Dynamic load spectrum acquisition method for key parts of electric vehicle transmission system

Abstract

The invention discloses a method for acquiring a dynamic load spectrum of key parts of an electric vehicle transmission system, which comprises the following steps of: establishing a dynamic model of the electric vehicle transmission system, and simulating and acquiring dynamic load data of the key parts of the transmission system based on an urban road cycle condition (UDDS); and processing the random dynamic load data by adopting a statistical analysis method, and compiling a uniform amplitude two-dimensional design spectrum and a fatigue test program loading spectrum of the key parts of the electric vehicle transmission system. And based on the load spectrum, realizing optimal design and reliability experiment of parts of the electric vehicle transmission system, and estimating the service life of the transmission system.

Description

Technical Field

[0001] The invention belongs to the field of obtaining dynamic load spectra of components, and in particular, relates to a method for obtaining dynamic load spectra of key components of an electric vehicle transmission system. Background Art

[0002] In the early stage of electric vehicle transmission system design, fatigue resistance design and reliability tests of key components of the transmission system are often implemented based on load spectra. The structure and working characteristics of electric vehicle transmission systems are quite different from those of traditional fuel vehicles, and their load spectra cannot refer to the load spectrum data of traditional fuel vehicle transmission systems. In terms of load spectrum acquisition methods, traditional fuel vehicles mainly use real vehicle road tests to obtain load data, and compile them into load spectra for reliability tests through data processing. The method of obtaining the load spectrum of the transmission system through real vehicle road tests has high requirements for the test system, long cycles, and high costs; in addition, the amount of random load data of the automobile transmission system obtained through the real vehicle test method is very large and not very practical. Therefore, based on specific driving conditions, there is currently a lack of simple and feasible methods for obtaining the load spectrum of the electric vehicle transmission system using computer simulation methods. Summary of the invention

[0003] The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a method for obtaining the dynamic load spectrum of key components of an electric vehicle transmission system, thereby solving the problems raised in the above-mentioned background technology.

[0004] In order to solve the above technical problems, the basic concept of the technical solution adopted by the present invention is:

[0005] A method for obtaining a dynamic load spectrum of key components of an electric vehicle transmission system comprises the following steps:

[0006] S1: Based on the actual operating environment of electric vehicles, the control model of the electric vehicle drive motor is established using the urban road cycle condition to simulate the output motor speed and torque;

[0007] S2: Based on the rigid body rotation and elastic vibration of the gear, the lumped parameter method is used to establish the elastic dynamics model of the multi-stage gear transmission system, which is organized into a matrix form to obtain the forced vibration equation of the gear transmission system;

[0008] S3: Substitute the motor speed and torque obtained by simulation and the transmission system load into the transmission system dynamics model, calculate the system load in combination with the vehicle driving resistance, obtain the vibration displacement response of key components, and then calculate the load history of key components;

[0009] S4: The dynamic stress-time history of key components is obtained by combining static stress calculation with dynamic load-time history. Then, the stress-time history of components is discretized into a series of peak-valley values ​​by using the rainflow counting method. After cycle counting processing, the load amplitude, mean and corresponding frequency relationship of the components are obtained. The counting results are subjected to probability distribution fitting and chi-square hypothesis test to obtain the joint probability density function of the load mean and amplitude.

[0010] S5: Based on the fitted joint probability density function, the average amplitude two-dimensional design load spectrum and fatigue test program loading spectrum of key components are generated.

[0011] In this embodiment, the dynamic equation in step S2 is: Where X is the system displacement vector, F(t) is the external force excitation, M, T L , E and T e denote the generalized mass matrix, system load, meshing error excitation vector and electromagnetic torque vector respectively, K m , K t , K b They are meshing stiffness matrix, torsional stiffness matrix, support stiffness matrix, C m , C t , C b They are meshing damping matrix, torsional damping matrix and support damping matrix respectively.

[0012] In this embodiment, the load history of key components calculated in step S3 includes the dynamic meshing force of the gear pair, the bearing support force, and the dynamic torque of the transmission shaft;

[0013] Among them, based on the dynamic meshing characteristics of the gear pair, the expression of the dynamic meshing force F(t) of the gear pair is: Among them, K m (t) is the time-varying mesh stiffness, C m (t) is the time-varying meshing damping, δ(t) is the relative displacement on the gear meshing line, is the first-order derivative of the relative displacement;

[0014] The timing starts when a pair of teeth just enters meshing, that is, the initial angular displacement of the driving and driven gears is θ p (0) = 0, θ g (0) = 0, then the system gap function f(δ) is defined as

[0015] Wherein, b′ is the tooth side clearance, and the expression of the tooth side clearance b′ is b′=2a0cosα·(invα′-invα)+b0, where a0 is the theoretical center distance, α is the pitch circle pressure angle, b0 is the tooth side clearance caused by the change of tooth thickness, and b0=0;

[0016] The expression of δ(t) is: δ(t)=R p θ p (t)-R g θ g (t)-e(t), represents the dynamic transmission error of the gear pair along the meshing line direction;

