Design method of elastic wheel structure capable of adjusting P2 frequency of wheel track

Abstract

The invention discloses a design method of an elastic wheel structure capable of adjusting the wheel track P2 frequency, which comprises the following steps of: based on an elastic wheel-continuous elastic support track system theoretical model, changing the mass ratio of a wheel core to a rim and the radial rigidity of a rubber layer to achieve the wheel track P2 frequency needing to be adjusted. The problem of bogie fatigue caused by wheel track P2 resonance can be solved under the condition that the track structure is not changed.

Description

Technical Field

[0001] This invention belongs to the field of rail transit, specifically relating to a design method based on a theoretical model of an elastic wheel-continuous elastic support track system, which changes the wheel-rail P2 frequency by adjusting the elastic wheel structure. Background Technology

[0002] In the rail transit industry, vibration and noise issues in wheel-rail systems have always been key factors affecting vehicle operating quality and service life. During operation, the P2 resonance frequency of ordinary rigid wheels can easily trigger resonant fatigue in the bogie. This resonant fatigue significantly accelerates bogie wear and damage, not only increasing vehicle maintenance costs but also potentially posing a threat to driving safety. Currently, existing technologies primarily address the P2 resonance problem by adjusting the track structure. However, this approach has several drawbacks. Firstly, adjusting the track structure is costly, requiring significant investment of manpower, resources, and capital. Secondly, it is difficult to implement, necessitating large-scale modifications to existing tracks, resulting in long construction periods and poor compatibility with existing track systems, making it difficult to modify without disrupting normal operations. Therefore, developing a method to regulate wheel-rail P2 frequency by adjusting the wheel structure alone, without altering the track structure, is of significant practical importance for improving the performance and reliability of rail transit vehicles. Summary of the Invention

[0003] The purpose of this invention is to provide a design method for an elastic wheel structure with adjustable wheel-rail P2 frequency. By changing the mass distribution of the wheel core and rim and the radial stiffness of the rubber layer in the wheel structure, the wheel-rail P2 frequency can be precisely adjusted, effectively solving the bogie fatigue problem caused by wheel-rail P2 resonance, and improving the running quality and service life of rail transit vehicles without changing the track structure.

[0004] This invention proposes a design method for an elastic wheel structure with adjustable wheel-rail P2 frequency, comprising the following steps: Step S1: Based on vehicle operating parameters, such as operating speed, load, and axle load distribution, as well as track structure parameters, including track type, sleeper spacing, ballast stiffness, and rail type, construct a dynamic model of the elastic wheel-continuous elastic support track system. By solving and analyzing this model, accurately determine the P2 resonance frequency of the wheel-rail system. Step S2: Conduct an in-depth study of the influence of parameters such as wheel core mass, rim mass, and radial stiffness of the rubber layer on the P2 frequency in the wheel structure. Using professional computer simulation software, perform comprehensive simulation calculations on the wheel-rail system under different parameter combinations. By analyzing the simulation results, determine the reasonable adjustment range and optimization direction for each parameter. Step S3: Based on the parameter adjustment range and optimization direction determined in Step S2, the natural frequency of the wheel-rail system is effectively adjusted by designing replaceable wheel cores and rim modules to change the mass distribution, and by selecting rubber materials with different formulations to adjust the radial stiffness of the rubber layer. Step S4: Based on the adjusted design, manufacture a prototype of the elastic wheel. Mount the prototype on a dedicated laboratory testing platform to simulate actual operating conditions and conduct comprehensive vibration tests. Detailed analysis of the test data verifies the effectiveness and efficiency of the designed wheel structure in regulating the P2 frequency.

[0005] As a further aspect of the present invention, step S1 specifically includes: Step S1.1: Construct the differential equations for the elastic wheel-rail system: ; ; Among them, M u Let p be the total mass of the half-elastic wheelset, and p be the percentage. Step S1.2: Let P0 = P1 = 0, and use the method of separation of variables to solve the differential equation of the elastic wheel-rail system as follows: ;in, , ; Step S1.3: Perform a Laplace transform on the equation in step S1.2 to obtain: ; Step S1.4: Perform an inverse Laplace transform on the equation in step S1.3 to obtain: ; Wherein, G(x) is the bending response curve of the rail beam under a unit impulse force, expressed as: ; Where u(x-x0) is a unit step function, and the coefficients A, B, C, and D are determined by the boundary conditions of the rail beam model; Step S1.5: Use boundary conditions Substituting this into the solution for the mode shape function of the rail, we get: ; When x = x0, Y(x) = Y(x0). Substituting this into the above equation, we obtain the characteristic equation for the system's natural frequency: ; Step S1.6: When the frequency is lower than the orbital natural frequency, i.e. , For two pairs of conjugate complex roots, when hour, Let each pair of conjugate complex roots and each pair of real roots have a real part of zero. We can obtain the transcendental equation: ; Will Substituting the values ​​will yield the solutions for each order. and The first root corresponds to the frequency, which is the P2 resonant frequency of the system.

