Research On The Digital Modeling Theory And Simulation Methods Of Planar Double-Enveloping Toroid Worm Gear Drive

Planar double-enveloping toroid worm gear drive is an excellent way to transmit torque and movement through two axes that are not parallel. It has many advantages such as several couples of teeth meshsing simultaneously, double touching lines on each interacting surface, high transmission ratio and heavy load, etc. And it's easy to form elastohydrodynamics lubricant film between two interacting surfaces. But this kind worm gear drive is not used widely in China. The reason is that its manufacturing method-dual generating method-is outdated. In order to manufacture this type of worm gear drive precisely and cheaply, we should explore a whole new dis- dual generating method. As a part of the project "the modeling and simulation of Planar double- enveloping toroid worm gear drive's intelligent manufacturing method", this dissertation focuses on the 3D modeling of Planar double-enveloping toroid worm gear in Computer. The author of this dissertation has completed lots of studies and researches in this field and has found some new methods for the 3D modeling of worm gear drive. Creative points and all tasks having be finished are briefly shown below:According to the classical space meshing theory, we have strictly deduced a series of formulae such as the equation of contacting line of worm, the equation of the second limiting curve of worm gear, and the equation of working surface and non-working surface, etc. And we have deeply studied the algorism of the actual contacting lines of worm gear drive.We have deeply studied the old design mode and point out that the lubricating advantages of this type of worm gear drive is not fully used. We put forward a new way which optimizes the lubricating property. The result of simulation proves our assumption.Based on the algorithm of contacting lines of worm, this dissertation uses 3D discrete contacting lines to depict a worm surface. Under OpenGL environment, we use four-side grids to reconstruct a worm surface and gain a solid modeling of worm.Under the computer virtual reality environment, we simulate the manufacturing process of dual generating method. Using "union", "subtract" and "interference" methods, a solid worm is formed in computer. Steering computation is used in this virtual manufacturing process.This dissertation strictly analyzes the worm gear surface. With regard to the restrains of geometries boundaries of the surface, we have finished the tooth contact analyses (TCA) and precisely drawn the actual contacting area on the surface. The relations between the total length of the actual contacting lines and the rotating angle of worm gear are also revealed in this dissertation.According to the TCA results, we use a series of planes which include the axis of worm gear to intersect with the worm gear surface, and calculate the intersecting points which belong to both plane and surface. Under this way, the surfaces are separated into lots of discrete points. Then we use Bernstain-Bezier triangles to interpolate these points and reconstruct the wormgear surface. A new digital model of worm gear is provided. We can use this digital model to CNC, RP&RM, Interference-detecting, etc.Finally, we refit a Y35J2 nobbing machine into a five- coordinate CNC machine. The simulation results show that the modeling method is correct and the CNC manufacturing scheme is feasible.