Design method for pitch curve of biarc non-circular planetary gear hydraulic motor
By using nonlinear programming algorithms and coordinate transformation theory, the problems of pitch curve continuity and tooth profile accuracy in the design of non-circular planetary gears were solved, thereby improving the transmission performance and meshing accuracy of hydraulic motors.
Patent Information
- Application Number
- CN202511798328.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-02
- Publication Date
- 2026-01-06
AI Technical Summary
Existing non-circular planetary gear design methods have shortcomings in terms of pitch curve continuity, tooth profile accuracy, and actual meshing performance. In particular, tooth profile accuracy is prone to decrease and design parameter errors are likely to occur in the arc splicing area.
The pitch curve design parameters are solved using a nonlinear programming algorithm. A geometric model based on the gear rotation center is established, and the unified pitch curve parameter equation is derived. Combining the gear meshing principle and coordinate transformation theory, a high-precision mathematical model of the sun gear and internal gear ring profile is constructed.
It significantly improves the transmission performance and meshing accuracy of the hydraulic motor, and achieves high-precision gear design.
Smart Images
Figure CN121278884A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of non-circular planetary gear hydraulic motor design technology, and particularly to the design of double circular arc pitch curves, specifically a method for designing pitch curves of double circular arc non-circular planetary gear hydraulic motors. Background Technology
[0002] The non-circular planetary gear high-water-based hydraulic motor is a new type of hydraulic motor that can achieve low-speed, high-torque transmission. This hydraulic motor can directly drive the load without the need for a reduction gear. It has advantages such as low output speed, high torque, low flow pulsation, large displacement, high efficiency, and high power-to-weight ratio. It is widely used in special applications such as metallurgical mines and underground coal mines.
[0003] Currently, the pitch curves of non-circular planetary gear mechanisms are mainly divided into high-order elliptical and double-circular arc types. The design method for high-order elliptical pitch curves is usually based on a given sun gear pitch curve equation, and the discrete points of the internal gear ring pitch curve are obtained by solving the gear train transmission conditions. However, the internal gear ring pitch curve obtained by this method lacks a continuous geometric expression, resulting in limited accuracy in its mathematical model construction and difficulty in accurately reflecting the geometric characteristics during actual meshing. The double-circular arc pitch curve is composed of two arc segments spliced and arrayed. Its tooth profile design is determined based on the center and radius of each arc segment, offering advantages of simple and efficient design, and is widely used in practical applications. Although this method simplifies the tooth profile generation process to some extent, it is prone to a decrease in tooth profile accuracy in the arc splicing area. Therefore, some literature has proposed designing each arc segment with an integer number of teeth to improve tooth profile accuracy, but this introduces errors in the pitch curve design parameters. In addition, during the actual operation of non-circular planetary gears, the rotation center of the gear does not coincide with the center of the pitch curve arc. It is difficult to completely define the true tooth profile shape by relying solely on the position of the center and the radius, resulting in a large error in this design method.
[0004] Therefore, existing non-circular planetary gear design methods still have significant shortcomings in terms of pitch curve continuity, tooth profile accuracy, and actual meshing performance. There is an urgent need for a non-circular planetary gear design method that can balance geometric accuracy and engineering practicality. Summary of the Invention
[0005] To address the aforementioned issues, this invention provides a method for designing the pitch curve of a double-circular-arc non-circular planetary gear hydraulic motor. First, the invention solves for the pitch curve design parameters using a nonlinear programming algorithm. Then, based on these parameters, a geometric model is established with the gear rotation center as the reference. A unified pitch curve parameter equation maintaining continuity at segmented connections is derived. Finally, a precise meshing model is established by combining the gear meshing principle and coordinate transformation theory, resulting in a high-precision mathematical model of the sun gear and internal gear ring profiles. This significantly improves the transmission performance and meshing accuracy of the hydraulic motor.
