Method, system and device for realizing vibration suppression and lightweight of gear transmission system

Abstract

The invention provides a gear transmission system vibration suppression and lightweight realization method, system and device, and the method comprises the steps: building a vibration amplitude model based on the electric field intensity, and the quality and rigidity of a gear transmission system; constructing a constraint model, a state space model, an action space model and a reward model; based on the constraint model, the state space model, the action space model and the reward model, optimizing the vibration amplitude model to obtain a minimum amplitude target model; and based on the minimum amplitude target model, constructing a multi-objective optimization model, and optimizing the multi-objective optimization model to obtain the global optimal electric field intensity, the minimum mass and the optimal rigidity, thereby obtaining the global minimum vibration amplitude, and realizing the minimum vibration amplitude and the minimum mass of the gear transmission system. The gear transmission system can obtain the minimum mass on the premise that the minimum vibration amplitude is ensured, and the requirements for vibration suppression and light weight of the gear transmission system are met.

Description

Technical Field

[0001] The present invention relates to the field of transmission systems, and in particular to a method, system and device for achieving vibration suppression and lightweighting of a gear transmission system. Background Art

[0002] With the increasing performance requirements of modern mechanical systems, gear transmission systems have been widely used in engineering. However, gear transmission systems often encounter vibration problems during operation, which not only affects the stability and accuracy of the machinery, but also causes premature wear or failure of the gear transmission system. At the same time, with the increasing attention to energy consumption and environmental impact, lightweight design has become an important goal of mechanical system optimization. The lightweight design of the gear transmission system can effectively reduce the energy loss of the machinery and improve the transmission efficiency, but in actual design, lightweight and vibration suppression often have a contradictory relationship.

[0003] Existing vibration suppression methods usually reduce the vibration amplitude by increasing stiffness or mass, but this often leads to increased mass and structural complexity, thus affecting the lightweight goal of the system. On the other hand, lightweight design reduces the stiffness of the system, resulting in increased vibration. Therefore, in the design of gear transmission systems, how to achieve lightweight while ensuring vibration suppression is a technical problem that needs to be solved urgently. In recent years, the application of smart materials has provided new ideas for solving this problem. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention provides a method, system and device for achieving vibration suppression and lightweighting of a gear transmission system.

[0005] In order to solve the above technical problems, the present invention is solved by the following technical solutions: A method for achieving vibration suppression and lightweighting of a gear transmission system, comprising the following steps: Based on relevant parameters of the gear transmission system and relevant parameters of the piezoelectric material, a vibration amplitude model is constructed, wherein the relevant parameters of the gear transmission system at least include the mass, stiffness, and vibration amplitude of the gear transmission system, and the relevant parameters of the piezoelectric material at least include the electric field intensity; Construct a constraint model of vibration amplitude and mass, construct a state space model based on the mass and stiffness of the gear transmission system, construct an action space model based on the electric field strength, and construct a reward model based on minimizing the vibration amplitude; Based on the constraint model, state space model, action space model and reward model, the vibration amplitude model is optimized to obtain the minimum amplitude target model. Specifically, under the constraint model, based on the reward value obtained by the reward model, the electric field strength in each state space is adjusted to adjust the vibration amplitude model until the optimization conditions are met, and the optimal electric field strength in each state space, i.e., the minimum amplitude target model, is obtained. Based on the mass, stiffness and electric field strength in the minimum amplitude target model, a multi-objective optimization model is constructed. The multi-objective optimization model is optimized to obtain the global optimal electric field strength, minimum mass and optimal stiffness, and then the global minimum vibration amplitude is obtained, thereby achieving the minimum vibration amplitude and minimum mass of the gear transmission system.

[0006] As an implementable embodiment, the vibration amplitude model is expressed as follows:

[0007] in, represents the vibration amplitude of the gear transmission system, represents the stiffness of the gear transmission system without the piezoelectric material control force, Indicates the quality of the gear transmission system, represents the electric field strength acting on the piezoelectric material, represents the initial external excitation force on the gear transmission system, represents the piezoelectric constant of the piezoelectric material, represents the effective force-bearing area of ​​the piezoelectric material, represents the deformation displacement of the gear transmission system, represents the frequency of the external excitation force on the gear transmission system, Represents the damping coefficient of the gear transmission system.

[0008] As an implementable method, the vibration amplitude and mass constraint model includes a first vibration amplitude constraint model and a first mass constraint model, and the first vibration amplitude constraint model and the first mass constraint model are respectively expressed as follows:

[0009]

[0010] The state space model is expressed as follows:

[0011] The action space model is expressed as follows:

[0012] The reward model is expressed as follows:

[0013] in, represents the vibration amplitude of the gear transmission system, Indicates the preset vibration amplitude threshold, Indicates the quality of the gear transmission system, represents the preset first quality threshold, represents the state space, A discrete value representing the mass of the gear transmission system, represents the discrete value of the gear transmission system stiffness, represents the total number of discrete values ​​of the quality of the gear transmission system, represents the total number of discrete values ​​of the gear transmission system stiffness, represents a state in the state space, represents the action space, The discrete value representing the electric field strength is the action in the action space, represents the total number of discrete values ​​of the electric field strength, Represents the reward value, represents the current state in the state space, Represents the action in the action space selected based on the current state.

[0014] As an implementable method, the vibration amplitude model is optimized based on the constraint model, the state space model, the action space model and the reward model to obtain the minimum amplitude target model, including the following steps: Based on the reward model, a reward value is obtained; based on the reward value, a Q-value update model of the Q-Learning algorithm is constructed to obtain a Q value; Under the constraint model, based on the Q value, the electric field strength in each state space is adjusted by the Q-Learning algorithm to adjust the vibration amplitude model; until the optimization condition is met, the optimal electric field strength in each state space, that is, the minimum amplitude target model, is obtained, wherein the optimization condition is that a preset number of adjustments is reached or the change in the Q value is less than a preset threshold or the reward value reaches a preset reward threshold; Among them, the Q value update model is expressed as follows:

[0015] in, represents the updated Q value, Indicates the current state. Indicates the current action. represents the Q value, represents the learning rate, Indicates the reward value for taking the current action in the current state, represents the discount factor, Indicates the next state, Indicates all actions that can be taken in the next state. It represents the maximum Q value among all the Q values ​​that can be obtained based on the next state and all the actions that can be taken in the next state.

