Method for evaluating frequency reliability of permanent magnet semi-direct drive transmission system

Abstract

The invention discloses a permanent magnet semi-direct drive transmission system frequency reliability evaluation method, which comprises the steps of S1, establishing an electromechanical coupling dynamic model of a permanent magnet semi-direct drive transmission system, and performing modal analysis on the system; s2, a coupling relation between system dynamic response and abrasion is constructed, and the meshing stiffness of the gear pair after different service times is calculated; s3, fitting a function relationship among the service time of the system, the random variable and the inherent frequency by adopting a BP neural network; and S4, constructing a system frequency reliability limit state function according to a reliability interference theory, and solving the time-varying frequency reliability of the system by adopting an active learning Kriging method. According to the method, the influence of a permanent magnet synchronous motor control strategy and an electromechanical coupling effect is comprehensively considered, the evolution rule of the meshing stiffness of the gear pair under vibration response and wear coupling is explored, and the BP neural network and the active learning Kriging method are combined; and rapid and accurate parametric analysis of modal characteristics and frequency reliability of the system under wear and dynamic response coupling is realized.

Description

Technical Field

[0001] The present invention relates to the field of transmission system reliability assessment, and in particular to a frequency reliability assessment method for a permanent magnet semi-direct drive transmission system applicable to the fields of aviation industry, rail transportation, mining machinery, etc. Background Art

[0002] High-power electromechanical equipment is widely used in the aviation industry, rail transit, mining machinery, and other fields. Its reliability directly determines the operational safety, production efficiency, and lifecycle cost of the entire system. Traditional transmission systems for high-power electromechanical equipment primarily consist of three-phase asynchronous motors, couplings, and multi-stage reducers. These systems suffer from long transmission lines and low transmission efficiency. In complex operating environments, transmission systems are prone to failure, especially in multi-stage reducers, which directly impacts the system's reliable operation time.

[0003] To address this issue, a low-speed, high-power permanent magnet synchronous motor (PMSM) drives a single-stage planetary gear reducer, forming a permanent magnet semi-direct drive transmission system. Compared to asynchronous motors, PMSMs offer advantages such as high energy density, high efficiency, excellent controllability, and safety and reliability. Furthermore, the simplified reduction gearing can reduce system vibration and noise, thereby improving the reliability of high-power electromechanical equipment. However, the presence of the PMSM introduces new electromechanical coupling characteristics into the system. Under electromagnetic excitation, gear mesh excitation, and load excitation, the PMSM exhibits a rich set of dynamic characteristics. Especially when the internal and external excitation frequencies approach the system's natural frequency, resonance is highly likely to occur, compromising the safe and stable operation of the system. Furthermore, the inevitable uncertainty in the dimensional and material parameters of various components in the transmission system is a significant factor affecting system reliability. Therefore, frequency reliability assessment of PMSMs has become an important issue that needs to be explored. Summary of the Invention

[0004] Technical problem: The purpose of the present invention is to overcome the shortcomings of the existing technology and provide a frequency reliability evaluation method for a permanent magnet semi-direct drive transmission system. By comprehensively considering the influence of the permanent magnet synchronous motor control strategy and the electromechanical coupling effect, and combining the BP neural network and the active learning Kriging method, a rapid and accurate parametric analysis of the modal characteristics and frequency reliability of the system under the coupling of wear and dynamic response is achieved, providing theoretical guidance for the anti-resonance optimization design of the permanent magnet semi-direct drive transmission system.

[0005] Technical solution: A method for evaluating the frequency reliability of a permanent magnet semi-direct drive transmission system of the present invention comprises the following steps:

[0006] S1: Establish an electromechanical coupling dynamic model of the permanent magnet semi-direct drive transmission system and perform modal analysis on the permanent magnet semi-direct drive transmission system;

[0007] The mechanical-electromagnetic global coupling relationship of the permanent magnet semi-direct drive transmission system is analyzed according to the Lagrange-Maxwell principle, and the electromechanical coupling dynamic model of the permanent magnet semi-direct drive transmission system is obtained. On this basis, modal analysis is carried out.

[0008] S2: Construct the coupling relationship between the dynamic response and wear of the permanent magnet semi-direct drive transmission system, and calculate the meshing stiffness of the gear pair after different service times;

[0009] A dynamic analysis of a permanent magnet semi-direct drive transmission system considering gear pair meshing wear was conducted to obtain the coupling relationship between dynamic response and wear. The energy method was used to calculate the meshing stiffness of the worn gear pair and to explore the evolution of the meshing stiffness with service time.

