ELEMENTS OF MACHINE TOOL DESIGN ELEMENTS OF MACHINE TOOL DESIGN Particular 25.5 Formula where Ft or Fc ẳFz ị ẳ tangential cutting force perpendicular to Fr (¼Fy ) and Ff (ẳFx ) in the vertical plane Fr ẳFy ị ẳ radial force perpendicular to the direction of feed and in the horizontal plane Ff ẳFx ị ẳ feed force in the horizontal plane against the direction of the feed x, y and z are machine reference axes along feed force Ff , radial force Fr , and cutting force Ft or Fc directions, respectively 25.1.2 Merchant’s circle for cutting forces for a single-point metal cutting tool F Fhc ỵ Fc tan ¼ Fn Fc À Fhc tan The co-efficient of friction in orthogonal cutting (Fig.25-3) ¼ tan ¼ The shear force F ¼ Fc cos À Fhc sin 25-5ị The friction force F ẳ Fhc cos ỵ Fc sin 25-6ị Mean shear stress ẳ Fc sin cos À Fhc sin2 Ai ð25-7Þ t2 Chip Fτ Fc t1 α Tool rn Fhτ = F hc 2φ Fτ ρ = tan—1µ φ rn φ FR α Fµ ρ α FIGURE 25-3 Force acting in orthogonal cutting with a continuous chip Courtesy: ASTME, Tool Engineers’ Handbook, 2nd Edition, McGraw-Hill Book Company, New York, 1959 d-rn ð25-4Þ d Feed θ Direction of chip flow FIGURE 25-4 Approximate chip flow direction Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ELEMENTS OF MACHINE TOOL DESIGN 25.6 CHAPTER TWENTY-FIVE Particular Formula Work done in shearing the material W ẳ ẵcot ỵ tan ị 25-8ị Work done in overcoming friction W ¼ F sin Ai cos ị 25-9ị Wt ẳ Fc Ai The total work done in cutting ð25-10Þ rc cos À rc sin The shear angle ( ) tan ¼ The tangential cutting force Ft ẳ KCs m1 d m2 25-11ị 25-12ị where d ẳ depth of cut, m (mm) m1 ¼ slope of Ft versus s graph (typical values 0.5 to 0.98) m2 ¼ slope of Ft versus d graph (typical values 0.90 to 1.4) K ¼ overall correction coefficient, depends on actual conditions of tool angles and working conditions (varies from 0.9 to 1.0) C ¼ coefficient characterized by material of job, condition of working tool, coolants, etc (Table 25-1) The values of K in Eq (25-12) are calculated from equation K ẳ Km K K Kc 25-12aị where Km ¼ material correction coefficient K ¼ correction coefficient, depends on back rack angle Kc ¼ correction coefficient for coolant used K ¼ correction coefficient, depends on top rack angle Values of Km , K , Kc , and K are taken from Tables 25-2 and 25-3 TABLE 25-1 Values of C and exponents Type of operation Material Turning and boring Facing and parting Turning and boring Parting and facing Steel Steel Gray cast iron Gray cast iron Ultimate strength, u , MPa Hardness, Brinell, HB C m1 m2 735 735 215 215 190 190 225 264 98 135 1.0 1.0 1.0 1.0 0.75 1.00 1.75 1.0 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ELEMENTS OF MACHINE TOOL DESIGN ELEMENTS OF MACHINE TOOL DESIGN Particular 25.7 Formula The chip flow angle for zero-degree rake angle (Fig 25-4) tan ẳ d rn ỵ d rn ị tan 25-13ị where rn ẳ nose radius ¼ side cutting edge angle, deg The equation relating the true rake angle to the corresponding chip flow angle tan tr ẳ tan sin ỵ tan cos The equation for locating the maximum rake angle tan max ¼ The metal removal rate ð25-14Þ Q¼ tan tan 25-15ị D dịsdn ẳ Vsd 1000 where 25-16ị s ¼ feed rate, mm/rev Q ¼ metal removal rate, cm3 /min d ¼ depth of cut, mm D ¼ diameter of work piece, mm V ẳ ẵD dịn=1000, m/min The approximate relationships between Ft ẳFz ị, Ff ẳFx ị and Fr ẳFy ị Ff ẳFx ị % 0:3 to 0:2 Ft ẳFz ị 27-17ị Fr ẳFx ị % 0:2 to 0:1 Ft ẳFz ị 27-18ị The turning moment on the work piece due to tangential cutting force Mtcut ¼ Ft TABLE 25-2 Material correction coefficient, Km