A contact analysis method and application of an arc tooth bevel gear based on tooth surface topology modification

Abstract

The application relates to a contact analysis method and application of an arc tooth bevel gear based on tooth surface topology modification, and belongs to the technical field of gear transmission analysis. The method is as follows: based on basic geometric parameters and machine tool machining parameters of the arc tooth bevel gear, a meshing equation and a pinion conjugate tooth surface equation are constructed, and then a topology modification model is obtained; based on the meshing equation and the pinion conjugate tooth surface equation, an instantaneous contact line Gamma0 on the pinion conjugate tooth surface is established, and then through projection and inverse projection, an actual pinion tooth surface instantaneous contact line Gamma1 corresponding to the Gamma0 is obtained; the contact area boundary of the tooth surface is demarcated through the topology modification model, and the Gamma0 and the Gamma1 are contact-aligned through an angular positioning angle; distance judgment and contact analysis are carried out on the contact-aligned instantaneous contact line, and corresponding contact characteristics, namely a contact trace, a contact mark and a transmission error, are obtained. The method is helpful to improve the calculation stability of the contact analysis method, reduces the calculation time, and can improve the design efficiency and quality of the arc tooth bevel gear.

Description

Technical Field

[0001] This invention belongs to the field of gear transmission analysis technology, specifically relating to a contact analysis method and application of spiral bevel gears based on tooth surface topology modification. Background Technology

[0002] With the increasingly widespread application of spiral bevel gears in aerospace and other fields, the requirements for their tooth surface contact characteristics are also becoming more stringent. Tooth surface contact analysis, by simulating the tooth surface contact state through contact imprints and transmission errors, is a key means of judging meshing performance. Existing methods are based on differential geometry and meshing principles, constructing contact conditions containing five independent nonlinear equations for contact analysis. This method uses an approximate algorithm at the contact point, resulting in generally low computational accuracy; moreover, the large number of nonlinear equations leads to computational complexity, long computation time, and numerical instability within certain parameter ranges. To address these issues, some researchers have reduced numerical instability by adding a condition for equal normal vectors; others have reduced computational complexity by establishing a meshed representation of the contact tooth surface and a distance field of the contact surface. While these methods improve upon the problems of existing contact analysis methods, they remain relatively complex.

[0003] The above background information is provided only to enhance the understanding of the background of this invention, and therefore may contain information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0004] The technical problem to be solved:

[0005] To avoid the shortcomings of existing technologies, this invention provides a contact analysis method for spiral bevel gears based on tooth surface topology modification. This method only constructs a nonlinear equation system consisting of two meshing equations, which is simple to calculate and takes less time. It can effectively solve the problems of complexity and time consumption of existing algorithms, reduce the calculation time, and improve the design efficiency and quality of spiral bevel gears.

[0006] The technical solution of this invention is: a contact analysis method for spiral bevel gears based on tooth surface topology modification, the specific steps of which are as follows:

[0007] Step S100: Based on the basic geometric parameters of the spiral bevel gear and the machining parameters of the machine tool, construct the meshing equation and the conjugate tooth surface equation of the pinion, and then obtain the topological modification model between the actual tooth surface of the pinion and the conjugate tooth surface of the pinion.

[0008] Step S200: Based on the meshing equation and the pinion conjugate tooth surface equation, establish the instantaneous contact line Γ0 on the pinion conjugate tooth surface, and then obtain the actual instantaneous contact line Γ1 of the pinion tooth surface that corresponds one-to-one with Γ0 through projection and inverse projection.

[0009] Step S300: Define the contact area boundary of the tooth surface using the topology modification model, and align Γ0 and Γ1 in contact using the angular positioning angle;

[0010] Step S400: Perform distance judgment and contact analysis on the instantaneous contact line after contact alignment to obtain the corresponding contact characteristics: contact trace, contact imprint and transmission error.

