - Cones
DIN ISO 5459
Technical drawings – Geometrical tolerancing - Datums and datum-systems for geometrical tolerances
DIN ISO 8015
Technical drawings - Fundamental tolerancing principle
DIN ISO 10578
Technical drawings - Tolerancing of orientation and location - Projected tolerance zone
DIN ISO 10579
Technical drawings – Dimensioning and tolerancing - Non-rigid parts
DIN EN ISO 5458
Geometrical Product Specifications (GPS) - Geometrical tolerance Positional tolerance Table 2: Summary of relevant DIN standards
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2.2.4
General Manufacturing Tolerances
Manufacturing process
Standard Indication example
Existing tolerances/comments
Molding
DIN 6930
DIN 6930m
Dimension, coaxiality, symmetry (partially), straightness, flatness (only for sections)
Bending/molding
DIN 6930
DIN 6930m s DIN 6935
Dimensions, radiuses, angles, coaxiality, symmetry (partially)
DIN 6935
Straightness, flatness (only for sections) Plastic moldings
DIN 16901
DIN 16901120
For longitudinal dimensions
Deep drawing
none
DIN ISO 2768-mH
Straightness, flatness, circularity, parallelism, perpendicularity, symmetry, runout
Pipe bending
none
DIN ISO 2768-mH
Straightness, flatness, circularity, parallelism, perpendicularity, symmetry, runout
(pipe as semiproduct)
DIN 2393 DIN 2394 DIN 2395
Welding
DIN 8570
DIN ISO 13920-AE
Dimension, angle, flatness, parallelism
Chip machining, turning
DIN ISO 2768
DIN ISO 2768-mH
Straightness, flatness, circularity, parallelism, perpendicularity, symmetry, runout
Disc springs
DIN 2093
DIN 2093 – see DIN
Cylindrical screws,
DIN 2095
DIN 2095 – see DIN
Pressure springs cold-molded from round bars
DIN 2096
DIN 2096 – see DIN
Heat-treated pressure springs from round steel sections
Pressure springs
DIN 2097
DIN 2097 – see DIN
Draw springs cold-molded from round wires
Cylindrical screws,
DIN 2098
DIN 2098 – see DIN
Pressure springs below 0.5mm cold-molded from round wires
pressure springs Cylindrical screws, pressure springs
pressure springs Table 3: General manufacturing tolerances
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2.2.5
Legislative Framework for Standards
DIN and ASME standards are the benchmarks for the engineering behavior, having certain legal relevance within a jurisdiction. Basically, they are recommendations the application of which is discretionary, which means that they may and may not be applied. Standards become binding only when references to them are incorporated in private contracts or laws and regulations, providing for their application. As specifications in standards are unambiguous, a specific agreement may be made on their binding effect in order to prevent litigations. References to standards in laws and regulations disburden governments and citizens from necessity of detailed legislations. Even in cases where parties have not incorporated standards into their agreement, if a dispute arises, such standards serve as guidance for rulings in respect of defects of substance in agreements or contracts. The basis here is the assumption that standards correspond to the current recognized development level of technology. Such assumption may be challenged (for example if a new draft standard is being prepared) or denied by a chartered expert’s specialist opinion.
2.2.6
OEM related overview for GD&T Standards
Daimler
ISO
BMW
ISO
VW
ISO
AUDI
ISO
FIAT
ISO
Peugeot
ISO
Porsche
ISO
GM / Opel
ASME
Chrysler
ASME
Ford
ASME
KIA
ISO
Hyundai
ISO
Toyota
ISO
Renault
ISO
Volvo
ASME Table 4: OEM related GD&T Standard
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2.3 Benefits of GD&T GD&T improves communication: 1) 2) 3) 4) 5) 6) 7) 8)
It facilitates more accurate definition of the “project intent”. Drawings are more easy-to-read. Mistaken interpretations arising from different technical backgrounds are minimized. After training in GD&T, this area is understandable to all of design engineers, production, quality control, inspection, buyers and all personnel engaged in a project. GD&T is internationally comprehensible. It protects suppliers against customers that are excessively critical and asking questions about missing drawing data. A supplier is able to present a more accurate quotation as GD&T is very precise. It gives a business extended legal protection in respect of, inter alia, wrong drawing interpretations.
GD&T raises business profits 1) 2) 3) 4) 5) 6)
GD&T increases productivity. GD&T minimizes returns, reworking and product and part defect rates. GD&T has higher CAD/CAM/CAM compatibility. GD&T helps to adhere to time plans. With bonus tolerances, lower cost levels can be maintained. GD&T guarantees interchangeability of parts.
GD&T enhances competitiveness 1) GD&T complies with ISO 9000 requirements. 2) Suppliers are able to reduce their quoted prices. “I had a supplier say to me at the end of my GD&T Seminar, that because of the bonus tolerance he would now be able to win bids from competitors that didn’t understand GD&T”. 3) GD&T reduces production costs.
It can be summed up under the line that with GD&T, drawings are read correctly and free interpretation is eliminated. Only with the precision and unambiguity of GD&T symbols correct “reading” of a drawing is really possible.
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3 Types of Tolerances 3.1
Tolerances of Form
Symbol
Designation
Explanation
Tolerance Zone =
Tolerance/ Deviation Sign
Datum
Point Space
Straightness
Line straightness tolerances
Tol.
Var.
between two planes/straight lines within a cylinder
Tg
Fg
no
between two planes
Te
Fe
no
between two concentric circles
Tk
Fk
no
between two concentric cylinders
Tz
Fz
no
The tolerated cylinder axis lies within a cylindrical tolerance zone with a diameter of 0.04. Flatness
Flatness tolerances
The area lies between two parallel planes with a distance of 0.04. Circularity
Circularity tolerances
The circumferential line of every cross-section lies between two concentric circles with a pitch of 0.06. Cylindricity
Cylindricity tolerances
The tolerated surface area of the cylinder lies between two coaxial cylinders with a pitch of 0.1. Table 5: Tolerances of form
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3.2 Symbol
Tolerances of Profile
Designation
Explanation
Tolerance Zone = Point Space
Line profile
Profile tolerance of any line profile shape
Tolerance/ Deviation Sign
Datum
Tol.
Var.
between two perfectly ideal equidistant curves
TIp
FIp
No or yes
space demarcated by a rightangled frame
Tfn
Ffn
No or yes
The tolerated profile lies in any parallel cross-section relative to the projection plane between two lines enclosing circles with a diameter of 0.06. Surface profile
Profile tolerance of any surface profile shape
The tolerated plane lies between two parallel planes enwrapping spheres with a diameter of 0.04. Table 6: Tolerances of profile
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3.3
Tolerances of Orientation
Symbol
Designation
Explanation
Tolerance Zone = Point Space
Gradient
Gradient tolerance, e.g. of a line relative to a datum plane
Tolerance/ Deviation Sign
Datum
Tol.
Va r.
within a cylinder
Tn
Fn
yes
within a cylinder
Tr
Fr
yes
between two parallel lines/planes
Tp
Fp
yes
The tolerated hole axis lies between two parallel planes with a distance of 0.08, inclined against the datum plane A with a gradient of 60° . Perpendicularly
Perpendicularity tolerance of e.g. a line relative to a datum plane.
The tolerated cylinder axis lies between two parallel planes with a distance of 0.1 that are perpendicular to the datum plane and the arrow-line’s direction Parallelism
Parallelism tolerance of e.g. a line relative to a datum line
The tolerated axis lies within a cylinder with a diameter of 0.04, which is parallel with the datum axis A.
Table 7: Tolerances of orientation
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3.4
Tolerances of Location
Symbol
Designation
Explanation
Tolerance Zone = Point Space
Position
Position tolerance of .e.g. a certain point
Tolerance/ Deviation Sign
Datum
Tol
very
symmetrical in a theoretically accurate location on a circular part relative to the diameter
Tps
Fps
yes
symmetrical in a theoretically accurate location on a circular part relative to the diameter
TCU
Fko
yes
symmetrical in a theoretically accurate location on a circular part relative to the diameter
Ts
Fs
yes
An actual point (intersection) is placed within a circle with a diameter of 0.2 the centre of which is identical to the theoretically precise position of the controlled point. Concentricity
Coaxiality tolerance of an axis
The tolerated cylinder axis lies within a cylinder with a diameter of 0.06 which is coaxial relative to the datum axis AB. Symmetry
Symmetry tolerance of e.g. a central plane
The tolerated center plane of a slot is placed between two parallel planes with a distance of 0.04 that lie symmetrically relative to the centerline of the datum feature A. Table 8: Tolerances of location (position)
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3.5 Runout Tolerances Symbol
Designation
Explanation
Tolerance Zone = Point Space
Runout
Circular runout tolerance plane of measurement
Tolerance/ Deviation Sign
Datum
Tol.
Var.
on a circular part relative to the diameter
TI
FI
yes
on a circular part relative to the diameter
TIg
FIg
yes
For one rotation around the datum axis A-B the circular runout deviation must not exceed 0.1 in any plane of measurement. Axial runout tolerance
For one rotation around the axis D, the axial plane deviation must not exceed 0.1 in any point of measurement.
Total runout
Total circular runout tolerance
For multiple rotations around the datum axis A-B and an axial shift of the part and the measuring device, all points of the tolerated feature’s surface must be within the total circular runout tolerance t=0.1.
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Total axial runout tolerance
For multiple rotations around the datum axis d and a radial shift of the part and the measuring device, all points of the tolerated feature’s surface must be within the total axial runout tolerance t=0,1. Table 9: Runout tolerances
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4 Representation of Tolerances 4.1 Summary: Standard Drawing Layout
Figure 10: Representation of a standard drawing layout
1) Datum triangle 2) Datum reference letter 3) Datum reference frame 4) Tolerated geometric feature 5) Datum/tolerance arrow 6) Information line 7) Feature Control Frame 8) Tolerance type symbol 9) Tolerance value in mm 10) Datum reference letter
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4.2
Baseline Dimensioning
Dimensional data and tolerances of a part are principally represented independently from each other. Baseline dimensioning is used to determine the: -
theoretically precise dimension
-
profile
-
orientation
-
position
-
references
Normally, the dimensioning unit is millimeter.
4.2.1 Tolerance/Datum Arrow Depending on functional requirements placed on a workpiece, the following rules concerning tolerated features / datums have been defined: ● where the auxiliary dimension line is terminated by an arrowhead, it relates to a tolerated feature ● where the auxiliary dimension line is terminated by a triangle, it relates to a datum feature
relates to a datum feature
relates to a tolerated feature
relates to a datum feature
Figure 11: Representation of a tolerated feature
● a datum arrow/triangle arrow must be indicated using an extension line in each instance where the tolerated element or the datum feature is an axis or a centerline.
37
The toleranced feature is the centreline of a groove
The toleranced feature is the central plane or the centerline of a rectangular prism
The toleranced feature is the central axis of a rotiational part
Figure 12: Representation of a tolerated feature (2)
•
A tolerance/datum dimension line indicates which geometric feature is being tolerated.
•
A tolerance arrow is to be placed on the contour line of the feature, or on an auxiliary dimension line in instances when the tolerance relates to the line or surface itself.
Figure 13: Representation of a tolerance arrow (datum arrow)
•
A tolerance arrow is to be drawn using an extension line if the tolerance relates to an axis or centerline of the dimensioned feature.
Figure 14: Representation of a tolerance arrow (datum arrow) (2)
38
•
A tolerance arrow is to be placed on the axis or central plane if the tolerated feature is a common axis or central plane of two or more features.
Figure 15: Representation of a tolerance arrow (datum arrow) (3)
A tolerance arrow is to be placed: •
always perpendicularly to the appropriate tolerated feature
•
by way of exemption, for tolerated circularity of a cone surface, at an angle when viewed from a side
4.2.2
Ideal/Theoretically Precise Dimension
A theoretically precise dimension, also referred to as ideal dimension, serves as indication of the geometrically ideal position of the tolerance zone. It is a numerical value used to describe the theoretically precise dimension, form, orientation or location of a geometric feature, or a datum location. It is the basis for determination of all permissible deviations.
Figure 16: Representation of the ideal/theoretically precise dimension
39
4.2.3
Controlled Dimension
The dimension being controlled is indicated by a circle (also referred to as bubble or zeppelin). It indicates a measure that requires specific control for the quality assurance.
Figure 17: Representation of a controlled dimension
4.2.4
Datums
Practically every workpiece is in some relation to its adjacent parts. Datum references are intended to provide information for precise fit of an assembly unit. Datums are indicated in squared boxes.
Figure 18: Representation of datums
Where more than one letter are used, they indicate the order of precedence to ensure proper working.
40
4.3
Feature Control Frame
Geometric tolerances are always indicated in a rectangular box referred to as feature control frame, which is split into several compartments. They are primarily information compartments which unambiguously define the requirements placed on the feature concerned. Tolerance data are indicated in the left to right order. Data are indicated in feature control frames that may be split into two or three parts: •
Simple feature control frames without a datum specify only the form tolerance, i.e. they relate to a geometric tolerance. The following data must be provided as minimum
•
Any other tolerances principally require indication of at least one datum! A datum provides an additional specification of the orientation and, where no orientation tolerance is provided, the position.
41
So meaning:
must be
must be
must may be
may
A feature control frame is basically split into the following compartments:
dimensioning Controlled characteristic
diameter position tolerance material condition
Figure 19: Representation of a feature control frame
The next figure shows a description of the left hole on the below metal plate.