[0017] When analyzing the gear meshing state, when f(δ)>0, it means that the tooth surface is in a normal meshing state, and its value is the deformation at the meshing point; when f(δ)=0, it means the tooth disengagement state, that is, due to the existence of tooth side clearance, the driving and driven wheel teeth are temporarily disengaged during the transmission process, but then the teeth of the two gears will contact again and produce tooth surface impact; when f(δ)<0, it means the tooth back contact and its corresponding deformation;

[0018] The bearing support force is derived based on the kinematics of rolling bearings and Hertz contact theory, and its expression is: In the formula, x b ,y b are the vibration displacements of the inner ring center in the x and y directions, respectively, and c is the rolling bearing clearance; is the position angle of the jth roller; N b is the number of rolling elements; K c The Hertzian contact stiffness is related to the bearing material and contact shape, and n is an index;

[0019] The index n is 2 / 3 when the bearing is a ball bearing and 10 / 9 when the bearing is a roller bearing; H(δ j ) is the Heaviside function, whose return value is 0 and 1; δ j It represents the total contact deformation of the jth roller, and its expression is: Among them, ω b Indicates the inner ring speed;

[0020] The dynamic torque of the transmission shaft is established using the Lagrangian dynamics equation, and its expression is: Where, T d represents the dynamic torque of the transmission shaft, J, c, and k represent the moment of inertia, torsional stiffness, and torsional damping of the transmission shaft, respectively.

[0021] In this embodiment, the steps for obtaining the dynamic stress-time history of key components are as follows:

[0022] Based on the finite element analysis software or the stress calculation formula of the fatigue risk position of the parts, the elastic stress of the key components is calculated under static load conditions to obtain the static stress value σ FEA ,Then, through simulation or experiment, the dynamic load time history p(t) of key components under dynamic conditions is obtained;

[0023] The static stress σFEA Combined with the dynamic load time history p(t), the dynamic stress-time history σ(t) of key components is calculated, and its expression is: Among them, PFEA represents the defined static load; σ represents the elastic stress caused by the load; p(t) represents the dynamic load-time history; σ(t) represents the stress-time history.

[0024] In this embodiment, rain flow counting is divided into two steps: data compression and cycle number extraction. Among them, data compression is divided into peak and valley value detection and invalid amplitude removal. The range of the random load history (the difference between the maximum stress amplitude and the minimum stress amplitude) is calculated, and 10% of the range is taken as the threshold. The small amplitude cycle data less than the threshold is compressed and processed to remove invalid data that has no significant effect on fatigue damage.

[0025] Cycle number extraction is to extract peak values ​​and valley values ​​from the load time history, discretize the random load history into a sequence of peak and valley values, count the cycles of the peak and valley value sequence, identify the starting point and closing point of the load cycle, obtain the cycle number of each load cycle, and then organize the rain flow counting results into a rain flow matrix, which is expressed as follows: Where R(i, j) represents the rain flow matrix; i represents the load level at the starting point of the rain flow cycle; j represents the load level at the closing point of the rain flow cycle; r ij It represents the number of cycles with the starting point i and the closing point j of the rain flow cycle; u and v are the number of columns and rows of the rain flow matrix respectively.

[0026] In this embodiment, after the rain flow matrix is ​​established, the steps of performing probability distribution fitting and chi-square hypothesis test on the counting results are as follows:

[0027] According to the load data obtained by the rain flow counting method, it is assumed that the load amplitude X obeys the three-parameter Weibull distribution and the load mean Y obeys the normal distribution. Based on this assumption, a joint probability density function is constructed, and its expression is: Where x represents the test load amplitude, y represents the test load mean, α represents the Weibull distribution shape parameter, β represents the Weibull distribution scale parameter, ε represents the Weibull distribution threshold parameter, μ represents the normal distribution mean, and σ represents the normal distribution standard deviation;

[0028] Based on the counting results of the rain flow matrix, the frequency distribution of the amplitude and mean at different load levels is calculated, and the chi-square value calculation formula is constructed to test the independence between the amplitude and the mean. The expression is: In the formula, n represents the sub-sample size; r represents the number of levels of amplitude; s represents the number of levels of mean; n j Indicates the frequency of the mean falling into the jth level; n i Indicates the frequency of the amplitude falling into the i-th level; n ijIt indicates the frequency that the amplitude falls in the i-th level and the mean falls in the j-th level;

[0029] The chi-square test is used to test the independence of the load mean and amplitude. If the amplitude and mean are independent of each other, according to Fisher's theorem, the random quantity approximately obeys the chi-square test with degrees of freedom (r-1)·(s-1) 2 Distribution, its expression is: Where U α represents the upper alpha quantile of the standard normal distribution;

[0030] If X and Y are not independent of each other, it is necessary to use linear or nonlinear regression analysis to finally determine the joint distribution density function of the mean amplitude. Finally, based on the load mean amplitude frequency histogram, the linear regression least squares method is used to fit the amplitude means respectively to obtain the estimation of the amplitude mean distribution parameters.

[0031] In this embodiment, after the above distribution verification is passed, the working condition cycle load needs to be expanded to 10 6 The total cumulative frequency of cycles is expressed as: Among them, N' i is the cumulative frequency after the cyclic load is expanded;

[0032] Since the mean follows the normal distribution and the load amplitude follows the three-parameter Weibull distribution, the extreme values ​​of the load amplitude X and the mean Y are calculated according to the probability density function and the probability of extreme value occurrence P, which are used to define the unfavorable load conditions. The expression is: Y max =μ P σ+μ, where μ p is the deviation value of the standard normal distribution.

