US-12618459-B2 - Internal meshing cylindrical gear pair with constant meshing characteristics constructed tooth pair

US12618459B2US 12618459 B2US12618459 B2US 12618459B2US-12618459-B2

Abstract

Provided is an internal meshing cylindrical gear pair with a constant meshing characteristics constructed tooth pair. The internal meshing cylindrical gear pair with a constructed tooth pair includes an external cylindrical gear with a constructed tooth pair and an internal cylindrical gear with a constructed tooth pair based on conjugate curves. In the present disclosure, normal tooth profile curves of the external cylindrical gear with a constructed tooth pair and the internal cylindrical gear with a constructed tooth pair are continuous combined curves with the same curve shape, which facilitates machining by the same cutter. A common normal at an inflection point or a tangent point of the continuous combined curve passes through a pitch point of the gear pair, and a position of the inflection point or the tangent point can be adjusted as required, so as to adjust a sliding ratio of the gear pair.

Inventors

Bingkui Chen
Fei Liu
Luhe ZHANG
Yonghong Chen
Changyan PENG
Wenjun Luo
Chaoyang Li

Assignees

CHONGQING UNIVERSITY
Chongqing Yisilun Technology Co., Ltd.

Dates

Publication Date: 20260505
Application Date: 20240502
Priority Date: 20230531

Claims (6)

