CAJ | 학술논문

在波发生器作用下，柔轮的中性层变形是谐波齿轮啮合分析的基础。柔轮变形分析基于小变形和中性层不伸长假定，但几何分析计算表明：柔轮的中性层出现伸长变形。为了真实揭示柔轮在双圆盘波发生器作用下的变形特征，提出基于强制几何约束条件和力平衡方程及连续性条件的柔轮中性层变形和内力计算方法。将波发生器作用下圆环受力分为接触区和非接触区，接触区由波发生器的强制位移条件确定柔轮中性层内力和变形；非接触区的变形和内力根据弯曲微分方程及其边界条件、连续性条件来确定。利用胡克定律，基于齿圈的周向力获得柔轮中性层周向应变和伸长变形。建立壳单元的柔轮有限元模型，实例表明理论解与有限元模型结果吻合良好，验证了柔轮中性层伸缩变形计算方法的正确性。获得的双圆盘波发生器作用下柔轮中性层变形及其周向应变分布，为后续的啮合分析、共轭齿廓设计及其侧隙计算提供了更准确的理论基础。
재파발생기작용하，유륜적중성층변형시해파치륜교합분석적기출。유륜변형분석기우소변형화중성층불신장가정，단궤하분석계산표명：유륜적중성층출현신장변형。위료진실게시유륜재쌍원반파발생기작용하적변형특정，제출기우강제궤하약속조건화력평형방정급련속성조건적유륜중성층변형화내력계산방법。장파발생기작용하원배수력분위접촉구화비접촉구，접촉구유파발생기적강제위이조건학정유륜중성층내력화변형；비접촉구적변형화내력근거만곡미분방정급기변계조건、련속성조건래학정。이용호극정률，기우치권적주향력획득유륜중성층주향응변화신장변형。건립각단원적유륜유한원모형，실례표명이론해여유한원모형결과문합량호，험증료유륜중성층신축변형계산방법적정학성。획득적쌍원반파발생기작용하유륜중성층변형급기주향응변분포，위후속적교합분석、공액치곽설계급기측극계산제공료경준학적이론기출。
Under the action of wave generator, the deformation of the neutral line of flexspline is the fundamental of mesh analysis in harmonic drive. The deformation analysis is built on assumption of small deformation and inextensible of the neutral line in flexspline tooth ring. However geometric analysis of flexspline has shown that stretch deformation is produced in neutral layer of flexspline. In order to truly describe the deformation of flexspline under two-disk wave generator, a calculation method to describe the deformation and the internal forces of neutral surface of flexspline is presented based on the force equilibrium equations and continuous conditions with geometric constraints. The ring model of the neutral line of flexspline under two-disk wave generator is divided into contact segment and non-contact segment. The internal forces and deformation in the ring in contact segment are solved by geometric constraint conditions from the wave generator. The deformation and internal forces in the non-contact segment is determined with geometric and forces boundary conditions, continuous conditions and the bending differential equation between bending deformation and bending moment. Finally, stretch deformation of neutral line of flexspline is obtained with the circumferential force in tooth ring by Hook’s law. A finite element model with shell element is built, and theoretical results of an example agree very well with results of the FEA model, which indicates that the theory of stretch of neutral line of flexspline is reasonable. Deformations and hoop strains of the neutral line of flexspline under two-disk wave generators provide reasonable theoretical basis for subsequent mesh analysis, conjugated tooth profile design, gap calculation and mesh status simulation.