According to the structural relationship of the non-circular gear stepless speed regulation mechanism shown in Fig. 1, as the generation part of the time variable ratio, the speed ratio function of the working section of the non-circular gear pair in the stepless speed regulation mechanism needs to be in the form of a first-order function; According to the inclusion of high-order function to low-order function, the corresponding transition section speed ratio function of non-circular gear pair can be constructed by Fourier series or polynomial. Taking eccentric non-circular gear as the research object, the transition section speed ratio function of non-circular gear pair is constructed by polynomial, and the periodic speed ratio function of non-circular gear pair is obtained, as shown in the formula.
Where, X is the working section angle of non-circular gear; X =4 π / 3,T =2 π 。
According to the speed ratio characteristics, pitch curve closure and function envelope of non-circular gear, it is known that the speed ratio function of non-circular gear transition section needs to be determined by six boundary conditions and one closure condition, as shown in the formula.
Finally, the periodic speed ratio function of non-circular gear pair is obtained as follows