[0033] In this embodiment, the average amplitude two-dimensional design load spectrum is generated by a non-equal interval amplitude grading method; the fatigue test program loading spectrum is converted into a one-dimensional load spectrum based on the Goodman equation according to the equal damage principle;

[0034] The average amplitude two-dimensional load spectrum is obtained based on the load average and amplitude extreme values ​​of the components throughout their life cycle, and the average is graded at equal intervals. The amplitude is divided into 8 levels according to the non-equal interval method through the formula Get the number of cycles n at each level corresponding to the mean and amplitude i , thus obtaining the two-dimensional spectrum matrix of the mean amplitude, where Sa1 and Sa2 represent the lower and upper limits of the integral of the load amplitude, respectively; Sm1 and Sm2 represent the lower and upper limits of the integral of the load mean, respectively; f j (x,y) represents the joint distribution probability density function;

[0035] Based on the two-dimensional design spectrum, the asymmetric cyclic stress is equivalent to the symmetric cyclic stress with a mean of zero. Then, the Goodman equation is used as the equal fatigue damage conversion formula, which is specifically expressed as Wherein, Sa represents the torque amplitude; Sb represents the torsional strength limit torque; Sm represents the torque mean; Seq represents the equivalent torque amplitude;

[0036] On the basis of obtaining the equivalent torque amplitude, the load amplitude is divided into 8 levels using the unequal interval method, and its expression is: k =K k ·x max , where x k is the k-th level load amplitude; K k is the proportionality coefficient between the k-th level amplitude and the limit value; x max is the limit value of equivalent torque amplitude; k represents load classification, k = 1, 2, 3...8;

[0037] According to the probability distribution function F(x) of the load amplitude, calculate the cumulative frequency N of the load amplitude from level 1 to level k k , its expression is: N k =10 6 ·F(x k ), where F(x) is the probability distribution function of the amplitude load. Finally, the number of occurrences of the k-th level load amplitude is calculated based on the cumulative frequency. k , its expression is: k =N k -N k-1 (k=2, 3, .. , 8), where N k and N k-1 They represent the cumulative frequencies of the kth level and the k-1th level respectively.

[0038] In this embodiment, the ratio coefficients are divided into 8 levels: 1, 0.95, 0.85, 0.725, 0.575, 0.425, 0.275, and 0.125.

[0039] After adopting the above technical solution, the present invention has the following beneficial effects compared with the prior art. Of course, any product implementing the present invention does not necessarily need to achieve all the advantages described below at the same time:

[0040] 1. The present invention establishes a dynamic model of the electric vehicle transmission system, obtains dynamic load data of key components of the transmission system based on the urban road cycle condition (UDDS) simulation, processes the random dynamic load data using statistical analysis methods, and compiles the average amplitude two-dimensional design spectrum and fatigue test program loading spectrum of key components of the electric vehicle transmission system. Based on the load spectrum, the optimization design and reliability experiment of the components of the electric vehicle transmission system, as well as the life estimation of the transmission system, are realized.

[0041] 2. Based on the urban road cycle working conditions, the load spectrum of the electric vehicle transmission system is obtained by computer simulation, which has the advantages of significant low cost and high efficiency. Compared with the traditional real vehicle test, this method can quickly and accurately simulate the dynamic load conditions of components such as motors, gears, and bearings in a virtual environment, greatly reducing the test time and capital investment. In addition, the present invention can be applied after the transmission system is initially finalized, without waiting for the actual vehicle to be manufactured, which provides great flexibility for early verification in product development. By obtaining the load spectrum of key components, it can not only provide a reliable numerical basis for the anti-fatigue design of components, but also help optimize the structural design and improve the service life and reliability of components. At the same time, the data in the load spectrum can also be used for experimental loading to simulate the fatigue state under real working conditions, further verify the reliability of the design scheme, and form a closed-loop process of design and verification.

[0042] The specific implementation modes of the present invention are further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The drawings described below are only some embodiments. For those skilled in the art, other drawings can be obtained based on these drawings without creative work.

[0044] In the figure:

[0045] Figure 1 Simulate control models for motors;

[0046] Figure 2 It is a schematic diagram of the rolling bearing model;

[0047] Figure 3 This is the flowchart of the rain flow counting method.

[0048] It should be noted that these drawings and textual descriptions are not intended to limit the conceptual scope of the present invention in any way, but are intended to illustrate the concept of the present invention for those skilled in the art by referring to specific embodiments. DETAILED DESCRIPTION

[0049] The present invention will now be described in further detail with reference to the accompanying drawings.