[0010] S3: Using BP neural network to fit the functional relationship between the service time, random variables and natural frequency of the permanent magnet semi-direct drive transmission system;

[0011] Determine the random parameters and distribution patterns of the permanent magnet semi-direct drive transmission system, extract random parameter samples and service time samples, obtain natural frequency samples based on the modal equation of the permanent magnet semi-direct drive transmission system, and use a BP neural network to fit the functional relationship between the system service time, random variables and natural frequency;

[0012] S4: Based on the reliability interference theory, the frequency reliability limit state function of the permanent magnet semi-direct drive transmission system is constructed, and the active learning Kriging method is used to solve the time-varying frequency reliability of the permanent magnet semi-direct drive transmission system;

[0013] The internal and external excitations of the permanent magnet semi-direct drive transmission system are analyzed, and the limit state function of the resonance of the permanent magnet semi-direct drive transmission system is established based on the reliability interference theory. The active learning Kriging method is used to construct a surrogate model of random samples, time and the resonance failure performance function of the permanent magnet semi-direct drive transmission system. The probability of resonance failure of the permanent magnet semi-direct drive transmission system in different time periods is calculated.

[0014] In step S1, the core driving unit of the permanent magnet semi-direct drive system is a permanent magnet synchronous motor. First, the stator voltage equation of the permanent magnet synchronous motor is combined with the control strategy to obtain the permanent magnet synchronous motor state equation and electromagnetic torque equation:

[0015]

[0016] Among them, ω m 、 are the angular velocity and angular velocity output reference value of the permanent magnet synchronous motor respectively; χ′ m The difference between the permanent magnet synchronous motor angular velocity output reference value and the current angular velocity; i d 、i qare the d-axis current and q-axis current of the permanent magnet synchronous motor respectively; are the reference values of d-axis and q-axis current output respectively; e′ d The difference between the d-axis current output reference value and the current d-axis current; e′ q The difference between the q-axis current output reference value and the current q-axis current; L d 、L q are the d-axis inductance and q-axis inductance of the permanent magnet synchronous motor respectively; R s is the stator resistance of the permanent magnet synchronous motor; f is the motor flux; p n is the number of pole pairs of the permanent magnet synchronous motor; B a is the damping coefficient of the permanent magnet synchronous motor; K pω , K iω are the PI control parameters of the permanent magnet synchronous motor speed loop; K pd , K id , K pq , K iq are the PI control parameters of the permanent magnet synchronous motor current loop;

[0017] Secondly, the mechanical-electromagnetic coupling relationship of the system is analyzed, and the bending-torsion coupling dynamic model of the mechanical part of the permanent magnet semi-direct drive transmission system is established according to the Lagrange equation:

[0018] [M]{x″}+[C]{x′}+[K]{x}={f(t)} (3)

[0019] Where [M], [C], [K], and [f(t)] are the mass matrix, damping matrix, stiffness matrix, and external excitation matrix of the mechanical part of the permanent magnet semi-direct drive transmission system, respectively; {x″}, {x′}, and {x} are the acceleration response matrix, velocity response matrix, and displacement response matrix of the mechanical part of the system, respectively;

[0020] Then, the state equation and electromagnetic torque equation of the permanent magnet synchronous motor are combined with the bending-torsion coupling dynamic equation to obtain the global electromechanical coupling model of the permanent magnet semi-direct drive transmission system and transform it into the state equation form:

[0021] [A]{X s ′}=[B]{X s}+[U] (4)

[0022] Among them, [A], [B], [U] are the coefficient matrices in the global state equation of the permanent magnet semi-direct drive transmission system, {X s ′} is the differential of the system state variable, {X s} is the system state variable;

[0023] Equation (4) can be further transformed into:

[0024] {X s ′}=[A] -1 [B]{X s}+[A] -1 [U] (5)

[0025] Among them, the matrix [A] -1 [B] The imaginary part of the eigenvalue is the natural frequency of the permanent magnet semi-direct drive transmission system, [A] -1 The eigenvectors of [B] are mode shapes.

[0026] In step S2, the coupling relationship between the dynamic response and wear of the permanent magnet semi-direct drive transmission system is established, and the meshing stiffness of the gear pair after different service times is calculated, specifically including:

[0027] S21. The design life of the permanent magnet semi-direct drive transmission system is T s Divide equally into N T stage, and assume that the dynamic response of the permanent magnet semi-direct drive transmission system remains unchanged in each stage;

[0028] S22. Use the energy method to calculate the initial time-varying meshing stiffness of each gear pair in the permanent magnet semi-direct drive transmission system, and expand the time-varying meshing stiffness into the gear angular displacement θ of the driving gear. i The associated Fourier series form:

[0029]

[0030] Among them, k i is the time-varying meshing stiffness of the i-th pair of driving gear and driven gear; a 0i is the mean meshing stiffness of the i-th gear pair; a i is the Fourier series expansion coefficient of the i-th gear pair; l is the Fourier series expansion order; Z i is the number of teeth of the driving gear in the i-th gear pair; γ i is the initial meshing phase of the i-th gear pair;

