Peng Quancheng, Li Minghao
College of Mechanical Engineering, Shenyang Ligong University, Shenyang, 110159, China.
Sci Rep. 2024 Aug 4;14(1):18023. doi: 10.1038/s41598-024-68556-8.
The meshing and limit equations of worm drive usually have strong nonlinearities such as multiple solutions, solution nonexistence and equation singularity. Meanwhile, the tooth surfaces of worm drive are in nonconforming line contact, which often requires mesh refinement of contact region for the loaded contact analysis. These two challenges cause that the modeling of worm drive heavily relies on manual adjustment and the loaded contact analysis of worm drive is still rare especially when edge contact and assembly error are concerned. Focusing on the double enveloping hourglass worm (DEHW) drive with planar generatrix, this work presents procedures to solve meshing and limit equations with global convergence. The instantaneous contact line, meshing limit line, curvature interference limit line and tooth surface grid discretization are adaptively generated, without manual trial or adjustment. On the basis of adaptive mesh refinement of tooth surface, the mortar virtual element method is adopted for loaded contact analysis of DEHW drive with edge contact and center distance error. Under sliding friction, the discrete system of governing equalities and inequalities is solved by semi-smooth Newton algorithm after constraint condensation. Numerical results for meshing theory and loaded contact analysis of DEHW drive with planar generatrix are discussed.
蜗杆传动的啮合和极限方程通常具有很强的非线性，如多解、无解和方程奇异性。同时，蜗杆传动的齿面为非协调线接触，在进行承载接触分析时通常需要对接触区域进行网格细化。这两个难题导致蜗杆传动的建模严重依赖人工调整，并且蜗杆传动的承载接触分析仍然很少见，尤其是在考虑边缘接触和装配误差的情况下。针对具有平面母线的双包络环面蜗杆（DEHW）传动，本文提出了具有全局收敛性的求解啮合和极限方程的方法。能够自适应生成瞬时接触线、啮合界限线、曲率干涉界限线和齿面网格离散化，无需人工试算或调整。在齿面自适应网格细化的基础上，采用mortar虚拟单元法对考虑边缘接触和中心距误差的DEHW传动进行承载接触分析。在滑动摩擦条件下，通过约束凝聚后采用半光滑牛顿算法求解离散的等式和不等式控制方程组。讨论了具有平面母线的DEHW传动的啮合理论和承载接触分析的数值结果。
