A method, system, storage medium and program product for calculating meshing contact deformation of gear pairs

Abstract

The present invention provides a method, system, storage medium and program product for calculating the meshing contact deformation of a gear pair, and belongs to the field of dynamic analysis of a gear transmission system. The method includes: setting gear model parameters, and establishing a gear model according to the parameters; setting a grid division plan based on the gear model, and establishing a full hexahedron subdivision model; establishing an equation of force and displacement to obtain an overall stiffness matrix; determining the gear contact line, and obtaining the load point information on the gear contact line; sequentially traversing each load point and its next load point, and assembling equations for different situations composed of information of two adjacent load points to obtain a final equation; solving the final equation to obtain the displacement of each node, and using finite element framework interpolation to obtain the normal displacement of each load point to obtain the gear pair meshing contact deformation result. The present invention does not need to perform additional subdivision processing on the grid for the contact load position at a certain moment, thereby simplifying the calculation of gear meshing analysis.

Description

Technical Field

[0001] The present invention relates to the field of dynamic analysis of gear transmission systems, and in particular to a method, system, storage medium and program product for calculating meshing contact deformation of gear pairs. Background Art

[0002] As one of the most common forms of mechanical transmission, gear transmission has been widely used in manufacturing industries such as machinery, electronics, automobiles, and aviation. With the rapid development of mechanical science and manufacturing technology, people have put forward higher requirements for the operating accuracy and quality of mechanical transmission. The excitation of gear meshing stiffness comes from the change of the meshing position of the gear teeth and the number of meshing teeth during the meshing process of the gear pair over time. Even under a constant load, the deformation of the gear teeth will change periodically, that is, the time-varying stiffness will be generated, causing vibration. During the gear meshing process, the determination of the gear meshing stiffness is very important for the quality assurance of the gear transmission. This requires accurate calculation of the elastic deformation of the tooth surface in the meshing area and the normal contact force on the tooth surface at each moment.

[0003] The finite element method (FEM) has proven to be an effective method for solving helical gear mesh contact deformation, offering high computational accuracy. However, for a pre-meshed gear mesh model, the contact line periodically shifts upwards or downwards during the gear meshing process, making it difficult to precisely apply the contact load to the mesh nodes at each moment. This necessitates additional mesh subdivision based on the contact load locations at different moments, complicating the gear mesh analysis calculations.

[0004] Therefore, a calculation method is urgently needed to use a unified calculation process throughout the gear meshing process, without the need to perform additional mesh subdivision processing based on the contact load position at a certain moment. The entire process can be calculated and a fairly accurate result can be obtained, thus simplifying the calculation of gear meshing analysis. Summary of the Invention

[0005] To address the shortcomings of the prior art, the present invention provides a method, system, storage medium, and program product for calculating contact deformation in gear meshing. These methods employ an artificially added load point approach, eliminating the need for overlap between load application points and finite element mesh nodes, allowing calculations to be performed throughout the entire process with highly accurate results. This contact load application method allows for a unified calculation process throughout the gear meshing process, eliminating the need for additional mesh subdivision based on contact load locations at specific moments, thus simplifying the calculations for gear mesh analysis.

[0006] In a first aspect, the present invention provides a method for calculating the meshing contact deformation of a gear pair, comprising the following steps:

[0007] Set the gear model parameters and build the gear model according to the parameters;

[0008] Based on the gear model, set the meshing plan and build a full hexahedron meshing model;

[0009] Establish force and displacement equations based on geometric equations and physical equations in elastic mechanics, derive unit stiffness matrices, and assemble the overall stiffness matrix;

[0010] Determine the gear contact line and obtain the load point information on the gear contact line;

[0011] Traverse each load point and the next load point in sequence, and assemble the right-hand side of the equation according to the different situations of the information of the two adjacent load points to obtain the final equation;

[0012] Boundary conditions are applied to the final equation and solved to obtain the displacement of each node. The normal displacement of each load point is obtained using finite element framework interpolation to obtain the gear pair meshing contact deformation results.

[0013] As a further improvement of the present invention, the gear model parameters include: the gear's tooth top circle radius, tooth root circle radius, tooth width, helix angle, pressure angle, module, number of teeth, material density, elastic modulus, and Poisson's ratio.

