Bevel gear power closed transmission system rapid loading vibration suppression method based on adaptive particle swarm optimization

Abstract

The invention discloses a bevel gear power closed transmission system rapid loading vibration suppression method based on adaptive particle swarm optimization, and belongs to the field of gear transmission system loading test method optimization. The problem that violent vibration is generated in the rapid loading test process of an existing bevel gear power closed transmission system is solved. According to the method, a kinetic equation of a bevel gear system under closed power is established by utilizing structural parameters of a bevel gear closed power transmission system, and a rotating speed-torque-vibration mapping model is constructed by utilizing the kinetic equation and combining historical operation data and quantitative vibration and load relations; based on the given rising rate of the bevel gear and the allowable maximum vibration amplitude, a double-target self-adaption function is constructed in combination with a rotating speed-torque-vibration mapping model; the loading torque of the bevel gear transmission system is used as an input variable of the adaptive particle swarm optimization algorithm; and iterating the particle position and speed to obtain the optimal parameter of the loading torque of the bevel gear transmission system. The method is mainly used for vibration suppression of a bevel gear power closed transmission system.

Description

Technical Field

[0001] This invention belongs to the field of optimization of loading test methods for gear transmission systems. Background Technology

[0002] Bevel gear transmission systems have wide applications in power units, power systems, and industrial production. To ensure the performance of bevel gears, they need to undergo no-load and loaded tests for verification. In the testing of bevel gear transmission systems, rapid and stable loading to the target operating condition is a core requirement. The bevel gear power closed transmission system is a highly efficient mechanical transmission device that achieves energy circulation and transfer through a closed structure. It is widely used in high-precision, high-load testing and industrial scenarios. This system combines the spatial transmission advantages of bevel gears with the high efficiency of power closed systems, and is an important branch of gear transmission technology.

[0003] However, during testing of bevel gear power closed transmission systems, severe vibrations often occur due to excessive acceleration rates and excessively high loading torques. This leads to unstable system output speeds, failing to meet the coordinated loading test conditions for the power closed transmission system. Consequently, the bevel gears within the system face complex dynamic loads and failure risks, potentially resulting in gear wear, breakage, and system malfunctions. Current gear loading methods primarily involve initially applying no load, increasing the speed to the rated speed, and then applying the rated torque, or initially applying the rated torque and then decreasing the load as the speed increases. In actual testing, this often results in excessive vibrations due to the real-time mismatch between speed and load. Therefore, while ensuring the gear acceleration rate, it is necessary to optimize the loading method of the bevel gear transmission system to minimize vibration and ensure smooth operation during the acceleration process, thereby guaranteeing that the bevel gear transmission system quickly reaches the test conditions.

[0004] Currently, numerous research teams have conducted extensive studies on optimizing rapid loading test methods for gear transmission systems. Most existing methods and systems focus on developing gear loading test methods and apparatus, primarily using additional mechanical devices and empirically adjusting the additional load on the gear transmission system, with limited attention paid to test optimization algorithms addressing the transmission's inherent motion characteristics. However, some intelligent algorithms for optimizing gear transmission system loading cannot solve the problem of severe vibrations caused by rapid loading. Summary of the Invention

[0005] This invention aims to solve the problem of severe vibration generated during rapid loading tests in existing bevel gear power enclosed transmission systems. It provides a rapid loading vibration suppression method for bevel gear power enclosed transmission systems based on adaptive particle swarm optimization.

[0006] The rapid loading vibration suppression method for bevel gear power closed transmission system based on adaptive particle swarm optimization described in this invention includes:

[0007] Step 1: Using the structural parameters of the bevel gear enclosed power transmission system, establish the dynamic equation of the bevel gear system under power enclosure. Using the dynamic equation and historical operating data, quantify the relationship between vibration and load, and construct a speed-torque-vibration mapping model.

[0008] Step 2: Based on the given rate of increase and maximum allowable vibration amplitude of the bevel gear, and combined with the speed-torque-vibration mapping model, construct a dual-objective adaptive degree function. ;

[0009] Step 3: The loading torque of the bevel gear transmission system is used as the input variable of the adaptive particle swarm optimization algorithm; a set of particles is randomly generated, each particle having a position and velocity representing the loading torque parameter; the particle swarm is initialized.

