Braking torque fluctuation analysis method

Abstract

The invention discloses a braking torque fluctuation analysis method, and belongs to the technical field of automobile braking. According to the method, a braking system concentrated mass-spring mathematical model is constructed, the dynamic characteristics of brake calipers, a brake disc, a friction block and other components are comprehensively considered, actually-measured brake disc wall thickness difference (DTV) data is used as excitation, a fourth-order-fifth-order Runge-Kutta method in Matlab is adopted for solving a differential equation, and a braking torque fluctuation (BTV) curve is calculated in a simulation mode. The accuracy of the model is verified by comparing measured data with a simulation result, and the deviation is controlled within 5%. The verified model can replace a bench test to analyze BTV characteristics, the development cost is saved, the development period is shortened, guidance is provided for design optimization of a braking system, and the braking jitter performance is remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of automotive braking, and relates to a method for analyzing the braking torque fluctuation. Background Art

[0002] Brake judder, as a typical NVH (Noise, Vibration, and Harshness) problem in the automotive braking system, is a low-frequency vibration phenomenon that usually occurs within a specific vehicle speed range (e.g., 20 - 80 km / h) when the driver applies medium or low braking intensity. Its main characteristics include the reciprocating swing of the steering wheel in its circumferential direction, the pulsating vibration of the brake pedal, and the obvious vibration of the vehicle body. These phenomena not only affect driving comfort but also may cause the driver to worry about vehicle safety. Therefore, the research and solution of the brake judder problem have always been an important topic in the design and optimization of automotive braking systems.

[0003] Brake judder is a system response phenomenon triggered by external excitation, and its influencing factors are complex and diverse, including suspension system design, tire force fluctuation, imbalance of rotating components, brake torque variation (BTV), road surface input, and driving habits, etc. Among them, brake torque variation (BTV) is widely regarded in the industry as the core factor inducing brake judder. Further research shows that the main source of brake torque variation is the disc thickness variation (DTV). Disc thickness variation refers to the uneven thickness of the two friction surfaces of the brake disc during rotation, resulting in periodic changes in the frictional force during braking, and thus triggering the fluctuation of the braking torque. This fluctuation is transmitted through the braking system to the suspension, steering wheel, and vehicle body, and finally manifests as vibrations perceptible to the driver.

[0004] In order to deeply study the influencing mechanism of brake torque fluctuation, the existing technologies usually start from the design parameters of key components of the braking system (such as brake calipers, brake discs), and discuss their influence on brake torque fluctuation through theoretical analysis and experimental verification. For example, by analyzing parameters such as brake caliper stiffness and brake disc geometric characteristics, the formation mechanism of brake torque fluctuation can be preliminarily revealed. However, traditional experimental methods rely on a large number of bench tests and on-vehicle tests, which are not only time-consuming and costly but also difficult to comprehensively cover various working conditions and parameter combinations of the braking system. Therefore, the method based on simulation analysis has gradually attracted attention. Existing simulation studies usually establish a dynamic model of the braking system, use the disc thickness variation (DTV) as the main excitation input, combine parameters such as the stiffness and mass of the brake caliper and brake disc, and use numerical methods (such as the Runge - Kutta method) to solve the dynamic equation, calculate the characteristic curve of brake torque fluctuation, and verify the accuracy of the simulation results through experimental data.

[0005] Although the above methods have promoted the research on the brake judder problem to a certain extent, there are still some deficiencies. First, the existing simulation models usually simplify the dynamic characteristics of the braking system and fail to fully consider the complex interactions among components such as brake calipers, brake discs, friction pads, and pistons, resulting in a large deviation between the simulation results and the actual working conditions. Second, the treatment of the brake disc thickness variation (DTV) in the existing research is relatively simple. Usually, the measured data is directly used as the input, lacking the dynamic fitting and analysis of the variation of DTV with time and phase, which limits the prediction ability of the simulation model. In addition, the verification process of the existing simulation methods is relatively single, lacking systematic model correction and optimization steps, and it is difficult to ensure the confidence level and engineering application value of the simulation results. Summary of the Invention

[0006] In view of this, the purpose of the present invention is to provide an analysis method for braking torque fluctuation. By establishing an accurate dynamic model of the braking system, combining measured data and dynamic fitting technology, high-precision simulation analysis of braking torque fluctuation is realized, the test cost is reduced, and guidance is provided for the design of the braking system.

