Question

2/1 A spur gearset has a module of 4 mm and a pressure angle of 25°, and a velocity ratio of 2.80. The pinion has 20 teeth. 1) Checok for interference; show your work. 2) Find: a) The number of teeth on the driven gear b)The circular pitch c) The pitch and base diameters d) The theoretical center distance e) The contact ratio

Answer 1

Given m = 4 mm: phi = 25 degree G = VR = 2.8 t_p = 20 1 (a) min no of teeth on the gear to avoid interference T_G = 2/squareroot 1 + 1/G (1/4 +2) s_n^2 = 2/squareroot 1 + 1/28 (1/2 +2) s_n^2 2s^2 -1 therefore , 28/2.8 = 10 since t_p greaterthan (t_p)_min - no interference 2 a) no of teeth on the driver gear T_4 = 20 times 2.8 = 56 b) The circular pitch i_c = pi times 4 = 12 times 6 mm d_p 4 times 20 = 80 mm: d_G = 56 times 4 = 224 mm d) centre distance = 152 mm e) contact ratio path of contact = squareroot R_a^2 - R^2 cos^2 p + squareroot r_a^2 - r^2 cos^2 p - (R + r) sin phi R_a = 116 mm , R = 224/2 = 112 mm , r = 40 mm Therefore path of contact = 16.843 mm Therefore area of contact = 78.58mm Therefore contact ratio x = area of contact/circular 18.58/12.56 = 1.479