Research On Reliability Algorithm Based On Improved Surrogate Models And Vibration Reduction Strategy Of Gears

Gear transmission is the most important equipment of power and motion transmission,and it plays a very important role on the mechanical transmission,this is because performance and life of machine system depend on dynamic characteristics and work status of gears.However,there are many random factors during gear transmission inevitably because machining technology,assembly technology and external loaded of gears are usually random,such as machining errors,assembly errors,loaded deformation,fluctuation of external load and rotary speed and so on.Therefore,shock and noise occur during gear engagement so the strength and vibration performance will become bad,and then the whole mechanical equipment’s reliability decreases dramatically.In order to solve above issues of gear transmission,reliability and reliability sensitivity of gear contact strength and vibration based on improved surrogate models(such as polynomial response surface,Kriging model),optimization of the gear modification and vibration reduction,random vibration reliability is carried out in this paper,the mainly studies are as follows:(1)In view of the spur gear contact strength failure,firstly,the gear parametric model with assembly errors and machining errors is established,and parametric dynamic simulation analysis is conducted.It provides a modeling basis for the next gear simulation;Secondly,the response surface method is improved,namely,Markov Chain Monte Carlo(MCMC)method is introduced into the response surface analysis.Because MCMC can simulate the points in failure region,the fitting accuracy nearby design point of gear contact stress response will improve.And then the problems of large computation and low precision of implicit response function can be solved.Finally,gear contact strength reliability sensitivity is calculated by using this method,and the efficiency and correctness are validated by comparison of different methods,and this will provide an important theoretical method for reliability design of gear contact strength.(2)The reliability research of gear nonlinear vibration is carried out.Firstly,Kriging model is introduced into reliability analysis because of strongly nonlinear feature of gear clearance vibration.In order to make full use of samples’ information and maximize reliability calculation accuracy,thanks to the stochastic property of Kriging prediction,an active reliability algorithm and more accurately stopping condition are proposed.And this algorithm is suitable for solving the problem with small failure probabilities and many dimensions.Secondly,three academic explicit examples from literatures is calculated by different methods,and through comparison with other surrogate model(such as polynomial response surface,ANN model),the accuracy and efficiency of AK-SSIS are validated.Finally,gear clearance nonlinear vibration reliability and reliability sensitivity are carried out by using AK-SSIS algorithm,and it is proved that AK-SSIS algorithm is more suitable for solving the gear clearance nonlinear vibration problem than other methods.And this research will provide a theoretical direction for design and optimization of gear vibration system.(3)In view of the gear modification and vibration reduction,firstly,the gear engagement composite stiffness formula with respect to gear modification parameters is derived based on energy method.This formula is validated through comparing with finite element method.Thanks to this formula,gear engagement composite stiffness can be calculated rapidly.Therefore,this is a good basis for gear modification optimization;Secondly,a gear modification optimization algorithm based on improved PSO is presented(also called PSO-D),and this optimization method’s objective is that minimize the range of gear dynamic transmission response,this will provide a new idea for gear modification.Through comparison of different methods,it is shown that PSO-D method has high accuracy,high efficiency and strong versatility,this will provide an important reference for vibration and noise reduction of gear system.(4)The research of gear random vibration system is conducted,firstly,gear nonlinear random vibration model with excitation frequency,engagement damping and backlash in circular tooth is built to simulate the response of random vibration system;Secondly,considering the complexity of gear nonlinear random vibration,a reliability model of gear random vibration based on process surpass theory is built,and surpassing the maximal or minimum safety limits is regarded as this model’s failure criterion,so the formula for reliability of gear random vibration system is derived.Last but not least,gear system response impacts of random parameters is analyzed by using phase plane diagram,Poincare section diagram,bifurcation diagram and the largest Lyapunov exponents,so that this research will provide a reference value for controlling or avoiding the irregular chaotic vibration.