Herringbone Gear Pair With Constant Meshing Characteristics Constructed Tooth Pair

Abstract

Provided is a herringbone gear pair with a constant meshing characteristics constructed tooth pair. The herringbone gear pair with a constructed tooth pair includes a herringbone gear I with a constructed tooth pair and a herringbone gear II with a constructed tooth pair based on conjugate curves. In the present disclosure, normal tooth profile curves of the herringbone gear pair 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 according to an actual demand. A contact ratio of the herringbone gear pair with a constructed tooth pair is designed as an integer.

Description

CROSS REFERENCE TO RELATED APPLICATION

This patent application claims the benefit and priority of Chinese Patent Application No. 202310633261.6, 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 a herringbone gear pair with a constant meshing characteristics constructed tooth pair that has the same tooth profile of continuous combined curves, and in particular, to a herringbone gear pair with a constructed tooth pair that is formed by a herringbone gear I with a constructed tooth pair and a herringbone 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, a constant sliding ratio, a constant meshing stiffness, and a constant direction of a meshing force action line.

BACKGROUND

A herringbone gear is a key basic component to achieve movement and power transmission, and is applied in aerospace, industrial automation devices, precision instruments, and other fields. Most of existing herringbone gear pairs are involute gear pairs, which have a large sliding ratio between tooth surfaces, a time-varying meshing stiffness, a time-varying meshing force action line, and other inherent characteristics, leading to limited transmission efficiency, service life and dynamic meshing performance improvement room of the herringbone gear pair.

Patents No. 103939575 A, No. 105202115 A and No. 105114542 A each disclose a point contact meshing gear pair based on conjugate curves. Each gear pair constructed in the above patents includes a convex-tooth gear and a concave-tooth gear, and a pair of gears with concave and convex tooth profiles in the gear pair needs machining by means of different cutters, which increases a manufacturing cost of the 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 gear pair. With regard to selection of a contact point, tooth surface interference occurs at a pitch point, making it difficult to achieve a zero sliding ratio. During meshing, the contact point moves in a tooth width direction, which leads to a time-varying meshing force. Therefore, there is an urgent need for an innovative tooth profile design based on an existing design theory of gears with spatial conjugate curves, so as to improve meshing performance of gears with a constructed tooth pair for transmission and reduce production and manufacturing costs of herringbone gears with a constructed tooth pair for transmission.

SUMMARY

An objective of the present disclosure is to provide a herringbone gear pair with a constant meshing characteristics constructed tooth pair, to solve the aforementioned problems existing in the prior art. The gear pair technically features low manufacturing cost, high bearing capacity, high transmission efficiency, and low vibration noise.

To achieve the above objective, the present disclosure provides the following technical solutions.

A herringbone gear pair with a constant meshing characteristics constructed tooth pair disclosed according to the present disclosure includes a herringbone gear I with a constructed tooth pair and a herringbone gear II with a constructed tooth pair based on conjugate curves, where a normal tooth profile curve Γ_s1 of the herringbone gear I with a constructed tooth pair and a normal tooth profile curve Γ_s2 of the herringbone gear II with a constructed tooth pair in the herringbone gear pair with a constant meshing characteristics constructed tooth pair are continuous combined curves Γ_L with the same curve shape, and the continuous combined curves Γ_L include a combined curve Γ_L1 of an odd power function curve and a tangent at an inflection point thereof, a combined curve Γ_L2 of a sine function curve and a tangent at an inflection point thereof, a combined curve Γ_L3 of an epicycloid function curve and a tangent at an inflection point thereof, a combined curve Γ_L4 of an odd power function, a combined curve Γ_L5 of a sine function, or a combined curve Γ_L6 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 a common normal at the inflection point or the tangent point of the continuous combined curve passes through a pitch point of the herringbone gear pair; and the normal tooth profile curves are swept along given conjugate curves to obtain tooth surfaces of the herringbone gear I with a constructed tooth pair and the herringbone gear II with a constructed tooth pair.

Further, in the herringbone gear pair with a constant meshing characteristics constructed tooth pair, 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:

$\{\begin{array}{c}{\Gamma }_{L11}:x_{10}=t,y_{10}=0\left(t_1\le t<0\right)\\ {\Gamma }_{L12}:x_{10}=t,y_{10}=A{t}^{2n-1}\left(0\le t\le t_2\right)\end{array},$

• • where x₁₀ and y₁₀ 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; t₁ and t₂ 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.

Further, in the herringbone gear pair with a constant meshing characteristics constructed tooth pair, when the continuous combined curve Γ_L is the combined curve Γ_L2 of the sine function curve and the tangent at the inflection point thereof, the continuous combined curve Γ_L is formed by a sine function curve Γ_L22 and a tangent Γ_L21 at an inflection point of the sine 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_L2 of the sine function curve and the tangent at the inflection point thereof is as follows:

$\{\begin{array}{c}{\Gamma }_{L21}:x_{20}=t,y_{20}=\mathrm{kt}\left(t_1\le t<0\right)\\ {\Gamma }_{L22}:x_{20}=t,y_{20}=A\sin \left(Bt\right)\left(0\le t\le t_2\right)\end{array},$

where x₂₀ and y₂₀ 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; t₁ and t₂ are value ranges of the continuous curve; k is a slope of the tangent at the inflection point of the sine function curve; and A and B are coefficients of the equation.