[0016] As an implementable method, under the constraint model, based on the Q value, the electric field strength in each state space is adjusted by the Q-Learning algorithm to adjust the vibration amplitude model; until the optimization conditions are met, the optimal electric field strength in each state space is obtained, including the following steps: Based on the state space and the action space, the Q-table of the Q-Learning algorithm is initialized to obtain an initialized Q-table, wherein the state space in the initialized Q-table satisfies the quality constraint model; Randomly obtain the initial state from the state space, and obtain the initial action based on the initial state and the initialized Q table; Based on the initial state and initial action, the current vibration amplitude and the next state are obtained; If the mass in the next state does not satisfy the first mass constraint model, the mass in the next state is adjusted to obtain the adjusted mass in the next state; if the current vibration amplitude does not satisfy the first vibration amplitude constraint model, the current vibration amplitude is adjusted to obtain the adjusted current vibration amplitude; Based on the current vibration amplitude, get the current reward value; Based on the initial state, initial action and current reward value, combined with the Q value update model, the updated Q value is obtained, and then the updated Q table is obtained; Based on the next state and the updated Q-table, the next action is selected to obtain the next reward value and the next Q-value, and the Q-table is updated until the optimization conditions are met to obtain the final Q-table. Extract each state in the final Q table, the maximum Q value corresponding to each state, and the action corresponding to each maximum Q value, and obtain the maximum Q value table, i.e., the minimum amplitude target model; Among them, the adjusted mass in the next state and the adjusted current vibration amplitude are expressed as follows:

[0017]

[0018] in, represents the quality in the next state after adjustment, represents the quality in the next state that does not satisfy the first quality constraint model, represents the preset quality adjustment amount, and , Indicates the current vibration amplitude after adjustment, Indicates the preset vibration amplitude threshold.

[0019] As an implementable method, the multi-objective optimization model is constructed based on the mass, stiffness and electric field strength in the minimum amplitude target model, including the following steps: The multi-objective optimization model includes an optimization variable model, an optimization target model and a second constraint model; Based on the mass, stiffness and electric field strength in the minimum amplitude target model, an optimization variable model is constructed; Based on the mass, stiffness and electric field strength in the minimum amplitude target model, an optimization target model is constructed; The second constraint model at least includes a second mass constraint model and a second vibration amplitude constraint model; Wherein, the optimization variable model is expressed as follows:

[0020] The optimization target model is expressed as follows:

[0021] The second quality constraint model is expressed as follows:

[0022] The second vibration amplitude constraint model is expressed as follows:

[0023] in, represents the optimization variable, represents the mass of the gear transmission system in the minimum amplitude target model, represents the stiffness of the gear transmission system in the minimum amplitude target model, represents the electric field strength in the minimum amplitude target model, represents the optimization target value, represents the optimization goal, and represents the weight factor, represents the preset second quality threshold, represents the minimum amplitude target model, represents the vibration amplitude in the minimum amplitude target model, Indicates the preset vibration amplitude threshold.

[0024] As an implementable method, the multi-objective optimization model is optimized to obtain the global optimal electric field strength, the minimum mass and the optimal stiffness, and then the global minimum vibration amplitude, including the following steps: Based on the optimization target model, the second mass constraint model and the second vibration amplitude constraint model, combined with Lagrangian multipliers, a Lagrangian model is constructed; The partial derivatives of the Lagrangian model are obtained based on the optimization variables and the Lagrangian multipliers to obtain a partial derivative model; Solve the partial derivative model to obtain the optimal solution of the optimization variables in the multi-objective optimization model, and then obtain the global optimal electric field intensity, global minimum mass and global optimal stiffness; Based on the global optimal electric field intensity, global minimum mass and global optimal stiffness, combined with the minimum amplitude target model, the global minimum vibration amplitude is obtained; The Lagrangian model is expressed as follows:

[0025] The partial derivative model is expressed as follows:

[0026] in, represents the Lagrangian value, and represents the Lagrange multiplier.

[0027] A gear transmission system vibration suppression and lightweight realization system, comprising an amplitude module, a modeling module, a local optimization module and a global optimization module; The amplitude module constructs a vibration amplitude model based on relevant parameters of the gear transmission system and relevant parameters of the piezoelectric material, wherein the relevant parameters of the gear transmission system at least include the mass, stiffness, and vibration amplitude of the gear transmission system, and the relevant parameters of the piezoelectric material at least include the electric field strength; The modeling module constructs a constraint model of vibration amplitude and mass, constructs a state space model based on the mass and stiffness of the gear transmission system, constructs an action space model based on the electric field intensity, and constructs a reward model based on minimization of vibration amplitude; The local optimization module optimizes the vibration amplitude model based on the constraint model, the state space model, the action space model and the reward model to obtain the minimum amplitude target model, specifically: under the constraint model, based on the reward value obtained by the reward model, the electric field strength in each state space is adjusted to adjust the vibration amplitude model until the optimization condition is met, and the optimal electric field strength in each state space, that is, the minimum amplitude target model, is obtained; The global optimization module constructs a multi-objective optimization model based on the mass, stiffness and electric field strength in the minimum amplitude target model, optimizes the multi-objective optimization model, obtains the global optimal electric field strength, minimum mass and optimal stiffness, and then obtains the global minimum vibration amplitude, thereby achieving the minimum vibration amplitude and minimum mass of the gear transmission system.