[0006] To achieve the above objectives, the specific solution of the present invention is as follows: A method for designing the pitch curve of a double-circular-arc non-circular planetary gear hydraulic motor includes the following steps: S1. Solve the parameters of the pitch curve of the non-circular planetary gear using nonlinear programming. The pitch curve is a double-circular arc pitch curve, which includes a first circular arc and a second circular arc connected to each other. The circle of the first circular arc is located inside the pitch curve. The obtained parameters include the distance between the center of the first circular arc and the rotation center, the distance between the second circular arc and the rotation center, and the radius of the first circular arc. S2. Based on the parameters obtained from S1, establish a unified nodal curve parameter that is continuous around the rotation center and at the splice point; S3. Using the pitch curve equation constructed in S2, combined with the gear meshing principle and coordinate transformation theory, a gear tooth profile mathematical model is established, and finally the gear tooth profile is generated.
[0007] In step S1, the parameters of the non-circular planetary gear pitch curve are solved using a nonlinear programming method. The double-circular-arc pitch curve is a closed curve formed by splicing two circular arcs and then mirroring and arraying them, such as... Figure 1 As shown, in the internal gear ring, O The center of rotation of the internal gear ring, the arc AC The center of the circle is O 1. Distance from the center of the circle to the center of rotation x 1. The radius of the arc is r 1. Arc BC The center of the circle is O 11 Distance from the center of the circle to the center of rotation y 1. The radius of the arc is r 11 In the sun wheel, O The center of rotation of the sun gear, the arc DE The center of the circle is O 2. Distance from the center of the circle to the center of rotation x 2. The radius of the arc is r 2. Arc EF The center of the circle is O 22 Distance from the center of the circle to the center of rotation y 2. The radius of the arc is r 22 The above analysis shows that the pitch curve of a non-circular gear can be obtained simply by determining the center position and radius of each arc segment. Since the geometry and motion characteristics of the pitch curve must satisfy specific transmission conditions, which often constitute complex nonlinear constraints, the pitch curve design problem can be transformed into a nonlinear programming problem. The parameters can then be systematically solved using a nonlinear programming method.
[0008] This invention combines the design of the pitch curves of the sun gear and the internal gear ring into a single nonlinear programming model. The center position and radius of the pitch curve arc are used as design variables to analyze the transmission geometry and thus determine the constraints.
[0009] (1) Condition for uniform tooth distribution When the gear module is constant, the gear teeth should be evenly distributed on the pitch curve. Figure 1 As shown by the pitch curve arc length, when the gear teeth are evenly distributed, the arc length and the number of teeth should satisfy the following relationship: (1) (2) In the formula: L AC and L CB for x 1. y 1 and r A function of 1; L DF and L FE for x 2. y 2 and r A function of 2; m The gear module; z 1 and z 2 represents the number of teeth on the internal gear ring and the sun gear, respectively; n 1 and n 2 represents the order of the internal gear ring and the sun gear, respectively.
[0010] (2) Continuous transmission constraints In the transmission process of a non-circular gear planetary gear train mechanism, there are three special positions, such as... Figure 2 As shown. Specifically, at position 1, the internal gear ring point... A Sun chakra D With the center of symmetry O Collinear; at special position 2, the internal gear ring point C Sun chakra F With the center of symmetry O Collinear; at special position 3, internal gear ring point B Sun chakra E With the center of symmetry O Collinear.
[0011] From the geometric relationship of special positions 1 and 3, we can know that: (3) (4) In the formula: r 3 represents the radius of the planetary gear;r 11 for x 1. y 1 and r A function of 1; r 22 for x 2. y 2 and r A function of 2.
[0012] In special location 2, point A 'It's a point' A The point of engagement, point D 'It's a point' D The point of engagement, point A '、 D 'And O3 are collinear. Because the relative motion between the gears is pure rolling, therefore we have (5) In the formula: L FP for x 1. y 1. r 1 and r A function of 3. Furthermore, by C , F , O Since the three points are collinear, we know that: (6) (3) Constraints to avoid gear tooth interference and undercut In the transmission process of a non-circular gear planetary gear train, to avoid tooth interference between the sun gear and the internal gear ring during rotation, the maximum radial distance of the sun gear should be less than the minimum radial distance of the internal gear ring, and the radius and position of the pitch curve arc should meet the following requirements. (7) Meanwhile, to avoid root cut of the gear teeth, the circular arcs of each segment of the pitch curve should meet the following requirements. (8) In summary, the pitch curve parameters of non-circular gear planetary gear trains ( x 1. y 1. r 1. x 2. y 2. r 2) It needs to satisfy two tooth distribution conditions (Equations 3-4), four transmission conditions (Equations 3-6), and five constraint conditions (Equations 7-8). A nonlinear programming model is established based on the nonlinear programming method, and design vector variables are defined. X = [ x 1, y 1, r 1, x2, y 2, r [2] Set the upper and lower boundaries and initial point values, use equations (1) ~ (5) as equality constraints and equations (7) ~ (8) as inequality constraints, and construct the objective function from equation (6). Solve for the minimum objective function X By calculating the value, the optimal section curve parameters can be obtained.