Further, in the herringbone gear pair with a constant meshing characteristics constructed tooth pair, when the continuous combined curve Γ_L is the combined curve Γ_L3 of the epicycloid function curve and the tangent at the inflection point thereof, the continuous combined curve Γ_L is formed by an epicycloid function curve Γ_L32 and a tangent Γ_L31 at an inflection point of the epicycloid 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_L3 of the epicycloid function curve and the tangent at the inflection point thereof is as follows:

$\{\begin{array}{c}{\Gamma }_{L31}:x_{30}=t,y_{30}=\mathrm{kt}\left(t_1\le t<0\right)\\ {\Gamma }_{L32}:\begin{array}{c}{x}_{30}=\left(R+r\right)\sin t-e\sin \left(\left(R+r\right)t/r\right)\left(0\le t<t_2\right)\\ x_{30}=\left(R+r\right)\cos t-e\cos \left(\left(R+r\right)t/r\right)-\left(R+r-e\right)\end{array}\end{array},$

• • where x₃₀ and y₃₀ 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; t₁ and t₂ are value ranges of the continuous curve; k is a slope of the tangent at the inflection point of the epicycloid function curve; R₁, r₁, R₂ and r₂ are radii of a cycloidal moving circle and fixed circle, respectively; and e is an eccentric distance.

Further, in the herringbone gear pair with a constant meshing characteristics constructed tooth pair, when the continuous combined curve Γ_L is the combined curve Γ_L4 of the odd power function, the continuous combined curve Γ_L is formed by a first odd power function curve Γ_L41 and a second odd power function curve Γ_L42; a rectangular coordinate system is established at the inflection point of the continuous combined curve, and an equation of the combined curve Γ_L4 of the odd power function is as follows:

$\{\begin{array}{c}{\Gamma }_{L41}:x_{40}=t,y_{40}=A{t}^{2n1-1}\left(t_1\le t<0\right)\\ {\Gamma }_{L42}:x_{40}=t,y_{40}=B{t}^{2n2-1}\left(0\le t\le t_2\right)\end{array},$

• • where x₄₀ and y₄₀ 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; t₁ and t₂ are value ranges of the continuous curve; A and B are coefficients of the equation; and n1 and n2 are degrees of the independent variable and are positive integers.

Further, in the herringbone gear pair with a constant meshing characteristics constructed tooth pair, when the continuous combined curve Γ_L is the combined curve Γ_L5 of the sine function, the continuous combined curve Γ_L is formed by a first sine function curve Γ_L51 and a second sine function curve Γ_L52; a rectangular coordinate system is established at the inflection point of the continuous combined curve, and an equation of the combined curve Γ_L5 of the sine function is as follows:

$\{\begin{array}{c}{\Gamma }_{L51}:x_{50}=t,y_{50}=A_1\sin \left(B_{1}t\right)\left(t_1\le t<0\right)\\ {\Gamma }_{L52}:x_{50}=t,y_{50}=A_2\sin \left(B_{2}t\right)\left(0\le t\le t_2\right)\end{array},$

• • where x₅₀ and y₅₀ 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; t₁ and 12 are value ranges of the continuous curve; and A₁, B₁, A₂ and B₂ are coefficients of the equation.

Further, in the herringbone gear pair with a constant meshing characteristics constructed tooth pair, when the continuous combined curve Γ_L is the combined curve Γ_L6 of the epicycloid function, the continuous combined curve Γ_L is formed by a first epicycloid function curve Γ_L61 and a second epicycloid function curve Γ_L62; a rectangular coordinate system is established at the inflection point of the continuous combined curve, and an equation of the combined curve Γ_L6 of the epicycloid function is as follows:

$\{\begin{array}{c}{\Gamma }_{L61}:\begin{array}{c}{x}_{60}=-\left(R_1+r_1\right)\sin t+e\sin \left(\left(R_1+r_1\right)t/r_1\right)\left(t_1\le t<0\right)\\ y_{60}=-\left(R_1+r_1\right)\cos t+e\cos \left(\left(R_1+r_1\right)t/r_1\right)+\left(R_1+r_1-e\right)\end{array}\\ {\Gamma }_{L62}:\begin{array}{c}{x}_{60}=\left(R_2+r_2\right)\sin t-e\sin \left(\left(R_2+r_2\right)t/r_2\right)\left(0\le t<t_2\right)\\ y_{60}=\left(R_2+r_2\right)\cos t-e\cos \left(\left(R_2+r_2\right)t/r_2\right)-\left(R_2+r_2-e\right)\end{array}\end{array},$

• • where a parameter t is an independent variable of the equation; t₁ and t₂ are value ranges of the continuous curves; R₁ and r₁ are radii of a first epicycloid moving circle and fixed circle, respectively, and R₂ and r₂ are radii of a second epicycloid moving circle and fixed circle, respectively; e is an eccentric distance; and x₆₀ and y₆₀ are x-axis and y-axis coordinate values of the combined curve in the rectangular coordinate system, respectively.

Further, in the herringbone gear pair with a constant meshing characteristics constructed tooth pair, a curve equation of the normal tooth profile curve Γ_s1 of the herringbone 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 α₁ is as follows:

$\{\begin{array}{c}{x}_{01}=x_{n0}\cos {\alpha }_1-y_{n0}\sin {\alpha }_1\\ y_{01}=x_{n0}\sin {\alpha }_1+y_{n0}\cos {\alpha }_1\end{array}\left(n=1,2,3,4,5,6\right),$

• • where x₀₁ and y₀₁ are x-axis and y-axis coordinate values of the normal tooth profile curve of the herringbone gear I with a constructed tooth pair in the rectangular coordinate system, respectively.

