A disc brake braking vibration stability evaluation method

Abstract

The present application relates to disc brake stability evaluation technical field, provide a kind of disc brake braking vibration stability evaluation method, comprising step 1, establish high-speed train disc brake dynamics simulation model;Step 2, the simulation test is carried out to high-speed train disc brake dynamics simulation model, obtains the braking disc axial excitation response result under different braking parameters;Step 3, the braking disc axial excitation response result is Fourier transformed and handled, obtains the braking disc FFT axial excitation response spectrum;Step 4, according to the corresponding braking disc FFT axial excitation amplitude in different vibration frequency under braking disc axial excitation response spectrum, calculate the braking disc axial vibration impact degree and braking disc axial vibration power under different time;Step 5, calculate stability index.The present application can obtain the stability index that can describe the severity of braking disc axial vibration, directly see the severity of braking disc vibration.

Description

Technical Field

[0001] This invention relates to the field of disc brake stability evaluation technology, and in particular to a method for evaluating the braking vibration stability of a disc brake. Background Technology

[0002] As the speed of high-speed trains continues to increase, the requirements for braking performance and stability also rise. Disc brakes play a crucial role in rail transit equipment, primarily achieving braking through the friction between brake pads and the brake disc. Typically, at the start of braking, the train speed is high. Due to uneven pressure distribution between the brake disc and brake pads, self-excited vibrations occur between the friction pairs, leading to brake vibration and accompanying braking noise, thus affecting passenger comfort. Strong vibrations can also impact the brake disc and brake pads, potentially causing premature cracking and fissures in the brake disc, impacting the safety and efficiency of high-speed train operation. Therefore, research on the braking stability assessment of disc brakes is of significant practical importance.

[0003] Current research on disc brakes is insufficient, leading to a series of problems such as premature brake disc failure, vibration noise, and traffic safety issues caused by vibration during braking. This results in high maintenance costs for train braking systems and unresolved issues related to traffic safety and noise pollution. Therefore, this paper proposes a method for evaluating the vibration stability of disc brakes, providing a valuable reference for addressing these challenges. Summary of the Invention

[0004] This invention helps to solve technical problems such as premature brake disc failure and low train braking efficiency. It proposes a method for evaluating the braking vibration stability of disc brakes, which will help optimize the design of disc brakes to improve train braking efficiency and save train maintenance costs.

[0005] This invention provides a method for evaluating the braking vibration stability of a disc brake, comprising the following steps:

[0006] Step 1: Establish a dynamic simulation model of the disc brake for high-speed trains;

[0007] Step 2: Conduct simulation tests on the dynamic simulation model of the high-speed train disc brake to obtain the axial excitation response results of the brake disc under different braking parameters; wherein, the axial excitation response results are the magnitude of the axial excitation amplitude of the brake disc at different angular frequencies.

[0008] Step 3: Perform Fourier transform processing on the axial excitation response results of the brake disc to obtain the FFT axial excitation response spectrum of the brake disc.

[0009] Step 4: Based on the axial excitation amplitude of the brake disc at different vibration frequencies in the axial excitation response spectrum, calculate the axial vibration impact JE and axial vibration power VP of the brake disc at different times.

[0010] The expression for impact JE:

[0011]

[0012] In the formula, Q is the axial vibration displacement of the brake disc, t is the braking time, and a n b represents the amplitude of the cosine wave in the signal corresponding to n times the fundamental frequency. n Let f represent the amplitude of the sine wave corresponding to n times the fundamental frequency in the signal, f represent the vibration frequency, and cos(2πnft) and sin(2πnft) represent the cosine wave and the sine wave, respectively.

[0013] The expression for the axial vibration power VP of the brake disc is:

[0014]

[0015] In the formula, P d denoted as , where is the axial vibration power of the brake disc, and m is the mass of the train brake disc.

[0016] Step 5: Calculate the stability index based on the axial vibration impact degree JE and the axial vibration power VP of the brake disc;

[0017] The expression for the stability index SI is:

[0018]

[0019] In the formula, the axial vibration impact degree JE of the brake disc and its vibration power VP are included, and α and β are the weighting coefficients of the impact degree and vibration power, respectively. The larger the stability index, the more unstable the brake disc vibration tends to be, the more obvious the change in the axial vibration acceleration of the brake disc, and the higher the vibration power, the worse its vibration stability.

