US-12618455-B2 - Bevel gear pair with constant meshing characteristics constructed tooth pair

Abstract

A bevel gear pair with constant meshing characteristics with a constructed tooth pair is provided. The bevel gear pair with a constructed tooth pair includes a bevel gear I with a constructed tooth pair and a bevel gear II with a constructed tooth pair based on conjugate curves. In the present disclosure, a normal tooth profile curve of the bevel gear I with a constructed tooth pair and a normal tooth profile curve of the bevel gear II 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 bevel gear pair with a constructed tooth pair, and a position of the inflection point or the tangent point can be adjusted according to an actual demand.

Inventors

• Bingkui Chen
• Dongyu Wang
• Luhe ZHANG
• Xinxin YE
• Wenjun Luo
• Yonghong Chen
• Chaoyang Li
• Changyan PENG
• Hehe LU

Assignees

• CHONGQING UNIVERSITY
• Chongqing Yisilun Technology Co., Ltd.

Dates

Publication Date

20260505

Application Date

20240502

Priority Date

20230531

Claims (5)

1. 1 . A bevel gear pair with constant meshing characteristics with a constructed tooth pair, comprising a bevel gear I with a constructed tooth pair and a bevel gear II with a constructed tooth pair as a pair based on conjugate curves, wherein a normal tooth profile curve Γ s1 of the bevel gear I with a constructed tooth pair and a normal tooth profile curve Γ s2 of the bevel gear II 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 Γ L 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 Γ L is a designated point located on a meshing force action line of the bevel gear pair with a constructed tooth pair; and the normal tooth profile curve Γ s1 and the normal tooth profile curve Γ s2 are swept along given conjugate curves to obtain tooth surfaces of the bevel gear I with a constructed tooth pair and the bevel gear II 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 Γ L , 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 ⁢ 1 ⁢ 1 : x 1 ⁢ 0 = t , y 1 ⁢ 0 = 0 ⁢ ( t 1 ≤ t < 0 ) Γ L ⁢ 1 ⁢ 2 : x 1 ⁢ 0 = t , y 1 ⁢ 0 = A ⁢ t 2 ⁢ n - 1 ⁢ ( 0 ≤ t ≤ t 2 ) , wherein x 10 and y 10 are x-axis and y-axis coordinate values of the combined curve in the rectangular coordinate system, respectively; a parameter t is 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; and n is a degree of the independent variable and is a positive integer.
2. 2 . The bevel gear pair with constant meshing characteristics with a constructed tooth pair according to claim 1 , wherein a curve equation of the normal tooth profile curve Γ s1 of the bevel gear I 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 Γ s1 of the bevel gear I with a constructed tooth pair in the rectangular coordinate system, respectively.
3. 3 . The bevel gear pair with constant meshing characteristics with a constructed tooth pair according to claim 2 , wherein a curve equation of the normal tooth profile curve Γ s2 of the bevel gear II with a constructed tooth pair obtained by rotating the normal tooth profile curve Γ s1 of the bevel gear I 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 01 ⁢ sin ⁡ ( 180 ⁢ ° ) y 0 ⁢ 2 = x 0 ⁢ 1 ⁢ sin ⁡ ( 180 ⁢ ° ) + y 01 ⁢ cos ⁡ ( 180 ⁢ ° ) , wherein x 02 and y 02 are x-axis and y-axis coordinate values of the normal tooth profile curve Γ s2 of the bevel gear II with a constructed tooth pair in the rectangular coordinate system, respectively.
4. 4 . The bevel gear pair with constant meshing characteristics with a constructed tooth pair according to claim 2 , wherein a tooth surface Σ 1 of the bevel gear I with a constructed tooth pair is obtained by sweeping the normal tooth profile curve Γ s1 of the bevel gear I with a constructed tooth pair along a given helix, with a tooth surface equation as follows: ( x ∑ 1 y ∑ 1 z ∑ 1 1 ) = M 1 ⁢ σ 1 · ( x 01 y 01 0 1 ) , wherein x Σ1 , y Σ1 and z Σ1 are coordinate values of the tooth surface of the bevel gear I with a constructed tooth pair; and M 1σ 1 is a sweep transformation matrix.
5. 5 . The bevel gear pair with constant meshing characteristics with a constructed tooth pair according to claim 3 , wherein a tooth surface Σ 2 of the bevel gear II with a constructed tooth pair is obtained by sweeping the normal tooth profile curve Γ s2 of the bevel gear II with a constructed tooth pair along a given helix, with a tooth surface equation as follows: ( x ∑ 2 y ∑ 2 z ∑ 2 1 ) = M 2 ⁢ σ 1 · ( x 02 y 02 0 1 ) , wherein x Σ2 , y Σ2 and z Σ2 are coordinate values of the tooth surface of the bevel gear II with a constructed tooth pair, respectively; and M 2σ 2 is a sweep transformation matrix.

