DESIGN OF SINGLE POINT CUTTING TOOL Objective: To remove greatest amount of material in the shortest length of time consistent with finish requirements, work and tool rigidity, available power of the machine, and relative cost of labour and cutting tools .[1]
In design of a single point cutting tool the following factors are to be considered. i) Type of work piece material and tool material; ii) Type of operation and surface finish required; iii) Optimum tool angles; iv) Permissible cutting speed, feed and depth of cut; v) Cutting forces; vi) Condition of work holding: a) Work held as a cantilever; b) Work held in between two centres, both of which can be live or one live and the other dead. c) Work held in chuck and tailstock centre. vii) Overhung of the tool from the tool post; viii) Accuracy of the work in terms of permissible deflection (maximum) of job with respect to the tool.
Figure 4.1: Various turning operations
Lecture Notes of Chinmay Das
1
General recommendations for geometry of single point turning tools Material
BHN
High Speed Steel and Cast Alloy Tools Back Rake
Gray or flake graphite cast iron Nodular or ductile cast iron Malleable cast iron Free machining plain carbon steel, plain carbon steel Free machining alloy steel Alloy steels, cast steels Hot work die steel, tool steel Ferritic stainless steel Austenitic stainless steel Martensitic stainless steel Precipitation hardening stainless steel Aluminium alloys Magnesium alloys Copper alloys Titanium alloys High temperature alloys
140 180 220 180
5 3 0 10
Side rake 10 8 5 12
End Relief
Side Relief
ECEA
250 350 500 180 200 180 440 220-320
8 0 0 5 5 5 0 0
10 8 5 8 6 8 5 5
6 5 5 6 6 6 5 5
6 5 5 6 6 6 5 5
5 5 5 6 6 6 5 5
40*-110 30*-80 120-185 280-360 260-320
20 20 5 0 5
15 15 10 5 6
12 12 8 5 5
10 10 8 5 5
5 5 5 5 5
6 5 5 8
6 5 5 8
6 5 5 5
Table-I: Recommended tool geometry for single point cutting turning tools [2]
Material Gray or flake graphite cast iron Nodular or ductile cast iron Malleable cast iron Free machining plain carbon steel, plain carbon steel Free machining alloy steel Alloy steels, cast steels Hot work die steel, tool steel Ferritic stainless steel Austenitic stainless steel Martensitic stainless steel Precipitation hardening stainless steel Aluminium alloys Magnesium alloys Copper alloys Titanium alloys High temperature alloys
BHN
Brazed
Carbide Tools Throwaway End
Back Rake 0 0 5 neg
Side rake 6 6 5 neg
Back Rake 5 neg 5 neg 5 neg
Side rake 5 neg 5 neg 5 neg
0
6
5 neg
250 350 500 180 200 180 440 220-320
0 0 5 neg 0 0 0 0
6 6 5 neg 6 6 6 6
0
40*-110 30*-80 120-185 280-360 260-320
3 3 5 0 0
140 180 220 180
Side ECEA Relief Relief 5 5 5
5 5 5
5 5 5
5 neg
5
5
5
5 neg 5 neg 5 neg 0 0 0 5 neg
5 neg 5 neg 5 neg 5 5 5 5 neg
5 5 5 5 5 5 5
5 5 5 5 5 5 5
5 5 5 5 5 5 5
6
0
5
5
5
5
15 15 8 6 6
0 0 0 0 0
5 5 5 5 5
8 8 5 5 5
8 8 5 5 5
5 5 5 5 5
Table-II: Recommended tool geometry for single point cutting turning tools [2]
Lecture Notes of Chinmay Das
2
Permissible Cutting Speed, Feed and Depth of Cut
Depth of cut has the greatest influence upon the cutting force, followed by feed, with cutting speed having the least influence. Feed has the greatest effect on surface finish when it is set according to nose radius. The cutting speed has maximum influence on temperature generated at cutting zone during machining. Considering all above factors, the tool designer has to make correct compromise so as to get best machining operation under the given condition. A general rule used by many production people to achieve the greatest machining efficiency is to use the heaviest feed that will allow the required surface finish, use the maximum depth of cut consistent with available power and rigidity of workpiece and machine, and then establish the cutting speed to give the desired tool life. Too fast a cutting speed will increase tool costs and down time for tool changing. Too slow a speed simply cannot produce enough pieces to make a profit. Somewhere between too fast and too slow is a cutting speed that will give the best tool life for overall efficiency. Usually the best cutting speed is the one that will reduce the total cost of machining to a minimum cost per piece. However, cost may be secondary, the objective may be to set the maximum production rate. Many variables like the cost of labour on the machines, over head costs, set up time, tool costs, tool changing time, time to machine the workpiece, tool grinding time, grinding room labour costs etc. determine the minimum cost and maximum production rate. The majority of these variables may be changed to known quantities for a particular job. When these quantities are determined, it is possible to plot costs and production rates vs. cutting speeds. The resulting graph will show speeds for minimum cost and maximum production rate. The theoretical best cutting speed will lie between the points of minimum cost and maximum production.