[0020] Preferably, in step 1, the dynamic simulation model of the high-speed train disc brake includes:

[0021] The inner and outer diameters of the brake disc, the total thickness of the disc body, the brake disc material, and the elastic modulus, Poisson's ratio, density, thermal conductivity, specific heat capacity, linear expansion coefficient, and surface emissivity of the brake disc material;

[0022] The inner and outer diameters of the brake pads, the total thickness of the brake pads, the brake pad material, and the elastic modulus, Poisson's ratio, density, thermal conductivity, specific heat capacity, linear expansion coefficient, and surface emissivity of the brake pad material.

[0023] Preferably, in step 2, the test parameters of the simulation test include the initial rotational speed v, braking pressure F, and friction coefficient μ.

[0024] This invention provides a method for evaluating the vibration stability of disc brakes. First, a dynamic simulation model of a high-speed train disc brake is established to obtain the axial vibration results of the brake disc under different braking parameters (braking pressure, initial speed, and friction coefficient). The simulation results are then processed using Fourier transform to obtain the axial excitation response spectrum of the brake disc. Second, based on the two key factors affecting vibration—impact intensity and vibration power—the vibration stability of the brake disc during braking is evaluated, resulting in a stability index that describes the severity of the axial vibration of the brake disc, thus providing a direct indication of the intensity of the brake disc vibration. This invention can determine the degree of influence of different braking parameters on vibration stability during braking. Based on the main parameters affecting vibration stability, valuable data references can be provided for subsequent structural optimization design, material selection, and lightweight design of disc brakes. This invention can provide important data references for achieving the ultimate goal, mainly in the following two aspects: First, it can extend the service life of disc brakes, reduce maintenance costs, improve operational economy, and help improve the availability and maintainability of railway systems. On the other hand, it can improve the braking efficiency of high-speed train disc brakes, shorten braking distance, improve train safety, help reduce accidents and improve transportation efficiency, reduce braking noise, improve passenger comfort, and promote the competitiveness and development of the railway industry. Attached Figure Description

[0025] Figure 1 This is a flowchart illustrating the implementation of the disc brake vibration stability evaluation method provided by the present invention.

[0026] Figure 2 This is a multibody dynamics model diagram of the high-speed train disc brake provided by the present invention;

[0027] Figure 3a This is the axial excitation response spectrum of the brake disc when the friction coefficient is 0.25, provided by the present invention.

[0028] Figure 3b This is the axial excitation response spectrum of the brake disc when the friction coefficient is 0.3, provided by the present invention.

[0029] Figure 3c This is the axial excitation response spectrum of the brake disc when the friction coefficient is 0.35, provided by the present invention.

[0030] Figure 4 This invention provides an index for the axial vibration stability of the brake disc under different friction coefficients. Detailed Implementation

[0031] To make the technical problems solved by this invention, the technical solutions adopted, and the technical effects achieved clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings, not all of them.

[0032] like Figure 1 As shown, the disc brake vibration stability evaluation method provided in this embodiment of the invention includes the following process:

[0033] Step 1: Establish a dynamic simulation model of the disc brake for high-speed trains.

[0034] As attached Figure 2 As shown, a high-speed train disc brake includes a brake disc and brake pads. The brake disc is connected to the axle or directly to the wheel and rotates with the axle or wheel. Brake pads are distributed on both sides of the brake disc. When the train needs to decelerate or stop, the brake piston applies pressure to the brake pads, causing friction between the brake pads and the brake disc to achieve braking. In actual braking, the brake disc and axle achieve high-speed rotation through an interference fit. This motion is simulated using a revolute joint, and the rigid node connecting the inner ring of the brake disc to the axle is selected as the rigid region. The remaining parts are made flexible. The rigid region, as the area where the flexible component connects to the axle, provides the kinematic joint application point and load-bearing point for the revolute joint. At the same time, the rigid region can also limit the displacement at the connection point to ensure that it does not deform, thus simulating the interference fit relationship between the brake disc and the axle. When the brake is working, the brake pads press against the brake disc through a translational joint under the action of braking pressure. The brake pads rub against the brake disc under the action of braking pressure to achieve the purpose of braking.

[0035] The dynamic simulation model of the high-speed train disc brake includes:

[0036] The inner and outer diameters of the brake disc, the total thickness of the disc body, the brake disc material, and the elastic modulus, Poisson's ratio, density, thermal conductivity, specific heat capacity, linear expansion coefficient, and surface emissivity of the brake disc material;

[0037] The inner and outer diameters of the brake pads, the total thickness of the brake pads, the brake pad material, and the elastic modulus, Poisson's ratio, density, thermal conductivity, specific heat capacity, linear expansion coefficient, and surface emissivity of the brake pad material.