Further, in the herringbone gear pair with a constant meshing characteristics constructed tooth pair, a curve equation of the normal tooth profile curve Γ_s2 of the herringbone gear II with a constructed tooth pair obtained by rotating the normal tooth profile curve Γ_s1 of the herringbone gear I with a constructed tooth pair around the origin of the rectangular coordinate system by an angle of 180° is as follows:

$\{\begin{array}{c}{x}_{02}=x_{01}\cos \left(180°\right)-y_{01}\sin \left(180°\right)\\ y_{02}=x_{01}\sin \left(180°\right)+y_{01}\cos \left(180°\right)\end{array},$

• • where x₀₂ and y₀₂ are x-axis and y-axis coordinate values of the normal tooth profile curve of the herringbone gear II with a constructed tooth pair in the rectangular coordinate system, respectively.

Further, in the herringbone gear pair with a constant meshing characteristics constructed tooth pair, a tooth surface Σ₁ of the herringbone gear I with a constructed tooth pair is obtained by sweeping the normal tooth profile curve Γ_s1 of the herringbone gear I with a constructed tooth pair along a given helix, with a tooth surface equation as follows:

$\{\begin{array}{c}{x}_{\mathrm{\Sigma 1}}=x_{01}+m\tan \beta \\ y_1=y_{01}\\ z_{\mathrm{\Sigma 1}}=\pm m\end{array}\left(m_1\le m\le m_2\right),$

• • where x_Σ1, y_Σ1 and z_Σ1 are coordinate values of the tooth surface of the herringbone gear I with a constructed tooth pair, respectively; β is a helix angle of the gear pair, a parameter m is an independent variable of the equation, and m₁ and m₂ are value ranges of a tooth width; in the sign “±”, the sign “+” indicates a left tooth surface of the herringbone gear with a constructed tooth pair, and the sign “−” indicates a right tooth surface of the herringbone gear with a constructed tooth pair.

Further, in the herringbone gear pair with a constant meshing characteristics constructed tooth pair, a tooth surface Σ₂ of the herringbone gear II with a constructed tooth pair is obtained by sweeping the normal tooth profile curve Γ_s2 of the herringbone gear II with a constructed tooth pair along a given helix, with a tooth surface equation as follows:

$\{\begin{array}{c}{x}_{\Sigma 2}=x_{02}\cos \theta -y_{02}\cos \beta s\mathrm{in}\theta +\left(a-r\right)\cos \theta \\ y_{\Sigma 2}=x_{02}\sin \theta +y_{02}\cos \beta \cos \theta +\left(a-r\right)\sin \theta \\ z_{\Sigma 2}=\pm \left(r\theta \cot \beta -y_{02}\sin \beta \right)\end{array},$

• • where x_Σ2, y_Σ2 and z_Σ2 are coordinate values of the tooth surface of the herringbone gear II with a constructed tooth pair, respectively; r is a pitch radius of the herringbone gear pair with a constant meshing characteristics constructed tooth pair, and θ is an angle of a given contact line; in the sign “±”, the sign “+” indicates a left tooth surface of the herringbone gear with a constructed tooth pair, and the sign “−” indicates a right tooth surface of the herringbone gear with a constructed tooth pair.

Further, in the herringbone gear pair with a constant meshing characteristics constructed tooth pair, a contact ratio of the herringbone gear pair with a constant meshing characteristics constructed tooth pair is designed as an integer, thereby achieving meshing transmission with a constant stiffness.

Further, in the herringbone gear pair with a constant meshing characteristics constructed tooth pair, the herringbone gear I with a constructed tooth pair and the herringbone gear II with a constructed tooth pair are designed to be symmetrical along the tooth width, thereby achieving a constant meshing force action line of the gear pair.

Compared with the prior art, the present disclosure has the following technical effects:

In the herringbone gear pair with a constant meshing characteristics constructed tooth pair according to the present disclosure, a herringbone gear I with a constructed tooth pair and a herringbone gear II with a constructed tooth pair have the same normal tooth profile, and can be machined by using the same cutter, thus reducing a manufacturing cost. A curvature radius at a meshing point is constant and tends to infinity, which improves the overall bearing capacity. A sliding ratio during meshing is constant and may be designed as a zero sliding ratio, which improves overall transmission efficiency and reduces wear during transmission. The herringbone gear I with a constructed tooth pair and the herringbone gear II with a constructed tooth pair are designed to be symmetrical along a tooth width, which can achieve a constant meshing force action line. A contact ratio of the herringbone gear pair with a constant meshing characteristics constructed tooth pair is designed as an integer, which can achieve a constant meshing stiffness, thus greatly reducing vibration noise of the herringbone gear pair with a constant meshing characteristics constructed tooth pair.

BRIEF DESCRIPTION OF THE DRAWINGS

To describe the technical solutions in embodiments of the present disclosure or in the prior art more clearly, the accompanying drawings required for the embodiments are briefly described below. Apparently, the accompanying drawings in the following description show merely some embodiments of the present disclosure, and those of ordinary skill in the art may still derive other accompanying drawings from these accompanying drawings without creative efforts.

FIG. 1 is a schematic diagram of a combined curve of an odd power function curve and a tangent at an inflection point thereof according to the present disclosure;

FIG. 2 is a schematic diagram illustrating formation of a normal tooth profile of a herringbone gear pair with a constant meshing characteristics constructed tooth pair having a combined curve of an odd power function curve and a tangent at an inflection point thereof as a tooth profile curve according to the present disclosure;

FIG. 3 is a schematic diagram illustrating construction of a tooth surface of a herringbone gear pair with a constant meshing characteristics constructed tooth pair having a combined curve of an odd power function curve and a tangent at an inflection point thereof as a tooth profile curve according to the present disclosure;

FIG. 4 is a schematic entity diagram of a herringbone gear pair with a constant meshing characteristics constructed tooth pair having a combined curve of an odd power function curve and a tangent at an inflection point thereof as a tooth profile curve according to the present disclosure;

FIG. 5 is a schematic diagram illustrating a curvature radius at a meshing point of a herringbone gear pair with a constant meshing characteristics constructed tooth pair having a combined curve of an odd power function curve and a tangent at an inflection point thereof as a tooth profile curve according to the present disclosure;

FIG. 6 is a schematic diagram of a designated point on a meshing force action line of a herringbone gear pair with a constant meshing characteristics constructed tooth pair according to the present disclosure;

FIG. 7 is a schematic diagram illustrating a sliding ratio at a meshing point of a herringbone gear pair with a constant meshing characteristics constructed tooth pair having a combined curve of an odd power function curve and a tangent at an inflection point thereof as a tooth profile curve according to the present disclosure; and

FIG. 8 is a schematic diagram illustrating a meshing force of a herringbone gear pair with a constant meshing characteristics constructed tooth pair according to the present disclosure.