Controlled characteristic
dimensioning diameter position tolerance material condition
datum
datums
datums
Figure 20: Representation of descriptions in a feature control frame
42
4.3.1
Controlled Properties
The first compartment of a feature control frame shows the symbol of the controlled properties of a part.
Figure 21: Representation of symbols of controlled properties
The following symbols of controlled properties are available:
Form tolerances: Symbol
Designation Tolerance Sign
Straightness
Tg
Fg
Flatness
Te
Fe
Circularity
Tk
Fk
Cylindricity
Tz
Fz
Table 10: Symbols for form tolerance indications
43
Deviation Sign
Profile tolerances: Tolerance Sign
Deviation Sign
Line profile
TIp
FIp
Surface profile
Tfn
FIn
Symbol Designation
Table 11: Symbols for profile tolerance indications
Orientation tolerances: Symbol
Tolerance Sign
Deviation Sign
Gradient
Tn
Fn
Perpendicularity
Tr
Fr
Parallelism
Tp
Fp
Designation
Table 12: Symbols for orientation tolerance indications
Location tolerances: Symbol Designation Tolerance Sign Position
Tps
Fps
Concentricity
Tko
Fko
Symmetry
Ts
Fs
Table 13: Symbols for location tolerance indications
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Deviation Sign
Runout tolerances: Symbol Designation Tolerance Sign
Deviation Sign
Runout
TI
FI
Total runout
TIg
FIg
Table 14: Symbols for runout tolerance indications
4.3.2
Diameter
The second compartment of a feature control frame shows whether the tolerance value applies to a circular or a square part. Where the first is the case, a diameter symbol must be used. It is normally not used in connection with flatness, circularity, cylindricity, profile of a line or surface, gradient, runout or total runout.
Figure 22: Diameter symbol
4.3.3
Tolerance Values
The third compartment shows the permissible tolerance range as value. The indication uses the same units as length. The unit typically used in Europe is millimeter. The value 1,0 is equal to a tolerance zone of ± 0,5.
Figure 23: Indication of tolerance values
45
4.3.4
Material Conditions
The fourth compartment of a feature control frame describes the material conditions applying to the given tolerance values. Any of the three material condition options may be used here:
Material condition
ASME Y14.5 and DIN ISO 2692 symbol
Maximum material condition Least material condition Regardless of feature size
NO symbol Table 15: Material conditions
4.3.5
Datums
The last compartment of a feature control frame contains part orientation data. Where the tolerated feature involves any datum, it is normally indicated by means of a datum reference letter which appears in a feature control frame according to the order of precedence, starting from capital A.
Figure 24: Datum reference letter indications in a feature control frame
For vehicle designs using coordinate systems, preferable use of appropriate X, Y, Z levels for all parts is advisable. Also known as RPS-System. Reference Point System.
Figure 25: Datum indication according to coordinates
46
Figure 26: XYZ coordinate system
4.3.6
Additional Textual Data
Additional texts for which symbols are not available can be placed: •
above the feature control frame
6 holes
6x ....
non-concave
convex
Figure 27: Additional textual data
●
next to the feature control frame
6 holes
non-concave Figure 28: Additional textual data (2)
47
Example:
Figure 29: Example – additional textual data
4.3.7
Single and Combined Feature Control Frames
Basically,, a feature control frame may be represented as a single feature control frame or a combined feature control frame, or a composite feature control frame.
4.3.7.1
Single Feature Control Frame
The next figure shows a single feature control frame. frame
Figure 30: Single feature control frame
4.3.7.2
Combined Feature eature Control Frame
A symbolic illustration of a feature control frame with two spate segments is provided in the figure below.
Figure 31: Combined feature control frame
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4.3.7.3
Example: Position Tolerance
Single feature control frame
Location/orientation tolerance
Combined feature control frame
Location/orientation tolerance
with a combined datum
(relative to another datum)
Figure 32: Single/combined feature control frame with a position tolerance example
4.3.7.3.1
Single Feature Position Control Frame
true axis
tolerance zone Ø 2.0
nominal zero
Figure 33: Single feature position control frame
With this position tolerance, a cylindrical tolerance zone is drawn for each hole, lying symmetrically around the nominal central point of a hole and related to the datum system. The tolerance zone may be applied to position, orientation and/or form deviations. All points must lie within the tolerance zone. For the quality assurance/measuring, a part is first orientated using the datum (reference) system, and then the hole to which the tolerance applies is measured. If the deviation is within the cylindrical tolerance zone of 2.0mm, the hole is considered to be within the tolerance.
49
4.3.7.3.2
Combined Feature Position Control Frame
true axis
Feature-related tolerance zone
Figure 34: Combined feature position control frame
The lower position limit indicated in the feature control frame defines relative positions of holes, and is therefore specified more narrowly. By this, second cylindrical tolerance zones are drawn for each hole, lying centrically around the holes’ nominal central points and interrelated. These interrelated cylindrical tolerance zones may be shifted and rotated within a larger tolerance zone. With the best fit approach to quality assurance/measuring, the required central point of a hole is measured relatively to the nominal central point. If deviations with the best-fit approach are within the tolerance (1.0mm), then the hole is positioned within the inner tolerance of the group of holes.
4.3.7.4
Example: Profile Tolerance
Single feature control frame
Location/orientation/form tolerance
Combined feature control frame
Location/orientation/form tolerance
with a combined datum
Location/orientation/form tolerance (relative to another datum)
Figure 35: Single/combined feature control frame with a profile tolerance example
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4.3.7.4.1
Single Feature Profile Control Frame
location/orientation/form tolerance width tolerance zone 1.0mm, even on both sides of the basic profile true profile
Figure 36: Single feature control frame
In this position tolerance a tolerance zone is drawn which lies symmetrically along both sides of the nominal profile and is related to the datum system. The tolerance zone may be applied to position, orientation and/or form deviations. All profile points must lie within the tolerance zone. For the quality assurance/measuring, a part is first orientated using the datum (reference) system, and then the profile to which the tolerance applies is measured. If deviations are within the tolerance zone (1.0mm = permissible deviation of +/- 0.5mm), the profile is considered to be within the tolerance.
4.3.7.4.2
Combined Feature Tolerance Frame with Directional Limit
Figure 37: Combined feature profile tolerance frame with a directional limit
51
The upper limit in the feature control frame controls the profile relative to its place within the datum (reference) system. A tolerance zone identical to a single feature profile control frame is created, lying along both sides, symmetrical relative to the nominal profile and aligned with the datum system. The lower limit further confines the profile orientation and form within the position tolerance. A second tolerance zone is created against the reference system, which may be, however, shifted within the large tolerance zone in parallel with the nominal profile. For the quality assurance/measuring, a part is first orientated using the datum (reference) system, and then the profile to which the tolerance applies is measured. If deviations are within the tolerance zone of the upper limit (2.0mm = permissible deviations of +/- 1.0mm), the profile is within the tolerance. To assess the direction (orientation) of the form, the difference between the maximum and minimum deviations is subsequently determined. If this range is within the tolerance of the lower limit (1.0mm), then the direction (orientation)/form are within the tolerance.
4.3.7.4.3
Combined Feature Control Frame with Form Variation Ratio location/orientation tolerance form variation rate
true surface
basic profile
The difference between X and Y (50mm) must not exceed 0.5
Figure 38: Combined feature control frame with a form deviation ratio
52
tolerance
4.3.7.5 Composite Feature Control Frame
A composite feature control frame contains a common beginning compartment with the symbol of the property being controlled, followed by the individual tolerance and datum requirements applying to both data.
It is an ASME-specific specific feature, not implemented in ISO. ISO
Figure 39:: Composite feature control frame
4.3.7.5.1
Example: Composite Position Tolerance
GD&T offers an application combining position tolerances for location of groups of geometric features, and mutual relationships relations (location and orientation) between geometric features within a group. This can be achieved by using a composite feature control frame.
Figure 40: Composite position tolerance
53
4.4
Additional Symbols Descriptions Toleranced feature reference
Symbols direct by a letter
Datum reference (only a letter) Datum location reference
ø2 = surface dimension of datum location A1 = datum feature and datum location number
Theoretically precise measure Projected (predefined) tolerance zone Maximum material condition Dependence on dimensional and geometric tolerances Least material condition A measure describing the minimum material condition of a geometric feature Free state condition (non-rigid parts) Envelope condition: a geometrically ideal envelope must not be broken by the maximum material measure
Table 16: Additional symbols
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4.5
General Table of Tolerances
This standard table contains all tolerance data that have not been specifically defined in a drawing. They are process-specific and constitute the basis of each drawing.
Table 17: General table of tolerances
Can be found at: „/Johnson_Controls_Catalogs/Johnson_Controls_2D_Catalogs/Johnson_Controls_2D_Catalogs_MM A_20APR2009.catalog/JC_Metal_Standards_Nov2007/Metal_Tables_Sep2008/JCGDT/JCGDT/JCGD T_GREATER_3“.
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5
Datums
A datum is the basis for the tolerancing and testing of geometric features. A datum provides information on the exact orientation of an assembly group. A datum represents an existing feature of a workpiece (e.g. edge, surface, hole wall, ...) to be used as reference for the location of another feature. A geometric feature to which a datum triangle with a datum leader is assigned in a drawing is datum (reference) feature. Both holes should be orientated perpendicularly to the workpiece’s upper
The upper surface of the workpiece represents the datum for the location of holes
Figure 41: Datum feature
As described earlier in this paper, a datum is generally designated by a datum reference letter. The same datum reference letter appears in the feature control frame. This indication:
means the following: datum A
datum A
geometrically precise counterpart A
geometrically precise counterpart A
embodiment parallel planes with the least distance Datum axis A
Datum axis A part Central plane of a geometrically precise
embodiment
parallel planes with the part
Central plane of a geometrically precise
Figure 42: Datum – datum feature relationship
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5.1
What are Datums good for?
The sequential order of datums has a major impact on the functionality. Should the order fail to be respected in the part manufacturing or testing, parts may be marked as defective though in fact they will be not. An example of different sequential orders and meanings:
Figure 43: Sequential order of datums
For the proper fit, a part is first laid on the primary surface (datum A) and then aligned according to the secondary feature (datum B).
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5.2
Datum References in Drawings 5.2.1
Datum Triangle
A datum feature is designated by a datum triangle. A datum triangle may be represented as either a filled frame or an empty frame. The datum reference letter assigned to a triangle is placed in a squared frame or a circle. Datums may be differentiated as follows:
a)
upper surface
c)
as datum
d)
rear surface as datum
central axis
front surface as datum
as datum
e)
b)
different positions and data of a datum leader
Figure 44: Representation options for datum triangles relating to different datum features
5.2.2 Datum Locations / Datum Features There are three types of datum locations: •
surface datum locations: designated by a hatched area demarcated by a two dots one dash line.
•
line datum locations: designated by a thin full line between two crosses
•
point datum locations: designated by a cross
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a) surface
b) line
Figure 45: Types of datum features/datum locations
Examples: Surface datum locations
Figure 46: Surface datum locations
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c) point
Line datum locations:
Figure 47: Line datum locations
Point datum locations:
Figure 48: Point datum locations
Datum locations are indicated in drawings by means of a circle with a horizontal dividing line.
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The datum reference letter is indicated in the lower part and the datum location size is defined in the upper part. Where there is insufficient space for the datum location indication, it may be indicated off the frame.
Figure 49: Off-frame indication of a datum
5.2.3
Sequential Order of Datum Indications According to MBN 11011
Datum location references should be indicated in a drawing using symbols according to the DIN ISO 5459 standard
etc.
The following referencing order is proposed.
= primary datum
= secondary datum
= tertiary datum
= further datums Figure 50: Datum referencing sequence
Where the tertiary datum should be the centre between two points, a or b will be added to the datum reference letter (e.g. Ca6 and Cb6).
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Then, the geometric central point between the two points will be interpreted as datum (C6).
Figure 51: Sequential order of datums
5.2.4 Axis / Plane as Datum In addition to a rounded cylinder, a plane is another most frequent datum element. A) Central plane of an outer datum feature datum plane
simulated datum / least test gap
Figure 52: Central plane of outer datum features
B) Central plane of an internal datum feature datum plane
simulated datum / least test cube
Figure 53:Central plane of an inner datum feature
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C) Datum axis of an outer dimensioned feature (shaft)
Figure 54: A datum axis of an outer dimensioned feature (shaft)
D) Datum axis of an inner dimensioned feature (hole)
Figure 55: Datum axis of an inner dimensioned feature (hole)
In the following example, the longer arm will be chosen as datum as it bears locating holes.
Figure 56: A datum plane with a flatness tolerance
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5.2.5 Coplanar Surface as Datum Here, the common datum plane of the two coplanar surfaces is designated as Datum A. Using a profile tolerance, which in this case represents a surface tolerance (since no datum is provided) and the “2 SURFACES” note indicates that it is the common flatness tolerance of the two surfaces.
Figure 57: Coplanar plane as datum
5.2.6 Unfolded State as Datum
Figure 58: Unfolded state as datum
This tolerancing approach is widely used for large sheet metals and for flexible parts where tolerance values will be designated by “F”. The sequence of datums are not in the right sequence related to the new best practice proposals.