[0007] To achieve the above purpose, the present invention provides the following technical solutions:

[0008] An analysis method for braking torque fluctuation, which establishes a lumped mass-spring mathematical model of the braking system. This model combines the dynamic characteristics of the brake caliper, brake disc, bracket, inner and outer brake pads, and piston in the brake caliper system. The dynamic characteristics include mass parameters, stiffness parameters, damping parameters, displacement parameters, and velocity parameters. Using the measured brake disc thickness variation (DTV) data as the external excitation, the measured stiffness parameters, mass parameters, and damping parameters as the system constraint conditions, and the initial values of displacement and velocity as the initial conditions, the fourth-fifth order Runge-Kutta method in Matlab is used to solve the differential equations, and the brake disc thickness variation (DTV) data and the braking torque fluctuation (BTV) curve are simulated and calculated. By comparing the measured brake disc thickness variation (DTV) and braking torque fluctuation (BTV) data with the simulation results, the accuracy and confidence level of the model are verified. The verified model simulation is used to replace the bench test for the analysis of braking torque fluctuation (BTV).

[0009] Furthermore, establishing the lumped mass-spring mathematical model of the braking system includes the following steps:

[0010] S1: Establish a differential equation set of the lumped mass-spring mathematical model of the braking system, which includes the mass parameters, stiffness parameters, damping parameters, displacement parameters, and velocity parameters of the brake caliper, brake disc, bracket, inner and outer brake pads, and piston.

[0011] S2: Determine the simulation parameters. Obtain the stiffness parameters through experimental tests, obtain the mass parameters from design data, and obtain the damping parameters by querying existing literature.

[0012] S3: Measure the input parameters required for the simulation model through experiments, including the stiffness parameters, the data of the brake disc thickness variation (DTV), and the initial values of displacement and velocity. The stiffness parameters, mass parameters, and damping parameters are used as system constraint conditions, the data of the brake disc thickness variation (DTV) is used as an external excitation, and the initial values of displacement and velocity are used as the initial conditions for solving the differential equations.

[0013] S4: Take the measured data of the brake disc thickness variation (DTV), stiffness parameters, mass parameters, damping parameters, and initial conditions in step S3 as inputs, and use the fourth-fifth order Runge-Kutta method in Matlab to solve the differential equation system in step S1 to generate simulation calculation data, which includes the data of the brake disc thickness variation (DTV).

[0014] S5: Measure the brake disc thickness variation (DTV) through the brake disc DTV test equipment to obtain the measured data of the brake disc thickness variation (DTV).

[0015] S6: Compare the data of the brake disc thickness variation obtained by simulation calculation in step S4 with the measured data of the brake disc thickness variation in step S5 to verify the accuracy of the simulation model.

[0016] S7: Based on the measured data of the brake disc thickness variation in step S5, fit it into a function of displacement and phase through the Fourier function. After converting the function of displacement with respect to phase into a function of displacement and time according to the settings of the braking process, use this function as an external excitation, combine it with the system constraint conditions and initial conditions in step S3, and use the fourth-fifth order Runge-Kutta method in Matlab to solve the differential equation system to generate the curve of the braking torque fluctuation (BTV) of the simulation calculation.

[0017] S8: Measure the braking torque fluctuation (BTV) of the brake disc tested in step S5 through a professional BTV test equipment to obtain the measured BTV data.

[0018] S9: Compare the curve of the braking torque fluctuation (BTV) obtained by simulation calculation in step S7 with the measured BTV data in step S8 to verify the confidence level of the simulation model analysis.

