BS 1134 1 1988

British Standard

A single copy of this British Standard is licensed to I S B ) c ( , y p o C d e l l o r t n o c n U , 3 0 0 2 r e b m e t p e S 6 1 , p u o r G r e v o R , t t e k c i r p l u a p : y p o C d e s n e c i L

paul prickett

16 September 2003

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BRITISH STANDARD

Assessment of surface texture — Part 1: Methods and instrumentation

I S B ) c ( , y p o C d e l l o r t n o c n U , 3 0 0 2 r e b m e t p e S 6 1 , p u o r G r e v o R , t t e k c i r p l u a p : y p o C d e s n e c i L

UDC 621.9.015:620.179.118:001 621.9.015:620.179.118:001.4 .4

BS 1134-1: 1988

BS 1134 1134-1: -1:19 1988 88

Committees responsible for this British Standard The preparation of this British Standard was entrusted by the General Mechanical Engineering Standards Committee (GME/-) to Technical Committee GME/10, upon which the following bodies were represented: Department of Trade and Industry (National Engineering Laboratory) Department of Trade and Industry (National Physical Laboratory) GAMBICA (BEAMA Ltd.) Gauge and Tool Makers’ Association Institution of Production Engineers Loughborough University of Technology University of Warwick Coopted member

I S B ) c ( , y p o C d e l l o r t n o c n U , 3 0 0 2 r e b mThis British Standard, having e been prepared under the t p direction direction of the General General e Mechanical Engineering S Standards Committee, was 6 published under the authority 1 BSI and comes , of the Board of BSI p into into effect effect on u 29 Februa ry 1988 1988 o February r G© BSI 11-1999 r e v BS 1134 first published o Decembe Decemberr 1950 1950 RFirst revision revision April April 1961 Amendments issued since publication , t First published pub lished as BS 1134-1 11341 t e Amd. No. Date of issue Comments k August 1972 revision February February 1988 c First revision i r p l u The following BSI references a relate to the work on this p : standard: y p Committee reference GME/10 o Draft for comment 85/74262 DC C d e ISBN 0 580 16269 9 s n e c i L

BS 1134-1:1988

Contents

Committees responsible Foreword

Page Inside front cover iii

Section 1. General 1 Scope 2 Definitions


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Section 2. Determination of surface roughness 3 Sampling lengths 4 Graphical determination of parameter values 5 Statements of surface roughness

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Section 3. Instrumentation 6 Stylus-type measuring instruments 7 Accuracy

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Appendix A Parameter values Appendix B Method divergence of instrument reading Appendix C Factors affecting the statement of accuracy

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Figure 1 — Surface characteristics and terminology Figure 2 — Traversed length Figure 3 — Profile departure Figure 4 — Local peak of the profile Figure 5 — Spacing of local peaks of the profile Figure 6 — Local valley of the profile Figure 7 — Profile peaks Figure 8 — Profile valleys Figure 9 — Spacing of profile irregularities Figure 10 — Profile section level Figure 11 — Profile bearing length Figure 12 — Arithmetical mean deviation of the profile (Ra) Figure 13 — Maximum height of the profile (Ry) Figure 14 — Graphical determination of Ra values Figure 15 — Graphical determination of Rz values Figure 16 — Graphical determination of S m values Figure 17 — Graphical determination of S values Figure 18 — Graphical determination of tp values Figure 19 — Stylus acting midway between two skids Figure 20 — Profile instrument frequency response Figure 21 — Permissible deviations of the transmission coefficient Figure 22 — Symbols for the direction of lay Figure 23 — Centre arithmetical mean lines (A) and electrical mean lines (B)

3 4 5 5 6 6 7 7 8 8 9 9 10 13 13 14 15 15 17 19 21 22

Table 1 — Sampling lengths Table 2 — Static measuring force of the stylus Table 3 — Evaluation lengths Table 4 — Nominal sinusoidal frequency response characteristics for a profile instrument Table 5 — Upper and lower limits of transmission coefficients Table 6 — Preferred nominal values for arithmetical mean deviation of the profile (Ra)

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Page Table 7 — Preferred nominal values for ten point height of irregularities (Rz), and maximum height of the profile (Ry) Table 8 — Preferred nominal values for mean spacing of profile irregularities (S m), and mean spacing of local peaks of the profile (S ) Table 9 — Comparison of Ra values obtained by graphical and instrumental means Publications referred to

I S B ) c ( , y p o C d e l l o r t n o c n U , 3 0 0 2 r e b m e t p e S 6 1 , p u o r G r e v o R , t t e k c i r p l u a p : y p o C d e s n e c ii i L

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Inside back cover

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BS 1134-1:1988

Foreword This Part of BS 1134 has been prepared under the direction of the General Mechanical Engineering Standards Committee and is a revision of BS 1134-1:1972, which is withdrawn. The definitions given in this Part of BS 1134 supersede those given in BS 6741-1 and BS 6741-2. BS 6741-1 and BS 6741-2 are accordingly withdrawn. BS 1134 was first issued in 1950 and revised in 1961 and 1972. This revision takes account of the 1982 edition of ISO 468 “Surface roughness — Parameters, their values and general rules for specifying requirements” published by the International Organization for Standardization. BS 1134-1:1972 dealt with two parameters, Ra and Rz, whereas this edition covers the additional parameters Ry, S m, S and tp. Additional parameters may be found in ISO 4287-1:1984 “Surface roughness — Terminology — Part 1: Surface and its parameters” and in ISO 4287-2:1984 “Surface roughness — Terminology — Part 2: Measurement of surface roughness parameters” . BS 1134-2 gives general information and guidance. I S B ) c ( , y p o C d e l l o r t n o c n U , 3 0 0 2 r e b m e t p e S 6 1 , p u o r G r e v o R , t t e k c i r p l u a p : y p o C d e s n e c i L

A British Standard does not purport to include all the necessary provisions of a contract. Users of British Standards are responsible for their correct application. Compliance with a British Standard does not of itself confer immunity from legal obligations.

