Design of a Noncircular Planetary Gear Mechanism for Hydraulic Motor

Dawei Li,Yongping Liu,Jun Gong,Tongcheng Wang,Nikunja Mohan Modak

doi:10.1155/2021/5510521

Abstract

Given the design difficulty and poor accuracy of tooth profile of noncircular gear used in noncircular gear hydraulic motor, it is proposed to reduce the design difficulty and improve the design accuracy by using arc-shaped pitch curve instead of noncircular pitch curve with continuously varying curvature. Based on the geometric relationship and transmission relationship of the noncircular planetary gear mechanism, a nonlinear programming model is constructed for the circular arc-shaped pitch curve. By solving the nonlinear programming model, a noncircular planetary gear mechanism with a modulus of m = 1.5 is designed. The noncircular gear mechanism with the arc-shaped pitch curve was machined and installed in a hydraulic motor, and an efficiency comparison experiment was conducted with a high-order elliptical noncircular gear mechanism with a continuously varying curvature. The experiment shows that the efficiency of the two noncircular gear mechanisms is basically the same, and the best speed range is 100–400 rpm. The noncircular planetary gear mechanism with an arc-shaped pitch curve designed in this paper has reasonable structure, correct transmission relationship, and simple design method, which shows that the design method proposed in this paper has a good engineering application value.

Highlights

A lot of researchers have studied noncircular gears, the design of a noncircular gear tooth profile is still complicated and difficult because the pitch curve of noncircular gears has continuously varying curvature, which brings great inconvenience to the promotion and use of such noncircular gear hydraulic motor
High-Order Elliptic Pitch Curve. e noncircular planetary gear mechanism is the core of a noncircular gear hydraulic motor. e geometry of the noncircular gear pitch curve directly determines whether the planetary gear mechanism can be properly meshed and continuously driven
In the previous noncircular planetary gear mechanism, the pitch curve of noncircular gears is of high-order elliptical type, which can be expressed in polar coordinates as

Summary

Nonlinear Programming Model for ArcShaped Pitch Curves

It is only necessary to determine the radius and the position of the center of the arc to obtain the model of the arc-shaped pitch curve. The geometry of the noncircular gears and their relative position to the central wheel need to satisfy defined constraints, which may be complex nonlinear relationships. Erefore, a nonlinear programming model of the pitch curve is constructed with the radius and center position of the arc as design variables, and a computer is used to help us find the optimal center position and radius of the arc that satisfies the defined constraints The geometry of the noncircular gears and their relative position to the central wheel need to satisfy defined constraints, which may be complex nonlinear relationships. erefore, a nonlinear programming model of the pitch curve is constructed with the radius and center position of the arc as design variables, and a computer is used to help us find the optimal center position and radius of the arc that satisfies the defined constraints

Constraints on Nonlinear Programming Models

Design of Arc-Shaped Pitch Curve

Experiment

C Figure 8

Conclusions