关键词: 类圆曲线, 偏心圆节曲线, 椭圆节曲线, 非圆齿轮

Abstract:

This paper studied the key design parameters, the eccentricity ratio e of eccentric circular curve and the eccentricity ε of elliptic curve, which were used commonly for non-circular gear transmission. By changing the pole of the polar coordinates, a new transformed elliptic curve named quasi-circular curve can be obtained, which can be regarded as generalized elliptic curve or generalized eccentric curve. Aiming at that the original elliptic curve and eccentric curve were just special cases of the quasi-circular curve, two key design parameters, eccentricity ratio e and eccentricity ε  were introduced into the mathematical expression of the quasi-circular curve to build a new expression of the pitch of  non-circular gear. The research indicates that the eccentricity ratio determines the minimum and the maximum radius of the quasi-circular curve and the eccentricity determines the shape of  the quasi-circular curve. The quasi-circular gear  transmission has the characteristics similar to the eccentric circular gears and elliptic gears, but it is more flexible and convenient to design.

Key words: quasi-circular curve, eccentric circular gear, elliptic gear, non-circular gear