In the figures: 1—Herringbone gear I with a constructed tooth pair, 2—Herringbone gear II with a constructed tooth pair.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The technical solutions of the embodiments of the present disclosure are clearly and completely described below with reference to the accompanying drawings in the embodiments of the present disclosure. Apparently, the described embodiments are merely some rather than all of the embodiments of the present disclosure. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present disclosure without creative efforts shall fall within the protection scope of the present disclosure.

An objective of the present disclosure is to provide a herringbone gear pair with a constant meshing characteristics constructed tooth pair, to solve the technical problems in the prior art that gears in a gear pair need machining by means of different cutters and have high manufacturing costs, high vibration noise and low transmission efficiency.

In order to make the above objective, features and advantages of the present disclosure clearer and more comprehensible, the present disclosure will be further described in detail below in combination with accompanying drawings and specific implementations.

As shown in FIGS. 1 to 8, this embodiment provides a herringbone gear pair with a constant meshing characteristics constructed tooth pair, with basic parameters as follows: Module m=8, number of teeth of a gear I with a constructed tooth pair: z₁=20, number of teeth of a gear II with a constructed tooth pair: z₂=85, addendum coefficient h_a*=0.5, tip clearance coefficient c*=0.2, addendum h_a=4 mm, dedendum h_f=5.6 mm, helix angle β=35°, and tooth width w=80 mm.

Taking a combined curve of an odd power function curve and a tangent at an inflection point thereof as a normal tooth profile as an example, FIG. 1 is a schematic diagram of a combined curve of an odd power function curve and a tangent at an inflection point thereof according to this embodiment. A local plane rectangular coordinate system σ₁(O₁-x₁,y₁) is established at the inflection point of the continuous curve, with a coefficient A=1.2 and n=2, and an equation of a combined curve Γ_L1 (formed by an odd power function curve Γ_L12 and a tangent Γ_L11 at an inflection point of the odd power function curve) of an odd power function curve and a tangent at an inflection point thereof is as follows:

$\{\begin{array}{cc}{\Gamma }_{L11}:x_{10}=t,y_{10}=0& \left(t_1\le t<0\right)\\ {\Gamma }_{L21}:x_{10}=t,y_{10}=1.2t^3& \left(0\le t\le t_2\right)\end{array},$

• • where x₁₀ and y₁₀ are x-axis and y-axis coordinate values of the combined curve in the rectangular coordinate system σ₁, respectively; a parameter t is an independent variable of the equation; and t₁ and t₂ are value ranges of the continuous curve.

FIG. 2 is a schematic diagram illustrating formation of a normal tooth profile of a herringbone gear pair with a constant meshing characteristics constructed tooth pair having a combined curve of an odd power function curve and a tangent at an inflection point thereof as a tooth profile curve according to this embodiment. An inflection point P is a meshing point. When the continuous combined curve Γ_L rotates around an origin of the rectangular coordinate system by an angle α₁ to obtain a normal tooth profile curve Γ_s1 of a sun gear with a constructed tooth pair, the value of the rotation angle α₁ needs to be determined according to specific parameters of the gear pair, with a general value range as follows: 0°<α₁<180°. A specific formation process and a tooth profile curve equation of the normal tooth profile of the herringbone gear pair with a constant meshing characteristics constructed tooth pair are as follows:

The combined curve Γ_L1 of the odd power function curve and the tangent at the inflection point thereof rotates around the rectangular coordinate system σ1 by an angle of α₁=120° to obtain the normal tooth profile curve Γ_s1 of the herringbone gear I 1 with a constructed tooth pair, with a curve equation as follows:

$\{\begin{array}{c}{x}_{01}=x_{10}\cos \left(120°\right)-y_{10}\sin \left(120°\right)\\ y_{01}=x_{10}\sin \left(120°\right)+y_{10}\cos \left(120°\right)\end{array},$

• • where x₀₁ and y₀₁ are x-axis and y-axis coordinate values of the normal tooth profile curve of the herringbone gear I 1 with a constructed tooth pair in the rectangular coordinate system σ₁, respectively.

A normal tooth profile curve Γ_s2 of the herringbone gear II 2 with a constructed tooth pair is obtained by rotating the normal tooth profile curve Γ_s1 of the herringbone gear I 1 with a constructed tooth pair around the origin of the rectangular coordinate system σ₁ by an angle of 180°, with a curve equation as follows:

$\{\begin{array}{c}{x}_{02}=x_{01}\cos \left(180°\right)-y_{01}\sin \left(180°\right)\\ y_{02}=x_{01}\sin \left(180°\right)+y_{01}\cos \left(180°\right)\end{array},$

• • where x₀₂ and y₀₂ are x-axis and y-axis coordinate values of the normal tooth profile curve of the herringbone gear II 2 with a constructed tooth pair in the rectangular coordinate system σ₁, respectively.

