Reliability Analysis And Modeling Of Gear System

Gear system is one of the important mechanical transmissions,which is widely used in the mechanical equipment.The working conditions of high speed and heavy load can result in the failures of static and fatigue strengths of gear systems.Its performance directly affects the working reliability and service life of mechanical equipment.So,it is vital to analyze and estimate the reliability of gear system.Most of the traditional reliability models are statistical strength models and ignore the dependent failure between the conponents and it is difficult to obtain the initial strength of component.Most of them are not convenient for engineering applications.In this paper,taking the vehicle gearbox and wind turbine gearbox for example,transmission characteristics of gear system are analyzed and the reliability models are develop with the stress-strength interference model,statistical weighted average algorithm,order statistic theory and Monte Carlo simulation method,as well as developing the P-S-N curve fitting method of minimum sample of fatigue lives following two-parameter Weibull distribution based on the principle of sample polymerization.The main contents are as follows.(1)The finite model of a vehicle gearbox is built and the deformations of gear shafts are calculated by the finite method,which is verified by the traditional method.Then,the tooth surface load distribution,gear ratio and meshing stiffness are analyzed because of the deformations of gear shafts.The tooth bending stresses are obtained,by which the gear reliability can be estimated based on the P-S-N curves of the gear bending fatigue life.(2)The gear time-varying meshing relationships are established according to the gear meshing characteristics and the dependent failure of meshing tooth-pair is analyzed.The reliability model with dependent failure is developed by the Monte Carlo method and stress-strength interfenrence model.The proposed method is compared with the traditional reliability models,which shows that the proposed method is more reasonable.(3)A reliability model of gear system considering the uncertainty of strength degradation is developed with the stress-strength interference model and order statistic theory.Then,the reliability of gear system considering the strength degradation is calculated and the influence of the uncertainty of material parameters on the system reliability is analyzed.The research shows that the proposed method can be used to estimate the reliability of the gear system more reasonably.(4)The fatigue life distributions of the gear system are obtained under four constant load histories based on the P-S-N curves of the gear bending fatigue life and the linear relationships are fitted between the load level and statistical parameters of fatigue life distribution of the gear system.Then,the system reliability model is built with the statistical weighted average algorithm.Due to the above method deficiency of using the Monte Carlo simulation method,a reliability model considering the dependent failure is developed with the statistical weighted average algorithm and order statistical theory based on the linear relationships between the stress level and statistic parameters of gear fatigue life distribution.Then,the influences of the input load on the reliability of the gear system are analyzed.(5)The mean is substituted by using the arithmetic mean value of minimum sample of fatigue lives following two-parameter Weibull distribution under each stress level.The standard deviation of maximum stress level and linear coefficient between the standard deviation and stress level are assumed.The linear relationships between the statistical parameters of fatigue life and stress level are fitted.The fatigue lives of each stress level are equipped to the maximum stress level by the consistency principle of fatigue life probability quantile.The reasonable statistic parameters can be obtained by the calculation of relative error of statistical parameters between the original fatigue lives and equivalent fatigue lives.Then,The P-S-N curves of minimum sample of fatigue lives following two-parameter Weibull distribution can be fitted.