[0028] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the following method is implemented: Based on relevant parameters of the gear transmission system and relevant parameters of the piezoelectric material, a vibration amplitude model is constructed, wherein the relevant parameters of the gear transmission system at least include the mass, stiffness, and vibration amplitude of the gear transmission system, and the relevant parameters of the piezoelectric material at least include the electric field intensity; Construct a constraint model of vibration amplitude and mass, construct a state space model based on the mass and stiffness of the gear transmission system, construct an action space model based on the electric field strength, and construct a reward model based on minimizing the vibration amplitude; Based on the constraint model, state space model, action space model and reward model, the vibration amplitude model is optimized to obtain the minimum amplitude target model. Specifically, under the constraint model, based on the reward value obtained by the reward model, the electric field strength in each state space is adjusted to adjust the vibration amplitude model until the optimization conditions are met, and the optimal electric field strength in each state space, i.e., the minimum amplitude target model, is obtained. Based on the mass, stiffness and electric field strength in the minimum amplitude target model, a multi-objective optimization model is constructed. The multi-objective optimization model is optimized to obtain the global optimal electric field strength, minimum mass and optimal stiffness, and then the global minimum vibration amplitude is obtained, thereby achieving the minimum vibration amplitude and minimum mass of the gear transmission system.

[0029] A device for realizing vibration suppression and lightweighting of a gear transmission system, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor implements the following method when executing the computer program: Based on relevant parameters of the gear transmission system and relevant parameters of the piezoelectric material, a vibration amplitude model is constructed, wherein the relevant parameters of the gear transmission system at least include the mass, stiffness, and vibration amplitude of the gear transmission system, and the relevant parameters of the piezoelectric material at least include the electric field intensity; Construct a constraint model of vibration amplitude and mass, construct a state space model based on the mass and stiffness of the gear transmission system, construct an action space model based on the electric field strength, and construct a reward model based on minimizing the vibration amplitude; Based on the constraint model, state space model, action space model and reward model, the vibration amplitude model is optimized to obtain the minimum amplitude target model. Specifically, under the constraint model, based on the reward value obtained by the reward model, the electric field strength in each state space is adjusted to adjust the vibration amplitude model until the optimization conditions are met, and the optimal electric field strength in each state space, i.e., the minimum amplitude target model, is obtained. Based on the mass, stiffness and electric field strength in the minimum amplitude target model, a multi-objective optimization model is constructed. The multi-objective optimization model is optimized to obtain the global optimal electric field strength, minimum mass and optimal stiffness, and then the global minimum vibration amplitude is obtained, thereby achieving the minimum vibration amplitude and minimum mass of the gear transmission system.

[0030] The present invention has significant technical effects due to the adoption of the above technical scheme: the present invention relates to a method, system and device for realizing vibration suppression and lightweighting of a gear transmission system, adopting piezoelectric material as intelligent material, adjusting the control force generated by the piezoelectric material by adjusting the electric field strength acting on the piezoelectric material, and then controlling the vibration amplitude of the gear transmission system in real time through the control force of the piezoelectric material, constructing an amplitude electric field strength model through the vibration amplitude, electric field strength, mass and stiffness of the gear transmission system, optimizing the amplitude electric field strength model based on the minimum vibration amplitude, obtaining the minimum vibration amplitude and the corresponding optimal electric field strength corresponding to different masses and different stiffnesses, further optimizing the mass and minimum vibration amplitude of the gear transmission system synchronously, obtaining the minimum mass of the gear transmission system and the final optimal electric field strength, thereby realizing vibration suppression and lightweighting of the gear transmission system. The method of the present invention deeply considers the interaction between the mass and vibration amplitude of the gear transmission system, ensuring that the mass of the gear transmission system is minimized while minimizing the vibration amplitude, effectively meeting the dual needs of vibration suppression and lightweighting, and thus improving the operating efficiency and stability of the gear transmission system. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, 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 paying creative labor.

[0032] Figure 1 It is a schematic flow diagram of the method of the present invention; Figure 2 It is an overall schematic diagram of the system of the present invention. DETAILED DESCRIPTION

[0033] The present invention is further described in detail below in conjunction with the embodiments, which are explanations of the present invention but are not limited to the following embodiments. In the absence of conflict, the features in the following embodiments can be combined with each other.

[0034] Embodiment 1: A method for achieving vibration suppression and lightweighting of a gear transmission system, such as Figure 1 As shown, the following steps are included: S100: constructing a vibration amplitude model based on relevant parameters of the gear transmission system and relevant parameters of the piezoelectric material, wherein the relevant parameters of the gear transmission system at least include mass, stiffness, and vibration amplitude of the gear transmission system, and the relevant parameters of the piezoelectric material at least include electric field strength; S200: Construct a constraint model of vibration amplitude and mass, construct a state space model based on the mass and stiffness of the gear transmission system, construct an action space model based on the electric field strength, and construct a reward model based on minimizing the vibration amplitude; S300: Based on the constraint model, the state space model, the action space model and the reward model, the vibration amplitude model is optimized to obtain a minimum amplitude target model, specifically: under the constraint model, based on the reward value obtained by the reward model, the electric field strength in each state space is adjusted to adjust the vibration amplitude model until the optimization condition is met, and the optimal electric field strength in each state space, that is, the minimum amplitude target model, is obtained; S400: Based on the mass, stiffness and electric field strength in the minimum amplitude target model, a multi-objective optimization model is constructed, and the multi-objective optimization model is optimized to obtain the global optimal electric field strength, minimum mass and optimal stiffness, and then the global minimum vibration amplitude is obtained to achieve the minimum vibration amplitude and minimum mass of the gear transmission system.

[0035] In S100, a vibration amplitude model is constructed based on relevant parameters of the gear transmission system and relevant parameters of the piezoelectric material, wherein the relevant parameters of the gear transmission system at least include the mass, stiffness, and vibration amplitude of the gear transmission system, and the relevant parameters of the piezoelectric material at least include the electric field strength, wherein the derivation process of the vibration amplitude model is as follows: (1) Construct the initial vibration amplitude model of the gear transmission system (without the control force of the piezoelectric material), which is expressed as follows:

[0036] in, Indicates the quality of the gear transmission system, represents the vibration displacement of the gear transmission system, represents the speed of vibration, represents the acceleration of vibration, represents the damping coefficient of the gear transmission system, represents the stiffness of the gear transmission system, Represents external incentive.

