学术论文

      齿轮综合啮合误差计算方法及对系统振动的影响

      Determination of Composite Meshing Errors and Its Influence on the Vibration of Gear System

      摘要:
      通过将轮齿变形分为线性宏观变形和非线性局部接触变形两部分,建立齿轮承载接触分析修正模型,并利用两层迭代将非线性接触问题转化为多个线性代数方程组进行求解。根据各接触点变形关系,提出已知齿面误差分布时啮合刚度和综合啮合误差的确定方法。通过引入刚度激振力将参变的运动微分方程组化为定常微分方程组,并利用傅里叶级数法求解其稳态解。以一对斜齿轮副为例,分析了齿轮误差在不同扭矩和转速下对系统振动的影响规律。研究发现,由于轮齿误差的存在,齿轮副啮合刚度在轻载时会减小,从而导致系统共振转速降低;受重合度和轮齿变形的影响,综合啮合误差的幅值远小于齿面原始制造误差幅值。此方法可用于分析不同误差类型及分布形式对系统振动的影响规律,为进一步建立齿轮误差控制原则提供了有效手段。
      Abstract:
      The tooth deformation is separated into linear global term and nonlinear local contact term, and a modified loaded tooth contact model is built. The nonlinear contact problem is transformed into solving a set of linear algebraic equations by considering two iterative loops. According to the deformation relationship of contact points, the mesh stiffness and composite meshing errors can be obtained when the error distribution on tooth surface has been known. By introducing the stiffness exciting force, the time-variant differential equations of motion are transformed into the time-invariant ones of which the steady-state solution can be calculated using Fourier series method. Taken a helical gear pair as an example, the influence of gear errors is studied under different torque levels and input speeds. The results show that the mesh stiffness will decrease for lightly loaded gears as the effect of gear errors, which will cause the system resonance speed decreased. As the impact of contact ratio and tooth deformation, the amplitude of composite meshing errors is much smaller than the original amplitude of manufacturing errors on tooth surface. The method can be used to analyze the influences of different types of manufacturing errors and different error distributions on system vibration, which provides an effective means to establish the control principles for gear errors.
      Author: CHANG Lehao LIU Geng WU Liyan
      作者单位: 西北工业大学机电学院西安 710072
      刊 名: 机械工程学报 ISTICEIPKU
      年,卷(期): 2015, (1)
      分类号: TH113
      机标分类号: TH1 TG8
      在线出版日期: 2015年2月4日
      基金项目: 国家自然科学基金,高等学校创新引智计划,长安大学高速公路筑养装备与技术教育部工程研究中心开放基金(2013G1502057)资助项目。