TABLE 25-3 Values of Kc , K , and K Material Steel Cast iron Ultimate strength , MPa Km Coolant 390–490 490–588 686–785 785–880 980–1175 1370–1570 1570–1765 1765–1960 2155–2355 2355–2745 0.76 0.82 1.00 1.10 1.28 0.88 0.94 1.00 1.12 1.17 D Dry Soda water Emulsion Mineral oil Hard mineral oil ð25-19Þ , deg K 15 10 ỵ5 ỵ5 ỵ10 ỵ15 þ20 1.40 1.30 1.23 1.13 1.06 1.00 0.94 0.89 , deg K Kc 30 45 60 75 1.05 1.00 0.96 0.94 1.03 1.10 1.15 90 0.92 1.20–1.25 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ELEMENTS OF MACHINE TOOL DESIGN 25.8 CHAPTER TWENTY-FIVE Particular The bending moment due to bending of the tool in the vertical plane by tangential cutting force Formula Mb ¼ Ft l 25-20ị where l ẳ cantilever length of the cutting tool, m 25.1.3 Power The total power at the cutting tool, Ptotal Ptotal ẳ Pc ỵ Pf ỵ Pr 25-21ị where Pc ¼ Ft Vt ¼ power required for turning cut, kW 1000 Pf ¼ Ff Vf ¼ power required to feed in a horizontal 1000 direction, kW The feed velocity is very low Power required to feed is approximately 1% of total power Hence it is neglected Pr ¼ Fr Vr ¼ power required to feed in radial direc1000 tion, kW The radial velocity is zero Therefore Pr is ignored After neglecting Pf and Pr , the power required at the cutting tool, taking Vc for Vt and Ptotal % Pc The gross or motor power Ft Vc KCs m1 d m2 Vc ẳ 25-22ị 1000 1000 where Pc in kW, Ft in N, Vc in m/s, s and d in m Pc ẳ Pg ẳ Pc ỵ Pt 25-23ị where ẳ mechanical eciency of machine tool Pt ¼ tare power, the power required at no-load, kW 25.1.4 Specific power or unit power consumption The specific power Pu ẳPs ị, required to cut a material Pu ẳ Pc (cubic meter or cubic millimeter of material removed by cut per minute) ð25-24Þ The specific power or unit power Pu ẳPs ị, for turning Pu ẳ Pc Ft C ¼ ¼ Vc sd 1000sd 1000s À m1 d À m2 ð25-25Þ where Pc , Pu in kW/m3 /min, Ft in N, s and d in m, and Vc in m/s Another relation connecting specific powers at different cutting feeds and depths of cuts Pu2 ¼ Pu1 s1 s2 À m1 d1 d2 À m2 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ð25-26Þ ELEMENTS OF MACHINE TOOL DESIGN ELEMENTS OF MACHINE TOOL DESIGN 25.9 Particular Formula TABLE 25-4 Typical values of specific power consumption Ps or Pu Refer to Table 25-4 for Pu (m3 /s) or Pu (mm3 /s) for various materials Brinell hardness number, HB Material Plain carbon steel Alloy steel Free cutting steel Cast iron Aluminum alloy Specific power consumption, Ps or Pu ; kW/m3 126 179 262 179 429 229 140 256 55 115 m1 and m2 are taken from Table 25-1 1.6 to 1.8 1.9 to 2.2 2.3 to 2.6 1.5 to 1.86 3.0 to 5.20 1.37 to 1.48 0.60 to 0.90 2.32 to 3.60 0.76 0.46 to 0.57 1.5 Brass 25.1.5 Tool design For comparison of Orthogonal Rake System (ORS), Normal Rake System (NRS) and American (ASA) tool nomenclature Refer to Table 25-5 25.1.6 Tool signatures ðASAÞ - o - p - rn ðORSÞ s - n - n - - o - p - rn n The tool signature for sintered carbide tipped single point tool p - f - p - f - o - s - rn s - o - o - o The tool signature of ASA, ORS and NRS ðNRSÞ Refer to Fig 25-5 TABLE 25-5 Comparison of tool nomenclature system Particular Orthogonal rake system (ORS)a Normal rake system (NRS)a American Standards Association (ASA)b Location of cutting edges Orientation of face Orientation of principal flank Orientation of Auxiliary flank Nose radius p , o o , s o 0o rn p , o n , s n 0n rn s , o p , f p , f — rn a Tool reference system b Machine reference system Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ELEMENTS OF MACHINE TOOL DESIGN 25.10 