A method for designing a non-circular intermittent gear pitch curve with quick-return characteristics

Abstract

The application discloses a kind of non-circular intermittent gear pitch curve design method with quick return characteristic, by analyzing the design process of pitch curve, pitch curve is divided into two categories of functional type and non-functional type, wherein functional type pitch curve is used to meet any given transmission requirement, non-functional pitch curve is used to compensate functional type pitch curve so that it can realize the repair of the defect of rotation.To improve the transmission efficiency of non-circular intermittent gear, a quick return characteristic repair model for non-functional pitch curve design is constructed based on the principle of variation, and the implementation mechanism of the model is studied.Based on the boundary conditions of functional type pitch curve, the analytical solution of the model is derived using Euler-Lagrange equation, and the pitch curve equation of the conjugate external meshing and internal meshing non-circular gear is given.The quick return characteristic repair model not only ensures that the designed N-leaf non-circular intermittent gear meets the rotation constraint requirement, but also makes the transmission efficiency of the non-circular intermittent gear highest.

Description

Technical Field

[0001] This invention relates to the field of non-circular gear transmission technology, and specifically to a method for designing pitch curves of non-circular intermittent gears with quick-return characteristics. Background Technology

[0002] Because non-circular gear pairs have the advantages of compact structure, smooth transmission, high motion accuracy and easy dynamic balancing between two parallel shafts, they have been used in mechanical products such as printing presses, gear shaping machines, and flow meters to replace traditional mechanisms such as Geneva wheels, cams, ratchet wheels or connecting rods, realizing speed change, differential or intermittent motion of mechanical products. Since the early 20th century, domestic and foreign researchers have conducted extensive research on the pitch curve design of non-circular gears: HECTOR et al. proposed a method for constructing Nth-order non-circular gear pitch curves using Bézier curves and B-spline curves; Liu Yongping and Wu Xutang et al. used common planar curves with unidirectional continuous rotation characteristics (ellipse, eccentric circle, Basgar worm curve, etc.) as pitch curves for non-circular gears, derived their conjugate external and internal meshing pitch curves, and compared and analyzed the transmission performance and ease of design and manufacturing of these three types of gear pairs; BAIR proposed a computer-aided design method for elliptical gear pairs based on the gear meshing principle; Tian Lijian proposed a method to replace non-circular gear pitch curves with segmented circular arc gear pitch curves; WEI developed an elliptical interpolation algorithm for elliptical gear design based on the central angle segmentation principle.

[0003] The aforementioned research methods all use specific planar curves as the pitch curves of non-circular gears, which cannot meet the increasingly complex engineering application requirements. This limitation has gradually been discovered by some researchers: Yao Wenxi first proposed using the same planar curves connected end to end to replace each side of a regular polygon, and using the resulting "regular curved polygon" as the pitch curve of the non-circular gear, thus constructing an arbitrary N-leaf non-circular gear pitch curve that satisfies the rotational constraint; LITVIN, LIU, and Ren Tingzhi, among others, have respectively elaborated on the function generation method for non-circular gear pitch curve design in different forms.

[0004] Non-circular gear pitch curves that meet any given transmission requirements may have rotational defects, meaning they cannot achieve unidirectional continuous full-circumference rotational motion. Summary of the Invention

[0005] To maximize the transmission efficiency of the designed non-circular intermittent gear, this invention provides a method for designing the pitch curve of a non-circular intermittent gear with quick-return characteristics, based on the principle of variational method.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A method for designing pitch curves of non-circular intermittent gears with quick-return characteristics, comprising the following steps: 1) Rotate the given non-circular gear pitch curve around the center of rotation to obtain the functional pitch curve. r 1( i The non-functional pitch curve is defined as the pitch curve used to compensate for the functional pitch curve and enable the non-circular gear to meet the rotational constraints. g 1( i ); 2) Obtain the functional joint curve based on rotational characteristics. r 1( i ) and non-functional section curves g 1( i The polar coordinate equation of ). 3) Based on the principles of kinematics and the differential principle, the interval time function is obtained. T [ g 1( i )]; 4) Utilizing the intermittent time function T [ g 1( i A quick-return characteristic repair model for non-functional nodal curve design was established; 5) Using the variational principle, the non-functional section curve is obtained by solving the quick-return characteristic repair model. g 1( i ) and its constraints; 6) Using the non-functional section curve obtained in step 5) g 1( i ) Functional section curve r 1( i Perform quick-return characteristic repair of turnover defects to complete the process and meet turnover constraints. N Pitch curve of non-circular intermittent gear R ( i ) design.