[0031] S23, the time-varying meshing stiffness k of each gear pair i (θ i ) is substituted into the global state equation (4) of the permanent magnet semi-direct drive transmission system to calculate the dynamic meshing force of the gear pair;

[0032] S24. Based on the dynamic meshing force of the gear pair at stage n and the Archard wear formula, calculate the wear depth of each gear pair of the i-th gear pair at stage n and the cumulative wear depth after n service stages:

[0033]

[0034] Among them, Nni is the number of meshing times of the gear pair in the nth stage; K is the dimensionless wear coefficient; p ni is the pressure on the contact surface of the gear pair; s pni is the relative sliding distance between the meshing points; h pni is the wear depth of stage n; H p(n-1)i and H pni are the cumulative wear depths after the end of the (n-1)th and nth stages, respectively;

[0035] S25. Update the dimensional parameters of the gear pairs and calculate the time-varying meshing stiffness of the gear pairs using the energy method again. Simultaneously, use Fourier series expansion to obtain the mean value and each order amplitude of the meshing stiffness of each gear pair.

[0036] S26. Repeat steps S23 to S25 until the meshing stiffness of the gear pair of the permanent magnet semi-direct drive transmission system in all time periods is obtained, and a polynomial is used to fit the relationship between the mean meshing stiffness of the gear pair and time.

[0037] In step S3, the use of the BP neural network to fit the functional relationship between the system service time, random variables and natural frequency includes:

[0038] (1) Latin hypercube sampling is used to generate 200 sets of random parameter samples and service time samples to form input samples. The gear meshing stiffness mean matrix corresponding to the random parameter samples and service time samples is substituted into the system natural frequency calculation formula to obtain the output sample.

[0039] (2) A BP neural network with two hidden layers is used to fit the relationship between random parameters, service time and natural frequency, and the "Tanh" function is selected as the transfer function of the hidden layer. Therefore, the fitting function of the BP neural network is expressed as:

[0040] Y=LW2×tanh[LW1×tanh(IW×X+Ib)+Lb1]+Lb2 (8)

[0041] Among them, X and Y are the input and output matrices of the neural network respectively; IW and LW i (i=1,2) are the weight matrices of the output layer and the hidden layer respectively; Ib and Lb i (i=1,2) are the bias matrices of the output layer and the hidden layer respectively.

[0042] In step S4, the frequency reliability limit state function of the permanent magnet semi-direct drive transmission system is constructed according to the reliability interference theory, and the time-varying frequency reliability of the permanent magnet semi-direct drive transmission system is solved by the active learning Kriging method, which includes:

[0043] S41. According to the reliability interference theory, the limit state function G of a certain order natural frequency resonance problem of the permanent magnet semi-direct drive transmission system under internal and external excitation is obtained. ij (X,t) is expressed as:

[0044] G ij (X,t)=|ω ej -ω hi (X,t)|-γ (9)

[0045] Among them, ω ej is the jth excitation frequency; ω hi (X,t) is the i-th order natural frequency calculated based on the BP neural network fitting function; γ is the threshold value of the system resonance failure;

[0046] Obviously, the performance functions of the resonance failure of the permanent magnet semi-direct drive transmission system are in series relationship, so the performance function of the resonance failure of the system under multi-frequency excitation G ss (X,t) is expressed as:

[0047]

[0048] S42. Use active learning Kriging model to establish the resonance failure performance function G of permanent magnet semi-direct drive transmission system ss (X,t) with time t and random variable X as the surrogate model G ALK , using the U function as the criterion for whether the Kriging model converges; after completing the construction of the proxy model, generate uniform time point samples in the time interval [0, T] according to Δt = 0.05, and substitute the N groups of random parameter samples generated by Latin hypercube sampling and the uniform time point samples in [0, T] into the proxy model G ALK , get the extreme value of the response of each random parameter sample in [0,T] Therefore, the probability of resonance failure of the permanent magnet semi-direct drive transmission system in [0, T] is:

[0049]

[0050] in, T is an arbitrary number of years in service;

[0051] S43, repeat step S42 until the system design life T is obtained s The time-varying resonance failure probability of all time periods within the system is calculated, thereby completing the frequency reliability evaluation of the system.