Figure 4.2: Cutting Speed vs. Production Rate
Lecture Notes of Chinmay Das
3
The recommended Cutting speeds and feeds for various work and tool materials. Steel
Condition
BHN
HSS Speed m/min
Low Carbon, free machining Medium Carbon, free machining Medium Carbon, free machining Plain low carbon Plain medium carbon( 0.4 to 0.5 C) Plain high carbon( 0.55 to 0.95 C) Plain medium carbon
Plain high carbon Resulfurized alloys Leaded alloy
Feed mm/rev
Speed m/min
Feed mm/rev
Carbide Speed m/min
Feed mm/rev
Oxide Speed m/min
Feed mm/rev
Cold drawn
170190
57
0.3
75
0.3
190
0.38
180-450
0.13-0.5
Cold drawn
200230
42
0.3
60
0.3
126
0.3
135-375
0.13-0.5
Quenched and tempered
250300
29
0.3
36
0.3
120
0.3
120-300
0.130.38
Annealed
110165
42
0.3
54
0.3
158
0.38 0.38
165-450
0.130.38
Annealed
120185
30
0.3
45
0.3
143
0.38 0.38
135-300
0.130.38
Annealed
170200
27
0.3
42
0.3
128
0.3
128-270
0.130.38
210250
24
0.25
38
0.25
120
0.3
120-240
0.130.38
260310
21
0.25
33
0.25
100
0.25
98-225
0.130.38
320375
15
0.25
21
0.25
68
0.25
75-210
0.130.38
38
0.3
53
0.3
128
0.38 0.38
135-300
0.130.38
45
0.3
68
0.3
143
0.38
180-600
0.13-0.5
24
0.25
33
0.25
120
0.3
150-300
0.13-0.5
24-33
0.25
32
0.25
90-128 90-128
0.38
100-300
0.13-0.5
240310
20
0.25
26
0.25
98
0.3
90-300
0.130.38
315370
14
0.25
20
0.25
83
0.25
90-270
0.130.38
380440
10
0.2
17
0.25
75
0.25
75-240
0.13-0.3
450500
8
0.2
14
0.25
54
0.25
80-210
0.130.25
510560
5
0.2
8
0.25
36
0.25
60-180
0.07-0.2
Quenched and tempered Quenched and tempered Quenched and tempered Annealed Annealed Normalised
Alloy steels
Cast Alloy
Annealed Normalised or Quenched and tempered Quenched and tempered Quenched and tempered Quenched and tempered Quenched and tempered
160210 140190 250300 150240
Table-III: Cutting speeds and feeds for turning steels [3]
Lecture Notes of Chinmay Das
4
Work material
Condition
BHN
HSS Speed m/min
Cast Alloy
Carbide
Feed mm/rev
Speed m/min
Feed mm/r ev
Speed m/min
Fee d mm /rev
Aluminium Alloys Non-heat-treatable Non-heat-tr eatable cast alloys Heat –treatable cast alloys
Non-heat-treatable Non-heat-tr eatable wrought alloys Heat-treatable Heat-treatabl e wrought alloys
Cast Solutiontreated and aged Cold-Drawn Solutiontreated and aged
50-70
300
0.3
360
0.3
Max
0.38
70-105
210
0.3
300
0.3
Max
0.38
40-70
210
0.3
360
0.3
Max
0.38
65-105
210
0.3
300
0.3
Max
0.38
Magnesium Alloys Cast alloys: A10,A12,AZ63,AZ63X,AZ101,AZ 92,AZ92X,AS100,AZ90,AZ90X, Wrought alloys: AT35,AZ31,AZ61,AZ80
Cast
Cold drawn
35-70
300
0.3
450
0.3
Max
0.3
40-80
300
0.3
450
0.3
Max
0.3
120-160
120
0.25
200
0.25
300
0.25
165-180
80
0.25
150
0.25
250
0.25 0.25
172-205
37
0.25
100
0.25
180
0.25 0.25
150-200
45
0.25
48
0.25
112
0.25
250-320
10
o.25
15
0.25
45
0.25
Over 320
5
o.25
7
0.25
40
0.25
Copper alloys Group-I Group-II Group-III
Wrought cast Wrought cast Wrought cast
or or or
Titanium Alloys Commercially pure Alloys: MST 5 A1-2.5Sn, RS110C,A110AT,Ti 6Ai-4Zr-1v,Ti, 8A11Mo-IV Ti6A1-4V,Ti 2A1-16V,Ti 4A1-4Mo-4V
Wrought or cast Wrought or cast
Wrought or cast
Table-IV: Cutting speeds and feeds for turning non-ferrous materials [3]
Cutting Forces during Turning The single point cutting tools being used for turning, shaping, planing, slotting, boring etc. are characterised by having only one cutting force during machining. But that force is resolved into two or three components for ease of analysis and exploitation. Tangential or Cutting Force, Pz This acts in the direction tangent to the revolving member and is sometimes referred to as turning force. It is usually the highest of the three forces and constitutes approximately 99 percent of the total power required by the tool.