[0038] Different models of trains use disc brakes with slightly different structures or materials, but their braking principles are not significantly different.

[0039] The following is an example of a dynamic simulation model of a disc brake for a certain type of high-speed train: The brake disc has an outer diameter of 660mm, an inner diameter of 380mm, and a total thickness of 108mm. The brake disc contains 72 fan-shaped cooling fins evenly distributed throughout its interior. The brake disc material is Q345B, with an elastic modulus of 2.1 × 10⁻⁶. 11 Its Pascal-Poisson ratio is 0.31, its density is 7850 kg / m³, its thermal conductivity is 48 W / (m°C), its specific heat capacity is 462 J / (kg°C), and its linear expansion coefficient is 12.8 × 10⁻⁶. -5 The surface emissivity is 0.28, and the brake pad has an outer diameter of 650 mm, an inner diameter of 390 mm, and a total thickness of 30 mm. The brake pad material is copper-based powder metallurgy with an elastic modulus of 1.8 × 10⁻⁶. 11 Its Pascal-Poisson ratio is 0.3, its density is 5250 kg / m³, its thermal conductivity is 30 W / (m°C), its specific heat capacity is 550 J / (kg°C), and its linear expansion coefficient is 1.5 × 10⁻⁶. -6 / degrees Celsius, surface emissivity 0.8.

[0040] Step 2: Conduct simulation tests on the dynamic simulation model of the high-speed train disc brake to obtain the axial excitation response results of the brake disc under different braking parameters.

[0041] In this invention, the test parameters for the simulation test include the initial rotational speed v, the braking pressure F, and the friction coefficient μ.

[0042] In this embodiment, the simulation test parameters are set as follows: initial braking speed v = 200 km / h, braking pressure F applied to the translational pair with a magnitude of 0.36 MPa, and the frictional contact between the brake disc and brake pads defined as a contact pair. The friction coefficient μ between the friction pairs during braking is used as a variable factor in comparative tests, with friction coefficients set to 0.25, 0.3, and 0.35 respectively. Simulation tests are conducted using COMSOL software, and the axial excitation response results under different friction coefficient conditions can be obtained based on the above test conditions.

[0043] The axial excitation response result is the magnitude of the axial excitation amplitude of the brake disc at different angular frequencies. The axial excitation response result can be used as input data for Fourier transform in step 3 to obtain the corresponding spectrum of the axial excitation of the brake disc.

[0044] Step 3: Perform Fourier transform processing on the axial excitation response results of the brake disc to obtain the FFT axial excitation response spectrum of the brake disc.

[0045] The specific brake disc FFT axial excitation response spectrum is as follows: Figure 3a -c is shown.

[0046] Step 4: Based on the axial excitation amplitude of the brake disc at different vibration frequencies in the axial excitation response spectrum, calculate the axial vibration impact JE and axial vibration power VP of the brake disc at different times.

[0047] Impact intensity represents the rate of change of brake vibration acceleration over time. Its value reflects the degree of impact on the brake disc, and thus the stability of the brake. Vibration power represents the rate of change of the kinetic energy of a disc brake during vibration over time. Its value reflects the change in the vibration energy of the brake disc, ultimately affecting the stability of the brake.

[0048] Impact Factor (JE): The impact factor is defined as the third derivative of the axial vibration displacement with respect to time when a disc brake vibrates, i.e., the rate of change of axial vibration acceleration over time. The rate of change of axial vibration acceleration of the brake disc can, to some extent, reflect the change in the axial force it experiences, thus characterizing the degree of impact on the brake disc. Drastic acceleration changes negatively impact the stability of the brake disc because rapid changes in vibration acceleration indicate more frequent impacts, leading to more severe vibrations and reduced stability. Therefore, JE is negatively correlated with brake disc stability; the larger the value, the worse the vibration stability and the more severe the brake vibration.

[0049] Assuming the axial vibration displacement of the brake disc is Q, then the third derivative of its axial vibration displacement with respect to time is equivalent to the rate of change of the axial vibration acceleration with time, which can be expressed as:

[0050]

[0051] In the formula, Q is the axial vibration displacement of the brake disc, a is the axial vibration acceleration of the brake disc, and t is the braking time.

