| The drive of single enveloped TI (Toroidal Involute) worm is the worm drivecomposed of involute helical gear and its conjugate tooth surface. The advantages ofthis worm drive, including stronger carrying capacity, higher drive efficiency etc., areproved in theory and testified in experiments by Chinese and foreign scholars. TIworm drive is not widely applied in industry because the key manufacture techniqueof accurately grinding has not been solved due to the complexity of its tooth surface,although it is considered a promising worm drive. For this type of worm-gear set, mathematical model is developed, correlativeequations are derived, numerical analysis is done and three-dimensional simulation isdrawn. Mathematical model of abrasion wheel for grinding TI worm is established toguide practical accurate manufacture. Equations related to single enveloped TI worm are deduced. These equationsinclude meshing functions, meshing equations, contact lines in the tooth flank ofinvolute helix gear, meshing face equations and tooth flank equations of TI worm.The equations of meshing limit lines, undercut limit lines and induced normalcurvature are derived too. The range of origin parameters and the boundary conditions of meshing flank areobtained. According to the numerical analysis, the curves of involute helix gear'stooth flank, contact lines, the curves of mating flank, the curve of TI worm's toothflank and meshing limit lines are plotted. The state of undercut is testified by thecharacters of undercut limit lines and inductive normal curvature. The threedimensional model of TI worm pair is pictured in software by two methods based onnumerical analysis and the principle of machining. The space coordinates system for grinding TI worm is built. By transforming inthe coordinates and dealing with parameters, the equations of profile curves ofabrasion wheel are derived based on the requirement in theory and practical process.Then the method of grinding TI worm is accurately attained. |
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