CHAPTER TWENTY-FIVE Particular Formula Tool signature Back rake angle Side rake angle End relief angle End clearance angle Top view 7 10 1/64 = 0.4 mm Side relief angle Side clearance angle End cutting edge angle Side cutting edge angle Nose radius Carbide insert 1/64 in = 0.4 mm 10 Right side view Front view FIGURE 25-5 A straight shank, right cut, sintered carbide tipped, single point tool Rake angles are negative Courtesy: American Society of Tool and Manufacture Engineers, Fundamentals of Tool Design, Prentice Hall of India Private Ltd., New Delhi, 1969 For general recommended various angles for HSS single-point tool Refer to Table 25-6 For general recommended various angle for carbide single-point tool Refer to Table 25-8 25.1.7 Tool life The relation between the tool life and cutting speed V according to Taylor Kc ẳ V m 25-27ị where Kc ẳ constant taken from Table 25-7 or constant equal to the intercept of the tool life and cutting speed curve and the ordinate (V curve) m ¼ slope of the V curve mẳ logV1 =V2 ị log 2 = 1 ị Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ð25-28Þ γp = back rack angle υp = true wedge angle φp F S φs O O1 P O1 P O F αo υ s N lip angle γo υ = wedge angle υn = true wedge angle = normal clearance angle Section N—N γn = normal rack angle γn υn αn orthogonal rack angle λs = inclination angle φp = principal cutting edge angle φs = side cutting edge angle N Section O—O φo = end cutting edge angle orthogonal clearance angle υo ELEMENTS OF MACHINE TOOL DESIGN Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website FIGURE 25-6 Single-point tool geometry (angles of machine reference system ASA, ORS and NRS) Courtesy: Principles of metal cutting—An introduction, Centre for Continuing Education, I.I.T., Madras, November, 1987.5 Section P—P γp υp α1 = α’0 αp = front or end clearance or relief angle Section O1 —O1 γ1 υ1 Section F—F αf = side clearance angle υf γf = side rack angle ELEMENTS OF MACHINE TOOL DESIGN 25.11 ∝ λs n N = 10° n N Section O–O Section N–N ∝ ° ∝ = 6° ° Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ∝n = 6° O φ = 8° ° φ ° F P P O1 Section F–F φs O1 P φ O 15' F φs = 15° S ∝f = 5° P ∝ = 22° 6' P ∝ ∝ Section P–P P P = 2° Section O1 –O1 ∝ 36' FIGURE 25-7 Left hand single-point tool geometry (angles of machine reference system ASA, ORS and NRS) Courtesy: Principles of metal cutting—An introduction, Centre for Continuing Education, I.I.T., Madras, November, 1987.5 υ =true wedge angle, deg ° φ =principal cutting edge angle, deg P φ =end cutting edge angle, deg ° φ =side cutting edge angle, deg s View S λs = 0° = 10° ∝ ∝ ° ° ∝ ∝f ∝ 25.12 ∝ ∝ f ELEMENTS OF MACHINE TOOL DESIGN CHAPTER TWENTY-FIVE ELEMENTS OF MACHINE TOOL DESIGN 25.28 CHAPTER TWENTY-FIVE Particular Formula 25.2.4 Broaching machine BROACHES (Figs 25-14 and 25-15) AND BROACHING For broach tooth form Refer to Fig 25-14 For nomenclature of round pull broach Refer to Fig 25-15 The allowable pull of internal or hole broach Fapl ¼ Asut n The permissible load on push type of round broach (Fig 25-15) using Euler’s column formula with both ends free but guided Fpps ¼ 2 EI 2 E ¼ nL2 nL The allowable push in case of push type round broaches when E ¼ 206:8 GPa in Eq (25-74) Faps ¼ Note: when (L=D) is greater than 25, a push broach is considered as a long column and strength is based on this If (L=D) is less than 25, the broach is considered to act as a short column which resist compressive load only Land Rake angle ð25-73Þ D4 r 64 100;000D4 r nL2 where 25-74ị 25-75ị