Machine Design Databook Episode 3 part 7 potx

MISCELLANEOUS MACHINE ELEMENTS MISCELLANEOUS MACHINE ELEMENTS Particular 24.81 Formula p h s2 r1 s1 h 2 d r2 FIGURE 24-53 Definitions and dimensions of ratchet wheel For external ratchet ẳ 148 to 178 24-266ị For internal ratchet ¼ 178 to 308 ð24-267Þ The ratio of a=d (internal ratchet) a=d ¼ 0:35 to 0:43 sffiffiffiffiffiffiffiffiffiffiffiffiffi Mt m¼2 z ba ð24-268Þ The module ð24-269Þ The bending moment on pawl Mb1 ẳ Fn e2 24-270ị The bending stress b ẳ 6Mb1 Fn ỵ ba bs1 bs2 s   b Fn ỵ th d1 ẳ 2:71 2ba 24-271ị The diameter of pawl pin where th ẳ thickness of hub on pawl TABLE 24-23 FÃ Material kN/m Cast iron 49–98 Steel or 98–196 cast steel Hardened 196–392 steel b lbf/in 280–560 560–1120 1120–2240 MPa kpsi 19.5–29.5 2.85–4.27 39–68.5 5.69–10.0 58.8–98 8.54–14.23 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 ð24-272Þ MISCELLANEOUS MACHINE ELEMENTS 24.82 CHAPTER TWENTY-FOUR 24.9 GENEVA MECHANISM SYMBOLS2,3 r1 sin  a¼ F1 F2 F2maxị Fmaxị Fimaxị iẳ z2 z k M1t M2t M2ti M2t n0 n P r1 r2 r02 ra2 rp r2 r1 m  gear ratio radius ratio total time required for a full revolution of the driver or crank, s time required for indexing Geneva wheel, s time during which Geneva wheel is at rest, s velocity, m/s number of slots on the Geneva wheel crank angle or angle of driver at any instant, deg (Fig 24-54) angular acceleration, m/s2 (ft/s2 ) angular acceleration of Geneva wheel, m/s2 (ft/s2 ) angular position of the crank or driver radius at which the product !2a is maximum, deg angle of the driven wheel or Geneva wheel at any instant, deg (Fig 24-54) t ti tr v z 2a ¼ the component of force acting on the crank or the driving shaft due to the torque, M1t , kN (lbf ) (Fig 24-57) the component of force acting on the driven Geneva wheel shaft due to the torque M2t , kN (lbf ) (Fig 24-57) maximum force (pressure) at the point of contact between the roller pin and slotted Geneva wheel, kN (lbf ) the component of maximum friction force at the point of contact due to the friction torque M2t , on the driven Geneva wheel shaft, kN (lbf ) the component of maximum inertia force at the point of contact due to the inertia torque on the driven Geneva wheel shaft, kN (lbf ) polar moment of inertia of all the masses of parts attached to Geneva wheel shaft, m4 (in4 ) the working time coefficient of the Geneva wheel total torque on the driver or crank, N m (lbf in) total torque on the driven or Geneva wheel, N m (lbf in) inertia torque on the Geneva wheel, N m (lbf in) friction or resistance torque on Geneva wheel, N m (lbf in) speed, rps speed, rpm power, kW (hp) radius to center of driving pin, m (in) radius of Geneva wheel, m (in) distance of center of semicircular end of slot from the center of Geneva wheel, m (in) outside radius of Geneva wheel, which includes correction for finite pin diameter, m (in) pin radius, m (in) J Rr ¼ center distance, m (in) r1 a the ratio of the driver radius to center distance efficiency of Geneva mechanism 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 MISCELLANEOUS MACHINE ELEMENTS MISCELLANEOUS MACHINE ELEMENTS   24.83 locking angle of driver or crank, rad or deg ratio of time of motion of Geneva wheel to time for one revolution of driver or crank ¼ 360 2z semi-indexing or Geneva wheel angle, or half the angle subtended by an adjacent slot, deg (Fig 24-54) crank or driver angle, deg (Fig 24-54) 2n !¼ 60 !1 , !2 a1 angular velocity of driver or crank (assumed constant), rad/s angular velocities of driver or crank and Geneva wheel, respectively, rad/s φ β r2 ω2 a a2 ω1 α a3 ψ r1 FIGURE 24-54 Design of Geneva mechanism Particular Formula The angular velocity (constant) of driver or crank !1 ¼ Gear ratio i¼ angle moved by crank or driver during rotation angle moved by Geneva wheel during rotation i¼ zÀ2 z 2n 60 360 2z The semi-indexing angle or Geneva wheel angle or half the angle subtended by two adjacent slots ¼ The angle through which the Geneva wheel rotates 2 ẳ 360 z 24-273ị 24-274ị or or  z ð24-275Þ 2 z ð24-276Þ EXTERNAL GENEVA WHEEL The angle of rotation of driver through which the Geneva wheel is at rest or angle of locking