Gear tooth direction modification method, system and equipment and medium

Abstract

The invention provides a gear tooth direction modification method, system and device and a medium, and belongs to the technical field of mechanical gear design, and the method comprises the following steps: constructing a tooth direction modification amount mathematical model and a meshing stiffness change rate mathematical model of a gear; constructing a self-adaptive function of gear tooth direction modification according to the tooth direction modification quantity mathematical model and the meshing stiffness change rate mathematical model; and taking the tooth direction modification quantity as particles of a particle swarm algorithm, performing iterative optimization on the adaptive function by using the particle swarm algorithm, searching a globally optimal solution of the particles, and if no globally optimal solution exists, performing target optimization on the adaptive function after iterative optimization by using a cosine annealing algorithm to obtain the optimal solution of the particles, and carrying out tooth modification on the gear according to the optimal solution. According to the method, target optimization is carried out on the constructed adaptive function by combining the global search capability of the particle swarm algorithm and the cosine annealing algorithm, and the optimal solution of the tooth modification amount can be efficiently searched in a complex solution space.

Description

Technical Field

[0001] The invention belongs to the technical field of mechanical gear design, and in particular relates to a gear tooth modification method, system, equipment and medium. Background Art

[0002] Gear transmission is an important field in mechanical engineering and is widely used in various mechanical equipment. However, gears often face problems such as noise, vibration, stress concentration, etc. during operation, which may lead to reduced performance, shortened life, and even failure of gears. In order to solve these problems, engineers have developed tooth profile modification technology. Tooth profile modification is a method to optimize gear performance by changing the geometry of the gear tooth surface. Appropriate tooth profile modification can improve the contact stress distribution of the gear, reduce noise and vibration, and improve transmission efficiency and gear life.

[0003] At present, traditional tooth modification methods are often based on experience or simplified theoretical models. These methods often find it difficult to find the optimal modification parameters under complex working conditions, resulting in low tooth modification accuracy. Summary of the invention

[0004] In order to overcome the above-mentioned shortcoming of low tooth profile modification accuracy, the present invention provides a gear tooth profile modification method, comprising the following steps:

[0005] Acquire relevant parameters of gear meshing, construct a gear tooth profile modification mathematical model and a meshing stiffness change rate mathematical model according to the relevant parameters, and construct an adaptive function of gear tooth profile modification according to the gear tooth profile modification mathematical model and the meshing stiffness change rate mathematical model;

[0006] The tooth modification amount is used as the particle of the particle swarm algorithm, and the adaptive function is iteratively optimized using the particle swarm algorithm to find the global optimal solution of the particles. If there is no global optimal solution, the cosine annealing algorithm is used to perform target optimization again on the iteratively optimized adaptive function to obtain the optimal solution of the particles, and the gear tooth modification is performed according to the optimal solution.

[0007] Preferably, the method for constructing the mathematical model of the tooth modification amount is specifically: obtaining the drum amount, helix angle, tooth surface width and tooth line length of the gear tooth modification, taking the tooth line length as the horizontal coordinate and the tooth surface width as the vertical coordinate, and constructing the mathematical model of the tooth modification amount in combination with the drum amount and helix angle.

[0008] Preferably, the method for constructing the mathematical model of meshing stiffness change rate is specifically: obtaining the meshing stiffness and meshing angle of the gear, and constructing the mathematical model of meshing stiffness change rate according to the meshing stiffness, meshing angle and the mathematical model of tooth modification amount.

[0009] Preferably, the method for constructing the adaptive function of the gear tooth modification is specifically as follows: obtaining the contact stress of the gear tooth modification, the weight coefficient of the contact stress and the weight coefficient of the meshing stiffness change rate, and constructing an adaptive function based on the contact stress, the weight coefficient of the contact stress and the weight coefficient of the meshing stiffness change rate.

[0010] Preferably, the method of iteratively optimizing the adaptive function using a particle swarm algorithm to find a global optimal solution of particles comprises the following steps:

[0011] A group of particles are randomly generated, each particle represents a specific tooth modification amount;

[0012] The initial value of the tooth modification amount is obtained according to the mathematical model of the tooth modification amount, the initial position and speed of each particle are set according to the initial value, the adaptive function is used as the target optimization function, the fitness value of each particle is calculated, the speed and position of each particle are updated according to the fitness value, and the global optimal solution of the particle is obtained.