[0014] As a further improvement of the present invention, the grid division plan setting method includes:

[0015] According to the gear parameters, set the number of spoke units, set the number of tooth width units, set the number of tooth root fillet units, set the number of tooth shape units, set the number of spoke units in the radial direction, and set the number of tooth top units.

[0016] As a further improvement of the present invention, the load point information includes a (r, h, f) triplet, wherein r is the distance from the load point to the gear rotation axis, h is the distance from the load point to the bottom surface of the gear, and f is the applied force per unit length.

[0017] As a further improvement of the present invention, for different situations where the information of two adjacent load points is formed, the right-hand side terms of the equation are assembled to obtain the final equation, including:

[0018] When two adjacent load points are on the same quadrilateral element surface, the right-hand side of the equation is assembled by directly calculating the line integral;

[0019] When two adjacent load points are on two quadrilateral element surfaces, and these two quadrilateral element surfaces have a common edge, a new load point is constructed on the common edge by interpolation, and line integrals are performed on the two quadrilateral element surfaces with the initial two load points to assemble the right-hand side of the equation;

[0020] When two adjacent load points are on two quadrilateral unit surfaces and these two quadrilateral unit surfaces have only one common vertex, a new load point is constructed on the common vertex by interpolation. This new load point is line integrated with the initial two load points on the two quadrilateral unit surfaces to assemble the right-hand side of the equation.

[0021] As a further improvement of the present invention, the interpolation method is linear interpolation, that is, for the original two load points, the unit length force is f1 and f2, and the unit length force of the new load point on the common edge is f * , suppose the distances between the two load points and the new load point are x1 and x2 respectively, then

[0022] As a further improvement of the present invention, boundary conditions are applied to the final equation and solved to obtain the displacement of each node. The normal displacement of each load point is obtained using finite element framework interpolation to obtain the gear pair meshing contact deformation results, including:

[0023] Take all gear vertices that are one or more times the module away from the calculated meshing tooth position as fixed points, that is, the displacement of these points is zero, apply this boundary condition to the final equation, and solve the equation to obtain the displacement value of each node;

[0024] According to the finite element framework, after obtaining the displacement of all nodes of the hexahedral unit where the load point is located, the displacement of the load point is obtained by interpolation, and the normal displacement of the load point is obtained to obtain the meshing contact deformation result of the gear pair.

[0025] In a second aspect, the present invention provides a computer system comprising a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method described in the first aspect.

[0026] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which implements the steps of the method described in the first aspect when executed by a processor.

[0027] In a fourth aspect, the present invention provides a computer program product, comprising a computer program, which implements the steps of the method described in the first aspect when executed by a processor.

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] This invention employs an artificially added load point approach, eliminating the need for load application points to coincide with finite element mesh nodes. This allows for calculations to be performed throughout the entire process, yielding highly accurate results. This approach to contact load application allows for a unified calculation process throughout the gear meshing process, eliminating the need for additional mesh subdivision based on contact load locations at specific moments, thus simplifying the calculations for gear mesh analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 A flow chart of a method for calculating meshing contact deformation of a gear pair provided in an embodiment of the present invention;

[0031] Figure 2 A diagram of a helical gear model divided into a full hexahedron according to an embodiment of the present invention;

[0032] Figure 3 Schematic diagram of the tooth surface and load points of the helical gear model provided by an embodiment of the present invention;

[0033] Figure 4 A schematic diagram of adjacent load points on the same unit surface provided by an embodiment of the present invention;

[0034] Figure 5 A schematic diagram of adjacent load points on two co-edge element surfaces provided by an embodiment of the present invention;

[0035] Figure 6 A schematic diagram of adjacent load points on two common point unit surfaces provided by an embodiment of the present invention;

[0036] Figure 7 A comparison chart of the contact deformation calculation results of the present invention (left) and the MASTA results (right) on three contact lines at a certain moment. DETAILED DESCRIPTION

[0037] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the present invention will provide a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Among them, steps S100, S200... in the embodiments described in the present invention do not limit the only execution steps of the present invention; the various models described in the present invention are not the only way to limit the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0038] In the present invention, a computer device / equipment / system refers to a computer-related entity, such as hardware, a combination of hardware and software, software, or software in execution. Specifically, for example, software includes, but is not limited to, a process running on a processor, a processor, an object, executable software, an execution thread, a program, and / or a computer. Furthermore, an application or script running on a server, or a server, can also be software. One or more software programs can be in an execution process and / or thread, and software can be localized on a single computer and / or distributed between two or more computers, and can be executed from various computer-readable media.