[0011] A further technical solution of the present invention is: in step S100, the actual tooth surface equation of the pinion, the conjugate tooth surface equation of the pinion, and the topological modification model are expressed as follows:

[0012]

[0013] In the formula, θ1 and φ1 represent the small wheel cutter angle and the small wheel rotation angle, which are surface parameters of the small wheel tooth surface; θ2 and φ2 represent the large wheel cutter angle and the large wheel rotation angle, which are surface parameters controlling the conjugate tooth surface of the small wheel; r1 and n1, The position vector equation and normal vector equation represent the actual tooth surface of the pinion before and after angular positioning; r 1c ,n 1c , The position vector equation and normal vector equation represent the conjugate tooth surface of the pinion before and after angular positioning; Δδ represents the error between the two tooth surfaces, which is the pinion tooth surface topological modification model.

[0014] A further technical solution of the present invention is: the specific solution process in step S100 is as follows:

[0015] S101: Based on the basic geometric parameters of spiral bevel gears and the initial contact parameters required for local synthesis, the machine tool machining parameters are calculated using the local synthesis method to determine the machine tool machining parameters of the working surface;

[0016] S102: Based on the principle of spiral bevel gear tooth surface generation, and combining the basic geometric parameters of S1 with the machine tool machining parameters, construct the actual tooth surface equations of the large and small gears under the machining parameters; then, based on the definition of the conjugate tooth surface of the small gear that is completely conjugate to the large gear, and combining the actual tooth surface equation of the large gear with the meshing equation, obtain the conjugate tooth surface equation of the small gear. The meshing equation and the conjugate tooth surface equation of the small gear are expressed as follows:

[0017] {A1sinφ 1c +A2cosφ 1c =A3

[0018]

[0019] In the formula, φ 1c This represents the rotation angle of the conjugate tooth surface of the pinion, and A1, A2, and A3 are the values ​​used to solve for φ. 1c The transition parameter, R 1cM represents the gear ratio between the large and small wheels. 1ch Represents coordinate system S h To coordinate system S 1c The transformation matrix, r 2x ,r 2y ,r 2z ,n 2x ,n 2y ,n 2z r h and n h The coordinate components, r h and n h Z1 and Z2 are the tooth surface position vector and normal vector of the large gear in the installation coordinate system, respectively; Σ is the intersection angle of the spiral bevel gear pair shaft; and z1 and z2 are the number of teeth of the small gear and the large gear, respectively.

[0020] S103: Based on the conjugate tooth surface equation of the pinion obtained in S102, the conjugate tooth surface is discretized and projected onto the coordinate system of the spiral bevel gear shaft section using a rotational projection method. Then, combined with the actual tooth surface equation of the pinion obtained in S102, the actual discrete tooth surface corresponding to the conjugate discrete tooth surface is obtained through inverse projection. The rotational projection method is expressed as follows:

[0021]

[0022] In the formula, x 1c ,y 1c ,z 1c r is the position vector of the conjugate tooth surface of the pinion. 1c The components, XL,RL, are the corresponding r components in the axial section coordinate system of the spiral bevel gear. 1c The rotated projected coordinates;

[0023] S104: Based on the actual discrete tooth surface and the conjugate discrete tooth surface obtained in S103, locate the midpoint angular direction of the two discrete tooth surfaces, calculate the normal distance between the corresponding points, and obtain the topological modification model between the actual tooth surface and the conjugate tooth surface of the pinion.

[0024] A further technical solution of the present invention is: the basic geometric parameters include the number of teeth, module and pressure angle of the spiral bevel gear; the initial contact parameters are the first-order transmission ratio derivative, the major axis of the contact ellipse, and the angle between the contact trace and the gear root cone.

[0025] A further technical solution of the present invention is: the specific solution process in step S200 is as follows:

[0026] S201: Based on the meshing equation in S102, the rotation angle at the midpoint of the tooth width and the tooth surface parameters are used as the initial values ​​for solving the rotation angle range. The tooth tip of the large gear and the tooth tip of the small gear are used as the rotation angle constraint conditions to solve for the meshing rotation angle range of the small gear.

