基于三维实体有限元模型的谐波齿轮装配状态应力分析

Stress analysis of harmonic gear driven in assemble state with 3D solid finite element model

为准确地反映谐波柔轮的齿廓及齿根的应力状态,提出了基于真实齿廓信息的柔轮三维实体的建模方法.以渐开线齿形为例,利用APDL语言建立包括渐开线齿廓、齿厚和齿根倒圆等参数的实体模型.定义波发生器与柔轮筒内表面间接触,求解获得波发生器作用下的柔轮应力,与基于圆环理论的理论值比较分析;为更真实反映柔轮在装配状态下的应力分布,构建柔轮三维实体模型,求解柔轮应力.通过路径定义,提取与理论计算截面相对应的中截面上的应力,与平面齿圈的有限元结果和理论值比较分析.研究发现:平面齿圈有限元实体模型中,沿周向应力波动均值与理论值基本吻合,验证了文中的有限元实体建模方法的有效性.三维实体模型周向应力比平面齿圈周向应力大,且最大周向应力发生在顶层.

In order to describe the tooth profile and dedendum stress distribution of harmonic flexspline correctly, a 3D solid model method based on real tooth profile is put forward. Using involute tooth profile as an example, a parameter-ized solid model based on language APDL is set up, which includes important parameters such as involute tooth profile, tooth thickness and tooth root fillet. The stress of flexspline under the action of wave generator is obtained by defining contact between the wave generator and flexspline＇s inner surface. The stress is compared with the theoretical value based on equivalent ring theory. In order to analyze the stress distribution of flexspline in assem-ble state more fully, a 3D solid model of flexspline is built and solved by ANSYS. The stress is extracted by defining the path in the middle section corresponding to the section calculated by theoretical formula and com-pared with the results obtained by the planar gear ring and theoretical value. The results show that in the finite el-ement model of planar gear ring, the mean value of the circumferential stress fluctuation is consistent with the theoretical value, which validates the validity of the finite element model method. In addition, the circumferen-tial stress extracted from 3D solid model is larger than that from planar gear ring, and the maximum circumferen-tial stress occurs at the top layer.