CN103089616B - A kind of internal messing flank profil is secondary - Google Patents

Abstract

An internal meshing tooth profile pair, the single tooth profile of the internal gear is composed of a cosine base composite curve that satisfies the first-order continuous straight line segment I, cosine curve I, straight line segment II and cosine curve II in polar coordinates, and the single tooth profile of the internal gear The single conjugate tooth profile of the external gear corresponding to the tooth profile is obtained through the meshing principle to form a conjugate tooth profile pair; the complete conjugate tooth profile pair is obtained by uniformly distributing the individual tooth profiles of the internal gear and the external gear around their centers respectively according to the number of teeth . In the present invention, the straight line segment I, the cosine curve I, the straight line segment II and the cosine curve II that satisfy the first-order continuous formation of a single tooth profile of the internal gear are sequentially determined in polar coordinates; According to the meshing principle, the single tooth profile corresponding to its conjugate external gear is obtained to form a single conjugate tooth profile pair; finally, the individual tooth profiles of the internal and external gears are evenly distributed around their centers according to the number of teeth to obtain a complete The conjugate tooth profile pair.

Description

A kind of internal meshing tooth profile pair

technical field

The invention belongs to the field of mechanical engineering, and in particular relates to an internal meshing tooth profile pair in the field of fluid machinery.

Background technique

Gear pumps mainly include external gear pumps and internal gear pumps. Internal gear pumps are widely used for their advantages of compact structure, small relative slip rate, long life, small flow pulsation, low noise, and high volumetric efficiency at high speed. The core component of the internal meshing pump is a pair of internal and external meshing gear pairs with conjugate tooth profiles. Whether the design of the tooth profile pair is reasonable or not will directly affect the performance of the pump. At present, internal gear pumps mainly include involute internal gear pumps, cycloid internal gear pumps and linear conjugated tooth profile internal gear pumps. The common design method is generally to directly design the tooth profile pair in the Cartesian coordinate system. Due to the small number of design parameters, this tooth profile pair design method can usually only be designed as an internal meshing pump with a symmetrical tooth profile.

Contents of the invention

The purpose of the present invention is to provide an internal meshing tooth profile pair to solve the problem that the existing internal meshing gear pair has few design parameters and can only be designed as an internal meshing pump with a symmetrical tooth profile.

Another object of the present invention is to provide a design method for the above-mentioned internal tooth profile pair.

Technical scheme of the present invention is as follows:

An internal meshing tooth profile pair, the single tooth profile of the internal gear is composed of a cosine-based compound curve composed of a straight line segment I, a cosine curve I, a straight line segment II and a cosine curve II that satisfy the first-order continuity in polar coordinates, and the internal gear The single conjugate tooth profile of the external gear corresponding to the single tooth profile is obtained through the meshing principle to form a conjugate tooth profile pair; the complete conjugate tooth profile pair is the single tooth profile of the internal gear and the external gear are distributed evenly around the center according to the number of teeth get.

The design method of the above-mentioned internal meshing tooth profile pair is to first determine the cosine of the single tooth profile of the internal gear in polar coordinates, which meets the first-order continuity requirement and is composed of a straight line segment I, a cosine curve I, a straight line segment II and a cosine curve II. base compound curve; then transform it into the Cartesian coordinate system, so that the single tooth profile of the corresponding internal gear is composed of dedendum arc, cosine curve I transformation curve, addendum arc, cosine curve II transformation curve; and then by A single tooth profile in the Cartesian coordinate system is obtained according to the meshing principle to obtain a single tooth profile corresponding to its conjugated external gear, forming a single conjugated tooth profile pair; finally, the single tooth profile of the internal and external gears is respectively wound around its center according to its The number of teeth is evenly distributed to obtain a complete conjugate tooth profile pair composed of the internal gear tooth profile and the external gear tooth profile.

The present invention is also characterized in that:

The design parameters of a single tooth profile include internal gear tooth number z ₂ , external gear tooth number z ₁ , modulus m, tooth profile half tooth height coefficient k ₁ , tooth root arc length coefficient k ₂ , tooth profile symmetry coefficient k ₃ , cosine Curve translation coefficient k ₄ and addendum arc length coefficient k ₅ ;

The angular range of a single tooth profile of an internal gear is Among them, the starting and ending angles of the straight line segment I are θ ₁ and θ ₂ respectively, and the equation is: r=r _b +H(θ ₁ ≤θ≤θ ₂ ), where: r _b is the average value of the cosine curve, H is Amplitude of the cosine-shaped curve;

Define tooth profile half tooth height factor

Define the dedendum arc length coefficient k ₂ to get from the start and end points of the straight line segment I:

${\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; ;</span>$

The starting and ending angles of the cosine curve I are θ ₂ and θ ₃ respectively, and the equation of the cosine curve I is:

$\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 180</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; ;</span>$

Define tooth profile symmetry factor

Define cosine curve translation factor

The starting and ending angles of the straight line section II are θ ₃ and θ ₄ respectively, and the equation is: r=r _b -H(θ ₃ ≤θ≤θ ₄ ),

The arc length coefficient k ₅ of the addendum arc is obtained from the starting and ending points of the straight line segment II:

The starting and ending angles of the cosine curve II are θ ₄ and θ ₅ respectively, and the equation of the cosine curve II is:

$r=h\&times;\cos (\frac{\mathrm{\&theta;}-{\mathrm{\&theta;}}_4}{{\mathrm{\&theta;}}_5-{\mathrm{\&theta;}}_4}\&times;180+180)+r_b,$ In the formula, θ ₅ satisfies a ₅ -θ ₁ =α.

Preferably, the value range of the tooth profile half tooth height coefficient k ₁ is 0≤k ₁ ≤1.5; the value range of the dedendum arc coefficient k ₂ is 0≤k ₂ ≤0.8; the value range of the tooth profile symmetry coefficient k ₃ The value range is 0.2≤k ₃ ≤0.8; the value range of cosine curve translation coefficient k ₄ is 0.5≤k ₄ ≤2; the value range of addendum arc length coefficient k ₅ is 0≤k ₅ ≤0.8; The number of teeth z ₂ of the gear and the number of teeth z ₁ of the external gear are both positive integers and satisfy: z ₂ -z ₁ ≥ 1, z ₁ ≥ 2; in the polar coordinate system θ ₁ can be any real number, and the angle range of a single tooth profile of the internal gear α Satisfy: θ ₅ −θ ₁ =α=360/z ₂ .

The present invention has following beneficial effect:

1) The present invention can obtain an asymmetric gear pump tooth profile by adjusting the tooth profile symmetry coefficient,

In this way, the long side of the two tooth sides of the gear is more suitable for transmission, and the short side is more suitable for sealing, which is conducive to the separation of transmission and sealing functions, and enhances the transmission performance and sealing function;

2) The present invention mainly changes the flow rate of the pump by changing the half-tooth height coefficient of the tooth profile when the module and the number of teeth remain unchanged;

3) The present invention is beneficial to processing detection through the setting of the addendum arc and the dedendum arc;

The strength of the gear pump can be adjusted by adjusting the arc length coefficient of the addendum arc and the arc length coefficient of the root arc;

4) The smoothness between tooth profile pairs of the present invention reaches the first-order continuity;

5) The present invention can reduce the phenomenon of oil trapping by adjusting the cosine curve translation coefficient k ₄ ;

6) The design method of the present invention establishes a mathematical model for the multivariate optimization of tooth profile pairs.

Description of drawings

Fig. 1 is the internal gear polar coordinate system cosine base composite curve diagram of the internal meshing tooth profile pair of the present invention;

Fig. 2 is the secondary figure of tooth profile in Cartesian coordinate system of embodiment 1 of the present invention;

Fig. 3 is the tooth profile pair and its comparison diagram in Cartesian coordinate system of embodiment 2 and embodiment 3 of the present invention;

Fig. 4 is the tooth profile pair and its comparison diagram in Cartesian coordinate system of embodiment 4 and embodiment 5 of the present invention;

Fig. 5 is a secondary diagram of the tooth profile in the Cartesian coordinate system of Embodiment 6 of the present invention.

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

The internal meshing tooth profile pair of the present invention, the single tooth profile of the internal gear is composed of cosine-based compound curves that satisfy the first-order continuous straight line segment I, cosine curve I, straight line segment II and cosine curve II in polar coordinates, and the single tooth profile of the internal gear The single conjugate tooth profile of the external gear corresponding to the tooth profile is obtained through the meshing principle to form a conjugate tooth profile pair; the complete conjugate tooth profile pair is obtained by uniformly distributing the individual tooth profiles of the internal gear and the external gear around their centers respectively according to the number of teeth .

The design method of the internal meshing tooth profile pair of the present invention: first determine the single tooth profile of the internal gear in the polar coordinates, which is sequentially composed of a cosine base composed of a straight line segment I, a cosine curve I, a straight line segment II and a cosine curve II satisfying the first-order continuity It is composed of a compound curve; then it is transformed into a rectangular coordinate system, so that the single tooth profile corresponding to the internal gear is sequentially composed of a dedendum arc, a cosine curve I transformation curve, an addendum circle arc, and a cosine curve II transformation curve; and then by a right angle A single tooth profile in the coordinate system is obtained from the corresponding single tooth profile on the conjugated external gear according to the meshing principle, forming a single conjugated tooth profile pair; finally, the single tooth profile of the internal and external gears is respectively wound around its center according to the number of teeth Perform uniform distribution to obtain a complete conjugate tooth profile pair composed of internal gear tooth profile and external gear tooth profile.