Fapl ẳ allowable pull, N Faps ¼ allowable push, N A ¼ area of the minimum cross-section of broach which occurs at the root of the first roughing tooth or at the pull end, mm2 Back off angle Pitch Straight land Depth Radius FIGURE 25-14 Broach tooth form Courtesy: American Broach and Machine Division, Sundstrand Machine Tools Company Pull end Shank Front pilot Semifinish Finishing teeth teeth Broach "length" Round hole broach Burnishing teeth Roughing teeth Round hole broach with burnishers Rear pilot Rear support Follow rest grip FIGURE 25-15 Nomenclature of a typical round pull broach Courtesy: American Broach and Machine Division, Sundstrand Machine Tools Company Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ELEMENTS OF MACHINE TOOL DESIGN ELEMENTS OF MACHINE TOOL DESIGN Particular 25.29 Formula n ¼ factor of safety to prevent broach damage because of sudden overloads due to hard spots in material, etc n ¼ or more dependent on slenderness ratio sut ¼ tensile strength of the broach material, N/mm2 Dr ¼ root diameter of the broach at 1=2L, mm L ¼ length of broach from push end of first cutting tooth, mm sa ¼ sut =n The safe tensile stress for high speed steel as ¼ 98 MPa for keyway broaches as ¼ 196 MPa for polygon broaches as ¼ 245 MPa for round/circular broaches The number of teeth cutting at a time in case of surface broaching zẳ lmax ỵ1 p 25-76ị where lmax ẳ maximum length of workpiece, mm p ¼ pitch of the broach teeth, mm L ¼ Dz for circular/round broach 25-77aị L ẳ bz for spline broach 25-77bị L ẳ lz for surface broach Sum of the length of all the teeth engaged at any instant in broaching 25-77cị ks ẳ 4415 ỵ 3 108 24;515sz The specific broaching/cutting force ð25-78Þ where ks in N/mm2 Also refer to Table 25-21 for ks TABLE 25-21 Specific broaching force, ks Rise per tooth, sz , mm 0.03 0.04 0.05 0.06 0.08 0.1 Specific broaching force, ks , MPa Material Mild steel Cast iron: Gray Malleable Alloy steel 4168 3580 3285 3040 2745 2550 3726 3334 5688 3236 2844 4505 2942 2648 4413 2648 2452 4168 2452 2206 3775 2305 2060 3530 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ELEMENTS OF MACHINE TOOL DESIGN 25.30 CHAPTER TWENTY-FIVE Particular Formula ¼ tensile strength of workpiece, N/mm2 ¼ rack angle, deg sz ¼ rise per tooth, mm The recommended speeds and feeds for broaching Refer to Table 25-22 The broaching force F ¼ kks Dzịsz for circular or round broaches 25-79aị F ẳ kks bzịus sz for spline or key broaches 25-79bị F ẳ kks lzịsz for surface broaches 25-79cị where b ẳ width of spline or key, mm D ¼ diameter of broached hole, mm l ¼ width to be broached in case of surface broach, mm k ¼ coefficient (may be taken as 1.1 to 1.3) z ¼ number of teeth engaged at a time us ¼ number of spline Another equation for the broaching force in case of key and splines broaching F ẳ Cszm5 bzịus TABLE 25-22 Recommended speeds and feeds for broaching TABLE 25-23 Broach angles for broaching with HSS broaching (Fig 25-14) Brinell hardness, HB Workpiece material Aluminum alloys Copper alloys Cast iron: Gray Malleable Low alloy steels Carbon steel Free cutting steel Rise per tooth, mm Cutting speed, m/min 30–150 40–200 0.15 0.12 10–20 8–10 110–140 190–220 250–320 110–400 85–125 120–375 100–200 275–325 325–375 0.13 0.07 0.05 0.15 0.10 0.08 0.10 0.07 0.05 4.5 5–30 3–8 10–12 6 Workpiece material Aluminum/ magnesium Copper alloys Cast iron Lead brass Mild steels Alloy steels Tool steels Stainless steel Titanium ð25-80Þ Brinell hardness, HB 30–150 40–200 100–320 — 225–325 130–423 