3D力热耦合磨齿模型与数值分析

3D Models of Thermo-mechanical Coupling of Grinding Tooth and Numerical Analysis

根据螺旋锥齿轮的数控磨齿原理,得出磨齿基本参数的理论模型和物理意义上的磨削力计算公式;应用单磨粒热模型计算了磨齿热量分配比,采用矩形分布热源得出磨齿热流量。以热弹塑性变形理论为基础,采用PRANDTL-REUSS方法建立磨齿界面应力应变场本构关系:齿轮材料采用双线性等向强化模型,用3D力热耦合有限元单齿模型和小步距载荷移动方法,实例进行瞬态温度场的仿真。结果表明,磨削瞬态最高温度位于磨削弧中心,其他各点的瞬态温度,随磨削条件、空间和时间等影响因素的不同,呈现相应的变化规律。试验与力热耦合仿真的数值比较分析表明,构造的3D力热耦合磨齿模型有较高的精度,能为螺旋锥齿轮磨齿质量的控制提供依据。

According to the principle of NC grinding tooth of spiral bevel gear, the theoretic models of basic grinding tooth parameters and the calculation formula of grinding forces in the physical sense are gotten. The heat distribution ratio is computed by using the thermal model of a single grinding grit, and the heat flux is obtained by applying rectangle heat source. Based on the thermo-elastic-plastic deformation theory, the constitutive relationship of stress-strain field on grinding tooth interface by applying PRANDTL-REUSS method is set up. According to the bilinear isotropic hardening model of gear material, the transient temperature field of a single tooth is simulated by using the 3D finite element model of thermo-mechanical coupling, and the method of small sub-step moving of loads. Many conclusions of the simulation are gotten. Firstly, the place of the highest transient temperature of grinding is located at the center of grinding arc. Secondly, while changing of the conditions, space, time of grinding, and so on, the transient temperature of other points has its corresponding changing rule. By the numerical analysis of comparing test data with simulation ones of thermo-mechanical coupling, the results show that the thermo-mechanical coupling model has relatively high precision. These conclusion provide a foundation for the control of grinding quality of sprial bevel gear.