[0010] Step 4: Utilize the bi-objective adaptive degree function The fitness value of each particle is calculated, and the optimal position of each particle is updated using the fitness value. The global optimal particle of the particle swarm is updated by combining the Stackelberg game model.

[0011] Step 5: Each particle adjusts its velocity and position based on the current global optimal particle position, and determines whether the current particle iteration meets the iteration termination condition. If so, the current global optimal particle position and velocity are used as the optimal parameters for loading torque in the bevel gear transmission system. Otherwise, the fitness value of each particle is calculated, and the process returns to step 4.

[0012] Furthermore, in step one of this invention, the dynamic equations of the bevel gear system under power closure are established using the structural parameters of the bevel gear closed power transmission system:

[0013]

[0014] In the formula, M is the mass of the bevel gear; q is the generalized displacement vector, which can be expressed in angular displacement or linear displacement form. The angular displacement form is... The linear displacement form is C is the damping matrix; K(t) is the time-varying stiffness matrix; External load force; Floss is the nonlinear meshing force loss; For dynamic meshing force; This represents the relative displacement. err represents the relative meshing error. Let q represent the first derivative of the generalized displacement vector with respect to time, and let q represent the generalized velocity vector. It is the second derivative of the generalized displacement vector q with respect to time, and represents the generalized acceleration vector. This represents a nonlinear function describing the geometric relationship or displacement-force transmission relationship of a gear pair. This represents the coefficient of friction between the gear teeth. This indicates the sliding speed between the meshing tooth surfaces of the gears. Indicates the angular velocity of the gear. The nonlinear quantization function representing the friction coefficient, sliding velocity, and angular velocity during gear meshing. The function represents the loss of meshing force, and c represents the meshing damping coefficient at the meshing interface of the gear pair.

[0015] Furthermore, in this invention, in step two, a dual-objective adaptive function is constructed. for:

[0016]

[0017] in, and To optimize function weights, they are adaptively adjusted based on operating conditions; The vibration amplitude of the transmission system; The maximum permissible vibration amplitude; The theoretically optimal loading torque; For loading torque; The maximum allowable load torque;

[0018] vibration amplitude satisfy:

[0019]

[0020] in, Given the bevel gear lifting rate; For loading torque; Here is the stiffness matrix. For the damping ratio, This represents a nonlinear relational function.

[0021] Furthermore, in this invention, the process of initializing the particle swarm in step three is as follows:

[0022] Step 3: Randomly generate N particles, each with a randomly generated initial position in D-dimensional space. and speed ;

[0023] Step 3.2: Set the initial optimal position for each individual. , Global optimal position ;

[0024] Step 3: Set the maximum number of iterations T0 and adjust the parameters adaptively.

[0025] Furthermore, in this invention, the method for updating the optimal position of each particle and the optimal position of the particle swarm in step four is as follows:

[0026] Compare the current fitness value of each particle with its historical best fitness value. If the current fitness value is better, then the current fitness value is taken as the best fitness value, and the particle position corresponding to that fitness value is taken as the best position. At the same time, compare the current best fitness value of each particle with the global best position g. best The corresponding fitness values ​​are compared, and the top 10% of particles with the highest fitness values ​​are selected as candidate particles. These candidate particles are then substituted into a Stackelberg game model to obtain the robustness of the particles. The position of the particle with the best robustness is determined as the new global optimum. .

[0027] Furthermore, in this invention, in step four, the optimal position of each particle is updated using the Metropolis criterion. If:

[0028]

[0029] Then the position of the particle is updated, where, To simulate the annealing temperature coefficient, The particle's historical best fitness value This represents the fitness value of the particle's current position. Indicates the fitness difference. This represents the fitness difference threshold; the specific data is determined based on actual needs.

[0030] Furthermore, in this invention, in step five, the formula for each particle to adjust its own velocity and position based on the current globally optimal particle position is as follows:

[0031]

[0032]

[0033] in, This represents the velocity of particle i. Indicates the position of particle i. The learning factor is dynamically adjusted based on population diversity. It is a random number. This represents the optimal position of particle i in the current iteration during the entire population optimization process. The learning factor represents the optimal position of particle i in the current iteration during its optimization process, k represents the current iteration number, and k represents the learning factor. The expression is:

[0034]

[0035] This indicates the maximum number of iterations.