300–402 135–325 110–402 Hook/rake angle, deg Clearance angle, deg 1015 13 010 68 to ỵ5 15–20 8–12 8–12 12–18 8–26 1–3 2–3 1–3 2–3 1–3 1–2 2–3 2–8 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ELEMENTS OF MACHINE TOOL DESIGN ELEMENTS OF MACHINE TOOL DESIGN Particular 25.31 Formula where C ¼ coefficient which takes into consideration condition of cutting and characteristic of workpiece Taken from Table 25-25 sz ¼ feed per tooth, mm (Table 25-25) m5 ¼ exponent taken from Table 25-25 Another equation for the broaching force in case of cylindrical broaching F ¼ Cszm5 Dz The velocity of broaching vẳ Kv m6 szm7 25-81ị 25-82ị where Kv ¼ velocity coefficient depends on the conditions of metal cutting (Table 25-24) ¼ life of tool, su ¼ stress of material, N/m2 , from Table 25-24 The power required for broaching by the broaching machine Fv 1000 where F in N, v in m/s, and P in kW Pẳ 25-83ị 25.2.5 Milling machines A knee horizontal-milling machine for plain or slab milling Refer to Fig 25-16 A knee-type vertical milling machine for face milling Refer to Fig 25-17 For nomenclature and tool geometry of milling cutters Refer to Figs 25-18 and 25-19a For tool angles of millings cutters Refer to Table 25-26 and Figs 25-18 and 25-19a rffiffiffiffi z h 25-84ị kẳ ẳ " D where The engagement parameter (Fig 25-19a) ¼ engagement angle for milling depth, h r h ẳ2 D 25-85ị " ẳ peripheral pitch angle, deg % 2 z Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ð25-86Þ 200 200 up to 200 200–230 above 200 — — up to 686 686–785 above 785 Stress su , MPa 14.0 11.5 16.8 15.5 11.2 Kv 0.50 0.50 0.62 0.62 0.62 m6 0.60 0.60 0.62 0.62 0.62 m7 sz as given in Table 25-25 Circular or round broaching Alloy steels Cast steel Cast iron 200 >200 200 200–230 >230 200 200–230 >230 Brinell hardness, HB Workpiece material — — 686 686–785 >785 686 686–785 >735 Stress su , MPa 2942 3472 6865 7472 8257 6865 7472 8257 C 6.2 5.1 9.2 8.8 6.3 Kv 0.04–0.08 0.03–0.06 0.02–0.03 0.02–0.05 0.02–0.03 0.02–0.03 0.02–0.04 0.02–0.03 sz sz 0.73 0.73 0.85 0.85 0.85 0.85 0.85 0.85 m5 Circular or round broaching TABLE 25-25 Values of C, sz and m5 for use in Eqs (25-80) and (25-81) Steels Cast iron Brinell hardness, HB Workpiece material 0.6 0.6 0.87 0.87 0.87 m6 1128 1344 1735 1980 2452 1735 1980 2452 C 6.2 5.1 7.7 7.0 5.0 Kv 0.6 0.6 0.87 0.87 0.87 m6 0.08–0.15 0.07–0.12 0.04–0.07 0.07–0.12 0.04–0.07 0.03–0.06 0.06–0.10 0.04–0.07 sz 0.73 0.73 0.85 0.85 0.85 0.85 0.85 0.85 m5 0.95 0.95 1.4 1.4 1.4 m7 sz > 0:07 mm Keyway broaching 0.95 0.95 1.4 1.4 1.4 m7 0.07 mm Keyway broaching 1490 2108 2079 2255 2785 2079 2255 2785 C 17.5 14.7 15.5 14.0 10.2 Kv 0.05–0.10 0.04–0.08 0.04–0.06 0.04–0.08 0.03–0.05 0.03–0.05 0.04–0.06 0.03–0.05 sz Spline broaching 0.5 0.5 0.6 0.6 0.6 m6 0.73 0.73 0.85 0.85 0.85 0.85 0.85 0.85 m5 0.6 0.6 0.75 0.75 0.75 m7 sz as given in Table 25-25 Spline broaching 25.32 TABLE 25-24 Values constant, Kv and exponents m6 and m7 for use in Eq (25-82) ELEMENTS OF MACHINE TOOL DESIGN CHAPTER TWENTY-FIVE Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ELEMENTS OF MACHINE TOOL DESIGN ELEMENTS OF MACHINE TOOL DESIGN Particular 25.33 Formula For up-milling and down-milling processes Refer to Fig 25-19 The minimum number of teeth for satisfactory cutting action (Fig 20-19a) 2 zmin ¼ p h=D 25-87ị where h ẳ depth of milling, mm For h=D ¼ 10 to The circumferential or circular pitch pc ¼ 20 the zmin lies between 20 and 28 D z ð25-88Þ Overarm Arbor Work table Column Saddle Knee Base (a) Knee - type horizontal milling