The design parameters of a single tooth profile mainly include: the number of teeth of the internal gear z ₂ , the number of teeth of the external gear z ₁ , the gear module m; the pitch circle radius r ₂ of the internal gear = m×z ₂ /2, and the pitch circle radius r ₁ of the external gear =m×z ₁ /2, the center distance of the gear d=r ₂ -r ₁ ; see Figure 2, the coordinate system fixedly connected with the internal gear is x ₂ o ₂ y ₂ , and its origin is the center of rotation of the internal gear is o _2. The coordinate system fixedly connected with the external gear is x ₁ o ₁ y ₁ , and the center of rotation of the external gear at its origin is o ₁ .

Referring to Figure 1, in the polar coordinate system, a single tooth profile of an internal gear is composed of a straight line segment I, a cosine curve I, a straight line segment II, and a cosine curve II, and the angle range of a single tooth profile is Among them, the starting and ending angles of straight line segment 1 are θ ₁ and θ ₂ respectively, and their equations are:

r=r _b +H(θ ₁ ≤θ≤θ ₂ )

In the formula: r _b is the average value of the cosine curve, that is, the pitch diameter of the internal gear; H is the amplitude of the cosine curve.

say is half tooth height coefficient, then H=k ₁ ×m.

From the start and end points of straight line segment 1: Call k ₂ the arc length coefficient of the dedendum arc.

The starting and ending angles of cosine curve 1 are θ ₂ and θ ₃ respectively, so the equation of cosine curve 1 is:

$\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 180</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}$

say is the tooth profile symmetry coefficient;

say Cosine curve translation coefficient.

The starting and ending angles of straight line segment 2 are θ ₃ and θ ₄ respectively, and their equations are:

r=r _b -H(θ ₃ ≤θ≤θ ₄ )

The starting and ending points of straight line segment 2 satisfy: Call k ₅ the arc length coefficient of the addendum arc;

The starting and ending angles of cosine curve 2 are respectively θ ₄ and θ ₅ , then the equation of cosine curve 2 is:

$\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}{{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 180</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 180</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}$

In the formula: θ ₅ satisfies θ ₅ -θ ₁ =α.

The corresponding tooth profile in the Cartesian coordinate system is composed of the root arc, the cosine curve I transformation curve in the polar coordinate system, the addendum arc, and the cosine curve II transformation curve in the polar coordinate system.

Transform from polar coordinates to rectangular coordinates according to the following formula:

x=r cos(θ)

y=r sin(θ)

So far, the parameters k ₁ , k ₂ , k ₃ , k ₄ , and k ₅ have become independent parameters for controlling the single tooth profile of the internal gear. The parameter θ ₁ controls the initial phase of the tooth profile and does not affect the shape of the tooth profile. The parameters of are such that the conjugate tooth profile of the internal gear tooth profile exists without any interference.

Usually the value range of the parameter satisfies the following constraints:

θ ₁ has no restrictions and can be any real number;

The gear modulus m satisfies: m>0;

Tooth profile half tooth height coefficient k ₁ , its value range is 0≤k ₁ ≤1.5;

Arc length coefficient k ₂ of the dedendum arc, whose value range is 0≤k ₂ ≤0.8;

Tooth profile symmetry coefficient k ₃ , its value range is 0.2≤k ₃ ≤0.8;

Cosine curve translation coefficient k ₄ , whose value range is 0.5≤k ₄ ≤2;

Addendum arc length coefficient k ₅ , its value range is 0≤k ₅ ≤0.8;

The number of teeth of the internal gear z ₂ and the number of teeth of the external gear z ₁ are both positive integers and satisfy: z ₂ -z ₁ ≥1; z ₁ ≥2;

The complete tooth profile on the internal gear is obtained by uniformly distributing the single tooth profile of the internal gear with its center o ₂ as the center and according to the number of teeth z ₂ .

The single tooth profile on the external gear is obtained from the single tooth profile of the internal gear according to the meshing principle. Similarly, the complete tooth profile on the external gear can be obtained by uniformly distributing the center o ₁ and the number of teeth z ₁ .