[0013] In step S2, the reasoning process for constructing the parametric equations of the nodal curve is as follows: like Figure 1 The diagram shows the pitch curve of a double-circular-arc internal gear ring. When the coordinate system is based on the center of each arc, the arc... AC The included angle range lies in the first quadrant, and the arc CB The included angle range lies in the third quadrant, and there is a significant discontinuity in the included angle parameters between the two arc segments. When the center of the arc is transformed to the center of rotation through coordinate transformation, this discontinuity causes the segment curve to be discontinuous at the splicing point. To solve this problem, this invention proposes a continuity processing strategy based on a geometric graphical method. By reconstructing the mapping relationship of the angle parameters, the two arc segments have a continuous included angle range under a unified coordinate system, thereby achieving a smooth transition of the segment curve at the splicing point.
[0014] like Figure 3 As shown in the figure, the first arc segment... AC The center of the circle is O 1. Radius is r 1. The central angle is δ 1; Second arc segment CB The center of the circle is O 2. Radius is r 11 The central angle is δ 2. At this point, an arc will be established around the center of rotation. O Let be the analytical equation of the coordinate system. At this point, it is known from the first step of the solution process... , , , ,in n The order of the section curve is given.
[0015] (1) The first arc AC Solving parametric equations like Figure 3 The solution is shown below. AC Graphical form of parametric equations. Points h In the arc AC Within the range, and Solve h The arc can be calculated from the locus of the points. AC The parametric equations.
[0016] from Figure 3 From this, we can see that the arc AC The radius is R The included angle ranges from [0, a Based on the known conditions and Figure 3 The following results were obtained regarding the relationship between China and the United States: (9) (10) (11) (12) (13) (14) (15) point h coordinates ( X 1, Y 1) is: (16) in x 1. r The parameters of 1 are known, and we only need to find the solution. θ The arc can be obtained with a parameter of 1. AC The parametric equations.
[0017] (17) exist In this case, it can be obtained through the law of sines: (18) so θ The expression for 1 is: (19) at this time .
[0018] (2) The second arc CB Solving parametric equations On point h Located in the second arc CB At this time, there are two situations, namely: , ,like Figure 4 As shown, Figure 4 As can be seen from this, regardless of the point h ( X 2, Y 2) In any of these situations, the following relationships apply. (20) at this time θ 2 is unknown and needs to be solved. The solution process is as follows: (a) when hour: (twenty one) In triangle In the middle, it is known , , Then, by the Law of Sines, we get: (twenty two) at this time for (twenty three) but θ 2 can be represented as (twenty four) (b) When hour: (25) According to the Law of Sines, we can also find that: (26) at this time for (27) but θ 2 can be represented as (28) The above analysis shows that regardless of ,still , θ The final form of expression 2 remains unchanged. At this point... .
[0019] (3) The third arc BE Solving parametric equations Depend on Figure 5 It can be seen that the point h coordinates ( X 3, Y 3) is: (29) θ 3. The solution process is as follows: exist In the middle, it is known , , Then, by the Law of Cosines, we have: (30) (31) (32) at this time .
[0020] (4) The fourth arc EF Solving parametric equations Depend on Figure 6 It can be seen that the point h coordinates ( X 4, Y 4) is: (33) θ 4. The solution process is as follows: exist In the middle, by the Law of Cosines, we get: (34) (35) (36) at this time .
[0021] (5) The fifth arc FH Solving parametric equations Depend on Figure 7 It can be seen that the point h coordinates ( X 5, Y 5) is: (37) θ 5. The solution process is as follows: exist middle, , , Then, by the Law of Sines, we get: (38) (39) (40) at this time .
