Machine Design I

A 17-tooth 20° pressure angle spur pinion rotates at 1800 rev/min and transmits 3 kW to a 52 tooth disk gear. The module of the gear is 2.54 mm, the face width 40 mm, and assume the suitable quality standard for the gear. The gears are straddle-mounted with bearings immediately adjacent. The pinion is a grade 1 steel with a hardness of 240 Brinell tooth surface and a through-hardened core. The gear is steel, through-hardened also, grade 1 material, with a Brinell hardness of 200, tooth surface and core. Poisson's ratio is 0.30 and Young's modulus is 205 MPa. The loading is smooth because of motor and load. Assume a pinion life of (10^8) cycles and a reliability of 0.90, and use (Y_N=1.3558N^{-0.0178}), (Z_N=1.4488N^{-0.023}). The tooth profile is uncrowned. This is a commercial enclosed gear unit. Find the factors of safety of the gears in bending. Find the factors of safety of the gears in wear. By examining the factors of safety identify the threat to each gear and to the mesh.