[0037] The external excitation force is a periodic external force acting on the gear transmission system, which is expressed as follows:

[0038] in, represents the initial external excitation force, i.e. the amplitude of the external excitation force, represents the frequency of the external excitation force, represents time, taking into account the forced vibration of the system, the vibration displacement of the gear transmission system is expressed as follows:

[0039] in, represents the initial vibration amplitude (without the control force of the piezoelectric material), Indicates the initial phase.

[0040] The updated initial vibration amplitude model is expressed as follows:

[0041] Will Expand to , it is expressed as follows:

[0042] In order to make the sine and cosine terms on both sides match, we get a system of equations, which is expressed as follows:

[0043] Eliminate phase , and square the two equations in the system and add them together to get:

[0044] right Solve and get another representation of the initial vibration amplitude model:

[0045] It can be seen that the initial vibration amplitude depends on the external excitation force , system quality , stiffness , damping coefficient and excitation frequency The model provides a mathematical basis for the subsequent control strategy design and lightweight design. By adjusting the mass, stiffness and damping coefficients, the vibration amplitude of the system can be effectively controlled, thus achieving a balance between vibration suppression and lightweight design.

[0046] The relationship between natural frequency and initial vibration amplitude, natural frequency is the natural frequency of the gear transmission system, , natural frequency and the frequency of the external excitation force The relationship between is critical. If the frequency of the external excitation force is close to the natural frequency of the system, the system will resonate, causing the initial vibration amplitude to increase sharply. Therefore, in order to control the vibration amplitude, it is necessary to avoid the excitation frequency Close to natural frequency When the external excitation frequency Close to natural frequency When , the vibration amplitude of the system is the largest. In actual design, it is necessary to avoid the occurrence of resonance, so the mass and stiffness are usually adjusted to ensure that the natural frequency is not close to the external excitation frequency.

[0047] (2) Match the piezoelectric material to the gear transmission system to obtain the target stiffness of the gear transmission system By matching the piezoelectric material to the gear transmission system, the control force of the piezoelectric material is obtained, which is expressed as follows:

[0048] in, represents the control force generated by the piezoelectric material, The piezoelectric constant of the piezoelectric material (indicates the stress generated under a unit electric field, and characterizes the ability to convert electric field into stress). represents the effective force-bearing area of ​​the piezoelectric material, Indicates the electric field strength applied to the piezoelectric material. The electric field strength is adjusted in real time. , the control force of the piezoelectric actuator can be precisely controlled to offset the unwanted vibration in the transmission system. According to the mechanical properties of the material, the control force of the piezoelectric material can change the stiffness of the gear transmission system. The piezoelectric material changes the stiffness of the gear transmission system by applying a control force to a certain position of the gear. The system stiffness of the gear transmission system after the control force of the piezoelectric material is applied is the target stiffness of the gear transmission system, which is expressed as follows:

[0049] in, It represents the stiffness of the gear transmission system after the piezoelectric material control force is applied, that is, the target stiffness. represents the initial (no piezoelectric material control force applied) stiffness of the gear transmission system, It represents the deformation displacement of the gear transmission system after being subjected to the control force of the piezoelectric material. The piezoelectric constant of the piezoelectric material (indicates the stress generated under a unit electric field, and characterizes the ability to convert electric field into stress), represents the effective force-bearing area of ​​the piezoelectric material, Indicates the electric field strength applied to the piezoelectric material. The electric field strength is adjusted in real time. , the control force of the piezoelectric actuator can be precisely controlled to offset the unwanted vibration in the gear transmission system. The control force of the piezoelectric material is an active control force that can change the stiffness and vibration mode of the gear by adjusting the electric field strength.

[0050] (3) The initial vibration amplitude model is updated through the target stiffness to obtain the vibration amplitude model of the gear transmission system. The vibration amplitude of the gear transmission system after the piezoelectric material control force is applied is obtained. The vibration amplitude model is expressed as follows:

[0051] in, represents the vibration amplitude of the gear transmission system, It represents the initial external excitation force of the gear transmission system, that is, the amplitude of the external excitation force. represents the stiffness of the gear transmission system, represents the piezoelectric constant of the piezoelectric material, represents the electric field strength and is an adjustable control variable. represents the effective force-bearing area of ​​the piezoelectric material, represents the deformation displacement of the gear, Indicates the quality of the gear transmission system, represents the frequency of the external excitation force on the gear transmission system, Represents the damping coefficient of the gear transmission system. By adjusting the electric field strength The control force of the piezoelectric material can be controlled to actively control the vibration amplitude of the gear transmission system. The control force generated by the piezoelectric material is an active control force, which can change the stiffness and vibration mode of the gear by adjusting the electric field strength.

[0052] In S200, a constraint model of vibration amplitude and mass is constructed, a state space model is constructed based on the mass and stiffness of the gear transmission system, an action space model is constructed based on the electric field strength, and a reward model is constructed based on minimization of the vibration amplitude. The constraint model of vibration amplitude and mass includes a first vibration amplitude constraint model and a first mass constraint model, and the first vibration amplitude constraint model and the first mass constraint model are respectively expressed as follows:

[0053]

[0054] The state space model is expressed as follows:

[0055] The action space model is expressed as follows:

[0056] The reward model is expressed as follows:

[0057] in, represents the vibration amplitude of the gear transmission system, Indicates the preset vibration amplitude threshold, Indicates the quality of the gear transmission system, represents the preset first quality threshold, represents the state space, A discrete value representing the mass of the gear transmission system, represents the discrete value of the gear transmission system stiffness, represents the total number of discrete values ​​of the quality of the gear transmission system, represents the total number of discrete values ​​of the gear transmission system stiffness, represents a state in the state space, represents the action space, The discrete value representing the electric field strength is the action in the action space, represents the total number of discrete values ​​of the electric field strength, Represents the reward value, which is the opposite of the vibration amplitude. This means that the smaller the vibration amplitude, the higher the reward value. represents the current state in the state space, Represents the action in the action space selected based on the current state.