action (Fig 24-55) The crank or driver angle  ẳ 2 ị ẳ  ỵ 2 ẳ ẳ  z ỵ 2ị z  z 2ị ẳ 2z 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 ð24-277Þ ð24-278Þ MISCELLANEOUS MACHINE ELEMENTS 24.84 CHAPTER TWENTY-FOUR Particular ro Formula r’2 a φ ω2 ψ ” 90 ω1 r1 FIGURE 24-55 External Geneva mechanism DISPLACEMENT r1 sin  The center distance (Fig 24-55) a¼ The radius ratio Rr ¼ The ratio of crank radius to center distance ¼ The relation between crank angle and Geneva wheel angle r2 ¼ cot  r1 r1  ¼ sin  ¼ sin a z   sin ¼ tanÀ1 À cos ð24-279Þ ð24-280Þ ð24-281Þ ð24-282Þ VELOCITY The angular velocity of the Geneva wheel !2 ẳ d cos ị ! ẳ dt cos ỵ sin=zịcos sin =zị !1 sin=zị cos ỵ sin2 =z   d !2maxị ẳ ẳ ! dt max À      À sin !1 ¼ sin z z !2 ¼ The maximum angular velocity of Geneva wheel at angle ¼ 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 ð24-283aÞ ð24-283bÞ ð24-283cÞ MISCELLANEOUS MACHINE ELEMENTS 24.85 MISCELLANEOUS MACHINE ELEMENTS Particular Formula ACCELERATION The angular acceleration, a 2a , of Geneva wheel d2 ị sin ẳ !2 dt ỵ cos ị2 a 2a ẳ a 2a ẳ ặ sin=zị cos2 =zị sin !2 1 sin=zị cos ỵ sin2 =zị cos maxị ẳ  ỵ The maximum angular acceleration of Geneva wheel which occurs at ẳ maxị p 2 ỵ 2a ịi; f ẳ ặ sin=zị cos3 =zị !2 ẵ1 sin2 =zị ỵ sin2 =zị ẳ ặ!2 tan  ẳ ặ!2 tan =z 1   r ẳ ặ!2 1 r2 Total time required for a full revolution of the crank or driver 2a 20 12 tẳ 60 n 24-285ị 24-286ị ω2 ω1 10 0 α α2a ω12 ω2 ω1 10 20 30 a ð24-284cÞ where   1 ẳ ỵ The angular acceleration of Geneva wheel at start and finish of indexing α2a ω12 ð24-284bÞ Refer to Fig 24-56 For angular velocity and angular acceleration curves for three-slot external Geneva wheel with driver velocity, !1 ¼ rad/s 30 ð24-284aÞ FIGURE 24-56 Angular velocity and angular acceleration curves for three-slot external Geneva wheel 2a is the symbol used for angular acceleration of Geneva wheel; is the crank or driver angle at any given instant 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   !1 , !2 Particular Formula SINGLE UNIVERSAL JOINT (Figs 24-59 and 24-61a) The relation between , , and tan  cos 24-323ị !2 cos ẳ !1 sin2 sin2  24-324ị tan  ẳ The relation between the angular velocities of driving shaft or driver (!1 ) to the driven shaft or the follower (!2 ) β R ω2 r cos β β r P d1 ω1 d2 β O Q S FIGURE 24-59 A single universal joint 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 MISCELLANEOUS MACHINE ELEMENTS 24.92 CHAPTER TWENTY-FOUR Particular The maximum value of !2 =!1 The minimum value of !2 =!1 Formula  !2 !1  ¼ max cos ¼ À sin2 cos 24-325ị when sin  ẳ ỵ1, i.e.,  ¼ 908, 2708, or =2 or 3=2, etc   !2 ẳ cos 24-326ị !1 when sin ẳ 0, i.e.,  ¼ 0, , 2, etc The angular acceleration of the driven shaft 2, if !1 is constant The value of  for which the angular acceleration of the driven shaft is maximum d  d!2 cos sin2 sin 2 ¼ !1 ¼ dt dt ð1 sin2  sin2 ị2 p cos 2maxị ẳ  2 ỵ 24-327ị 24-328ị where  ẳ À sin Þ=2 sin 2 The angular acceleration of driven shaft is maximum when  is approximately equal to 458, 1358, etc., when the arms of cross are inclined at 458 to the plane containing the axes of the two shafts The power transmitted by universal joint P ¼ Mt !=1000 SI ð24-329aÞ where P in kW, Mt in N m, and ! in rad/s P ¼ Mt n=63,000 USCS ð24-329bÞ where P in hp, Mt in lbf in, and n in rpm The design torque of universal joint Mtd ẳ Mt Ks Kct 24-330ị The design power of universal joint Pd ẳ P KCN 24-331ị For calculation of torque and power transmitted by universal joint for various angles of inclination ... 2.414 3. 078 0. 134 0.2 93 0.500 0.6 17 0.690 30 08 270 8 2408 2258 2168 0.1 67 0.250 0 .33 3 0 . 37 5 0.400 6.46 2.41 1.00 0.620 0.4 47 1. 73 2 1.000 0. 577 0.414 0 .32 5 48460 118240 228540 31 838 0 38 830 0 31 .44... 25 16 32 20 40 25 50 32 63 40 50 75 90 34 40 52 48 62 56 74 68 86 82 108 105 132 130 166 160 190 45 0 .39 2 0.04 40 0.10 32 0. 17 28 3. 334 0 .34 25 5.296 0.54 20 14 .71 0 1.5 18 0.12 21. 575 27. 458... 458 30 8 22 830 0 188 i  30 8 458 608 67 830 0 72 8 r1 =a r2 =a Rr r02 =a   !2ðmaxÞ 2aðinitialÞ ¼ À ðmaxÞ Jmax J ¼ 0.5 0.886 0 .70 7 0.500 0 .38 3 0 .30 9 0.500 0 .70 7 0.866 0.924 0.951 0. 577 1.000 1. 73 2