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2-in full journal bearing at 1,800 rpm and 500 lb: Reynolds-equation solution against the NACA Report 1157 short-bearing forms and Petroff

Tool	Journal Bearing and Wear
Source	DuBois, G. B., and Ocvirk, F. W. (1953). Analytical Derivation and Experimental Evaluation of Short-Bearing Approximation for Full Journal Bearings. NACA Report 1157, National Advisory Committee for Aeronautics, Washington (eqs 13-28, 32); Hamrock, B. J. (1991). Fundamentals of Fluid Film Lubrication. NASA Reference Publication 1255, NASA, Washington (chapter 10, Table 4-12).
Level	Undergraduate

Problem

A plain journal bearing of 1.0 in radius, 0.001 in radial clearance and 1.0 in length runs at 1,800 rpm under a 500 lb radial load on a 4 microreyn oil entering at 110 °F (density 54.7 lb/ft³, specific heat 0.469 Btu/(lb·°F)). Find the eccentricity ratio, minimum film thickness, attitude angle, peak pressure, friction force, torque and power, inlet and side oil flow and the adiabatic temperature rise from the Reynolds equation with the Reynolds cavitation boundary on a 120 × 24 grid, and compare with Petroff's no-load friction and the short-bearing closed forms of Report 1157 at the same Sommerfeld number. Then estimate the sliding wear of the bushing (K = 10⁻⁴, 200 HB) over 10⁶ in at 500 lb and its PV product.

Inputs to Enter

r = 1.0 in, c_r = 0.001 in, l = 1.0 in (l/d = 0.5), N = 1,800 rpm, W = 500 lb, μ = 4 microreyn constant, T_in = 110 °F, ρ = 54.7 lb/ft³, c_p = 0.469 Btu/(lb·°F)
Reynolds (Swift–Stieber) boundary, 120 × 24 grid, mesh table on; wear K = 1e-4, 200 HB, s = 1,000,000 in, W_w = 500 lb

Open the Journal Bearing and Wear tool (loaded with this example)

Answers

p′ = W/(l d) = 250 psi, S = (r/c)² μ N′/p′ = 0.4800, C_n = S (l/d)² = 0.1200
Reynolds solution: ε = 0.5143, h_0 = 0.000486 in, φ = 54.35°, p_max = 627.2 psi at α = 18.0° past the load line (k = 2.51), film rupture 70.9° past the load line
Friction: F = 5.629 lb, f = 0.01126, (r/c) f = 11.26, T = 5.629 lb·in, 0.1608 hp (409 Btu/h); Petroff F_o = 4.737 lb, (r/c) f_o = 2π²S = 9.475, F/F_o = 1.188
Flow: Q = 0.1340 in³/s in, Q_s = 0.0891 in³/s side leakage (Q_s/Q = 0.665); ΔT = 85.6 °F by F U = ρ c_p Q ΔT (1 − Q_s/2Q), T_out = 195.5 °F
Report 1157 short-bearing forms at C_n = 0.120: n = 0.4746, φ = 55.53°, F/F_o = 1.136, k = 2.700 (p_max = 674.9 psi), Q_r = 0.0895 in³/s; mesh table 60 × 12 / 120 × 24 / 240 × 48: S at ε 0.4828 / 0.4800 / 0.4793
Archard: V = K W s/H = 0.1758 in³, mean depth 0.0879 in over 2 r l; PV = 250 psi × 942.5 ft/min = 235,600 psi·ft/min

Notes

The tool's default inputs are this bearing; press Submit. The case is illustrative (no printed worked example has it) and every number is reproduced by the independent numpy/scipy solution in References/Journal-Bearing/checks/ (test_journal_bearing.php, 396 checks, which also reproduce the Report 1157 printed cases of its page 20 and Table IV). The numerical S differs from Ocvirk's at l/d = 0.5 because the short-bearing approximation neglects the circumferential pressure flow; the long-bearing Sommerfeld forms are printed on the page as the other bound.