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AGMA rating of a 17/52-tooth spur mesh at 4 hp: bending and contact stresses, S_F and S_H for pinion and gear (Shigley Example 14-4)

Tool	Gear Stress
Source	Budynas, R. G., and Nisbett, J. K. (2015). Shigley's Mechanical Engineering Design, 10th ed. McGraw-Hill Education, New York. Example 14-4 (Eqs. 14-15 to 14-18, 14-23, 14-27 to 14-38, Tables 14-8 and 14-10, Figs. 14-2, 14-5, 14-14 and 14-15); American Gear Manufacturers Association (2004). Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth. ANSI/AGMA 2001-D04, Alexandria, VA.
Level	Undergraduate

Problem

A 17-tooth 20° spur pinion at 1,800 rev/min transmits 4 hp to a 52-tooth gear; diametral pitch 10 teeth/in, face width 1.5 in, quality number 6, straddle-mounted pinion, commercial enclosed unit, uncrowned teeth, smooth loading. Both are grade 1 through-hardened steels, the pinion 240 HB and the gear 200 HB; J_P = 0.30, J_G = 0.40, C_p = 2300 √psi, reliability 0.90, 10⁸ pinion cycles. Find the AGMA bending and contact stresses and the safety factors S_F and S_H of both members.

Inputs to Enter

N_P 17, N_G 52, P 10 teeth/in, 20°, F 1.5 in, 4 hp at 1,800 rev/min, K_o 1.0
Q_v 6, commercial enclosed, straddle-mounted (C_pm 1), uncrowned, not adjusted, solid gears, K_T 1, R 0.90, 10⁸ cycles, upper life lines
J entered 0.30 / 0.40, C_p 2300 (Table 14-8); pinion through-hardened grade 1 at 240 HB, gear the same at 200 HB

Open the Gear Stress tool (loaded with this example)

Answers

d_P 1.7 in, V = 801.1 ft/min, W_t = 164.8 lbf; K_v = 1.377 (B 0.8255, A 59.77), K_s 1.043 / 1.052, K_m = 1 + (0.0695 + 0.150) = 1.22, I = 0.121
Y_N 0.977 / 0.996, Z_N 0.948 / 0.973, C_H = 1.005 (A′ 2.49 × 10⁻³), S_t 31,350 / 28,260 psi, S_c 106,400 / 93,500 psi
Pinion: σ = 6,417 psi, σ_all 36,030 psi, S_F = 5.62; σ_c = 70,330 psi (book 70,360), σ_c,all 118,700 psi, S_H = 1.69, S_H² = 2.85 (book 2.86): wear governs
Gear: σ = 4,852 psi (book 4,854), S_F = 6.83 (book 6.82); σ_c = 70,620 psi (book 70,660), σ_c,all 107,600 psi, S_H = 1.52, S_H² = 2.32 (book 2.31): wear governs
Power rating at unit safety factor 4 × 2.32 = 9.29 hp; the Lewis check with the Barth factor (1200 + V)/1200 gives 6,046 / 4,450 psi; computed J by the AGMA 908 layout 0.317 / 0.405 against the chart readings 0.30 / 0.40

Notes

The tool's default inputs are this example; press Submit. The book carries the factors rounded to three or four digits, so the printed stresses differ from the tool's by up to 0.1 %; test_gear_stress.php checks every printed factor and stress (and the Lewis Examples 14-1 and 14-3) and the geometry-factor layout against a numpy brute-force sweep of the generating rack (References/Gear-Stress/gear_check.py).