[0019] Furthermore, in step S1, the differential equation system of the lumped mass-spring mathematical model of the braking system is as follows:

[0020]

[0021] Where:

[0022] mC -- Mass of the brake caliper; m D -- Mass of the brake disc; m P -- Mass of the friction pad; m P- -- Mass of the piston;

[0023] -- Velocity of the brake caliper; -- Acceleration of the brake caliper; x C -- Displacement of the brake caliper;

[0024] -- Velocity of the outer friction pad; -- Acceleration of the outer friction pad; x PO -- Displacement of the outer friction pad;

[0025] -- Velocity of the outer end face of the brake disc; -- Acceleration of the outer end face of the brake disc; x DO -- Displacement of the outer end face of the brake disc;

[0026] -- Velocity of the inner end face of the brake disc; -- Acceleration of the inner end face of the brake disc; x DI -- Displacement of the inner end face of the brake disc;

[0027] -- Velocity of the inner friction pad; -- Acceleration of the inner friction pad; x PI -- Displacement of the inner friction pad;

[0028] -- Velocity of the piston; -- Acceleration of the piston; x PT -- Displacement of the piston;

[0029] k FP -- Stiffness between the brake caliper jaw and the outer friction pad; k DP -- Stiffness between the friction pad and the brake disc;

[0030] k PP -- Stiffness between the inner friction pad and the piston; k HS -- Equivalent stiffness of the piston including hydraulic influence;

[0031] k BC -- Sliding stiffness of the brake caliper against the bracket; x B -- Displacement of the bracket;

[0032] c FP -- Damping between the brake caliper jaw and the outer friction pad; c DP -- Damping between the friction pad and the brake disc;

[0033] c PP -- Damping between the inner friction block and the piston; c HS -- Equivalent piston damping including hydraulic influence;

[0034] c BC -- Sliding damping of the brake caliper on the bracket; -- Speed of the bracket

[0035] F DO-D -- Generalized force on the outer surface of the brake disc; F DI-D -- Generalized force on the inner surface of the brake disc.

[0036] Furthermore, in the lumped mass-spring mathematical model of the braking system, the stiffness parameters k FP 、k HS 、k DP 、k PP 、k BC are all obtained through tests, the mass parameters m C 、m D 、m P 、m PT are obtained from design parameters, and the damping parameters c FP 、c DP 、c PP 、c HS 、c BC are obtained by querying existing literature.

[0037] Furthermore, in step S6, the original data of x DI and x DO measured in the bench test are imported into Matlab, and the Fourier function is used to fit them into functions of displacement versus phase x DI (θ) and x DO (θ), then the function of the brake disc thickness variation (DTV) obtained by fitting is:

[0038] DTV(θ) = x DI (θ) - x DO (θ);

[0039] The function of the brake disc thickness variation DTV obtained by fitting is compared with the data of the brake disc thickness variation calculated by simulation in S4, and the model is corrected to control the deviation within 5%.

[0040] Furthermore, in step S7:

[0041] Let: x1 = x C , x3 = x PO , x5 = x PI, x7 = x PT , The differential equations of the lumped mass-spring mathematical model of the braking system are reduced to:

[0042]

[0043] According to the braking process:

[0044]

[0045] where ω0 is the initial braking speed, a is the braking deceleration, and R is the tire rolling radius;

[0046] The functions x DI (θ) and x DO (θ) of displacement with respect to phase in step S6 are transformed into functions x DI (t) and x DO (t) of displacement with respect to time;

[0047] The fourth-fifth order Runge-Kutta method in Matlab is used to solve the differential equations, and we get:

[0048]

[0049] Substitute it into the differential equations of the lumped mass-spring mathematical model of the braking system, and then F DO-D and F DI-D can be obtained:

[0050] Moreover,

[0051] BTV = μ × (F DI-D - F DO-D ) × Reff

[0052] where BTV - braking torque fluctuation; μ - braking friction coefficient; Reff - effective braking radius;

[0053] Substitute F DO-D and F DO-D , and then the BTV curve can be obtained.

[0054] Furthermore, in step S9, the measured BTV data is fitted using the Fourier function to obtain the BTV fitting curve, and the BTV fitting curve is compared with the BTV curve obtained by simulation to correct the model so that the deviation is controlled within 5%.