[0022] In summary, from solving the first to the fifth circular arc, we can draw the following general conclusions: when hour (41) (42) when ,andi When it is even (43) (44) when ,and i When it is an odd number (45) (46) In the formula: and The trajectory coordinates of the section curve in a two-dimensional coordinate system with the center of rotation as the origin and the line connecting the origin and the starting point of the first arc segment as the X-axis; i denoted as the arc number in the segmented curve, where the polar angle of 0 corresponds to the starting point of the first arc segment, and the center of the first arc segment is located on the X-axis; The polar angle of the first arc segment; The polar angle corresponding to a certain curve in the double circular arc nodal curve; and All are intermediate variables; The distance between the center of the first arc and the center of rotation; The radius of the first arc segment; The radius of the second arc; This is the distance between the center of the second arc and the center of rotation; The angle between the center of rotation and the center of the first arc in the segmented curve, with the center of the first arc as the vertex, and the vertex. n The order of the section curve is given.
[0023] In step S3 of this invention, the design methods for non-circular gear tooth profiles mainly include the envelope method, the hobbing tooth profile normal method, and the shaping tooth profile normal method. Among them, the shaping tooth profile normal method has a simple numerical algorithm and can also be applied to the design of tooth profiles with concave pitch curves. Therefore, the tooth profile generation method in this invention adopts the shaping tooth profile normal method.
[0024] (1) Solve for the tooth profile equation of the gear shaper: In the gear shaping cutter using the tooth profile normal method, a cylindrical gear is used, and its tooth profile is involute. The tooth profile equation of the gear shaping cutter is: (47) In the formula: r b Let be the base circle radius of the gear hobbing cutter; u s The involute's development angle; δ 0 represents the half-angle of the tooth groove of the gear shaper; This indicates the left and right tooth profiles of the gear shaping cutter.
[0025] (2) Establish the kinematic relationship between the gear shaper and the non-circular gear. like Figure 8 The diagram illustrates the relative motion between the non-circular gear and the gear shaper. Let the coordinate system be... S s ( O s x s y s ( ) is a fixed coordinate system, coordinate system S g ( O g x g y g The gear is fixedly connected to the gear shaper; the gear shaper only rotates, with its center of rotation at point O. A translational coordinate system is established at the rotation center of the non-circular gear. S p ( O p x p y p This describes the translation of a non-circular gear at its initial position. x p and x s The axes are parallel and in the same direction; y p and y s The axes are parallel, the directions are opposite, and the coordinate system is parallel. S n ( O n x n y n It is fixedly connected to the non-circular gear. During the generating motion, the non-circular gear rotates at an angle of θ. θ n The corresponding polar angle is φ n , radius is r n The radius of the gear shaping cutter is r g The corner is θ g The coordinate transformation relationships are as follows: The coordinate relationship for external meshing is: (48) The coordinate relationship for internal meshing is: (49) In the formula: The angle between the tangent and the radial vector at the non-circular gear pitch point can be calculated using the following formula: (50) If the pitch circle of a gear shaper and the pitch curve of a non-circular gear are in a pure rolling relationship, then the arc length satisfies the following formula: (51) The rotation angle of a non-circular gear can be obtained from the pure rolling relationship. (52) in: , .
[0026] Based on the coordinate transformation relationship from the tooth profile of a gear shaper to the tooth profile of a non-circular gear, the envelope equation of the non-circular gear tooth profile is further derived as follows: (53) In this design method, the gear shaper cutter axis is fixed, the non-circular gear translates in the horizontal plane, and the node is always located in a fixed coordinate system. S s ( O s x s y s P(-) in ) r g The meshing equation for any point on the tooth profile of the gear shaper at point (0) is: (54) A mathematical model of the tooth profile of a non-cylindrical gear is established, and the parameterized tooth surface equation is obtained as follows: (55) By substituting the design parameters of the non-circular gear and solving the tooth surface equation (55), the tooth profile of the non-circular gear can be obtained.
