Design of piecewise deformed elliptical gear with closed pitch curve and its conjugate pair

Abstract

The family of elliptical gears with closed pitch curves includes elliptical gears and deformed elliptical gears. Elliptical gears are not only the most widely used non-circular gears but also the research hotspot in the field of non-uniform transmission. However, adjusting the shape of its pitch curve is difficult, which seriously restricts its popularization. This article proposes a piecewise deformed elliptical gear with a closed pitch curve, which realizes the unity of all kinds of elliptical gears in the mathematical model, makes the shape of the pitch curve and gear ratio easier to adjust, and expands the connotation and application scope of the family of elliptical gears. Moreover, the design approach of transmission with piecewise deformed elliptical gear was studied, and the inspection method of transmission performance was provided. The internal relationship between piecewise deformed elliptical gears and the family of elliptical gears was then analyzed. Finally, the method of computer-aided design (CAD) system developed was also provided. Additionally, a case was provided to verify the above theories. The designed conjugate pair can realize a correct meshing and adjust the gear ratio more flexibly, laying a theoretical foundation to expand the application field of non-uniform transmission.

Rounding theory and method for the pitch curves of the variable center distance non-circular gear pair based on working conditions

“…Under the condition of transmission ratio unknown, based on the aforementioned ideas, by adjusting the parameters in the base curves such as eccentric circular curves, 7–12 higher-order elliptical curves, 13–19 Pascal’s limaçon, 20,21 Hermite cubic parameter curves, 22 epitrochoids, 23 Aronhold’s first principle regression curve, 24,25 etc., it is possible to design non-circular gear pair’s pitch curves which can be divisible by the pitch. 26…”

“…To address this issue, Xutang and Guihai suggest that designers should dynamically adjust the known conditions, such as the parameters that control the base curve used to fit the gear pair's pitch curves, and the modulus that directly related to the pitch, until the pitch curve length for both driving gear and driven gear are multiple of the standard pitch. 6 Under the condition of transmission ratio unknown, based on the aforementioned ideas, by adjusting the parameters in the base curves such as eccentric circular curves, [7][8][9][10][11][12] higher-order elliptical curves, [13][14][15][16][17][18][19] Pascal's limac xon, 20,21 Hermite cubic parameter curves, 22 epitrochoids, 23 Aronhold's first principle regression curve, 24,25 etc., it is possible to design non-circular gear pair's pitch curves which can be divisible by the pitch. 26 Under the condition of transmission ratio known, by scaling the theoretical pitch curve proportionally, at the expense of changing the center distance of the gear pair 27 ; or adjusting the gear modulus, at the expense of increasing the gear pair's design and manufacturing costs dramatically, it is also possible to design pitch curves which can be divisible by the pitch and meshes same as the known transmission ratio.…”