Study On Reliability Of Small Sample Gear With Strength Degradation And Failure Correlation

Milling machine is widely used in industry,which can be used to process plane,groove,gear parts,spiral surface and various curved surfaces.As an important part of the transmission system of milling machine,gears work in harsh environment and bear highly uncertain load.Long time service leads to fatigue damage accumulation and strength degradation.When the gear failure occurs,the repair time is long,the cost is high,and even greater accidents and economic losses will occur.With the improvement of reliability requirements of parts in engineering,the traditional theory of reliability evaluation will have some limitations.Aiming at the problems of data missing,strength degradation and failure correlation in gear reliability evaluation,it has certain research significance and value to use fatigue reliability theory to realize reliability evaluation.Therefore,this paper takes the milling machine gear as the research object,around the three problems of data missing,strength degradation and failure related,establishes a small sample gear reliability evaluation model considering strength degradation and failure related(1)Based on the reliability theory of gear transmission,the variation law of parameters in the gear reliability evaluation model is clarified,and the distribution parameters of each parameter are solved.(2)Aiming at the small sample test data of 45 steel for milling machine gear material,the grey theory is introduced to reveal the relationship between the data.The standard deviation of the test data is obtained by resampling bootstrap method,and the P-S-N curve of 45 steel for small sample gear material is obtained by means of sample aggregation algorithm.(3)With the help of gamma process,the strength degradation law of milling machine gear is described.In order to solve the problem of lack of gear strength degradation data,the parameters of gamma process are estimated by using the strength degradation information hidden in P-S-N curve,and the strength degradation model of milling machine gear is established.(4)Considering the correlation between the contact fatigue failure and the bending fatigue failure of the tooth root of milling machine,based on Copula theory and EM algorithm,a hybrid copula model of the correlation between the two failure modes is established,and the Monte Carlo algorithm is used to solve the reliability of milling machine gear with strength degradation and failure.