[0050] See also Figure 1-3 As shown, in this embodiment, a method for obtaining a dynamic load spectrum of key components of an electric vehicle transmission system is provided, comprising the following steps:

[0051] S1: Based on the actual operating environment of electric vehicles, the urban road cycle condition is adopted to establish a control model of the electric vehicle drive motor, and simulate the output motor speed and torque; specifically, a control model of the vehicle motor is established, and the speed and torque output of the vehicle motor is obtained based on the cycle condition simulation. Electric vehicles are mainly used in cities or suburbs, so the urban road cycle condition (UDDS) formulated by the US Environmental Protection Agency EPA is selected as the simulation cycle condition. Common motors used in electric vehicles include DC motors, AC induction motors, permanent magnet synchronous motors and switched reluctance motors, but with the increasing number of complex controls for vehicle motors, AC speed regulation has shown outstanding advantages. Therefore, the mainstream and future development trend of electric vehicle drive motors is the AC speed regulation system, including AC asynchronous motors and permanent magnet synchronous motors. According to the dynamic mathematical models of AC asynchronous motors and permanent magnet synchronous motors, the corresponding control strategies are selected to establish the simulation model of the motor. The control speed of the motor simulation model is the vehicle speed of the urban road cycle condition (UDDS), and the output is the motor speed and torque. The motor simulation control model is as follows Figure 1 shown.

[0052] It should be noted that by building a vehicle motor control model and combining it with actual working conditions (such as UDDS), the performance output of the motor in a real driving environment can be simulated. This can not only ensure the reliability and accuracy of the input data, but also reflect the dynamic response differences of different motor types (such as AC asynchronous motors and permanent magnet synchronous motors) in actual applications, providing high-quality input data for subsequent dynamic simulation of power transmission.

[0053] S2: The transmission system of electric vehicles can be divided into two categories: fixed transmission ratio systems represented by multi-stage reducers and variable transmission ratio systems with 2 to 4 gears; their structural forms are all complex mechanical systems composed of many parts such as gears, shafts, and bearings. Taking into account the rigid body rotation and elastic vibration of each gear, the lumped parameter method is used to establish the elastic dynamics model of the multi-stage gear transmission system, which is organized into a matrix form to obtain the forced vibration equation of the gear transmission system;

[0054] It should be noted that the elastic dynamics model of the transmission system simplifies the modeling of complex mechanical systems through the lumped parameter method, which helps to accurately capture the dynamic characteristics of each component. This process provides a clear description of the mechanical behavior of key components such as gears, bearings and transmission shafts, ensuring that the model can fully reflect the power transmission and vibration characteristics of the transmission system, laying the foundation for dynamic stress analysis.

[0055] S3: Substitute the motor speed and torque obtained by simulation and the transmission system load into the transmission system dynamics model, calculate the system load in combination with the vehicle driving resistance, obtain the vibration displacement response of key components, and then calculate the load history of key components;

[0056] Furthermore, by clarifying the physical parameters of each component of the transmission system, the vehicle motor speed n and torque Te obtained by the cyclic working condition (UDDS) simulation and the transmission system load (vehicle driving resistance) TL calculated by the vehicle driving equation are substituted into the forced vibration equation () to concretize the forced vibration equation of the gear transmission system, and the vibration displacement response of the key components is obtained, and then the load history of the key components is calculated.

[0057] It should be noted that by substituting the motor output data obtained by simulation into the dynamic model, the stress-time history of key components under different working conditions can be dynamically calculated. This process provides dynamic stress data for fatigue analysis, which can capture the extreme loads that key components may encounter in long-term use, thereby providing strong support for their reliability and durability design.

[0058] S4: The dynamic stress-time history of key components is obtained by combining static stress calculation with dynamic load-time history. Then, the stress-time history of components is discretized into a series of peak-valley values ​​by using the rainflow counting method. After cycle counting processing, the load amplitude, mean and corresponding frequency relationship of the components are obtained. The counting results are subjected to probability distribution fitting and chi-square hypothesis test to obtain the joint probability density function of the load mean and amplitude.

[0059] Specifically, the stress-time history of key components of electric vehicle transmission system obtained based on cyclic driving conditions is essentially random stress, so statistical analysis methods are used to describe it, and cycle counting of random stress is the premise of statistical analysis. The rain flow counting method is used to discretize the stress-time history of components into a series of peak and valley values. After cycle counting processing, the load amplitude, mean and corresponding frequency relationship of the components are obtained; the counting results are statistically analyzed and chi-square hypothesis tested to obtain the probability distribution characteristics of dynamic stress.

[0060] It should be noted that the load data is discretized using the rainflow counting method, and the joint distribution function of the load mean and amplitude is established through probability distribution fitting and chi-square test. This statistical process can extract core features from a large amount of load data, ensuring that the load model can reflect the randomness and uncertainty under long-term working conditions, and providing important data support for load spectrum generation.

[0061] S5: Based on the fitted joint probability density function, the average amplitude two-dimensional design load spectrum and fatigue test program loading spectrum of key components are generated.

[0062] More specifically, the rainflow counting computer processing program flow is as follows Figure 3As shown in the figure, it is divided into two steps: data compression and cycle number extraction. Data compression is divided into peak and valley value detection and invalid amplitude removal. 10% of the random load history range (maximum stress amplitude - minimum stress amplitude) is taken to compress a small number of cycles that cannot cause fatigue damage; the filtering and denoising method in signal processing can also be used to process load data.

[0063] It should be noted that the compilation of two-dimensional design spectrum and fatigue test program loading spectrum provides a direct basis for the fatigue design and fatigue life verification of parts. The two-dimensional design spectrum is used to optimize the structural design of parts and improve their fatigue resistance; the one-dimensional loading spectrum is verified by test to ensure that the design can meet the reliability requirements of actual working conditions, thereby realizing closed-loop management from design to verification.