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5.2.7 Difference Between Datum Plane and Datum Location When defining a complete plane as datum feature, there is a danger – especially in cases when the plane involves relatively large form deviations – that it will be impossible to define the datum plane unambiguously. When creating a datum plane using a gage, the datum plane position will depend on which points of the plane will be measured to create the datum plane. Since a complete plane is defined as datum plane, but for economy reasons the complete plane cannot be measured to obtain the datum, the points will be chosen on a random basis. This may lead to a situation that different machine operators come to different datum planes, and thus to different measurements.
part datum feature datum plane 1
datum plane 2 Measurement points to create the datum planes
Measurement points to create the datum planes
Figure 59: Difference between a datum plane and a datum location
Definition of individual datum locations instead of a complete plane will reduce the susceptibility to inaccuracies of the created datum plane due to form deviations. To determine the primary datum, three datum locations are required. Two datum locations are needed or a secondary datum and one datum location for a tertiary datum. Conformity exists where more than three datum locations are provided for a primary datum. Such conformity is required for highly non-rigid workpieces (e.g. sheet metals). Datum locations designate certain points, lines or surfaces on a workpiece that are used to establish the datum system.
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Examples may include rough or uneven surfaces resulting from casting, forging or molding, weld surfaces and surfaces of thin parts that are subjected to bending or twisting, or other existing or emerging distortions. Datum locations and datum features may be combined to create a datum system. A datum location is designated using a circle from which an arrow line is drawn to the datum location. If the arrow line is dashed, the datum location lies on a plane that is not visible in the drawing. The position of a datum location will be determined by theoretically precise dimensions.
5.2.8 Sequence of Datums related to Datum Reference Frame The datums of a workpiece should be normally defined with capital letters starting with A It is helpful for avoid misunderstandings to keep it simple and use only a small number of datums. General this cases are possible:
•
Single datum, e.g. defined by element A
•
Multiple datum, e.g. defined by elements A,B,C
•
Common datum, e.g. defined by elements A and B as axis
•
Common datum, e.g. defined by elements A and B and C as surface
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The sequence of the datums have a big effect related to efficiency of a workpiece and should be considered for manufactoring and proofing. The following example shows two position tolerances with different sequences for datums A and B. The following pictures show the different proofing methods related to this sequences. The workpiece have different contact to proofing fixture related to the defined primary datum and we will get also different measuring results.
Figure 60: Effects related to different datum sequences
The pictures display in a clear kind of way the different proofing conditions related to the sequence of datums for the hole position 10mm or 40mm.
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5.3 Datum System If we wish to unambiguously define geometric tolerances within a space, we need to define several datums. A datum system comprises a group of one or more datums.
5.3.1 6 Degrees of Freedom For locating a body in a 3D space, three turns (rotations) and 3 shifts (translations) must be specified. Motions of solid bodies include shift motions along x-, y-, z-axes and rotational motions around translation axes.
Shift motion along Z-axis Rotation around Z-axis
Shift motion along Y-axis Rotation around Y-axis
Shift motion along Xaxis
Figure 61: 6 degrees of freedom
datum system beginning
datum axis
measuring direction datum axis
datum planes datum axis
startig point for mesuring Figure 62: 6 degrees of freedom (2)
This is referred to as determination of 6 degrees of freedom, needed to define the complete datum system to achieve the specified fastening of a body.
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5.3.2 The 3-2-1 Rule To determine 3 datum planes that should make up a right-angled datum system, the 6 degrees of freedom must be defined. The datum planes will be created using a number of datum points. They will be referred to as primary datum, secondary datum and tertiary datum in line with their respective sequential positions. To provide an unambiguous and non-redundant reference, the three datum planes require a minimum number of datum points. •
● primary datum: 3 datum points
•
● secondary datum: 2 datum points
•
● tertiary datum: 1 datum point
As shown in the figure, the following direction will be thus determined:
Figure 63: 3-2-1 rule
1st datum plane / primary datum ● -
translation in the Z-direction rotation around X-axis rotation around Y-axis
2nd datum plane / secondary datum - translation in the X-direction - rotation around Z-axis 3rd datum plane / tertiary datum - translation in the Y-direction
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Generally, datum locations are surface points or small surfaces areas, and they may be substituted by datum features, such as holes or oblong holes. Conventional application of the 3-2-1 rule to metal-sheets and boards looks like this:
Figure 64: 3-2-1 rule (2)
Spatial representation of examples of the 3-2-1 rule:
Example 1: Board
tertiary datum plane
secondary datum plane
primary datum plane Figure 65: Example 1 for the 3-2-1 rule (1)
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The figure shows three datum planes to which appropriate reference letters are assigned as follows: -
primary datum plane (A)
-
secondary datum plane (B)
-
tertiary datum plane (C)
tertiary datum plane C
secondary datum plane
primary datum plane A
Figure 66: Example 1 for the 3-2-1 rule(2)
There are three datums within the primary plane - A1, A2 and A3, and each of them is represented by a single zone with a 5mm diameter. On the other side there are two datums B1, B2 for the secondary plane and one datum for the tertiary plane. Example 2: Rotational body
datum plane A datum axis B
datum central plane B
Figure 67: Example 2 for the 3-2-1 rule
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Housing Seal Cover
Aligned insertion
Figure 68: Example2 for the 3-2-1 rule (2)
Example 3: Point-defined datums
This data in the drawing This data in the drawing
Means this
Workpiece
Means this
Workpiece Point contact at the theoretically precise location
Locating pin
Locating pin
Figure 69: Example 3 for the 3-2-1 rule
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Example 4: Datum locations on a bullhorn Datum locations on the cover
Figure 70: Example 4 for the 3-2-1 rule
Bullhorn tolerances derived from the cover fastening:
Figure 71: Example 4 for the 3-2-1 rule (2)
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Example 5: Datum locations for a bent pipe
These data in the drawing
mean this:
Effective condition equaling to the maximum material condition of the geometric feature plus a 4mm position tolerance diameter Theoretically precise counterpart relative to the datum feature B
Theoretically precise counterpart relative to the datum feature A
(effective locating pin condition at MMC)
(effective locating pin condition at MMC) The workpiece must fit within confines corresponding to the maximum material condition of the outer diameter, plus a 4mm tolerance zone Figure 72: Example 5 for the 3-2-1 rule
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5.3.3 Determination of Datum System Determination of a datum system will largely affect measurement results.
Oblong hole
Figure 73: Determination of a datum system
Measurement 1 Datum points of a plane
points of measurement are ok
Measurement 2 Datum points of a plane
points of measurement are not ok
Figure 74: Determination of a datum system influencing measurement results
Without defined and transient datums, workpieces cannot be unambiguously verified.
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5.3.4 Datum System Requirements Determination of datums or a datum system is subject to the following rules: •
Where possible, avoid any redundancies in the datum determination (3-2-1 rule).
•
Datum points must be functional, i.e. datums should be the most important geometric features of a workpiece.
•
Appropriate geometric distribution of datum points should be ensured.
•
Continuity of datum points should be ensured, starting from an individual part, through assembly groups, to the final product.
•
Standardized shaft (opening) diameters should be used.
•
Instead of camber pin holes, oblong holes with cylindrical pins should be used.
5.3.5 Datum System Arrangement Wherever possible, datum locations should be defined on network-parallel surfaces to prevent a part defect from distribution over different vectors. Every datum location should operate only in a single vector direction. The advantage of selecting a network-parallel datum location lies in that a datum point within the system may be changed without affecting the other directions. On the other hand, for single- or double-inclined surfaces, two or three coordinates, respectively, will be changed.
part defect Figure 75: Datum system arrangement – part defect
A part with a specified tolerance will be captured in two different systems: once in the network-parallel manner shown in Representation 1 and once in the network-parallel manner shown in Representation 1 .
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Representation
Representation The part tolerance operates only in Xdirection
The parts will be captured in a networkparallel manner
Deviation in Xdirection When the part is defective, an additionl deviation in Z-direction will emerge here
With a capture that is not network-parallel, inclination of the defective part will occur.. Figure 76: A part with a defined tolerance in different systems
5.3.6
Determination of Datum/Locating Distance (Effective Distance)
With the hole/oblong hole principle, an important role is played by the locating (effective) distance. The effective distance is always measured perpendicularly to the acting direction within the vehicle’s coordinate system. Process-safe locating is ensured when the effect of the effective distance is the largest and the locating point is within a stable area. The absolute distance between a hole and a longitudinal hole is not always consistent with the actual effective distance. The maximum process safety is achieved with the least difference between the absolute distance and the actual effective distance In an optimum case, the actual effective distance corresponds to the absolute distance.
Figure 77.Determination of an effective/locating distance
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The oblong hole must be always reasonably orientated relatively to the vehicle’s coordination system to ensure that on equipment adjustment parts/assembly groups will need to be adjusted only in a single vector direction. The equipment should be designed in a manner allowing for individual adjustment of each coordinate only in the direction corresponding to the vehicle’s coordinates. When designing the combination of a hole and a oblong hole, care should be taken to avoid a situation that their ratio falls within the critical area.
Pin/hole clearance
Acting direction Larger pin/hole clearance
Figure 78. Determination of the datum/locating distance (2)
Due to the locating pin/oblong hole clearance, a threat emerges that further process tolerancing within the critical area will be needed as the locating pin does not act perpendicularly to the oblong hole’s cut edge any more.
Critical area
Figure 79. Determination of the datum (locating) distance (critical area)
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5.3.7
Determination of Unilateral Surface Tolerances
Where unilateral surface tolerances are to be used, they should be designated by “U” as shown below.
Figure 80. Determination of unilateral surface tolerances
This modifier (characteristic) is used for profile tolerances (of lines or surfaces) with a nonsymmetrical tolerance array. The characteristic is followed by the off-material tolerance area value. The tolerance array always extends in the direction of the material side, i.e. the value following the characteristic U refers to the biggest measure of the part. If the biggest measure is lesser than the nominal measure, the value is negative. Example 1:
Meaning:
Tolerance symbol Tolerance value symbol Off-material value Datum (if necessary)
1.0 mm off the material
Figure 81: Determination of unilateral surface tolerances (Example 1)
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Example 2:
Meaning:
1.0mm off the material Nominal measure (TED) Figure 82: Determination of unilateral surface tolerances (Example 2)
Example 3:
Meaning:
1.0mm off the material Figure 83: Determination of unilateral surface tolerances (Example 3)
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5.3.8 Definition of Datums through Coordinate Data
Unless determined otherwise, the geometric tolerances and the datum features indicated in each individual frame apply to a fastened workpiece . The drawing is intentionally incomplete. Figure 84: Definition of datums through coordinate data
These datums are defined by means of coordinate data, as shown in Figure 86.
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5.4
Locator Selection Strategy 5.4.1
Hole/Oblong Hole Principle
The hole/oblong hole principle is applied in the part -
fastening
-
aligning
-
locating
‘Oblong hole’ refers to an oblong opening or slot. Its narrow sides are enclosed by semicircles with diameters corresponding to the oblong hole’s length. Longitudinal sides of an oblong hole are mutually parallel. They may be linear or curvilinear- e.g. taking shape of a circle arch. An oblong hole is thus one drawn along a defined track.
Hole/oblong hole principle
Hole/oblong hole principle
Figure 85: The hole/oblong hole principle
Locator selection strategy:
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-
unambiguous mounting, first by fastening through the hole and then through the oblong hole, and then complemented by additional securing
-
no additional hole boring or hole adjustment operations are necessary
-
independency from the operator staff
Initial design
Consideration of deviations
Figure 86: The hole/oblong hole principle (2)
5.4.2
Opening
Locator selection strategy:
-
no unambiguous tensioning order is visible; any of the tensioning locations may be tensioned first
-
boring and filing operations are likely; the last mounting element cannot be always positioned
-
dependence on the operator staff and their “daily condition” Initial design
Consideration of deviations
Figure 87: Locator selection strategy
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5.4.3
Distance between Locators
Principal rule: Whenever possible, locators must be placed as far from each other as possible so that the part can be located with the utmost stability.
Hole – oblong hole principle
Opening Initial design
Initial design
Consideration of deviations
Consideration of deviations
Figure 88: Distance between locators
5.4.4 Low Strain Arrangement with Locators The clear “3-2-1” locator concept will not induce any strain in a part or assembly group and the positioning is always unambiguous. A redundant locator concept will induce strains and lead to unforeseeable distortions. Reproducible precision is not assured.
Advantages of the low strain arrangement:
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-
eliminates non-linear, unforeseeable deviations from the manufacturing process
-
“springback” effects in parts are easier to localize and resolve
5.4.5
Curvilinear Surfaces as Locator
Where locators are needed on slant or curvilinear surfaces of a part, efforts should be made to place them on offset surfaces that are orientated relative to the XYZ planes of the vehicle’s main coordinate system. Advantages: -
accentuation of the surface where the locator is placed improved reproducible precision simple and cheap design of tooling
5.4.6
Pressing Tools and Locators
Locator designs should be developed in parallel with the development of the pressing process. Locator principle: – a hole/oblong hole should be introduced into a part in a single operation – as soon as possible. It can be thus used for later operations. Functionally critical holes should be applied concurrently with the locators. All holes should be applied to a surface at an angle of max. 7 degrees. All determining surface locators should be introduced in a single working operation.
5.4.7 Locators on Vertical Surfaces Principal rule: Locators on vertical surfaces should be avoided. The “springback“ effect can be then prevented only by clamping means. Also, do not use any: -
cut edges
-
shears without guides
-
crosscuts
-
tapped holes
-
interconnected holes
These are features with great deviations that are not suitable for process-safe fastening of a part.
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5.4.8
Locator Block and Pin Layout
Principal rule: Wherever possible, locator blocks and pins should be orientated relative to the vehicle’s raster grid.
Locator pins must be always arranged on parallel axes. Wherever possible, locator blocks should be arranged on parallel planes.