[0052] The actual motion of the train brake disc is complex and variable. After processing with Fourier transform, the actual axial motion equation of the brake disc can be expressed as:

[0053]

[0054] In the formula, q0 represents the amplitude of the average component of the signal over one complete cycle, ω is the axial vibration angular frequency, and a n b represents the amplitude of the cosine wave in the signal corresponding to n times the fundamental frequency. n The amplitude of the sine wave corresponding to n times the fundamental frequency in the signal is represented by cos(nωt) and sin(nωt), which represent the cosine wave and the sine wave, respectively, and t is the braking time.

[0055] From the above expression, the impact force JE when the brake disc vibrates can be expressed as:

[0056]

[0057] The impact intensity JE in the above formula is a function of time and is constantly changing dynamically. For ease of calculation, the angular frequency (ω) is replaced with the vibration frequency (f), resulting in the following expression for the impact intensity JE:

[0058]

[0059] In the formula, Q is the axial vibration displacement of the brake disc, t is the braking time, and a n b represents the amplitude of the cosine wave in the signal corresponding to n times the fundamental frequency. n Let f represent the amplitude of the sine wave corresponding to n times the fundamental frequency in the signal, f represent the vibration frequency, and cos(2πnft) and sin(2πnft) represent the cosine wave and the sine wave, respectively.

[0060] Vibration power (VP): Vibration power is defined as the rate of change of the kinetic energy of a disc brake as a function of time during vibration. Its magnitude reflects the change in the vibration energy of the brake disc. Brake disc instability is caused by vibration. The greater the vibration energy per unit time, the more intense the vibration, ultimately leading to reduced operational stability of the brake disc. Therefore, VP is negatively correlated with brake disc stability; the higher the value, the worse the vibration stability and the more severe the brake vibration.

[0061] Using the kinetic energy theorem, the kinetic energy of the axial vibration of the train brake disc is calculated as follows:

[0062]

[0063] The vibration power P can be obtained by differentiating the kinetic energy of the axial vibration of the brake disc with respect to time. d The expression is:

[0064]

[0065] In the formula, E k This indicates the kinetic energy of the train's brake disc. The rotational speed of the train brake disc is represented by m, the mass of the train brake disc is represented by ω, and the axial vibration angular frequency is represented by a. n b represents the amplitude of the cosine wave in the signal corresponding to n times the fundamental frequency. n The amplitude of the sine wave corresponding to n times the fundamental frequency in the signal is represented by cos(nωt) and sin(nωt), which represent the cosine wave and the sine wave, respectively, and t is the braking time.

[0066] After removing the mass factor, the vibration power VP can be expressed as:

[0067]

[0068] Similarly, by expressing the angular frequency (ω) in terms of the vibration frequency (f), we obtain the following expression for the axial vibration power VP of the brake disc:

[0069]

[0070] In the formula, P d Let m be the axial vibration power of the brake disc, t be the mass of the train brake disc, and a be the braking time. n b represents the amplitude of the cosine wave in the signal corresponding to n times the fundamental frequency. n Let f represent the amplitude of the sine wave corresponding to n times the fundamental frequency in the signal, f represent the vibration frequency, and cos(2πnft) and sin(2πnft) represent the cosine wave and the sine wave, respectively.

[0071] The axial vibration impact degree JE of the brake disc is calculated according to the expression of the impact degree JE (Formula 4), and the axial vibration power VP of the brake disc is calculated according to the expression of the vibration power VP.

[0072] Step 5: Calculate the stability index based on the axial vibration impact degree JE and the axial vibration power VP of the brake disc.

[0073] In actual braking, the vibration frequency and amplitude of the brake disc are randomly distributed and change continuously as braking progresses. Multiple vibration frequencies may coexist simultaneously. The simulated brake disc vibration acceleration-time curve can be transformed using Fourier transform to calculate the axial excitation amplitude for each frequency range. The impact intensity JE and vibration power VP corresponding to each frequency range are then calculated. Finally, these values ​​are summed to obtain the overall vibration stability index SI for the entire braking process. The stability index (SI) is designed using both JE and VP to characterize the axial vibration stability of the brake disc. The formula is as follows, where α and β are the weighting coefficients for impact intensity and vibration power, respectively, ranging from 0 to 1 (here, 0.5 is used). The expression for the stability index SI is:

[0074]

[0075] In the formula, includes the axial vibration impact degree JE of the brake disc and its vibration power VP, α and β are the weighting coefficients of the impact degree and vibration power, respectively. n b represents the amplitude of the cosine wave in the signal corresponding to n times the fundamental frequency. nThe stability index (SI) represents the amplitude of the sine wave corresponding to n times the fundamental frequency in the signal, f represents the vibration frequency, and cos(2πnft) and sin(2πnft) represent the cosine wave and sine wave, respectively. A larger SI value indicates that the brake disc vibration is more unstable; that is, the larger the SI value, the more obvious the change in axial vibration acceleration of the brake disc, the higher the vibration power, and the worse its vibration stability.