1 . An internal meshing cylindrical gear pair with a constant meshing characteristics constructed tooth pair, comprising an external cylindrical gear with a constructed tooth pair and an internal cylindrical gear with a constructed tooth pair as a pair based on conjugate curves, wherein a normal tooth profile curve Γ s1 of the external cylindrical gear with a constructed tooth pair and a normal tooth profile curve Γ s2 of the internal cylindrical gear with a constructed tooth pair are continuous combined curves Γ L with the same curve shape, and the continuous combined curves Γ L comprise a combined curve Γ L1 of an odd power function curve and a tangent at an inflection point thereof; the continuous combined curve is formed by two continuous curves, a connection point of the two continuous curves is an inflection point or a tangent point of the continuous combined curve, and the inflection point or the tangent point of the continuous combined curve is a designated point located on a meshing force action line of the internal meshing cylindrical gear pair with a constructed tooth pair; and the normal tooth profile curves are swept along given conjugate curves to obtain tooth surfaces of the external cylindrical gear with a constructed tooth pair and the internal cylindrical gear with a constructed tooth pair; wherein when the continuous combined curve Γ L is the combined curve Γ L1 of the odd power function curve and the tangent at the inflection point thereof, the continuous combined curve Γ L is formed by an odd power function curve Γ L12 and a tangent Γ L11 at an inflection point of the odd power function curve; a rectangular coordinate system is established at the tangent point of the continuous combined curve, and an equation of the combined curve Γ L1 of the odd power function curve and the tangent at the inflection point thereof is as follows: { Γ L ⁢ 11 ∶ x 10 = t , y 10 = 0 ⁢ ( t 1 ≤ t < 0 ) Γ L ⁢ 12 ∶ x 10 = t , y 10 = at 2 ⁢ n - 1 ⁢ ( 0 ≤ t ≤ t 2 ) , wherein a parameter tis an independent variable of the equation; t 1 and t 2 are value ranges of the continuous curve; a is a coefficient of the equation; n is a degree of the independent variable and is a positive integer; and x 10 and y 10 are x-axis and y-axis coordinate values of the combined curve in the rectangular coordinate system, respectively.
2 . The internal meshing cylindrical gear pair with a constant meshing characteristics constructed tooth pair according to claim 1 , wherein a curve equation of the normal tooth profile curve Γ s1 of the external cylindrical gear with a constructed tooth pair obtained by rotating the continuous combined curve Γ L around an origin of the rectangular coordinate system by an angle α 1 is as follows: { x 0 ⁢ 1 = x n ⁢ 0 ⁢ cos ⁢ α 1 - y n ⁢ 0 ⁢ sin ⁢ α 1 y 0 ⁢ 1 = x n ⁢ 0 ⁢ sin ⁢ α 1 + y n ⁢ 0 ⁢ cos ⁢ α 1 ⁢ ( n = 1 , 2 , 3 , 4 , 5 , 6 ) , wherein x 01 and y 01 are x-axis and y-axis coordinate values of the normal tooth profile curve of the external cylindrical gear with a constructed tooth pair in the rectangular coordinate system, respectively.
3 . The internal meshing cylindrical gear pair with a constant meshing characteristics constructed tooth pair according to claim 2 , wherein a curve equation of the normal tooth profile curve Γ s2 of the internal cylindrical gear with a constructed tooth pair obtained by rotating the normal tooth profile curve Γ s1 of the external cylindrical gear with a constructed tooth pair around the origin of the rectangular coordinate system by an angle of 180° is as follows: { x 0 ⁢ 2 = x 0 ⁢ 1 ⁢ cos ⁡ ( 180 ⁢ ° ) - y 0 ⁢ 1 ⁢ sin ⁡ ( 180 ⁢ ° ) y 0 ⁢ 2 = x 0 ⁢ 1 ⁢ sin ⁡ ( 180 ⁢ ° ) + y 0 ⁢ 1 ⁢ cos ⁡ ( 180 ⁢ ° ) , wherein x 02 and y 02 are x-axis and y-axis coordinate values of the normal tooth profile curve of the internal cylindrical gear with a constructed tooth pair in the rectangular coordinate system, respectively.
4 . The internal meshing cylindrical gear pair with a constant meshing characteristics constructed tooth pair according to claim 2 , wherein a tooth surface Σ 1 of the external cylindrical gear with a constructed tooth pair is obtained by sweeping the normal tooth profile curve Γ s1 of the external cylindrical gear with a constructed tooth pair along a given helix, with a tooth surface equation as follows: { x ∑ 1 = x 0 ⁢ 1 ⁢ cos ⁢ φ 1 - y 01 ⁢ cos ⁢ β ⁢ sin ⁢ φ 1 + r 0 ⁢ 1 ⁢ cos ⁢ φ 1 y ∑ 1 = x 0 ⁢ 1 ⁢ sin ⁢ φ 1 + y 01 ⁢ cos ⁢ β ⁢ cos ⁢ φ 1 + r 0 ⁢ 1 ⁢ sin ⁢ φ 1 z ∑ 1 = r 0 ⁢ 1 ⁢ φ 1 ⁢ cot ⁢ β - y 01 ⁢ sin ⁢ β , wherein x Σ1 , y Σ1 and z Σ1 are coordinate values of the tooth surface of the external cylindrical gear with a constructed tooth pair, respectively; β is a helix angle of the gear pair; φ 1 is an angle of a given contact line; and r 01 is a pitch radius of the external cylindrical gear with a constructed tooth pair.
5 . The internal meshing cylindrical gear pair with a constant meshing characteristics constructed tooth pair according to claim 3 , wherein a tooth surface Σ 2 of the internal cylindrical gear with a constructed tooth pair is obtained by sweeping the normal tooth profile curve Γ s2 of the internal cylindrical gear with a constructed tooth pair along a given helix, with a tooth surface equation as follows: { x ∑ 2 = x 0 ⁢ 2 ⁢ cos ⁢ φ 1 - x 0 ⁢ 2 ⁢ cos ⁢ β ⁢ sin ⁢ φ 1 + r 0 ⁢ 2 ⁢ cos ⁢ φ 1 y ∑ 2 = x 0 ⁢ 2 ⁢ sin ⁢ φ 1 + y 0 ⁢ 2 ⁢ cos ⁢ β ⁢ cos ⁢ φ 1 + r 0 ⁢ 2 ⁢ sin ⁢ φ 1 z ∑ 2 = r 0 ⁢ 2 ⁢ φ 1 ⁢ cot ⁢ β - y 02 ⁢ sin ⁢ β , wherein x Σ2 , y Σ2 and z Σ2 are coordinate values of the tooth surface of the internal cylindrical gear with a constructed tooth pair, respectively, and r 02 is a pitch radius of the internal cylindrical gear with a constructed tooth pair.
6 . The internal meshing cylindrical gear pair with a constant meshing characteristics constructed tooth pair according to claim 1 , wherein a contact ratio of the internal meshing cylindrical gear pair with a constructed tooth pair is designed as an integer to achieve transmission at a constant meshing stiffness.