[0036] Furthermore, in this invention, in step five, the iteration termination condition is that the current iteration number reaches the maximum iteration number or the rate of change of the fitness function value is within the threshold range.

[0037] Furthermore, in this invention, the formula for the rate of change of the fitness function value within the threshold range is:

[0038]

[0039] in, Let be the fitness function corresponding to a certain position globally. The fitness function corresponding to another position globally. This represents the threshold range for the rate of change of the fitness function value.

[0040] The method described in this invention directly optimizes the torque parameters of a bevel gear power closed transmission system, directly reducing system vibration, eliminating the need for vibration damping devices, and lowering testing difficulty and cost. Verification using this method shows that the vibration acceleration amplitude can be controlled within 0.3g, an additional 15–35% reduction compared to the damper method. The torque optimization response time is <100ms, meeting the requirements for rapid loading (traditional methods >500ms); furthermore, this method can be directly integrated into the existing closed test bench electrical control system; it adapts to variable speed and load conditions, avoiding gear fatigue damage. Attached Figure Description

[0041] Figure 1 This is a flowchart of the method described in this invention;

[0042] Figure 2 Schematic diagram of a bevel gear power closed transmission system architecture;

[0043] Figure 3 The flowchart shows the adaptive particle swarm optimization algorithm during its implementation. Detailed Implementation

[0044] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0045] Specific implementation method one: Refer to Figure 1 This embodiment specifically describes the rapid loading vibration suppression method for a bevel gear power closed transmission system based on adaptive particle swarm optimization, which includes:

[0046] Step 1: Using the structural parameters of the bevel gear enclosed power transmission system, establish the dynamic equation of the bevel gear system under power enclosure. Using the dynamic equation and historical operating data, quantify the relationship between vibration and load, and construct a speed-torque-vibration mapping model.

[0047] Step 2: Based on the given rate of increase and maximum allowable vibration amplitude of the bevel gear, and combined with the speed-torque-vibration mapping model, construct a dual-objective adaptive degree function. ;

[0048] Step 3: The loading torque of the bevel gear transmission system is used as the input variable of the adaptive particle swarm optimization algorithm; a set of particles is randomly generated, each particle having a position and velocity representing the loading torque parameter; the particle swarm is initialized.

[0049] Step 4: Utilize the bi-objective adaptive degree function The fitness value of each particle is calculated, and the optimal position of each particle is updated using the fitness value. The global optimal particle of the particle swarm is updated by combining the Stackelberg game model.

[0050] Step 5: Each particle adjusts its velocity and position based on the current global optimal particle position, and determines whether the current particle iteration meets the iteration termination condition. If so, the current global optimal particle position and velocity are used as the optimal parameters for loading torque in the bevel gear transmission system. Otherwise, the fitness value of each particle is calculated, and the process returns to step 4.

[0051] Furthermore, in step one of this invention, the dynamic equations of the bevel gear system under power closure are established using the structural parameters of the bevel gear closed power transmission system:

[0052]

[0053] In the formula, M is the mass of the bevel gear; q is the generalized displacement vector, which can be expressed in angular displacement or linear displacement form. The angular displacement form is... The linear displacement form is C is the damping matrix; K(t) is the time-varying stiffness matrix; For external load force; F loss This represents a nonlinear meshing force loss. For dynamic meshing force; Here, 'err' represents the relative displacement, and 'err' represents the relative meshing error. Let q represent the first derivative of the generalized displacement vector with respect to time, and let q represent the generalized velocity vector. It is the second derivative of the generalized displacement vector q with respect to time, and represents the generalized acceleration vector. This represents a nonlinear function describing the geometric relationship or displacement-force transmission relationship of a gear pair. This represents the coefficient of friction between the gear teeth. This indicates the sliding speed between the meshing tooth surfaces of the gears. Indicates the angular velocity of the gear. The nonlinear quantization function representing the friction coefficient, sliding velocity, and angular velocity during gear meshing. The function represents the loss of meshing force, and c represents the meshing damping coefficient at the meshing interface of the gear pair.

