变双曲圆弧齿线圆柱齿轮非线性振动特性分析

In order to get the vibration rule of a cylindrical gear with variational hyperbola and circular-arc-tooth-trace (CHATT) at work and design a stable and efficient gear,it's necessary to analyze its nonlinear vibration characteristics.The time-varying stiffness of meshing curve and axial error excitation were calculated by load tooth contact analysis (LTCA),and meshing impact excitation was received according to meshing impact model.The twelve-degree of bending-torsion-shaft multi-factor coupling dynamical model of CHATT was established based on the theory of concentrated parameter,and vibration differential equations were built on the basis of Newton's second law.Then,equations were solved by adopting fourth-order Runge-Kutta algorithm with variable step lengths.Vibration displacement,vibration velocity,vibration acceleration,dynamic load of bearing,vibration displacement & velocity phase and Poincaré section of driving gear and driven gear were calculated,and response amplitude spectrums of above signals were obtained with FFT method.The comparison of numerical solutions of driving gear and driven gear in verticality,torsion,and axial direction showed that the vibration law of driving gear always keeps consistent with driven gear,quasi-periodic motion occurs in verticality and torsion direction,and vibration in axial direction shows a nearly chaotic state of steady state response.Moreover,the influence rule on system vibration characteristics was researched by changing tooth-trace radius,loading torque and inputing speed,and results of vibration displacement & velocity phase indicated that vibration regularity of driving gear and driven gear in axial direction gradually becomes poor,which evolutes from quasi-periodic motion to nearly chaotic motion.The regularity of axial direction vibration is more susceptible by changing these three parameters.The establishment and solution of CHATT vibration model and parameter influencing analysis provide theoretical foundation for the later dynamic design,prediction of vibration response under different parameters,and noise reduction.