FIG. 3 is a schematic diagram illustrating construction of a tooth surface of a herringbone gear pair with a constant meshing characteristics constructed tooth pair having a combined curve of an odd power function curve and a tangent at an inflection point thereof as a tooth profile curve according to this embodiment. A specific construction process and a tooth surface equation of the tooth surface of the herringbone gear pair with a constant meshing characteristics constructed tooth pair are as follows:

A tooth surface Σ₁ of the herringbone gear I 1 with a constructed tooth pair is obtained by sweeping the normal tooth profile curve Γ_s1 of the herringbone gear I 1 with a constructed tooth pair along a given helix, with a tooth surface equation as follows:

$\{\begin{array}{c}{x}_{\mathrm{\Sigma 1}}=x_{01}+0.268m\\ y_{\mathrm{\Sigma 1}}=y_{01}\\ z_{\mathrm{\Sigma 1}}=\pm m\end{array}\left(m_1\le m\le m_2\right),$

• • where x_Σ1, y_Σ1 and z_Σ1 are coordinate values of the tooth surface of the herringbone gear I 1 with a constructed tooth pair, respectively; a parameter m is an independent variable of the equation, and m₁ and m₂ are value ranges of a tooth width; in the sign “±”, the sign “+” indicates a left tooth surface of the herringbone gear with a constructed tooth pair, and the sign “−” indicates a right tooth surface of the herringbone gear with a constructed tooth pair.

Similarly, a tooth surface Σ₂ of the herringbone gear II 2 with a constructed tooth pair is obtained by sweeping the normal tooth profile curve Γ_s2 of the herringbone gear II 2 with a constructed tooth pair along a given helix, with a tooth surface equation as follows:

$\{\begin{array}{c}{x}_2=\left(x_{02}+80\right)\cos \theta -0.966x_{02}\sin \theta \\ y_2=\left(x_{02}+80\right)\sin \theta +0.966y_{02}\cos \theta \\ z_2=\pm \left(298.564\theta -0.259y_{02}\right)\end{array},$

• • where x_Σ2, y_Σ2 and z_Σ2 are coordinate values of the tooth surface of the herringbone gear II 2 with a constructed tooth pair, respectively; θ is an angle of a given contact line; in the sign “±”, the sign “+” indicates a left tooth surface of the herringbone gear with a constructed tooth pair, and the sign “−” indicates a right tooth surface of the herringbone gear with a constructed tooth pair.

FIG. 4 is a schematic entity diagram of a herringbone gear pair with a constant meshing characteristics constructed tooth pair having a combined curve of an odd power function curve and a tangent at an inflection point thereof as a tooth profile curve according to this embodiment. An entity model of the herringbone gear pair with a constant meshing characteristics constructed tooth pair having the same tooth profile of continuous combined curves is obtained by defining dimensions of addendum circles and dedendum circles of the herringbone gear I 1 with a constructed tooth pair and the herringbone gear II 2 with a constructed tooth pair, and performing trimming, stitching, rounding, and other operations on the tooth surfaces.

In this embodiment, the normal tooth profile curves of the herringbone gear I 1 with a constructed tooth pair and the herringbone gear II 2 with a constructed tooth pair each may alternatively be a combined curve Γ_L2 of a sine function curve and a tangent at an inflection point thereof, a combined curve Γ_L3 of an epicycloid function curve and a tangent at an inflection point thereof, a combined curve Γ_L4 of an odd power function, a combined curve Γ_L5 of a sine function, or a combined curve Γ_L6 of an epicycloid function, with a curve equation as follows.

When the continuous combined curve Γ_L is the combined curve Γ_L2 of the sine function curve and the tangent at the inflection point thereof, the continuous combined curve Γ_L2 is formed by a sine function curve Γ_L22 and a tangent Γ_L21 at an inflection point of the sine 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_L2 of the sine function curve and the tangent at the inflection point thereof is as follows:

$\{\begin{array}{cc}{\Gamma }_{L21}:x_{20}=t,y_{20}=\mathrm{kt}& \left(t_1\le t<0\right)\\ {\Gamma }_{L22}:x_{20}=t,y_{20}=A\sin \left(\mathrm{Bt}\right)& \left(0\le t\le t_2\right)\end{array},$

• • where x₂₀ and y₂₀ 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; t₁ and t₂ are value ranges of the continuous curve; k is a slope of the tangent at the inflection point of the sine function curve; and A and B are coefficients of the equation.

When the continuous combined curve Γ_L is the combined curve Γ_L3 of the epicycloid function curve and the tangent at the inflection point thereof, the continuous combined curve Γ_L3 is formed by an epicycloid function curve Γ_L32 and a tangent Γ_L31 at an inflection point of the epicycloid 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_L3 of the epicycloid function curve and the tangent at the inflection point thereof is as follows:

$\{\begin{array}{cc}{\Gamma }_{L31}:x_{30}=t,y_{30}=\mathrm{kt}& \left(t_1\le t<0\right)\\ {\Gamma }_{L32}:x_{30}=\left(R+r\right)\sin t-e\sin \left(\left(R+r\right)t/r\right)& \left(0\le t\le t_2\right)\\ y_{30}=\left(R+r\right)\cos t-e\cos \left(\left(R+r\right)t/r\right)-\left(R+r-e\right)& \end{array},$

• • where x₃₀ and y₃₀ 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; t₁ and t₂ are value ranges of the continuous curve; k is a slope of the tangent at the inflection point of the epicycloid function curve; R₁, r₁, R₂ and r₂ are radii of a cycloidal moving circle and fixed circle, respectively; and e is an eccentric distance.