[0039] The purpose of the present invention is to use a method of artificially adding load points so that the load application points do not need to coincide with the finite element mesh nodes, and the entire process can be calculated and a fairly accurate result can be obtained. Using this method to apply contact loads, a unified calculation process can be used throughout the gear meshing process, eliminating the need to perform additional mesh subdivision processing based on the contact load position at a specific moment, thereby simplifying the calculation of gear mesh analysis. It should be noted that the embodiments and features in the embodiments of this application can be combined with each other unless they conflict.

[0040] In a first aspect, an embodiment of the present invention provides a method for calculating the meshing contact deformation of a gear pair, such as Figure 1 As shown, the specific steps can be as follows:

[0041] S100: setting gear model parameters and establishing a gear model according to the parameters;

[0042] Preferably, the tooth tip circle radius, tooth root circle radius, tooth width, helix angle, pressure angle, module, number of teeth, material density, elastic modulus, and Poisson's ratio of the gear are set.

[0043] In the embodiment of the present invention, a pair of helical gears are used with the following parameters: density 7800kg / m 3 , elastic modulus 207GPa, Poisson's ratio 0.3, the number of teeth of the large wheel is 64, the number of teeth of the small wheel is 15, the module is 2.25mm, the pressure angle is 17.5°, the helix angle is 30°, the small wheel is left-handed and the large wheel is right-handed, the tooth width is 25mm, the tool tooth top height coefficient is 1, the tool tooth root height coefficient is 1.4, the small wheel modification coefficient is 0.7416, the large wheel modification coefficient is 0.4, the small wheel tooth top circle diameter is 46.808mm, the tooth root circle diameter is 36.008mm, the large wheel tooth top circle diameter is 172.577mm, and the tooth root circle diameter is 161.777mm.

[0044] S200: Based on the gear model, set the meshing plan and build a full hexahedron meshing model;

[0045] According to the gear parameters, set the number of spoke units (excluding the spoke circumferential direction of the part connected to the gear), set the number of tooth width units, set the number of tooth root fillet units, set the number of tooth shape units, set the radius (the number of spoke units in the radial direction), and set the number of tooth top units.

[0046] In the embodiment of the present invention, Figure 2 As shown, according to the set gear model parameters and the meshing plan obtained in step S200, a fully hexahedral helical gear model is established.

[0047] S300: Establish force and displacement equations based on geometric equations and physical equations in elastic mechanics, derive unit stiffness matrices, and assemble the overall stiffness matrix;

[0048] S400: Determine the gear contact line and obtain load point information on the gear contact line;

[0049] Extract the tooth surface of a tooth and determine the absolute coordinates of all load points on this tooth surface and their corresponding unit indices. The gear contact line is calculated based on the gear size and involute equation. The data structure of the load point information is generally a triple (r, h, f). Where r is the distance from the load point to the gear axis of rotation, h is the distance from the load point to the bottom surface of the gear, and f is the applied force per unit length.

[0050] In the embodiment of the present invention, Figure 2 In the fully hexahedral helical gear model shown in Figure 3 As shown, the tooth surface of one tooth is extracted, and the absolute coordinates of all load points on this tooth surface and their corresponding unit indexes are determined.

[0051] S500: traverse each load point and its next load point in order, and assemble the right-hand side of the equation according to different situations of the information of two adjacent load points to obtain the final equation;

[0052] Among them, the left-hand side of the final equation is obtained by transforming the overall stiffness matrix combined with the boundary conditions.

[0053] For a given set of load points on a fixed hexahedral meshed gear model, the load points do not necessarily coincide with the mesh nodes. Furthermore, the contact line position constantly changes as a tooth engages and disengages, necessitating a unified framework to address the misalignment between contact and load points.