[0006] As a further aspect of the present invention, step S2 specifically includes: Step S2.1: Define the total mass of the elastic wheel half-wheel pair as Mu, the total mass of the wheel core and half-axle as (1-p)Mu, and the rim mass as pMu, where p is a percentage; Mass distribution adjustment: While keeping the total mass Mu constant, the mass of the wheel core and rim is redistributed by changing the mass distribution coefficient p. Step S2.2: By changing the total mass Mu, percentage p, and radial stiffness of the rubber layer of the elastic wheel half-pair in the theoretical model. Adjusting the P2 resonance frequency of the elastic wheel-rail system by selecting rubber materials with different elastic moduli can change the radial stiffness of the rubber layer.

[0007] Furthermore, step S3 specifically includes: Step S3.1: Modular Structure Design Based on parameter adjustment requirements, a modular design concept was adopted, with wheel core modules and rim modules of different radial thicknesses, as well as rubber blocks of different radial stiffnesses, designed separately. During the design of the wheel core and rim modules, finite element analysis software was used to simulate the mechanical properties of different thickness schemes, ensuring that each module possesses sufficient strength and stability while meeting quality adjustment requirements. For the rubber blocks, by changing the rubber material formulation (such as adjusting the ratio of natural to synthetic rubber, adding different types of fillers, etc.) and vulcanization process parameters (vulcanization temperature, vulcanization time, vulcanization pressure), rubber blocks with gradient radial stiffness were prepared, covering the adjustment range required for actual engineering. Step S3.2: Parameter Adjustment and Assembly Based on the parameter adjustment range and optimization direction determined in step S2, and combined with actual engineering requirements, select and match pre-designed wheel core modules, rim modules, and rubber blocks. In specific operation, the selected wheel core module and rim module are first preliminarily assembled using positioning structures (such as keyways and locating pins). Then, rubber blocks with suitable radial stiffness are precisely embedded in the annular groove between the wheel core and rim. A stable connection is achieved through interference fits or bonding, forming a complete elastic wheel structure. By replacing wheel core modules, rim modules, and rubber blocks of different specifications, the mass distribution of the wheel and the radial stiffness of the rubber layer are changed, thereby achieving precise adjustment of the natural frequency of the wheel-rail system, ensuring that the wheel-rail P2 frequency meets the target design requirements.

[0008] As a further aspect of the present invention, step S4 specifically includes: Step S4.1: Experimental platform setup and sample installation A multi-functional experimental rig conforming to the standards for testing the dynamics of rail transit vehicles was selected. This rig is equipped with a high-precision drive system, loading device, and track simulation module, which can simulate wheel-rail contact conditions under different track conditions. The manufactured sample wheels were fixed to the wheelset axle seats of the experimental rig using special tooling fixtures according to the actual vehicle wheelset installation requirements, ensuring that parameters such as wheel installation angle and coaxiality met the standards. The power connection between the wheel and the rig's drive system and loading device, as well as the laying of signal transmission lines, were also completed. Step S4.2: Operating Condition Simulation and Data Acquisition Based on actual rail transit operation scenarios, various typical operating parameters were set, including but not limited to operating speed (covering a speed range of 20-350 km / h), axle load (different levels of load were set according to vehicle design standards), and track irregularity excitation (simulating various track defects such as elevation irregularities and track alignment irregularities). Different excitations and operating conditions were sequentially applied through the control system of the experimental bench. Accelerometers, displacement sensors, and force sensors located on the wheels, wheelset axles, and key parts of the experimental bench were used to collect real-time vibration response data of the wheels under different operating conditions, including parameters such as vibration acceleration, displacement amplitude, and vibration frequency. Simultaneously, a dynamic data acquisition instrument and signal analysis system were used to synchronously record and preliminarily process the collected data, extracting the P2 frequency data of the wheel-rail system. Step S4.3: Data Analysis and Structure Optimization The collected P2 frequency data is compared and analyzed with the design target frequency range determined in step S2. Statistical analysis methods (such as error analysis and spectrum comparison analysis) are used to evaluate the effect of the designed wheel structure on adjusting the P2 frequency. If the test data shows that the P2 frequency does not meet the design requirements, based on the frequency deviation and the parameter influence law established in step S2, the wheel structure parameters that need to be adjusted (such as the wheel core / rim mass ratio, rubber layer radial stiffness, etc.) are analyzed and determined. A new parameter adjustment scheme is recalculated using optimization algorithms (such as genetic algorithms and particle swarm optimization algorithms), and the process returns to step S3 to perform targeted optimization and improvement of the wheel structure. The sample manufacturing, testing, and verification process is repeated until the P2 frequency of the wheel structure meets the design target requirements.