[0007] Preferably, in step 3), a non-functional section curve is obtained. g 1( i The rotational linear velocity on ) v ( i )for Based on the principles of kinematics and the differential principle, the first differential of the intermittent time function is obtained. Integrating both sides simultaneously yields the intermittent time function. T [ g 1( i )]for ,in ds ( i ) represents a single-leaf non-functional segment curve g 1( i The arc length on ) Minimum interval time, i Polar angle, ,symbol" "Indicates no more than" m The largest integer, m For non-circular gears, the number of blades is... w It is the angular velocity of a non-circular intermittent gear transmission.

[0008] Preferably, in step 4), the intermittent time function is used. T [ g 1( i Establish a quick-return characteristic repair model for non-functional nodal curve design. .

[0009] Preferably, in step 5) First, obtain the first-order integral of the Euler-Lagrange equation. , express F right g 1′( i The first partial derivative of ) h It is the integration constant; Secondly, this first-order integral is used to obtain... ,use ,get The combination of the two yields ,in ; Then to Integrating both sides simultaneously yields ,in h 1. h 2 is an undetermined constant; Furthermore, the undetermined constants are obtained by utilizing the constraints of the non-functional section curve. h 1 and h The formula for calculating 2 is: ; Finally, the analytical solution of the quick-return characteristic repair model for the non-functional nodal curve design is obtained. , Through the Differentiating both sides simultaneously yields , according to Obtain non-functional section curves g 1( i The corresponding rotation angle is .

[0010] Preferred, judgment Is the value an integer? mIf the given value is an integer, then the given nodal curve can be directly obtained by rotating it around the center of rotation to satisfy the circumduction constraint. m The pitch curve of a non-circular gear; if m If it is not an integer, then let and according to Paired curves r 1( i Perform quick-return characteristic repair of turnover defects to complete the process that meets turnover constraints. N Pitch curve of non-circular intermittent gear R ( i ) design.

[0011] Preferably, the result obtained in step 6) N Pitch curve of non-circular intermittent gear R ( i The single-leaf pitch curves of conjugate external and internal meshing non-circular gears and their single-leaf pitch curves. R o1( i o) and R i1( i i) as follows: ,

[0012] , a o and a i They refer to and N Pitch curve of non-circular intermittent gear R ( i Pitch curves of conjugate external and internal meshing non-circular gears R o( i o) and R i( i i) center distance.

[0013] Preferred, according to and Adjust center distance a o and a i So that the obtained section curve R o( i o) and R i( i i) Meets the given closure design requirements. N o and N i are the curves that satisfy the given closure design requirements. R ( i Pitch curves of conjugate external and internal meshing non-circular gearsR o( i o) and R i( i i) number of leaves and N Pitch curve of non-circular intermittent gear R ( i Pitch curves of conjugate external and internal meshing non-circular gears R o( i o) and R i( i The formula for calculating i) is: ; .

[0014] Preferably, the solution and N Pitch curve of non-circular intermittent gear R ( i The steps for constructing conjugate external and internal meshing non-circular gear pitch curves are as follows: I. Determine the number of leaves based on actual project needs. N o and N i; II. By adjusting the center distance a o and a i Make each and Established, the external meshing center distance that meets the closed design requirements is obtained. a o and the distance between the internal meshing centers a i III. Utilization and Find the pitch curve of the conjugate single-lobe non-circular gear. R o1( i o) and R i1( i i); IV. Through

[0015] and

[0016] Obtain the complete pitch curve of the non-circular gear R o( i o) and R i( i i).