[0013] Preferably, the adaptive function is specifically:

[0014] F=w1(1 / σ)+w2(1 / |dK / dθ|);

[0015] Among them, w1 and w2 are weight coefficients, σ ​​is the contact stress of tooth modification, and dK / dθ is the change rate of meshing stiffness.

[0016] The present invention also provides a gear tooth profile modification system, comprising:

[0017] An adaptive function construction module is used to obtain relevant parameters of gear meshing, construct a mathematical model of gear tooth profile modification and a mathematical model of meshing stiffness change rate according to the relevant parameters, and construct an adaptive function of gear tooth profile modification according to the mathematical model of tooth profile modification and the mathematical model of meshing stiffness change rate;

[0018] The tooth profile modification module is used to use the tooth profile modification amount as the particle of the particle swarm algorithm, and use the particle swarm algorithm to iteratively optimize the adaptive function to find the global optimal solution of the particles. If there is no global optimal solution, the cosine annealing algorithm is used to perform target optimization again on the iteratively optimized adaptive function to obtain the optimal solution of the particles, and the gear tooth profile is modified according to the optimal solution.

[0019] The present invention also provides a computer device, comprising a memory and a processor; the memory stores a computer program, and the processor is used to run the computer program in the memory to execute the gear tooth modification method.

[0020] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and the computer program is suitable for being loaded by a processor to execute the gear tooth profile modification method.

[0021] The gear tooth modification method, system, equipment and medium provided by the present invention have the following beneficial effects:

[0022] The present invention can construct a mathematical model of the gear tooth profile modification amount and a mathematical model of the meshing stiffness change rate according to the gear meshing related parameters, and construct an adaptive function of the gear tooth profile modification according to the mathematical model of the tooth profile modification amount and the mathematical model of the meshing stiffness change rate. The adaptive function can adjust the weight coefficients of the gear meshing related parameters according to the actual situation, so as to output the tooth profile modification amount under specific conditions, and can be applicable to various working conditions; by combining the particle swarm algorithm and the cosine annealing algorithm to perform target optimization on the constructed adaptive function, the optimal solution of the tooth profile modification amount can be efficiently found in the complex solution space, so as to obtain the tooth profile modification amount with higher accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the embodiment of the present invention and its design scheme, the following briefly introduces the drawings required for this embodiment. The drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0024] Figure 1 Flow chart of a gear tooth modification method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0025] In order to enable those skilled in the art to better understand the technical solution of the present invention and implement it, the present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the scope of protection of the present invention.

[0026] In the description of the present invention, it is to be understood that the terms “center”, “longitudinal”, “lateral”, “length”, “width”, “thickness”, “up”, “down”, “front”, “back”, “left”, “right”, “vertical”, “horizontal”, “top”, “bottom”, “inside”, “outside”, “axial”, “radial”, “circumferential”, etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing the technical solutions of the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0027] In addition, the terms "first", "second", etc. are used for descriptive purposes only and are not to be understood as indicating or implying relative importance. In the description of the present invention, it should be noted that, unless otherwise clearly specified or limited, the terms "connected" and "connected" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to the specific circumstances. In the description of the present invention, unless otherwise specified, "plurality" means two or more, which will not be described in detail here.

[0028] Example

[0029] The present invention provides a gear tooth modification method, specifically as follows Figure 1 As shown, the following steps are included:

[0030] Step 1: Obtain relevant parameters of gear meshing, construct a gear tooth profile modification mathematical model and a meshing stiffness change rate mathematical model based on the relevant parameters, and construct an adaptive function of gear tooth profile modification based on the tooth profile modification mathematical model and the meshing stiffness change rate mathematical model. The specific process is as follows:

[0031] (1) Construct a mathematical model of tooth modification.

[0032] The method for constructing the mathematical model of tooth profile modification is as follows: extract the basic parameters of the meshing gear pair, such as the crowning amount, helix angle, tooth surface width and tooth line length of the gear tooth profile modification, perform mathematical modeling of the tooth profile development diagram, and establish the mathematical model of the local tooth profile modification by defining the abscissa (tooth line length direction) and ordinate (tooth surface width direction) on the measuring cylindrical development plane, as follows:

[0033]

[0034] In the formula, δ a is the crowning amount of the tooth modification, β is the helix angle, b is the tooth width, l is the tooth line length, and s is the tooth modification amount.

