Reliability Analysis Of Gear Transmission Based On The Stress-strength Interference Theory

Gear transmission is widely used in various mechanical devices.Its dynamic performance is very essential to the normal operation of the whole equipments.To meet the requirements of lower noise,longer life,higher reliability,it is necessary to investigate the influence of random factors of a gear system occurred in the design,manufacturing,installation and operation stages.Previous studies on the effects of stochastic parameters on dynamics and reliability of gear systems were carried out based on the assumption that all stochastic parameters conform to a certain distribution function.Few of them have used the method of interval mathematics to considere the influences of parameter randomness such as the manufacturing errors,the installation errors,the load fluctuations and the modification deviations on gear dynamics,not to mention the evaluation of gear transmission reliability.In view of this,this thesis will establish a lumped-parameter dynamic model for the spur gear transmission,which contains the random parameters of design,manufacturing,installation and operation.With the method of interval mathematics,the effects of these stochastic parameters on the dynamic behaviors of the gear system are studied.Based on the stress-strength interference theory,a reliability analysis is carried out to reveal the reliability of spur gear transmission under random parameters,which is then compared with the results obtained from Monte Carlo simulation.The main contents of the thesis include:1.A lumped-parameter dynamic model is established for the spur gear transmission system by including the random factors such as the manufacturing errors,the installation errors,the load fluctuations and the modification deviations.The parameter settings in the proposed dynamic model are briefly described followed by the derivation of differential motion equations of the gear system.This provides a theoretical foundation for the following interval-mathematics-based dynamic analysis,parametric analysis of random factors and reliability analysis of the gear transmission.2.By combined the Chebyshev expansion function method with the 4th order variable-step Runge-kutta method,the differential motion equaiotns of the gear system with interval parameters is solved to obtain the dynamic responses.The effects of interval length of installation errors,pitch deviations,tooth profile deviations,load fluctuations and modification deviations on the dynamic characteristics of the gear transmission system are analyzed.The results indicate that the impact intensity of these random factors follows the order of the installation errors,the load fluctuations,the pitch deviations,the tooth profile deviations and modification deviations.3.Based on the stress-strength interference theory,a reliability analysis is carried out to investigate the reliability of the spur gear system with comprehensive random parameters that subject to the indices of gear dynamic transmission error,tooth root bending fatigue strength and tooth surface contact fatigue strength.The reliability analysis results are compared to those obtained from Monte Carlo simulation.The results show that the interval changes of random parameters have the ‘strongest' influence on the reliability of gear transmission accuracy,less impact on the reliability of tooth root bending fatigue strength and the ‘weakest' effects on the reliability of tooth surface contact fatigue strength.