When the continuous combined curve Γ_L is the combined curve Γ_L4 of the odd power function, the continuous combined curve Γ_L4 is formed by an odd power function curve Γ_L41 and a second odd power function curve Γ_L42; a rectangular coordinate system is established at the inflection point of the continuous combined curve, and an equation of the combined curve Γ_L4 of the odd power function is as follows:

$\{\begin{array}{cc}{\Gamma }_{L41}:x_{40}=t,y_{40}=A{t}^{2n1-1}& \left(t_1\le t<0\right)\\ {\Gamma }_{L42}:x_{40}=t,y_{40}=B{t}^{2n2-1}& \left(0\le t\le t_2\right)\end{array},$

• • where x₄₀ and y₄₀ 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; t₁ and t₂ are value ranges of the continuous curve; A and B are coefficients of the equation; and n1 and n2 are degrees of the independent variable and are positive integers.

When the continuous combined curve Γ_L is the combined curve Γ_L5 of the sine function, the continuous combined curve Γ_L5 is formed by a sine function curve Γ_L51 and a second sine function curve Γ_L52; a rectangular coordinate system is established at the inflection point of the continuous combined curve, and an equation of the combined curve Γ_L5 is of the sine function is as follows:

$\{\begin{array}{cc}{\Gamma }_{L51}:x_{50}=t,y_{50}=A_1\sin \left(B_{1}t\right)& \left(t_1\le t<0\right)\\ {\Gamma }_{L52}:x_{50}=t,y_{50}=A_2\sin \left(B_{2}t\right)& \left(0\le t\le t_2\right)\end{array},$

• • where x₅₀ and y₅₀ 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; t₁ and t₂ are value ranges of the continuous curve; and A₁, B₁, A₂ and B₂ are coefficients of the equation.

When the continuous combined curve Γ_L is the combined curve Γ_L6 of the epicycloid function, the continuous combined curve Γ_L6 is formed by an epicycloid function curve Γ_L61 and a second epicycloid function curve Γ_L62; a rectangular coordinate system is established at the inflection point of the continuous combined curve, and an equation of the combined curve Γ_L6 of the epicycloid function is as follows:

$\{\begin{array}{cc}{\Gamma }_{L61}:x_{60}=-\left(R_1+r_1\right)\sin t+e\sin \left(\left(R_1+r_1\right)t/r_1\right)& \left(t_1\le t<0\right)\\ y_{60}=-\left(R_1+r_1\right)\cos t+e\cos \left(\left(R_1+r_1\right)t/r_1\right)+& \\ \left(R_1+r_1-e\right)& \\ {\Gamma }_{L62}:x_{60}=\left(R_2+r_2\right)\sin t-e\sin \left(\left(R_2+r_2\right)t/r_2\right)& \left(0\le t<t_2\right)\\ y_{60}=\left(R_2+r_2\right)\cos t-e\cos \left(\left(R_2+r_2\right)t/r_2\right)-& \\ \left(R_2+r_2-e\right)& \end{array},$

• • where a parameter t is an independent variable of the equation; t₁ and t₂ are value ranges of the continuous curves; R₁ and r₁ are radii of a first epicycloid moving circle and fixed circle, respectively, and R₂ and r₂ are radii of a second epicycloid moving circle and fixed circle, respectively; e is an eccentric distance; and x₆₀ and y₆₀ are x-axis and y-axis coordinate values of the combined curve in the rectangular coordinate system, respectively.

In the herringbone gear pair with a constant meshing characteristics constructed tooth pair disclosed according to the embodiment of the present disclosure, normal tooth profile curves of the herringbone gear I 1 with a constructed tooth pair and the herringbone gear II 2 with a constructed tooth pair are continuous combined curves with the same curve shape, and a meshing point of the herringbone gear I 1 with a constructed tooth pair and the herringbone gear II 2 with a constructed tooth pair is at an inflection point or a tangent point of the continuous combined curve.

In this embodiment, the inflection point or the tangent point of the continuous combined curve is as follows:

• • 1. When the continuous combined curve is a combined curve of an odd power function, a combined curve of a sine function or a combined curve of an epicycloid function, a connection point of the continuous combined curve is an inflection point, that is, a concave-convex boundary point of the curve, a second derivative of the curve is zero at this point, and second order derivative signs near two sides of this point are opposite;
  • 2. when the combined curve is a combined curve of an odd power function curve and a tangent at an inflection point thereof, a combined curve of a sine function curve and a tangent at an inflection point thereof, or a combined curve of an epicycloid and a tangent at an inflection point thereof, a connection point of the combined curve is an inflection point of the odd power function curve, the sine function curve or the epicycloid (meaning the same as 1), which is also a tangent point of the odd power function curve, the sine function curve or the epicycloid at the tangent.

At the inflection point or the tangent point of the continuous combined curve, the curvature is zero, and the curvature radius tends to infinity. When the continuous combined curve is the combined curve of the odd power function, the combined curve of the sine function, or the combined curve of the epicycloid function, the curvature radii on two sides of the inflection point tend to infinity; or when the continuous combined curve is the combined curve of the odd power function curve and the tangent at the inflection point thereof, the curvature radius on the side of the odd power function curve tends to infinity, and the curvature radius on the side of the tangent is infinite.

The curvature radius of the combined curve is calculated based on given parameters in the embodiment, as shown in FIG. 5. The curvature radius of a straight line segment in the combined curve in FIG. 5 is infinite, the curvature radius at the inflection point tends to infinity, and the curvature radius of the cubic power function curve segment gradually decreases and then increases, but is still far less than the curvature radius at the inflection point. This means that the curvature radius at a contact point of the gear pair with a constructed tooth pair tends to infinity, which improves the bearing capacity of the gear pair with a constructed tooth pair.