[0052] Beneficial effects: Due to the adoption of the above technical solution, the present invention solves the problem of frequency reliability evaluation of permanent magnet semi-direct drive transmission system, constructs a coupling relationship model between system dynamic response and gear wear, and improves the accuracy of gear wear depth and meshing stiffness calculation. Based on the active learning Kriging algorithm, a proxy model of random samples, time and system resonance failure performance function is constructed to achieve efficient and accurate evaluation of the frequency reliability of permanent magnet semi-direct drive transmission system. The electromagnetic effect of permanent magnet synchronous motor and the influence of control algorithm are taken into account in the electromechanical coupling dynamics equation of permanent magnet semi-direct drive transmission system, so that the dynamic response and modal characteristics of the system are more in line with actual working conditions. The BP neural network is used to establish the functional relationship between system service time, random parameter variables and system natural frequency, which improves the efficiency of natural frequency calculation of permanent magnet semi-direct drive transmission system. The main advantages of this invention over the prior art are: it comprehensively considers the influence of the permanent magnet synchronous motor control strategy and electromechanical coupling effects, explores the evolution of the gear pair meshing stiffness under the coupling of vibration response and wear, and combines the BP neural network with the active learning Kriging method to achieve rapid and accurate parametric analysis of the system's modal characteristics and frequency reliability under the coupling of wear and dynamic response, providing a reference for the anti-resonance design and long-term safe operation of permanent magnet semi-direct drive transmission systems. The method is simple and easy to operate, achieving rapid and accurate parametric analysis of the system's modal characteristics and frequency reliability under the coupling of wear and dynamic response, providing theoretical guidance for the anti-resonance optimization design of permanent magnet semi-direct drive transmission systems. It has practical application in this technical field. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a design flow chart of the present invention.

[0054] Figure 2 It is a schematic diagram of the implementation structure of the permanent magnet semi-direct drive transmission system of the present invention.

[0055] Figure 2 In: 1. Permanent magnet synchronous motor; 2. Flexible coupling at the motor output end; 3. Gear reducer; 4. Flexible coupling at the reducer output end; 5. Load end.

[0056] Figure 3 (a) is a time-varying meshing stiffness diagram of the sun gear-planet gear after different service times using the present invention.

[0057] Figure 3 (b) is a time-varying meshing stiffness diagram of the inner ring gear and the planetary gear after different service times using the present invention.

[0058] Figure 4 (a) is a diagram showing the change in mean square error during the BP neural network training process using the present invention.

[0059] Figure 4(b) is a diagram of a regression model of training samples using the BP neural network training process of the present invention.

[0060] Figure 5 This is a flow chart of calculating the resonance failure probability of a permanent magnet semi-direct drive transmission system based on the active learning Kriging method in the present invention.

[0061] Figure 6 It is a time-varying resonance failure probability diagram of the permanent magnet semi-direct drive transmission system using the present invention. DETAILED DESCRIPTION

[0062] The present invention will be further described below with reference to the embodiments in the accompanying drawings:

[0063] like Figure 1 As shown, a method for evaluating the frequency reliability of a permanent magnet semi-direct drive transmission system of the present invention has the following specific steps:

[0064] S1: Establish an electromechanical coupling dynamics model of the permanent magnet semi-direct drive transmission system and perform modal analysis on the permanent magnet semi-direct drive transmission system: Figure 2 As shown in the simplified diagram of the model structure, the permanent magnet semi-direct drive transmission system includes a low-speed, high-power permanent magnet synchronous motor 1, an elastic coupling 2, a planetary gear reducer 3, an elastic coupling 4, and a load end 5. The elastic coupling 2 is connected to the planetary gear reducer 3, and then connected to the load end 5 through the elastic coupling 4. Through the above transmission path, the permanent magnet synchronous motor drives the load end. Based on the structure of the model, the system modeling work is first carried out starting from the low-speed, high-power permanent magnet synchronous motor 1. According to the Lagrange-Maxwell principle, the mechanical-electromagnetic global coupling relationship of the permanent magnet semi-direct drive transmission system is analyzed to obtain the electromechanical coupling dynamic model of the permanent magnet semi-direct drive transmission system, and modal analysis is carried out on this basis.

[0065] The permanent magnet synchronous motor is the core drive unit of the permanent magnet semi-direct drive system. First, the stator voltage equation of the permanent magnet synchronous motor is combined with the control strategy to obtain the permanent magnet synchronous motor state equation and electromagnetic torque:

[0066]

[0067] Among them, ω m 、 are the angular velocity and angular velocity output reference value of the permanent magnet synchronous motor respectively; χ' m The difference between the permanent magnet synchronous motor angular velocity output reference value and the current angular velocity; i d 、i q are the d-axis current and q-axis current of the permanent magnet synchronous motor respectively; are the reference values of d-axis and q-axis current output respectively; e′ dThe difference between the d-axis current output reference value and the current d-axis current; e′ q The difference between the q-axis current output reference value and the current q-axis current; L d 、L q are the d-axis inductance and q-axis inductance of the permanent magnet synchronous motor respectively; R s is the stator resistance of the permanent magnet synchronous motor; f is the motor flux; p n is the number of pole pairs of the permanent magnet synchronous motor; B a is the damping coefficient of the permanent magnet synchronous motor; K pω , K iω are the PI control parameters of the permanent magnet synchronous motor speed loop; K pd , K id , K pq , K iq are the PI control parameters of the permanent magnet synchronous motor current loop;

