Tools › Mechanical Design › Shafts › Interference and Press Fit › Example

2 in steel shaft pressed in a 4 in hub: Lamé contact pressure, hub stresses, holding torque, shrink temperature and release speed

Tool	Interference and Press Fit
Source	Oswald, F. B., Zaretsky, E. V., and Poplawski, J. V. (2008). Interference-Fit Life Factors for Roller Bearings. NASA Technical Memorandum 2008-215153, Glenn Research Center, Cleveland, OH, eq. 7 and p. 9; Coe, H. H., and Zaretsky, E. V. (1986). Effect of Interference Fits on Roller Bearing Fatigue Life. NASA Technical Memorandum 87165, eqs. 21-31; U.S. Department of Defense (2003). MIL-HDBK-5J, Table 2.3.1.0(c1) and Figure 2.3.1.0.
Level	Undergraduate

Problem

A 2.000 in solid AISI 4130 shaft (E = 29.0 Msi, ν = 0.32, F_ty = 75 ksi, ρ = 0.283 lb/in³) carries a 4.000 in OD hub of the same steel over 2.0 in with a nominal diametral interference of 0.002 in, ±0.0005 in on each part, μ = 0.15, design factor 1.5, at 3,600 rpm with 5,000 lb-in of torque. Find the contact pressure of the loose, nominal and tight fits, the hoop and von Mises stresses at the hub bore, the first-yield pressure and the largest elastic interference, the holding torque and press force, the hub heating for a shrink assembly with a 0.001 in gap, the pressure at speed and the release speed, and the margins on yield and slip.

Inputs to Enter

d 2.000 in, D_o 4.000 in, solid shaft, L 2.0 in; δ_d 0.002 in, shaft and bore tolerances ±0.0005 in, finish loss 0, assembly gap 0.001 in, μ 0.15, μ_a 0.15, n_d 1.5
Hub and shaft: E 29.0 Msi, ν 0.32, F_ty 75 ksi, ρ 0.283 lb/in³, α 6.5 µin/in/°F; speed 3,600 rpm, outside pressure 0, T_app 5,000 lb-in, F_app 0

Open the Interference and Press Fit tool (loaded with this example)

Answers

C_h + C_s = (r_c/E)[(r_o² + r_c²)/(r_o² − r_c²) + ν + 1 − ν] = (8/3)/29e6 in/psi; p = δ_r/(C_h + C_s) = 0.001 × 29e6 × 3/8 = 10,875 psi nominal (5,437.5 loose, 16,312.5 tight), the same as E δ_d (D_o² − d²)/(2 d D_o²)
Hub bore: σ_θ = 5p/3 = 18.125 ksi, σ_r = −p, von Mises 7p/3 = 25.38 ksi (25.38 with the 0.21 ksi torsional shear), Tresca 8p/3 = 29.0 ksi; shaft −p, −p, von Mises 12.19 ksi with τ = 3.18 ksi
First yield of the hub p_Y = F_ty (1 − r_c²/r_o²)/2 = 28.125 ksi (Tresca), 32.14 ksi (von Mises); shaft 75 ksi; largest elastic interference 2 (C_h + C_s) p_Y = 0.005172 in
T_hold = 2π r_c² L p μ = 20,499 lb-in (10,005 lb-in for the loose fit at speed), F_hold = F_press = 20,499 lb (30,748 lb tight); ΔT_h = (0.003 + 0.001)/(6.5e-6 × 2) = 307.7 °F
At 3,600 rpm the hub bore grows 12.5 µin and the shaft 0.6 µin, p = 10,745 psi; release speed √[4 E δ_r/(ρ r_c (3 + ν) r_o²)] = 32,965 rpm (23,310 loose); M.S. hub yield +0.31, shaft +1.90, slip +0.33 (design factor 1.5)

Notes

The tool's default inputs are this case; press Submit. The geometry, interference, friction and design factor are illustrative and said so on the page; the material is MIL-HDBK-5J's AISI 4130 row with α read from Figure 2.3.1.0. The equal-material equation and the four printed 50-mm bearing-ring pressures of NASA/TM-2008-215153 (5.00 / 7.55 / 8.67 / 12.21 MPa for 0.017 mm) are reproduced by test_press_fit.php (799 checks), together with an independent numpy solve of the boundary-condition system in References/Press-Fit/checks/.