Benefits of these requirements: -
simple design of tooling
-
easy adjustment of tooling
-
improved reproducible precision
5.4.9
Locator Pins on Plastic Parts
Example :4-way locator
Example :2-way locator
Figure 89: Locator pins on plastic parts
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6
Material Conditions
Applicability of material conditions is confined to geometric features that are subject to dimensional deviations. They can be datum features or their geometric features whose axis or central plane is determined by geometric tolerances.
6.1
Regardless of Feature Size (RFS) Material Conditions
Where any geometric tolerance is applied on the RFS basis, the tolerance is independent from the actual size of the geometric feature concerned. The tolerance is limited to the value indicated irrespective of the actual size of the geometric feature. In relation to a RFS-based datum feature it also means that alignment according to its axis or central plane is required, irrespective of the actual size of the geometric feature. In relation to a hole or a pin it means that the hole tolerance values are always the same, regardless of whether the hole diameter is at the lower or upper limit.
6.2
Maximum Material Condition (MMC)
Where the MMC principle is applied in geometric tolerance, the permissible tolerance depends on the actual matching rate of the geometric feature concerned. A tolerance is limited to a specific value if the geometric feature is made at its MMC limit value. Where the actual matching rate of a geometric feature deviates from MMC, an increased tolerance is permissible, depending on the amount of such deviation. The total permissible deviation of a specific geometric characteristic is the maximum if the geometric feature lies at LMC. Identically, application of MMC to a datum feature means that for the MMC limit the datum is the geometric feature’s axis or central plane. Where the actual matching rate of a datum feature departs from MMC, a shift between its axis or central plane and the datum axis or central plane is permissible.
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⇒
6.3
A condition when a dimensional element contains the maximum possible amount of material within defined dimensional limits.
Least Material Condition (LMC)
Where the LMC principle is applied in geometric tolerance, the permissible tolerance depends on the actual matching rate of the geometric feature concerned. A tolerance is limited to a specific value if the geometric feature is made at its LMC limit value. Where the actual matching rate of a geometric feature deviates from LMC, an increased tolerance is permissible, depending on the amount of such deviation. The total permissible deviation of a specific geometric characteristic is the maximum if the geometric feature lies at MMC. Identically, application of LMC to a datum feature means that for the LMC limit the datum is the geometric feature’s axis or central plane. Where the actual matching rate of a datum feature departs from LMC, a shift between its axis or central plane and the datum axis or central plane is permissible. ⇒
A condition when a dimensional element contains the least possible amount of material within defined dimensional limits.
6.4 Bonus Tolerance For conventional drawings with +/- tolerances without application of GD&T, the position tolerance of a borehole is indicated in form of a target frame.
Figure 90: Representation of bonus tolerances
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The expected tolerance array then looks like this:
Figure 91: Representation of tolerance array
The MMC tolerance range is 57 % larger than the old +/- value and is referred to as bonus tolerance.
6.5 Comparison between MMC and RFS
The hole has a diameter of 10, with a tolerance of +/0.5mm. The position tolerance is 1.0mm.
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⇒ The tolerance depends on the feature’s actual size
⇒ The tolerance is independent from the feature’s actual size
nominal measure
lower size limit 9,5 upper size limit 10,5
actual geometric feature size
position tolerance
(hole diameter)
actual geometric feature size
position tolerance
(hole diameter)
ø 9.5mm
ø 1.0mm
ø 9.5mm
ø 1.0mm
ø 10.0mm
ø 1.5mm
ø 10.0mm
ø 1.0mm
ø 10.5mm
ø 2.0mm
ø 10.5mm
ø 1.0mm
The hole position tolerance vary depending on the hole size.
The hole position size remains constant.
Table 18: Comparison between MMC and RFS
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6.6 Comparison of MMC and LMC
⇒ The tolerance depends on the feature’s actual size ⇒ The tolerance applies to the geometrically precise size of the least possible hole (9.5) ⇒ i.e. the maximum possible material
⇒ The tolerance depends on the feature’s actual size ⇒ The tolerance applies to the geometrically precise size of the maximum possible hole (10.5) ⇒ i.e. the least possible material
nominal measure
lower size limit 9,5 upper size limit 10,5
actual geometric feature size
position tolerance
actual geometric feature size
position tolerance
(hole diameter) (hole diameter) MMC
LMC
ø 9.5mm
ø 1.0mm
ø 10.0mm
ø 1.5mm
ø 10.5mm
ø 2.0mm
⇒ When the hole approaches its upper size limit (10.5), the target area for the hole position extends
MMC
LMC
ø 9.5mm
ø 2.0mm
ø 10.0mm
ø 1.5mm
ø 10.5mm
ø 1.0mm
⇒ When the hole approaches its lower size limit (9.5), the target area for the hole position shrinks
Table 19: Comparison between MMC and LMC
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6.7
Hole-Piston Interplay 6.7.1
Example of MMC
An inner feature: e.g. a hole A hole is to be made in the following example. The hole may have a diameter of 30.5 to 30.1. The maximum material condition is set.
Figure 92:Example of MMC
actual geometric feature size
position tolerance
(hole diameter) LCM
MMC
30.5
0.5
30.4
0.4
30.3
0.3
30.2
0.2
30.1
0.1
Table 20: Comparison between MMC and LMC for an inner feature:
The table shows that the tolerance applies to the theoretically precise size of the least hole.
With an outer feature it is just the opposite.
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An outer feature: e.g. a pin
The pin may have a diameter of 29.5 to 29.9. Again, MMC is set. It implies the following table.
actual geometric feature size
position tolerance
(hole diameter)
MMC
Figure 93:Comparison between MMC and LMC for an outer feature
LMC
29.9
0.1
29.8
0.2
29.7
0.3
29.6
0.4
29.5
0.5
Table 21: Comparison between MMC and LMC for an outer feature
The table shows that the tolerance applies to the theoretically precise size of the largest pin. With MMC, the hole and the pin in their common ideal position can be connected in any tolerance situation. It is just the same with LMC!
6.8 Effective Condition Depending on its function, a geometric feature is defined by its size and the appropriate geometric designation. A MMC or LMC material condition may be also suitable. To determine the dimensions of a functional gage, the aggregate effect of MMC and applicable tolerances must be taken in account in order to properly define clearances between the different parts. To determine the dimensions, the aggregate effect of MMC and applicable tolerances must be taken in account in order to correctly determine the guaranteed contact area to ensure proper thin wall thicknesses and positioning of the hole.
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6.8.1
Example: Effective condition
A reference is made to the preceding example: the same tables have been adopted and extended to incorporate the effective condition. Hole table: actual geometric feature size
position tolerance
effective condition
(hole diameter)
LCM
MMC
30.5
0.5
30.4
0.4
30.3
0.3
30.2
0.2
30.1
0.1
30
Table 22: Effective condition with an inner feature ( MMC)
Piston table: actual geometric feature size
position tolerance
effective condition
(hole diameter)
MMC
LMC
29.9
0.1
29.8
0.2
29.7
0.3
29.6
0.4
29.5
0.5
30
Table 23: Effective condition table of an outer feature (MMC)
In simple words:
⇒ MMC for an inner feature: effective condition of an inner geometric feature is the constant value of its MMC size minus its position tolerance.
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⇒ MMC for an outer feature: effective condition of an outer geometric feature is the constant value of its MMC size plus its position tolerance.
With LMC it is similar: Hole table: actual geometric feature size
position tolerance
effective condition
(hole diameter) LCM
MMC
30.5
0.5
30.4
0.4
30.3
0.3
30.2
0.2
30.1
0.1
30.0
Table 24: Effective condition table of an inner feature (LMC)
Piston table: actual geometric feature size
position tolerance
effective condition
(hole diameter)
MMC
LMC
29.9
0.1
29.8
0.2
29.7
0.3
29.6
0.4
29.5
0.5
30.0
Table 25: Effective condition table of an outer feature ( LMC)
In simple words:
⇒ LMC for an inner feature: effective condition of an inner geometric feature is the constant value of its LMC size minus its position tolerance. ⇒ LMC for an outer feature: effective condition of an outer geometric feature is the constant value of its MMC size plus its position tolerance.
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7 Tolerance Principles Problem formulation: Already long before the introduction of geometric tolerances it was broadly understood that for part fitting adherence to dimensional tolerances was not sufficient; form deviations also required limitation. This will be explained using an example. Figure 94 represents a flat guide consisting of a carrying plate and a guide block. To ensure a minimum clearance of 0.1mm, the parts were tolerated as shown in the figure.
Figure 94: Tolerance principles
If both parts have such MMC that the guide block height is 25.2mm and the carrying plate slot height is 25.3mm, the minimum clearance of 0.1mm is just maintained. But none of the parts may have any other form deviations. If the guide block features any other form deviations, to maintain the minimum clearance in matching with the carrying plate at MMC, its total height must be lower than MMC. In the figure below, the guide block has a height corresponding to its LMC (24.8). Since it must not exceed its effective size (25.2) in order to meet the minimum clearance requirement, the flatness deviation is limited to 25.2mm -24.8mm = 04.mm.
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A carrying plate and a guide block with maximum material sizes
A carrying plate with the minimum material size and a guide block with the maximum material size and the maximum form deviation
Figure 95: Tolerance principles (2)
In other words: The guide block height may not be lesser than 24.8mm in any location, or otherwise the dimensional tolerance would not be observed, and it must fit an envelope with a height of 25.2mm. This corresponds to the Taylor testing principle.
7.1 Tolerance Principle A tolerance principle indicates whether the permissible form deviation of simple geometric features (surface areas of a cylinder, pairs of planar areas) does or does not depend on permissible dimensional deviations. Two principles are distinguished: the envelope (envelope curve) principle and the independence principle. To prevent confusion, the tolerance principle should be always indicated in a drawing. Where the drawing bears a “DIN 717 Tolerance“ indication, the envelope (envelope curve) principle applies. If the indication is “ISO 8015 Tolerance”, the independence principle applies.
7.1.1 Basics of Envelope Principle The envelope principle applies to all tolerated dimensions in all drawings that do not contain any reference to DIN ISO 8015. For the sake of clarity, however, the “DIN 7167 Tolerance” indication should be always provided.
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The tolerance principle says that all geometric features will be bounded within envelopes corresponding to their ideal design and have the Maximum Material Condition. The effective actual size of a simple geometric feature must not exceed its Maximum Material Condition. Effective actual size ≤ Maximum Material Condition Maximum permissible form deviations are thus limited by the envelope. It means that a geometric feature with the “Maximum Material Condition” size must not have any form deviation. In case its size is lesser than the “Maximum Material Condition” but not lesser than the “Least Material Condition”, form deviations are permissible.
7.1.2 Tolerance by Envelope Principle The following rules must be respected when the envelope principle of tolerancing is being applied: -
The envelope principle may be applied only to simple geometric features (surface areas of a cylinder, pairs of planar areas, in extreme cases also to circles or parallel straight lines). The envelope principle must not be applied to complex features.
-
The envelope principle puts limits only on form deviations (circularity, flatness, straightness, cylindricity deviations). Generally, position deviations are not limited by the envelope principle. The only exception is deviations from parallelism that are directly limited by the envelope principle.
-
The envelope principle applies only to geometric features that are directly dimensioned using inner or outer dimensions and for which dimensional tolerances are set. They may take form of general tolerance data. The envelope principle must not be applied to geometric features whose dimensions are derived from a calculation. Also, the envelope principle must not be applied to stepped dimensions and distances as they determine a position, not a form.
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The following are examples illustrating cases where the envelope principle cannot be applied:
Straightness of a slant line or flatness of a slant plane cannot be determined by means of the envelope principle, because no envelope is defined for these
The envelope principle cannot be applied to the slot because its width is not directly dimensioned
Straightness and parallelism of horizontal lines cannot be determined by means of the envelope principle because they do not lie opposite each other
Straightness and parallelism of horizontal lines can be determined by means of the envelope principle only within the overlapping area. This is, however, unsuitable for the practice
Perpendicularity deviations will not be limited by the envelope principle because they are position deviations
Coaxiality deviation swill not be limited by the envelope principle because they are position deviations
Figure 96: Examples of applications where the envelope principle cannot be used
In the figure below, a thickness tolerance of 0.1mm is prescribed for a board with a length of 1000mm. With application of the envelope principle, for the Maximum Material Condition of 8mm no flatness deviation would be permissible, and for the Least Material Condition of 7.9mm a flatness deviation of 0.1mm would be permissible. It is impossible to make this.
DIN 7167 Tolerancing
Figure 97: DIN 7167 Tolerance
⇒ The envelope principle may lead to tolerance specifications that cannot be met In such cases, the DIN 7167 standard permits the use of the envelope principle for individual geometric features. The board must have a larger form tolerance.
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DIN 7167 Tolerancing
Figure 98: DIN 7167 Tolerance (2)
7.1.3
Basics of Independence Principle
The independence principle says that form tolerances and dimensional tolerances should be considered independently from each other. A geometric feature with the “Maximum Material Condition” may also have form deviations, which is not permitted with the envelope principle. Permissible form deviations must be indicated in a suitable manner, as either individual form or position tolerance data, or general tolerances. The independence principle is provided for in DIN ISO 8015; and it says that a tolerance dimension is considered as observed if no actual local dimensions exceed the size limits upward or downward. Every tolerance of dimension, form or position must be independently complied with. Thus, no matching testing is carried out. Where the independence principle is to be applied, the “ISO 8015 Tolerance” indication must be provided in the drawing’s text filed, or otherwise the envelope principle applies. With application of the independence principle, a larger form tolerance may be achieved for the “Maximum Material Condition”.