[0068] Secondly, the mechanical-electromagnetic coupling relationship of the permanent magnet semi-direct drive transmission system is analyzed, and the bending-torsion coupling dynamic model of the mechanical part of the permanent magnet semi-direct drive transmission system is established according to the Lagrange equation:

[0069] [M]{x″}+[C]{x′}+[K]{x}={f(t)} (3)

[0070] Where [M], [C], [K], and [f(t)] are the mass matrix, damping matrix, stiffness matrix, and external excitation matrix of the mechanical part of the permanent magnet semi-direct drive transmission system, respectively; {x″}, {x′}, and {x} are the acceleration response matrix, velocity response matrix, and displacement response matrix of the mechanical part of the system, respectively;

[0071] Then, the permanent magnet synchronous motor state equation, electromagnetic torque equation and bending-torsion coupling dynamics equation are combined to obtain the global electromechanical coupling model of the permanent magnet semi-direct drive transmission system and transform it into the state equation form:

[0072] [A]{X s ′}=[B]{X s}+[U] (4)

[0073] Among them, [A], [B], [U] are the coefficient matrices in the global state equation of the permanent magnet semi-direct drive transmission system, {X s ′} is the differential of the system state variable, {X s} is the system state variable.

[0074] Equation (4) can be further transformed into:

[0075] {X s ′}=[A] -1 [B]{X s}+[A] -1 [U] (5)

[0076] Among them, the matrix [A] -1 [B] The imaginary part of the eigenvalue is the natural frequency of the permanent magnet semi-direct drive transmission system, [A] -1 The eigenvector of [B] is the mode shape;

[0077] S2: Construct the coupling relationship between the dynamic response and wear of the permanent magnet semi-direct drive transmission system, and calculate the meshing stiffness of the gear pair after different service times:

[0078] The design life of the permanent magnet semi-direct drive transmission system is T s Divide equally into N T The energy method is used to calculate the initial time-varying meshing stiffness of each gear pair in the permanent magnet semi-direct drive transmission system, and the time-varying meshing stiffness is expanded into the gear angular displacement θ of the driving gear. i The associated Fourier series form:

[0079]

[0080] Among them, k i is the time-varying meshing stiffness of the i-th pair of driving gear and driven gear; a 0i is the mean meshing stiffness of the i-th gear pair; a i is the Fourier series expansion coefficient of the i-th gear pair; l is the Fourier series expansion order; Z i is the number of teeth of the driving gear in the i-th gear pair; γ i is the initial meshing phase of the i-th gear pair;

[0081] Substitute the time-varying mesh stiffness of each gear pair into the global state equation (4) of the permanent magnet semi-direct drive transmission system to calculate the dynamic meshing force of the gear pair. Based on the dynamic meshing force of the gear pair at stage n and the Archard wear formula, calculate the wear depth of each gear pair in stage n and the cumulative wear depth after n service stages of the i-th gear pair:

[0082]

[0083] Among them, N ni is the number of meshing times of the gear pair in the nth stage; K is the dimensionless wear coefficient; p ni is the pressure on the contact surface of the gear pair; s pni is the relative sliding distance between the meshing points; h pni is the wear depth of stage n; H p(n-1)i and H pni are the cumulative wear depths after the end of the (n-1)th and nth stages, respectively;

[0084] Update the dimensional parameters of the gear pair and use the energy method again to calculate the time-varying mesh stiffness of the gear pair. At the same time, use the Fourier series expansion to obtain the mean value and order amplitude of the mesh stiffness of each gear pair. Repeat the above process until the mesh stiffness of the permanent magnet semi-direct drive transmission system gear pair at each stage during the service period is obtained, and use a polynomial to fit the relationship between the mean value of the mesh stiffness of the gear pair and time. The time-varying mesh stiffness of the sun gear-planet gear and the inner ring gear-planet gear under vibration wear coupling is as follows: Figure 3 (a) (b)

[0085] S3: BP neural network is used to fit the functional relationship between the service time of permanent magnet semi-direct drive transmission system and the random variable and natural frequency:

[0086] The distribution types of each random variable are shown in Table 1. The Latin supersampling method is used to generate 10 5 Group random parameter sample X R , the service life of the permanent magnet semi-direct drive transmission system [0,20] is generated into a uniform time sample X according to Δt = 0.05 t , randomly select 200 groups of random parameter samples and service time samples to form the input sample X * And substitute the gear meshing stiffness mean matrix corresponding to the random parameter sample and service time sample into the system natural frequency calculation formula to obtain the output sample Y * A BP neural network with two hidden layers is used to fit the relationship between random parameters, service time and natural frequency. The number of nodes in the hidden layer of the BP neural network is set to 5 and 10 respectively, and the "Tanh" function is selected as the transfer function of the hidden layer. Therefore, the fitting function of the BP neural network can be expressed as:

[0087] Y=LW2×tanh[LW1×tanh(IW×X+Ib)+Lb1]+Lb2 (8)

[0088] Among them, X and Y are the input and output matrices of the neural network respectively; IW and LW i (i=1,2) are the weight matrices of the output layer and the hidden layer respectively; Ib and Lb i (i=1,2) are the bias matrices of the output layer and the hidden layer respectively.