[0058] In this embodiment, the vibration amplitude model is optimized by constructing a reinforcement learning model. Because the lightweight design of the gear transmission system is usually achieved by reducing the mass of the gear transmission system. However, reducing the mass will affect the natural frequency of the gear transmission system, thereby affecting the vibration amplitude. Therefore, the mass and vibration amplitude must be constrained. The mass cannot be lower than the preset mass threshold to ensure the vibration amplitude of the system, and the vibration amplitude must be lower than the preset vibration amplitude threshold to ensure that the vibration is effectively suppressed. Since the reward value is the opposite of the vibration amplitude, constraining the vibration amplitude is equivalent to constraining the reward value. In order to ensure that the vibration amplitude is not too large, only the minimum mass constraint is imposed on the mass, which is a weak constraint on the mass.

[0059] In S300, based on the constraint model, the state space model, the action space model and the reward model, the vibration amplitude model is optimized to obtain the minimum amplitude target model, specifically: under the constraint model, based on the reward value obtained by the reward model, the electric field strength in each state space is adjusted to adjust the vibration amplitude model until the optimization conditions are met, and the optimal electric field strength in each state space, that is, the minimum amplitude target model, is obtained, including the following steps: S310: Based on the reward model, a reward value is obtained; based on the reward value, a Q-value update model of the Q-Learning algorithm is constructed to obtain a Q value. In this embodiment, the Q-learning algorithm is used to obtain the optimal control strategy of reinforcement learning. The Q-learning algorithm approximates the optimal strategy by iteratively updating the Q value of each state-action pair. The Q value represents the expected return of taking an action in a given state. The Q-value update model is expressed as follows:

[0060] in, represents the updated Q value, Indicates the current state. Indicates the current action. represents the Q value, Represents the learning rate, which usually ranges from 0 to 1 and is used to control the speed of learning. Indicates the reward value for taking the current action in the current state, which is the immediate reward value. Represents the discount factor, which ranges from 0 to 1 and indicates the importance of future rewards. Indicates the current status The next state to which we transfer is Indicates all actions that can be taken in the next state. Indicates the maximum Q value among all the Q values ​​that can be taken based on the next state and the next state, that is, the next state The Q value corresponding to the best action is, It is an estimate of the best future action and is used to calculate the expected future return. By continuously updating the Q value, the reinforcement learning model can gradually find the strategy for taking the best action in each state. This strategy can minimize the vibration amplitude and satisfy the lightweight constraint at the same time.

[0061] S320: Under the constraint model, based on the Q value, the electric field strength in each state space is adjusted by the Q-Learning algorithm to adjust the vibration amplitude model; until the optimization condition is met, the optimal electric field strength in each state space, that is, the minimum amplitude target model, is obtained, wherein the optimization condition is to reach a preset number of adjustments or the change in the Q value is less than a preset threshold or the reward value reaches a preset reward threshold. Specifically including: S321: Based on the state space and action space, the Q table of the Q-Learning algorithm is initialized to obtain an initialized Q table. The Q table is a state space and action space The size of the Q table is the size of the state space multiplied by the size of the action space. Each element of the Q table represents the state of the action space. Next action The expected Q value is usually initialized to 0 or a small random number. Since the quality in the state space is constrained in this application, the state space that does not meet the first quality constraint model is eliminated when the Q table is initialized.

[0062] S322: Randomly obtain an initial state from the state space, and obtain an initial action based on the initial state and the initialized Q table; Select state and action: Randomly select a state from the state space of the initialized Q table as the initial state, the initial state is also the current state, and use the current state and Q table to select the initial state and action. Greedy strategy, selects an action from the action space with probability Randomly choose an action with probability The action with the largest Q value is selected as the best initial action.

[0063] S323: Based on the initial state and initial action, obtain the current vibration amplitude and the next state; If the mass in the next state does not satisfy the first mass constraint model, the mass in the next state is adjusted to obtain the adjusted mass in the next state. If the current vibration amplitude does not satisfy the first vibration amplitude constraint model, the current vibration amplitude is adjusted to obtain the adjusted current vibration amplitude. The adjusted mass in the next state and the adjusted current vibration amplitude are respectively expressed as follows:

[0064]

[0065] in, represents the quality in the next state after adjustment, represents the quality in the next state that does not satisfy the first quality constraint model, represents the preset quality adjustment amount, and For easy processing, you can , or search in state space for the same mass Closest and greater than or equal to The quality of is taken as the quality of the next state. Indicates the current vibration amplitude after adjustment, Indicates the preset vibration amplitude threshold.

[0066] S324: Based on the current vibration amplitude, obtain the current reward value; S325: Based on the initial state, initial action and current reward value, combined with the Q value update model, an updated Q value is obtained, and then an updated Q table is obtained; S326: Based on the next state and the updated Q-table, the next action is selected, and the next reward value and the next Q-value are obtained, and the Q-table is updated until the optimization condition is met (the optimization condition is that the preset number of adjustments is reached or the change in the Q-value is less than the preset threshold or the reward value reaches the preset reward threshold), and the final Q-table is obtained. The final Q-table is a mapping of all states in the state space and all optional actions in the action space, as well as the corresponding Q-values.

[0067] S327: Extract each state in the final Q table, the maximum Q value corresponding to each state, and the action corresponding to each maximum Q value, and obtain the maximum Q value table, i.e., the minimum amplitude target model. (stiffness and mass), the action corresponding to the maximum Q value is the optimal action under this state, and the optimal action is the optimal electric field strength under this state. The best action in each state in the final Q table is extracted, and the obtained maximum Q value table is the state space optimal action mapping table, that is, the electric field strength mapping table that minimizes the vibration amplitude under different stiffnesses and different masses.