[0054] Preferably, after obtaining Figure 3 After the load point information on the gear contact line is obtained, the right-hand side of the equation is assembled for different situations formed by the two adjacent load point information to obtain the final equation, including:

[0055] The first case, such as Figure 4 As shown in the figure, when two adjacent load points are on the same quadrilateral element surface, the right-hand side of the equation is assembled by directly calculating the line integral.

[0056] The second case, such as Figure 5 As shown in the figure, when two adjacent load points are on two quadrilateral element surfaces, and there is a common edge between the two quadrilateral element surfaces, a new load point is constructed on the common edge by interpolation, and line integrals are performed on the two quadrilateral element surfaces with the initial two load points to assemble the right-hand side of the equation;

[0057] The interpolation method is linear interpolation, that is, the unit length force of the original two load points is f1 and f2, and the unit length force of the new load point on the common edge is f * , suppose the distances between the two load points and the new load point are x1 and x2 respectively, then

[0058] The third case, such as Figure 6 As shown in the figure, when two adjacent load points are on two quadrilateral unit surfaces, these two quadrilateral unit surfaces have only one common vertex, and a new load point is constructed on the common vertex by interpolation. This new load point is line-integrated with the initial two load points on the two quadrilateral unit surfaces to assemble the right-hand side of the equation. The interpolation method is the same as the second case.

[0059] S600: Apply boundary conditions to the final equation and solve it to obtain the displacement of each node. Use finite element framework interpolation to obtain the normal displacement of each load point and obtain the gear pair meshing contact deformation result.

[0060] Preferably, the step of applying boundary conditions to the final equation and solving it to obtain the displacement of each node, using finite element framework interpolation to obtain the normal displacement of each load point, and obtaining the gear pair meshing contact deformation result includes:

[0061] All gear vertices outside the positions far away from the calculated meshing tooth position (for example, three times the module) are taken as fixed points, that is, the displacement of these points is zero. This boundary condition is applied to the final equation, and the equation is solved to obtain the displacement value of each node; according to the finite element framework, after obtaining the displacement of all nodes of the hexahedral unit where the load point is located, the displacement of the load point can be obtained by interpolation, and the normal displacement of the load point can be obtained to obtain the meshing contact deformation result of the gear pair.

[0062] It should be noted that the embodiments of the present invention are preferred embodiments, and a prerequisite is preferably set here, namely that two adjacent load points must be on at least two adjacent quadrilateral unit faces. The two adjacent quadrilateral unit faces refer to two quadrilateral unit faces that have a common edge or a common vertex. Based on this premise, the above two adjacent load points can only be formed in the three cases in step S500. That is, the three cases in step S500 cover all cases of information formation of two adjacent load points.

[0063] It should be noted that, based on the exemplary technical solutions provided by the embodiments of the present invention, the situations where the positions of two load points are not adjacent and / or the two quadrilateral unit faces are not adjacent also fall within the scope of protection of the present invention. At the same time, all other embodiments obtained by ordinary technicians in this field without creative work fall within the scope of protection of the present invention. For example, regarding the situation where the positions of two load points are not adjacent, they can be converted into two adjacent load point positions and calculated using the technical solution of the present invention; for another example, the situation where two adjacent load points are located on two other quadrilateral unit faces separated by a quadrilateral unit face, and the separated unit faces have common edges with the other two unit faces, at this time, two new load points are constructed on the two common edges by interpolation, forming a situation where the separated unit face has two load points on each of the other two unit faces, and the two load points on each face are used to perform line integrals to assemble the right-hand side of the equation.

[0064] In the embodiment of the present invention, the gear meshing process is divided into 32 time steps, and the right-hand side of the overall equation is assembled at each time step and the normal displacement at the load is calculated.

[0065] After actual testing, such as Figure 7 As shown in the figure, the same gear model and the same load are processed by the software MASTA. During the entire process from engagement to engagement of the entire gear pair, the error between the calculated gear deformation results and the results of the software MASTA is within an average of 3%, ensuring the accuracy of the calculation process.