[0055] The beneficial effects of the present invention are as follows:

[0056] The present invention provides an analysis method for braking torque fluctuation. By establishing an accurate dynamic model of the braking system and combining measured data and dynamic fitting techniques, the simulation analysis accuracy of braking torque fluctuation (BTV) is significantly improved, the test cost is reduced, and scientific guidance is provided for the design of automotive braking systems. Compared with the prior art, the beneficial effects of the present invention are specifically reflected in the following aspects:

[0057] 1. High-precision simulation analysis ability

[0058] The present invention constructs a lumped mass-spring mathematical model of the braking system, comprehensively considering the dynamic characteristics of the brake caliper, brake disc, bracket, inner and outer brake pads, and piston, including mass parameters, stiffness parameters, damping parameters, displacement parameters, and velocity parameters. This refined modeling method with multiple components and multiple parameters fully restores the complex interactions between components in the braking system, and significantly improves the authenticity and reliability of the simulation results compared with traditional simplified models.

[0059] In addition, the present invention uses measured data of brake disc thickness variation (DTV) as an external excitation, and performs dynamic fitting on it through the Fourier function to generate the functional relationship between displacement, phase, and time. This dynamic fitting method overcomes the limitations of directly using static DTV data in traditional methods, can more accurately describe the dynamic changes of brake disc thickness variation during braking, and thus improves the accuracy of braking torque fluctuation (BTV) simulation. The deviation between the simulation results and the measured data is controlled within 5%, indicating that the model has a high confidence level and can effectively predict the occurrence mechanism and characteristics of brake judder problems.

[0060] 2. Significantly reduce development costs and cycle

[0061] The research on traditional brake judder problems highly relies on bench tests and on-vehicle tests. These tests require a large amount of sample preparation, equipment operation, and manual operation, with high costs and long cycles. The present invention can replace most bench tests with computer simulations at the early stage of design through a high-precision simulation analysis method, greatly reducing the number of physical tests and related resource consumption. For example, the influence of different brake disc thickness variations (DTV) on braking torque fluctuation (BTV) can be quickly evaluated through simulation, without repeatedly manufacturing and testing various brake disc samples, saving material costs and processing fees.

[0062] At the same time, the fast iteration characteristic of simulation analysis enables designers to complete the analysis of multiple parameter combinations in a short time, shortening the development cycle of the braking system. Compared with traditional test methods, the present invention can shorten the analysis cycle of brake judder problems, winning a valuable time window for automobile manufacturers in the development of new models and enhancing market competitiveness.

[0063] Other advantages, objects, and features of the present invention will, to some extent, be set forth in the following description, and to some extent, will be obvious to those skilled in the art based on an examination of the following, or can be learned from the practice of the present invention. The objects and other advantages of the present invention can be achieved and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] In order to make the objects, technical solutions, and advantages of the present invention clearer, the present invention will be described in detail preferably with reference to the accompanying drawings, where:

[0065] Figure 1 is a schematic flow diagram of the present invention.

[0066] Figure 2 is the centralized mass-spring mathematical model of the braking system;

[0067] Figure 3 is x DI 、x DO original data fitting;

[0068] Figure 4 are the DTV curves of the new brake disc and the faulty brake disc;

[0069] Figure 5 is the BTV simulation result;

[0070] Figure 6 is the BTV bench test result. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0071] The following describes the embodiments of the present invention through specific examples. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments. The details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the drawings provided in the following embodiments only illustrate the basic concept of the present invention schematically. Without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0072] Among them, the drawings are only for illustrative purposes, showing only schematic diagrams, not physical diagrams, and should not be construed as a limitation on the present invention; in order to better illustrate the embodiments of the present invention, some components in the drawings will be omitted, enlarged, or reduced, and do not represent the dimensions of the actual product; for those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0073] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "rear", etc. indicating the orientation or positional relationship, they are based on the orientation or positional relationship shown in the accompanying drawings. This is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the terms describing the positional relationship in the accompanying drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those of ordinary skill in the art, the specific meanings of the above terms can be understood according to specific circumstances.