machine Y Z Machined surface Tool X Primary motion (C) Continuous feed motion(X’) Workpiece Work surface (b) Helical milling cutter FIGURE 25-16 Knee-type horizontal milling machine for plane milling Courtesy: G Boothroyd, Fundamentals of Metal Machining and Machine Tools, McGraw-Hill Book Company, New York, 1975.9 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ELEMENTS OF MACHINE TOOL DESIGN 25.34 CHAPTER TWENTY-FIVE Particular Formula pc D ¼ tan z tan The axial pitch pa ¼ The number of teeth in engagement in case of plain milling cutter whose helix angle is z b tan ỵ zs ẳ D The design equation for the number of teeth on milling cutter 25-89ị r! h D 25-90ị where b ẳ width of cutter, mm p zẳm D 25-91aị where m is a function of helix angle Table 25-27 gives values of m for various helix angles Head Table Column Saddle Knee Z X Y Base (a) Knee - type vertical milling machine Cutting Edge Primary motion ( C) Tool Relief Angle Primary clearance angle (α) Secondary clearance angle (α1) Lip Angle Machined surface Back of Tooth Face of Tooth Radial Rake Angle = γ1 Land (f) Gash or Chip space BODY OF CUTTER (b) Face milling cutter FIGURE 25-17 Knee-type vertical milling machine for face milling Courtesy: G Boothroyd, Fundamentals of Metal Machining and Machine Tools, McGraw-Hill Book Company, New York, 1975.9 Direc Work surface tion Root diameter (Dr) f Rota Workpiece tion o Continuous feed motion ( X’) Fillet or Root radius Tooth depth Outside diameter (D ) ¡ FIGURE 25-18 Nomenclature and geometry of milling cutter Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ELEMENTS OF MACHINE TOOL DESIGN ELEMENTS OF MACHINE TOOL DESIGN Particular Formula R= γ α1 ψ V D f ∋ h δ Feed α δ = gullet angle, deg γ = rake angle α = primary clearance angle α1 = secondary clearance angle h = depth of cut or depth of mmilling, Feed = peripheral pitch angle or angular pitch, deg = engagement angle for milling depth, h = (ψ / = engagement parameter = land, mm (∋ ∋ ψ k f 25.35 (b) Up-milling (a) Down-milling FIGURE 25-19 Horizontal milling process The gullet angle (Fig 25-19a) ẳ"ỵ if rack angle ẳ 25-91bị where ¼ wedge angle, deg CHIP FORMATION IN MILLING OPERATION PLAIN MILLING (Fig 25-21) The maximum undeformed chip thickness in case of plain or slab milling (Fig 25-21) as per Martellotti10,11 tucðmaxÞ 91=2 D > > > > > > À1 < = h cos 6s ¼6 z 2 > D vf vf D> > > > > ầ 1ặ : ; 2h V Vh 25-92ị The length of undeformed chip (Fig 25-21) lẳ The inherent roughness height R¼ D 1=2 vf D Ỉh À1 h V D sz sz ặ z 25-93ị 25-94ị where the upper sign (ỵ) refers to up-milling and the lower sign (À) refers to down-milling The feed s which is equal to the distance moved by the workpiece during one resolution of tool (Fig 25-21) vf n where s in mm/rev s¼ Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ð25-95aÞ ... 2 93? ? ?30 2 402 286 ? ?30 2 225? ?32 5 32 5–425 85 –225 4 23 510 135 ? ?32 5 402 110–402 149–170 187 –202 187 –217 90–104 — — 90–100 90–100 1 18 1 18 1 18 1 18 1 18? ?? 135 1 18 1 18? ?? 135 150 1 18 150 1 18? ?? 135 1 18 1 18 130 1 18. .. 125– 135 125– 135 125– 135 125– 135 125– 135 125– 135 125– 135 125– 135 135 135 24? ?32 24? ?32 24? ?32 24? ?32 24? ?32 24? ?32 24? ?32 24? ?32 24? ?32 24? ?32 24? ?32 24? ?32 20? ?32 24? ?32 24? ?32 24? ?32 32 –45 24? ?32 24 -32 Dry Dry Dry,... 0. 08 0.1 Specific broaching force, ks , MPa Material Mild steel Cast iron: Gray Malleable Alloy steel 41 68 35 80 32 85 30 40 2745 2550 37 26 33 34 5 688 32 36 284 4 4505 2942 26 48 44 13 26 48 2452 41 68 2452