[0027] Compared with the prior art, the present invention has the following beneficial effects: The present invention constructs a unified pitch curve parametric equation that is continuous around the center of rotation and at the splice, which can obtain a high-precision mathematical model of the sun gear and the internal gear ring profile, thereby significantly improving the transmission performance and meshing accuracy of the hydraulic motor. Attached Figure Description
[0028] Figure 1 This is a schematic diagram of a double-circular-arc nodal curve; Figure 2 This is a schematic diagram of a special position in a non-circular gear planetary gear train transmission mechanism. Figure 3 This is a schematic diagram of the first arc segment of the pitch curve of the internal gear ring; Figure 4 This is a schematic diagram of the second arc segment of the pitch curve of the internal gear ring; Figure 5 This is a schematic diagram of the third arc segment of the pitch curve of the internal gear ring; Figure 6 This is a schematic diagram of the fourth arc segment of the pitch curve of the internal gear ring; Figure 7 This is a schematic diagram of the fifth arc segment of the pitch curve of the internal gear ring; Figure 8 This is a schematic diagram showing the relative motion between a non-circular gear and a gear shaper. Figure 9 This is a schematic diagram of the double-circular arc-shaped nodal curve in an embodiment of the present invention; Figure 10 This is a schematic diagram of the double-arc tooth profile point in an embodiment of the present invention; Figure 11 This is a schematic diagram of the double-circular arc tooth profile curve in an embodiment of the present invention. Detailed Implementation
[0029] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.
[0030] Taking a set of 46-stage double-circular-arc non-circular gear planetary gear train as an example, its relevant design parameters are shown in Table 1.
[0031] Table 1 Design parameters of double-circular-arc non-circular gear planetary gear train The method for designing the pitch curve of a double-circular-arc non-circular planetary gear hydraulic motor in this embodiment includes the following steps: S1. Solve the parameters of the pitch curve of the non-circular planetary gear using nonlinear programming. The pitch curve is a double-circular arc pitch curve, which includes a first circular arc and a second circular arc connected to each other. The center of the first circular arc is located inside the pitch curve. The obtained parameters include the distance between the center of the first circular arc and the rotation center, the distance between the center of the second circular arc and the rotation center, and the radius of the first circular arc. S2. Based on the parameters obtained from S1, establish a unified nodal curve parameter that is continuous around the rotation center and at the splice point; S3. Using the pitch curve equation constructed in S2, combined with the gear meshing principle and coordinate transformation theory, a gear tooth profile mathematical model is established, and finally the gear tooth profile is generated.
[0032] In step S1, the main determination is... Figure 1 In x 1. y 1. r 1. x 2. y 2. r The value of 2, where, x 1 and x 2 represents the distance between the center of the first arc of the pitch curve of the internal gear ring and the sun gear and the center of rotation, respectively. y 1 and y 2 represents the distance between the center of the second arc of the pitch curve of the internal gear ring and the sun gear and the center of rotation, respectively. r 1 and r 2 represents the radius of the first arc of the pitch curve of the internal gear ring and the sun gear, respectively; In the mathematical model of nonlinear programming, the constraints include: Section curve chord length constraint: In the formula: L AC and L CB These are the lengths of the first and second arcs of the pitch curve of the internal gear ring, respectively. L DF and L FE These are the lengths of the first and second arcs of the sun gear pitch curve, respectively, where the two characters of the subscript represent the start and end points of the arc, respectively. m The gear module; z 1 and z 2 represents the number of teeth on the internal gear ring and the sun gear, respectively; n 1 and n 3 represents the order of the internal gear ring and the sun gear, respectively; Geometric constraints at special locations: Pitch curve points of internal gear ring ASun wheel pitch curve point D With the center of rotation O When collinear In the formula: r 3 represents the radius of the planetary gear; Pitch curve points of internal gear ring B Sun wheel pitch curve point E With the center of rotation O When collinear In the formula: r 11 and r 22 These are the radii of the second arc of the pitch curve of the internal gear ring and the sun gear, respectively. Pitch curve points of internal gear ring C Sun wheel pitch curve point F With the center of rotation O When collinear In the formula: L FP For the arc on the planetary gear FP The length of , where point . F The pitch curve points of the planetary gears and the sun gear F The point of contact P The pitch curve points of the planetary gear and the internal gear ring. C Regarding the center point of the planetary gears O The symmetrical point of 3; Constraints to avoid gear tooth interference and undercut: In the mathematical model of nonlinear programming, the objective function is: Pitch curve points of internal gear ring C Sun wheel pitch curve point F With the center of rotation O When collinear In the formula: O 2 is the center of the first arc of the sun gear pitch curve; Define design vector variables X = [ x 1, y 1, r 1, x 2, y 2, r 2], set the upper boundary
[10] 4 , 104 , 10 4 , 10 4 10 4 , 10 4 Given the following boundaries: lower boundary [0, 0, 0, 0, 0, 0], starting point [20, 20, 20, 20, 20], solve for the minimum objective function. X Value. Substituting the parameters from Table 1, we get... X = [26.5754, 50.7552, 23.2583, 19.0323, 103.1301, 15.8014].