[0089] Table 1 Distribution types of random variables

[0090]

[0091]

[0092] In the table: B s is the sun gear tooth width in the planetary gear reducer; B r B is the width of the inner ring gear in the planetary gear reducer;p is the width of the planetary gear teeth in the planetary gear reducer; B c is the width of the planet carrier in the planetary gear reducer; m n is the module of the sun gear, internal gear ring and planet gear in the planetary gear reducer; ρ is the density of the gear material in the planetary gear reducer; E is the elastic modulus of the gear material in the planetary gear reducer.

[0093] After 100 iterations, the mean square error of the training dataset and the test dataset changes as shown below: Figure 4 As shown in (a), the test set achieved the minimum mean square error of 3.055×10 at the 98th iteration. -4 . Figure 4 (b) is the input sample X * The correlation coefficient of the regression model with the predicted output value is 0.99914. This shows that the function fitted by the BP neural network has high accuracy and can be used to subsequently construct the limit state function of the frequency reliability of the permanent magnet semi-direct drive transmission system.

[0094] S4: Construct the frequency reliability limit state function of the permanent magnet semi-direct drive transmission system and use the active learning Kriging method to solve the time-varying frequency reliability of the permanent magnet semi-direct drive transmission system:

[0095] According to the reliability interference theory, the limit state function G of a certain order natural frequency resonance problem of the permanent magnet semi-direct drive transmission system under internal and external excitation is obtained. ij (X,t) can be expressed as:

[0096] G ij (X,t)=|ω ej -ω hi (X,t)|-γ (9)

[0097] Among them, ω ej is the jth excitation frequency; ω hi (X, t) is the i-th order natural frequency calculated based on the BP neural network fitting function; X is the system random variable; γ is the threshold value for the system to fail due to resonance, which is generally 5% to 10% of the natural frequency.

[0098] Obviously, the performance functions of the resonance failure of the permanent magnet semi-direct drive transmission system are in series relationship, so the performance function of the resonance failure of the permanent magnet semi-direct drive transmission system under multi-frequency excitation G ss (X,t) can be expressed as:

[0099]

[0100] Directly using the MCS method to evaluate the resonance failure probability of the permanent magnet semi-direct drive transmission system requires repeated calls to formulas (9) and (10), which is extremely computationally intensive. Therefore, the active learning Kriging method is used to construct a proxy model of the performance function of the permanent magnet semi-direct drive transmission system, thereby improving the efficiency of reliability evaluation. Figure 5 As shown. Using active learning Kriging model to fit the resonance failure performance function G ss The functional relationship G between (X,t) and time t and random variable X ALK , and the U function is used as the criterion for whether the Kriging model converges. After completing the construction of the proxy model, the time interval [0, T] is generated according to Δt = 0.05 to generate uniform time point samples, and the random parameter sample X R Substitute the uniform time point samples in [0,T] into G ALK , get the extreme value of the response of each random parameter sample in [0,T] Therefore, the probability of frequency resonance failure of the permanent magnet semi-direct drive transmission system in [0, T] is:

[0101]

[0102] in, N is the number of random samples;

[0103] The above process is repeated until the resonance failure probability of the system in all time periods is obtained, thus completing the time-varying frequency reliability evaluation of the system.

[0104] In a permanent magnet semi-direct drive transmission system without this method, the influence of gear wear is ignored, the natural frequency of the system will remain unchanged during the service life, and therefore no resonance failure will occur. After applying this method, the threshold value γ for resonance failure is set to 5% and 10% of the natural frequency of each order of the system, respectively. The change in the dynamic resonance failure probability of the permanent magnet semi-direct drive transmission system can be obtained, as shown in Figure 2. Figure 6 The results show that as the resonance failure threshold increases, the time for the permanent magnet semi-direct drive transmission system to enter the failure stage and completely resonant failure is advanced. This is because the larger resonance failure threshold causes the system's natural frequency to enter the resonance range earlier as the gear wears.

