基于分段啮合刚度的双圆弧斜齿轮转子系统的振动响应分析

Vibration response analysis on double-arc helicalgear rotor system based on sectional engaging stiffness

以双圆弧斜齿轮平行轴转子系统为研究对象,结合其啮合过程的变形特点,导出了其动能和势能的计算公式,根据拉格朗日方程建立了齿轮啮合的动力学模型;根据转子系统齿轮多点和多齿的啮合特点,采用分段式的方法计算其啮合刚度,将其与动力学模型相结合,采用有限元法,求解平行轴转子的弯曲振动和弯扭耦合振动特征值,并分析了系统在不平衡力作用下随激振频率变化的振动响应曲线.研究表明,采用分段式计算啮合刚度的方法来分析双圆弧齿轮是可行的,以此为根据求解的响应曲线符合转子动力学的振动规律,可为双圆弧齿轮平行轴转子系统的动力学分析提供理论基础.

With regard to the double-arc helical gear rotor system with parallel shafts,the formulae of kinetic and potential energies are derived in combination with engaging deformation features.The dynamical model of gear engaging is established based on the Lagrange equation.According to the multipoint and multi-tooth engaging features,the engaging stiffness is calculated using sectional method.By integrating with the dynamical model,the feature values of banding and twisting coupled vibrations are solved for parallel shafts.Meanwhile,the response curve of exciting vibration frequency variations is analyzed under unbalanced system loading conditions.Therein,it is found that this proposed method is feasible due that the response curve is coincided with vibration principle.Accordingly,this approach sets a basis on relevant system dynamical analysis.