[0064] In this embodiment, the dynamic equation in step S2 is: Where X is the system displacement vector, F(t) is the external force excitation, M, T L , E and T e denote the generalized mass matrix, system load, meshing error excitation vector and electromagnetic torque vector respectively, K m , K t , K b They are meshing stiffness matrix, torsional stiffness matrix, support stiffness matrix, C m , C t , C b They are meshing damping matrix, torsional damping matrix and support damping matrix respectively.

[0065] In this embodiment, the load history of key components calculated in step S3 includes the dynamic meshing force of the gear pair, the bearing support force, and the dynamic torque of the transmission shaft;

[0066] Among them, based on the dynamic meshing characteristics of the gear pair, the expression of the dynamic meshing force F(t) of the gear pair is: Among them, K m (t) is the time-varying mesh stiffness, C m (t) is the time-varying meshing damping, δ(t) is the relative displacement on the gear meshing line, is the first-order derivative of the relative displacement;

[0067] The timing starts when a pair of teeth just enters meshing, that is, the initial angular displacement of the driving and driven gears is θ p (0) = 0, θ g (0) = 0, then the system gap function f(δ) is defined as

[0068] Wherein, b′ is the tooth side clearance, and the expression of the tooth side clearance b′ is b′=2a0cosα·(invα′-invα)+b0, where a0 is the theoretical center distance, α is the pitch circle pressure angle, b0 is the tooth side clearance caused by the change of tooth thickness, and b0=0;

[0069] The expression of δ(t) is: δ(t)=R p θ p (t)-R g θ g (t)-e(t), represents the dynamic transmission error of the gear pair along the meshing line direction;

[0070] When analyzing the gear meshing state, when f(δ)>0, it means that the tooth surface is in a normal meshing state, and its value is the deformation at the meshing point; when f(δ)=0, it means the tooth disengagement state, that is, due to the existence of tooth side clearance, the driving and driven wheel teeth are temporarily disengaged during the transmission process, but then the teeth of the two gears will contact again and produce tooth surface impact; when f(δ)<0, it means the tooth back contact and its corresponding deformation;

[0071] The bearing support force is derived based on the kinematics of rolling bearings and Hertz contact theory, and its expression is: In the formula, x b ,y b are the vibration displacements of the inner ring center in the x and y directions, respectively, and c is the rolling bearing clearance; is the position angle of the jth roller; N b is the number of rolling elements; K c The Hertzian contact stiffness is related to the bearing material and contact shape, and n is an index;

[0072] The index n is 2 / 3 when the bearing is a ball bearing and 10 / 9 when the bearing is a roller bearing; H(δ j ) is the Heaviside function, whose return value is 0 and 1; δ j It represents the total contact deformation of the jth roller, and its expression is: Among them, ω b Indicates the inner ring speed;

[0073] The dynamic torque of the transmission shaft is established using the Lagrangian dynamics equation, and its expression is: Where, T d represents the dynamic torque of the transmission shaft, J, c, and k represent the moment of inertia, torsional stiffness, and torsional damping of the transmission shaft, respectively.

[0074] In this embodiment, the steps for obtaining the dynamic stress-time history of key components are as follows:

[0075] Based on the finite element analysis software or the stress calculation formula of the fatigue risk position of the parts, the elastic stress of the key components is calculated under static load conditions to obtain the static stress value σ FEA ,Then, through simulation or experiment, the dynamic load time history p(t) of key components under dynamic conditions is obtained;

[0076] The static stress σ FEA Combined with the dynamic load time history p(t), the dynamic stress-time history σ(t) of key components is calculated, and its expression is: Among them, PFEA represents the defined static load; σ represents the elastic stress caused by the load; p(t) represents the dynamic load-time history; σ(t) represents the stress-time history.

[0077] In this embodiment, rain flow counting is divided into two steps: data compression and cycle number extraction. Among them, data compression is divided into peak and valley value detection and invalid amplitude removal. The range of the random load history (the difference between the maximum stress amplitude and the minimum stress amplitude) is calculated, and 10% of the range is taken as the threshold. The small amplitude cycle data less than the threshold is compressed and processed to remove invalid data that has no significant effect on fatigue damage.

[0078] Cycle number extraction is to extract peak values ​​and valley values ​​from the load time history, discretize the random load history into a sequence of peak and valley values, count the cycles of the peak and valley value sequence, identify the starting point and closing point of the load cycle, obtain the cycle number of each load cycle, and then organize the rain flow counting results into a rain flow matrix, which is expressed as follows: Where R(i, j) represents the rain flow matrix; i represents the load level at the starting point of the rain flow cycle; j represents the load level at the closing point of the rain flow cycle; r ij It represents the number of cycles with the starting point i and the closing point j of the rain flow cycle; u and v are the number of columns and rows of the rain flow matrix respectively.