Longitudinal or Feed Force, Px This acts in a direction parallel to the axis of the work. It averages about 40 percent as high as the tangential force. Since the feeding velocity is very low, the power required is usually 1 percent of the total. Lecture Notes of Chinmay Das
5
Figure 4.3: Cutting Forces in Turning
Radial Force, Py This acts in a radial direction from the centre of the work piece. It is the force that holds the tool to the correct depth of cut. It is the smallest of the three tool forces-only 20 percent as large as the tangential force. It requires no power in that there is no velocity in the radial direction. It should be kept to a minimum to reduce deflection, vibration and chatter. Calculation of Cutting Forces
From Merchant’s Circle Diagram for turning operation, we have Tangential or Cutting Force Force [1]
{t so τs cos (η- γ0)} ⁄ { Sinβ0 cos(β0 + η- γ0)} Where, t = depth of cut so = feed τs = dynamic shear stress η = coefficient of friction at chip-tool interface γ0 = orthogonal rake β0 = shear angle in orthogonal cutting Pz =
[4.1]
o
For brittle work materials, like grey cast iron, usually, 2 β0 + η - γ0 = 90 and τs remains almost unchanged . Then for turning brittle material, the cutting force 0 0 Pz = {t so τs cos (90 – 2 β0)} ⁄ { Sinβ0 cos(90 – 2 β0)} [4.2] Or, Pz = 2 t so τs cot β0 [4.3] Where, cot β0 = ζ – tan γ0 [4.4] Lecture Notes of Chinmay Das
6
And ζ = chip reduction coefficient = a2 ⁄ a1 = a2 ⁄ so sin Φ Where, a2 = chip thickness and Φ = principal cutting edge angle
[4.5]
It is difficult to measure chip thickness and evaluate the values of ζ while machining brittle materials and the value of τ of τs is roughly estimated from τs = 0.175 BHN [4.6] Where, BHN= Brinnel Hardness Number But most of the engineering materials are ductile in nature and even some semibrittle materials behave ductile under the cutting condition. The angle relationship reasonably accurately applicable for ductile metals is β0 + η - γ0 = 450 [4.7] And the value of τ of τs is obtained from, τs = 0.186 BHN ( approximate) [4.8] 0.6 ∆ ( more suitable and accurate) Or, τs = 0.74 σu ε [4.9] Where, σu = ultimate tensile strength of the work material ε = cutting strain ≈ ζ – tan γ0 ∆ = % elongation Substituting Equation 4.7 in Equation 4.1, we get Pz = t so τs (cot β0 + 1) [4.10] Again, cot β0 = ζ – tan γ0 So, Pz = t so τs(ζ – tan γ0 + 1) [4.11] Longitudinal or Feed Force, Px and Radial Radial Force, Py
From Merchant’s Circle Diagram for turning operation, we have
Pxy = Pz tan (η– γ0)
[4.12]
Combining Equation 4.12 in Equation 4.1, we get 0
0
Pxy = {t so τs sin (90 –2 β0)} ⁄ { Sin β0 cos(90 – 2 β0)}
[4.13]
0
Again, using the angle relationship β0 + η - γ0 = 45 , for ductile material
Pxy = t so τs (cot β0 – 1) Pxy = t so τs (ζ – tan γ0 – 1) 0.6 ∆ Where, τs is 0.74 σu ε or 0.186 BHN
[4.14] [4.15]
It is already known, Px = Pxy sinΦ and
Py = Pxy cosΦ Therefore,
Px= t so τs (ζ – tan γ0 – 1) sinΦ Py= t so τs (ζ – tan γ0 – 1) cosΦ
Lecture Notes of Chinmay Das
[4.16] [4.17]
7
Calculation of Tool Cross Section
Figure 4.4: Cutting Tool Cross Section
The shank of a cutting tool is generally analyzed for strength and rigidity. The tool is assumed to be loaded as a cantilever by tool forces at the cutting edge as shown in Figure 4.4. The deflection at the cutting edge is limited to a certain value depending on the size of the machine, cutting conditions and tool overhung. The tool overhung (L e) is related also to the shank size as well as to end fixity conditions. The recommended value of (Le / / H) is between 1.2 and 2. The common value for L e is 25 to 40 mm. Checking for strength: We know that the bending moment due to cutting force P z is P z Le at the tool post. If the height and width of cutting tool are H and B respectively, then 2 Pz Le = 1/6 BH σ1 [4.18] Where, σ1= tensile stress induced in the cutting tool body 2 = 6 Pz Le / BH [4.19] If the effect of P x is included, then it becomes a case for unsymmetrical bending. 