Summary of pages This document comprises a front cover, an inside front cover, pages i to iv, pages 1 to 26, an inside back cover and a back cover. This standard has been updated (see copyright date) and may have had amendments incorporated. This will be indicated in the amendment table on the inside front cover. © BSI 11-1999

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I S B ) c ( , y p o C d e l l o r t n o c n U , 3 0 0 2 r e b m e t p e S 6 1 , p u o r G r e v o R , t t e k c i r p l u a p : y p o C d e s n e c iv i L

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Section 1. General 1 Scope This Part of BS 1134 describes methods for the assessment of surface texture of machined, self-finished and other surfaces and describes the characteristics and parameters standardized for use in industry. It embraces the following. a) The terminology to be employed in statements relating to surfa ce texture and measurement of surface texture. b) Preferred values for the grading of surface texture (see Appendix A). c) Sampling lengths and cut-off values to be used in graphical procedures and instrument construction. d) The graphical determination of the following parameters: 1) Ra, arithmetical mean deviation of the profile; 2) Rz, ten point height of irregularities; 3) Ry, maximum height of the profile; 4) S m, mean spacing of profile irregularities; 5) S , mean spacing of local peaks of the profile; I S B ) c ( , y p o C d e l l o r t n o c n U , 3 0 0 2 r e b m e t p e S 6 1 , p u o r G r e v o R , t t e k c i r p l u a p : y p o C d e s n e c i L

6) tp, profile bearing length ratio. e) The determination of parameter values by instrumental means. f) The essential instrument requirements to ensure repeatability of performance. g) The information to be given in statements relating to surface texture requirements. NOTE

The titles of the publications referred to in this standard are listed on the inside back cover.

2 Definitions For the purposes of this Part of BS 1134 the following definitions apply. 2.1 Terms relating to the surface, profile and datum 2.1.1 real surface the surface limiting the body, separating it from surrounding space 2.1.2 real profile the profile that results from the intersection of the real surface by a plane conventionally defined with respect to the geometrical surface (see Figure 1) 2.1.3 geometrical surface the surface determined by the design, and defined by the drawing and/or other technical document, neglecting errors of form and surface roughness (see Figure 1) 2.1.4 geometrical profile the profile that results from the intersection of the geometrical surface by a plane conventionally defined with respect to this surface (see Figure 1) 2.1.5 effective surface the close representation of a real surface obtained by instrumental means (see Figure 1) 2.1.6 effective profile the profile that results from the intersection of the effective surface by a plane conventionally defined with respect to the geometrical surface (see Figure 1)

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2.1.7 profile transformation an action (operation) that results int entionally or unintentionally in the transformation of a p rofile at any stage in the process of measurement, e.g. traversing with a stylus, filtering, recording 2.1.8 transformed profile a profile produced as a result of transformation 2.1.9 intentional profile transformation a profile transformation that is made in order that measurements are performed in accordance with the specified requirements for a given measurement NOTE The following are examples of intentional profile transformations. a) Transformation of the surface profile into an electric signal to make it possible to use electronic measuring instruments. b) Transformation of the effective profile by defined filter means of suppressing those undulations of the real profile that are not or are not fully to be included in the measured roughness parameters of the surface.

2.1.10 unintentional profile transformation

I Sa profile transformation arising from the imperfection of the measuring instrument or of its sep arate parts Band usually seen as distortions of the information about the profile ) c NOTE An example of an unintentional profile transformation is the distortion of the information about the profile when traversing ( , y it with a stylus having a finite tip radius. p 2.1.11 o Csurface texture d e those irregularities with regular or irregular spacing that tend to form a pattern or texture on the surface l l o r NOTE This texture may contain components of roughness (see 2.1.12) and waviness (see 2.1.13). t n 2.1.12 o c roughness n Uthe irregularities in the surface texture that are inherent in the production process but excluding waviness , 3 and errors of form (see Figure 1) 0 0 2 r e b m e t p e S 6 1 , p u o r G r e v o R , t t e k c i r p l u a p : y p o C d e s n e © BSI 11-1999 c 2 i L

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Figure 1 — Surface characteristics and terminology

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2.1.13 waviness that component of surface texture upon which roughness is superimposed (see Figure 1) NOTE Waviness may result from such factors as machine or work deflections, vibrations, chatter, heat treatment or warping strains.

2.1.14 lay the direction of the predominant surface pattern, ordinarily determined by the production method used (see Figure 1) 2.1.15 traversed length the complete length of the pick-up movement along the surface being measured (see Figure 2) 2.1.16 reference line the line chosen by convention as a reference to serve for the quantitative evaluation of t he roughness of the effective profile (see Figure 2)

I S2.1.17 Bsampling length, l ) c the length of the reference line used for identifying the irregularities characterizing the su rface roughness ( , y (see Figure 2). The sampling length is measured in the general direction of the profile p o C d e l l o r t n o c n U , 3 0 0 2 r e b m e t p e S Figure 2 — Traversed length 6 1 , p 2.1.18 u evaluation length, ln o r Gthe length over which the profile is assessed. It may contain one or more sampling lengths (see Figure 2) r 2.1.19 e v profile departure, y o Rthe distance between a profile point and the reference line in the direction of measurement (see Figure 3) , t t 2.1.20 e k mean line system, system M c i r the calculation system used for the profile evaluation in which a mean line is taken as a reference line p l u 2.1.21 a p least-squares mean line of the profile : y a reference line having the form of the geometrical profile and dividing the profile so that, within the p o sampling length, the sum of the squares of the profile departures from this line is the minimum C d e s n e © BSI 11-1999 c 4 i L

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2.1.22 centre arithmetical mean line of the profile a reference line representing the form of the geometrical profile and parallel to th e general direction of the profile throughout the sampling length, such that the sums of the areas contained between it and those parts of the profile that lie on each side of it are equal NOTE The centre line (centre arithmetical mean line) is defined and used for graphical convenience. When the centre line has a distinguishable periodicity and its general direction is therefore determinate, the “equal area” centre li ne is unique. When the profile is irregular, the assessment of the general direction becomes uncertain over a certain range. Within this range a family of “equal area” centre lines can be drawn, one of which will be identical with the least-squares mean line.