[0054] Furthermore, in this invention, in step two, a dual-objective adaptive function is constructed. for:

[0055]

[0056] in, and To optimize function weights, they are adaptively adjusted based on operating conditions; The vibration amplitude of the transmission system; The maximum permissible vibration amplitude; The theoretically optimal loading torque; For loading torque; The maximum allowable load torque;

[0057] vibration amplitude satisfy:

[0058]

[0059] in, Given the bevel gear lifting rate; For loading torque; Here is the stiffness matrix. For the damping ratio, This represents a nonlinear relational function.

[0060] Furthermore, in this invention, the process of initializing the particle swarm in step three is as follows:

[0061] Step 3: Randomly generate N particles, each with a randomly generated initial position in D-dimensional space. and speed ;

[0062] Step 3.2: Set the initial optimal position for each individual. , Global optimal position ;

[0063] Step 3: Set the maximum number of iterations T0 and adjust the parameters adaptively.

[0064] Furthermore, in this invention, the method for updating the optimal position of each particle and the optimal position of the particle swarm in step four is as follows:

[0065] Compare the current fitness value of each particle with its historical best fitness value. If the current fitness value is better, then the current fitness value is taken as the best fitness value, and the particle position corresponding to that fitness value is taken as the best position. At the same time, compare the current best fitness value of each particle with the global best position g. best The corresponding fitness values ​​are compared, and the top 10% of particles with the highest fitness values ​​are selected as candidate particles. These candidate particles are then substituted into the Stackelberg game model to obtain the robustness of the particles. The position of the particle with the best robustness is determined as the new global optimum. .

[0066] Furthermore, in this invention, in step four, the optimal position of each particle is updated using the Metropolis criterion. If:

[0067]

[0068] Then the position of the particle is updated, where, To simulate the annealing temperature coefficient, The particle's historical best fitness value This represents the fitness value of the particle's current position. This represents the fitness difference, and rand() represents the fitness difference threshold. The specific data should be determined according to actual needs.

[0069] Furthermore, in this invention, in step five, the formula for each particle to adjust its own velocity and position based on the current globally optimal particle position is as follows:

[0070]

[0071]

[0072] in, This represents the velocity of particle i. Indicates the position of particle i. The learning factor is dynamically adjusted based on population diversity. It is a random number. This represents the optimal position of particle i in the current iteration during the entire population optimization process. The learning factor represents the optimal position of particle i in the current iteration during its optimization process, k represents the current iteration number, and k represents the learning factor. The expression is:

[0073]

[0074] This indicates the maximum number of iterations.

[0075] Furthermore, in this invention, in step five, the iteration termination condition is that the current iteration number reaches the maximum iteration number or the rate of change of the fitness function value is within the threshold range.

[0076] Furthermore, in this invention, the formula for the rate of change of the fitness function value within the threshold range is:

[0077]

[0078] in, Let be the fitness function corresponding to a certain position globally. The fitness function corresponding to another position globally. This represents the threshold range for the rate of change of the fitness function value.

[0079] This invention provides a rapid loading vibration suppression method for a bevel gear power enclosed transmission system based on adaptive particle swarm optimization. Specifically, it utilizes the optimization function of the adaptive particle swarm algorithm, combined with the rotational speed and vibration amplitude of the bevel gears in the bevel gear power enclosed transmission system, to optimize the loading torque input to the system, thereby controlling the vibration amplitude within a defined range. The architecture of the bevel gear power enclosed transmission system involved in this invention is as follows: Figure 1 As shown, it includes components such as: test object bevel gear, power closed bevel gear, rotating shaft, power loss compensation motor, torque loader, etc.

[0080] The specific algorithm flow is as follows: Figure 2 As shown, the specific steps are as follows:

[0081] Step 1: Establishment of the bevel gear enclosed power transmission system model. Establish the dynamic equations of the bevel gear system under power enclosure, quantify the relationship between vibration and load, and construct a speed-torque-vibration mapping model;

[0082] The dynamic equations of the bevel gear system under power closure are specifically expressed as follows:

[0083]

[0084] In the formula, M is the mass of the bevel gear; q is the generalized displacement vector, which can be expressed in angular displacement or linear displacement form. The angular displacement form is... The linear displacement form is C is the damping matrix; K(t) is the time-varying stiffness matrix; For external load force; F loss This represents a nonlinear meshing force loss. For dynamic meshing force; represents the relative displacement. err represents the relative meshing error.