In this embodiment, 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 gear pair. The designated point is specifically defined as a given point at a pitch point or near the pitch point on the meshing force action line of the herringbone gear pair with a constant meshing characteristics constructed tooth pair that is a straight line which forms a certain angle (pressure angle) with a horizontal axis by means of the pitch point. FIG. 6 is a schematic diagram of a designated point on a meshing force action line of a herringbone gear pair with a constant meshing characteristics constructed tooth pair. In the figure, P is the designated point on the meshing force action line of the gear pair; P₁ and P₂ are limit points of the position range of the designated point; the straight line N₁N₂ is the meshing force action line of the gear pair; α_k is a pressure angle; O₁ is a central point of the herringbone gear II 2 with a constructed tooth pair, and O₁-x₁y₁ and O₂-x₂y₂ are local rectangular coordinate systems of the herringbone gear I 1 with a constructed tooth pair and the herringbone gear II 2 with a constructed tooth pair, respectively; and r₁ and r₂, r_a1 and r_a2, and r_f1 and r_f2 are pitch radii, addendum circle radii, and dedendum circle radii of the herringbone gear I 1 with a constructed tooth pair and the herringbone gear II 2 with a constructed tooth pair, respectively. The designated point P is a given point usually located at a pitch point or near either of two sides of the pitch point, and a variation area of the designated point does not exceed a half of a tooth height.

According to the principle of gear meshing, it can be known that there is no relative sliding between tooth surfaces when the herringbone gear pair with a constant meshing characteristics constructed tooth pair meshes at the pitch point. FIG. 7 is a schematic diagram illustrating a sliding ratio at a meshing point of a herringbone gear pair with a constant meshing characteristics constructed tooth pair having a combined curve of an odd power function curve and a tangent at an inflection point thereof as a tooth profile curve according to this embodiment. Since the herringbone gear pair with a constant meshing characteristics constructed tooth pair having the same tooth profile of continuous combined curves meshes at a pitch point at any time in the embodiment, the herringbone gear pair with a constant meshing characteristics constructed tooth pair can achieve zero-sliding meshing. When the inflection point or the tangent point of the combined curve does not coincide with the pitch point, the sliding ratio of the herringbone gear pair with a constant meshing characteristics constructed tooth pair is also constant but is not zero. A closer inflection point or tangent point of the continuous curve to the pitch point indicates a smaller sliding ratio of the herringbone gear pair with a constant meshing characteristics constructed tooth pair, vice versa. When the inflection point or the tangent point coincides with the pitch point, the herringbone gear pair with a constant meshing characteristics constructed tooth pair can achieve zero-sliding meshing transmission, which reduces the wear between tooth surfaces and improves the transmission efficiency of the herringbone gear pair with a constant meshing characteristics constructed tooth pair.

Further, when a contact ratio of the herringbone gear pair with a constant meshing characteristics constructed tooth pair in the embodiment is designed as an integer, the meshing stiffness is constant. At this time, a magnitude of a meshing force of the herringbone gear pair at any meshing position is determined, and a position and a direction of the meshing force at any time are also determined. Therefore, the herringbone gear pair with a constructed tooth pair has a constant meshing state at any time, which effectively ensures stability of dynamic meshing performance of the herringbone gear pair with a constructed tooth pair and can effectively reduce vibration noise of the gear pair with a constructed tooth pair.

A schematic diagram illustrating a meshing force of a herringbone gear pair is established with the herringbone gear pair with a constant meshing characteristics constructed tooth pair in the embodiment as an example, as shown in FIG. 8. For a right side of the herringbone gear pair with a constant meshing characteristics constructed tooth pair, a meshing force F_n1 on a herringbone gear with a constructed tooth pair may be decomposed into an axial force F_a1, a radial force F_r1, and a circumferential force F_t1. For a left side of the herringbone gear pair with a constructed tooth pair, a meshing force F_n2 on the herringbone gear with a constructed tooth pair may be decomposed into an axial force F_a2, a radial force F_r2, and a circumferential force F_t2. When only the right side of the herringbone gear pair is considered, during meshing, with the movement of the meshing point in a tooth width direction, the meshing force F_n1 also translates in the tooth width direction, and a change in stress state leads to a periodic change in excitation factors of the herringbone gear pair, which seriously affects dynamic meshing performance of the herringbone gear pair. When two sides of the herringbone gear pair with a constructed tooth pair are both considered, since left and right side teeth are completely symmetrical, the axial forces F_a1 and F_a2 on tooth surfaces of the two sides cancel out each other, the radial forces F_r1 and F_r2 on the two sides are simplified to a central position of the herringbone gear with a constructed tooth pair in the tooth width direction, and the circumferential forces F_t1 and F_t2 on the two sides are also simplified to the central position of the herringbone gear with a constructed tooth pair in the tooth width direction. Therefore, a position and a direction of an action line of a combined force F_n of the meshing forces F_n1 and F_n2 are determined at any time, which improves stability of the herringbone gear pair with a constant meshing characteristics constructed tooth pair during meshing.

Specific examples are used in this description to illustrate the principles and implementations of the present disclosure. The description of the above embodiments is merely used to help understand the method and its core ideas of the present disclosure. In addition, those of ordinary skill in the art can make changes in terms of specific implementations and the application scope according to the ideas of the present disclosure. In conclusion, the content of this description shall not be construed as a limitation to the present disclosure.

Claims

1. A herringbone gear pair with a constant meshing characteristics constructed tooth pair, comprising a herringbone gear I with a constructed tooth pair based on conjugate curves and a herringbone gear II with a constructed tooth pair based on conjugate curves, wherein a normal tooth profile curve Γs1 of the herringbone gear I with a constructed tooth pair and a normal tooth profile curve Γs2 of the herringbone gear II with a constructed tooth pair are continuous combined curves ΓL with the same curve shape, and the continuous combined curves ΓL comprise 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 a common normal at the inflection point or the tangent point of the continuous combined curve passes through a pitch point of the herringbone gear pair; and the normal tooth profile curves are swept along given conjugate curves to obtain tooth surfaces of the herringbone gear I with a constructed tooth pair and the herringbone gear II with a constructed tooth pair.