[0027] S202: By combining the meshing equation obtained in S102 with the conjugate tooth surface equation of the pinion, the contact line equation on the single-parameter conjugate tooth surface of the pinion is obtained. Then, starting from the initial engagement angle obtained in S201, the instantaneous contact line Γ0 of the conjugate tooth surface of the pinion is calculated within the angle range. The single-parameter contact line equation of the conjugate tooth surface of the pinion is expressed as:

[0028]

[0029] In the formula, u2 represents the surface parameters, f represents the meshing equation, p represents the functional relationship between the small wheel rotation angle and the large wheel rotation angle, and g represents u2 and θ2, φ obtained from solving the meshing equation. 1c The relationship between φ 1c,i F represents the turning angle position of the i-th small wheel. 0,i This represents the single-parameter function relationship of the instantaneous contact line;

[0030] S203: According to the rotational projection method in S103, the instantaneous contact line Γ0 of the conjugate tooth surface of the pinion is projected onto the coordinate system of the axial section of the spiral bevel gear. Then, Γ0 is converted into the actual instantaneous contact line Γ1 of the pinion tooth surface that corresponds to it through inverse projection.

[0031] A further technical solution of the present invention is: the specific solution process in step S300 is as follows,

[0032] S301: Determine the maximum boundary of the tooth surface contact area based on the topological modification model and the contact criteria specified by Gleason;

[0033] S302: Based on the instantaneous contact lines Γ0 and Γ1 obtained from S202 and S203, angular positioning of Γ0 and Γ1 is performed using the angular positioning described in S104, and then the geometric deviation between Γ0 and Γ1 is calculated.

[0034] A further technical solution of the present invention is: the specific solution process in step S400 is as follows,

[0035] S401: Based on the geometric deviation between the contact lines calculated in S302, determine the minimum geometric deviation between each pair of contact lines and the corresponding data position to determine the contact point position, and obtain the contact trace within the small wheel meshing angle range calculated in S201.

[0036] S402: Based on the geometric deviation between the contact lines calculated in S302, determine the geometric deviation between each pair of contact lines that meets the Gleason standard, and determine the actual contact length based on the corresponding data position. The contact imprint is obtained within the range of the pinion meshing angle calculated in S201.

[0037] S403: Based on the minimum geometric deviation at the contact point obtained in S101, and combining the conversion between the minimum geometric deviation and the transmission error, the geometric transmission error is obtained, which is expressed as:

[0038]

[0039] In the formula, Δφ2 represents the geometric transmission error, and Δδ min This indicates the deviation value at the contact point.

[0040] An application of a contact analysis method for spiral bevel gears based on tooth surface topology modification is presented, which is used to determine the geometric transmission error of spiral bevel gears.

[0041] Beneficial effects

[0042] The beneficial effects of this invention are as follows: Based on the construction of the conjugate tooth surface equation of the pinion that is completely conjugate with the tooth surface of the large gear and the actual tooth surface equation of the pinion, this invention only needs to solve two nonlinear equations, the tooth surface equation and the meshing equation, to obtain the instantaneous contact line of the conjugate tooth surface of the pinion. Then, the instantaneous contact line of the actual tooth surface of the pinion is obtained through projection and inverse projection. After that, the instantaneous contact line is discretized, and angular positioning is performed based on the positioning angle in the tooth surface topology modification model, so that the instantaneous contact lines of the two tooth surfaces come into contact. Then, within the maximum contact area determined by the topology modification, the normal deviation of the discrete points corresponding to each pair of instantaneous contact lines is calculated. The point corresponding to the minimum deviation value is the contact point. The minimum deviation value and the rotational projection radius of the contact point are used to obtain the geometric transmission error. The deviation range of each pair of instantaneous contact lines within the maximum contact range is the contact line at that meshing moment.

[0043] This invention requires only two nonlinear equations to determine the tooth surface contact point, improving computational stability and reducing computational time. Furthermore, the contact line calculation is no longer approximated by a straight line, eliminating the complex calculations of principal curvature and principal direction, thus improving computational efficiency and accuracy. This method can be applied to various gears, contributing to the simplification and standardization of contact analysis methods and solving the problems of complexity and incompleteness in current contact analysis methods.

