Check the gear for wear if the surface endurance limit is 600MPa

Question

A pair of straight teeth spur gears having 20^o full depth involute teeth is to transmit 20kW. The pinion runs at 300 r.p.m and the speed ratio is 3:1

The following data are given :

Number of teeth on pinion =15

Service factor C_s = 1

Velocity factor C_v =  3/3+v where v is the pitch line velocity in m/sec

Tooth form factor ‘y’ = 0.154-0.912/T

Where,  T  = Number of Teeth

Face width = 14m,  where m = module in mm.

Allowable static stress for pinion and gear materials are 120 MPa and 100MPa respectively.

Check the gear for wear if the surface endurance limit is 600MPa and modulus of elasticity for pinion and gear materials are 200GPa and 100 GPa respectively.