[0079] In this embodiment, after the rain flow matrix is ​​established, the steps of performing probability distribution fitting and chi-square hypothesis test on the counting results are as follows:

[0080] According to the load data obtained by the rain flow counting method, it is assumed that the load amplitude X obeys the three-parameter Weibull distribution and the load mean Y obeys the normal distribution. Based on this assumption, a joint probability density function is constructed, and its expression is: Where x represents the test load amplitude, y represents the test load mean, α represents the Weibull distribution shape parameter, β represents the Weibull distribution scale parameter, ε represents the Weibull distribution threshold parameter, μ represents the normal distribution mean, and σ represents the normal distribution standard deviation;

[0081] Based on the counting results of the rain flow matrix, the frequency distribution of the amplitude and mean at different load levels is calculated, and the chi-square value calculation formula is constructed to test the independence between the amplitude and the mean. The expression is: In the formula, n represents the sub-sample size; r represents the number of levels of amplitude; s represents the number of levels of mean; n j Indicates the frequency of the mean falling into the jth level; n i Indicates the frequency of the amplitude falling into the i-th level; n ij It indicates the frequency that the amplitude falls in the i-th level and the mean falls in the j-th level;

[0082] The chi-square test is used to test the independence of the load mean and amplitude. If the amplitude and mean are independent of each other, according to Fisher's theorem, the random quantity approximately obeys the chi-square test with degrees of freedom (r-1)·(s-1) 2 Distribution, its expression is: Where U α represents the upper alpha quantile of the standard normal distribution;

[0083] If X and Y are not independent of each other, it is necessary to use linear or nonlinear regression analysis to finally determine the joint distribution density function of the mean amplitude. Finally, based on the load mean amplitude frequency histogram, the linear regression least squares method is used to fit the amplitude means respectively to obtain the estimation of the amplitude mean distribution parameters.

[0084] In this embodiment, after the above distribution verification is passed, the working condition cycle load needs to be expanded to 10 6 The total cumulative frequency of cycles is expressed as: Among them, N' i is the cumulative frequency after the cyclic load is expanded;

[0085] Since the mean follows the normal distribution and the load amplitude follows the three-parameter Weibull distribution, the extreme values ​​of the load amplitude X and the mean Y are calculated according to the probability density function and the probability of extreme value occurrence P, which are used to define the unfavorable load conditions. The expression is: Y max =μ P σ+μ, where μ p is the deviation value of the standard normal distribution.

[0086] In this embodiment, the average amplitude two-dimensional design load spectrum is generated by a non-equal interval amplitude grading method; the fatigue test program loading spectrum is converted into a one-dimensional load spectrum based on the Goodman equation according to the equal damage principle;

[0087] The average amplitude two-dimensional load spectrum is obtained based on the load average and amplitude extreme values ​​of the components throughout their life cycle, and the average is graded at equal intervals. The amplitude is divided into 8 levels according to the non-equal interval method through the formula Get the number of cycles n at each level corresponding to the mean and amplitude i, thus obtaining the two-dimensional spectrum matrix of the mean amplitude, where Sa1 and Sa2 represent the lower and upper limits of the integral of the load amplitude, respectively; Sm1 and Sm2 represent the lower and upper limits of the integral of the load mean, respectively; f j (x,y) represents the joint distribution probability density function;

[0088] Based on the two-dimensional design spectrum, the asymmetric cyclic stress is equivalent to the symmetric cyclic stress with a mean of zero. Then, the Goodman equation is used as the equal fatigue damage conversion formula, which is specifically expressed as Wherein, Sa represents the torque amplitude; Sb represents the torsional strength limit torque; Sm represents the torque mean; Seq represents the equivalent torque amplitude;

[0089] On the basis of obtaining the equivalent torque amplitude, the load amplitude is divided into 8 levels using the unequal interval method, and its expression is: k =K k ·x max , where x k is the k-th level load amplitude; K k is the proportionality coefficient between the k-th level amplitude and the limit value; x max is the limit value of equivalent torque amplitude; k represents load classification, k = 1, 2, 3…8;

[0090] According to the probability distribution function F(x) of the load amplitude, calculate the cumulative frequency N of the load amplitude from level 1 to level k k , its expression is: N k =10 6 ·F(x k ), where F(x) is the probability distribution function of the amplitude load. Finally, the number of occurrences of the k-th level load amplitude is calculated based on the cumulative frequency. k , its expression is: k =N k -N k-1 (k=2, 3, ..., 8), where N k and N k-1 They represent the cumulative frequencies of the kth level and the k-1th level respectively.

[0091] In this embodiment, the ratio coefficients are divided into 8 levels: 1, 0.95, 0.85, 0.725, 0.575, 0.425, 0.275, and 0.125.

[0092] The present invention is not limited to the above-mentioned embodiments. Anyone should be aware that any structural changes made under the enlightenment of the present invention, and any technical solutions that are the same or similar to the present invention, fall within the protection scope of the present invention. The technology, shape, and structural parts not described in detail in the present invention are all well-known technologies.