[0035] (2) Construct a mathematical model of the meshing stiffness change rate.

[0036] The method for constructing the mathematical model of meshing stiffness change rate is as follows: obtaining the meshing stiffness and meshing angle of the gear, and constructing the mathematical model of meshing stiffness change rate according to the mathematical models of meshing stiffness, meshing angle and tooth modification amount. The obtained mathematical model of meshing stiffness change rate is as follows:

[0037]

[0038] Where K is the meshing stiffness, θ is the meshing angle, and f(s) is the function of the local tooth surface tooth modification amount.

[0039] (3) Construct an adaptive function for gear tooth modification.

[0040] Specifically, the contact stress of gear tooth modification, the weight coefficient of contact stress and the weight coefficient of meshing stiffness change rate are obtained, and an adaptive function is constructed according to the contact stress, the weight coefficient of contact stress and the weight coefficient of meshing stiffness change rate. The obtained adaptive function is as follows:

[0041] F=w1(1 / σ)+w2(1 / |dK / dθ|);

[0042] Among them, w1 and w2 are weight coefficients, σ ​​is the contact stress of tooth modification, and dK / dθ is the change rate of meshing stiffness.

[0043] Step 2: Use the tooth modification amount as the particle of the particle swarm algorithm, use the particle swarm algorithm to iteratively optimize the adaptive function, and find the global optimal solution of the particle. If there is no global optimal solution, use the cosine annealing algorithm to perform target optimization again on the iteratively optimized adaptive function to obtain the optimal solution of the particle, and perform tooth modification on the gear according to the optimal solution. The specific process is as follows:

[0044] A group of particles are randomly generated, each particle represents a possible solution, that is, a specific tooth modification amount. The initial value of the tooth modification amount is obtained according to the mathematical model of the tooth modification amount, and each particle is set to have an initial position and speed according to the initial value. The adaptive function is used as the target optimization function to calculate the fitness value F of each particle, update the individual optimal position (pbest) and global optimal position (gbest) of each particle, and update the speed and position of each particle.

[0045] The speed update formula is as follows:

[0046] v i+1 =wv i +c1r1*(pbest-x i )+c2r2*(gbest-x i );

[0047] The position update formula is as follows:

[0048] x i+1 =x i +v i+1 ;

[0049] Where w is the inertia weight, c1 and c2 are acceleration constants, r1 and r2 are random numbers, and v i is the speed before update, v i+1is the updated speed, x i is the position before update, x i+1 is the updated position.

[0050] If the global optimal solution is not obtained after multiple iterations of optimization, the cosine annealing algorithm is used to decay the acceleration constant and then update the parameters to perform target optimization again to prevent the iteration from stopping after the local optimal solution is obtained. The specific method is as follows:

[0051]

[0052] In the formula, and are the lower and upper limits of the acceleration constant respectively; T cur is the number of epochs that have been completed; T is the total number of epochs in the experiment.

[0053] When F reaches the global minimum, the iteration stops and the tooth modification amount s at this time is the output solution.

[0054] The present invention also provides a gear tooth profile modification system, comprising:

[0055] An adaptive function construction module is used to obtain relevant parameters of gear meshing, construct a mathematical model of gear tooth profile modification and a mathematical model of meshing stiffness change rate according to the relevant parameters, and construct an adaptive function of gear tooth profile modification according to the mathematical model of tooth profile modification and the mathematical model of meshing stiffness change rate;

[0056] The tooth profile modification module is used to use the tooth profile modification amount as the particle of the particle swarm algorithm, and use the particle swarm algorithm to iteratively optimize the adaptive function to find the global optimal solution of the particles. If there is no global optimal solution, the cosine annealing algorithm is used to perform target optimization again on the iteratively optimized adaptive function to obtain the optimal solution of the particles, and the gear tooth profile is modified according to the optimal solution.

[0057] The present invention also provides a computer device, comprising a memory and a processor; the memory stores a computer program, and the processor is used to run the computer program in the memory to execute the gear tooth modification method.