2.1.23 electrical mean line in an electrical instrument, a reference line that is established by the circuits determining the meter cut-off and which divides equally those parts of the transformed profile lying above and below it 2.1.24 local peak of the profile a part of the profile between two adjacent minima of the profile (see Figure 4) I S B ) c ( , y p o C d e l l o r t n o c n U , 3 0 0 2 r e b m e t p e S 6 1 , p u o r G r e v o R , t t e k c i r p l u a p : y p o C d e s n e c i L

NOTE Figure 3 represents a profile graph which, due to the difference in the vertical and horizontal magnifications, is a distorted representation of the real profile. For this reason, the profile departures should be measured in the same direction as that used to determine the real profile. On the real profile, the angles, µ , between the reference line and the general direction of the profile within the evaluation length are very small. Thus, the difference between the profile departures measured perpendicular to the reference line and those measured perpendicular to the general direction of the profile may be negligible. Hence, on the real surface, the profile departures should be considered perpendicular to the reference line.

Figure 3 — Profile departure

Figure 4 — Local peak of the profile

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2.1.25 spacing of local peaks of the profile the length of a mean line section between the two highest points of adjacent local peaks of the profile projected on the mean line (see Figure 5)

I S B ) c ( Figure 5 — Spacing of local peaks of the profile , y p o 2.1.26 Clocal valley of the profile d e a part of the profile between two adjacent maxima of the profile (see Figure 6) l l o r t n o c n U , 3 0 0 2 r e b m e t p e S 6 Figure 6 — Local valley of the profile 1 , p 2.1.27 u o r local irregularity Ga local peak and the adjacent local valley r e 2.1.28 v o profile peak R , an outwardly directed (from material to surrounding medium) portion of the profile connecting two t t adjacent points of the intersection of the profile with the mean line (see Figure 7) e k c i r p l u a p : y p o C d e s n e © BSI 11-1999 c 6 i L

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NOTE The outwardly directed portion of the profile at the beginning or end of the sampling length should always be considered as a profile peak.


Figure 7 — Profile peaks 2.1.29 profile valley an inwardly directed (from surrounding medium to material) portion of the profile connecting two adjacent points of the intersection of the profile with the mean line (see Figure 8)

NOTE The inwardly directed portion of the profile at the beginning or end of the sampling length should always be considered as a valley.

Figure 8 — Profile valleys 2.1.30 profile irregularity a profile peak and the adjacent profile valley 2.1.31 spacing of profile irregularities the length of a mean line section containing a profile peak and the adjacent profile valley (see Figure 9)

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Figure 9 — Spacing of profile irregularities I S2.1.32 Bline of profile peaks ) c a line parallel to the mean line and passing through the highest point of the profile within the sampling ( , y length (see Figure 7) p o 2.1.33 Cline of profile valleys d e l l a line parallel to the mean line and passing through the lowest point within the sampling length o r (see Figure 8) t n 2.1.34 o c profile section level, c n Uthe distance between the line of profile peaks and a line intersecting the profile, the latter being parallel to , 3 the line of profile peaks (see Figure 10) 0 0 NOTE The profile section level can be determined in micrometres or in percent of Ry, the maximum height of the profile (s ee 2.2.2). 2 r e b m e t p e S 6 1 , p u o r G r e v o R , t t e k c Figure 10 — Profile section level i r p l u a p : y p o C d e s n e © BSI 11-1999 c 8 i L

BS 1134-1:1988

2.1.35 profile bearing length, ½p the sum of the section lengths obtained by cutting the profile peaks by a line parallel to the mean line within the sampling length (see Figure 11)


Figure 11 — Profile bearing length 2.2 Terms associated with surface roughness parameters 2.2.1 arithmetical mean deviation of the profile, Ra the arithmetical average value of the departure of the profile above and below the mean line (centre or electrical mean line) throughout the specified sampling length (see Figure 12). The arithmetical mean deviation is given by the equations:

or approximately:

where l is the sampling length; y is the profile departure; n is the number of profile departures. NOTE In practice, the values of Ra are determined within the evaluation length which includes several sampling lengths. The sampling length is equal to the cut-off.

Figure 12 — Arithmetical mean deviation of the profile (Ra)

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2.2.2 maximum height of the profile, Ry the distance between the line of profile peaks and the line of profile valleys within the sampling length (see Figure 13)

I S Figure 13 — Maximum height of the profile (Ry) B ) c 2.2.3 ( , y ten point height of irregularities, Rz p o the average distance between the five highest profile peaks and the five deepest profile valleys within the Csampling length, measured from a line parallel to the mean line and not crossing the profile (see Figure 15) d e l l 2.2.4 o r mean spacing of profile irregularities, S m t n the mean value of the spacing of the profile irregularities within the sampling length (see Figure 16) o c n 2.2.5 Umean spacing of local peaks of the profile, S , 3 0 the mean value of the local peak spacing of the profile within the sampling length (see Figure 17) 0 2 2.2.6 r e profile bearing length ratio, tp b mthe ratio of the profile bearing length to the sampling length e t p 2.3 Terms associated with instruments for the measurement of surface roughness by the profile e method S 6 2.3.1 1 profile recording instrument , p u an instrument recording the coordinates of the profile of the surface texture o r 2.3.2 G profile instrument r e an instrument used for the measurement of surface roughness parameters v o R2.3.3 , t t contact profile instrument, system M e k a contact (stylus) instrument of consecutive profile transformation used for the measurement of surface c roughness parameters according to system M (the mean line system) i r p l NOTE See ISO 3274:1975. u a 2.3.4 p modified profile : y p the effective profile defined by the combination of a stylus and profile filter, the filter being used for o Cselecting a part of the spectrum of the real profile to be taken into consideration in the measurement of d surface roughness parameters e s n e © BSI 11-1999 c 10 i L

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2.3.5 profile instrument with predetermined evaluation length an instrument in which the length used for measurement has a defined beginning and end NOTE These instruments generally indicate and hold the reading of the measured parameter obtained at the end of the stated measuring length.