Claims

1. A method for obtaining dynamic load spectrum of key components of electric vehicle transmission system, characterized in that: The following steps are involved: S1: Based on the actual operating environment of electric vehicles, the control model of the electric vehicle drive motor is established using the urban road cycle condition to simulate the output motor speed and torque; S2: Based on the rigid body rotation and elastic vibration of the gear, the lumped parameter method is used to establish the elastic dynamics model of the multi-stage gear transmission system, which is organized into a matrix form to obtain the forced vibration equation of the gear transmission system; S3: Substitute the motor speed and torque obtained by simulation and the transmission system load into the transmission system dynamics model, calculate the system load in combination with the vehicle driving resistance, obtain the vibration displacement response of key components, and then calculate the load history of key components; S4: The dynamic stress-time history of key components is obtained by combining static stress calculation with dynamic load-time history. Then, the stress-time history of components is discretized into a series of peak-valley values ​​by using the rainflow counting method. After cycle counting processing, the load amplitude, mean and corresponding frequency relationship of the components are obtained. The counting results are subjected to probability distribution fitting and chi-square hypothesis test to obtain the joint probability density function of the load mean and amplitude. S5: Based on the fitted joint probability density function, the average amplitude two-dimensional design load spectrum and fatigue test program loading spectrum of key components are generated.

2. The method for acquiring dynamic load spectrum of key components of electric vehicle transmission system according to claim 1, characterized in that: The dynamic equation in step S2 is: Where X is the system displacement vector, F(t) is the external force excitation, M, T L , E and T e denote the generalized mass matrix, system load, meshing error excitation vector and electromagnetic torque vector, respectively, K m , K t , K b They are meshing stiffness matrix, torsional stiffness matrix, support stiffness matrix, C m , C t , C b They are meshing damping matrix, torsional damping matrix and support damping matrix respectively.

3. The method for acquiring dynamic load spectrum of key components of electric vehicle transmission system according to claim 1, characterized in that: In step S3, the load history of key components is calculated, including the dynamic meshing force of the gear pair, the bearing support force, and the dynamic torque of the transmission shaft; Among them, based on the dynamic meshing characteristics of the gear pair, the expression of the dynamic meshing force F(t) of the gear pair is: Among them, K m (t) is the time-varying mesh stiffness, C m (t) is the time-varying meshing damping, δ(t) is the relative displacement on the gear meshing line, is the first-order derivative of the relative displacement; The timing starts when a pair of teeth just enters meshing, that is, the initial angular displacement of the driving and driven gears is θ p (0) = 0, θ g (0) = 0, then the system gap function f(δ) is defined as Wherein, b′ is the tooth side clearance, and the expression of the tooth side clearance b′ is b′=2a0cosα·(invα′-invα)+b0, where a0 is the theoretical center distance, α is the pitch circle pressure angle, b0 is the tooth side clearance caused by the change of tooth thickness, and b0=0; The expression of δ(t) is: δ(t)=R p θ p (t)-R g θ g (t)-e(t), represents the dynamic transmission error of the gear pair along the meshing line direction; When analyzing the gear meshing state, when f(δ)>0, it means that the tooth surface is in a normal meshing state, and its value is the deformation at the meshing point; when f(δ)=0, it means the tooth disengagement state, that is, due to the existence of tooth side clearance, the driving and driven wheel teeth are temporarily disengaged during the transmission process, but then the teeth of the two gears will contact again and produce tooth surface impact; when f(δ)<0, it means the tooth back contact and its corresponding deformation; The bearing support force is derived based on the kinematics of rolling bearings and Hertz contact theory, and its expression is: In the formula, x b ,y b are the vibration displacements of the inner ring center in the x and y directions, respectively, and c is the rolling bearing clearance; is the position angle of the jth roller; N b is the number of rolling elements; K c The Hertzian contact stiffness is related to the bearing material and contact shape, and n is an index; The index n is 2 / 3 when the bearing is a ball bearing and 10 / 9 when the bearing is a roller bearing; H(δ j ) is the Heaviside function, whose return value is 0 and 1; δ j It represents the total contact deformation of the jth roller, and its expression is: Among them, ω b Indicates the inner ring speed; The dynamic torque of the transmission shaft is established using the Lagrangian dynamics equation, and its expression is: Where, T d represents the dynamic torque of the transmission shaft, J, c, and k represent the moment of inertia, torsional stiffness, and torsional damping of the transmission shaft, respectively.

4. The method for acquiring dynamic load spectrum of key components of electric vehicle transmission system according to claim 1, characterized in that: The steps to obtain the dynamic stress-time history of key components are: Based on the finite element analysis software or the stress calculation formula of the fatigue risk position of the parts, the elastic stress of the key components is calculated under static load conditions to obtain the static stress value σσ FEA ,Then, through simulation, the dynamic load time history p(t) of key components under dynamic conditions is obtained; The static stress σ FEA Combined with the dynamic load time history p(t), the dynamic stress-time history σ(t) of key components is calculated, and its expression is: Among them, PFEA represents the defined static load; σ represents the elastic stress caused by the load; p(t) represents the dynamic load-time history; σ(t) represents the stress-time history.

5. The method for acquiring dynamic load spectrum of key components of electric vehicle transmission system according to claim 1, characterized in that: Rainflow counting is divided into two steps: data compression and cycle number extraction. Data compression is divided into peak and valley value detection and invalid amplitude removal. The range of random load history is calculated, and 10% of the range is taken as the threshold. The small amplitude cycle data less than the threshold is compressed and processed to remove invalid data that has no significant effect on fatigue damage. Cycle number extraction is to extract peak values ​​and valley values ​​from the load time history, discretize the random load history into a sequence of peak and valley values, count the cycles of the peak and valley value sequence, identify the starting point and closing point of the load cycle, obtain the cycle number of each load cycle, and then organize the rain flow counting results into a rain flow matrix, which is expressed as follows: Where R(i, j) represents the rain flow matrix; i represents the load level at the starting point of the rain flow cycle; j represents the load level at the closing point of the rain flow cycle; r ij It represents the number of cycles with the starting point i and the closing point j of the rain flow cycle; u and v are the number of columns and rows of the rain flow matrix respectively.