[0009] As a further aspect of the present invention, the parameter adjustment method is as follows: Based on the dynamic characteristics of elastic wheels and the requirements for wheel-rail P2 frequency adjustment, a modular design concept and material property control technology are adopted to achieve precise parameter adjustment by designing wheel components of different specifications. In terms of mass parameter adjustment, the mass distribution of the wheel is altered by designing wheel core and rim modules with different radial thicknesses. Finite element analysis software is used to simulate the mechanical properties and calculate the mass of different thickness designs, determining wheel core and rim modules that meet strength requirements and have a mass adjustment gradient. While maintaining the overall wheel dimensions, the ratio of the total mass of the wheel core and half-axle to the rim mass is adjusted by replacing wheel core and rim modules with different thicknesses, thereby changing the wheel's moment of inertia and vibration characteristics. In terms of stiffness parameter adjustment, rubber blocks with different radial stiffnesses were prepared by developing rubber materials with different formulations. The relationship between the composition of the rubber materials (such as the ratio of natural rubber to synthetic rubber, and the proportion of fillers such as carbon black and silica), vulcanization process (vulcanization temperature, time, and pressure), and the radial stiffness of the rubber blocks was studied in depth to establish a rubber stiffness control model. Based on the wheel-rail P2 frequency adjustment target, rubber blocks with suitable radial stiffness were selected from the pre-prepared rubber blocks and embedded between the wheel core and the rim to adjust the radial stiffness of the wheel rubber layer and change the dynamic characteristics of the wheel-rail system. By coordinating the mass distribution of the wheel core and rim, and the radial stiffness of the rubber layer, the natural frequency of the wheel-rail system can be effectively controlled, thereby achieving the purpose of adjusting the wheel-rail P2 frequency.

[0010] As a further aspect of this invention, while maintaining a constant total wheel mass, the core objective is to precisely control the wheel-rail P2 frequency. This involves a deep analysis of the influence mechanisms of the wheel core-rim mass ratio and the radial stiffness of the rubber layer on the dynamic characteristics of the wheel-rail system. Modular design and material optimization techniques are employed to achieve precise adjustment of the inherent frequency of the wheel-rail system. Specifically: Utilizing a modular design concept, wheel core and rim modules with varying radial thicknesses were pre-designed. Based on the law of conservation of mass, while maintaining a constant total wheel mass, the ratio of the total mass of the wheel core and half-axle to the rim mass was flexibly adjusted by replacing wheel core and rim modules of different specifications. Using finite element analysis software, mechanical performance simulations and dynamic analyses were performed on the wheel structure under various mass distribution schemes to clarify the impact of changes in mass distribution on the wheel's moment of inertia and vibration characteristics, thereby altering the dynamic response of the wheel-rail system.

[0011] Simultaneously, focusing on the control of the radial stiffness of the rubber layer, this study delves into the intrinsic relationship between the composition of rubber materials (such as the ratio of natural rubber to synthetic rubber, and the addition ratio of fillers such as carbon black and silica), vulcanization process parameters (vulcanization temperature, time, and pressure), and the radial stiffness of the rubber block, establishing a systematic rubber stiffness control model. Based on this model, rubber blocks with different radial stiffnesses are prepared. According to the specific adjustment requirements of the wheel-rail P2 frequency, rubber blocks with suitable stiffness are selected from the pre-made rubber blocks and precisely embedded between the wheel core and the wheel rim, achieving effective adjustment of the radial stiffness of the rubber layer, thereby changing the dynamic characteristics of the wheel-rail system.

[0012] By coordinating and optimizing the two key parameters of the wheel core and rim mass ratio and the radial stiffness of the rubber layer, the natural frequency of the wheel-rail system is precisely changed, ultimately achieving directional adjustment of the wheel-rail P2 frequency and effectively solving the related problems caused by wheel-rail P2 resonance.

[0013] As a further aspect of this invention, the elastic wheel structure adopts a modular elastic connection design, consisting of three core components: the wheel core, the wheel rim, and the rubber block. The wheel core, as a key component bearing the vehicle's axle load and transmitting driving force, is integrally molded from high-strength alloy material to ensure structural strength and stability. The wheel rim is made of wear-resistant and impact-resistant special steel, and its outer surface undergoes a special process to optimize wheel-rail contact performance. The rubber block, embedded between the wheel core and the wheel rim, is the core element for achieving the elastic connection. It uses a specially formulated rubber compound, precisely controlling the ratio of natural and synthetic rubber, adding specific fillers and additives, and combining customized vulcanization process parameters (temperature, time, pressure) to give the rubber block precise elastic modulus and damping characteristics.

[0014] As a further aspect of the present invention, the wheel-rail system under different parameter combinations is simulated and analyzed in the model simulation, and the relationship curve between the parameters and the P2 frequency is plotted to determine the adjustment range of the key parameters.

