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By means of meshing theory, vector and matrix, a new manufacturing method what is called helix generating method is developed in the thesis. Manufacturing theory and machine-calculation method of helix generating method are researched, model of cutting driving hypoid gears with new manufacturing method is built, machine-tool setting expression of relation is developed based tooth cutting model, and mathematical model of hypoid gears is built. Validity and practicability of the method were proved by a numerical example.

This paper presents the mathematical definition of cylindricity tolerance and mathematical model for cylindricity error evaluation firstly, and then the mathematical models and efficient methodology are proposed for the evaluation of cylindricity error based on projection theory and geometrical approximation theory for geometrical error evaluation. The search technique is efficient and easy to code, and the simulation calculation results indicate that it can provide accurate results quickly.

TI worm drive consists of involute helical gear and its enveloping Hourglass worm. Accurate grinding for TI worm is the key manufacture technology for TI worm gearing being popularized and applied. According to the theory of gear mesh, the equations of tooth surface of worm drive are gained, and the equation of the axial section profile of grinding wheel that can accurately grind TI worm is extracted. Simultaneously, the relation of position and motion between TI worm and grinding wheel are expounded. The method for precisely grinding single enveloping TI worm is obtained.