| This essay takes the method of listing equations of gears' surface directly and installing them in appropriate coordinate system to establish the mathematic model for analyzing engagement of spiral helical gear. Programs use this mathematic model to make numerical computation as well as to output the contact domains diagram and the relative velocity diagram on this foundation. This essay made computerized simulation on scene of two gears contact in three-dimensional space. And it also described the direction and magnitude of relative velocity in three-dimensional space. Normal section linear diagram of two gears' surfaces, which is on the arbitrary section, has also been protracted .The writing validated the correctness of the mathematical model and experimenting on contact region of spiral helical gear's surface validates theoretical analysis. Through systemic analyzing on spiral helical gear transmission with different basic parameters , the essay found out rules of how can such basic parameters influence spiral helical gear engagement characteristics .So it brings forward the auxiliary assembling mode of adopting one straight gear and one helical gear on condition of little axial angle as well as treasures to ameliorate ill engagement performance on condition of large axial angle, Another two jobs of the essay are to clarify the wrong concept that spiral helical gear can only transmit movement but not impetus and to provide a brief and practical method of analyzing contact for gear pairs whose surface equations can be written out directly.
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