Question

Homework 6: The figure below shows a gear train where gear 1, on shaft a (input shaft), drives gear 2 with 32 teeth (denoted 32T) on shaft b, gear 3 (20T) also is on shaft b and drives gear 4 (507) on shaft c (output shaft). The pitch diameter of gears 1 and 2 are d = 24 mm and d = 48 mm. The center distance between gears 3 and 4 (distance between shafts b and c is 70mm. (a) How many teeth are there on gear 1? (10 pts) (b) What is the circular pitch of gear 2? (10 pts) (c) What are the pitch diameters of gears 3 and 4? (10 pts) (d) If gear 4 on shaft c is to rotate at 75 rpm clockwise, what is the required speed and direction (CW or CCW) of the input shaft a. (10 pts) (e) If the input torque delivered to gear 1 is 6 N-m and the efficiency of the gear train is 90%, what is the expected output torque? (10 pts) 507 v Omm

Answer 1

6. (Pc), - 7 m2 = 7 dz. ** 32) = 4.712 mm © dg + dy = 2x70 =140, -0. m3 = my 48 ds. dy + du = (he) ds = 620) dz = 91503 32 (-16 from eqr o dz=40mm & dy = 100 mm 0. N Ng = (3) X75 = 187.5 rpm = No (compared years) Nu N I N ,= N₂ (72) = 187.5 (32) = 375 rpm (cw) ! o exr, = 6 = 6410 - 500 N = F2, T2 2 ₂ X 2 = 12 N.m but eff is 90%, so I2 = 0.9x12= 10. 8 N.m = T3 (Compound gear) F = I3 - 10.8410 = 540N=fy, Ty=fu x ry=540x50 - 27 Nm but eff 90%, so Tg = 0.9827 = 24.3 Nm. +3- 20 103