[0017] The beneficial effects of the present invention: NIn practical engineering applications, non-circular intermittent gears only need to have corresponding teeth meshed on their functional pitch curve and their conjugate non-circular gear pitch curve to meet the given transmission design requirements; while the non-functional pitch curve is a toothless part to meet the unidirectional continuous rotation and specific intermittent time requirements of non-circular intermittent gears.

[0018] This quick-return characteristic repair model can not only ensure the design N The non-circular intermittent gear meets the circumferential constraint requirements and maximizes the transmission efficiency of the non-circular intermittent gear.

[0019] By selecting different angular velocities, one can... N Non-circular intermittent gears have different interval times, which allows them to adapt to different engineering application requirements. Attached Figure Description

[0020] Figure 1(a) and Figure 1(b) show the pitch curves of arbitrary multi-leaf non-circular or non-circular intermittent gears.

[0021] Figure 2 Flowchart of the quick-return characteristic repair algorithm designed for non-circular intermittent gears.

[0022] Figure 3 To meet the conditions r 1( i 1)> r 1( i 2) Pitch curve of a 3-lobe non-circular intermittent gear R ( i ).

[0023] Figure 4 shows the relationship with Figure 3 Middle section curve R ( i (a) Conjugate non-circular gear pitch curves: External meshing R o( i o), (b) internal meshing R i( i i).

[0024] Figure 5 To meet the conditions r 1( i 1)= r 1( i 2) Pitch curve of a two-lobe non-circular intermittent gear R ( i ).

[0025] Figure 6 shows the relationship with Figure 5 Middle section curve R ( i (a) Conjugate non-circular gear pitch curves: External meshing R o( io), (b) internal meshing R i( i i).

[0026] Figure 7 To meet the conditions r 1( i 1) r 1( i 2) Pitch curve of a two-lobe non-circular intermittent gear R ( i ).

[0027] Figure 8 shows the relationship with Figure 7 Middle section curve R ( i (a) Conjugate non-circular gear pitch curves: External meshing R o( i o), (b) internal meshing R i( i i)

[0028] Figure 9 For different angular velocities w The corresponding shortest interval time function T min . Detailed Implementation

[0029] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0030] This invention provides a method for designing pitch curves of non-circular intermittent gears with quick-return characteristics, comprising the following steps: 1) Rotate the given non-circular gear pitch curve around the center of rotation to obtain the functional pitch curve. r 1( i The non-functional pitch curve is defined as the pitch curve used to compensate for the functional pitch curve and enable the non-circular gear to meet the rotational constraints. g 1( i ); 2) Obtain the functional joint curve based on rotational characteristics. r 1( i ) and non-functional section curves g 1( i The polar coordinate equation of ). 3) Based on the principles of kinematics and the differential principle, the interval time function is obtained. T [ g 1( i )]; 4) Utilizing the intermittent time function T [ g 1( i A quick-return characteristic repair model for non-functional nodal curve design was established; 5) Using the variational principle, the non-functional section curve is obtained by solving the quick-return characteristic repair model. g 1( i ) and its constraints; 6) Using the non-functional section curve obtained in step 5) g 1( i ) Functional section curve r 1( i Perform quick-return characteristic repair of turnover defects to complete the process and meet turnover constraints. N Pitch curve of non-circular intermittent gear R ( i ) design.

[0031] As shown in Figure 1(a), the fixed coordinate system o- xyz Rigidly connected to the center of rotation o, assuming an arbitrary curve in the plane. r 1( i ) ( i ∈[ i 1, i 2]) is a given non-circular gear pitch curve, polar angle i by x The positive axis is measured counterclockwise. Points a and b are nodal curves. r 1( i If the two boundary points of the curve are (), then the rotation angle corresponding to that section of the curve is ∠aob. If ∠aob = 2π / m ,and m If the value is an integer, then rotating the curve around the center of rotation will yield the result that satisfies the circumference constraint. m Leaf is not a circular gear.

