Coupled Vibration Analysis And Dynamic Performance Optimization Of Gear System Considering Temperature Effect

Gearings in large-scal ship have high input speed and heavy working load,which inevitably affects the frictional heat and temperature distribution of the gear system.And the thermal stress and deformation of the structure will be generated further so that the internal dynamic excitation will be changed.The gearing is simultaneously subjected to the internal excitation caused by the time-varying stiffness,transmission error and backlash and the external excitation introduced by the driving and load system.Vibration characteristics of the gear system are extremely complex and show serious non-linear coupling features.Therefore,carring out coupled vibration analysis and dynamic performance optimization of the gear system with temperature effect have important theoretical significance and engineering value for the reduction of vibration and noise,as well as the reliable operation of the gear device.Focusing on a CODAD marine gearbox,researches on the analytic algorithm of time-varing mesh stiffness of helical gears considering temperature effect,characterization of the internal dynamic excitation,coupled vibration analysis and dynamic performance optimization of the transmission system are conducted.The main researches in this paper are as follows:(1)An analytic algorithm of time-varing mesh stiffness of helical gears with temperature is proposed based on slicing method and integral thought.In this algorithm,the thermal deformation of the base circle,the tooth profile deformation caused by the change of contact temperature,and the elastic deformation of contact,bending,shear,axial compression and the wheel are taken into account.The accuracy of the algorithm is verified by using finite element method.Then the influence of friction coefficient,input torque and input speed on the mesh stiffness of gears is analyzed.(2)The quantitative relationship of the thermal deformation of gears,transmission shafts and the box,as well as the radial clearance of bearings on backlash is studied.And then the bending-torsion-axis lumped parameter model of the transmission system which considers mesh stiffness,transmission error,backlash and friction is established.The time-frequency response of the transmission system and the dynamic meshing force of gear pairs are solved by adopting Runge-Kutta method.Then the influence of working parameters on the internal excitation is analyzed.(3)Combining with the characterization of internal dynamic excitation in time domain with temperature effect,the analytical model of coupled vibration about the marine gearbox including gear pairs,bearings,shafts and the box is established.The modal superposition method is used to calculate the vibration response of the gear system before and after considering temperature effect.The vibration results are compared with the test results on the comprehensive performance testing bench of marine gearbox.It is concluded that the calculation results considering temperature effect are closer to the measured values.(4)Considering non-linear factors such as backlash and friction,the multi-objective hybrid discrete optimization mathematical model is established,in which basic parameters of the gear pair are taken as optimization design variables,the total transmission ratio,the actual center distance and the load capacity are taken as constraints,the vibration acceleration and the weight of the system are taken as optimum objectives.The Kriging surrogate model is introduced to simulate the mapping relationship between the optimization objective about vibration response and design variables.And then optimal design parameters are obtained by programming based on the branch and bound algorithm.The effect of this optimization is evident.