Description

CROSS REFERENCE TO RELATED APPLICATION This patent application claims the benefit and priority of Chinese Patent Application No. 202310633244.2, 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, in particular, to a bevel gear pair with constant meshing characteristics with a constructed tooth pair, and especially to a bevel gear pair with a constructed tooth pair that is formed by a bevel gear I with a constructed tooth pair and a bevel gear II 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, and a constant sliding ratio. BACKGROUND Bevel gears are key basic components for motion transmission and power transformation between intersecting shafts or staggered shafts, and are widely used in the fields of aerospace, vehicles and vessels, industrial automation equipment, and the like. Patents No. 103075493 A and No. 105202152 A each disclose a bevel gear pair based on conjugate curves. Each bevel gear pair constructed in the above two patents includes a convex-tooth bevel gear and a concave-tooth bevel gear, and a pair of bevel gears with concave and convex tooth profiles in the bevel gear pair needs machining by means of different cutters, which increases a manufacturing cost of the bevel gear pair. The 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 bevel gear pair. Therefore, there is an urgent need to innovate a tooth profile design based on an existing gear design theory with spatial conjugate curves, improve meshing performance of the bevel gear pair with a constructed tooth pair, and reduce a production and manufacturing cost of the bevel gear pair with a constructed tooth pair. SUMMARY In view of this, the present disclosure provides a bevel gear pair with constant meshing characteristics with a constructed tooth pair. The gear pair is formed by a bevel gear I with a constructed tooth pair and a bevel gear II 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 and a constant sliding ratio, and technically features low manufacturing cost, high bearing capacity, high transmission efficiency, and the like. To achieve the above objective, the present disclosure provides the following solution. The present disclosure provides a bevel gear pair with constant meshing characteristics with a constructed tooth pair, including a bevel gear I with a constructed tooth pair and a bevel gear II with a constructed tooth pair as a pair based on conjugate curves, where a normal tooth profile curve Γs1 of the bevel gear I with a constructed tooth pair and a normal tooth profile curve Γs2 of the bevel gear II 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 of an odd power function, a combined curve ΓL5 of a sine function, or a combined curve ΓL6 of an epicycloid function; 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 bevel gear pair with a constructed tooth pair; and the normal tooth profile curve Γs1 and the normal tooth profile curve Γs2 are swept along given conjugate curves to obtain tooth surfaces of the bevel gear I with a constructed tooth pair and the bevel gear II with a constructed tooth pair. Further, in the bevel gear pair with constant meshing characteristics with a constructed tooth pair, when the continuous combined curve ΓL is the combined curve ΓL1 of the odd power function curve and the tangent at the inflection point thereof, the continuous combined curve ΓL is formed by an odd power function curve ΓL12 and a tangent ΓL11 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 ΓL1 of the odd power function curve and the tangent at the inflection point thereof is as follows: {ΓL⁢11:x10=t,y10=0⁢ (t1≤t<0) ΓL⁢12:x10=t,y10=At2⁢n-1⁢