2.3.6 profile instrument with “running” evaluation length a profile instrument with running evaluation length giving a running average 2.3.7 static measuring force the force which the stylus exerts along its axis on the examined surface without taking into account the dynamic components that arise from the traversing of the surface by the stylus 2.3.8 rate of change of the static measuring force the change of the static measuring force per unit displacement of the stylus along its axis I S B ) c ( , y p o C d e l l o r t n o c n U , 3 0 0 2 r e b m e t p e S 6 1 , p u o r G r e v o R , t t e k c i r p l u a p : y p o C d e s n e c i L

2.3.9 cut-off, 2 B the value of the wavelength 2 numerically equal to the sampling length and conventionally taken as the upper limit of transmission of the instrument NOTE The given upper limit conventionally separates the nominally transmitted components of the effective profile spectrum from those that are nominally suppressed.

2.3.10 vertical magnification of a profile record, V v the ratio of the recorded horizontal displacement to the displacement of the stylus along the surface 2.3.11 horizontal magnification of a profile record, V h the ratio of the recorded length of the recorder chart to that of the stylus displacement along the surface 2.3.12 error of vertical magnification of a profile record the percentage difference between the nominal and the actual values of the vertical magnification referred to the nominal value 2.3.13 error of horizontal magnification of a profile record the percentage difference between the nominal and the actual values of the horizontal magnification referred to the nominal value 2.3.14 basic error of a profile instrument reading the percentage difference between the instrument reading and the value of the surface roughness parameter as defined by the stylus and cut-off (without skid) of the instrument 2.3.15 method divergence of the instrument reading for a given measured profile, the percentage difference between the value of the surface roughness parameter determined with respect to the electrical mean line of the defined wave filter and a succession of straight centre arithmetical mean lines each equal in length to the cut-off, both determinations being referred to the same part and overall length of the same cross section (see Appendix B)

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Section 2. Determination of surface roughness 3 Sampling lengths Normally the appropriate sampling length of surface, which determines the corresponding cut-off to be used (see 6.3), shall be selected from the range of sampling lengths given in Table 1. In special cases which require the choice of values of sampling length other than those specified in Table 1, sampling and evaluation lengths shall be stated on all records of the test. Table 1 — Sampling lengths mm

in

0.08 0.25

0.003 0.01

0.8 2.5

0.03 0.1

8.0

0.3

4 Graphical determination of parameter values 4.1 Graphical determination of Ra values I 4.1.1 Observe the procedure in 4.1.2 to 4.1.8 when determining R values from graphical recordings. a S BNOTE If the surface is intentionally curved, the curvature will generally be neutralized, prior to recording, by some form of guiding ) or filter device. c ( , 4.1.2 Assume the surface is nominally flat, and that the record is produced in rectilinear coordinates in y which a truly flat surface is represented by a straight line. p o C4.1.3 First determine the centre arithmetical mean line of the profile for each successive sampling length, d l, contained within the evaluation length of the record, as given in 4.1.4 to 4.1.6. e l l 4.1.4 Draw a straight line A“B” through the lowest profile valley and parallel to the general course of the o r record over the sampling length l [see Figure 14a)]. t n NOTE 1 The slope of the line A“B” can usually be determined by eye with sufficient accuracy. o c NOTE 2 Where the texture has a distinguishable periodicity it is essential that the sampling length should be chosen to include a n whole number of wavelengths. U , 4.1.5 Determine the area, P , between the profile and the line A“B” either by measuring equally-spaced 3 0 ordinates or by the use of a planimeter, through the chosen sampling length. 0 2 4.1.6 The height, H m, of the centre arithmetical mean line above A“B” (the line of profile valleys) is given r e by the equation: b m H = P ---m e l t p e where S 6 P is the area between the profile and line of profile valleys (A“B”); 1 , l is the sampling length. p u o r 4.1.7 Draw the centre arithmetical mean line AB parallel to the line of profile valleys (A“B”) at the height GH m above it [see Figure 14a)]. r 4.1.8 Determine the areas r , r , r ... and s , s ... above and below the centre arithmetical mean line 1 2 3 1 2 e v [see Figure 14b)]. The value of Ra (in 4m) is calculated from the equation: o R , t t e k c i r p l where u a r is the area (in mm2) of the ith profile peak; i p : y si is the area (in mm2) of the ith profile valley; p o l is the sampling length (in mm); C d V v is the vertical magnification of the profile record. e s n e © BSI 11-1999 c 12 i L

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4.1.9 The required value of Ra over the evaluation length is taken as the mean of the successive values of the sampling length.


Figure 14 — Graphical determination of Ra values 4.2 Graphical determination of Rz and Ry values For some purposes it is convenient to have an assessment of average peak-to-valley height of surface irregularities. The Rz or “ten point height” method (see Figure 15) is an arbitrary way of avoiding the effect of exceptional peaks and valleys in the final computation, and is used in determining average peak-to-valley values. Rz values are generally from four to seven times the corresponding Ra values, the ratio depending upon the shape of the profile.

