Prediction Of Vibration Fatigue Life About Double Involute Gears Based On Grey Bootstrap Model

The poor information means that the information presented by the research object is incomplete or inadequate,and lacks a priori knowledge.Under the background of low carbon economy,the gear drive is developing towards the direction of light weight and high power density,its strength and reliability issues are more prominent.For a long time,the evaluation of gear fatigue performance is mainly based on classical mechanics and fatigue life test.The reliability analysis is carried out by using Weibull,exponential distribution or lognormal distribution.The traditional fatigue test analysis method is based on the classical statistical theory of large samples,not only requires a lot of experimental work,but also has huge manpower and material consumption,the development lags behind.With the rapid development of new energy,new materials and heavy load transportation machinery,the extreme working conditions of power transmission machinery put forward higher requirements for the fatigue life and reliability of the related gears.The traditional theory of gear fatigue evaluation has been unable to meet the needs of the society,forcing people to have to deal with a large number of poor information system problem.The author takes double involute gear as the research object,studied on the influence of random vibration on the gear fatigue life based on the poor information theory.Specific contents are as follows:(1)The poor information theory is introduced into the evaluation of the fatigue performance of the double involute gear,and the P-N-S model based on the classical geometry,mechanics theory and large sample test statistics is broken through.Based on the poor information theory,the mathematical model of the GM(1,1)model,bootstrap method and Monte Carlo method are established,and the validity of the three kinds of methods is verified by the analysis of the gear parameters.(2)Combined with the advantages of the grey GM(1,1)model and the Bootstrap sampling principle,a new method of dynamic prediction based on the poor information theory is proposed,and the Grey Bootstrap model is established.MATLAB software is used to simulate the reliability of the Grey Bootstrap model,and the statistical analysis of the uniform distribution and Weibull distribution is carried out to analyze the reliability of the Grey Bootstrap model.(3)The random vibration error of double involute gear is predicted using Grey Bootstrap model,compared with the predicted values of GM(1,1)prediction model and Monte Carlo method,determine the feasibility and accuracy of the grey bootstrap model.(4)Based on the poor information theory,the peak probability density function and the power spectrum density method are introduced into the Grey Bootstrap model,studied on the prediction of contact fatigue life under the action of random vibration about double involute gears.(5)Predicted the fatigue life of double involute gears in axial,circumferential and radial vibration using Grey Bootstrap model,The error distribution range of the model is simulated by comparing the experimental data,and the accuracy of the model is analyzed.Verify that the model can solve the fatigue life problem of double involute gear based on the poor information.