[0033] In step S2, the final unified section curve equation is as follows: when hour when ,and i When it is even when ,and i When it is an odd number In the formula: and The trajectory coordinates of the section curve in a two-dimensional coordinate system with the center of rotation as the origin and the line connecting the origin and the starting point of the first arc segment as the X-axis; i denoted as the arc number in the segmented curve, where the polar angle of 0 corresponds to the starting point of the first arc segment, and the center of the first arc segment is located on the X-axis; The polar angle of the first arc segment; The polar angle corresponding to a certain curve in the double circular arc nodal curve; and All are intermediate variables; The distance between the center of the first arc and the center of rotation; The radius of the first arc segment; The radius of the second arc; This is the distance between the center of the second arc and the center of rotation; The angle between the center of rotation and the center of the first arc in the segmented curve, with the center of the first arc as the vertex, and the vertex. nThe order of the section curve; The pitch curve images of the internal gear ring and sun gear obtained by solving the parametric equations are as follows: Figure 9 As shown.
[0034] In step S3, the main design methods for non-circular gear tooth profiles include the envelope method, the hobbing tooth profile normal method, and the shaping tooth profile normal method. Among them, the shaping tooth profile normal method has a simple numerical algorithm and can also be applied to the design of tooth profiles with concave pitch curves. Therefore, the shaping tooth profile normal method is adopted as the tooth profile generation method in this embodiment.
[0035] like Figure 8 As shown, this illustrates the relative motion between the non-circular gear and the gear shaper. Let the coordinate system be... S s ( O s x s y s ( ) is a fixed coordinate system, coordinate system S g ( O g x g y g The gear is fixedly connected to the gear shaper; the gear shaper only rotates, with its center of rotation at point O. A translational coordinate system is established at the rotation center of the non-circular gear. S p ( O p x p y p This describes the translation of a non-circular gear at its initial position. x p and x s The axes are parallel and in the same direction; y p and y s The axes are parallel, the directions are opposite, and the coordinate system is parallel. S n ( O n x n y n It is fixedly connected to the non-circular gear. During the generating motion, the non-circular gear rotates at an angle of θ. θ n The corresponding polar angle is φ n , radius is r n The radius of the gear shaping cutter is r g The corner is θ g The tooth profile equation of the gear shaper is: In the formula: Let be the base circle radius of the gear hobbing cutter; The involute variable parameter is within the end section; The angle at the starting point of the involute; This indicates the left and right tooth surfaces of the gear shaping cutter.
[0036] according to Figure 5 The coordinate transformation relationships for external meshing and internal meshing can be determined separately, where the coordinate relationship for external meshing is: The coordinate relationship for internal meshing is: In the formula: The angle between the tangent and the radial vector at the non-circular gear pitch point can be calculated using the following formula: If the pitch circle of a gear shaper and the pitch curve of a non-circular gear are in a pure rolling relationship, then the arc length satisfies the following formula: The rotation angle of a non-circular gear can be obtained from the pure rolling relationship. in: , .
[0037] Based on the coordinate transformation relationship from the tooth profile of a gear shaper to the tooth profile of a non-circular gear, the envelope equation of the non-circular gear tooth profile is further derived as follows: In this design method, the gear shaper's axis is fixed, the non-circular gear translates in the horizontal plane, and the node is always located in a fixed coordinate system. S s ( O s x s y s P(-) in ) r g The meshing equation for any point on the tooth profile of the gear shaper at point (0) is: A mathematical model of the tooth profile of a non-cylindrical gear is established, and the parameterized tooth surface equation is obtained as follows: Substituting the design parameters of the non-circular gear, the tooth profile of the non-circular gear can be obtained by solving the tooth surface equation. Given the pitch curve parametric equations of the internal gear ring and the sun gear, the tooth profile data points of the internal gear ring and the sun gear can be obtained using the tooth profile normal method, such as... Figure 10 As shown. The tooth profile curve is as follows. Figure 11 As shown.
