摘要
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。
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.
出处
《机械工程学报》
EI
CAS
CSCD
北大核心
2014年第21期189-196,共8页
Journal of Mechanical Engineering
基金
天津市应用基础与前沿技术研究计划(14JCYBJC19200)
浙江大学CAD&CG国家重点实验室开放课题(A1114)
国家自然科学基金(61173126)资助项目
关键词
谐波齿轮传动
柔轮
伸缩变形
力学分析
双圆盘波发生器
harmonic drive
flexspline
stretch deformation
mechanical analysis
two-disk wave generator
