Tools › Structures › Contact › Contact Stress › Example
AGMA 2001-D04: spur gear pair at the pitch point against the Grade 1 through-hardened allowable at 300 HB
| Tool | Contact Stress |
| Source | American Gear Manufacturers Association (2004). Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth. ANSI/AGMA 2001-D04, Alexandria, VA. Figure 11, allowable contact stress number for through-hardened steel, Grade 1, as fitted by Budynas, R. G., and Nisbett, J. K. (2011), Shigley's Mechanical Engineering Design, 9th ed., McGraw-Hill, New York, Fig. 14-5. |
| Level | Professional |
Problem
A 2 in pinion drives a 6 in gear, 20° pressure angle, 1.0 in face width, transmitting a tangential load of 500 lb; both gears are through-hardened steel of 300 HB (E = 30 MSI, ν = 0.3). Find the Hertz contact stress at the pitch point and the margin against the AGMA Grade 1 allowable contact stress number.
Inputs to Enter
- Case: spur gear teeth at the pitch point; d_p1 = 2.0 in, d_p2 = 6.0 in, φ = 20°, F_w = 1.0 in, W_t = 500 lb
- E_1 = E_2 = 30 MSI, ν = 0.3; HB_1 = HB_2 = 300; pitting allowable: AGMA through-hardened steel, Grade 1
Answers
- Pitch-point radii R_1 = (d_p1/2) sin φ = 0.3420 in, R_2 = 1.0261 in; normal load P_n = W_t / cos φ = 532.1 lb; E* = 16.48 MSI
- Line contact half-width b = 0.003247 in; peak pressure σ_H = p_0 = 104.3 ksi; mean pressure 81.9 ksi
- τ_max = 31.3 ksi at z = 0.00255 in; von Mises equivalent 58.2 ksi
- Allowable contact stress number σ_HP = 322 HB + 29,100 psi = 125.7 ksi at 300 HB (AGMA Figure 11, Grade 1)
- M.S. = σ_HP / σ_H − 1 = +0.205 (changelog harness value +0.20)
Notes
The gear dimensions are the form's gear-case defaults, but the Contact select opens on the ball-on-raceway case, so choose the gear case, enter 300 HB for both bodies and the Grade 1 allowable. Only the allowable is the published value; the stresses are the tool's Hertz line-contact solution (equal to the AGMA contact stress with C_p = √(E*/π) and no rating factors).