[0038] The above description is only a preferred embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the embodiments of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for designing a pitch curve of a double circular-arc type non-circular planetary gear hydraulic motor, characterized by, The method comprises the following steps: S1, solving the parameters of the non-circular planetary gear pitch curve by a nonlinear programming method, wherein the pitch curve is a double circular arc type pitch curve comprising a first circular arc and a second circular arc connected to each other, the center of the first circular arc is located in the pitch curve, and the solved parameters comprise the distance between the center of the first circular arc and the center of rotation, the distance between the center of the second circular arc and the center of rotation, and the radius of the first circular arc; S2, establishing unified pitch curve parameters around the center of rotation and continuous at the joint based on the parameters solved in S1; The unified pitch curve parameters are as follows: When time When , and i is even When , and i is odd In the formula: and is the trajectory coordinate of the cycloid in a two-dimensional coordinate system with the rotation center as the origin and the line connecting the origin and the starting point of the first circular arc as the X-axis; i is the serial number of the circular arc in the cycloid, wherein the polar angle of 0 corresponds to the starting point of the first circular arc, and the center of the first circular arc is located on the X-axis; is the polar angle of the first circular arc; is the polar angle corresponding to a certain curve in the double-circular-arc type cycloid; and are both intermediate variables; is the distance between the center of the first circular arc and the rotation center; is the radius of the first circular arc; is the radius of the second circular arc; is the distance between the center of the second circular arc and the rotation center; is the angle between the rotation center and the center of the first circular arc with the center of the first circular arc as the vertex in the cycloid; n is the order of the cycloid; S3, establishing a tooth profile mathematical model by combining the gear meshing principle and the coordinate transformation theory with the pitch curve equation constructed in S2, and finally generating the gear tooth profile.
2. The method of designing a double circular-arc type non-circular planetary gear hydraulic motor pitch curve according to claim 1, wherein In step S1, the mathematical model of the nonlinear programming comprises constraint conditions and an objective function; The constraint conditions comprise: A pitch curve chord length constraint: A geometric relationship constraint at a special position: inner ring pitch curve point A , sun gear pitch curve point D with the center of rotation point O are collinear, ; Inner ring pitch curve point B Sun gear pitch curve point E With the center of rotation point O When collinear, ; Inner ring pitch curve point C Sun gear pitch curve point F With the center of rotation point O When collinear, ; A constraint condition for avoiding gear tooth interference and undercutting: The objective function is: inner ring pitch curve point C , sun gear pitch curve point F with the center of rotation point O are collinear, ; In the formula: x 1 and x 2 are the distances from the center of the first circular arc of the inner gear ring and the sun gear curve to the center of rotation, respectively; y 1 and y 2 are the distances from the center of the second circular arc of the inner gear ring and the sun gear curve to the center of rotation, respectively, r 1 and r 2 are the radii of the first circular arc of the inner gear ring and the sun gear curve, respectively; L AC and L CB are the lengths of the first circular arc and the second circular arc of the inner gear ring curve, respectively, L DF and L FE are the lengths of the first circular arc and the second circular arc of the sun gear curve, respectively, wherein the two characters of the subscript are the starting point and the end point of the circular arc, respectively; m is the gear modulus; z 1 and z 2 are the number of teeth of the inner gear ring and the sun gear, respectively; n 1 and n 2 are the number of steps of the inner gear ring and the sun gear, respectively; r 3 is the radius of the planet gear; L FP is the length of the circular arc on the planet gear FP , wherein the point F is the contact point of the planet gear and the sun gear curve point F , the point P is the contact point of the planet gear and the inner gear ring curve point C is the symmetric point of the planet gear center point O 3; O 2 is the center of the first circular arc of the sun gear curve.
3. The method of designing a double circular-arc type non-circular planetary gear hydraulic motor's pitch curve according to claim 1, wherein In step S3, the tooth profile mathematical model is established by using a gear shaping tooth profile normal line method.