[0015] This invention offers the following advantages: Existing technologies address P2 resonance by adjusting the track structure, but suffer from drawbacks such as long construction periods, high modification costs (requiring sleeper replacement, track bed stiffness adjustment, etc.), and poor adaptability. This invention achieves P2 frequency control through the adjustment of elastic wheel structure parameters, eliminating the need for modifications to existing tracks, significantly reducing modification costs, and greatly shortening the construction period. Multi-parameter coordinated control: By coordinating the adjustment of the wheel core / rim mass ratio (adjustment range p=35%~65%) and the radial stiffness of the rubber layer (200~500MN / m), the P2 frequency control range can be expanded to 45~70Hz, covering the avoidance requirements of the natural frequency (50~65Hz) of existing rail transit vehicle bogies, with a frequency adjustment accuracy of ±1.5Hz. Based on the dynamic model established by the differential equations of the elastic wheel-continuous elastic support track system, the quantitative correlation between P2 frequency and structural parameters is achieved through Laplace transform and mode shape function solving. Simulation verification shows that the error between the model calculation value and the experimental test value is less than 3.2%, providing a precise theoretical basis for parameter adjustment. The wheel core / rim adopts a detachable modular design with a radial thickness gradient of 5mm / level (e.g., wheel core thickness ranges from 80mm to 120mm, with a total of 9 specifications). Combined with 5 different stiffness rubber blocks (stiffness gradient of 50MN / m / level), the wheel parameters can be reconstructed within 2 hours to meet the dynamic adjustment needs of different routes (such as mountain slopes and plains routes).

[0016] To more clearly illustrate the structural features and effects of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the method flow of the present invention.

[0018] Figure 2 This is a schematic diagram of the method model of the present invention.

[0019] Figure 3 This is a schematic diagram comparing the solution obtained by the method in this invention with the P2 frequency of a rigid wheel.

[0020] Figure 4 This is a schematic diagram illustrating the influence of the radial stiffness of the rubber layer and the mass ratio of the rim on the P2 resonant frequency in this invention.

[0021] Figure 5 This is a schematic diagram showing the P2 resonance frequency distribution of the elastic wheel-rail system under different masses in this invention.

[0022] Figure 6 This is a schematic diagram showing the P2 frequency test results at different speeds.

[0023] Figure 7 Cross-sectional views of three different types of elastic wheels, a, b, and c. Detailed Implementation

[0024] The present invention will now be further described in conjunction with the accompanying drawings and relevant knowledge, and will be described clearly and completely. Obviously, the described applications are only some embodiments of the present invention, and not all embodiments.

[0025] Reference Figures 1-7 As shown, the core idea of ​​this invention is to precisely adjust the wheel-rail P2 frequency by changing the mass distribution of the wheel core and rim, as well as the radial stiffness of the rubber layer, thereby solving the bogie fatigue problem caused by wheel-rail P2 resonance. Based on the theoretical model of an elastic wheel-continuous elastic support track system, this invention designs an elastic wheel structure with adjustable wheel-rail P2 frequency.

[0026] (a) Establishing a dynamic model to determine the P2 resonance frequency S1. Based on vehicle operating conditions (such as operating speed and load capacity) and track parameters (such as track type, sleeper spacing, and track stiffness), establish a dynamic model of the elastic wheel-continuously elastically supported track system. Determine the P2 resonance frequency of the wheel-rail system by solving this model. The specific process is as follows: Step S1.1: Construct the differential equation of the elastic wheel-rail system as follows: ; ; ; Among them, M u Let p be the total mass of the half-elastic wheelset, and p be the percentage. Step S1.2: Consider the system's free vibration problem, let P0 = P1 = 0, and solve using the method of separation of variables. The system's differential equation is expressed as: ; in, , ; Step S1.3: Perform a Laplace transform on the equations in step S1.2: ; Step S1.4: Perform an inverse Laplace transform on the equations in step S1.3: ; Wherein, G(x) is the bending response curve of the rail beam under unit impulse force, which can be expressed as: ; Where u(x-x0) is a unit step function, and the coefficients A, B, C, and D can be determined by the boundary conditions of the rail beam model; Step S1.5: Consider simply supported ends of the track, boundary conditions Substituting this into the solution for the mode shape function of the rail, we get: ; When x = x0, Y(x) = Y(x0). Substituting into the above equation, we can obtain the characteristic equation of the system's natural frequency. ; Step S1.6: When the frequency is lower than the orbital natural frequency, i.e. , For two pairs of conjugate complex roots, when hour, Let each pair of conjugate complex roots and each pair of real roots have a real part of zero. We can obtain the transcendental equation: ; Will Substituting the values ​​will yield the solutions for each order. and The first root corresponds to the frequency, which is the P2 resonant frequency of the system.

[0027] (II) Analysis of the influence of wheel structure parameters on P2 frequency S2. Analyze the influence of wheel structural parameters on the P2 frequency, including wheel core mass, rim mass, and radial stiffness of the rubber layer, and determine the adjustment range of key parameters through model simulation. Details are as follows: The total mass of the half-wheel pair of the elastic wheel is defined as Mu, the total mass of the wheel core and half-shaft is (1-p)Mu, and the rim mass is pMu, where p is a percentage. By changing the total mass Mu, percentage p, and radial stiffness of the rubber layer of the elastic wheel half-wheel pair in the theoretical model, the P2 resonance frequency of the elastic wheel-rail system is adjusted. Using computer simulation software, the wheel-rail system under different parameter combinations is simulated and analyzed, and the relationship curves between each parameter and the P2 frequency are plotted. This allows for the determination of reasonable adjustment ranges for each parameter to meet the requirements for P2 frequency adjustment under different operating conditions.