Description

CROSS REFERENCE TO RELATED APPLICATION This patent application claims the benefit and priority of Chinese Patent Application No. 202310630490.2, filed with the China National Intellectual Property Administration on May 31, 2023, the disclosure of which is incorporated by reference herein in its entirety as part of the present application. TECHNICAL FIELD The present disclosure relates to the technical field of gear transmission, and in particular, to an internal meshing cylindrical gear pair with a constant meshing characteristics constructed tooth pair, especially an internal meshing cylindrical gear pair with a constructed tooth pair that is formed by an external cylindrical gear with a constructed tooth pair and an internal cylindrical gear with a constructed tooth pair as a pair, and has the same normal tooth profile, a constant curvature radius at a meshing point that tends to infinity, a constant sliding ratio, and a constant meshing stiffness. BACKGROUND An internal meshing cylindrical gear pair as one of main forms of mechanical transmission functions to keep the same direction of mechanical rotation and transmit power, and decelerate to increase a torque or accelerate to reduce the torque, and is widely used in the fields of high-end equipment, aerospace, precision instruments, and the like. Most of existing internal meshing cylindrical gear pairs are involute gear pairs, which have problems such as large sliding ratio between tooth surfaces and time-varying meshing stiffness, leading to reduction of transmission efficiency, service life and dynamic meshing performance, and the like of the internal meshing cylindrical gear pairs. With the development of science and technology and the popularization in application scenarios, it is difficult for the conventional internal meshing cylindrical gear pairs to meet high performance requirements in the fields of national defense technology, industrial manufacturing, production and life, and the like. In the paper Research on the basic theory of internal meshing gear drive with curve element constructed tooth pairs, based on the research of the basic theory of conjugate curve meshing, related application work was further performed on an internal meshing gear with a constructed tooth pair, and a basic principle of convex-concave internal meshing gear drive with curve element constructed tooth pairs was established. An internal meshing gear pair with convex teeth and concave teeth constructed in this paper need machining by means of different cutters, which increases a manufacturing cost of the gear pair. Concave and convex tooth profiles lead to a limited curvature radius at a meshing point of the gear pair, thereby limiting further improvement of the bearing capacity of the gear pair. With regard to selection of contact points, tooth surface interference occurs at pitch points, making it difficult to achieve a zero sliding ratio. Therefore, there is an urgent need for an innovative tooth profile design based on an existing design theory of gears with a constructed tooth pair having conjugate curves, so as to improve meshing performance of an internal meshing cylindrical gear pair with a constructed tooth pair and reduce production and manufacturing costs of the gear pair. SUMMARY An objective of the present disclosure is to provide an internal meshing cylindrical gear pair with a constant meshing characteristics constructed tooth pair, to solve the aforementioned problems existing in the prior art. The gear pair is formed by an external cylindrical gear with a constructed tooth pair and an internal cylindrical gear with a constructed tooth pair that have the same normal tooth profile, with a constant curvature radius at a meshing point that tends to infinity, a constant sliding ratio, and a constant meshing stiffness, and technically features low manufacturing cost, high bearing capacity, high transmission efficiency, low vibration noise, and the like. To achieve the above objective, the present disclosure provides the following technical solutions. The present disclosure provides an internal meshing cylindrical gear pair with a constant meshing characteristics constructed tooth pair, including an external cylindrical gear with a constructed tooth pair and an internal cylindrical gear with a constructed tooth pair as a pair based on conjugate curves, where a normal tooth profile curve Γs1 of the external cylindrical gear with a constructed tooth pair and a normal tooth profile curve Γs2 of the internal cylindrical gear with a constructed tooth pair are continuous combined curves ΓL with the same curve shape, and the continuous combined curves ΓL include a combined curve ΓL1 of an odd power function curve and a tangent at an inflection point thereof, a combined curve ΓL2 of a sine function curve and a tangent at an inflection point thereof, a combined curve ΓL3 of an epicycloid function curve and a tangent at an inflection point thereof, a combined curve ΓL4