Figure 15 — Graphical determination of Rz values Measure the five highest peaks and five deepest valleys from an arbitrary base line A“B” drawn parallel to the centre arithmetical mean line AB of the chosen sampling length l. Rz (in 4m) is then given by the equation:

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where Y 1, Y 2, . . . Y 10 V v

is the distance (in mm) of peaks and valleys from the arbitrary base line A“B”;

is the vertical magnification of the profile record.

The value of Ry (in 4m) is calculated from the equation:

where Y y

is the maximum height (in mm) of the profile record;

V v

is the vertical magnification of the profile record.

4.3 Graphical determination of S m values Draw the centre arithmetical mean line AB (see Figure 16) for the sampling length, l, and identify the profile peaks, noting that the minimum height of the profile peaks to be taken into consideration is specified as 10 % of Ry. The mean spacing of the profile irregularities S m (in 4m) is calculated from the equation: I S B ) c ( , y where p S is the length (in mm) of mean line section containing the nth profile peak and the adjacent profile mn o C valley; d e n is the number of sections included in the determination; l l o V h is the horizontal magnification of the profile record. r t n o c n U , 3 0 0 2 r e b m e t p e S 6 1 , p u o r G r Figure 16 — Graphical determination of S m values e v o R4.4 Graphical determination of S values , t t Draw the centre arithmetical mean line AB (see Figure 17) for the sampling length, l, and identify the local e k peaks, noting that the minimum spacing of the local peaks that is to be ta ken into consideration is specified c as 1 % of the sampling length, while the minimum height of the local peaks that is to be taken into i r p consideration is specified as 10 % of Ry. The mean spacing of local peaks of the profile, S , (in 4m) is l u calculated from the equation: a p : y p o C d e s n e © BSI 11-1999 c 14 i L

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where S 1 . . . S n n

is the number of spacings included;

V h


are the spacing of local peaks of the profile (in mm);

is the horizontal magnification of the profile record.

Figure 17 — Graphical determination of S values 4.5 Graphical determination of tp values Determine the profile bearing length, ½p, which is the sum of the section lengths obtained by cutting the profile peaks by a line (A“B” in Figure 18) parallel to the arithmetical mean line within the sample length, l, at the profile section level, c, below the line of profile peaks. The profile bearing length, ½p, is given by the equation:

½p + a + b + c + d + e where a, b, c . . . are the section lengths. The profile bearing length ratio, tp, expressed as a percentage, is given by the equation:

where

½p and l are in the same units.

Figure 18 — Graphical determination of tp values

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5 Statements of surface roughness 5.1 General The following information is that which shall be given in statements relating to surface roughness. 5.2 Surface roughness values For requirements specified by the maximum value (in 4m) of the surface roughness parameter, none of the measured values of the parameter of the whole surfa ce being inspected shall exceed the value specified on the drawings or in technical documents. In such cases, the suffix “max” shall be added to the parameter symbol, as shown in the following example: Ry max 12.5 5.3 Limiting values When both lower and upper limit values need to be specified, these shall be expressed (in 4m) as shown in the following examples: Ra 0.8

Rz 12.5

Ra 0.4

Rz 6.3

I If a single value is stated it shall be the upper limit value and shall be expressed (in 4m) as shown in the S Bfollowing examples: ) Ra 0.8, Rz 12.5 c ( , Variations in the value of the surface roughness parameter in most engineering surfaces are found to approximate y NOTE p sufficiently closely to the normal (Gaussian) distribution for the properties of the normal distribution to be applied. Thus, the lower o and upper limits of the roughness parameter values are the limits between which 68 % of all the measured values of the parameter Care expected to fall. d For requirements specified by the upper limit of the surface roughness parameter, the surface is considered to be acceptable if not e l l more than 16 % of all the measured values of the parameter exceed the value specified on the drawings or in technical documents. In o r cases where the lower limit is specified, the surface is considered to be acceptable if not more than 16 % of all the measured values of t the roughness parameter can be exceeded by the specified value. n o 5.4 Cut-off values c n UWhen the cut-off value is other than 0.8 mm the value shall be indicated in parentheses following the , surface roughness value (in 4m), as shown in the following example: 3 0 R 0.2 (2.5) a 0 2 NOTE Apart from indicating the cut-off to be used in assessment, the cut-off value denotes that dominant peak spacings greater r e than the cut-off are not present on a surface. b m5.5 Lay e t It is sometimes necessary to specify the direction of lay, in which case it shall be as defined as in Figure 22 p e and expressed in accordance with the following example: S 6 Ra 0.8 C 1 NOTE C refers to the symbol for lay which is circular (see Figure 22). Unless otherwise specified, the implication is that the surface , p roughness should be measured across the direction of the lay. u o r 5.6 Production process GWhen production of a surface is to be limited to the use of one particular process, the process shall be stated. r e v o R , t t e k c i r p l u a p : y p o C d e s n e © BSI 11-1999 c 16 i L

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Section 3. Instrumentation 6 Stylus-type measuring instruments 6.1 Stylus 6.1.1 Tip radius of the stylus. The nominal value of the tip radius of the stylus shall be one of the following: a) 2 ± 0.5 4m; b) 5 ± 1 4m; c) 10 ± 2.5 4m. See also Appendix C. 6.1.2 Stylus angle. The nominal value of the stylus angle shall be one of the following: a) 1.57 radians (90°); b) 1.05 radians (60°). 6.1.3 Static measuring force. The static measuring force shall be sufficient to ensure continuous contact between the stylus and the surface being measured and shall be not greater than that given in Table 2. Table 2 — Static measuring force of the stylus I S B ) c ( , y p o C d e l l o r t n o c n U , 3 0 0 2 r e b m e t p e S 6 1 , p u o r G r e v o R , t t e k c i r p l u a p : y p o C d e s n e c i L

Nominal tip radius of stylus

Maximum static measuring force at mean level of stylus

Maximum rate of change of measuring force

4m

mN

N/m

2 ± 0.5

0.7

35

5 ± 1

4.0

200

16.0

800

10 ± 2.5 6.2 Skid

6.2.1 Skid dimensions. If a skid is employed, its radius in the direction of the traverse shall be not less than 50 times the meter cut-off used. If two simultaneously operative skids, as shown in Figure 19, are used, their radii shall be not less than eight times the meter cut-off. NOTE Although the use of the skid may, when applied under suitable conditions, introduce no error of any great practical significance, external datum units should be used in all serious metrological work such as, for example, calibration procedures, and in the case of surfaces of limited area or requiring the use of cut-off values of 2.5 mm or greater.