[0044] As attached Figure 10 The figure shows the geometric transmission error curve of the spiral bevel gear obtained by the analysis method of the present invention. It can be seen from the figure that the transmission error curve is symmetrical and the gear transmission has good stability. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of an improved contact analysis method for spiral bevel gears based on tooth surface topology modification, provided by a specific embodiment of the present invention.

[0046] Figure 2This is a flowchart illustrating an improved contact analysis method for spiral bevel gears based on tooth surface topology modification, provided in a specific embodiment of the present invention.

[0047] Figure 3 This is a scatter plot of the shaft section of the spiral bevel gear provided in a specific embodiment of the present invention;

[0048] Figure 4 This is a scatter plot of the conjugate tooth surface of the pinion and the actual tooth surface of the pinion in the pinion coordinate system, provided in a specific embodiment of the present invention.

[0049] Figure 5 This is a discrete point diagram of the tooth surface of the pinion after angular positioning and the actual tooth surface of the pinion in the pinion coordinate system, provided by a specific embodiment of the present invention.

[0050] Figure 6 This is a topological model diagram of the tooth surface modification of an arc-shaped bevel gear provided in a specific embodiment of the present invention;

[0051] Figure 7 This is a diagram of the instantaneous contact line of the conjugate tooth surface of the pinion within the rotation angle range of the spiral bevel gear provided in a specific embodiment of the present invention;

[0052] Figure 8 This is a contact trace diagram of the tooth surface of an arc-shaped bevel gear provided in a specific embodiment of the present invention;

[0053] Figure 9 This is a diagram of the contact imprint on the tooth surface of an arc-shaped bevel gear provided in a specific embodiment of the present invention;

[0054] Figure 10 This is a geometric transmission error curve diagram of an arc bevel gear provided in a specific embodiment of the present invention; Detailed Implementation

[0055] The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the invention, and should not be construed as limiting the invention.

[0056] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0057] Example 1

[0058] A specific embodiment of the improved contact analysis method for spiral bevel gears based on tooth surface topology modification according to the present invention is shown in the appendix. Figure 1 This is a schematic diagram illustrating a specific embodiment of the present invention, including the following steps:

[0059] S100: Based on the basic geometric parameters and machine tool processing parameters of spiral bevel gears, the actual tooth surface equations of the large and small gears are first established, and the definition of the conjugate tooth surface of the small gear that is completely conjugate with the large gear is obtained. The actual tooth surface equation and meshing equation of the large gear are obtained, and the conjugate tooth surface equation of the small gear is obtained. Then, the tooth surface topology modification model is established through angular positioning.

[0060] S200: Based on the conjugate tooth surface meshing equation, establish the instantaneous contact line Γ0 on the conjugate tooth surface, and then obtain the actual instantaneous contact line Γ1 on the tooth surface that corresponds one-to-one with Γ0 through projection and inverse projection.

[0061] S300: The feasible contact area of ​​the tooth surface can be defined by the topology modification model, which defines the contact boundary for subsequent calculations, and the contact alignment of Γ0 and Γ1 is performed by the angular positioning angle.

[0062] S400: Determine the normal distance at the corresponding discrete points of the instantaneous contact line after contact alignment to obtain the corresponding contact characteristics: contact trace, contact imprint and transmission error.

[0063] Example 2

[0064] A specific embodiment of the improved contact analysis method for spiral bevel gears based on tooth surface topology modification according to the present invention is shown in the appendix. Figure 2 This is a flowchart illustrating a specific embodiment of the present invention, including the following steps:

[0065] S1: Calculation of geometric parameters and machine tool machining parameters for spiral bevel gears;

[0066] Specifically, the geometric parameters and machine tool processing parameters of the spiral bevel gear are shown in Table 1 and Table 2;

[0067] Table 1. Geometric parameters of spiral bevel gears;

[0068]

[0069] Table 2. Machining parameters for spiral bevel gears;