[0066] In a second aspect, an embodiment of the present invention provides a computer system comprising a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method described in the first aspect.

[0067] In a third aspect, an embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon, which implements the steps of the method described in the first aspect when executed by a processor.

[0068] In a fourth aspect, an embodiment of the present invention provides a computer program product, comprising a computer program, which implements the steps of the method described in the first aspect when executed by a processor.

[0069] This invention employs an artificially added load point approach, eliminating the need for load application points to coincide with finite element mesh nodes. This allows for calculations to be performed throughout the entire process, yielding highly accurate results. This approach to contact load application allows for a unified calculation process throughout the gear meshing process, eliminating the need for additional mesh subdivision based on contact load locations at specific moments, thus simplifying the calculations for gear mesh analysis.

Claims

1. A method for calculating the meshing contact deformation of a gear pair, characterized in that: The following steps are involved: Set the gear model parameters and build the gear model according to the parameters; Based on the gear model, set the meshing plan and build a full hexahedron meshing model; Establish force and displacement equations based on geometric equations and physical equations in elastic mechanics, derive unit stiffness matrices, and assemble the overall stiffness matrix; Determine the gear contact line and obtain the load point information on the gear contact line; Traverse each load point and the next load point in sequence, and assemble the right-hand side of the equation according to the different situations of the information of the two adjacent load points to obtain the final equation, which includes: When two adjacent load points are on the same quadrilateral element surface, the right-hand side of the equation is assembled by directly calculating the line integral; When two adjacent load points are on two quadrilateral element surfaces, and these two quadrilateral element surfaces have a common edge, a new load point is constructed on the common edge by interpolation, and line integrals are performed on the two quadrilateral element surfaces with the initial two load points to assemble the right-hand side of the equation; When two adjacent load points are on two quadrilateral element surfaces and these two quadrilateral element surfaces have only one common vertex, a new load point is constructed on the common vertex by interpolation. This new load point is then line-integrated with the initial two load points on the two quadrilateral element surfaces to assemble the right-hand side of the equation. Boundary conditions are applied to the final equation and solved to obtain the displacement of each node. The normal displacement of each load point is obtained using finite element framework interpolation to obtain the gear pair meshing contact deformation results.

2. The method for calculating gear pair meshing contact deformation according to claim 1, characterized in that: The gear model parameters include: the gear's tooth tip circle radius, tooth root circle radius, tooth width, helix angle, pressure angle, module, number of teeth, material density, elastic modulus, and Poisson's ratio.

3. The method for calculating the meshing contact deformation of a gear pair according to claim 1, characterized in that: The grid division plan setting method includes: According to the gear parameters, set the number of spoke units, set the number of tooth width units, set the number of tooth root fillet units, set the number of tooth shape units, set the number of spoke units in the radial direction, and set the number of tooth top units.

4. The method for calculating gear pair meshing contact deformation according to claim 1, characterized in that: The load point information includes a (r, h, f) triplet, where r is the distance from the load point to the gear rotation axis, h is the distance from the load point to the bottom surface of the gear, and f is the applied force per unit length.

5. The method for calculating gear pair meshing contact deformation according to claim 1, characterized in that: The interpolation method is linear interpolation, that is, the force per unit length of the original two load points is and , the force per unit length of the new load point on the common edge is , suppose the distances between the two load points and the new load point are and ,So .

6. The method for calculating gear pair meshing contact deformation according to claim 1, characterized in that: The boundary conditions are applied to the final equation and solved to obtain the displacement of each node. The normal displacement of each load point is obtained using the finite element framework interpolation to obtain the gear pair meshing contact deformation results, including: Take all gear vertices that are one or more times the module away from the calculated meshing tooth position as fixed points, that is, the displacement of these points is zero, apply this boundary condition to the final equation, and solve the equation to obtain the displacement value of each node; According to the finite element framework, after obtaining the displacement of all nodes of the hexahedral unit where the load point is located, the displacement of the load point is obtained by interpolation, and the normal displacement of the load point is obtained to obtain the meshing contact deformation result of the gear pair.

7. A computer system comprising a memory, a processor, and a computer program stored in the memory, wherein: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

9. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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