7.1.4
Tolerance by Independence Principle
The independence principle may be formulated as follows: Every tolerance is subject to separate testing. A workpiece is ok if all tolerances have been respected.
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However, independence does not mean that any individual design deviation must be always fully exhausted, as some types of tolerances are mutually excluded. With the independence principle, all tolerances (i.e. all dimensional tolerances and all geometric tolerances) must be always indicated – either explicitly or generally by means of general tolerances. Where such data are missing, the drawings is considered to be incomplete. With the envelope principle, important form tolerances may be defined through dimensional tolerances. In such case, however, it is impossible to determine whether the envelope tolerancing automatically produces completely tolerated drawings. ISO 8015 enables targeted application of the envelope principle to individual geometric features. This is effective because with the envelope principle the fitting functionality of such features can be easily achieved. This is, however, referred to as ‘envelope condition’, rather than ‘envelope principle’.
Difference between the envelope condition and the envelope principle : The “envelope principle” says that the principle can be generally applied to all simple geometric features, unless the principle has been explicitly rescinded by indication of a form tolerance. The “envelope condition” says that the condition should be purposefully applied to the geometric feature to which it relates. The envelope condition is represented in a drawing by means of attaching letter “E” (as envelope) enclosed in a circle to the fit value.
ISO 8015 Tolerancing
Figure 99: ISO 8015 Tolerancing
The figure below shows form deviations and envelopes for different geometric features. An envelope limits not only individual effects, but also the resulting effect of multiple form deviations.
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simple geometric feature
deviation captured
envelope
Cylinder outside: shaft
Straightness, circularity, cylindricity, parallelism
Cylinder – inside: hole
Straightness, circularity, cylindricity, parallelism
Parallel planes – outside: rectangular prism
Straightness, flatness, parallelism
Parallel planes – inside: slot
Straightness, flatness, parallelism Table 26: Form deviations and envelopes of simple geometric features
The envelope condition compliance check is based on the Tylor testing principle: •
determine MMC of the geometric feature being checked
•
create the envelope area (= the ideal design of the geometric feature with the MMC)
•
check whether the geometric feature being checked matches the envelope without any projections
•
check whether the Least Material Condition has been complied with. For outer dimensions, it must not be exceeded downward in any location, and for inner dimensions it must not be exceeded upward in any location.
Figure 100: Taylor testing principle
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The following figure shows a shaft with the Least Material Condition - LMC = 9.8mm. A form deviation may exhaust the entire value of the dimensional tolerance of T=0.4mm, without any projection off the envelope. Figure b shows a shaft with a central dimension of 10mm. Since half of the dimensional tolerance has been exhausted, only T/2 = 0.2mm is available for the form tolerance. Figure c shows a shaft with the Maximum Material Condition - MMC = 10.2mm. Since the dimensional tolerance has been fully exhausted, no form deviations are permissible. Since in practice it is impossible to create a geometric feature without any form deviations, compliance with the envelope conditions requires that it must never have MMC in all locations.
Figure 101: Taylor testing principle (2)
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8 Differences between ASME and ISO Standard Standardization: In addition to the international standardization of geometric tolerances according to ISO 1101 and other standards, the ANSI Y 14.5 standard had been in place in the USA for decades, largely differing from ISO. In 1994, it was replaced by the ASME Y 14.5 standard and in many points harmonized with ISO (in line with the approximation of ISO to ASME that had occurred in the meantime). Despite that, some differences still persist, lying partially in that ASME offers some extended options as compared to ISO.
Meaning: ASME Y 14.5 – 1994 ([ASM 94], in the text shortly referred to as “ASME”) covers on 133 pages the complete geometric tolerancing issues. In the meantime, a German translation has become available ([ASM 98]. Since this standard is generally applied, inter alia, across the automotive industry, the following text provides a concise summary of major differences against ISO. However, exhaustive completeness is impossible and we don’t pursue it. “p.” indications in the text refer to pages of the ASME standard, or the page-identical German translation.
The following Figure clarifies a)
Representation of dimensions: dimension lines (p.5) are interrupted for the dimension data. Dimension data (p.9) are normally read in the bottom-to-top direction. Auxiliary dimension lines (p.7/8) feature gaps opposite to corresponding edges of bodies and when crossing dimension lines.
b)
Rising dimensioning sequence (p.19): dimension arrows are omitted
c)
Size limits: instead of nominal sizes with limit dimensions (here ø 20 ± 1), size limits are also directly indicated (in two different versions)
d)
Simplified representation of a hole: (p.15/16). Meanings: ● ø 10 through hole ● ø 15 recess hole, depth of 20 to 20.8 from the workpiece surface ● ø 22 cylindrical recess, depth of 5 to 5.5 from the surface
e)
Radius: (p. 28): the tolerance zone lies between the two tolerance limits.
f)
Controlled radius (controlled radius, p.38): the tolerance zone is identical to (e), except that the actual outline must be free of any flattened spots or waves (term of curvature)
g)
Statistical tolerance (p. 38,45): ST sign in a hexagonal box following the dimension being tolerated indicates that the tolerance is subject to statistical tolerated.
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Figure 102: Drawing representations
Tolerated geometric features: ASME partially limits the range of types of geometric features than can be tolerated as compared to ISO: -
flatness applies only to actual geometric features. On the other hand, surprisingly, it uses the straightness symbol for central planes (see under “Tolerance Principle”)
-
position and symmetry are applied only to derived features. For actual features, ASME resorts to surface profiles
Tolerance principle (p. 26/27): generally, the envelope principle is applied (here, it is referred to as “Rule One”). Examples may include the following: -
the envelope condition does not apply to semi-finished products (sheet-metals, timber, pipes etc.) and to corresponding unmachined workpiece surfaces
-
where a straightness tolerance for an axis or a central plane is specified for a feature of size (e.g. a circular cylinder or a pair of parallel planes, p.26), the envelope condition is annulled by that (differently from ISO). Where a feature of size consist of two parallel planes, then the straightness tolerance controls flatness of the central plane.
However, where a straightness tolerance relates to actual lines (e.g. straight lines of a circular cylinder surface), the envelope conditions remains effective. In addition, the following notes can be provided (p.195): “Perfect form at MMC not required“ – either for the entire drawing (this corresponds to the independence principle) or as addition to an individual feature of size (then the envelope condition is locally annulled). MMC means “Maximal Material Condition”. The material condition may be alternatively introduced by means of a straightness tolerance of 0 M for the axis or the central plane.
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Figure 103: Geometric tolerance notations
a) different ways of connecting a feature control frame; b) simplified hole tolerance and datum indication; c) datum location: visible vs. hidden.
Tolerance leader line (p. 49): it is normally drawn from the right or left side of the feature control frame at an angle relative to the tolerated feature (alike an informational arrow line). However, if a position tolerance operates only in a certain direction (except a cylindrical tolerance zone), it is drawn perpendicularly to the tolerance zone also in ASME. The tolerance leader line may be entirely omitted; then, the feature control frame is hung directly on the auxiliary line, or is placed under the dimension indication. For types of tolerances that may relate to both actual and derived features (in ASME, these include only straightness and orientation tolerances), it must be clearly distinguished (identically to ISO) whether the tolerance leader line is connected with the appropriate dimension line or the dimension indication (then a derived feature is being tolerated), or it is not (then an actual feature is being tolerated). However, for other types of tolerances where no risk of mistake is present, ASME’s approach to the positioning of tolerance leader lines is rather generous. Datum triangle: for derived features (such as an axis), the datum triangle is placed on the dimension line (alike ISO; it was different with ANSI in the past). Generally, it may be also hung on the feature control frame pertaining to the datum feature (b). It applies as if the datum triangle was placed at the end point of the tolerance leader line. Datum locations (p. 72,74): the contact point of a straight line lying in parallel with the projection plane is represented by a one dash – two dots line. The informational arrow line is omitted. If the informational arrow line is dashed, the location in the drawing is hidden (it is in the rear) – it is very synoptic. Special tolerance data: the figure below explains the following cases a) Bounded tolerance zone (p.162): a square test region with a size of 25 x 25mm may be placed wherever within the tolerated surface. b) Position tolerance without form tolerance (p.187):U this says that only the tangentially aligned ideal feature rather than actual geometric features must lie within he tolerance zone. In such case it is a flat plate designed on a least condition basis. Form deviations of the actual surface are thus not captured.
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Figure 104: Fig. 104: Special tolerancing a) bounded tolerance zone; b) position tolerance without form tolerancing; c) tolerancing lines within an area; d) projected tolerance zone
c) Projected tolerance zone (p. 48/134): the projected tolerance zone length is indicated in a feature control frame in a box following Q. It applies from the workpiece’s surface on the indicated side. Alternatively, a position and the (minimum) length may be dimensioned using a thick dot-dash line.
Axes/central planes as tolerated features (p.152): unlike ISO, a derived feature is not created from individual cross-sections but from the pertaining ideal counterpart, alike datum features, e.g. for a hole by means of a pin without clearance (this is normally more simple and consistent with the functionality). With this, form deviations are not covered by the position tolerance. Only with the concentricity symbol a and the symmetry symbol d the derived feature will be created either from individual cross-sections or point-by-point. Also, the M symbol M is not used for these. Where M or any other measuring is required, the position symbol I refers to both other location tolerances.
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Special Location Tolerance Data
Figure 105: Special location tolerances
a) position in terms of coaxiality; b) conical tolerance zone; c) crescent-shaped tolerance zone
a) Coaxiality with the maximum material condition: recesses should be always coaxial relative to their holes. The testing is carried out by means of a caliper (M). Therefore, a notation is provided for the position rather than coaxiality. b) Conical tolerance zone: the tolerance zone has ø 0,5mm at surface C, ø 1mm at surface D (due to possible placement of a hole), and it is conical in between. The testing is carried out by means of a caliper. c) Crescent-shaped tolerance zone: it is located at +/-002mm relative to the ideal radius R78 and +/-01mm from an arm of the ideal angle of 15°.
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Edge-based position tolerance and floating position tolerance: ASME uses dozens of examples of this hole series tolerance:
-
Pattern-locating tolerance zone framework (PLTZF): the tolerance zone location is determined using the edge-based system
-
Feature-relating tolerance zone framework (FRTZF): the floating tolerance system (“freely”) relates mutual positions of features. At least a primary relationship regularly occurs here.
Figure 106: Special feature control frames
a) composite frame; b) bounded maximum material condition
This is accommodated by a composite feature control frame, fig. a. It has two lines with the common first compartment containing the tolerance symbol. It is used only for tolerances of position and profile. Both lines have the same datum system, but in the second line the datums may be omitted, starting from the end. The first line is always PLTZF; the second line is FRTZF and it has a lesser tolerance value than the first one. It determines the direction between the datum feature and the tolerated feature. However, theoretical measures determining the location do not apply here. It may even happen that both lines have the same datums. Then, the FRTZF hole series can be only shifted but not rotated. (However, where the first compartment of the frame does not extend, each line applies only to itself, as is generally the case in ISO). Bounded maximum material condition: in figure b, a perpendicularity deviation may be as large as is the deviation of the actual measure from the maximum material limit ø, but not larger than 0.1mm.
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Figure 107: Profile tolerancing
a) different tolerance zone positions; b) bounded tolerance zone; c) position of an actual geometric feature; d) common tolerance zone (coplanarity)
Profile tolerances: they are more versatile than with ISO, fig. 107
a) Non-centric tolerance zone: it may be unilaterally shifted internally or externally (designated by a thin one dash – two dots line), or arbitrarily (with dimensioning). The one dash – two dots line must not be mistaken with the thick one dash – two dots line used by ISO for designation of a bounded tolerance zone. b) Bounded tolerance zone: a profile tolerance is valid only between the points C and D – this is a very effective representation, better than ISO c) Position of an actual geometric feature: the common front surface is the actual plane. However, in ASME, position tolerances are used only for derived geometric features. Here, therefore, we will resort to a surface profile tolerance. d) Common tolerance zone: unfortunately, this term and the “CZ” symbol do not exist in ASME. For flat surfaces, a common tolerance zone is referred to as coplanarity. Again, instead of flatness – which is applied only to individual geometric features – surface profile will be used here. The tolerance arrow is seated on a one dash – two dots line between the surfaces concerned. Moreover, the number of surfaces is indicated – 2 surf(aces) in this illustration. For other types of tolerances, a “2 surf sim.” (2 surfaces simultaneously) notice may be provided below the feature control frame.
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nominal profile
least break
boundary (outline)
Figure 108: Boundary control
a) drawing with an enclosed profile (break); b) boundary
Boundary control of an enclosed profile: Under both ASME and ISO, the maximum material condition may be applied only to simple features of size (circular cylinders and pairs of parallel planes). The boundary control extends the application to any shaped features. The break outline in figure 108a is encircled by a surface profile tolerance zone with a width of 1.2mm. The outline is perpendicular to the primary datum A; or otherwise it is just form tolerance. The break position must leave free the hatched boundary area in b. This will be achieved as follows: -
The nominal profile of the break will take the nominal position defined by the datum system A / B / C.
-
The maximum material condition of the break (the least break) will be shifted all around by the half profile tolerance, i.e. 0.6mm, inwards.
-
This least break may be shifted at all sides by the half profile tolerance, i.e. +/- 0.25 mm, but it must not be turned.
With this, a hatched area will remain that must stay free. This may be checked by means of a functional gage embodying the boundary area in its drawn position.
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9
Specifics of Use of MBN 11011
9.1 Surface Lines as Datums Surface lines must not be used as datums. Only axes of dimensioned geometric features or datum locations may be used.