[0028] (iii) Adjusting the natural frequency of the wheel-rail system S3. By designing replaceable wheel cores or rim modules, altering their mass distribution, and selecting rubber materials with different formulations, the radial stiffness of the rubber layer can be changed, thereby adjusting the natural frequency of the wheel-rail system. Specific operations are as follows: Design wheel core and rim modules with different radial thicknesses. By changing the radial thickness of the wheel core and rim, the mass of the wheel core and rim can be adjusted, thereby changing the mass distribution of the wheel. At the same time, design rubber blocks with different radial stiffnesses. Based on different rubber formulas and structural designs, rubber blocks with different radial stiffnesses can be manufactured. Based on actual needs, rubber blocks of different radial stiffness are selected and embedded between the wheel core and rim to form an elastic wheel structure. By replacing different rubber blocks and wheel core / rim modules, the wheel structure parameters can be flexibly adjusted, thereby regulating the natural frequency of the wheel-rail system.

[0029] (iv) Verify the adjustment effect S4. Manufacture a sample wheel and conduct vibration tests in a laboratory environment to verify the effect of the designed wheel structure on regulating the P2 frequency. Manufacture a sample wheel according to the design parameters and install it on a specialized test bench to simulate actual operating conditions. By applying different excitations and operating conditions, measure the vibration response of the wheel under different states to obtain the P2 frequency data of the wheel-rail system. Compare and analyze the test results with the design objectives to evaluate the effect of the designed wheel structure on regulating the P2 frequency. If the test results do not meet the design requirements, further optimize and adjust the wheel structure parameters until the design requirements are met.

[0030] Reference Figure 2 As shown, the elastic wheel is simplified as a dual-mass-spring system. (1-p)Mu represents the equivalent mass of the wheel core and half-axle components (p is the proportion of the rim mass to the total wheel mass, and Mu is the total wheel mass). It is connected to the equivalent mass of the pMu rim through a spring with stiffness kz (simulating the axial stiffness of elastic connection structures such as rubber layers), and acts on the track through a spring with stiffness kH (simulating the contact between the rim and the track and related elastic effects). P0 is the external force applied to the upper structure such as the wheel core (such as the vehicle's vertical load), and P1 is the vertical dynamic force acting on the rim.

[0031] Reference Figure 3 As shown, the effect of wheel mass on the P2 resonant frequency. Comparison of rigid wheels: When the mass of a rigid wheel changes, the P2 resonance frequency changes accordingly. For example, as the mass of the rigid wheel gradually increases from 300kg to 900kg, the P2 resonance frequency shows a decreasing trend. Furthermore, the P2 resonance frequency curve of a rigid wheel with a mass of m1 = 1.15m (where m is the base rigid wheel mass) is generally lower than that of a rigid wheel with a mass of m, indicating that under the same mass change trend, the P2 resonance frequency of the rigid wheel with increased mass is lower.

[0032] Comparison of elastic wheels: When the mass of the elastic wheel is m2 = 1.15m, its P2 resonance frequency curve is lower than that of the rigid wheel with a mass of m. Furthermore, substituting the P2 resonance frequency corresponding to the mass of the elastic wheel (585.6kg) in the experiment, compared with the frequency corresponding to the rigid wheel (509kg), the P2 resonance frequency of the elastic wheel is lower. This indicates that under the influence of the total mass of the wheel and its variation, the elastic wheel can, through its own structural characteristics, maintain a relatively lower P2 resonance frequency, thus avoiding the risk of resonance.

[0033] Reference Figure 4 As shown, the influence of rim mass percentage and rubber layer radial stiffness on the P2 resonant frequency is illustrated. The effect of rim mass percentage is as follows: as the rim mass percentage gradually increases from 0% to 100%, the P2 resonant frequency increases with different rubber layer radial stiffnesses (75MN / m, 350MN / m, 1200MN / m). For example, when the rubber layer radial stiffness is 75MN / m, as the rim mass percentage increases from 10% to 100%, the P2 resonant frequency increases from approximately 42Hz to around 56Hz. This indicates that increasing the rim mass percentage can effectively improve the P2 resonant frequency, providing a controllable parameter for frequency adjustment.

[0034] The effect of radial stiffness of the rubber layer: Under the same rim mass percentage, the greater the radial stiffness of the rubber layer, the higher the P2 resonance frequency. When the rim mass percentage is 50%, a radial stiffness of 75MN / m corresponds to a P2 resonance frequency of approximately 47Hz, 350MN / m corresponds to approximately 54Hz, and 1200MN / m corresponds to approximately 56Hz. Figure 5 The three-dimensional curved surface provides a more intuitive view. The increase in radial stiffness of the rubber layer and the increase in the proportion of rim mass together cause the P2 resonance frequency to rise. Moreover, this pattern remains stable under different wheel masses (400kg-700kg), verifying the technical effect of precisely controlling the P2 resonance frequency by adjusting the radial stiffness of the rubber layer and the proportion of rim mass.

[0035] Reference Figure 6 As shown, the P2 resonance frequencies of flexible and rigid wheels differ at different speeds. A comparison of frequency values ​​reveals that within the speed range of 40-80 km / h, the P2 resonance frequency of the flexible wheel is generally lower than that of the rigid wheel. For example, at 50 km / h, the P2 resonance frequency of the rigid wheel is mostly around 58 Hz, while that of the flexible wheel is around 55 Hz; at 70 km / h, the average frequency of the rigid wheel is approximately 61 Hz, while the average frequency of the flexible wheel is approximately 56 Hz.

[0036] Speed-related patterns: As the speed increases from 40 km / h to 80 km / h, the P2 resonance frequencies of both rigid and flexible wheels fluctuate slightly, but the flexible wheel maintains a relatively lower and more stable P2 resonance frequency level. This indicates that the flexible wheel can effectively reduce the P2 resonance frequency at different operating speeds, avoiding resonance caused by coupling with the inherent frequencies of other vehicle components, thus improving the stability and safety of vehicle operation and highlighting its advantage over rigid wheels in frequency regulation.

[0037] Reference Figure 7 As shown, cross-sectional diagrams of three different types of elastic wheels (a, b, and c) are presented, with corresponding wheelset mass ratios of 508 kg, 586 kg, and 618 kg, respectively. When the wheels wear down to their limit ( Figure 7The dashed line represents the tread profile when the wheel wear reaches its limit. The wheelset mass is reduced to half of 414 kg, 491 kg, and 524 kg, respectively. Table 1 shows the range of P2 resonance frequency of the wheel-rail system for these three types of elastic wheels from new wheel condition to wear limit under different radial stiffness of rubber layers, and also gives the results for rigid wheels (traditional integral rolled steel wheels) corresponding to the three types of wheels.

[0038] When all three types of wheels (a, b, and c) are rigid wheels, the P2 resonance frequencies of type a, b, and c wheels from new wheels to worn-out wheels are 60.7~65.5Hz, 57.4~61.5Hz, and 56.2~60.0Hz, respectively. The P2 resonance frequency can be adjusted by 4~6Hz from the lightest type a wheel to the heaviest type c wheel. The adjustable range is small, and none of the three types of rigid wheels can avoid the bogie's natural frequency.

[0039] For elastic wheels, the highest and lowest wheel-rail P2 resonance frequencies are for the type a (1200MN / m) scheme and the type c (75MN / m) scheme, respectively. The corresponding P2 resonance frequencies from new wheel to wear limit are 59.9~64.5Hz and 44.4~46.2Hz, respectively. This indicates that the P2 resonance frequency of type a, b, and c elastic wheels with different radial stiffnesses can be adjusted from 15.5 to 18.3Hz, offering a wide adjustment range. To avoid the natural frequency of typical bogies in the range of 56.6~62.5Hz, the six elastic wheel schemes highlighted in Table 1 can be selected. Therefore, for different bogie structures, the P2 resonance frequency of the wheel-rail system can be adjusted by optimizing the design parameters of the elastic wheel structure, thereby reducing the risk of bogie fatigue failure caused by wheel-rail P2 resonance.

[0040]

[0041] Specifically, refer to Figure 7As shown in Table 1, for rigid wheels, from the lightest type A (508kg) to the heaviest type C (618kg), the P2 resonance frequency can only be adjusted by 4-6Hz, and none of them can avoid the bogie's natural frequency (56.6-62.5Hz). However, for flexible wheels, taking the type A-1200MN / m and type C-75MN / m schemes as examples, the P2 resonance frequency adjustment range from new wheel to wear limit reaches 15.5-18.3Hz, a significantly wider adjustment range. The six flexible wheel schemes highlighted in bold in Table 1 (such as type A 75MN / m, 150MN / m, and 300MN / m schemes) have P2 resonance frequency ranges that do not overlap with the bogie's natural frequency range, effectively avoiding resonance and reducing the risk of bogie fatigue failure. As the weight of the flexible wheel decreases by half from new wheel to wear limit (e.g., type A from 508kg to 414kg), the P2 resonance frequency changes accordingly. Taking the 75MN / m type a wheel as an example, the P2 resonance frequency is 49.7-52.4Hz when the wheel is new and 47.3-49.6Hz when worn to the limit, indicating a decrease in frequency. This demonstrates that reducing wheel mass lowers the P2 resonance frequency. For the same type of elastic wheel, increasing the radial stiffness of the rubber layer increases the P2 resonance frequency. For example, for type a wheel, increasing the radial stiffness of the rubber layer from 75MN / m to 1200MN / m increases the P2 resonance frequency from 49.7-52.4Hz to 59.9-64.5Hz when the wheel is new and from 47.3-49.6Hz to 56.7-60.6Hz when worn to the limit, verifying the regulating effect of the radial stiffness of the rubber layer on the P2 resonance frequency.

[0042] Type A elastic wheels: Relatively lightweight (half the wheelset weight of a new wheel, 508kg), with different radial stiffnesses of the rubber layers, the P2 resonance frequency coverage is wide. For example, the frequency is low at 75MN / m (49.7-52.4Hz for a new wheel), and high at 1200MN / m (59.9-64.5Hz for a new wheel). The stiffness parameters can be flexibly selected according to the bogie's natural frequency to avoid resonance.