The above is the complete design process of the internal meshing tooth profile pair. The internal meshing tooth profile pair provided by the present invention is composed of the tooth profile of the internal gear and the tooth profile of the external gear conjugated thereto. The tooth profiles of the internal and external gears are an organic an indivisible whole.

Cosine-based internal gear pump tooth profiles of different shapes can be obtained by changing the combination of parameters. Because of different parameter combinations, different design results can be obtained. Since there are infinitely many combinations of parameters, it is impossible to list them all. Only different parameter states are given. The following design examples are shown in the examples below.

Figure 2 to Figure 5 are design examples under different parameter combinations, and the parameters are shown in Table 1.

Fig. 2 and Fig. 5 are each an embodiment, and the main curve meaning among the figure is shown on the figure;

Embodiment 1 shown in Fig. 2 is the combination of the smallest number of teeth, the difference between the number of teeth is 1, and the ratio of internal and external gears is: z ₂ :z ₁ =3:2.

Fig. 3 shows two embodiments of embodiment 2 and embodiment 3, the gear ratio of internal and external gears: z ₂ :z ₁ =7:5, the symmetrical tooth profile and the asymmetrical tooth profile are compared, and the A tooth profile with a rounded arc was compared with a tooth profile without a rounded arc.

Fig. 4 shows the two embodiments of embodiment 4 and embodiment 5, the gear ratio of internal and external gears: z ₂ : z ₁ = 8:5, and the cosine curve translation coefficient k ₄ is mainly compared.

Embodiment 6 shown in FIG. 5 , the gear ratio of internal and external gears: z ₂ :z ₁ =13:10, and the tooth difference is 3.

The design parameters of the embodiment shown in Fig. 2 to Fig. 5 in table 1

The invention provides a parameterized original tooth profile design method in the polar coordinate system, and then transforms the polar coordinate tooth profile into rectangular coordinates to obtain its common tooth profile to obtain a pair of conjugate tooth profiles.

The design principle of the present invention is: in polar coordinates, a single tooth profile of an internal gear is sequentially composed of a straight line I, a cosine curve I, a straight line II, and a cosine curve II; Arc, cosine curve I conversion curve, addendum arc, cosine curve II conversion curve. The design of a single tooth profile of an internal gear is carried out in a parametric way. In addition to the number of teeth z ₂ of the internal gear, the number of teeth z ₁ of the external gear, and the modulus m, the parameters include: tooth profile half-tooth height coefficient k ₁ , arc of the dedendum The length coefficient k ₂ , tooth profile symmetry coefficient k ₃ , cosine curve translation coefficient k ₄ , addendum circular arc length coefficient k ₅ , these parameters ultimately jointly control the tooth profile pair shape of the gear. After the single tooth profile of the internal gear is constructed in polar coordinates, it is transformed into the rectangular coordinate system x ₂ o ₂ y ₂ , and a complete single tooth profile corresponding to its conjugate external gear is obtained according to the meshing principle. The single tooth profile of the gear is distributed evenly around its center according to the number of teeth to obtain a complete conjugate internal gear tooth profile and conjugate external gear tooth profile.

Claims (4)