Figure 109: Surface line as datum
9.2 Angular Measure Tolerances (± Tolerances) Plus/minus tolerances for angles should be avoided. Surface profile tolerances should be used instead.
Figure 110: Angular measure tolerances
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9.3 Stepped Measures Stepped measures must be always aligned with surface profile tolerances with a datum.
Figure 111: Stepped measures
9.4 Surface Profile Outline Symbols Pursuant to ASME Y 14.5M, a drawing may bear only an arrow symbol placed above the feature control frame of the geometric feature, indicating that a certain specification should be applied between the two points referenced by the letters. In 3D-Master the symbol must not be used.
Figure 112: Surface profile outline symbols
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9.5
Concentricity / Coaxiality, Symmetry
Concentricity, coaxiality and symmetry must not be used any more. Tolerances of position should be used instead.
Figure 113: Concentricity / coaxiality and symmetry
9.6
Combined Feature Control Frame for Position and Surface Tolerances
Where combined tolerance is required for a certain geometric feature, two or more individual segments should be used. The lower tolerances set are independent from the upper tolerances set and they may have different datums, or the same datums in a different order of precedence.
Figure 114: Combined feature control frame for position and surface tolerances
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9.7 Use of Unilateral Surface Tolerances Meaning Data set
side
Data set
side
Data set
side
Data set
side
Data set
side
Data set
side
Table 27:Use of unilateral surface tolerances
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10 Best Business Practice (Simplified GD&T) 10.1 Position vs. Concentricity Best Practice:
Figure 115: Best Practice: Positon vs. Concentricity
In order to keep the two holes in the same axis, axi a composite position should be used. Both holes are held within 1-mm mm back to datums A| B | C. In addition, each hole is held to within 0.3-mm mm back to each other. Unlike the concentricity call-out, call out, the composite position can be checked using a simple gage.
Non-Preferred (IS NOT):
In a majority of applications, only 3 datums are required. req In this example, the D-datum datum has been added so that the opposite hole can be checked back to "D".
Position tolerance should be used in place of concentricity, whenever possible. Concentricity call-outs outs require CMM checks and/or expensive gages.
Figure 116: Not preferred: Position vs. Concentricity
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10.2 PROFILE VS. PERPENDICULARITY Best Practice:
Figure 117: Best Practice: Profile vs Perpendicularity
The profile control feature controls both orientation and location of the outer walls. The respective surfaces must lie within (2) theoretical planes spaced 0.5-mm 0.5 mm apart a distance of 189.1-mm and 77.9-mm mm from datum-B. datum
Non-Preferred (IS NOT):
Perpendicularity call-outs outs are not required on a majority of holes. Due to the fact our structures applications use thin steel thicknesses, this application is not necessary. essary. In addition, this call-out call is very difficult to measure.
The perpendicularity control feature only controls the orientation of the outer walls back to Datum surface A. It does not control location because there are no controls to Datum B. Therefore, the basic dimensions (189.1 and 77.9-mm) 7 are not applicable. To correct that, one would have to have ± dimensions.
Figure 118: Not preferred: Position vs. Perpendicularity
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10.3 PROFILE VS. PARALLELISM Best Practice:
The profile control feature controls both orientation and location of the outer walls. The right surface must lie within (2) theoretical planes spaced 0.2-mm 0.2 apart a distance of 4.4-mm. 4.4 Figure 119: Best Practice: Profile vs. Parallelism
Non-Preferred (IS NOT):
As with perpendicularity, a parallelism feature only controls the orientation of a surface relative to the datum. Therefore, the top surface must be parallel to datum -A-,, but the location of the surface is not controlled. Since no distance dimension is provided on the drawing, a measurement would have to be taken from CAD. The tolerance for that dimension would default to the title block tolerance.
Figure 120: Non-Preferred: Profile. vs Parallelism
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10.4 PROFILE VS. ANGULARITY Best Practice:
A profile call-out is required to control both orientation and location.
Figure 121: Best Pracice: Profile vs. Angularity
Non-Preferred (IS NOT):
Angularity only controls the orientation of the surface .
Figure 122: Non-Preferred: Profile vs. Angularity
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10.5 PROFILE VS. POSITION Best Practice: In this example, the hatched areas represent weld zones to a back frame tube. This weld surface is critical to ensure a proper welded joint. By using a profile tolerance, the hatched weld zones are controlled for both orientation and location.
Figure 123: Best Practice: Profile vs. Position
The profile tolerance applies to DIM R15.5; therefore, that dimension becomes a box dimension. .
Non-Preferred (IS NOT):
Again, the primary purpose of this drawing is to ensure a repeatable surface for welding. However, the positional control feature is only controlling the location of arc centerline, not the weld zone surfaces. .
Figure 124: Non-Preferred: Profile vs. Position
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11 Measurement Uncertainty and Tolerances International and national standards as well as associations’ regulations and some industrial standards require knowledge of the measurement uncertainty attributed to a certain measuring result, or verification of capability for a particular control process. The determination of measurement uncertainties involves estimation of the limits – at a defined confidence level – between which the true value of the measurement result lies. Normally, before using a production control gage, its capacity for the appropriate measuring operation is first verified to ensure that the measurement result uncertainty will be reasonably related to the tolerance of the characteristic. Measurement results so obtained may be used in the calculation of measurement uncertainty. Both approaches, whether related or non-related to characteristic tolerances, eventually bear on the tolerancing requirement compliance and testing. Therefore, their outcome should be taken in account in the tolerancing exercise. The figure below shows some implied measurements, represented by means of an Ishikawa diagram. Depending on the objective of measuring and the process situation, the measurement result may be influenced in many ways. With excessive measurement uncertainty due to an unsuitable measuring process, unrealistic concepts of dimensions may be arrived at and unnecessary costs incurred.
Figure 125: Measurement result and measurement uncertainty
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11.1 Measuring and Manufacturing Process Capability Capability of a certain measuring process used to measure parts of a certain selection sample is related to a later review of the manufacturing process. This will be further clarified in an example of simple statistical considerations based on simplified assumptions (normal distribution, without systematic measurement deviations). The measured variance σ2 of a certain characteristic of part is defined as the sum of the “actual“ variance σ2F of the characteristic (manufacturing variance) and the measuring process variance σ2F .
σ2 = σ2F + σ2M
Actual process variance Observed process variance
Large measuring process variance
Figure 126: Overlay of manufacturing process and measuring process variances
Since in the standard formula of process capability Cp
the estimated value of the standard process variance σ is the denominator value, Cp will be as lesser as bigger is the variance σ of the measuring process. The same applies to Cpk.
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The following figure illustrates the value of Cp as function of the characteristic measurand %GRR as measure for relative values of the measuring process variance (standard deviation related to the tolerance of the characteristic) with consideration of additional influences (e.g. from the machine operator).
Actual value of Cp
The higher this value, the more “uncertain” the measurement.
Observed value of Cp
Figure 127: Effect of %GRR on the characteristic quality process capability variable Cp
The illustration shows that the effect of the measuring process variance on the calculated characteristic manufacturing process capability value is for %GRR < 10% non-critical, and for 10% ≤ %GRR ≤ 30% it may be still acceptable, depending on the application situation.
11.2 Determination of Measurement Uncertainty A range of standards and regulations concerning measurement uncertainty have been issued. VDA has stipulated for the German automotive industry and its suppliers that substantial uncertainty components of a measuring process must be determined and estimated using statistical means.
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As an example, Volume VDA 5 [2] mentions concrete effects of influencing components of the surrounding environment, operator staff and the measured object.
In addition, uncertainty of calibration and workpiece fastening may be of some significance, as well as the type of the testing process and other uncertainty components. The different uncertainty components are then aggregated into so called extended measurement uncertainty U as follows:
Their meanings here:
k
Extension factor (the value of k for a confidence level of 95% is approx. 2) 2 c
Standard uncertainty indicated in the calibration sheet
u
Calibration uncertainty of a calibrated workpiece 2 p
Standard uncertainty from the measuring process, i.e. standard deviation of repeated measuring
2 w
Standard uncertainty from material and manufacturing variances (based on variances from the expansion coefficient, form deviations, roughness, elasticity and plasticity)
2 b
The systematic deviation between yi values and the calibration value of the calibrated workpiece XC, expressed as standard deviation
u
u
u
Table 28: Overview of uncertainty components
With deployment of a suitable software, these uncertainty components may be reported individually, which will enhance visibility of the maximum “performance capacity” of the measuring process. This will help to identify improvement potentials and optimize the measuring process, where appropriate. Also, the measuring process may help to establish the “minimum measurable tolerance”.
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11.3 Measurement Uncertainty Considerations unilateral
bilateral
area of tolerance a) area of conformity
area of tolerance a) area of conformity
area of tolerance b) area of nonconformity
area of tolerance b) area of nonconformity
area of tolerance c) area of uncertainty
area of tolerance c) area of uncertainty
Table 29: Measurement uncertainty considerations for limit values (tolerance zone boundaries)
The figure below illustrates how an area of conformity, area of nonconformity and area of uncertainty depend on the extended measurement uncertainty U. extended measurement uncertainty
area of conformity
area of nonconformity
Figure 128: extended area on uncertainty, area of conformity, area of nonconformity
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Growing measurement uncertainty (U)
area of tolerance
rejection
area of conformity
acceptance
area of nonconformity
area of uncertainty area of conformity
rejection
area of nonconformity
Figure 129: Areaof tolerance (USG – OSG)
Significance of a sufficiently small measurement uncertainty, particularly with “small” tolerances, is obvious. Any measurement uncertainty further constrains the manufacturing tolerance. On the other hand, specification of a too small tolerance necessarily leads to increased requirements for the appropriate testing process and, accordingly, to higher costs of production.
11.4 Measurement Uncertainty Implications Consideration of measurement uncertainty at the upper and/or lower limit has different implications for a customer and a supplier. A supplier must always constrain the tolerance zone at the upper and lower limits to provide for the measurement uncertainty, while a customer must always extend the tolerance zone by adding the measurement uncertainty at both limits when accepting a product. If measurement uncertainty was not taken in account, defective parts could be dispatched, with justified rejection of products as a result.
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12 Tolerancing Processes and Concepts 12.1 Product Definition -
The purpose and objective of product definition is complete and unambiguous communication of the proposed intent.
-
Product definition must be sufficiently unambiguous to be equally clear to all stakeholders involved in the product development process. This path leads from the designer, through the manufacturer and the inspector, up to the customer.
12.2 Illustration of Tolerancing Process by Means of General Car Development Process An important success factor of the continuous tolerancing work within the general car development process is coordination of all stakeholders involved in the process and interdisciplinary communication. The common objective should be satisfaction of final customer’s requirements for the whole vehicle product in terms of functionality, reliability and appearance, all that with due regard to cost effectiveness. This chapter provides an exemplary illustration of how the process of tolerancing geometric features in the general vehicle development work could look like.
Step 1: Selection of qualitative characteristics The research starts from the vehicle as a whole. Relevant geometric features having a significant effect on functionality, reliability and appearance of the entire vehicle are identified. Those features will be then grouped under the umbrella term “qualitative characteristics”. In addition to such functional aspects, also the testing process should be taken in account so that a qualitative characteristic may be measured at a later time in the series manufacturing. The qualitative characteristics so identified will be then documented in a suitable manner, e.g. in a characteristic catalogue. As soon as possible, ideally already at this stage, tolerance requirements for the qualitative characteristics so chosen must be considered and documented, e.g. in the characteristic catalogue or a gap and radius plan.
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Step 2: Tolerance analysis of a complete vehicle The complete vehicle will be decomposed into large system components – ideally such that they correspond to assembly groups. For the complete car, this could be for instance the rough design of the bodyworks, engine, chassis, lamps, driver compartments, doors, roofing system of the front compartment, rear module, etc. Using tolerance simulations at the complete vehicle level, tolerance specifications for qualitative characteristics of individual components will be now fine-tuned. The components as such will be further examined only as “black-boxes”. To do that, we need the tolerance specifications identified in Step 1 on the one hand, and components’ datum systems as well as information about assembling and coupling concepts for the components in the complete vehicle on the other. Already at this stage there is a significant potential for optimization through balanced finetuning of tolerance specifications for qualitative characteristics of components, and through possible improvement of the assembling and coupling concepts. Results, together with appropriate tolerance simulations, and the underlying assembling and coupling concepts are documented in a suitable form. Schematic representation of system boundaries of a complete vehicle:
complete vehicle
component
system boundary
part system boundary
Figure 130: System boundaries of a complete vehicle
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Example of a part and a component in a complete vehicle:
Figure 131: A part and a component in a complete vehicle
Step 3: Tolerance analysis at the component level Step 3 will be carried out by different persons who are responsible for the relevant components. They may be system suppliers. The tolerance specifications identified in Step 2 for qualitative characteristics of components must be verified through the tolerance simulation. It often happens that tolerance specifications of a component characteristic cannot be met. In such case, the first step is to look for optimization possibilities before the problem is escalated to the complete vehicle level for resolution. In addition to externally specified tolerances at system boundaries, there is, naturally, a range of qualitative characteristics within a component that require a review by the person responsible for the component.
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Step 4: General dimensioning concept The tolerancing process is closely interrelated with other processes involved in the general car development. They are particularly the following : -
Preparation and approval of a gap and radius plan
-
Documentation of datum systems/reference point systems in drawings
-
Documentation of geometric tolerances in drawings or CAD models
-
Identification of special characteristics in drawings
-
Designing manufacturing and assembling tools
-
Planning prototype, pilot run ad series manufacturing tests
-
Arrangement of the testing process
The objective of Step 4 is to ensure loss-free, insofar as possible, assessment of the acquired learning for the purposes of the above development processes. It requires intensive information sharing with relevant entities involved in the process. Losses of information are as lesser as better are the entities participating in the development engaged in the Simultaneous Engineering work. The objective of the tolerancing process systems, which is pursued across all project stages, can be best attained with suitable team structures and actively cooperating partners within the frame of Simultaneous Engineering.
