Question

A gear reduction unit uses the countershaft shown A gear A receives power from another gear with the transmitted force FA applied at the 20° pressure angle as shown. The power is transmitted through the shaft and delivered through gear B through a transmitted force Fa at the pressure angle shown 16 in in in 20° 1.25-in dia (a)Determine the minimum factor of safety for fatigue based on infinite life, using the modified Goodman criterion Gear A 20-in dia. (b)Determine the actual life (number of cycles) of the shaft Gear B 8-in dia. 300 lbf", The shaft rotates at a constant speed, has a constant diameter, and is made from cold-drawn AISI 1045 steel Ans

Answer 1

Given data a gear reduction unit uses the counter shaft shown in the question that gear receives power from other gear with transmitted force F_A at pressure = 20 degree angle the power is transmitted through shaft & delivered with gear B * finding the slope of the shaft at each bearing by using super position with a deflection equation rightarrow at each bearings shift values are given such as 16 inch , 14 inch & 9 inch rightarow also given gear A = 16 in diameter gear B = 8 in diameter F_A = 300 lbf F_B = 20 degree when sigma T = 0 when F_A = 300 lbf by substituting values we get = F_A (cos 20 degree) times 10 + F_B (cos 20 degree) times 4 50 = 300 (cos 20) times 10 + F_B (cos 20 degree) times 4 after calculations , we get that 50 = (cos 20) times 14 [75 times 10 + F_B] 50 = 13.758 [750 + F_B] 750 + F_B = 50 /3.758 F_b = 750 lbf