[0068] Through the Q-Learning algorithm, the electric field strength that minimizes the vibration amplitude in reinforcement learning is found, and the lightweight design requirements are maintained in the process. The Q-learning algorithm updates the Q value through continuous iteration, and can eventually approach the optimal value of each state-action pair. After the training is completed, for any state, the action with the largest Q value (the smallest vibration amplitude and meets the lightweight requirements) is selected as the optimal action. This method does not require a transition probability model of the environment, so it is applicable to many practical problems.

[0069] In S400, based on the mass, stiffness and electric field strength in the minimum amplitude target model, a multi-objective optimization model is constructed, and the multi-objective optimization model is optimized to obtain the global optimal electric field strength, minimum mass and optimal stiffness, and then obtain the global minimum vibration amplitude, so as to achieve the minimum vibration amplitude and minimum mass of the gear transmission system. The minimum amplitude target model obtained by the above steps is the optimal electric field strength mapping model that should be adopted when the vibration amplitude is minimized under different stiffness and different mass. The optimal electric field strength here is only the optimal electric field strength under a specific mass and a specific stiffness, which belongs to the local optimal electric field strength. In other words, the minimum amplitude target model obtains a series of stiffness, mass and local optimal electric field strength sets, and it is not possible to determine which set of data to select to achieve the minimum vibration amplitude and the minimum mass of the gear transmission system. Therefore, it is necessary to further select this series of data sets to obtain the global optimal electric field strength, global minimum mass and global optimal stiffness that minimize the vibration amplitude and the minimum mass, and then obtain the global minimum vibration amplitude, including the following steps: S410: constructing a multi-objective optimization model based on the mass, stiffness and electric field strength in the minimum amplitude target model, wherein the multi-objective optimization model includes an optimization variable model, an optimization target model and a second constraint model; Based on the mass, stiffness and electric field strength in the minimum amplitude target model, an optimization variable model is constructed. The optimization variable model is expressed as follows:

[0070] Based on the mass, stiffness and electric field strength in the minimum amplitude target model, an optimization target model is constructed. In order to achieve a balance between vibration suppression and lightweight design, the optimization target model needs to comprehensively consider the vibration amplitude and mass, and minimize the mass while ensuring the minimum vibration amplitude. In order to obtain better numerical results during the optimization process, the vibration amplitude is normalized or squared for better gradient optimization. A common method is to square it and introduce a weight factor. The optimization target model is expressed as follows:

[0071] The second constraint model at least includes a second mass constraint model and a second vibration amplitude constraint model. The second constraint model further constrains the mass and vibration amplitude. The mass cannot be greater than a preset mass threshold to ensure that the system meets the lightweight requirements. The vibration amplitude must be less than a preset vibration amplitude threshold to ensure that the vibration is effectively suppressed, thereby ensuring that the optimization result not only meets the requirements of lightweight design but also guarantees the effect of vibration suppression. The second constraint model constrains the mass not to exceed the preset mass threshold, which is a strong constraint on the mass. The second mass constraint model and the second vibration amplitude constraint model are respectively expressed as follows:

[0072]

[0073] in, represents the optimization variable, represents the mass of the gear transmission system in the minimum amplitude target model, represents the stiffness of the gear transmission system in the minimum amplitude target model, represents the electric field strength in the minimum amplitude target model, represents the optimization target value, represents the optimization goal, and represents the weight factor, represents the preset second quality threshold, represents the minimum amplitude target model, represents the vibration amplitude in the minimum amplitude target model, Indicates the preset vibration amplitude threshold.

[0074] S420: Optimizing the multi-objective optimization model to obtain the global optimal electric field strength, minimum mass and optimal stiffness, and then obtaining the global minimum vibration amplitude, including the following steps: (1) Based on the optimization target model, the second mass constraint model and the second vibration amplitude constraint model, a Lagrangian model is constructed in combination with Lagrangian multipliers. The Lagrangian model is expressed as follows:

[0075] (2) The partial derivatives of the Lagrangian model are calculated based on the optimization variables and the Lagrangian multipliers to obtain a partial derivative model, which is expressed as follows:

[0076] in, represents the Lagrangian value, and represents the Lagrange multiplier.

[0077] (3) Solve the partial derivative model. The solution of the partial derivative model is It is the optimal solution of the Lagrangian model, which includes the optimal optimization variables The optimal stiffness , best quality And the optimal electric field strength Optimal Optimization Variables The gear transmission system is made to minimize the vibration amplitude and the mass under the constraint model that satisfies the vibration suppression and lightweight design, thus achieving the global optimal electric field strength, the global minimum mass and the global optimal stiffness.

[0078] (4) Based on the global optimal electric field strength, the global minimum mass, and the global optimal stiffness, combined with the minimum amplitude target model, the global minimum vibration amplitude is obtained, thereby achieving the minimum vibration amplitude and minimum mass of the gear transmission system.

[0079] Embodiment 2: A gear transmission system vibration suppression and lightweight realization system, such as Figure 2 As shown, it includes an amplitude module 100, a modeling module 200, a local optimization module 300 and a global optimization module 400; The amplitude module 100 constructs a vibration amplitude model based on relevant parameters of the gear transmission system and relevant parameters of the piezoelectric material, wherein the relevant parameters of the gear transmission system at least include the mass, stiffness, and vibration amplitude of the gear transmission system, and the relevant parameters of the piezoelectric material at least include the electric field strength; The modeling module 200 constructs a constraint model of vibration amplitude and mass, constructs a state space model based on the mass and stiffness of the gear transmission system, constructs an action space model based on the electric field strength, and constructs a reward model based on minimization of vibration amplitude; The local optimization module 300 optimizes the vibration amplitude model based on the constraint model, the state space model, the action space model and the reward model to obtain the minimum amplitude target model, specifically: under the constraint model, based on the reward value obtained by the reward model, the electric field strength in each state space is adjusted to adjust the vibration amplitude model until the optimization condition is met, and the optimal electric field strength in each state space, that is, the minimum amplitude target model, is obtained; The global optimization module 400 constructs a multi-objective optimization model based on the mass, stiffness and electric field strength in the minimum amplitude target model, optimizes the multi-objective optimization model, obtains the global optimal electric field strength, minimum mass and optimal stiffness, and then obtains the global minimum vibration amplitude, thereby achieving the minimum vibration amplitude and minimum mass of the gear transmission system.