Step 5: Evaluation of results for prototype and series manufacturing Where conspicuous deviations of prototype and pilot series testing results from simulation results occur, it is necessary to check whether the toleration simulations were not based on wrong or adverse assumptions. Where appropriate, the assumption must be corrected so that the derived experience may be applied to further projects. Where appropriate, decisions concerning approval of geometric deviations of part measures must be adopted within the frame of the manufacturing process and product approval procedures (“Produktionsprozesse- und Produktfreigabe” (PPF)). The learning derived from the tolerancing process may provide an important guidance here. Such knowledge may be also used in the analysis of problems in the series manufacturing in relation to dimensional deviations.
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12.3 Tolerance Assessment in FMEA In the Failure Modes and Effects Analysis (FMEA) a potential failure is often described only in qualitative terms, e.g. “the insulating coat thickness is too small”. Particularly with a flat quality characteristic curve the potential consequence of a failure strongly depends on the quantitative measure of the failure, e.g. “little significance if the insulating coat thickness is 5% lesser, but great significance if the insulating coat thickness is 5o% lesser”. Therefore, quantitative description of a failure should be preferred (e.g. “the coat thickness is 5% to 30% lesser”). Determination of classes of characteristics is an integral component of the quality planning process and it reflects the classification of failures related to a qualitative characteristics. A general classification of failures is focused on the consequences of failures, and it classifies failures into three classes: “critical failure”, “major failure” and “minor failure”, which may be complemented by further sub-classification. However, there is no supporting generally accepted or standardized text or interpretation on which the classification of characteristic failures could be built. Today, estimations of process or product risks for functional characteristics or other qualitative characteristics are typically based on system FMEA ratings. If the classification of characteristics has been completed, for the sake of expediency we will further focus on the classification of risks. If the classification by risk class has been already done as part of the system FMEA of a product, tolerances of functional characteristics or qualitative characteristics will follow such classification. Logically, as the risk is reduced, tolerances will be set, with due regard to manufacturing capacities, at such levels that decisive factors in the tolerance selection exercise are costefficiency considerations and that small tolerances are set only in instances where the existing risk is proportionally high.
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12.3.1 Example for Assignment of FMEA Ratings to Characteristic Classes FMEA Rating
Severity/significance Probability of occurrence
Probability of detection
Severity/significance Probability of occurrence
Probability of detection
Severity/significance Probability of occurrence
Probability of detection
Class of characteristics Rating
Critical characteristic
9 -10
typical requirements
---
Cpk > 1.67
---
No value of the characteristic out of the area of tolerance is permissible (0 ppm)
Rating
Major characteristic
5-8
typical requirements
---
---
A rate of characteristic values outside the area of tolerance of up to 62 ppm is permissible
Rating
Minor characteristic
1-4
typical requirements
---
Cpk > 1.00
---
A rate of characteristic values outside the area of tolerance of up to 2700 ppm is permissible
Table 30: Assignment of FMEA ratings to characteristic classes
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Cpk > 1.33
12.4 Process Prerequisites for Functional Dimensioning Concept
Concept stage
Development
Prototypes
Manufacturings
Figure 132: Dimensional quality implementation process
Instructions for the implementation of dimensional quality: -
Concept stage: requirements placed on the product are clearly defined
-
Development: design complies with the product requirements; the product documentation has been prepared
-
Prototypes: the proposed product design has been verified by means of planned testing; manufacturing capacities enable series manufacturing
-
Manufacturing: process data processing has been implemented and feedback data flow from production to development is provided
12.4.1 Required Data and Information Concept stage: -
work plan of functional dimensions, assembly plan
-
reports and documentation o
○ product-specific definition of measures
o
○ competitiveness targets
o
○ comparison of concepts - evaluation
-
preparation of detailed task formulations
-
existing measure data
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Figure 133: Concept stage
Development: -
structural composition plan, assembly plan
-
identification of part location points (locators)
-
3D summary tolerance analysis o
○ optimized tolerancing and determination of assembling methods
o
○ design verification
o
○ weighted process control points
-
measurement plan
-
verified dimensioning and tolerancing documentation
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product structure / assembly plan
geometry, datums and tolerances assembling methods
Figure 134: Development
Prototypes: -
verification of the functional dimension plan, assembly plan
-
prototype measurements
-
3D summary tolerance analysis
-
o
simulation/process comparison
o
fine-tuning on changes
o
communication for problem resolution
documentation of deviations between development specifications and the actual prototype
Manufacturing: -
-
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3D summary tolerance analysis o
verification of calculation results
o
targeted process optimization
o
problem identification and resolution
problem resolution database (expert system) as source of information for future projects
12.5 VDA Standardized Tolerancing Process Draft Tolerancing process – 1.Information gathering ▪ Drawings, sketches ▪ Bill of materials ▪ Assembly structure ▪ Catalogue of requirements ▪ Functional description ▪ ...
2. Definition of critical functional areas and identification of requirements ▪ Function ▪ Life cycle ▪ Optics ▪ Input from FMEA Produkt ▪ ...
3. Identification of datum systems ▪ Assembly/layout/arrangement concepts ▪ Measuring concepts ▪ ...
4. Execution of tolerance simulation
Tolerancing process
▪ Examination of the worst-case scenario ▪ Error propagation law ▪ CA-tools (3D simulation) ▪ Effects of forces and distortions ▪ ...
5. Confirmation of feasibility ▪ Manufacturing ▪ Measuring equipment ▪ ...
6. Plan/actual comparisons and corrective actions ▪ Optimization of assembly structure ▪ Provision of adjustment options ▪ Tolerance fine-tuning ▪ Reduction of tolerance sensitivity ▪ Tolerance narrowing ▪ ...
7. Documentation of outcome ▪ Datum system and tolerances in drawing ▪ Catalogue of functional measures ▪ Computation documentation
▪ ... 8. Product verification and validation ▪ Comparison of simulation results against prototype testing results ▪ Manufacturing process and product approval (PPF) ▪ ...
9. Process management and care in series manufacturing ▪ Problem analysis of lot in progress ▪ Documentation of capability ▪ Change management ▪ Lessons Learned review ▪ ...
10. Service ▪ Field monitoring ▪ Product management ▪ Supply chain processes
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13 Tolerance Analysis and Tolerance Simulation 13.1 What Is Tolerance Analysis? The term ‘analysis’ generally refers to systematic examination of a certain object or substance with regard to all its determining individual components and factors. Accordingly, tolerance analysis means an analysis of: -
geometry
-
function
-
material
-
assembling sequence
13.2 What Do We Need Tolerance Analysis for? ⇒ To obtain results for verification of quality- and function-related customer requirements.
Figure 135 Representation of results (quality- and function-related customer requirements)
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13.3 Prerequisites for Effective Tolerance Analysis Principal Rule: The basis of an effective tolerance analysis is always effective tolerancing. Product requirements
Function
Manufacture
Testing
The tolerancing of a workpiece must be carried out in a manner assuring that its specified function will be complied with. Since a product without functional requirements is useless, this is the top-priority requirement
A workpiece must be able of manufacturing within the tolerances, with due regard to cost-efficiency and process arrangements.
When testing of a workpiece using measuring and testing instruments is carried out, the testing work must be as easy and safe as possible. Critical factors in this are the chosen type of tolerance (e.g. form or position) and tolerancing principle (envelope
Figure 136: Product requirements for the tolerance analysis
It is obvious that determination of a “proper” tolerance is a process in which a broad array of different aspects needs to be taken in account. Tolerancing which is optimal in both functionality and economy terms unconditionally requires close cooperation between the Development, Engineering, Manufacturing and Quality units.
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13.3.1 Requirements Placed on Drawings Completeness and unambiguity
Technical drawings of individual parts must provide a complete and unambiguous product description. complete:
unambiguous:
i.e. it must indicate all substantial properties
i.e. it must not allow for any differing interpretations
Figure 137: : Requirements placed on drawings
Further, a drawing must comply with all technical and economic requirements, i.e. it must satisfy the same criteria as product requirements: it must be fit for the
FUNCTION
MANUFACTURING
TESTING
Figure 138: Requirements placed on drawings (2)
Functional fitness of a part: ⇒ Every structural part must be toleranced so that it is able to perform its intended function throughout its life cycle. This generally implies the following: a part must always be capable of being analyzed.
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The following rules apply to this: -
A part must be geometrically described.
-
Tolerances (degrees of freedom and arrangement) must be limited.
-
All functional parameters of a part must be described.
-
A part must be capable of being tested according to its description (specification of points of measurement)
-
To enable an optimum analysis, it must be possible to describe a part by means of metrological procedures and their assessment within an assembly.
-
This requires general assignment of datum points to a part for assembling.
-
Metrological assessment of different parts and assembly units must provide an outcome that clearly evidences quality and provides the basis for corrections. (Position and deviations).
13.4 Tolerance Simulation Basically, 1D and 3D simulators can be distinguished.
The difference depends on the method
Figure 139: 1D and 3D simulation
As part of statistical tolerancing, it is possible to simulate assembling of individual components or a combination of individual characteristics in mathematical terms. This
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involves observation of each characteristic of a dimensional chain as a random sequence whose distribution is known, or at least it can be considered as known. Mathematical “linking” of random variables eventually yields values for the fitting dimension, or the gap/flush. Such linking may be a simple summation (taking regard of the appropriate counting direction or spatial direction), but computation of complex functional relationships between different measures is also feasible. Moreover, tolerance chains of multidimensional characteristics (such as position within a plane or space) can be also simulated. Such simulations are often undertaken as part of the development work to determine whether, and with what multitude, a design may induce problems in a later manufacturing or assembling process (e.g. difficulties with coupling two components). The major problem in mathematical modeling of a tolerance chain typically lies in estimating what the distribution of a characteristic in the future manufacturing process will be like. Looking at SPC’s of real processes or histograms of such data we can see that normal distribution is often not more than a rough approximation. Particularly characteristics having zero limits (e.g. characteristics of form or position) may have only values greater than zero, which may produce distributions that are inclined on the right-hand side, with zero as lower limit. Linking characteristics with normal distributions normally generates a “favorable” distribution of the coupling dimension, i.e. the resulting distribution is “small” relative to the tolerance of the coupling dimension. On the other hand, if we apply a rectangular distribution to individual features, the resulting distributions will be significantly wider. A rectangular distribution is thus a rather pessimistic assumption. A user usually has no other choice than to adopt, in cooperation with the production planning unit, assumptions regarding supposed manufacturing distributions that are as realistic as possible. This may be naturally aided by appropriate experience of similar ongoing processes. However, examination of Cp and Cpk values is not sufficient as they do not show the distribution of characteristics. Commercial summation programs offer a choice of model distributions for different dimensions (triangle, trapezoidal or skew distribution) and enable for example: -
representation of the resulting distribution of a coupling dimension as well as its statistical parameters;
-
representation of theoretical shares within and outside an area of tolerance;
-
information on individual tolerance percentages of the overall coupling dimension tolerance, i.e. the relative changes in this value if a tolerance is applied as zero.
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13.4.1 One-dimensional Simulation / Calculation One-dimensional (1D) tolerance simulation examines each (spatial) direction individually, and is based on quite simple mathematical models. In most cases, the basis is one of the three simple mathematical computation methods: (direct summation of tolerances of individual parts T = t1 + t2 + t3 + ... = Σ ti
simple statistical calculation: Formel 6
Square root method : Formel 7
It should be taken in account that 1D simulation fails to consider certain important mutual effects, because e.g. mutual effects of three spatial dimensions are a priori excluded. The 1D simulation is sometimes used as pre-stage of the 3D simulation to obtain the first rough estimate of the tolerance situation, and it may be carried out using simpler tools (e.g. the standard MS-Excel software).
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13.4.1.1 Example of One-dimensional Simulation / Calculation
Figure 140: Execution of 1D Studies
13.4.1.2 Excel Spreadsheet for One-dimensional Simulation / Calculation
Figure 141: 1D Excel spreadsheet
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13.4.2 3D Analysis Process As opposed to the above approaches, 3D analyses take account of the statistical nature of tolerances. We at JC currently use the VisVSA (VSA) 3D simulation software. During a simulation, VSA alternates all tolerances within a defined statistical distribution. The simulation outcome thus provides a picture of tolerance fluctuations and the casual nature of manufacturing processes.
Figure 142: 3D analysis overview
Another advantage of a 3D analysis is in that the simulation may yield statements as to process characteristic values (e.g. Cp/Cpk) and their appropriate originators or contributors. The identification of originators/contributors, including percentages of their variance impacts, is referred to as sensitivity analysis (HLM analysis). The VSA simulation reflects both influence of individual part tolerances and process tolerance implications (coupling sequence, layout concept). If a critical low-level assembly group is assembled (coupled) in a too early point of time, the subsequent components and assemblies will appear in the sensitivity analysis. They will not appear if the critical component is assembled in a later point of the coupling process. The VSA analysis further represents the effect of process-dependent contingent tolerances. Such tolerances (such as clearance in pin/hole couplings) will also appear in the list of originators, sorted by percentage weight.