[0043] Type B elastic wheels: The mass is between that of Type A and Type C (half the wheelset mass of a new wheel, 586 kg), and the P2 resonance frequency is also in the middle range. For example, when the radial stiffness of the rubber layer is 300 MN / m, the frequency of a new wheel is 57.5-61.7 Hz, and when it wears down to the limit, it is 54.5-58.0 Hz, providing more adjustment options for adapting to different bogies.

[0044] Type C elastic wheels have the largest mass (618kg, half the mass of a new wheel pair) and the lowest P2 resonance frequency (44.4-46.2Hz for new wheels) under low rubber layer radial stiffness (e.g., 75MN / m), providing an effective solution for scenarios requiring a significant reduction in P2 resonance frequency.

[0045] In summary, this invention significantly broadens the range of wheel-rail P2 resonance frequency adjustment by coordinating the adjustment of parameters such as the mass ratio of the wheel core and rim (which affects the total mass of the wheel) and the radial stiffness of the rubber layer. Furthermore, different types of elastic wheels can be adapted to different bogie structures, effectively avoiding the resonance range and reducing the risk of bogie fatigue failure, fully demonstrating the practicality and effectiveness of the technical solution.

[0046] Example 1: This example provides a specific elastic wheel structure design for adjusting the wheel-rail P2 frequency. The elastic wheel structure includes a wheel core and a rim, with a rubber block embedded between the wheel core and the rim. The radial stiffness of the rubber layer can be adjusted by replacing different rubber blocks to meet different wheel-rail P2 frequency adjustment requirements. The specific steps are as follows: A theoretical model of the elastic wheel-continuous elastic support track system is established. Using the method described above for establishing a dynamic model, the relationship between the wheel-rail P2 frequency and the wheel structural parameters is determined.

[0047] Determine the target bogie natural frequency. Based on the actual vehicle operating conditions and bogie performance parameters, determine the range of bogie natural frequencies to be avoided. By adjusting wheel structure parameters, the P2 frequency of the wheel-rail system is made to avoid the bogie natural frequency, thus preventing bogie fatigue caused by wheel-rail resonance. Based on the target P2 frequency, calculate the required mass ratio of the wheel core and rim, and adjust the radial stiffness of the rubber layer. For example, if the goal is to reduce the P2 frequency, while keeping the total wheel mass constant, the proportion of the wheel core mass to the total mass can be increased, and the radial stiffness of the rubber layer can be decreased, thereby reducing the system's natural frequency. Manufacture flexible wheels, assemble wheel cores, rims and rubber layers according to design parameters, and ensure the installation accuracy and connection reliability of each component. The manufactured elastic wheels are installed on the vehicle and tested on the track. Professional vibration testing equipment is used to measure the vibration data of the wheels during operation to verify whether their P2 frequency meets the design requirements.

[0048] Example 2: First, based on the theoretical model of the elastic wheel-continuous elastic support track system, the P2 frequency of the wheel-rail system is calculated. By changing the mass ratio of the wheel core and rim, and the radial stiffness of the rubber layer, the required wheel-rail P2 frequency is achieved. For a certain type of rail vehicle, assuming its operating speed range is 40-80 km / h, the corresponding P2 resonance frequency needs to be avoided from 56-62 Hz. A theoretical model is established based on the track parameters, and the calculated P2 frequency of the current wheel structure is 60 Hz. Adjusting the mass ratio of the wheel core from 45% to 55% lowers the P2 frequency to 56 Hz; adjusting the radial stiffness of the rubber layer from 350 MN / m to 300 MN / m further lowers the P2 frequency to 55 Hz. Experimental verification shows that this wheel structure can effectively avoid the resonance frequency range, significantly reducing the vibration and fatigue of the bogie.

[0049] Example 3: Taking high-speed rail as an example, the vibration of the wheel-rail system directly affects the stability and safety of train operation. The P2 resonance frequency of the wheel-rail system is a key issue. If the P2 resonance frequency happens to overlap with a natural frequency of the bogie, it will cause resonance, further leading to bogie fatigue and damage. To avoid these problems, the elastic wheel structure invented in this paper can be used in the wheel-rail system design of high-speed rail. By adjusting the structural parameters of the wheel (such as wheel core mass, rim mass ratio, and stiffness of the elastic layer), the P2 resonance frequency can be adjusted to avoid the bogie's natural frequency. For example, for the P2 resonance problem at high speeds (above 350 km / h), the manufacturer optimized the rim mass distribution and used a highly durable rubber layer, reducing the P2 resonance frequency from 58 Hz to 45 Hz, effectively avoiding the bogie's natural frequency (55 Hz). Experimental verification: In simulated track experiments, by comparing ordinary rigid wheels and optimized elastic wheels, it was found that the vibration amplitude of the elastic wheel was reduced by about 30%, and the fatigue life of the bogie was extended by 20%.

[0050] The technical principles of the present invention have been described above with reference to specific embodiments, which are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments; all technical solutions falling within the scope of the present invention's concept are within its protection scope. Those skilled in the art can conceive of other specific embodiments of the present invention without creative effort, and these embodiments will all fall within the protection scope of the present invention.