[0032] In practical engineering applications, m The gears are often not integers, making it impossible to obtain non-circular gears that satisfy the circumferential constraints through rotation. To address this issue, this application proposes an isochronous intermittent method. N Design method of non-circular gears (of which) ,symbol" "Indicates no more than" m The largest integer), and introduce the following definition: Definition 1: The given non-circular gear pitch curve and the pitch curve obtained by rotating around the center of rotation are collectively referred to as functional pitch curves (as shown by the solid line in Figure 1(b)).

[0033] Definition 2: The pitch curve used to compensate for the functional pitch curve and enable the non-circular gear to meet the rotational constraints is called the non-functional pitch curve (as shown by the dashed line in Figure 1(b)).

[0034] Referring to Figure 1(b), any N Single-lobe functional pitch curve in non-circular intermittent gears r 1( i The corresponding rotation angle ∠aob and the non-functional section curve g 1( i The corresponding rotation angle ∠boc satisfies the following relationship: (1) Based on rotational characteristics, functional nodal curves r k ( i ) and non-functional section curves g k ( i The polar equations of ) are as follows: (2) (3) In the formula, k =1, 2, ..., N .

[0035] like w If the angular velocity is that of a non-circular intermittent gear transmission, then the single-lobe non-functional pitch curve... g 1( i The rotational linear velocity on ) v ( i )for: (4) Based on the principles of kinematics and the principle of differentiation, the first derivative of the intermittent time function dt ( i This can be represented as: (5) In the formula, ds ( i ) represents a single-leaf non-functional segment curve g 1( i The arc length on the surface.

[0036] Integrating both sides of equation (5) simultaneously yields the intermittent time function. T [ g 1( i )]for: (6) As can be seen from equation (6), for different single-leaf non-functional segment curvesg 1( i ), N Non-circular intermittent gear passes through g 1( i The interval between point b and point c T They are all different. By designing different single-leaf non-functional section curves... g 1( i )of N Non-circular intermittent gears can meet specific intermittent time requirements in practical engineering applications.

[0037] N Pitch curve of non-circular intermittent gear R ( i ) and the single-leaf pitch curves of external and internal meshing non-circular gears conjugate with its single-leaf pitch curve. R o1( i o) and R i1( i i) are respectively: (7) (8) (9) In the formula, a o and a i They refer to and N Pitch curve of non-circular intermittent gear R ( i Pitch curves of conjugate external and internal meshing non-circular gears R o( i o) and R i( i i) center distance.

[0038] Considering only equations (8) and (9) may not guarantee the design of the nodal curve. R o( i o) and R i( i i) Meets the closed-loop design requirements for non-circular gears.

[12] Therefore, in the design process of the section curve, the center distance needs to be adjusted according to equations (10) and (11) respectively. a o and a i So that the obtained section curve R o( i o) and R i( i i) Meets the given closed-loop design requirements.

[0039] (10) (11) In the formula, N o and N i are the curves that satisfy the given closure design requirements. R ( i Pitch curves of conjugate external and internal meshing non-circular gears R o( i o) and R i( i i) The number of leaves.

[0040] and N Pitch curve of non-circular intermittent gear R ( i Pitch curves of conjugate external and internal meshing non-circular gears R o( i o) and R i( i The calculation formulas for i) are as follows: (12) (13) Should N In practical engineering applications, non-circular intermittent gears only need to have corresponding teeth meshed on their functional pitch curve and their conjugate non-circular gear pitch curve to meet the given transmission design requirements; while the non-functional pitch curve is a toothless part to meet the unidirectional continuous rotation and specific intermittent time requirements of non-circular intermittent gears.

[0041] and N As a key transmission component in modern mechanical products, the transmission efficiency of non-circular intermittent gears plays a crucial role in the function and performance of these products. This application uses the intermittent time function shown in equation (6) as a basis. T [ g 1( i A quick-return characteristic repair model for non-functional nodal curve design was established: (14) As shown in the above equation, this quick-return characteristic repair model is a simplest functional and belongs to a variational problem with fixed boundaries. According to the variational principle...

