Computational Design and Optimization of Non‐Circular Gears

Abstract

We study a general form of gears known as non‐circular gears that can transfer periodic motion with variable speed through their irregular shapes and eccentric rotation centers. To design functional non‐circular gears is nontrivial, since the gear pair must have compatible shape to keep in contact during motion, so the driver gear can push the follower to rotate via a bounded torque that the motor can exert. To address the challenge, we model the geometry, kinematics, and dynamics of non‐circular gears, formulate the design problem as a shape optimization, and identify necessary independent variables in the optimization search. Taking a pair of 2D shapes as inputs, our method optimizes them into gears by locating the rotation center on each shape, minimally modifying each shape to form the gear's boundary, and constructing appropriate teeth for gear meshing. Our optimized gears not only resemble the inputs but can also drive the motion with relatively small torque. We demonstrate our method's usability by generating a rich variety of non‐circular gears from various inputs and 3D printing several of them.

Manufacturing of Screw Rotors Via 5-axis Double-Flank CNC Machining

“…This approach has also been used recently for design of 2D gears [7]. For two given 2D shapes to form a pair of non-circular gears, an optimization-based framework that looks for position of rotational centers that admit gearing configuration is presented in [8].…”

A Novel Curve for the Generation of the Non-circular Gear Tooth Profile

“…Therefore, the NCGs have drawn a lot of interest from scientists with the following trends: (1) Generation of centrodes based on a transfer function of mechanisms [4,5,9]; (2) Design of the NCGs tooth profile by a number of methods such as: (a) Using shaper cutter [10,11]; (b) Using rack cutter with an isosceles trapezoidal profile or circular arc profile [12][13][14]; (3) Design noncircular gearing systems for various applications [15][16][17]. Recently, Hao et al [18] proposed methods to design an *Corresponding Author Email: thai.nguyenhongr@hust.edu.vn (N. H. Thai) NCGs pair based on an arbitrary centrode. However, those NCGs pairs could only be used for low-load application because the effect of undercutting and interference was not taken into the design process; (4) Methods for manufacturing the NCGs spur and the NCGs helical were the research object of other researchers [19][20][21].…”

Design of a Noncircular Planetary Gear Mechanism for Hydraulic Motor

“…Han [13][14][15] studied the design method of noncircular gear tooth profile and established a multiaxis linkage model of CNC hobbing to realize digital manufacturing of noncircular gears. Xu [16] studied the design method of noncircular gear vice, which can design the noncircular gear pitch curve with its conjugate as well as the tooth profile. Lyashkov [17] established an automated model for the geometric design of noncircular gears, using multisegment arcs instead of complex tooth profile curves to shorten the design cycle of noncircular gears.…”