2. The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 1, wherein 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:

3. The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 1, wherein when the continuous combined curve ΓL is the combined curve ΓL2 of the sine function curve and the tangent at the inflection point thereof, the continuous combined curve ΓL is formed by a sine function curve ΓL22 and a tangent ΓL21 at an inflection point of the sine function curve; a rectangular coordinate system is established at the tangent point of the continuous combined curve, and an equation of the combined curve ΓL2 of the sine function curve and the tangent at the inflection point thereof is as follows:

4. The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 1, wherein when the continuous combined curve ΓL is the combined curve ΓL3 of the epicycloid function curve and the tangent at the inflection point thereof, the continuous combined curve ΓL is formed by an epicycloid function curve ΓL32 and a tangent ΓL31 at an inflection point of the epicycloid function curve; a rectangular coordinate system is established at the tangent point of the continuous combined curve, and an equation of the combined curve ΓL3 of the epicycloid function curve and the tangent at the inflection point thereof is as follows:

5. The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 1, wherein when the continuous combined curve ΓL is the combined curve ΓL4 of the odd power function, the continuous combined curve ΓL is formed by a first odd power function curve ΓL41 and a second odd power function curve ΓL42; a rectangular coordinate system is established at the inflection point of the continuous combined curve, and an equation of the combined curve ΓL4 of the odd power function is as follows:

6. The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 1, wherein when the continuous combined curve ΓL is the combined curve ΓL5 of the sine function, the continuous combined curve ΓL is formed by a first sine function curve ΓL51 and a second sine function curve ΓL52; a rectangular coordinate system is established at the inflection point of the continuous combined curve, and an equation of the combined curve ΓL5 of the sine function is as follows:

7. The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 1, wherein when the continuous combined curve ΓL is the combined curve ΓL6 of the epicycloid function, the continuous combined curve ΓL is formed by a first epicycloid function curve ΓL61 and a second epicycloid function curve ΓL62; a rectangular coordinate system is established at the inflection point of the continuous combined curve, and an equation of the combined curve ΓL6 of the epicycloid function is as follows:

8. The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 2, wherein a curve equation of the normal tooth profile curve Γs1 of the herringbone gear I with a constructed tooth pair obtained by rotating the continuous combined curve ΓL around an origin of the rectangular coordinate system by an angle α1 is as follows:

9. The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 8, wherein a curve equation of the normal tooth profile curve Γs2 of the herringbone gear II with a constructed tooth pair obtained by rotating the normal tooth profile curve Γs1 of the herringbone gear I with a constructed tooth pair around the origin of the rectangular coordinate system by an angle of 180° is as follows:

10. The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 8, wherein a tooth surface Σ2 of the herringbone gear II with a constructed tooth pair is obtained by sweeping the normal tooth profile curve Γs2 of the herringbone gear II with a constructed tooth pair along a given helix, with a tooth surface equation as follows:

11. The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 1, wherein a tooth surface Σ1 of the herringbone gear I with a constructed tooth pair is obtained by sweeping the normal tooth profile curve Γs1 of the herringbone gear I with a constructed tooth pair along a given helix, with a tooth surface equation as follows:

12. The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 1, wherein a contact ratio of the herringbone gear pair with a constant meshing characteristics constructed tooth pair is designed as an integer, thereby achieving meshing transmission with a constant stiffness.

13. The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 1, wherein the herringbone gear I with a constructed tooth pair and the herringbone gear II with a constructed tooth pair are designed to be symmetrical along the tooth width, thereby achieving a constant meshing force action line of the herringbone gear pair.

14. The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 3, wherein a curve equation of the normal tooth profile curve Γs1 of the herringbone gear I with a constructed tooth pair obtained by rotating the continuous combined curve ΓL around an origin of the rectangular coordinate system by an angle α1 is as follows:

15. The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 4, wherein a curve equation of the normal tooth profile curve Γs1 of the herringbone gear I with a constructed tooth pair obtained by rotating the continuous combined curve ΓL around an origin of the rectangular coordinate system by an angle α1 is as follows:

16. The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 5, wherein a curve equation of the normal tooth profile curve Γs1 of the herringbone gear I with a constructed tooth pair obtained by rotating the continuous combined curve ΓL around an origin of the rectangular coordinate system by an angle α1 is as follows:

17. The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 6, wherein a curve equation of the normal tooth profile curve Γs1 of the herringbone gear I with a constructed tooth pair obtained by rotating the continuous combined curve ΓL around an origin of the rectangular coordinate system by an angle α1 is as follows:

18. The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 7, wherein a curve equation of the normal tooth profile curve Γs1 of the herringbone gear I with a constructed tooth pair obtained by rotating the continuous combined curve ΓL around an origin of the rectangular coordinate system by an angle α1 is as follows:

19. The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 14, wherein a curve equation of the normal tooth profile curve Γs2 of the herringbone gear II with a constructed tooth pair obtained by rotating the normal tooth profile curve Γs1 of the herringbone gear I with a constructed tooth pair around the origin of the rectangular coordinate system by an angle of 180° is as follows:

20. The herringbone gear pair with a constant meshing characteristics constructed tooth pair according to claim 15, wherein a curve equation of the normal tooth profile curve Γs2 of the herringbone gear II with a constructed tooth pair obtained by rotating the normal tooth profile curve Γs1 of the herringbone gear I with a constructed tooth pair around the origin of the rectangular coordinate system by an angle of 180° is as follows: