Orthogonal optimization method for wheel-rail modal frequency staggering design for inhibiting wheel-rail resonance

Abstract

The invention discloses a wheel-rail modal frequency-shifting design orthogonal optimization method for inhibiting wheel-rail resonance, and the method can achieve the frequency-shifting design of a wheel set and a steel rail modal through the decoupling design of the wheel set and the steel rail. An optimal wheel-rail parameter matching scheme is determined through an orthogonal test design and a range method, and resonance between a wheel-rail coupling mode and a wheel set mode and resonance between the wheel-rail coupling mode and a steel rail are further avoided; and according to the constructed train-rail three-dimensional rigid-flexible coupling dynamic model, whether abnormal vibration exists in the train-rail coupling system is judged, and if yes, the wheel rail parameters are changed again until the abnormal vibration is inhibited successfully. The method not only can evaluate the wheel-rail matching condition of the existing line and the service train, but also can be used for forward design of a new line or a new high-speed motor train unit; and compared with a traditional multi-rigid-body model, a result obtained by calculation of the rigid-flexible coupling model is closer to a real situation.

Description

Technical Field

[0001] The invention belongs to the technical field of rail transportation, and in particular relates to an orthogonal optimization method for wheel-rail modal frequency deviation design for suppressing wheel-rail resonance. Background Art

[0002] By the end of 2023, my country's railway operating mileage will reach 159,000 kilometers, of which high-speed railways account for 45,000 kilometers, forming the world's largest high-speed railway network. High-speed train-track is a large system that disturbs each other. The modal matching of key components such as the car body, frame, wheelset, and track largely determines the dynamic response of the vehicle-track coupling system. Poor modal matching will lead to abnormal vibration and deterioration of dynamic indicators. Among them, the wheel-rail relationship is the most critical constraint relationship among many coupling relationships. Mismatched wheel-rail modes may lead to enhanced wheel-rail dynamic effects and deteriorate the stability and safety of vehicle operation. Therefore, according to the modal matching principle, it is of great significance to optimize the wheel-rail modal frequency mismatching design from the perspective of staggering the fundamental frequency of wheel-rail vibration, so as to avoid the adverse effects of wheel-rail resonance on the dynamic performance of the vehicle-track coupling system.

[0003] At present, modal matching mainly focuses on the modes of the vehicle or rail system itself. As a large system with mutual interference, the high-speed train-track needs to consider the modal matching of different components, especially the wheel-rail modal matching. In recent years, my country's rail transportation has been changing with each passing day, and the structures and forms of key components have gradually diversified, which has brought huge challenges to the modal matching between vehicles and tracks. In addition, with the high-speed operation and lightweight design of EMUs, the influence of the flexible vibration of each component on the dynamic response of the whole vehicle system cannot be ignored. The traditional multi-rigid body model ignores the flexible vibration and it is difficult to reproduce the vibration of the high-speed train during service. Therefore, in order to fully consider the influence of the flexible vibration of the key components of the high-speed EMU on the dynamic performance of the vehicle-track coupling system, it is necessary to establish a high-speed train-track rigid-flexible coupling dynamic model.

[0004] The wheel-rail modal frequency staggered orthogonal optimization design method for suppressing wheel-rail resonance proposed in the present invention optimizes the wheel-rail parameters from the perspective of wheel-rail matching, effectively and efficiently avoids wheel-rail resonance, and improves the dynamic performance of the large train-track coupling system. Summary of the invention

[0005] In order to overcome the above-mentioned shortcomings, an orthogonal optimization method for wheel-rail modal frequency mismatch design to suppress wheel-rail resonance is proposed. This method can not only evaluate the wheel-rail matching of existing lines and in-service trains, but also be used for the forward design of new lines or new high-speed EMUs. Compared with the traditional multi-rigid body model, the results calculated by the rigid-flexible coupling model are closer to the actual situation.

[0006] To achieve the above-mentioned purpose, the technical solution adopted by the present invention is to provide an orthogonal optimization method for wheel-rail modal frequency deviation design to suppress wheel-rail resonance. The method comprises the following steps:

[0007] S1, select wheelset parameters and rail parameters from the high-speed EMU parameter library, extract unsprung mass and fastener spacing as optimization content, and calculate wheelset mode and rail mode respectively;

[0008] S2, using staggered frequency design to avoid resonance as the design criterion for modal matching, to determine whether the wheelset mode and rail mode meet the staggered frequency design requirements;

[0009] If the frequency offset design is not satisfied, return to step S1 and reselect different unsprung masses and fastener spacings to ensure that there is no resonant frequency between the wheelset mode and the rail mode.

[0010] S3, orthogonal test design is conducted on the unsprung mass, fastener spacing and fastener stiffness that meet the staggered frequency design;

[0011] S4, input the parameter combination designed by the orthogonal test into the constructed vehicle-rail vertical coupling model to obtain the wheel-rail vertical coupling system mode, and determine whether the wheel-rail coupling mode, wheelset mode, and rail mode also meet the staggered frequency design. If they do, the optimal parameter combination is obtained;

[0012] If the staggered frequency design is not satisfied, return to step S3 and re-perform the orthogonal experimental design until the staggered frequency design is satisfied;

[0013] S5, according to the optimal parameter combination selected by the staggered frequency design, the constructed train-track three-dimensional rigid-flexible coupling dynamic model is input to perform dynamic simulation calculation to determine whether there is abnormal vibration during operation;

[0014] S6, if there is abnormal vibration, return to step S1, reselect the parameters to be optimized to perform wheel-rail mismatch optimization design; if there is no abnormal vibration, complete an orthogonal optimization of the wheel-rail modal mismatch design to suppress wheel-rail resonance.

[0015] According to the orthogonal optimization method for wheel-rail modal frequency deviation design for suppressing wheel-rail resonance described in the present invention, a further preferred technical solution is: the values ​​of the unsprung mass and the fastener spacing in S1 are selected from a high-speed train parameter library.

[0016] According to the orthogonal optimization method for wheel-rail modal frequency deviation design for suppressing wheel-rail resonance described in the present invention, a further preferred technical solution is: the fastener stiffness in S3 includes the longitudinal, transverse and vertical stiffness of the fastener, all of which are selected from the high-speed EMU parameter library.

[0017] According to the orthogonal optimization method for wheel-rail modal frequency deviation design for suppressing wheel-rail resonance described in the present invention, a further preferred technical solution is: in the orthogonal experimental design in S3, the number of tests for different values ​​of different optimization parameters is the same, so as to achieve the result equivalent to the minimum number of tests and a large number of comprehensive tests.

[0018] According to the orthogonal optimization method for wheel-rail modal frequency mismatch design for suppressing wheel-rail resonance described in the present invention, its further preferred technical solution is: the optimal parameter combination in S4 is determined by: calculating the mean of the test results corresponding to the same level value of the same parameter to be optimized, determining the optimal value of the parameter to be optimized according to the size of the mean, further calculating the range of the mean of different level values ​​of the factor, the larger the range, the greater the influence of the parameter on the optimization result, determining the priority order of each parameter to be optimized according to the size of the range; finally, determining the optimal parameter combination according to the priority order and the optimal value of each parameter to be optimized.

[0019] According to the orthogonal optimization method for wheel-rail modal frequency deviation design for suppressing wheel-rail resonance described in the present invention, a further preferred technical solution is: the train-track three-dimensional coupling dynamic model in S5 is divided into a train system dynamic model, a track system dynamic model, a wheel-rail spatial dynamic contact model, and a train / track coupling interface excitation model, and the flexible modes of key structural components such as tracks, wheelsets, frames and car bodies are considered, and the required parameters are obtained from the high-speed EMU parameter library, and the parameters include marshaling, traction braking, and track irregularities.

[0020] According to the orthogonal optimization method for wheel-rail modal frequency stagger design for suppressing wheel-rail resonance described in the present invention, a further preferred technical solution is: the train-track three-dimensional coupled dynamic model in S5 is a three-dimensional coupled dynamic performance analysis model that takes into account the mutual influence of the longitudinal, lateral and vertical vibrations of the vehicle and the track.

[0021] According to the orthogonal optimization method for wheel-rail modal frequency deviation design for suppressing wheel-rail resonance described in the present invention, a further preferred technical solution is: the vibration state of the S6 medium- and high-speed EMU is determined based on dynamic indicators, including vehicle operation safety evaluation indicators: derailment coefficient, wheel weight reduction rate; vehicle operation stability evaluation indicators: vehicle body acceleration, stability index; wheel and track dynamic action evaluation indicators: wheel-rail vertical force, wheel axle lateral force.

[0022] Compared with the prior art, the technical solution of the present invention has the following advantages / benefits:

[0023] 1. The present invention is not limited to the modal matching of vehicle systems, but expands the modal matching principle to the high-speed train-track coupling large system level, focusing on analyzing the wheel set mode and rail mode. According to the full-band modal matching design criteria, the fundamental frequencies of the wheelset and the rail are completely offset, making the modal matching design more comprehensive, forming a general rule, and having a wide range of applications.

[0024] 2. The present invention not only considers the "static matching" of the wheelset and rail modes, but also carries out "dynamic matching" from the perspective of the dynamic response of the high-speed EMU under the condition that the fundamental frequencies of the wheelset and rail are staggered, and analyzes the dynamic performance of the high-speed EMU during running.

[0025] 3. When performing staggered frequency optimization design, the present invention adopts an orthogonal optimization method for optimizing the unsprung mass, fastener spacing, and fastener stiffness parameters, which greatly improves the optimization design efficiency compared to the traditional test scheme design method.

[0026] 4. When evaluating the dynamic performance of high-speed EMUs, the present invention adopts a three-dimensional rigid-flexible coupling dynamic performance analysis model of train-track, which comprehensively considers the rigid-flexible coupling vibrations of the vehicle structure and the track structure in the longitudinal, lateral and vertical directions. Compared with the settlement results of the traditional multi-rigid body model that ignores the flexible mode, it is closer to the actual situation, and its advantages have been reflected in specific applications.

[0027] 5. The orthogonal optimization method for wheel-rail modal frequency mismatch design for suppressing wheel-rail resonance proposed in the present invention can not only evaluate the wheel-rail matching of existing lines and in-service trains, but also be used for the forward design of new high-speed railway lines and new high-speed EMUs. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0029] Figure 1 It is a flow chart of the orthogonal optimization method of wheel-rail modal frequency deviation design for suppressing wheel-rail resonance of the present invention.

[0030] Figure 2 The present invention provides a wheelset finite element model and vibration mode.

[0031] Figure 3 It is the rail finite element model and vibration mode constructed by the present invention.

[0032] Figure 4 This is the wheel-rail vertical coupling model constructed by the present invention.

[0033] Figure 5 It is a train-track three-dimensional rigid-flexible coupling numerical simulation model constructed by the present invention. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention are clearly and completely described below. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in the field without creative work are within the scope of protection of the present invention. Therefore, the detailed description of the embodiments of the present invention provided below is not intended to limit the scope of the claimed invention, but merely represents the selected embodiments of the present invention.

[0035] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and thus, once an item is defined in one drawing, it may not be further defined or explained in the subsequent drawings.

[0036] Embodiment 1:

[0037] like Figure 1 As shown, an orthogonal optimization method for wheel-rail modal frequency mismatch design for suppressing wheel-rail resonance comprises the following steps:

[0038] S1, select wheelset parameters and rail parameters from the high-speed EMU parameter library, extract unsprung mass and fastener spacing as optimization content, and calculate wheelset mode and rail mode respectively;

[0039] S2, according to the full-band modal matching design criteria, determine whether the wheelset mode and rail mode meet the staggered frequency design;

[0040] If the frequency offset design is not satisfied, return to step S1 and reselect different unsprung masses and fastener spacings to ensure that there is no resonant frequency between the wheelset mode and the rail mode.

[0041] S3, conducts orthogonal test design on the unsprung mass, fastener spacing and fastener stiffness that meet the requirements of staggered frequency design; orthogonal test design is an efficient, fast and economical test design method involving multiple factors and multiple levels. Representative tests are selected from comprehensive tests based on orthogonality, in which the number of tests for different levels of each parameter to be optimized is the same, and the number of tests for the combination of any two different levels of the parameters to be optimized is also the same, so as to achieve a balance between the matching of each parameter and each level, and achieve the result equivalent to a large number of comprehensive tests with the least number of tests. Taking the three levels of the three parameters to be optimized, namely, unsprung mass, fastener spacing and fastener stiffness, as an example, an orthogonal test design is carried out according to orthogonality. The results are shown in Table 1 (the three optimization parameters are represented by A, B and C respectively). It can be found that the three levels of each parameter to be optimized appear 3 times, and the different level value combinations of any two parameters to be optimized (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2) and (3, 3) appear once, which meets the requirements of orthogonal test design.

[0042] Table 1 Orthogonal test design

[0043]

[0044] S4, input the parameter combination designed by the orthogonal test into the constructed vehicle-rail vertical coupling model to obtain the wheel-rail vertical coupling system mode, and judge whether the wheel-rail coupling mode, wheelset mode, and rail mode also meet the frequency deviation design. If they do, the optimal parameter combination is obtained; the optimal parameter combination screening method takes the above-mentioned orthogonal test scheme design as an example. After completing the working condition calculation, the optimization target is the frequency deviation degree k of the wheel-rail coupling mode, wheelset mode, and rail mode. i 、m i 、n i Calculate the mean K of the test results corresponding to the same level value of the same parameter to be optimized ij 、M ij 、N ij (where i is the parameter to be optimized, i = A, B, C; j is the different level values ​​of each optimization parameter, j = 1, 2, 3), such as K A1 =(k1+k6+k7) / 3, determine the optimal value of the parameter to be optimized based on the mean value; further calculate the range K of the mean of different level values ​​of this factor i 、M i , R i (i is the parameter to be optimized, i = A, B, C), such as K A =max(K A1 ,K A2 ,K A3 )-min(K A1 ,K A2,K A3 ), the larger the range, the greater the influence of the parameter on the optimization result. The priority order of each parameter to be optimized is determined according to the size of the range; finally, the optimal parameter combination is determined according to the priority order and optimal value of each parameter to be optimized.

[0045] If the staggered frequency design is not satisfied, return to step S3 and re-perform the orthogonal experimental design until the staggered frequency design is satisfied;

[0046] S5, according to the optimal parameter combination selected by the staggered frequency design, the constructed train-track three-dimensional rigid-flexible coupling dynamic model is input to perform dynamic simulation calculation to determine whether there is abnormal vibration during operation;

[0047] S6, if there is abnormal vibration, return to step S1, reselect the parameters to be optimized to perform wheel-rail mismatch optimization design; if there is no abnormal vibration, complete an orthogonal optimization of the wheel-rail modal mismatch design to suppress wheel-rail resonance.

[0048] The following is a practical example. When calculating the wheel-rail mode in step S1, the geometric model of the wheelset and rail is imported into the finite element software according to the wheelset information and rail information from the high-speed EMU parameter database, the unit properties are defined, the material parameters are set, the grid is divided, the constraints are set, and the Block Lanczos method is used to extract the modal parameters. The low-order modal frequencies of the wheelset and rail are as follows: Figure 3 , Figure 4 shown.

[0049] from Figure 3 It can be seen that the low-frequency modal frequencies of the wheelset are 116.87Hz, 194.98Hz, 326.23Hz, and 437.08Hz. Figure 4 It can be seen that the modal frequencies of the rail part are 12.28Hz, 44.49Hz, 110.85Hz, and 185.33Hz, which basically meet the requirements of the staggered frequency design. The fastener stiffness value is selected from the high-speed EMU parameter library, and the unsprung mass and fastener spacing selected in S1 are used to select a suitable orthogonal table for test scheme design. The fastener in this embodiment is the WJ-8 fastener commonly used in high-speed ballastless track, and the more sensitive fastener vertical stiffness (analysis range is 20-60MN / m) is selected as an example, and the orthogonal test scheme design is performed with the selected fastener spacing and unsprung mass. The specific parameter values ​​and orthogonal test scheme design are shown in Tables 2 and 3.

[0050] Table 2 Optimization factors at various levels

[0051]

[0052] Table 3 Orthogonal experimental design

[0053]

[0054]

[0055] According to the design plan, the vehicle-rail vertical coupling model constructed by S4 is input to calculate the wheel-rail coupling mode, and the optimization goal is to stagger the coupling modal frequency of the wheel-rail system with the wheel set modal and rail modal frequency. According to the range method, the optimization factors (in this embodiment, fastener stiffness, fastener spacing, and unsprung mass) are calculated. The range of the mean results under different value conditions is used to determine the priority order of each factor. The higher the priority level, the greater the impact of the optimization factor on the optimization goal. Then, according to the optimal value of each factor, the optimal matching scheme of different factors is determined by comprehensively considering the importance of each factor, and the three-dimensional rigid-flexible coupling dynamic model of the train-track constructed by S5 is input to perform dynamic simulation calculations.

[0056] The three-dimensional rigid-flexible coupling numerical simulation model of train-track in S5 is established based on the vehicle-track coupling dynamic theory, such as Figure 5 As shown in the figure, it includes four sub-models: train system dynamics model, track system dynamics model, wheel-rail spatial dynamic contact model, and train / track coupling interface excitation model. In the train system dynamics model and track system dynamics model, the rigid-flexible coupling dynamics model of key structural components (car body, frame, wheelset, rail, track plate, etc.) is established by hybrid coordinate system method, and the vibration deformation of key structural components in large-scale translation and rotation rigid body coordinate system and local flexible body coordinate system is solved by modal superposition method. The parameters required for model construction (such as key structural parameters, suspension parameters, track unevenness, etc.) are all selected from the high-speed EMU parameter database. The vehicle model selected in this embodiment is CRH380BG. The track plate is modeled by taking the CRTSⅡ type longitudinal slab ballastless track adopted by the Beijing-Shanghai High-speed Railway, the most representative high-speed railway in my country, as an example. The slab track is simplified into a spatial layered viscoelastic body, which is divided into rails, fasteners, track slab layers, CA mortar layers, support layers, and roadbed layers; the rails are Timoshenko beam models supported by continuous elastic discrete points, considering lateral, vertical, and torsional vibrations; fasteners are simulated by linear spring-damper units; the mortar layer and the supporting structure are considered as continuous viscoelastic units, and the vibration of the bottom plate and the roadbed is not considered. Track unevenness information is track unevenness information collected from the actual line. The wheel-rail spatial contact geometric relationship is solved by the trace method and the minimum distance method, the wheel-rail normal force is solved by the Hertz nonlinear theoretical model, the wheel-rail tangential force is calculated by "FASTSIM", and the integral calculation is performed by the new fast numerical calculation method of Zhai style, thus building a three-dimensional rigid-flexible coupling numerical simulation model of train-track.

[0057] In step S6, based on the wheel-rail force, acceleration, etc. calculated in the train-track three-dimensional rigid-flexible coupling numerical simulation model, the operation safety, stability, and dynamic interaction indicators of the wheels and tracks of the high-speed EMU are evaluated to determine whether there is abnormal vibration of the high-speed EMU.

[0058] The vehicle operation safety evaluation indicators include derailment coefficient and wheel load reduction rate. The derailment coefficient is the ratio of the lateral force Q and the vertical force P acting on the wheel at a certain moment (Q / P), and its limit value is:

[0059]

[0060] The wheel weight reduction rate is the ratio of the load reduction of the wheel on the load-reducing side to the average static wheel weight of the wheelset. Its safety standard is:

[0061]

[0062] The vehicle running stability includes the vehicle body acceleration and stability index. The test assessment limit of the vertical and lateral vibration acceleration of the vehicle body is 2.5m / s. 2 , the calculation formula of the stability index is:

[0063]

[0064] Where: A—vibration acceleration, in meters per second squared (m / s 2 );

[0065] f—vibration frequency, in Hertz (Hz);

[0066] F(f)—Frequency correction coefficient, see Table 4.

[0067] Table 4 Frequency Correction Coefficient Table

[0068]

[0069] The table of passenger car and EMU stability index grades is shown in Table 5.

[0070] Table 5 Passenger car and EMU stability index grade table

[0071] Stability level Stationarity index W assessment Level 1 W<2.50 excellent Level 2 2.50<W≤2.75 good Level 3 2.75<W≤3.00 qualified

[0072] The evaluation indicators of the dynamic interaction between vehicles and tracks include the wheel-rail vertical force and the wheel-axle lateral force. The maximum limit of the wheel-rail vertical force is 170 kN, and the calculation formula for the allowable limit of the wheel-axle lateral force is:

[0073]

[0074] Where: P W is the static axle weight.

[0075] If the safety, stability, and wheel-track dynamic action evaluation indicators obtained from the above analysis exceed the standard, the vehicle track-coupling system has abnormal vibration, and then return to step S1, reselect the fastener spacing and unsprung mass to perform the staggered frequency design of the wheelset mode and the rail mode, and reselect the fastener stiffness parameters in S4 for orthogonal test design.

[0076] If there is no abnormal vibration in the vehicle-track coupling system, an orthogonal optimization method for wheel-rail modal frequency mismatch design for suppressing wheel-rail resonance is completed. In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, which are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the equipment or elements referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention.

[0077] In the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0078] The above are only preferred embodiments of the present invention. It should be noted that the above preferred embodiments should not be regarded as limiting the present invention, and the protection scope of the present invention should be based on the scope defined by the claims. For ordinary technicians in this technical field, several improvements and modifications can be made without departing from the spirit and scope of the present invention, and these improvements and modifications should also be regarded as the protection scope of the present invention.

Claims

1. An orthogonal optimization method for wheel-rail modal frequency deviation design to suppress wheel-rail resonance, characterized in that: The following steps are involved: S1, select wheelset parameters and rail parameters from the high-speed EMU parameter library, extract unsprung mass and fastener spacing as optimization content, and calculate wheelset mode and rail mode respectively; S2, using staggered frequency design to avoid resonance as the design criterion for modal matching, to determine whether the wheelset mode and rail mode meet the staggered frequency design requirements; If the frequency offset design is not satisfied, return to step S1 and reselect different unsprung masses and fastener spacings to ensure that there is no resonant frequency between the wheelset mode and the rail mode. S3, orthogonal test design is conducted on the unsprung mass, fastener spacing and fastener stiffness that meet the staggered frequency design; S4, input the parameter combination designed by the orthogonal test into the constructed vehicle-rail vertical coupling model to obtain the wheel-rail vertical coupling system mode, and determine whether the wheel-rail coupling mode, wheelset mode, and rail mode also meet the staggered frequency design. If they do, the optimal parameter combination is obtained; If the staggered frequency design is not satisfied, return to step S3 and re-perform the orthogonal experimental design until the staggered frequency design is satisfied; S5, according to the optimal parameter combination selected by the staggered frequency design, the constructed train-track three-dimensional rigid-flexible coupling dynamic model is input to perform dynamic simulation calculation to determine whether there is abnormal vibration during operation; S6, if there is abnormal vibration, return to step S1 and reselect the parameters to be optimized to perform wheel-rail mismatch frequency optimization design; If there is no abnormal vibration, an orthogonal optimization of the wheel-rail modal frequency offset design for suppressing wheel-rail resonance is completed.

2. The orthogonal optimization method for wheel-rail modal frequency deviation design for suppressing wheel-rail resonance according to claim 1 is characterized in that: The values ​​of unsprung mass and fastener spacing in S1 are selected from the high-speed EMU parameter library.

3. The orthogonal optimization method for wheel-rail modal frequency deviation design for suppressing wheel-rail resonance according to claim 1 is characterized in that: The fastener stiffness in S3 includes the longitudinal, transverse and vertical stiffness of the fastener, all of which are selected from the high-speed EMU parameter library.

4. The orthogonal optimization method for wheel-rail modal frequency deviation design for suppressing wheel-rail resonance according to claim 1 is characterized in that: In the orthogonal experimental design in S3, the number of trials with different values ​​of different optimization parameters is the same, achieving the result of the minimum number of trials and the equivalent of a large number of comprehensive tests.

5. The orthogonal optimization method for wheel-rail modal frequency deviation design for suppressing wheel-rail resonance according to claim 1 is characterized in that: The method for determining the optimal parameter combination in S4 is as follows: calculate the mean of the test results corresponding to the same level value of the same parameter to be optimized, determine the optimal value of the parameter to be optimized based on the size of the mean, and further calculate the range of the mean of different levels of the factor. The larger the range, the greater the influence of the parameter on the optimization result. Determine the priority order of each parameter to be optimized based on the size of the range; finally, determine the optimal parameter combination based on the priority order and optimal value of each parameter to be optimized.

6. The orthogonal optimization method for wheel-rail modal frequency deviation design for suppressing wheel-rail resonance according to claim 1 is characterized in that: The train-track three-dimensional coupling dynamic model in S5 is divided into train system dynamics model, track system dynamics model, wheel-rail spatial dynamic contact model, and train / track coupling interface excitation model. It also considers the flexible modes of key structural components such as tracks, wheelsets, frames, and car bodies. The required parameters are obtained from the high-speed EMU parameter library, including marshalling, traction braking, and track irregularities.

7. The orthogonal optimization method for wheel-rail modal frequency deviation design for suppressing wheel-rail resonance according to claim 1 or 6, characterized in that: The train-track three-dimensional coupled dynamic model in S5 is a three-dimensional coupled dynamic performance analysis model that takes into account the mutual influence of longitudinal, lateral and vertical vibrations between the vehicle and the track.

8. The orthogonal optimization method for wheel-rail modal frequency deviation design for suppressing wheel-rail resonance according to claim 1 is characterized in that: The vibration state of the S6 medium- and high-speed EMU is determined based on dynamic indicators, including vehicle operation safety evaluation indicators: derailment coefficient, wheel weight reduction rate; vehicle operation stability evaluation indicators: vehicle body acceleration, stability index; wheel and track dynamic action evaluation indicators: wheel-rail vertical force, wheel axle lateral force.

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