[0080] Various changes and modifications can be made without departing from the spirit and scope of the present invention, and all equivalent technical solutions also belong to the scope of the present invention.

[0081] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0082] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, devices, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0083] The present invention is described with reference to the flowcharts and / or block diagrams of the method, terminal device (system), and computer program product according to the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of the processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing terminal device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing terminal device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1A device that provides the functions specified in a block or multiple blocks.

[0084] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing terminal device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce a manufactured product including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0085] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal device so that a series of operating steps are executed on the computer or other programmable terminal device to produce a computer-implemented process, thereby providing instructions for executing on the computer or other programmable terminal device to implement the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0086] It should be noted that: The "one embodiment" or "embodiment" mentioned in the specification means that the specific features, structures or characteristics described in conjunction with the embodiment are included in at least one embodiment of the present invention. Therefore, the phrases "one embodiment" or "embodiment" appearing in various places throughout the specification do not necessarily refer to the same embodiment.

[0087] In addition, it should be noted that the shapes and names of the parts and components of the specific embodiments described in this specification may be different. Any equivalent or simple changes made based on the structure, features and principles described in the patent concept of the present invention are included in the protection scope of the patent of the present invention. The technicians in the technical field of the present invention can make various modifications or supplements to the specific embodiments described or replace them in a similar manner, as long as they do not deviate from the structure of the present invention or exceed the scope defined by the claims, they should all fall within the protection scope of the present invention.

Claims

1. A method for achieving vibration suppression and lightweighting of a gear transmission system, characterized in that: The following steps are involved: Based on relevant parameters of the gear transmission system and relevant parameters of the piezoelectric material, a vibration amplitude model is constructed, wherein the relevant parameters of the gear transmission system at least include the mass, stiffness, and vibration amplitude of the gear transmission system, and the relevant parameters of the piezoelectric material at least include the electric field intensity; Construct a constraint model of vibration amplitude and mass, construct a state space model based on the mass and stiffness of the gear transmission system, construct an action space model based on the electric field strength, and construct a reward model based on minimizing the vibration amplitude; Based on the constraint model, state space model, action space model and reward model, the vibration amplitude model is optimized to obtain the minimum amplitude target model. Specifically, under the constraint model, based on the reward value obtained by the reward model, the electric field strength in each state space is adjusted to adjust the vibration amplitude model until the optimization conditions are met, and the optimal electric field strength in each state space, i.e., the minimum amplitude target model, is obtained. Based on the mass, stiffness and electric field strength in the minimum amplitude target model, a multi-objective optimization model is constructed. The multi-objective optimization model is optimized to obtain the global optimal electric field strength, minimum mass and optimal stiffness, and then the global minimum vibration amplitude is obtained, thereby achieving the minimum vibration amplitude and minimum mass of the gear transmission system.

2. The method for achieving vibration suppression and lightweighting of a gear transmission system according to claim 1, characterized in that: The vibration amplitude model is expressed as follows: in, represents the vibration amplitude of the gear transmission system, represents the stiffness of the gear transmission system without the piezoelectric material control force, Indicates the quality of the gear transmission system, represents the electric field strength acting on the piezoelectric material, represents the initial external excitation force on the gear transmission system, represents the piezoelectric constant of the piezoelectric material, represents the effective force-bearing area of ​​the piezoelectric material, represents the deformation displacement of the gear transmission system, represents the frequency of the external excitation force on the gear transmission system, Represents the damping coefficient of the gear transmission system.

3. The method for achieving vibration suppression and lightweighting of a gear transmission system according to claim 1, characterized in that: The vibration amplitude and mass constraint model includes a first vibration amplitude constraint model and a first mass constraint model, and the first vibration amplitude constraint model and the first mass constraint model are respectively expressed as follows: The state space model is expressed as follows: The action space model is expressed as follows: The reward model is expressed as follows: in, represents the vibration amplitude of the gear transmission system, Indicates the preset vibration amplitude threshold, Indicates the quality of the gear transmission system, represents the preset first quality threshold, represents the state space, A discrete value representing the mass of the gear transmission system, represents the discrete value of the gear transmission system stiffness, represents the total number of discrete values ​​of the quality of the gear transmission system, represents the total number of discrete values ​​of the gear transmission system stiffness, represents a state in the state space, represents the action space, The discrete value representing the electric field strength is the action in the action space, represents the total number of discrete values ​​of the electric field strength, Represents the reward value, represents the current state in the state space, Represents the action in the action space selected based on the current state.

4. The method for achieving vibration suppression and lightweighting of a gear transmission system according to claim 1, characterized in that: The vibration amplitude model is optimized based on the constraint model, the state space model, the action space model and the reward model to obtain the minimum amplitude target model, including the following steps: Based on the reward model, a reward value is obtained; based on the reward value, a Q-value update model of the Q-Learning algorithm is constructed to obtain a Q value; Under the constraint model, based on the Q value, the electric field strength in each state space is adjusted by the Q-Learning algorithm to adjust the vibration amplitude model; until the optimization condition is met, the optimal electric field strength in each state space, that is, the minimum amplitude target model, is obtained, wherein the optimization condition is that a preset number of adjustments is reached or the change in the Q value is less than a preset threshold or the reward value reaches a preset reward threshold; Among them, the Q value update model is expressed as follows: in, represents the updated Q value, Indicates the current state. Indicates the current action. represents the Q value, represents the learning rate, Indicates the reward value for taking the current action in the current state, represents the discount factor, Indicates the next state, Indicates all actions that can be taken in the next state. It represents the maximum Q value among all the Q values ​​that can be obtained based on the next state and all the actions that can be taken in the next state.