[0058] The present invention also provides a computer-readable storage medium, which stores a computer program. The computer program is suitable for being loaded by a processor to execute the gear tooth profile modification method.

[0059] The embodiments described above are only preferred specific implementation modes of the present invention, and the protection scope of the present invention is not limited thereto. Any simple changes or equivalent replacements of the technical solutions that can be obviously obtained by any technician familiar with the field within the technical scope disclosed in the present invention belong to the protection scope of the present invention.

Claims

1. A gear tooth modification method, characterized in that: The steps include: Acquire relevant parameters of gear meshing, construct a gear tooth profile modification mathematical model and a meshing stiffness change rate mathematical model according to the relevant parameters, and construct an adaptive function of gear tooth profile modification according to the gear tooth profile modification mathematical model and the meshing stiffness change rate mathematical model; The tooth modification amount is used as the particle of the particle swarm algorithm, and the adaptive function is iteratively optimized using the particle swarm algorithm to find the global optimal solution of the particles. If there is no global optimal solution, the cosine annealing algorithm is used to perform target optimization again on the iteratively optimized adaptive function to obtain the optimal solution of the particles, and the gear tooth modification is performed according to the optimal solution.

2. The gear tooth modification method according to claim 1, characterized in that: The method for constructing the mathematical model of the tooth profile modification is specifically as follows: obtaining the crowning amount, helix angle, tooth surface width and tooth line length of the gear tooth profile modification, taking the tooth line length as the horizontal coordinate and the tooth surface width as the vertical coordinate, and constructing the mathematical model of the tooth profile modification in combination with the crowning amount and the helix angle.

3. The gear tooth modification method according to claim 2, characterized in that: The method for constructing the meshing stiffness change rate mathematical model is specifically as follows: obtaining the meshing stiffness and meshing angle of the gear, and constructing the meshing stiffness change rate mathematical model according to the meshing stiffness, meshing angle and the tooth profile modification amount mathematical model.

4. The gear tooth modification method according to claim 1, characterized in that: The method for constructing the adaptive function of the gear tooth modification is specifically as follows: obtaining the contact stress of the gear tooth modification, the weight coefficient of the contact stress and the weight coefficient of the meshing stiffness change rate, and constructing an adaptive function according to the contact stress, the weight coefficient of the contact stress and the weight coefficient of the meshing stiffness change rate.

5. The gear tooth modification method according to claim 1, characterized in that: The particle swarm algorithm is used to iteratively optimize the adaptive function to find the global optimal solution of particles, including the following steps: A group of particles are randomly generated, each particle represents a specific tooth modification amount; The initial value of the tooth modification amount is obtained according to the mathematical model of the tooth modification amount, the initial position and speed of each particle are set according to the initial value, the adaptive function is used as the target optimization function, the fitness value of each particle is calculated, the speed and position of each particle are updated according to the fitness value, and the global optimal solution of the particle is obtained.

6. The gear tooth modification method according to claim 1, characterized in that: The adaptive function is specifically: F=w1(1 / σ)+w2(1 / |dK / dθ|), Among them, w1 and w2 are weight coefficients, σ ​​is the contact stress of tooth modification, and dK / dθ is the change rate of meshing stiffness.

7. A gear tooth modification system, characterized in that: include: An adaptive function construction module is used to obtain relevant parameters of gear meshing, construct a mathematical model of gear tooth profile modification and a mathematical model of meshing stiffness change rate according to the relevant parameters, and construct an adaptive function of gear tooth profile modification according to the mathematical model of tooth profile modification and the mathematical model of meshing stiffness change rate; The tooth profile modification module is used to use the tooth profile modification amount as the particle of the particle swarm algorithm, and use the particle swarm algorithm to iteratively optimize the adaptive function to find the global optimal solution of the particles. If there is no global optimal solution, the cosine annealing algorithm is used to perform target optimization again on the iteratively optimized adaptive function to obtain the optimal solution of the particles, and the gear tooth profile is modified according to the optimal solution.

8. A computer device, characterized in that: It comprises a memory and a processor; the memory stores a computer program, and the processor is used to run the computer program in the memory to execute the gear tooth modification method according to any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and the computer program is suitable for being loaded by a processor to execute the gear tooth modification method according to any one of claims 1 to 6.

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