Claims

1. A method for evaluating the frequency reliability of a permanent magnet semi-direct drive transmission system, characterized in that The following steps are involved: S1: Establish an electromechanical coupling dynamic model of the permanent magnet semi-direct drive transmission system and perform modal analysis on the permanent magnet semi-direct drive transmission system; The mechanical-electromagnetic global coupling relationship of the permanent magnet semi-direct drive transmission system is analyzed according to the Lagrange-Maxwell principle, and the electromechanical coupling dynamic model of the permanent magnet semi-direct drive transmission system is obtained. On this basis, modal analysis is carried out. S2: Construct the coupling relationship between the dynamic response and wear of the permanent magnet semi-direct drive transmission system, and calculate the meshing stiffness of the gear pair after different service times; A dynamic analysis of a permanent magnet semi-direct drive transmission system considering gear pair meshing wear was conducted to obtain the coupling relationship between dynamic response and wear. The energy method was used to calculate the meshing stiffness of the worn gear pair and to explore the evolution of the meshing stiffness with service time. S3: Using BP neural network to fit the functional relationship between the service time, random variables and natural frequency of the permanent magnet semi-direct drive transmission system; Determine the random parameters and distribution patterns of the permanent magnet semi-direct drive transmission system, extract random parameter samples and service time samples, obtain natural frequency samples based on the modal equation of the permanent magnet semi-direct drive transmission system, and use a BP neural network to fit the functional relationship between the system service time, random variables and natural frequency; S4: Based on the reliability interference theory, the frequency reliability limit state function of the permanent magnet semi-direct drive transmission system is constructed, and the active learning Kriging method is used to solve the time-varying frequency reliability of the permanent magnet semi-direct drive transmission system; The internal and external excitations of the permanent magnet semi-direct drive transmission system are analyzed, and the limit state function of the resonance of the permanent magnet semi-direct drive transmission system is established based on the reliability interference theory. The active learning Kriging method is used to construct a surrogate model of random samples, time and the resonance failure performance function of the permanent magnet semi-direct drive transmission system. The probability of resonance failure of the permanent magnet semi-direct drive transmission system in different time periods is calculated.

2. The method for evaluating frequency reliability of a permanent magnet semi-direct drive transmission system according to claim 1, wherein: In step S1, the core driving unit of the permanent magnet semi-direct drive system is a permanent magnet synchronous motor. First, the stator voltage equation of the permanent magnet synchronous motor is combined with the control strategy to obtain the permanent magnet synchronous motor state equation and electromagnetic torque equation: Among them, ω m 、 are the angular velocity and angular velocity output reference value of the permanent magnet synchronous motor respectively; X′ m The difference between the angular velocity output reference value of the permanent magnet synchronous motor and the current angular velocity; i d 、i q are the d-axis current and q-axis current of the permanent magnet synchronous motor respectively; are the reference values of d-axis and q-axis current output respectively; e′ d The difference between the d-axis current output reference value and the current d-axis current; e′ q The difference between the q-axis current output reference value and the current q-axis current; L d 、L q are the d-axis inductance and q-axis inductance of the permanent magnet synchronous motor respectively; R s is the stator resistance of the permanent magnet synchronous motor; f is the motor flux; p n is the number of pole pairs of the permanent magnet synchronous motor; B a is the damping coefficient of the permanent magnet synchronous motor; K pω , K iω are the PI control parameters of the permanent magnet synchronous motor speed loop; K pd , K id , K pq , K iq are the PI control parameters of the permanent magnet synchronous motor current loop; Secondly, the mechanical-electromagnetic coupling relationship of the system is analyzed, and the bending-torsion coupling dynamic model of the mechanical part of the permanent magnet semi-direct drive transmission system is established according to the Lagrange equation: [M]{x″}+[C]{x′}+[K]{x}={f(t)} (3) Where [M], [C], [K], and [f(t)] are the mass matrix, damping matrix, stiffness matrix, and external excitation matrix of the mechanical part of the permanent magnet semi-direct drive transmission system, respectively; {x″}, {x′}, and {x} are the acceleration response matrix, velocity response matrix, and displacement response matrix of the mechanical part of the system, respectively; Then, the state equation and electromagnetic torque equation of the permanent magnet synchronous motor are combined with the bending-torsion coupling dynamic equation to obtain the global electromechanical coupling model of the permanent magnet semi-direct drive transmission system and transform it into the state equation form: [A]{X s ′}=[B]{X s }+[U] (4) Among them, [A], [B], [U] are the coefficient matrices in the global state equation of the permanent magnet semi-direct drive transmission system, {X s ′} is the differential of the system state variable, {X s } is the system state variable; Equation (4) can be further transformed into: {X s ′}=[A] -1 [B]{X s }+[A] -1 [U] (5) Among them, the matrix [A] -1 [B] The imaginary part of the eigenvalue is the natural frequency of the permanent magnet semi-direct drive transmission system, [A] -1 The eigenvectors of [B] are mode shapes.