5. The method for achieving vibration suppression and lightweighting of a gear transmission system according to claim 4, characterized in that: The electric field strength in each state space is adjusted based on the Q value by the Q-Learning algorithm under the constraint model to adjust the vibration amplitude model until the optimization condition is met to obtain the optimal electric field strength in each state space, including the following steps: Based on the state space and the action space, the Q-table of the Q-Learning algorithm is initialized to obtain an initialized Q-table, wherein the state space in the initialized Q-table satisfies the quality constraint model; Randomly obtain the initial state from the state space, and obtain the initial action based on the initial state and the initialized Q table; Based on the initial state and initial action, the current vibration amplitude and the next state are obtained; If the mass in the next state does not satisfy the first mass constraint model, the mass in the next state is adjusted to obtain the adjusted mass in the next state; if the current vibration amplitude does not satisfy the first vibration amplitude constraint model, the current vibration amplitude is adjusted to obtain the adjusted current vibration amplitude; Based on the current vibration amplitude, get the current reward value; Based on the initial state, initial action and current reward value, combined with the Q value update model, the updated Q value is obtained, and then the updated Q table is obtained; Based on the next state and the updated Q-table, the next action is selected to obtain the next reward value and the next Q-value, and the Q-table is updated until the optimization conditions are met to obtain the final Q-table. Extract each state in the final Q table, the maximum Q value corresponding to each state, and the action corresponding to each maximum Q value, and obtain the maximum Q value table, which is the minimum amplitude target model; Among them, the adjusted mass in the next state and the adjusted current vibration amplitude are expressed as follows: in, represents the quality in the next state after adjustment, represents the quality in the next state that does not satisfy the first quality constraint model, represents the preset quality adjustment amount, and , Indicates the current vibration amplitude after adjustment, Indicates the preset vibration amplitude threshold.

6. The method for achieving vibration suppression and lightweighting of a gear transmission system according to claim 1, characterized in that: The multi-objective optimization model is constructed based on the mass, stiffness and electric field strength in the minimum amplitude target model, including the following steps: The multi-objective optimization model includes an optimization variable model, an optimization target model and a second constraint model; Based on the mass, stiffness and electric field strength in the minimum amplitude target model, an optimization variable model is constructed; Based on the mass, stiffness and electric field strength in the minimum amplitude target model, an optimization target model is constructed; The second constraint model at least includes a second mass constraint model and a second vibration amplitude constraint model; Wherein, the optimization variable model is expressed as follows: The optimization target model is expressed as follows: The second quality constraint model is expressed as follows: The second vibration amplitude constraint model is expressed as follows: in, represents the optimization variable, represents the mass of the gear transmission system in the minimum amplitude target model, represents the stiffness of the gear transmission system in the minimum amplitude target model, represents the electric field strength in the minimum amplitude target model, represents the optimization target value, represents the optimization goal, and represents the weight factor, represents the preset second quality threshold, represents the minimum amplitude target model, represents the vibration amplitude in the minimum amplitude target model, Indicates the preset vibration amplitude threshold.

7. The method for achieving vibration suppression and lightweighting of a gear transmission system according to claim 6, characterized in that: The multi-objective optimization model is optimized to obtain the global optimal electric field strength, the minimum mass and the optimal stiffness, and then the global minimum vibration amplitude, including the following steps: Based on the optimization target model, the second mass constraint model and the second vibration amplitude constraint model, combined with Lagrangian multipliers, a Lagrangian model is constructed; The partial derivatives of the Lagrangian model are obtained based on the optimization variables and the Lagrangian multipliers to obtain a partial derivative model; Solve the partial derivative model to obtain the optimal solution of the optimization variables in the multi-objective optimization model, and then obtain the global optimal electric field intensity, global minimum mass and global optimal stiffness; Based on the global optimal electric field intensity, global minimum mass and global optimal stiffness, combined with the minimum amplitude target model, the global minimum vibration amplitude is obtained; The Lagrangian model is expressed as follows: The partial derivative model is expressed as follows: in, represents the Lagrangian value, and represents the Lagrange multiplier.

8. A gear transmission system vibration suppression and lightweight realization system, characterized in that: Includes amplitude module, modeling module, local optimization module and global optimization module; The amplitude module constructs a vibration amplitude model based on relevant parameters of the gear transmission system and relevant parameters of the piezoelectric material, wherein the relevant parameters of the gear transmission system at least include the mass, stiffness, and vibration amplitude of the gear transmission system, and the relevant parameters of the piezoelectric material at least include the electric field strength; The modeling module constructs a constraint model of vibration amplitude and mass, constructs a state space model based on the mass and stiffness of the gear transmission system, constructs an action space model based on the electric field intensity, and constructs a reward model based on minimization of vibration amplitude; The local optimization module optimizes the vibration amplitude model based on the constraint model, the state space model, the action space model and the reward model to obtain the minimum amplitude target model, specifically: under the constraint model, based on the reward value obtained by the reward model, the electric field strength in each state space is adjusted to adjust the vibration amplitude model until the optimization condition is met, and the optimal electric field strength in each state space, that is, the minimum amplitude target model, is obtained; The global optimization module constructs a multi-objective optimization model based on the mass, stiffness and electric field strength in the minimum amplitude target model, optimizes the multi-objective optimization model, obtains the global optimal electric field strength, minimum mass and optimal stiffness, and then obtains the global minimum vibration amplitude, thereby achieving the minimum vibration amplitude and minimum mass of the gear transmission system.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

10. A device for achieving vibration suppression and lightweighting of a gear transmission system, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that: When the processor executes the computer program, the method according to any one of claims 1 to 7 is implemented.

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