2 2 σ = σ1 + σ2 = (6 Pz Le / BH ) + (6 Px Le / HB ) [4.20] Where, σ is permissible stress for cutting tool material = σut / factor of safety σut = ultimate tensile strength of cutting tool materials 2 = 1000 N / mm for HSS 2 = 700 N / mm for HCS factor of safety = 10 for rough machining = 4 for finish machining The Standard Cutting Tool Cross Section:
Figure 4.5: Types of Cutting Tool Cross section
The numerical values obtained for height and width of cutting tool from above equation should be standardized as per BIS specification. The designation of a tool shank section shall indicate the diameter, or the height and width in case of rectangular or square shanks and IS number.
Lecture Notes of Chinmay Das
8
Example 1: A shank having a circular cross section of 8 mm diameter shall be designated as: Shank Section 08 IS: 1983 Example 2: A shank having a square cross section h = 8 mm and b = 8 mm shall be designated as: Shank Section 0808 IS: 1983 Round d
Square hxb
6 6x6 8 8x8 10 10 x 10 12 12 x 12 16 16 x 16 20 20 x 20 25 25 x 25 32 32 x 32 40 40 x40 50 50 x 50 63 63 x 63 * Non preferred sizes are in brackets.
Rectangular hxb height to width ratio ( approx) 1.25 : 1 1.6 : 1 2:1 (6 x 5) 6x4 (6 x 3) (8 x6) 8x5 (8 x 4) (10 x 8) 10 x 6 (10 x 5) (12 x 10) 12 x 8 (12 x 6) (16 x 12) 16 x 10 (16 x 8) (20 x 16) 20 x 12 (20 x 10) (25 x 20) 25 x 16 (25x 12) (32 x 25) 32 x 20 (32 x 16) (40 x 32) 40 x 25 (40 x 20) (50 x 40) 50 x 32 (50 x 25) (63 x 50) 63 x 40 (63x 32)
Checking for deflection: The deflection of tool tip due to cutting force, P z is given as 3
δ = (4 Pz Le ) / EBH
3
[4.21]
Where, E = Modulus of elasticity for tool materials 2 = 224000 N / mm for HSS 2 = 700000 N / mm for C2 Carbide 2 = 560000 N / mm for C6 Carbide 2 = 420000 N / mm for TiC and Ceramics The permissible deflection of shank ranges from 0.04 mm in finishing cuts to 0.1 mm in roughing cuts. [4] Design of Chip Breakers During the high speed machining of ductile materials, long chips are continuously produced which must be broken into small pieces for easy disposal and to protect the finished surface from coiling chips. Chip breakers may be added to a cutting tool for this purpose. Types of Chip Breaker : Several types of chip breaking devices are in use. Sometimes a small step or shelf is ground on the tool face for this purpose. Its depth is usually from 0.3 mm to 0.8 mm (its width depends on feed and depth of cut). If the size of the shelf is properly chosen, it will break a continuous chip into short pieces. This type of chip breaker considerably increases the tool cost on carbide tools. A cutting tool with a groove and ridge type chip breaker has a groove of 2.5 mm to 13 mm width, 0.1 mm to 0.15 mm depth and a radius of 0.5 mm to 3 mm. A narrow Lecture Notes of Chinmay Das
9
ridge or land is provided along the cutting edge for strength. With this form of tool face , the chip flows into the groove and is forced into curl. The closer the groove is to the cutting edge, the smaller the radius will be and the tighter the chip will curl. In semifinish and finish turning of steel, the chip will break into short coiled pieces. This type of chip breaker, requiring power consumption and depending less upon feed or depth of cut than other types, is suitable for high feeds. Separate type chip breakers, often adjustable are also in use in tipped tools, particularly with throwaway type inserts.