[0074] Please refer to Figures 1 - 2 , which is an analysis method for the braking torque fluctuation. A lumped mass-spring mathematical model of the braking system is established. This model combines the dynamic characteristics of the brake caliper, brake disc, bracket, inner and outer brake pads, and piston in the brake caliper system. The dynamic characteristics include mass parameters, stiffness parameters, damping parameters, displacement parameters, and velocity parameters. Using the measured brake disc thickness variation (DTV) data as the external excitation, the measured stiffness parameters, mass parameters, and damping parameters as the system constraint conditions, and the initial values of displacement and velocity as the initial conditions, the fourth-fifth order Runge-Kutta method in Matlab is used to solve the differential equations, and the brake disc thickness variation (DTV) data and the braking torque fluctuation (BTV) curve are simulated and calculated. By comparing the measured brake disc thickness variation (DTV) and braking torque fluctuation (BTV) data with the simulation results, the accuracy and confidence of the model are verified. The verified model simulation is used to replace the bench test for the analysis of the braking torque fluctuation (BTV).

[0075] Specifically, when implementing, establishing the lumped mass-spring mathematical model of the braking system includes the following steps:

[0076] S1: Establish the differential equations of the lumped mass-spring mathematical model of the braking system. The differential equations include the mass parameters, stiffness parameters, damping parameters, displacement parameters, and velocity parameters of the brake caliper, brake disc, bracket, inner and outer brake pads, and piston.

[0077] S2: Determine the simulation parameters. Obtain the stiffness parameters through experimental tests, obtain the mass parameters through design data, and obtain the damping parameters through existing literature queries.

[0078] S3: Measure the input parameters required for the simulation model through experiments, including the stiffness parameters, brake disc thickness variation (DTV) data, and the initial values of displacement and velocity. The stiffness parameters, mass parameters, and damping parameters are used as the system constraint conditions, the brake disc thickness variation (DTV) data is used as the external excitation, and the initial values of displacement and velocity are used as the initial conditions for solving the differential equations.

[0079] S4: Using the measured brake disc thickness variation (DTV) data, stiffness parameters, mass parameters, damping parameters, and initial conditions in step S3 as inputs, solve the differential equations of the model in step S1 using the fourth-fifth order Runge-Kutta method in Matlab to generate simulation calculation data, which includes brake disc thickness variation (DTV) data;

[0080] S5: Measure the brake disc thickness variation (DTV) through the brake disc DTV test equipment to obtain the measured brake disc thickness variation (DTV) data;

[0081] S6: Compare the brake disc thickness variation data obtained from the simulation calculation in step S4 with the measured brake disc thickness variation data in step S5 to verify the accuracy of the simulation model;

[0082] S7: Based on the measured brake disc thickness variation data in step S5, fit it into a function of displacement and phase through the Fourier function. After converting the function of displacement versus phase into a function of displacement and time according to the settings of the braking process, use this function as an external excitation, combine with the system constraint conditions and initial conditions in step S3, and solve the differential equations using the fourth-fifth order Runge-Kutta method in Matlab to generate the braking torque variation (BTV) curve of the simulation calculation;

[0083] S8: Measure the braking torque variation (BTV) of the brake disc tested in step S5 through a professional BTV test equipment to obtain the measured BTV data;

[0084] S9: Compare the braking torque variation (BTV) curve obtained from the simulation calculation in step S7 with the measured BTV data in step S8 to verify the confidence level of the simulation model analysis.

[0085] Among them, in step S1, the differential equations of the brake system lumped mass-spring mathematical model are as follows:

[0086]

[0087] Where:

[0088] m C -- Caliper mass; m D -- Brake disc mass; m P -- Friction block mass; m PT -- Piston mass;

[0089] -- Caliper velocity; -- Caliper acceleration; x C -- Caliper displacement;

[0090] -- Outer friction block velocity; -- Outer friction block acceleration; x PO -- Outer friction block displacement;

[0091] -- Brake disc outer end face velocity; -- Brake disc outer end face acceleration; x DO -- Brake disc outer end face displacement;

[0092] -- Brake disc inner end face velocity; -- Brake disc inner end face acceleration; x DI -- Brake disc inner end face displacement;

[0093] -- Inner friction block velocity; -- Inner friction block acceleration; x PI -- Inner friction block displacement;

[0094] -- Piston velocity; -- Piston acceleration; x PT -- Piston displacement;

