Research On Reliability Of Gears Based On Kriging Model

Gear is one of the most widely used mechanism and transmission equipment.It has a significant impact on reliability of mechanical equipment.In the meshing process of gear,the teeth bear the contact stress and contact deformation which has a significant impact on its carrying capacity and reliability.In the process of gear transmission,the gear transmission system suffers dynamic excitation which causes vibration and noise.The dynamic excitation of gear transmission system includes internal excitation and external excitation.The external excitation is caused by changes in the engine and the load.While,the internal one is resulted from gear meshing,which mainly includes meshing stiffness excitation,gear error excitation and meshing impact excitation.To solve the problems above,this paper researches the reliability for contact strength of gears and for transmission error of gears.The main contributes of this paper are summarized as follows.(1)To improve the efficiency of Kriging based structural reliability analysis,a new adaptive learning function V_PDF is proposed.The learning function V_PDF takes variance and probability density function into consideration both of which can affect the accuracy of estimated failure probability.This learning function can avoid wasting samples caused by sampling in the area where the value of joint probability density function is negligible,and increase learning efficiency.Besides,a suitable stopping condition is proposed and the V_PDF-MCS algorithm is constructed by combining Monte Carlo method.Finally,examples are analyzed to show that the proposed method has high convergence speed,good accuracy and stability.(2)In view of the gear contact strength failure,the traditional theory of gear contact is based on the Hertz formula to calculate the gear contact strength.However,the contact problem is so complex that it is difficult to calculate the tooth contact strength directly.The finite element method is an effective method to calculate it.The ANSYS software is used to build parametric modeling of a pair of spur gears.Then,reliability of gear contact strength is calculated by the using the method which combines finite element simulation and surrogate model.(3)The reliability of gear transmission error can measure the probability of failure caused by vibration of gear meshing.In engineering,the vibration response of the gear system is difficult to express by explicit expression.In this paper,the finite element simulation and the surrogate model are combined to analyze the reliability of gear transmission error.Firstly,the model of a pair of gears made by ANSYS is used to simulate the instantaneous meshing stiffness and transmission error.The reliability of gear transmission error is calculated by V_PDF-MCS algorithm.