[16] To make the interval time T To reach the minimum T min , F The Euler-Lagrange equations must be satisfied. This is because the repair model contains... F No parameters included i Therefore, the first integral of the Euler-Lagrange equation is: (15) In the formula, express F right g 1′( i The first-order partial derivative of ) h is the integration constant.

[0042] In equation (14) F Substituting the expression into equation (15), we get: (16) Assumption Then we have: (17) Substituting the above equation into equation (16), we get: (18) In the formula, .

[0043] Integrating both sides of equation (18) simultaneously, we get: (19) In the formula, h 1. h 2 is an undetermined constant.

[0044] The single-leaf non-functional segment curve in equation (8) g 1( i Substituting the constraints into equation (19), we can obtain the undetermined constants. h 1 and h The formula for calculating 2 is: (20) Combining equations (19) and (20), the analytical solution for the quick-return characteristic repair model of the single-leaf non-functional nodal curve design is obtained as follows: (twenty one) Differentiating both sides of equation (19) simultaneously, we get: (twenty two) From equation (1), it can be seen that the single-leaf non-functional segment curve g 1( i The corresponding rotation angle is: (twenty three) exist N During the design of the pitch curve of the non-circular intermittent gear, the rotation angle always satisfies: From equations (21) to (23), it can be seen that the monotonicity of the quick-return characteristic repair section curve is determined by the given single-leaf functional section curve.r 1( i Polar radius of the left and right boundaries r 1( i 1) r 1( i 2) Determine: (twenty four) when r 1( i 1)= r 1( i 2) When the quick-return characteristic is repaired, the single-leaf non-functional segment curve g 1( i ) is an arc; and when r 1( i 1)≠ r 1( i 2) g 1( i ) is an exponential function with the natural constant e as its base.

[0045] Figure 2 This is a flowchart of the quick-return characteristic repair algorithm for non-circular intermittent gear design. The known parameters are the given non-circular gear pitch curve. r 1( i ) ( i ∈[ i 1, i 2]). judge m ( Is the value of ) an integer: If m If the given value is an integer, then the given nodal curve can be directly obtained by rotating it around the center of rotation to satisfy the circumduction constraint. m The pitch curve of a non-circular gear; if m If it is not an integer, then let And according to equation (21), the section curve r 1( i Perform quick-return characteristic repair of turnover defects to complete the process that meets turnover constraints. N Pitch curve of non-circular intermittent gear R ( i ) design.

[0046] In practical engineering applications of non-circular intermittent gears, a pair of conjugate gears is often used as the transmission component, with the non-circular intermittent gear being the driving gear. To obtain the conjugate driven non-circular gear, this paper presents the following steps for solving the pitch curves of the conjugate external and internal meshing non-circular gears: 1) Determine the number of blades based on actual project needs. N o and N i; 2) By adjusting the center distancea o and a i By making equations (10) and (11) true respectively, the external meshing center distance that meets the closed design requirements is obtained. a o and the distance between the internal meshing centers a i ; 3) Use equations (8) and (9) to obtain the pitch curve of the conjugate single-lobe non-circular gear. R o1( i o) and R i1( i i).

[0047] 4) Obtain the complete pitch curve of the non-circular gear through equations (12) and (13). R o( i o) and R i( i i).

[0048] Example meet the conditions r 1( i 1)> r 1( i 2) The planar curve is used as the given non-circular gear pitch curve. r 1( i The polar equation and boundary conditions of the curve in this section are as follows: (25) (26) because m =10 / 3 is not an integer, then Substituting equations (25) and (26) into equation (21), we can obtain the undetermined constants. h 1. h 2. Non-functional section curves repaired by quick return characteristics g 1( i They are respectively: (27) (28) Equation (7) is combined with the condition obtained by repairing the quick-return property. r 1( i 1)> r 1( i 2) Pitch curve of a 3-lobe non-circular intermittent gear R ( i )like Figure 3 As shown in equation (29). The pitch curve of this 3-lobe non-circular intermittent gear.R ( i Pitch curves of conjugate external and internal meshing non-circular gears R o( i o) and R i( i i) As shown in Figures 4(a) and 4(b) respectively, the relevant design parameters are shown in Table 1.

