Design and extraction of tooth profile of denatured elliptical gear

Abstract

Elliptical gear is a common type of non-circular gear; it’s theory and design methods are mature. But the research on denatured elliptical gear was not enough, the design method of tooth profile was single, low precision, and there may occur tooth overlap at the splice when the denatured elliptical gear is generated by the envelope method. The denatured elliptical gear design in the existing literature did not include tooth profile point extraction, so the denatured elliptical gear design only exists in theory, it can’t obtain the necessary data for processing and production. Given this situation, a design method is proposed to design denatured elliptical gear, and the tooth profile data are extracted. The main steps are as follows: firstly, the arc length of gear was calculated, and the arc length corresponding to the rotation angle is obtained. The piecewise interpolation of the gear with equal arc length was spliced together to get a complete envelope image, then, the image was binary processed. Finally, using the designed program, the tooth profile pixels were extracted by the eight-neighborhood algorithm. This method provides a new way of designing denatured elliptical gear, this method is stable and has a fast operation speed. The tooth profile data can be directly used for 3D modeling or wire cutting machining.

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

“…Put the formulas ( 28) and ( 29) into the formula (19), the result can be obtained as shown in formula (32):…”

“…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.…”