Figure 4.6: Types of Chip Breakers-I
Figure 4.7: Types of Chip Breakers-II
Lecture Notes of Chinmay Das
10
Design of Tool Tips The extensive application of cemented carbides in single point metal cutting practice has led to the introduction of tipped tools when an insert is either brazed or clamped on to the shank. The carbide tip must be so designed as to ensure that the resultant force P always passes through the nest of tip in the shank and keeps the tip in compression. Various tip designs are employed depending on the type of processing, feed and depth of cut. The seat or recess for the tip in the shank may be either open, semi-open, closed or of the slot type.
Figure 4.8: Typical Tip Styles
Figure 4.9: Seat for Tip in the Shank
Lecture Notes of Chinmay Das
11
The Tip Dimensions:
Figure 4.10: Dimensions of Tip in the Shank 0
0
The Seat Angle = θ = 25 to 30 2 G≥ H 3 The thickness of standard tip = c= 2.5 mm to 12 mm b/ c = 1.6 to 2.7 and E = G + b sin θ + c cos θ ≥ H Where H = Tool shank height F = Dimension for line of centres of lathe [ 5] Problem 1: Design a HSS cutting tool to machine mild steel work piece in a lathe. Assume suitable data. Solution: Since not much data available to solve above problem, we have to make following assumptions. 2 1. BHN of material = 200 Kg/ mm 2. Back Rake Angle, Side Rake Angle and Side Cutting Edge Angle for HSS tool for 0 0 0 machining mild steel are 10 , 12 , 45 respectively. 2 3. Dynamic Shear Stress of mild steel can be calculated using τs = 0.186 BHN Kg/ mm 2 4. Ultimate Tensile Strength of HSS is 1000 N / mm . 5. Factor of Safety for rough machining is 10. 6. Shank of Tool Section is square. 7. Tool Over Hung is 30 mm. 8. Chip Reduction Co-efficient is 2.5 for rough machining. Calculation: Conversion of tool angles from ASA system to ORS
tan γ0 = tan γy cosΦ cosΦ + tan γx sinΦ sinΦ = tan 10 cos 45 + tan 12 sin 45 = 0.273 0 or, γ0 = 15.26 Lecture Notes of Chinmay Das
12
2
Dynamic Shear Stress of mild steel is τs = 0.186 BHN Kg/ mm 2 2 = 0.186 x 200 = 37.2 Kg/ mm = 372 N / mm Selecting depth of cut 2 mm and feed 0.3 mm/ rev, we have
Pz = t so τs(ζ – tan γ0 + 1) = 2 x 0.3 x 372 ( 2.5 – tan15.26 + 1) = 720.26 ≈ 720 N
Px = t so τs (ζ – tan γ0 – 1) sinΦ = 2 x 0.3 x 372 ( 2.5 – tan15.26– 1)sin 45 = 193.6 ≈ 194 N 2
2
σ = σ ut / FOS = 1000/ 10 = σ 1 + σ 2 = (6 Pz Le / BH ) + (6 Px Le / HB ) Here Le = 30 mm, and H=B 3 3 So, 100 = {( 6 x 720 x 30 ) / B } + {( 6 x 194 x 30 ) / B } or, B = 11.805 mm The nearest standard cross section value is 12 mm. Therefore cross section of tool shank selected is 12 mm x 12mm. Checking for deflection: 3
3
3
4
δ = (4 Pz Le ) / EBH = ( 4 x 720 x 30 ) / ( 224000 x 12 ) = 0.016 mm , which is within the permissible limit. Power consumed = P z x Vc = 720 x { 50 / 60}= 599 W ≈ 0.6 KW Cutting Tool Specification 1212 IS: 1983 Cutting Tool Material can be M2 (T83 W6 Mo5 Cr4 V2) or T1 ( T72 W18 Cr4 V1) Generally M type HSS materials are cheaper compared to T type material. The various M type HSS materials are M1, M2, M3, M4, M7, M10, M33, M36, M41, M42, M43, M44, M45, and M46. The various T type HSS materials are T1, T2, T4 and T6. The design of chip breaker is optional.
Reference: 1. Manufacturing Science-II by A.B. Chattopadhyay, NPTEL website at www.nptel.iitm.ac.in 2. Tool Design by Cyril Donaldson, page 304 3. ASTME, “Manufacturing, Planning and Estimating Hand Book”, F.W.Wilson(ed), McGraw-Hill, New York, 1963 4. Metal Cutting- Theory and Practice by A. Bhattacharyya, page 577 5. Metal Cutting- Theory and Practice by A. Bhattacharyya, page 580
Lecture Notes of Chinmay Das
13
