Empirical Efficiency Estimation for Three-Stage Cylindrical Gearboxes in the Preliminary Design Phase

Established gearbox efficiency methods disagree and require inputs, such as friction coefficients and face widths, that are often unknown in preliminary design. This study develops an efficiency estimate based only on parameters available at that stage. For a three-stage cylindrical gearbox, we combined the tooth-friction models of Niemann and Duda with bearing, seal, oil-churning and windage losses, evaluated Klein’s single-step total-loss formula, and compared the results with efficiencies measured at four load levels. The loss-based approaches overestimated the measured efficiency; Klein’s formula underestimated it and did not follow the operating conditions. We replaced the friction term of Klein’s formula with an empirical factor fitted, as a function of output speed, to four operating points at which torque and speed varied together; the factor therefore reflects their combined effect, and its exponent is not statistically resolved. The resulting correlation requires only the tooth numbers and the output speed. It reproduced the measured efficiencies of this gearbox and, without refitting, of a second gearbox with a different center distance and ratio within 0.41 percentage points, inside the measurement uncertainty. Both gearboxes have z1 = 19 and z2 = 58–61; the correlation applies only to this design family and load–speed path.