Question

Calculate the power that can be transmitted safely by a pair of spur gears with the data given below. Calculate also the bending stresses induced in the two wheels when the pair transmits this power.

         No.of the teeth in the pinion  = 20

         No. of teeth in the gear = 80

         Module  = 4mm

         Width of the teeth = 60mm

         Tooth profile  = 20^oinvolute

         Allowable bending strengths :

         Materials of the pinion  = 20 kgf/mm²

         Materials of the gear = 16 kgf/mm²

         Speed of the pinion  = 400 r.p.m

         The Lewis equation , given below may be used:

                        U_n = $\sigma _{0}$ b p y k_v k_s

         Where U_n = nominal tangential force

        $\sigma _{b}$ = bending strength

         b = width of the teeth

         p = circular pitch

         y = form factor=0.154–(0.912/z)

         z = No. of teeth 

         k_v = velocity factor = 3/(3+v)

         v = peripheral velocity in m/sec

         k_­s = service factor = 0.8