Meshing theory and contact analysis of double enveloping hourglass worm drive with planar generatrix.

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.