[0085] The speed-torque-vibration mapping model is established based on traveling wave resonance theory, and the vibration amplitude... satisfy:

[0086]

[0087] in, Given the bevel gear lifting rate; For loading torque; Here is the stiffness matrix. This is the damping ratio. In this embodiment,

[0088] Step 2: Determine the fitness function based on the adaptive particle swarm optimization algorithm.

[0089] The fitness function of the adaptive particle swarm optimization algorithm is composed of the given bevel gear's lifting rate and the maximum allowable vibration amplitude, and is specifically expressed as follows.

[0090] Design a dual-objective adaptive optimization fitness function F. f The expression is:

[0091]

[0092] in, and To optimize function weights, they can be adaptively adjusted according to operating conditions; The vibration amplitude of the transmission system; The maximum permissible vibration amplitude; The theoretically optimal loading torque; For loading torque; This represents the maximum permissible load torque. In this embodiment, , .

[0093] Step 3: Design the load torque input variable for the bevel gear transmission system; initialize the particle swarm. Randomly generate a group of particles in the problem space, each particle having a position and velocity.

[0094] The input variable for a bevel gear transmission system is the applied torque. The main process of particle swarm initialization is as follows:

[0095] (1) Randomly generate N particles, and each particle is randomly initialized in D-dimensional space. and speed ;

[0096] (2) Set the initial optimal position of the individual ,i= Global optimal position ;

[0097] (3) Set the maximum number of iterations Parameter adaptive adjustment rules, such as the range of inertia weights. .

[0098] in, and Let the minimum and maximum values ​​be the inertia weight adaptive function. The expression is:

[0099]

[0100] Where a, b, and d are parameters. For the number of iterations, This represents the maximum number of iterations. In this embodiment, .

[0101] Step 4: Calculate the fitness value. Evaluate the current position of each particle and calculate its fitness value. Calculating particle fitness involves calculating the bi-objective optimization function based on the particle's current torque value, vibration amplitude, and other parameters. .

[0102] Step 5: Update individual and global optima. Compare the fitness value of each particle with its individual optimal position. and the global optimal position If the current fitness value is better, then update. and .

[0103] Updating individual optimal and global optimal positions, specifically updating the individual optimal position using the Metropolis criterion. ,like Then accept the new solution. To simulate the annealing temperature coefficient. Global optimal position update refers to selecting the top 10% of particles from the population, substituting them into a Stackelberg game model to verify robustness, and then updating the global optimal position. .

[0104] Step 6: Update particle velocity and position. Update the velocity and position of each particle using the velocity and position update formula.

[0105] Particle velocity and position refer to each particle's individual search for the optimal solution in the search space, recording it as its current individual extreme value. This individual extreme value is shared with all other particles in the swarm. The optimal individual extreme value is then used as the current global optimal solution for the entire swarm. All particles in the swarm adjust their velocity and position based on their own current individual extreme value and the shared global optimal solution. and location The update expression is:

[0106]

[0107]

[0108] in, The learning factor is dynamically adjusted based on population diversity. These are random numbers. The expression for the learning factor is:

[0109]

[0110] Step 7: Determine if the adaptive particle swarm optimization conditions are met. Check if the adaptive particle swarm optimization termination criteria are met (e.g., reaching the maximum number of iterations or a sufficiently good fitness value). If met, output the optimal solution for the loaded torque of the bevel gear transmission system; otherwise, return to step 4 and continue the iterative optimization.

[0111] The adaptive particle swarm optimization conditions are as follows: whether the number of iterations reaches a standard value, or whether the rate of change of the fitness function value of the bi-objective adaptive optimization is stable within a threshold range, determines whether to terminate the loop. After the optimization is terminated, the optimized solution is output.

[0112] The termination condition is:

[0113] (1) Whether the number of iterations has reached the standard value;

[0114]

[0115] When the number of iterations reaches the maximum value, the loop terminates and the optimal loading torque value is output; if the number of iterations is less than the maximum value, the loop continues. In this embodiment, .