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This detailed analysis enables a target-oriented analysis of: -
assembling methods
-
layout concepts
-
functional testing of motion processes
-
design of individual parts
Development process pursuing : Quality enhancement through assessment of ensuing factors
Cost reduction through preliminary tolerancing
Development process assessment: Is the assembly group functional?
Can the parts be coupled?
How should parts be mutually arranged ? Which tolerance is critical with regard to the entire assembly group? Figure 143: Development process assessment
Optimization potentials implied by a 3D simulation can be integrated into an existing analysis model. With this, verification of effects of tolerance changes may be accomplished with lower time intensity. Changes in coupling sequences, layout concepts and engineering improvements require, depending on the type of change to be implemented, more time-intensive adjustments of the simulation model. However, any modification of a model should be made only within the area being changed. Verification of alternative options does not require development of an entirely new simulation model. Only the affected parts need to be modified. Another important benefit of the VSA simulations, as compared to one-dimensional analysis methods, is in that it captures geometric effects. Particularly in complex assemblies threedimensional geometric effects occur whose existence is difficult to prove without deployment of simulation tools .
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In addition to its direct benefit for the process of optimizing a particular design series, the learning from simulation may be used as a knowledge base for future analyses. Drawbacks of the VSA simulation include significant time intensity of the analysis model development work and limitation to examination of ideally solid parts only. The time intensity ensues from the fact that complete description of a manufacturing process requires ex ante gathering of extensive amounts of data, which must be then compiled into a computer simulation model. One positive side effect of this approach is a very high degree of detail of examination exercises. With this, problems like missing input parameters can be detected at a very early stage. Limitation to coupling methods that are free of any tension means that distortions emerging in the part coupling process cannot be represented in a simulation model. In practice such distortions appear when elastic distortion of parts occurs as result of the action of clamping forces (tool, welding pliers). A detailed analysis of all coupling processes and specialist experience of the simulation tool may help to significantly reduce any uncertainties resulting from the limitation to solid parts. When all relevant data have been entered into the computation model, VSA generates two simulation outputs: -
Monte Carlo (MC) simulation with assumed dimensional values and process indicators (capability, variance spread, repair percentage...)
-
Sensitivity analysis (HLM rating) with percentages of impact of contributors as Pareto diagram.
13.4.2.1
Monte Carlo Simulation and Sensitivity Analysis ( HLM Analysis)
The Monte Carlo analysis examines variance values of a particular qualitative characteristic, defective part/repair percentages and the capability indices Cp and Cpk. The sensitivity analysis provides an accurate analysis and optimization of a simulation model. It generates a list of originators/contributors of the variance identified in the Monte Carlo simulation, sorted by percentage weight. It is also referred to as High-Low-Median (HLM) analysis.
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Monte Carlo and High-Low-Median simulation results embody a significant optimization potential. With application of targeted measures such as: •
change of the part coupling sequence
•
change of datum systems
•
optimization of the part and assembly group layout
•
tolerance narrowing
•
widening of “tolerances of concern”, etc.
a user is able to comply with applicable criteria and ensure safe, reproducible and costeffective processes.
Graphical representation of dimensional tolerance
Output diagram
Monte Carlo Simulation (process capability, variance width, repair percentage) Sensitivity analysis Percentage weights of identified process Figure 144: Comparison between the Monte Carlo simulation and the sensitivity analysis
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13.4.2.1.1 Monte Carlo Simulation
n-simulations
Aufteilung von Block und Winkel
nominal assembly
n blocks
nominal gap
Block
random component sampling, assembling and measuring
n angle
n-fold repetition
angle
disposal of used components
Figure 145: Monte Carlo simulation procedure
Normal (Gaussian) distribution:
This is the basis of statistical research. This distribution describes the probability of occurrence of a certain spread of variance for certain random configuration of events. Process results are dispersed around their mean values and the variances have a certain spread. The process spread is typically referred to as standard deviation.
Figure 146: Normal distribution
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13.4.2.1.2 Sensitivity Analysis (HLM Analysis)
The sensitivity (High Low Median Simulation = HLM) analysis examines the question what measures/tolerances bear on the process indicators determined through the Monte Carlo simulation and lists these originators ordered by their respective percentage weight.
⇒ HLM determines the percentage of influence of each tolerance on the qualitative characteristic and represents originators. nominal assembly
tolerance value
nominal value
Qualitative characteristic
component
Figure 147: Sensitivity analysis procedure
Figure 148: HLM Report
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13.4.3 Characteristic Values of Process Capabilities Cp and Cpk For the sake of simplification, processes or distributions of process results are often described using a number of characteristic values – indicators. One important indicator is process capability. Distributions of process results typically follow the Gaussian normal distribution. The variance spread is then defined by the standard deviation - sigma. The process situation is described by the distribution mean value. Every process has its specification limits within which the results must fall to meet the specification and be able of dispatch to a customer. Process capability compares the spread and position of the process distribution to those of the specification limits. In the automotive industry, the basic requirement is that the standard deviation sigma must fall at least six times within the specification limits, and three times between the lower specification limit and the mean value of the distribution and three times between the upper specification limit and the mean value (+/- 3 sigma from the mean value). This requirement describes the ideal condition when a process is in the middle between specification limits.
6 sigma region
Six Sigma = 99.73 % of all parts is within this region Figure 149: Six Sigma region in a HLM Report
150
Then the process capability Cp does not respect the position of the mean value of the process, and it only describes the spread of the process distribution. When looking at the Cp value, a process may seem to be appropriate as to the specification limit interval, but even though it may be outside the specification limits. Where the distribution is narrow and specification limits lie far from each other, Cp is always large regardless of where exactly the distribution is positioned relative to the specification limits.
The calculation of Cp from the upper and lower specification limits (OSG (Obere Spezifikationsgrenze) = upper specification limit; and USG – (Untere Spezifikationsgrenze) = lower specification limit) and the standard deviation sigma uses the below formula:
The process capability indicator Cpk reflects the mean value position. In addition to the requirement that the process distribution must be narrow and specification limits must be wide, now it is important to have the mean value of distribution as close to the centre between the specification limits as possible. Only if the three requirements are met the Cpk value is high. Where the process is not positioned close to the centre between the specification limits, the lesser distance between the mean value of distribution and that of the specification limits will be applied in the calculation of Cpk. With this, Cpk will be in most cases lesser than the respective Cp. Definition of Cpk using the mean value µ, the respective standard deviation σ and the upper/lower specification limit(OSG; USG) will be as follows:
Or more simply:
• • •
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Xmin = 3, then Cpk = 1 (corresponds to the 3σ requirement, which is a standard in the automotive industry) Xmin = 4, then Cpk = 1.33 (corresponds to 4σ) Xmin = 5, then Cpk = 1.67 (corresponds to 5σ)
13.4.3.1 Tolerance and Manufacturability Calculation
predefined tolerance Process variance
The Sigma value describes the number of parts with sound quality”
arithmetical average Meas. values
upper tolerance limit
lower tolerance limit
Tolerances in a drawing must be sufficiently large to achieve a reasonable cp / cpk value ! Figure 150: Tolerance and manufacturability calculation
13.4.3.2 Examples of Manufacturability for cp and cpk
capability indicators
Figure 151: Example of a garage for cp and Cpk
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13.5 Example: 3D / 1D Method Workflow for Interiors individual part data
quality requirements in assembling
assembling work sequence
customer-defined points of measurement
calculation results
Figure 152: Example of 1D and 3D workflow for interiors
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14 Tolerance Management at JC: Dimensional Management 14.1 Dimensional Management Objectives “Product Development puts on a drawing anything they want.... ...and then, Production makes it somehow .“
Dimensional Management provides support for the: •
definition of the tolerancing concept (GD&T)
•
definition of, and compliance with, quality standards relating to GD&T
•
definition of the part assembling sequence
•
designing of concepts for tooling, gages and testing instruments, and reference point systems
•
preparation and updates of tolerance calculations
•
integration of customer feedback, manufacturing and Quality Engineering
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The Dimensional Management methodology and VSA-3D software are well suited to help achieve dimensionally reproducible production solutions, provided that the methodology is deployed in a new project at the right moment. •
● Setup of a cross-functional team between the Planning, Development, Engineering, Manufacturing, suppliers and the Dimensional Management team is one of keys to success
•
● Unambiguous quality targets are irreplaceable
•
● Necessary changes and modification must be able of implementation with regard to time and cost considerations, and recognized and initiated as soon as possible
Costs Required for Manufacturability
Figure 153: Costs needed for manufacturability
155
Costs /quality
quality
costs time Figure 154: Cost reduction through preventive action by DM
Quality improvement through optimization of process parameters (Robust Engineering)
Engagement of Dimensional Management at the kickoff of a project
Summary: Tolerance calculations •
are possible only with a good drawing GD&T concept
•
are needed for verification of all part drawings
•
are needed for the “green” DSO Review report
•
must be carried out together with the Engineering team, or alternatively with the Dimensional Management team
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14.2 General neral Tolerance Analysis Process at JC
• ▪ Information gathering • Definition of critical functional areas and identification of requirements • Identification of datum systems • Execution of tolerance simulation • Confirmation of feasibility • Plan/actual comparisons and corrective action • Documentation of outcome • Product verification and validation • Process management and care in series manufacturig • Service
Figure 155: General tolerance analysis process at JC
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14.2.1 Relevant GD&T Reports According to PLUS Action Plan
Activity planning and support
Verify manufacturability through calculation of tolerances
Define GD&T concepts and test interface positions (e.g. footprint study)
Verify calculations based on feedback from the Manufacturing and/or suppliers
Verify calculations based on part prototypes
Figure 156: GD&T reports in the PLUS plan
13.2.2 Relevant GD&T Points in DSO Form Sheet Every DSO audit at JC involves, inter alia, a check of the following GD&T points from the DSO Form Sheet:
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14.2.2 Support Options for Individual PLUS Stages PLUS stage 0-1: Concept review using experience values for GD&T Input:
Output:
- part structure according to BOM
- verification of the position within the vehicle (BIW)
- experience value for part tolerances, tooling concept, assembling sequence, BIW tolerances
PLUS stage 1-2: Definition of the tolerancing and tooling concept Input:
Output:
- part tolerances, tooling concepts
- verification of tooling concepts from the Engineering
- assembling sequence agreed with the Engineering
- verification of individual part tolerances and drawing tolerances - verification of the position within the vehicle (BIW)
PLUS stage 2-3: Confirmation of the tolerancing and tooling concept Input:
Output:
- individual part and assembly group tolerances approved by the customer
-
verification of the supplier's tooling concept
-
verification of drawing tolerances of individual parts and assembly groups
-
verification of the position within the vehicle (BIW)
- the tooling concept confirmed by the customer - BIW tolerance confirmed by OEM
PLUS stage 3-5+: Support for the Engineering and the series manufacturing management
Figure 157: Support options in the PLUS plan
159
14.2.3 Tolerancing Communication Platform: Workgroup on Tolerancing The workgroup on tolerancing integrates all necessary units -
Engineering
-
Product Manufacturing
-
Dimensional Management
-
Quality Department
to recognize and optimize different tolerance analysis aspects, issues and topics.
Figure 158: Workgroup on tolerancing
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14.3 Quality Objectives at Johnson Controls
Figure 159: Quality objectives at JC
assembly drawing tolerances with SC / CC = +/- 5 sigma (cp / cpk = 1.67) all other assembly drawing tolerances = +/- 4 sigma (cp / cpk = 1.33)
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15 Annex 15.1 Guidance for Practice Dimensional and geometric tolerances must be functional and fit for manufacturing and testing. This aim is supported by respecting the following principles: 1) Tolerances – as few as possible and as many as necessary 2) General tolerances should encompass not only dimensions, but also the form and position 3) Tolerance notations must be unambiguous 4) Tolerance notations must be faultless 5) Reasonable datum features/datum systems should be always used 6) The tolerancing principle applied should be always indicated in a drawing 7) Unambiguous measuring requirements for tolerance testing should be always laid down
1. Tolerances - as few as possible and as many as necessary! Redundancy of tolerances compromises clarity and comprehensibility of a drawing, and gives raise to increased demands during the manufacturing and testing. Since position tolerances also control the form, form tolerances for the same geometric feature may be redundant.
2. General tolerances should encompass not only dimensions, but also the form and position A drawing should provide clear information about the general tolerances used. Since a drawing missing geometric tolerances is normally incomplete, geometric tolerances should be covered by at least general tolerances. As a rule, functionally important geometric tolerances of form and position should be explicitly stated in a drawing. This will simplify the test planning.
3. Tolerance notations must be unambiguous Toleranced features and datum features must be clearly recognizable in a drawing.
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4. Tolerance notations must be faultless I case of doubts, relevant standards should be consulted or appropriate qualified specialist assistance sought.
5. Reasonable datum features/datum systems should be always used Datum features should be chosen in such manner that is appropriate to the clamping/locating conditions during the testing. Datum surfaces should be sufficiently large and feature high stability of form and quality of surface.
6. The tolerancing principle applied should be always indicated in a drawing This warning is necessary because international practices and German practices are different. While the independence principle is preferred at the international level, the envelope principle is considered as generally agreed in Germany, unless a drawing contains a notice to the contrary. For the sake of clarity with regard to the internationalization of economy, a drawing should always indicate whether it has been toleranced according to DIN 7167 or ISO 8015.
7. Unambiguous measuring requirements for tolerance testing should be always laid down Since standardized regulations for tolerance measuring practices are still missing, adequate regulations should be incorporated into working instructions or internal rules.
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15.2 Wikipedia Page on Dimensional Management
Search term: Dimensional Management
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