Figure 19 — Stylus acting midway between two skids 6.2.2 Skid surface roughness. The surface roughness of the skid as determined by the ten point height of irregularities, Rz, shall be not greater than 0.1 4m when measured in the direction of traverse. 6.2.3 Skid force. The force exerted by the skid on the surface to be measured shall be not greater than 0.5 N. 6.3 Traverse In profile instruments with predetermined or running evaluation lengths, the length shall depend on the meter cut-off value 2 B within the limits given in Table 3.

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BS 1134-1:1988

Table 3 — Evaluation lengths Type of profile meter

Cut-off 2 B mm

Predetermined evaluation length

Running evaluation length

Evaluation length Min.

Max.

mm

mm

0.08 0.25 0.8 2.5 8

0.4 1.25 2.4 5 16

2 5 8 15 40

0.25 0.8

2.5 5

16 16

6.4 Values of vertical and horizontal magnification The values of vertical and horizontal magnification for profile recording instruments shall be selected from the following series: Vertical (V v): 100, 200, 500, 1 000, 2 000, 5 000, 10 000, 20 000, 50 000, 100 000, 200 000, 500 000, 1 000 000.

I S B Horizontal (V h): 10, 20, 50, 100, 200, 500, 1 000, 2 000, 5 000, 10 000, 20 000, 50 000. ) c 6.5 Transmission characteristics in the long wavelength ( , y 6.5.1 Rate of attenuation. The rate of attenuation shall be equivalent to that p roduced by two independent p o C-R networks of equal time constant in series. This describes a system in which the maximum slope of the Ctransmission curve is 12 dB per octave and in which the phase shift at the 75 % cut-off 2 is 60°. B d e l l The transmission coefficient of such a system shall be given by the equation: o r t n o c n U , 3 0 where 0 2 j = Æ – 1; r e 2 is the wavelength; b m 2 B is the meter cut-off. e t p The effective cut-off wavelengths shall be taken at 75 % transmission. These are deemed to be equivalent e to the sampling lengths in Table 1. S 6 NOTE In a practical determination, the values of the transmission coefficients for the characteristics shown are measured relative 1 to the flat part of the transmission curve (see Figure 20). , p 6.5.2 Cut-off values. The cut-off values (in mm) t o be used in instrument construction sh all be selected from u the following series: o r G 0.08, 0.25, 0.8, 2.5, 8.0. r NOTE 1 A cut-off of 0.8 mm is found adequate for most of the finer surfaces. e v NOTE 2 Nominal sinusoidal frequency response characteristics for a profile instrument are shown by the ratios given in Table 4 o (see also Figure 20). R , The permitted deviations from the nominal values of the transmission coefficients shall be as given t t e in Table 5, and graphically presented in Figure 21, and these allow the cut-off to be assessed at k between 70 % and 80 % of maximum transmission. c i r p l u a p : y p o C d e s n e © BSI 11-1999 c 18 i L

BS 1134-1:1988


Figure 20 — Profile instrument frequency response Table 4 — Nominal sinusoidal frequency response characteristics for a profile instrument Wavelength

Percentage transmission Cut-off 0.25 mm

Cut-off 0.8 mm

Cut-off 2.5 mm

Cut-off 8.0 mm

%

%

%

%

mm

0.025 0.05 0.08

99.7 98.7 96.7

— — 99.7

— — —

— — —

0.10 0.25 0.5

94.9 75.0 42.9

99.5 96.8 88.5

— 99.7 98.7

— — —

0.8 1.0 2.5

22.7 15.8 2.9

75.0 65.8 23.5

96.7 94.9 75.0

99.7 99.5 96.8

7.1 2.9 1.8

42.9 22.7 15.8

88.5 75.0 65.8

2.9 0.75 —

23.5 7.1 2.9

5.0 8.0 10.0

0.75 — —

25.0 50.0 80.0

— — —

— — —

NOTE Because of practical difficulties in measurement at the very short wavelengths involved, the electrical transmission characteristic for 0.08 mm cut-off, although nominally of the same form as for the longer cut-off values, has not been tabulated.

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BS 1134-1:1988

7 Accuracy 7.1 Statement of basic error of calibration of Ra instruments The basic error of profile instrument reading (as defined in 2.3.14) given within the cut-off by an instrument in optimum adjustment and use (see C.5), and expressed as a percentage of the designated value of the surface roughness parameter of an instrument calibration specimen complying with BS 6393, shall be determined from the formula: --- + q x

where x is the fraction of the range indicated by the instrument; p

is a percentage of full range;

q

is a percentage of reading.

NOTE The admissible basic error of calibration thus expressed does not include the effect of deviations in the transmission characteristic which will be additional thereto.