1. A pair of internal meshing tooth profiles, characterized in that the single tooth profile of the internal gear is composed of cosine bases that satisfy first-order continuous straight line segment I, cosine curve I, straight line segment II and cosine curve II in polar coordinates The single conjugate tooth profile of the external gear corresponding to the single tooth profile of the internal gear is obtained through the meshing principle to form a conjugate tooth profile pair; the complete conjugate tooth profile pair is a single tooth profile of the internal gear and the external gear respectively. The center is uniformly distributed according to the number of teeth, Set the angle range of a single tooth profile of the internal gear as Among them, the starting and ending angles of the straight line segment I are θ ₁ and θ ₂ respectively, and the equation is: r=r _b +H, at this time θ ₁ ≤θ≤θ ₂ , In the formula, θ is the polar coordinate angle of the point on the single tooth profile curve of the external gear, r is the polar diameter corresponding to the change of the single tooth profile of the external gear with the polar coordinate angle θ, z ₂ is the number of teeth of the internal gear; r _b is the cosine The average value of the curve is the pitch diameter of the internal gear; H is the amplitude of the cosine curve; say is the half-tooth height coefficient of the tooth profile, m is the gear module, then H=k ₁ ×m; From the start and end points of the straight line segment I: Call k ₂ the arc length coefficient of the dedendum arc; The starting and ending angles of the cosine curve I are θ ₂ and θ ₃ respectively, then the equation of the cosine curve I is: $\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 180</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; ,</span>$ say is the tooth profile symmetry coefficient; say is the cosine curve translation coefficient, r ₁ is the pitch circle radius of the external gear; The starting and ending angles of the straight line section II are θ ₃ and θ ₄ respectively, and the equation is: r=r _b -H, at this time θ ₃ ≤θ≤θ ₄ ; The starting and ending points of straight line segment II satisfy: Call k ₅ the arc length coefficient of the addendum arc; The starting and ending angles of cosine curve II are θ ₄ and θ ₅ respectively, then the equation of cosine curve II is: $r=h\&times;\cos (\frac{\mathrm{\&theta;}-{\mathrm{\&theta;}}_4}{{\mathrm{\&theta;}}_5-{\mathrm{\&theta;}}_4}\&times;180+180)+r_b,$ In the formula, θ ₅ satisfies θ ₅ -θ ₁ =α. 2. The design method of internal meshing tooth profile pair as claimed in claim 1, is characterized in that, first determines the single tooth profile of internal gear in polar coordinates, and it is successively by satisfying first-order continuous straight line segment I, cosine curve I, straight line Segment II and cosine curve II are composed of a cosine base composite curve; then it is transformed into a rectangular coordinate system, so that the single tooth profile corresponding to the internal gear is sequentially composed of dedendum arc, cosine curve I transformation curve, addendum arc, Cosine curve II transformation curve; then a single tooth profile corresponding to its conjugate external gear is obtained from a single tooth profile in the rectangular coordinate system according to the meshing principle, forming a single conjugate tooth profile pair; finally, the internal and external gears A single tooth profile is uniformly distributed around its center according to the number of teeth to obtain a complete conjugate tooth profile pair consisting of an internal gear tooth profile and an external gear tooth profile. 3. The design method of the internal meshing tooth profile pair according to claim 2, characterized in that: the design parameters of the single tooth profile include internal gear tooth number z ₂ , external gear tooth number z ₁ , gear module m, tooth profile half-tooth height coefficient k ₁ , dedendum arc length coefficient k ₂ , tooth profile symmetry coefficient k ₃ , cosine curve translation coefficient k ₄ and addendum arc length coefficient k ₅ ; The angular range of a single tooth profile of an internal gear is Among them, the starting and ending angles of the straight line segment I are θ ₁ and θ ₂ respectively, and the equation is: r=r _b +H, at this time θ ₁ ≤ θ ≤ θ ₂ , where θ is the angle on the single tooth profile curve of the external gear The polar coordinate angle where the point is located, r is the pole diameter corresponding to the change of a single tooth profile of the external gear with the polar coordinate angle θ, r _b is the average value of the cosine curve, and H is the amplitude of the cosine curve; Define tooth profile half tooth height factor Define the dedendum arc length coefficient k ₂ to get from the start and end points of the straight line segment I: The starting and ending angles of the cosine curve I are θ ₂ and θ ₃ respectively, and the equation of the cosine curve I is: $\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 180</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; ;</span>$ Define tooth profile symmetry factor Define cosine curve translation factor r ₁ is the pitch circle radius of the external gear; The starting and ending angles of the straight line section II are θ ₃ and θ ₄ respectively, and the equation is: r=r _b -H, at this time θ ₃ ≤θ≤θ ₄ ; The arc length coefficient k ₅ of the addendum arc is obtained from the starting and ending points of the straight line segment II: The starting and ending angles of the cosine curve II are θ ₄ and θ ₅ respectively, and the equation of the cosine curve II is: $r=h\&times;\cos (\frac{\mathrm{\&theta;}-{\mathrm{\&theta;}}_4}{{\mathrm{\&theta;}}_5-{\mathrm{\&theta;}}_4}\&times;180+180)+r_b,$ θ ₅ in the formula satisfies θ ₅ -θ ₁ =α. 4. The design method of internal meshing tooth profile pair as claimed in claim 3, characterized in that, the value range of the half tooth height coefficient k ₁ of the tooth profile is 0≤k ₁ ≤1.5; the dedendum arc The value range of the arc length coefficient k ₂ is 0≤k ₂ ≤0.8; the value range of the tooth profile symmetry coefficient k ₃ is 0.2≤k ₃ ≤0.8; the value range of the cosine curve translation coefficient k ₄ is 0.5≤k ₄ ≤2; the value range of the addendum arc length coefficient k ₅ is 0≤k ₅ ≤0.8; the number of teeth z ₂ of the internal gear and the number z ₁ of the external gear are both positive integers and satisfy: z ₂ -z ₁ ≥1, z ₁ ≥2, θ ₁ can be any real number in the polar coordinate system, and the angle range α of a single tooth profile of the internal gear satisfies: θ ₅ -θ ₁ =α=360/z ₂ .