Claims

1. A design method for an elastic wheel structure with adjustable wheel-rail P2 frequency, characterized in that, Includes the following steps: Step S1: Based on the vehicle operating condition parameters and track structure parameters, construct a dynamic model of the elastic wheel-continuous elastic support track system to determine the P2 resonance frequency of the wheel-rail system; Step S2: Based on the influence of parameters such as wheel core mass, wheel rim mass, and radial stiffness of rubber layer on the P2 frequency in the wheel structure, perform simulation calculations on the wheel-rail system under different parameter combinations to determine the adjustment range and optimization direction of each parameter; Step S3: By changing the adjustment range and optimization direction of the parameters, the natural frequency of the wheel-rail system can be effectively adjusted; Step S4: Based on the adjustment, manufacture a sample of the elastic wheel to verify the effect and effectiveness of the designed wheel structure in adjusting the P2 frequency.

2. The design method of an adjustable wheel-rail P2 frequency elastic wheel structure as described in claim 1, characterized in that, Step S1 specifically includes: Step S1.1: Construct the differential equations for the elastic wheel-rail system: ； ； Among them, M u Let p be the total mass of the half-elastic wheelset, and p be the percentage. Step S1.2: Let P0 = P1 = 0, and use the method of separation of variables to solve the differential equation of the elastic wheel-rail system as follows: ;in, , ; Step S1.3: Perform a Laplace transform on the equation in step S1.2 to obtain: ； Step S1.4: Perform an inverse Laplace transform on the equation in step S1.3 to obtain: ； Wherein, G(x) is the bending response curve of the rail beam under a unit impulse force, expressed as: ； Where u(x-x0) is a unit step function, and the coefficients A, B, C, and D are determined by the boundary conditions of the rail beam model; Step S1.5: Use boundary conditions Substituting this into the solution for the mode shape function of the rail, we get: ； When x = x0, Y(x) = Y(x0). Substituting this into the above equation, we obtain the characteristic equation for the system's natural frequency: ； Step S1.6: When the frequency is lower than the orbital natural frequency, i.e. , For two pairs of conjugate complex roots, when hour, Let each pair of conjugate complex roots and each pair of real roots have a real part of zero. We can obtain the transcendental equation: ； Will Substituting the values ​​will yield the solutions for each order. and The first root corresponds to the frequency, which is the P2 resonant frequency of the system.

3. The design method of an adjustable wheel-rail P2 frequency elastic wheel structure as described in claim 1, characterized in that, Step S2 specifically includes: Step S2.1: Define the total mass of the elastic wheel half-wheel pair as Mu, the total mass of the wheel core and half-shaft as (1-p)Mu, and the rim mass as pMu, where p is a percentage; Step S2.2: By changing the total mass Mu, percentage p, and radial stiffness of the rubber layer of the elastic wheel half-pair in the theoretical model. Adjust the P2 resonance frequency of the elastic wheel-rail system.

4. The design method of an adjustable wheel-rail P2 frequency elastic wheel structure as described in claim 1, characterized in that, In step S3, wheel cores and rim modules with different radial thicknesses and rubber blocks with different radial stiffnesses are designed. According to actual needs, rubber blocks with different radial stiffnesses are selected and embedded between the wheel core and the rim. The natural frequency of the wheel-rail system is adjusted by replacing the wheel core, rim module and rubber blocks.

5. The design method of an adjustable wheel-rail P2 frequency elastic wheel structure as described in claim 1, characterized in that, In step S4, the manufactured sample wheel is installed on the test bench to simulate actual operating conditions. Different excitations and operating conditions are applied, and the wheel vibration response is measured to obtain the P2 frequency data of the wheel-rail system. The data is compared and analyzed with the design target. If the requirements are not met, the wheel structure parameters are optimized.

6. The design method of an adjustable wheel-rail P2 frequency elastic wheel structure as described in claim 1, characterized in that, The parameters can be adjusted by designing wheel cores and rims with different radial thicknesses, as well as rubber blocks with different radial stiffnesses.

7. The design method of an elastic wheel structure with adjustable wheel-rail P2 frequency as described in claim 1, characterized in that, When adjusting the natural frequency of the wheel-rail system, the total mass of the wheel remains constant. The wheel-rail P2 frequency is adjusted by changing the mass ratio of the wheel core and the wheel rim, as well as the radial stiffness of the rubber layer.

8. The design method of an adjustable wheel-rail P2 frequency elastic wheel structure as described in claim 1, characterized in that, The flexible wheel structure includes a wheel core, a wheel rim, and a rubber block embedded between the wheel core and the wheel rim. The wheel core and the wheel rim are elastically connected by the rubber block.

9. The design method of an elastic wheel structure with adjustable wheel-rail P2 frequency as described in claim 1, characterized in that, In the model simulation, the wheel-rail system under different parameter combinations is simulated and analyzed, and the relationship curve between the parameters and the P2 frequency is plotted to determine the adjustment range of key parameters.

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