7.2 Deviations of transmission coefficients I The permissible deviations of the amplitude transmission coefficient (see Table 5 and Figure 21) of a profile Sinstrument from the nominal transmission coefficient shall be given by the equations: B ) c ( , y p o C d e l l o r t n o c n Uwhere , 3 2 is the wavelength; 0 0 2 B is the meter cut-off. 2 r Table 5 — Upper and lower limits of transmission coefficients e b Wavelength, 2 Transmission coefficient m e t Cut-off, 2 B Lower limit Upper limit p e % dB % dB S 6 0.1 96.6 – 0.30 102.7 – 0.23 1 95.5 – 0.40 101.8 + 0.15 , 0.2 p 0.3 93.7 – 0.56 100.4 + 0.03 u o 88.4 – 1.07 96.0 – 0.26 r 0.5 G 0.7 81.4 – 1.78 90.2 – 0.90 r 69.8 – 3.13 79.8 – 1.96 e 1.0 v 1.5 51.7 – 5.74 62.3 – 4.12 o R 2.0 37.9 – 8.43 47.7 – 6.44 , t t 3.0 21.5 – 13.5 28.5 – 10.9 e k 5.0 9.0 – 20.9 12.5 – 18.1 c i r 10.0 2.4 – 32.3 3.4 – 29.3 p l NOTE An explanation of the method divergence of the instrument reading (see 2.3.15) is u a given at Appendix B, and factors affecting the statement of accuracy are explained at p Appendix C. : y p o C d e s n e © BSI 11-1999 c 20 i L

BS 1134-1:1988


Figure 21 — Permissible deviations of the transmission coefficient

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BS 1134-1:1988

Symbol

Interpretation

Parallel to the plane of projection of the view in which the symbol is used

Perpendicular to the plane of projection of the view in which the symbol is used

Crossed in two slant directions relative I to the plane of projection of the view in S B which the symbol is used ) c ( , y p o C d Multi-directional e l l o r t n o c n U , Approximately circular relative to the 3 0 centre of the surface to which the 0 2 symbol is applied r e b m e t p e S Approximately radial relative to 6 the centre of the surface to which 1 , the symbol is applied p u o r G r NOTE Should it be necessary to specify a direction of lay not clearly defined by these symbols, this may be done by a suitable note e on the drawing. v o Figure 22 — Symbols for the direction of lay R , t t e k c i r p l u a p : y p o C d e s n e © BSI 11-1999 c 22 i L

BS 1134-1:1988

Appendix A Parameter values Values are normally determined as mean results from the measurement of several sampling lengths taken consecutively along the profile. These may be determined graphically in accordance with clause 4 or by direct reading instruments. The direction in which the measurement is made should in general be approximately at right angles to the lay if the surface texture has a directional quality (see Figure 22). The parameter values specified should be selected from the ranges of preferred values given in Table 6, Table 7 and Table 8. Table 6 — Preferred nominal values for arithmetical mean deviation of the profile (Ra) 4m

4in

400 200 100


16 000 8 000 4 000

50 25 12.5

2 000 1 000 500

6.3 3.2 1.6

250 125 63

0.8 0.4 0.2

32 16 8

0.1 0.05 0.025 0.0125

4 2 1 0.5

Table 7 — Preferred nominal values for ten point height of irregularities (Rz), and maximum height of the profile (Ry) 4m

4in

4m

4in

1 600

64 000

3.2

125

800

32 000

1.6

63

400

16 000

0.8

32

200

8 000

0.4

16

100

4 000

0.2

8

50

2 000

0.1

4

25

1 000

0.05

2

12.5

500

0.025

1

6.3

250

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BS 1134-1:1988

Table 8 — Preferred nominal values for mean spacing of profile irregularities (S m), and mean spacing of local peaks of the profile (S ) mm

in

mm

in

12.5

0.500

0.2

0.008

6.3

0.250

0.1

0.004

3.2

0.125

0.05

0.002

1.6

0.062

0.025

0.001

0.8

0.032

0.0125

0.0005

0.4

0.016

0.006

0.0003

NOTE The values given in Table 6, Table 7 and Table 8 are expressed as “preferred” in order to discourage unnecessary variation of the values expressed on drawings. It should be realized that in some circumstances, other values may be specified.

Appendix B Method divergence of instrument reading B.1 General When two methods of measurement which are both standardized give results which are nominally but not I Sprecisely equal, the numerical difference is referred to as “method divergence”. B ) Thus the two methods referred to in this standard for selecting the texture to be measured (by sampling c length and cut-off), although deemed to be acceptable equivalent s of each other, treat the profile in different ( , y ways that may lead to slightly different numerical evaluations. p o B.2 Effective cut-off C Reference to Figure 20 will show that transition occurs gradually from the fully transmitting to the d substantially rejecting part of the standardized characteristic. From consideration of filter theory, e l l experimental results and various practices, the effective cut-off has now become rated, by accepted o r t n convention, at the wavelength for which there is 75 % of the full transmission of a pure sinusoidal o waveform, with a tolerance permitting a range from 70 % to 80 %. This means that for a sine wave having c n a wavelength equal to the sampling length, an instrument calibrated in the usual way for a sine wave Uoccurring on the flat part of the characteristic would indicate an R value equal to 75 % of the value a , 3 obtained from the profile graph by planimetry. For short wavelengths and most machined surfaces the 0 0 divergence is usually small, and this is generally the case for random profiles. It is usual to accept the 2 instrument reading as the operative basis for grading workpieces in the workshop, and to avoid extreme r e divergences by use of a sufficient cut-off. b mB.3 Range of method divergence e t p The typical and extremes of method divergence found by comparing metered Ra values with the values e computed from the least squares mean line are shown in Table 9. S Table 9 — Comparison of Ra values obtained by 6 1 graphical and instrumental means , p Ra from least squares Ra from Type of Cut-off Method u o mean line of graph instrument surface divergence r G 4m 4m mm % r 2.5 0.80 0.86 +7 e Milled v o Milled 2.5 2.66 2.67 0 R , End-milled 2.5 0.90 0.81 – 11 t t e Turned 2.5 6.74 6.86 +2 k c Turned i 2.5 0.83 0.81 –2 r p Ground 0.8 0.71 0.66 –8 l u 0.8 0.48 0.53 +9 a Ground p : Lapped 0.8 0.02 0.02 0 y p NOTE Mean method divergence for 2.5 mm cut-off: 0 %; standard deviation: 4 %. o Mean method divergence for 0.8 mm cut-off: 1 %; standard deviation: 7 %. C These mean method divergences and standard deviations were obtained from measurements d on 22 surfaces. e s n e © BSI 11-1999 c 24 i L

BS 1134-1:1988

B.4 Electrical mean line A further point concerns the shape of the self-determined electrical mean line found by the filter. This is generally not a straight line but an undulating one which weaves its way through the profile as shown in Figure 23. The undulations account for the method divergence. Equations and computing tables for the electrical mean line found by the standard filter are available from manufacturers, and these can serve as a basis for determining precisely, by computation from digitized profile records, the errors of instruments complying with this standard. In practice, however, it is generally only in the case of precise instrument calibration that it is necessary to take the details of filter behaviour fully into account.