6. A method for acquiring dynamic load spectrum of key components of electric vehicle transmission system according to claim 5, characterized in that: After the rain flow matrix is ​​established, the steps for probability distribution fitting and chi-square hypothesis test of the counting results are as follows: According to the load data obtained by the rain flow counting method, it is assumed that the load amplitude X obeys the three-parameter Weibull distribution and the load mean Y obeys the normal distribution. Based on this assumption, a joint probability density function is constructed, and its expression is: Where x represents the test load amplitude, y represents the test load mean, α represents the Weibull distribution shape parameter, β represents the Weibull distribution scale parameter, ε represents the Weibull distribution threshold parameter, μ represents the normal distribution mean, and σ represents the normal distribution standard deviation; Based on the counting results of the rain flow matrix, the frequency distribution of the amplitude and mean at different load levels is calculated, and the chi-square value calculation formula is constructed to test the independence between the amplitude and the mean. The expression is: In the formula, n represents the sub-sample size; r represents the number of levels of amplitude; s represents the number of levels of mean; n j Indicates the frequency of the mean falling into the jth level; n i Indicates the frequency of the amplitude falling into the i-th level; n ij It indicates the frequency that the amplitude falls in the i-th level and the mean falls in the j-th level; The chi-square test is used to test the independence of the load mean and amplitude. If the amplitude and mean are independent of each other, the random quantity approximately obeys the chi-square test with degrees of freedom (r-1)·(s-1) according to Fisher's theorem. 2 Distribution, its expression is: Where U α represents the upper alpha quantile of the standard normal distribution; If X and Y are not independent of each other, nonlinear regression analysis is required to determine the joint distribution density function of the mean amplitude. Finally, based on the load mean amplitude frequency histogram, the linear regression least squares method is used to fit the mean amplitudes separately to obtain the estimated distribution parameters of the mean amplitude.

7. A method for acquiring dynamic load spectrum of key components of electric vehicle transmission system according to claim 6, characterized in that: After the above distribution verification is passed, the working cycle load needs to be expanded to 10 6 The total cumulative frequency of cycles is expressed as: Among them, N' i is the cumulative frequency after the cyclic load is expanded; Since the mean follows the normal distribution and the load amplitude follows the three-parameter Weibull distribution, the extreme values ​​of the load amplitude X and the mean Y are calculated according to the probability density function and the extreme value occurrence probability P, which are used to define the unfavorable load conditions. The expression is: Y max =μ P σ+μ, where μ p is the deviation value of the standard normal distribution.

8. The method for acquiring dynamic load spectrum of key components of electric vehicle transmission system according to claim 1, characterized in that: The average amplitude two-dimensional design load spectrum is generated by the non-equal interval amplitude classification method; the fatigue test program loading spectrum is converted into a one-dimensional load spectrum based on the Goodman equation according to the equal damage principle; The average amplitude two-dimensional load spectrum is obtained based on the load average and amplitude extreme values ​​of the components throughout their life cycle, and the average is graded at equal intervals. The amplitude is divided into 8 levels according to the non-equal interval method through the formula Get the number of cycles n at each level corresponding to the mean and amplitude i , thus obtaining the two-dimensional spectrum array of the average amplitude, where Sa1 and Sa2 represent the lower and upper limits of the load amplitude integral respectively; Sm1 and Sm2 represent the integral lower and upper limits of the load mean, respectively; f j (x,y) represents the joint distribution probability density function; Based on the two-dimensional design spectrum, the asymmetric cyclic stress is equivalent to the symmetric cyclic stress with a mean of zero. Then, the Goodman equation is used as the equal fatigue damage conversion formula, which is specifically expressed as Wherein, Sa represents the torque amplitude; Sb represents the torsional strength limit torque; Sm represents the torque mean; Seq represents the equivalent torque amplitude; On the basis of obtaining the equivalent torque amplitude, the load amplitude is divided into 8 levels using the unequal interval method, and its expression is: k =K k ·x max , where x k is the k-th level load amplitude; K k is the proportionality coefficient between the k-th level amplitude and the limit value; x max is the limit value of equivalent torque amplitude; k represents load classification, k = 1, 2, 3...8; According to the probability distribution function F(x) of the load amplitude, calculate the cumulative frequency N of the load amplitude from level 1 to level k k , its expression is: N k =10 6 ·F(x k ), where F(x) is the probability distribution function of the amplitude load. Finally, the number of occurrences of the k-th level load amplitude is calculated based on the cumulative frequency. k , its expression is: k =N k -N k-1 (k=2, 3, ..., 8), where N k and N k-1 They represent the cumulative frequencies of the kth level and the k-1th level respectively.

9. A method for acquiring dynamic load spectrum of key components of electric vehicle transmission system according to claim 8, characterized in that: The ratio coefficients divided into 8 levels are 1, 0.95, 0.85, 0.725, 0.575, 0.425, 0.275, and 0.125.

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