A method to determine kinematic accuracy reliability of gear mechanisms with truncated random variables

Gears are widely used as transmission components in various types of precision machinery, such as machine tools, vehicles and robots. The performance of these mechanical systems is directly related to the kinematic accuracy of the gear mechanism. This paper presents a novel method to evaluate the reliability of the kinematic accuracy of gear mechanisms with truncated random variables. The influence of errors originating from factors such as the gear eccentricity, profile deviation and assembly error on the transmission error are systematically analyzed and discussed. The statistical moments of the transmission error were obtained combined with the international standards for gear accuracy, tolerances, deviations and fits. A fit of the probability density function and cumulative distribution function of the transmission error was obtained using the saddlepoint approximation technique. A model was established to enable reliability analysis for gear mechanisms. Finally, a discussion of the practical applications along with a detailed analysis to evaluate the efficiency of the proposed method is presented.