Monte Carlo Simulation of Tests for the Determination of Gear Design Allowable Stresses Available to Purchase

In this work the design of fatigue test experiments to be performed on a new high-speed gear test rig is discussed. Several methods are compared and an optimal design is derived using a new statistical criterion of analysis. The main problem is to determine the minimum number of gears to be tested in order to obtain, with a given confidence level, correct indications of the distribution of bending and pitting fatigue resistance of such test gears. To solve this problem the most efficient experimental method has to be chosen first. From the statistical point of view the fatigue resistance is a random quantity that cannot be directly sampled. The methods currently used for the estimate of the distribution of this quantity are based on sequential tests like the stair-case (or up-down) method and its variants. In this paper we analyze the performance of a set of these methods by means of Monte-Carlo (MC) simulations. The emphasis is on the identification of an efficient procedure to estimate both the mean and the standard deviation of the unknown resistance distribution of the gears. Efficiency is here understood in terms of the amplitude of the confidence intervals at fixed confidence level when the size of the samples is relatively small (10–30). Finally, a Combined Robbins-Monro Random Step (CRMRS) method is herein proposed. The CRMRS method, for its stability, proved to be most suitable among the methods we considered when a-priori estimates for the mean and the standard deviation are not available. This is indeed the case when dealing with new materials. Moreover the CRMRS method achieves the best accuracy in the estimation of the variance. A similar but separated investigation has been performed for the case of gear scuffing tests. A sampling method, that can be used to reduce the number of inspections necessary to estimate (at a given confidence level) the minimum load at which scuffing takes place, is here proposed.