[0049] (29) Table 1 Design parameters for the pitch curve of conjugate non-circular gears

[0050] Examples 2 and 3 respectively satisfy the conditions r 1( i 1)= r 1( i 2) and r 1( i 1) r 1( i 2) The planar curve is used as the given non-circular gear pitch curve. r 1( i Since the solution process is the same as in Example 1, the design process will not be repeated; only the design results will be given, as follows: Figure 5 As shown in Figure 8 and Table 2.

[0051] As shown in Figures 4, 6, and 8, only when the given non-circular gear pitch curve... r 1( i (Meets the conditions) r 1( i 1)> r 1( i 2) When the non-functional pitch curve of the non-circular intermittent gear interferes with the pitch curves of its conjugate external and internal meshing non-circular gears (as shown in Figure 4), since the non-functional pitch curve is the toothless part of the non-circular intermittent gear and only serves as a unidirectional continuous rotation, interference during transmission can be avoided by appropriately designing the gear body and tooth profile of the non-circular intermittent gear and its conjugate non-circular gear. How to design the tooth profile of this gear pair and analyze and repair its interference will be the focus of our next research.

[0052] Figure 9 In the quick return characteristic repair model g 1( i Given a fixed value, different angular velocities w The corresponding shortest interval time function T min Curve. With angular velocity w As the value increases, the corresponding steepest intermittent time function Tmin The lower the value, the better. In practical engineering applications, an appropriate angular velocity can be selected. w To meet N Different interval time requirements for non-circular intermittent gears.

[0053] Table 2 meets the conditions r 1( i 1)= r 1( i 2) and r 1( i 1) r 1( i 2) Pitch curve design parameters for non-circular intermittent gears and their conjugate non-circular gears

[0054] In conclusion, the present invention has the following advantages: (1) To address the limitations of existing non-circular gear pitch curve designs and potential turnover defects, a design capable of meeting arbitrary transmission requirements is proposed. N A method for designing pitch curves of non-circular intermittent gears and a quick-return characteristic repair model for non-functional pitch curve design.

[0055] (2) Numerical examples show that this quick-return characteristic repair model can not only guarantee the design N The non-circular intermittent gear meets the circumferential constraint requirements and maximizes the transmission efficiency of the non-circular intermittent gear.

[0056] (3) By selecting different angular velocities, it is possible to... N Non-circular intermittent gears have different interval times, which allows them to adapt to different engineering application requirements.

[0057] The embodiments should not be regarded as limitations on the present invention, but any improvements made based on the spirit of the present invention should be within the protection scope of the present invention.

Claims

1. A method for designing pitch curves of non-circular intermittent gears with quick-return characteristics, characterized in that: It includes the following steps: 1) Rotate the given non-circular gear pitch curve around the center of rotation to obtain the functional pitch curve. r 1( θ The non-functional pitch curve is defined as the pitch curve used to compensate for the functional pitch curve and enable the non-circular gear to meet the rotational constraints. g 1( θ ); 2) Obtain the functional joint curve based on rotational characteristics. r 1( θ ) and non-functional section curves g 1( θ The polar coordinate equation of ). 3) Based on the principles of kinematics and the differential principle, the interval time function is obtained. T [ g 1( θ )]; 4) Utilizing the intermittent time function T [ g 1( θ A quick-return characteristic repair model for non-functional nodal curve design was established; 5) Using the variational principle, the non-functional section curve is obtained by solving the quick-return characteristic repair model. g 1( θ ) and its constraints; 6) Using the non-functional section curve obtained in step 5) g 1( θ ) Functional section curve r 1( θ Perform quick-return characteristic repair of turnover defects to complete the process and meet turnover constraints. N Pitch curve of non-circular intermittent gear R ( θ ) design, In step 4), the intermittent time function is used. T [ g 1( θ Establish a quick-return characteristic repair model for non-functional nodal curve design. ， in θ Polar angle, ,symbol" "Indicates no more than" m The largest integer.