3. The method for evaluating frequency reliability of a permanent magnet semi-direct drive transmission system according to claim 1, wherein: In step S2, the coupling relationship between the dynamic response and wear of the permanent magnet semi-direct drive transmission system is established, and the meshing stiffness of the gear pair after different service times is calculated, specifically including: S21. The design life of the permanent magnet semi-direct drive transmission system is T s Divide equally into N T stage, and assume that the dynamic response of the permanent magnet semi-direct drive transmission system remains unchanged in each stage; S22. Use the energy method to calculate the initial time-varying meshing stiffness of each gear pair in the permanent magnet semi-direct drive transmission system, and expand the time-varying meshing stiffness into the gear angular displacement θ of the driving gear. i The associated Fourier series form: Among them, k i is the time-varying meshing stiffness of the i-th pair of driving gear and driven gear; a 0i is the mean meshing stiffness of the i-th gear pair; a i is the Fourier series expansion coefficient of the i-th gear pair; l is the Fourier series expansion order; Z i is the number of teeth of the driving gear in the i-th gear pair; γ i is the initial meshing phase of the i-th gear pair; S23, the time-varying meshing stiffness k of each gear pair i (θ i ) is substituted into the global state equation (4) of the permanent magnet semi-direct drive transmission system to calculate the dynamic meshing force of the gear pair; S24. Based on the dynamic meshing force of the gear pair at stage n and the Archard wear formula, calculate the wear depth of each gear pair of the i-th gear pair at stage n and the cumulative wear depth after n service stages: Among them, N ni is the number of meshing times of the gear pair in the nth stage; K is the dimensionless wear coefficient; p ni is the pressure on the contact surface of the gear pair; s pni is the relative sliding distance between the meshing points; h pni is the wear depth of stage n; H p(n-1)i and H pni are the cumulative wear depths after the end of the (n-1)th and nth stages, respectively; S25. Update the dimensional parameters of the gear pairs and calculate the time-varying meshing stiffness of the gear pairs using the energy method again. Simultaneously, use Fourier series expansion to obtain the mean value and each order amplitude of the meshing stiffness of each gear pair. S26. Repeat steps S23 to S25 until the meshing stiffness of the gear pair of the permanent magnet semi-direct drive transmission system in all time periods is obtained, and a polynomial is used to fit the relationship between the mean meshing stiffness of the gear pair and time.

4. The method for evaluating frequency reliability of a permanent magnet semi-direct drive transmission system according to claim 1, wherein: In step S3, the use of the BP neural network to fit the functional relationship between the system service time, random variables and natural frequency includes: (1) Latin hypercube sampling is used to generate 200 sets of random parameter samples and service time samples to form input samples. The gear meshing stiffness mean matrix corresponding to the random parameter samples and service time samples is substituted into the system natural frequency calculation formula to obtain the output sample. (2) A BP neural network with two hidden layers is used to fit the relationship between random parameters, service time and natural frequency, and the "Tanh" function is selected as the transfer function of the hidden layer. Therefore, the fitting function of the BP neural network is expressed as: Y=LW2×tanh[LW1×tanh(IW×X+Ib)+Lb1]+Lb2 (8) Among them, X and Y are the input and output matrices of the neural network respectively; IW and LW i (i=1,2) are the weight matrices of the output layer and the hidden layer respectively; Ib and Lb i (i=1,2) are the bias matrices of the output layer and the hidden layer respectively.

5. The method for evaluating frequency reliability of a permanent magnet semi-direct drive transmission system according to claim 1, wherein: In step S4, the frequency reliability limit state function of the permanent magnet semi-direct drive transmission system is constructed according to the reliability interference theory, and the time-varying frequency reliability of the permanent magnet semi-direct drive transmission system is solved by the active learning Kriging method, which includes: S41. According to the reliability interference theory, the limit state function G of a certain order natural frequency resonance problem of the permanent magnet semi-direct drive transmission system under internal and external excitation is obtained. ij (X,t) is expressed as: G ij (X,t)=|ω ej -oh hi (X,t)|-γ (9) Among them, ω ej is the jth excitation frequency; ω hi (X,t) is the i-th order natural frequency calculated based on the BP neural network fitting function; γ is the threshold value of the system resonance failure; Obviously, the performance functions of the resonance failure of the permanent magnet semi-direct drive transmission system are in series relationship, so the performance function of the resonance failure of the system under multi-frequency excitation G ss (X,t) is expressed as: S42. Use active learning Kriging model to establish the resonance failure performance function G of permanent magnet semi-direct drive transmission system ss (X,t) with time t and random variable X as the surrogate model G ALK , using the U function as the criterion for whether the Kriging model converges; after completing the construction of the proxy model, generate uniform time point samples in the time interval [0, T] according to Δt = 0.05, and substitute the N groups of random parameter samples generated by Latin hypercube sampling and the uniform time point samples in [0, T] into the proxy model G ALK , get the extreme value of the response of each random parameter sample in [0,T] Therefore, the probability of resonance failure of the permanent magnet semi-direct drive transmission system in [0, T] is: in, T is an arbitrary number of years in service; S43, repeat step S42 until the system design life T is obtained s The time-varying resonance failure probability of all time periods within the system is calculated, thereby completing the frequency reliability evaluation of the system.

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