[0070] Tool pressure angle (°) 18.7500 20.0000 Blade tip radius (mm) 192.3798 189.4850 Radial tool path (mm) 161.9484 172.3086 Angular tool position (°) 74.7813 -73.2270 Axial wheel position (mm) -1.9084 0 Beds (mm) 0.5706 0.9191 Rolling ratio 2.9595 1.0531 Vertical wheel position (mm) -11.3674 0 Installation angle (°) 17.3975 69.0984

[0071] S2: Construct the equations for the actual tooth surface of the pinion and the conjugate tooth surface of the pinion in an arc bevel gear;

[0072] Specifically: the actual tooth surface of the small wheel is: r1=r1(u1,θ1), and the actual tooth surface of the large wheel is: r2=r2(u2,θ2);

[0073] In the formula, u1,θ1 are the surface coordinates of the small gear tooth surface, and u2,θ2 are the surface coordinates of the large gear tooth surface;

[0074] The conjugate tooth surface of the pinion is solved by combining the tooth surface equation of the large gear with the meshing equation. The solution process is as follows:

[0075]

[0076] In the formula, φ2, φ 1c These represent the rotation angles of the large wheel and the conjugate small wheel, respectively, n h This represents the unit normal vector of the large wheel in the mounting coordinate system Sh. Let f represent the relative velocity between the large wheel and the conjugate small wheel in the mounted coordinate system Sh, and let f represent the meshing equation. Z1 and Z2 represent the initial rotation angles of the large wheel and the conjugate small wheel, respectively, and the number of teeth of the small wheel and the large wheel, respectively.

[0077] S3: Based on the conjugate tooth surface equation obtained in S2, the conjugate tooth surface is discretized and projected onto the coordinate system of the spiral bevel gear shaft section using a rotational projection method. Then, combined with the actual tooth surface equation of the pinion obtained in S2, the actual discrete tooth surface corresponding to the conjugate discrete tooth surface is obtained through inverse projection. The rotational projection method is expressed as follows:

[0078]

[0079] In the formula, x 1c ,y 1c ,z 1c r is the position vector of the conjugate tooth surface of the pinion. 1c The components, XL,RL, are the corresponding r components in the axial section coordinate system of the spiral bevel gear. 1c The rotated projected coordinates;

[0080] As attached Figure 3 The attached diagram shows the rotational projection of the conjugate discrete tooth surface of the pinion onto the axial section of the spiral bevel gear, obtained by the analytical method of the present invention. Figure 4 The diagram shows the scatter plot of the conjugate discrete tooth surface of the pinion and the actual discrete tooth surface of the pinion in the pinion coordinate system obtained by the analysis method of the present invention.

[0081] S4: Construct the topology modification model of the spiral bevel gear tooth surface;

[0082] Specifically: Based on the actual discrete tooth surface and conjugate discrete tooth surface of the pinion obtained in S3, the two discrete tooth surfaces are angularly positioned at the midpoint C of the tooth width. The positioning formula is as follows:

[0083]

[0084] In the formula, This represents the Y and Z coordinate components of the actual tooth surface of the pinion at the midpoint C of the tooth width. λ represents the Y and Z coordinate components of the conjugate tooth surface of the pinion at the midpoint C of the tooth width, and λ1 represents the positioning angle of the actual discrete tooth surface of the pinion. 1cThis represents the positioning angle of the conjugate discrete tooth surface of the pinion;

[0085] As attached Figure 5 This diagram illustrates the discrete points of the pinion conjugate tooth surface and the actual tooth surface of the pinion in the pinion coordinate system after angular positioning, obtained by the analysis method of the present invention.

[0086] Then, the normal distance between corresponding points of the discrete tooth surface after angular positioning is calculated to obtain the topological modification model between the actual tooth surface and the conjugate tooth surface;

[0087] Specifically:

[0088] In the formula, θ1 and φ1 represent the small wheel cutter angle and the small wheel rotation angle, which are surface parameters of the small wheel tooth surface; θ2 and φ2 represent the large wheel cutter angle and the large wheel rotation angle, which are surface parameters controlling the conjugate tooth surface of the small wheel; r1 and n1, The position vector equation and normal vector equation represent the actual tooth surface of the pinion before and after angular positioning; r 1c ,n 1c , The position vector equation and normal vector equation represent the conjugate tooth surfaces of the front and rear pinions in angular positioning; M1(λ1), M 1c (λ1) represent the angular positioning transformation matrices of the actual tooth surface of the pinion and the conjugate tooth surface of the pinion, respectively, L1(λ1), L 1c (λ1) represents M1(λ1), M... 1c (λ1) The transformation matrix obtained by removing the last row and one column at the same time, Δδ represents the error between the two tooth surfaces, which is the topological modification model of the small gear tooth surface;

[0089] As attached Figure 6 The diagram shown represents the topological modification model of the arc bevel gear tooth surface obtained by the analysis method of the present invention.

[0090] S5: Based on the meshing equation of the large and small gears, the rotation angle at the midpoint of the tooth width and the tooth surface parameters are used as the initial values ​​for solving the rotation angle range. The tooth tip of the large gear and the tooth tip of the small gear (i.e., the working tooth height) are used as the rotation angle constraint conditions to solve for the initial meshing rotation angle and the meshing rotation angle range of the small gear.

[0091] S6: Combining the meshing equation expressed in S2 with the conjugate tooth surface equation of the pinion, we obtain the contact line equation on the single-parameter conjugate tooth surface of the pinion. Then, starting from the initial engagement angle obtained in S5, we calculate the instantaneous contact line Γ0 of the conjugate tooth surface of the pinion within the angle range. The single-parameter contact line equation of the conjugate tooth surface of the pinion is expressed as:

[0092]

[0093] In the formula, u2 represents the surface parameters, f represents the meshing equation, p represents the functional relationship between the small wheel rotation angle and the large wheel rotation angle, and g represents u2 and θ2, φ obtained from solving the meshing equation. 1c The relationship between φ 1c,i F represents the turning angle position of the i-th small wheel. 0,i This represents the single-parameter function relationship of the instantaneous contact line;

[0094] Starting from the initial turning angle, traverse all turning angles within the entire range to obtain the instantaneous contact line Γ at turning angle position i. 0,i Here, i = 1, ..., n; n represents the number of corner points within the corner range.

[0095] Based on the rotational projection method in S3, the instantaneous contact line Γ of the conjugate tooth surface of the pinion is... 0,i Projected onto the coordinate system of the spiral bevel gear shaft section, and then Γ is projected inversely. 0,i (expression is F) 0,i (θ2) is converted into the instantaneous contact line of the actual tooth surface of the pinion, which corresponds to it. 1,i (expression is F) 1,i (θ1)).

[0096] As attached Figure 7 The diagram shown represents the instantaneous contact line of the conjugate tooth surface of the pinion within the rotation angle range of the spiral bevel gear obtained by the analysis method of the present invention.

[0097] S8: Determine the maximum boundary of the tooth surface contact area based on the topological modification model described in S4 and the contact criteria specified by Gleason.

[0098] Specifically:

[0099] I: Based on the topology modification model in S4, obtain the normal deviation at each discrete point on the tooth surface;

[0100] II: Determine the Δδ at the k-th discrete point of the topologically modified model. k Whether it is equal to the coating thickness (0.00635mm) of the Gleason roller test, all the selected discrete points that meet the conditions are the maximum boundary of the tooth surface contact area.

[0101] S9: Instantaneous contact line Γ obtained from S6 and S7 0,i With Γ 1,i Using the angular positioning pair Γ described in S4 0,i With Γ 1,i Perform angular positioning;

[0102] Specifically:

[0103] In the formula, The equations of the instantaneous contact lines of the conjugate tooth surfaces of the pinion after angular positioning and the equations of the instantaneous contact lines of the actual tooth surfaces of the pinion are respectively represented.

[0104] Then calculate the instantaneous contact line Γ for each group. 0,i With Γ 1,i Geometric deviations between them.

[0105] S10: Based on the geometric deviation between the contact lines calculated in S9, compare each pair of contact lines Γ 0,i With Γ 1,i The minimum geometric deviation is obtained from the geometric deviation between the two, and the contact point position is determined according to the corresponding minimum deviation data position. The contact trace is obtained within the rotation range calculated by S5 and the maximum boundary of S8.