[0116] (2) The rate of change of the fitness function value remains stable within the threshold range;

[0117]

[0118] in, Let be the fitness function corresponding to a certain position globally. The fitness function corresponding to another position globally. This represents the threshold range for the rate of change of the fitness function value. In this embodiment, , .

[0119] The specific process of the rapid loading vibration suppression method for the bevel gear power closed transmission system based on adaptive particle swarm optimization in this embodiment is as follows:

[0120] According to the "speed-torque-vibration" mapping model of the bevel gear closed power transmission system in step 1 of this invention, the expected amplitude is solved by inputting the predetermined acceleration rate, system stiffness matrix, system damping ratio, and maximum loading torque. Then, based on the fitness function of the adaptive particle swarm optimization algorithm in step 2, the fitness function value is calculated based on parameters such as the given acceleration rate of the bevel gear and the maximum allowable vibration amplitude.

[0121] According to the adaptive particle swarm optimization algorithm for bevel gear closed power transmission systems involved in steps 3 to 7 of this invention, by substituting relevant system parameters and setting parameters such as the predetermined acceleration rate, system stiffness matrix, system damping ratio, and expected amplitude threshold in the algorithm, the optimal loading torque value under the corresponding acceleration rate condition is obtained. By continuously changing the acceleration rate of the transmission system, the optimal loading torque value corresponding to different acceleration rates and expected amplitude thresholds is obtained.

[0122] The speed-optimal loading torque curves under different amplitude threshold conditions, obtained by combining model calculations and optimization algorithms, were experimentally verified on a test bench for a bevel gear power closed transmission system. The verification method specifically involved installing vibration acceleration sensors and sound sensors on the bevel gear drive shaft, comparing the vibration magnitudes of the bevel gear transmission system under different loading methods and optimal loading torque conditions, and verifying the vibration suppression effect of the present invention on bevel gears.

[0123] The different loading methods are mainly of two types:

[0124] 1. Do not apply load initially; increase the speed to the rated speed before applying load to the rated torque.

[0125] 2. First apply the load to the rated torque, then reduce the load as the speed increases.

[0126] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A rapid loading vibration suppression method for bevel gear power closed transmission systems based on adaptive particle swarm optimization, characterized in that, include: Step 1: Using the structural parameters of the bevel gear enclosed power transmission system, establish the dynamic equation of the bevel gear system under power enclosure. Using the dynamic equation and historical operating data, quantify the relationship between vibration and load, and construct a speed-torque-vibration mapping model. Step 2: Based on the given rate of increase and maximum allowable vibration amplitude of the bevel gear, and combined with the speed-torque-vibration mapping model, construct a dual-objective adaptive degree function. ; Step 3: The loading torque of the bevel gear transmission system is used as the input variable of the adaptive particle swarm optimization algorithm; a set of particles is randomly generated, each particle having a position and velocity representing the loading torque parameter; the particle swarm is initialized. Step 4: Utilize the bi-objective adaptive degree function The fitness value of each particle is calculated, and the optimal position of each particle is updated using the fitness value. The global optimal particle of the particle swarm is updated by combining the Stackelberg game model. Step 5: Each particle adjusts its velocity and position based on the current global optimal particle position, and determines whether the current particle iteration meets the iteration termination condition. If so, the current global optimal particle position and velocity are used as the optimal parameters for loading torque in the bevel gear transmission system. Otherwise, the fitness value of each particle is calculated, and the process returns to step 4.

2. The rapid loading vibration suppression method for a bevel gear power closed transmission system based on adaptive particle swarm optimization according to claim 1, characterized in that, In step one, the dynamic equations of the bevel gear system under power closure are established using the structural parameters of the bevel gear closed power transmission system: In the formula, M is the mass of the bevel gear; q is the generalized displacement vector, which can be expressed in angular displacement or linear displacement form. The angular displacement form is... The linear displacement form is C is the damping matrix; The time-varying stiffness matrix; External load force; This represents a nonlinear meshing force loss. For dynamic meshing force; This represents the relative displacement. err represents the relative meshing error. Let q be the first derivative of the generalized displacement vector with respect to time, and let q be the generalized velocity vector. It is the second derivative of the generalized displacement vector q with respect to time, and represents the generalized acceleration vector. This represents a nonlinear function describing the geometric relationship or displacement-force transmission relationship of a gear pair. This represents the coefficient of friction between the gear teeth. This indicates the sliding speed between the meshing tooth surfaces of the gears. Indicates the angular velocity of the gear. The nonlinear quantization function representing the friction coefficient, sliding velocity, and angular velocity during gear meshing. The function represents the loss of meshing force, and c represents the meshing damping coefficient at the meshing interface of the gear pair.