2. The method for designing the pitch curve of a non-circular intermittent gear with quick-return characteristics according to claim 1, characterized in that: In step 3), the non-functional section curve is obtained. g 1( θ The rotational linear velocity on ) v ( θ )for Based on the principles of kinematics and the differential principle, the first differential of the intermittent time function is obtained. Integrating both sides simultaneously yields the intermittent time function. T [ g 1( θ )]for ,in ds ( θ ) represents a non-functional section curve g 1( θ The arc length on ) Minimum interval time, θ Polar angle, ,symbol" "Indicates no more than" m The largest integer, m For non-circular gears, the number of blades is... w It is the angular velocity of a non-circular intermittent gear transmission.

3. The method for designing the pitch curve of a non-circular intermittent gear with quick-return characteristics according to claim 1, characterized in that: Step 5) First, obtain the first-order integral of the Euler-Lagrange equation. , express F right g 1′( θ The first partial derivative of ) h It is the integration constant; Secondly, this first-order integral is used to obtain... ,use ,get The combination of the two yields ,in ; Then to Integrating both sides simultaneously yields ,in h 1. h 2 is an undetermined constant; Furthermore, the undetermined constants are obtained by utilizing the constraints of the non-functional section curve. h 1 and h The formula for calculating 2 is: ; Finally, the analytical solution of the quick-return characteristic repair model for the non-functional nodal curve design is obtained. ， Through the Differentiating both sides simultaneously yields ， according to Obtain non-functional section curves g 1( θ The corresponding rotation angle is .

4. The method for designing the pitch curve of a non-circular intermittent gear with quick-return characteristics according to claim 3, characterized in that: judge Is the value an integer? m If the given value is an integer, then the given nodal curve can be directly obtained by rotating it around the center of rotation to satisfy the circumduction constraint. m The pitch curve of a non-circular gear; if m If it is not an integer, then let and according to Paired curves r 1( θ Perform quick-return characteristic repair of turnover defects to complete the process that meets turnover constraints. N Pitch curve of non-circular intermittent gear R ( θ ) design.

5. The method for designing the pitch curve of a non-circular intermittent gear with quick-return characteristics according to claim 1, characterized in that: The result obtained in step 6) N Pitch curve of non-circular intermittent gear R ( θ The single-leaf pitch curves of conjugate external and internal meshing non-circular gears and their single-leaf pitch curves. R o1( θ o) and R i1( θ i) as follows: ， ， a o and a i They refer to and N Pitch curve of non-circular intermittent gear R ( θ Pitch curves of conjugate external and internal meshing non-circular gears R o( θ o) and R i( θ i) center distance.

6. The method for designing the pitch curve of a non-circular intermittent gear with quick-return characteristics according to claim 5, characterized in that: according to and Adjust center distance a o and a i So that the obtained section curve R o( θ o) and R i( θ i) Meets the given closure design requirements. N o and N i are the curves that satisfy the given closure design requirements. R ( θ Pitch curves of conjugate external and internal meshing non-circular gears R o( θ o) and R i( θ number of leaves (i) and N Pitch curve of non-circular intermittent gear R ( θ Pitch curves of conjugate external and internal meshing non-circular gears R o( θ o) and R i( θ The formula for calculating i) is: ； 。 7. The method for designing the pitch curve of a non-circular intermittent gear with quick-return characteristics according to claim 1, characterized in that: Solve and N Pitch curve of non-circular intermittent gear R ( θ The steps for constructing conjugate external and internal meshing non-circular gear pitch curves are as follows: I. Determine the number of leaves based on actual project needs. N o and N i; II. By adjusting the center distance a o and a i Make each and Established, the external meshing center distance that meets the closed design requirements is obtained. a o and the distance between the internal meshing centers a i III. Utilization and Find the pitch curve of the conjugate single-lobe non-circular gear. R o1( θ o) and R i1( θ i); IV. Through and Obtain the complete pitch curve of the non-circular gear R o( θ o) and R i( θ i).

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