Meshing Performance Optimization And Nonlinear Dynamics Analysis Of Hypoid Gear Pair

As a gear mechanism that transfers power between two crossed axes,the hypoid gear pair is widely used in the final drive of the vehicle,which has become a critical component in the front and rear drive axles.In recent years,due to the increasingly strict requirements of the automotive industry for the transmission accuracy,bearing capacity and vibration and noise performance,the development of the hypoid gear is mainly directed towards higher performance.The shape of the tooth surface of the hypoid gear is closely related to the machining process,and the cutting process parameters have a significant impact on the meshing and transmission performance.Therefore,it is valuable to explore new meshing and transmission performance optimization methods based on the existing machining technology and methods,and theoretically analyze the causes and influencing mechanism of the vibration of the system in order to provide theoretical foundation for the design,machining and assembly the hypoid gear pair.Based on the forming principle and the meshing theory of the hypoid gear drive and the tooth contact analysis technology,the machine-tool parameters calculation model,virtual machining model,tooth meshing model have been established in this paper.Furthermore,the meshing performance evaluation and optimization model,misalignments sensitivity analysis and optimization model of the hypoid gear drive have also been proposed.Based on the Newtonian mechanics,a multi-DOF coupled dynamics model of the hypoid gear transmission system has been established by using the centralized parameter method.The details are as follows:(1)The calculation method of the geometric paramaters of the tooth blank,the machine-tool parameters calculation theory and the unloaded tooth contact analysis method of a hypoid gear pair processed by the HFT method has been studied,in which the gear is machined by the formatted method,and the pinion is machined by the tilted method.An optimization method of the meshing performance has been proposed,which takes the area and the direction angle of the contact pattern,and the ordinate of the intersection of the transmission error curves as the optimization targets,and uses the curvatures of the cutting cone of the pinion as the control variables and the machine-tool settings of the pinion as the adjustment variables.The adjustment and control of the meshing characteristics of the entire tooth surface can be realized by performing this optimization method.(2)A meshing model of the hypoid gear drive with consideration of the axial error of the gear and the pinion,the offset error and the angular error of the axes has been established.The influence of each installation error on the contact pattern has been analyzed quantitatively,and a mathematical model of the sensitivity of the contact pattern to the misalignments has been established.According to the conclusion of the sensitivity analysis,a comprehensive sensitivity optimization model is established using a weighted method to increase the tolerance of the gear pair to the misalignments and reduce the sensitivity of the meshing performance to the installation errors.(3)Based on the virtual machining model,a geometric model of the gear pair including the working surface and the fillet surface between the root surface and the tooth surface has been established,then a finite element model of the gear drive has been constructed.The loaded tooth contact analysis of the gear pair under different loads has been completed.The time-varying meshing parameters such as equivalent meshing force,loaded transmission error,comprehensive elastic deformation and meshing stiffness under different load torques have been obtained.The changing rules of the above-mentioned parameters and the actual contact ratio and the contact pattern of the gear pair have been analyzed.(4)A multi-DOF coupled dynamics model of the studied hypoid gear drive with consideration of the bending,torsional and axial vibration has been established,in which the bearings,the meshing stiffness excitation,transmission error excitation,meshing shock excitation and the backlash between the tooth surfaces are considered.The time history curves,phase diagram,Poincaré mapping,frequency spectrum and bifurcation characteristics are used to investigate the response characteristics of the system.The effects of the time-dependent meshing parameters on the vibration characteristics of the system under different loads are compared.(5)The milling processing test,rolling test,tooth surface measurement test and vibration test of the studied hypoid gear pair processed by the HFT method has been completed.The test results are basicly consisted with the theoretical analysis and optimized results,which verifies the correctness of the theory and methods discussed in this paper.