3. The rapid loading vibration suppression method for a bevel gear power closed transmission system based on adaptive particle swarm optimization according to claim 1, characterized in that, In step two, a dual-objective adaptive function is constructed. for: in, and To optimize function weights, they are adaptively adjusted based on operating conditions; The vibration amplitude of the transmission system; The maximum permissible vibration amplitude; This is the theoretically optimal loading torque; For loading torque; This represents the maximum allowable load torque.

4. The rapid loading vibration suppression method for a bevel gear power closed transmission system based on adaptive particle swarm optimization according to claim 3, characterized in that, Vibration amplitude of the transmission system satisfy: in, Given the bevel gear lifting rate; For loading torque; Here is the stiffness matrix. For the damping ratio, This represents a nonlinear relational function.

5. The rapid loading vibration suppression method for a bevel gear power closed transmission system based on adaptive particle swarm optimization according to claim 4, characterized in that, Step three involves initializing the particle swarm as follows: Step 3: Randomly generate N particles, each with a randomly generated initial position in D-dimensional space. and speed ; Step 3.2: Set the initial optimal position for each individual. , Global optimal position ; Step 3: Set the maximum number of iterations T0 and adjust the parameters adaptively.

6. The rapid loading vibration suppression method for a bevel gear power closed transmission system based on adaptive particle swarm optimization according to claim 1 or 5, characterized in that, In step four, the method for updating the optimal position of each particle and the optimal position of the particle swarm is as follows: Compare each particle's current fitness value with its historical best fitness value. If the current fitness value is better, then the current fitness value is taken as the best fitness value, and the particle position corresponding to that fitness value is taken as the best position. Simultaneously, compare each particle's current best fitness value with the global best position. The corresponding fitness values ​​are compared, and the top 10% of particles with the highest fitness values ​​are selected as candidate particles. These candidate particles are then substituted into the Stackelberg game model to obtain the robustness of the particles. The position of the particle with the best robustness is determined as the new global optimum. .

7. The rapid loading vibration suppression method for a bevel gear power closed transmission system based on adaptive particle swarm optimization according to claim 5, characterized in that, In step four, the optimal position of each particle is updated using the Metropolis criterion. If it exists: Then the position of the particle is updated, where, To simulate the annealing temperature coefficient, The particle's historical best fitness value This represents the fitness value of the particle's current position. Indicates the fitness difference. This represents the fitness difference threshold.

8. The rapid loading vibration suppression method for a bevel gear power closed transmission system based on adaptive particle swarm optimization according to claim 7, characterized in that, In step five, the formula for each particle to adjust its velocity and position based on the current globally optimal particle position is as follows: in, This represents the velocity of particle i. Indicates the position of particle i. The learning factor is dynamically adjusted based on population diversity. It is a random number. This represents the optimal position of particle i in the current iteration during the entire population optimization process. The learning factor represents the optimal position of particle i in the current iteration during its optimization process, k represents the current iteration number, and k represents the learning factor. The expression is: This indicates the maximum number of iterations.

9. The rapid loading vibration suppression method for a bevel gear power closed transmission system based on adaptive particle swarm optimization according to claim 8, characterized in that, In step five, the iteration termination condition is that the current iteration number reaches the maximum iteration number or the rate of change of the fitness function value is within the threshold range.

10. The rapid loading vibration suppression method for a bevel gear power closed transmission system based on adaptive particle swarm optimization according to claim 9, characterized in that, The formula for the rate of change of the fitness function value within the threshold range is: in, Let be the fitness function corresponding to a certain position globally. The fitness function corresponding to another position globally. This represents the threshold range for the rate of change of the fitness function value.

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