[0076] This invention aims to conduct an in-depth study on the vibration stability of disc brakes for high-speed trains using two key parameters: impact intensity and vibration power. For disc brakes, the uneven distribution of contact stress is caused by the self-excited vibration phenomenon between the friction pairs, resulting in strong nonlinearity in their vibration. In the analysis process, it is necessary to transform the nonlinear characteristics into equivalent linear characteristics.

[0077] This invention takes a disc brake of a certain type of high-speed train as the research object. Through braking simulation tests and multi-physics coupled simulation analysis, the axial acceleration results of the brake disc under various braking parameters are obtained, and the axial excitation response spectrum of the brake disc is obtained through Fourier transform. Based on the two key factors affecting vibration—impact intensity and vibration power—a method for evaluating the braking vibration stability of disc brakes is proposed. This method can assess the vibration stability during braking and obtain a stability index that describes the severity of the axial vibration of the brake disc. Substituting the simulated axial excitation response spectrum of the brake disc into the stability index expression, the vibration of the brake disc under different braking parameters can be intuitively reflected. The stability indices calculated under different braking parameter conditions are plotted as curves, as shown below. Figure 4 As shown, the main factors affecting brake disc vibration during service can be determined based on the stability index calculation results, providing valuable theoretical reference for the subsequent optimization design of disc brakes.

[0078] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications to the technical solutions described in the foregoing embodiments, or equivalent substitutions for some or all of the technical features, do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for evaluating the braking vibration stability of a disc brake, characterized in that, Includes the following processes: Step 1: Establish a dynamic simulation model of the disc brake for high-speed trains; Step 2: Conduct simulation tests on the dynamic simulation model of the high-speed train disc brake to obtain the axial excitation response results of the brake disc under different braking parameters; wherein, the axial excitation response results are the magnitude of the axial excitation amplitude of the brake disc at different angular frequencies. Step 3: Perform Fourier transform processing on the axial excitation response results of the brake disc to obtain the FFT axial excitation response spectrum of the brake disc. Step 4: Based on the axial excitation amplitude of the brake disc at different vibration frequencies in the axial excitation response spectrum, calculate the axial vibration impact JE and axial vibration power VP of the brake disc at different times. The expression for impact JE: In the formula, Q is the axial vibration displacement of the brake disc, t is the braking time, and a n b represents the amplitude of the cosine wave in the signal corresponding to n times the fundamental frequency. n Let f represent the amplitude of the sine wave corresponding to n times the fundamental frequency in the signal, f represent the vibration frequency, and cos(2πnft) and sin(2πnft) represent the cosine wave and the sine wave, respectively. The expression for the axial vibration power VP of the brake disc is: In the formula, P d denoted as , where is the axial vibration power of the brake disc, and m is the mass of the train brake disc. Step 5: Calculate the stability index based on the axial vibration impact degree JE and the axial vibration power VP of the brake disc; The expression for the stability index SI is: In the formula, the axial vibration impact degree JE of the brake disc and its vibration power VP are included, and α and β are the weighting coefficients of the impact degree and vibration power, respectively. The larger the stability index, the more unstable the brake disc vibration tends to be, the more obvious the change in the axial vibration acceleration of the brake disc, and the higher the vibration power, the worse its vibration stability.

2. The method for evaluating the braking vibration stability of a disc brake according to claim 1, characterized in that, In step 1, the dynamic simulation model of the high-speed train disc brake includes: The inner and outer diameters of the brake disc, the total thickness of the disc body, the brake disc material, and the elastic modulus, Poisson's ratio, density, thermal conductivity, specific heat capacity, linear expansion coefficient, and surface emissivity of the brake disc material; The inner and outer diameters of the brake pads, the total thickness of the brake pads, the brake pad material, and the elastic modulus, Poisson's ratio, density, thermal conductivity, specific heat capacity, linear expansion coefficient, and surface emissivity of the brake pad material.

3. The method for evaluating the braking vibration stability of a disc brake according to claim 1, characterized in that, In step 2, the test parameters of the simulation test include the initial rotational speed v, braking pressure F, and friction coefficient μ.

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