[0106] As attached Figure 8 The diagram shown represents the contact trace of the bevel gear tooth surface obtained by the analysis method of the present invention.

[0107] S11: Based on the geometric deviation between each pair of contact lines calculated in S9, by judging whether the geometric deviation between each pair of contact lines meets the Gleason standard, the actual contact length is determined according to the corresponding data position, and the contact imprint is obtained within the corner range calculated in S5 and the maximum boundary of S8.

[0108] As attached Figure 9 The figure shows the contact imprint diagram of the spiral bevel gear tooth surface obtained by the analysis method of the present invention. It can be seen from the figure that the tooth surface contact imprint conforms to the actual contact imprint shape.

[0109] S12: Based on the minimum geometric deviation at the contact point obtained in S10, and according to the conversion between the minimum geometric deviation and the transmission error, the geometric transmission error is obtained, which is expressed as:

[0110]

[0111] In the formula, Δφ2 represents the geometric transmission error, and Δδ min This indicates the deviation value at the contact point;

[0112] As attached Figure 10 The figure shows the geometric transmission error curve of the spiral bevel gear obtained by the analysis method of the present invention. It can be seen from the figure that the transmission error curve is symmetrical and the gear transmission has good stability.

[0113] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A contact analysis method for spiral bevel gears based on tooth surface topology modification, characterized in that... The specific steps are as follows: Step S100: Based on the basic geometric parameters and machine tool machining parameters of the spiral bevel gear, construct the meshing equation and the conjugate tooth surface equation of the pinion, and then obtain the topological modification model between the actual tooth surface and the conjugate tooth surface of the pinion; the actual tooth surface equation, the conjugate tooth surface equation, and the topological modification model of the pinion are expressed as follows: In the formula, The pinion tool rotation angle and pinion rotation angle are surface parameters of the pinion tooth surface; The large wheel tool rotation angle and the large wheel rotation angle are surface parameters that control the conjugate tooth surface of the small wheel; , , , The position vector equation and normal vector equation represent the actual tooth surface of the pinion before and after angular positioning; , , , The position vector equation and normal vector equation represent the conjugate tooth surfaces of the front and rear pinions in angular positioning; This is expressed as the error between the two tooth surfaces, which is the pinion tooth surface topology modification model; The specific solution process is as follows: S101: Based on the basic geometric parameters of spiral bevel gears and the initial contact parameters required for local synthesis, the machine tool machining parameters are calculated using the local synthesis method to determine the machine tool machining parameters of the working surface; S102: Based on the principle of spiral bevel gear tooth surface generation, and combining the basic geometric parameters of S101 with the machine tool machining parameters, construct the actual tooth surface equations of the large and small gears under the machining parameters; then, based on the definition of the conjugate tooth surface of the small gear that is completely conjugate to the large gear, and combining the actual tooth surface equation of the large gear with the meshing equation, obtain the conjugate tooth surface equation of the small gear. The meshing equation and the conjugate tooth surface equation of the small gear are expressed as follows: In the formula, This indicates the rotation angle of the conjugate tooth surface of the pinion. It is to solve Transition parameters, This indicates the transmission ratio between the large wheel and the small wheel. Representing the coordinate system To coordinate system The transformation matrix, They are respectively and coordinate components, and These are the tooth surface position vector and normal vector of the large wheel in the installation coordinate system, respectively. It is the angle between the shafts of the spiral bevel gear. These are the number of teeth on the pinion and the gear, respectively. S103: Based on the conjugate tooth surface equation of the pinion obtained in S102, the conjugate tooth surface is discretized and projected onto the coordinate system of the spiral bevel gear shaft section using a rotational projection method. Then, combined with the actual tooth surface equation of the pinion obtained in S102, the actual discrete tooth surface corresponding to the conjugate discrete tooth surface is obtained through inverse projection. The rotational projection method is expressed as follows: In the formula, , , Position vector of conjugate tooth surface of pinion The components, XL,RL, are the corresponding components in the coordinate system of the spiral bevel gear shaft section. The rotated projected coordinates; S104: Based on the actual discrete tooth surface and the conjugate discrete tooth surface obtained in S103, locate the midpoint angular direction of the two discrete tooth surfaces, calculate the normal distance between the corresponding points, and obtain the topological modification model between the actual tooth surface and the conjugate tooth surface of the pinion. Step S200: Establish the instantaneous contact line on the conjugate tooth surface of the pinion based on the meshing equation and the pinion conjugate tooth surface equation. Then, through projection and inverse projection, the result is obtained with... One-to-one correspondence of the instantaneous contact line of the actual tooth surface of the pinion ; Step S300: Define the contact area boundary of the tooth surface using the topology modification model, and position the tooth surface using angular positioning angles. and Perform contact alignment; Step S400: Perform distance judgment and contact analysis on the instantaneous contact line after contact alignment to obtain the corresponding contact characteristics: contact trace, contact imprint and transmission error.

