Tutorial Problems – Gear Calculations
Machine Design
1.
A 24-tooth pinion has a module of 2 mm, rotates 2400 rpm, and drives an 800-rpm gear. Determine the number of teeth on the gear, the circular pitch, and the theoretical center distance.
2.
Figure P15.21 shows a two-stage gear reducer. Identical pairs of gears are used. (This enables input shaft a and output shaft c to be co-linear, which facilitates machining of the housing.) Shaft b , called the countershaft, turns freely in bearings A and B, except for the gear-tooth forces. a. Determine the rpm of shafts b and c , the pitch diameters of the pinion and gear, and the circular pitch. b. Determine the torque carried by each of the shafts a , b , and c : i. Assuming 100% gear efficiency, and (ii) assuming 95% efficiency of each gear pair. ii. For the 100% gear efficiency case, determine the radial loads applied to bearings A and B, and sketch the countershaft as a free body in equilibrium. (Note: This problem illustrates a machine designed using SI units except for the gear teeth, which are dimensioned in inches.) [Partial ans.: (b) T b = 23.88 N - m, T c = 71.64 N - m for 100% efficiency; T b b = 22.69 N - m, T c = 64.65 N - m for 95% efficiency]
3.
A pair of mating gears has 20º full-depth teeth with a diametral pitch of 8. Both gear and pinion are made of steel heat-treated to 350 Bhn, and both have a face width of 1.0 in. The teeth are cut with a top-quality hobbing operation. The accuracy of the gears correspond to “no sharing” in Figure 15.23, has less rigid mounting. The pinion has 20 teeth and rotates 1100 rpm. The design life corresponds to 5 years of 60 hours/week, 50 weeks/year operation. Using a reliability of 99% and a safety factor of 1.5, with uniform source of power and driven machinery, estimate the horsepower that can be transmitted, based only on bending fatigue. [Ans.: Approximately 11.7 hp]
Gear Calculations
Tutorial Problems – Gear Calculations
Machine Design
4. The four helical gears shown in Figure P16.16 have a module in the normal plane of 4 mm and a pressure angle in the normal plane of 0.35 rad. The motor shaft rotates 550 rpm and transmits 20 kW. Other data are on the drawing. a. What is the speed ratio between the motor (input) and output shafts? [Ans. 5] b. Determine all force components that the 20-tooth pinion applies to the 50-tooth gear. Make a sketch showing these forces applied to the gear. [Ans. F t = 7618 N, F r = 3169 N, F a = 4162 N]
5.
For an identical pair of 20° full-depth spur gears, the gears have 60 teeth, and rotate together at 5000 rpm. The module is 2 mm, and the face width is 25 mm. The gears are made of alloy steel, case-hardened to 680 Bhn. The tooth profiles are finished with a fine-grinding operation that gives a degree of precision justifying the use of curve A of Figure 15.24. The loading involves only very mild shock, justifying the use of K o = 1.1. The gears have accurate mounting, small bearing clearances and minimum deflection. Estimate the power that can be transmitted for 109 cycles with 90% reliability, based on surface fatigue.
Gear Calculations
Tutorial Problems – Gear Calculations
Gear Calculations
Machine Design
Tutorial Problems – Gear Calculations
Gear Calculations
Machine Design
Tutorial Problems – Gear Calculations
Gear Calculations
Machine Design
Tutorial Problems – Gear Calculations
Gear Calculations
Machine Design
Tutorial Problems – Gear Calculations
Gear Calculations
Machine Design
Tutorial Problems – Gear Calculations
Gear Calculations
Machine Design
Tutorial Problems – Gear Calculations
Gear Calculations
Machine Design