Figure 23 — Centre arithmetical mean lines (A) and electrical mean lines (B)

Appendix C Factors affecting the statement of accuracy C.1 General Many instruments are responsive to a single variable (e.g. length, angle, electric current) and have few sources of error. These errors can be expressed simply, and it is a normal expectation that this should be done. Surface instruments are more complicated, for the quantity to be measured has generally to be derived from a fluctuating signal representing the profile of a sample of the surface. Errors can arise from different sources having quite different error laws, and the total error does not lend itself to expression in a simple yet meaningful way. C.2 Calibration Workshop calibration is generally effected with the aid of instrument calibration specimens complying with BS 6393. Ideally, in addition to being marked with substantially its full value, assuming negligible instrument losses, each specimen should be accompanied by a statement of the reading that should be obtained from it by an instrument having given stylus dimensions and for each mean transmission characteristic. This is a refinement that has still to be treated in a formal way. The overall amplification is left as an adjustment for the user to make by means of one or more potentiometers which have to be set in conjunction with an instrument calibration specimen or with a calibrated test specimen. The attainable accuracy therefore starts with the calibration specimen and the user’s skill in allowing for its characteristics and in securing with it the best overall adjustment of the instrument. It is envisaged that the use of more than one test specimen will become normal practice.

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BS 1134-1:1988

C.3 Instrument error If the instrument is set up to give the correct reading for t he calibration specimen allowing for all relevant characteristics, the basic instrument error at this point in its range of operation will be that of the specimen, often assumed to be zero. However, the working range of the instrument may be considerable, extending vertically from around 0.025 4m to several micrometres, and horizontally from around 2 4m to several millimetres. Even if there is, after initial adjustment, no error in the calibrated region of the range, there may be errors in other regions unless all parts of the instrument function perfectly. These errors would be revealed by other precisely calibrated specimens. It is to the expression of the error throughout the range, relative to the setting-up point, that 7.1 refers. Instrument errors can arise from the condition of the stylus and datum device, various electronic sources, and the errors inherent in the output behaviour and reading. Assuming that the stylus is in good order, the radius of its t ip may influence the indication. Differences between a 2 4m and a 10 4m tip, while negligible for many surfaces, may be quite significant for others, and especially for very fine ones. It d oes not follow that the blunter tip will always give the lower reading, for on some surfaces (e.g. turned surfaces with sharp peaks) its own radius added to the radii of the peaks may more than compensate for the losses in the valleys. Instrument errors, apart from an error in overall amplification, may include errors due to electrical and I mechanical noise, to residual non-linearity, to ratio errors in range switching and, where applicable, to Serrors in the transmission characteristic. B ) C.4 Noise c ( , The effect of noise depends mainly on its proportion to the value of the signal. For most purposes, the noise y can be taken as the reading given by a well-polished optical flat, free from scratches. When the proportion p o of noise in the reading is small, say less than one-third, the noise can be neglected. When the two are equal C (as can happen with smooth surfaces) it can account for 70 % to 80 % of the reading. When it is twice as d great as the signal, it becomes dominant. The noise cannot be allowed for by simple subtraction, for if the e l l two signals have values of en and es, the nearest simple assessment of their combination will be given o r t 2 2 n by Æ ( en + es ) . The actual value of the noise, for a given instrument, may vary over a wide range according o to the rigidity of the set-up and the amount of vibration in the instrument and its environment. c n C.5 Optimum adjustment U , 3 The reference in 7.1 to optimum adjustment and use may call for qualification. If an instrument were 0 required to give maximum accuracy over a small range of operation, its adjustment would naturally be 0 2 optimized for that range. On t he other hand, if the instrument were required to perform as well as possible r over a wide range without readjustment, the adjustment would be optimized so as to minimize the residual e b errors throughout the range. m e The concept of optimum use will refer to environmental conditions, rigidity of workpiece mounting, and the t p fact that readings near the top of the scale will generally be less subject to error than those near the bottom. e SC.6 Statement of accuracy 6 1 If it is accepted that a useful statement of accuracy should neither under-rate nor over-rate the capability , p of an instrument, it becomes clear that no single figure can be expected to give fair information. On the u other hand, a specification attem pting to cover all possible combinations would become impossibly complex o r and again meaningless. G r e v o R , t t e k c i r p l u a p : y p o C d e s n e © BSI 11-1999 c 26 i L

BS 1134-1:1988

Publications referred to BS 308, Engineering drawing practice. BS 308-2, Recommendations for dimensioning and tolerancing of size. BS 1134, Method for the assessment of surface texture 1). BS 1134-2, General information and guidance. BS 6393, Specification for calibration of stylus instruments. ISO 468, Surface roughness — Parameters, their values and general rules for specifying requirements. ISO 3274, Instruments for the measurement of surface roughness by the profile method — Contact (stylus) instruments of consecutive profile transformation — Contact profile meters, system M. ISO 4287, Surface roughness — Terminology. ISO 4287-1, Surface and its parameters1). ISO 4287-2, Measurement of surface roughness parameters 1).


1)

Referred to in the foreword only.

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BS 1134 1 1988

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