2. The contact analysis method for spiral bevel gears based on tooth surface topology modification according to claim 1, characterized in that: The basic geometric parameters include the number of teeth, module, and pressure angle of the spiral bevel gear; the initial contact parameters are the first-order transmission ratio derivative, the major axis of the contact ellipse, and the angle between the contact trace and the gear root cone.

3. The contact analysis method for spiral bevel gears based on tooth surface topology modification according to claim 2, characterized in that: The specific solution process in step S200 is as follows: S201: Based on the meshing equation in S102, the rotation angle at the midpoint of the tooth width and the tooth surface parameters are used as the initial values ​​for solving the rotation angle range. The tooth tips of the large gear and the tooth tips of the small gear are used as rotation angle constraints to solve for the small gear meshing rotation angle range. S202: Combine the meshing equation obtained in S102 with the conjugate tooth surface equation of the pinion to obtain the contact line equation on the single-parameter conjugate tooth surface of the pinion. Then, starting from the initial engagement angle obtained in S201, calculate the instantaneous contact line of the conjugate tooth surface of the pinion within the angle range. The equation for the contact line of the conjugate tooth surface of the single-parameter pinion is expressed as: In the formula, Represents surface parameters. Represents the meshing equation. This represents the functional relationship between the rotation angle of the smaller wheel and the rotation angle of the larger wheel. The expression obtained by solving the meshing equation and The relationship between them This indicates the turning position of the i-th small wheel. This represents the single-parameter function relationship of the instantaneous contact line; S203: Based on the rotational projection method in S103, the instantaneous contact line of the conjugate tooth surface of the pinion is... Projected onto the coordinate system of the spiral bevel gear shaft section, and then projected inversely. Converted into the instantaneous contact line of the actual tooth surface of the pinion, corresponding one-to-one. .

4. The contact analysis method for spiral bevel gears based on tooth surface topology modification according to claim 3, characterized in that: The specific solution process in step S300 is as follows: S301: Determine the maximum boundary of the tooth surface contact area based on the topological modification model and the contact criteria specified by Gleason; S302: Instantaneous contact line obtained from S202 and S203 and Using the angular positioning pair described in S104 and Perform angular positioning, then calculate the corresponding... and Geometric deviations between them.

5. The contact analysis method for spiral bevel gears based on tooth surface topology modification according to claim 3, characterized in that: The specific solution process in step S400 is as follows: S401: Based on the geometric deviation between the contact lines calculated in S302, determine the minimum geometric deviation between each pair of contact lines and the corresponding data position to determine the contact point position, and obtain the contact trace within the small wheel meshing angle range calculated in S201. S402: Based on the geometric deviation between the contact lines calculated in S302, determine the geometric deviation between each pair of contact lines that meets the Gleason standard, and determine the actual contact length based on the corresponding data position. The contact imprint is obtained within the range of the pinion meshing angle calculated in S201. S403: Based on the minimum geometric deviation at the contact point obtained in S401, and combining the conversion between the minimum geometric deviation and the transmission error, the geometric transmission error is obtained, which is expressed as: In the formula, Indicates geometric transmission error. This indicates the deviation value at the contact point.

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