Dynamics Of Anti-backlash Double Roller Enveloping Hourglass Worm Gearing System

Based on the roller enveloping hourglass worm gearing, a new kind of worm transmission—anti-backlash double roller enveloping hourglass worm gearing has been presented. It not only inherits the characteristics of roller enveloping hourglass worm gearing such as high precision and high load capacity, but also can eliminate hysteresis error of the transmission system. So, this transmission has good application prospect in many fields such as precise indexer. Taking anti-backlash double roller enveloping hourglass worm gearing as the research object, the 3D modeling, moving performance, load capacity, mesh stiffness and dynamics performance of this drive are studied. The main contents of the course are as follows:Work principle, compositions and structures of the anti-backlash double roller enveloping hourglass worm gearing are reviewed and method and procedure of the 3D modeling of this worm on Pro/E are introduced.Kinematics performance of the anti-backlash double roller enveloping hourglass worm gearing is systematically analyzed. Based on the numerical calculation for meshing performance parameters, the impact of throat diameter coefficient, roller radius and roller installation offset distance on the tooth contact parameters are analyzed, which include induced normal curvature, entrainment velocity, lubrication angle, and roller's rotation angle with the two different conditions—the same center distance and the different center distance.The load capacity of the anti-backlash double roller enveloping hourglass worm gearing is studied. The contact finite element model of the anti-backlash double roller enveloping hourglass worm gearing is created through the interaction between Pro/E and ANSYS Workbench. Using the ANSYS Workbench, stress distribution curve along contact lines, bar chart of the load distribution among gear teeth and stress, and deformation cloud chart of this drive are obtained and analyzed.The analysis model for the mesh stiffness of the anti-backlash double roller enveloping hourglass worm gearing is proposed. Mesh stiffness is equivalent to contact deformation stiffness, bending deformation stiffness of worm wheel tooth and bending deformation stiffness of worm tooth with a series connection. The calculation methods of the three deformation stiffness are presented. And then, the mathematical model of the mesh stiffness of this transmission is built and numerical results are obtained for illustration.Dynamics performance of the anti-backlash double roller enveloping hourglass worm gearing is researched. The computing models of bend stiffness, torsion stiffness, axial stiffness of worm shaft and worm wheel shaft are built and then the equivalent mesh stiffness is proposed. According to the structural characteristic of the anti-backlash double roller enveloping hourglass worm gearing and considering contact deformation of the mesh profile, twist deformation, bending deformation and axial deformation, a multi-DOFs nonlinear dynamic model is established. The natural frequency and corresponding modes of the anti-backlash double roller enveloping hourglass worm gearing system are analyzed.