[0095] k FP -- Stiffness between the brake caliper jaw part and the outer friction block; k DP -- Stiffness between the friction block and the brake disc;

[0096] k PP -- Stiffness between the inner friction block and the piston; k HS -- Equivalent stiffness of the piston including hydraulic influence;

[0097] k BC -- Sliding stiffness of the brake caliper on the bracket; x B -- Displacement of the bracket;

[0098] c FP -- Damping between the brake caliper jaw part and the outer friction block; c DP -- Damping between the friction block and the brake disc;

[0099] c PP -- Damping between the inner friction block and the piston; c HS -- Equivalent damping of the piston including hydraulic influence;

[0100] c BC -- Sliding damping of the brake caliper on the bracket; -- Velocity of the bracket

[0101] F DO-D -- Generalized force on the outer surface of the brake disc; FDI-D -- Generalized force on the inner surface of the brake disc.

[0102] In the lumped mass-spring mathematical model of the braking system, the stiffness parameters k FP 、k HS 、k DP 、k PP 、k BC are all obtained through tests, the mass parameters m C 、m D 、m P 、m PT are obtained from design parameters, and the damping parameters c FP 、c DP 、c PP 、c HS 、c BC are obtained by querying existing literature.

[0103] In step S6, the original data of x DI and x DO measured in the bench test are imported into Matlab, and the Fourier function is used to fit them into functions of displacement versus phase x DI (θ) and x DO (θ). Then, the function of the brake disc thickness variation (DTV) obtained by fitting is:

[0104] DTV(θ) = x DI (θ) - x DO (θ);

[0105] The function of the brake disc thickness variation DTV obtained by fitting is compared with the data of the brake disc thickness variation calculated by simulation in S4, and the model is corrected to control the deviation within 5%.

[0106] In step S7:

[0107] Let: x1 = x C , x3 = x [O , x5 = x PI , x7 = x [T , The differential equations of the lumped mass-spring mathematical model of the braking system are reduced to:

[0108]

[0109] According to the braking process:

[0110]

[0111] where ω0 is the initial braking speed, a is the braking deceleration, and R is the tire rolling radius;

[0112] Convert the functions of displacement with respect to phase x DI (θ) and x DO (θ) in step S6 into functions of displacement with respect to time x DI (t) and x DO (t);

[0113] Use the fourth-fifth order Runge-Kutta method in Matlab to solve the differential equation system, and obtain:

[0114]

[0115] Substitute it into the differential equation system of the lumped mass-spring mathematical model of the braking system, and then calculate F DO-D and F DI-D :

[0116] And,

[0117] BTV = μ × (F DI-D - F DO-D ) × Reff

[0118] where BTV - braking torque fluctuation; μ - braking friction coefficient; Reff - effective braking radius;

[0119] Substitute F DO-D and F DI-D , and then calculate the BTV curve.

[0120] In step S9, fit the measured BTV data using the Fourier function to obtain the BTV fitting curve, and compare the BTV fitting curve with the BTV curve obtained by simulation to modify the model so that the deviation is controlled within 5%.

[0121] In implementation, use this method to conduct actual measurement and simulation processing for new brake discs and faulty brake discs respectively, and the comparison diagrams obtained are as Figures 3 - 6 shown.

[0122] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not restrictive. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the purpose and scope of the present technical solution, and they should all be covered by the scope of the claims of the present invention.

Claims

1. An analysis method for braking torque fluctuation, characterized in that: A lumped mass-spring mathematical model of the braking system is established. This model combines the dynamic characteristics of the brake caliper, brake disc, bracket, inner and outer brake pads, and piston in the brake caliper system. The dynamic characteristics include mass parameters, stiffness parameters, damping parameters, displacement parameters, and velocity parameters. Using the measured brake disc wall thickness difference data as the external excitation, the measured stiffness parameters, mass parameters, and damping parameters as the system constraint conditions, and the initial values of displacement and velocity as the initial conditions, the fourth-fifth order Runge-Kutta method in Matlab is used to solve the differential equation system, and the brake disc wall thickness difference data and the braking torque fluctuation curve are simulated and calculated. By comparing the measured brake disc wall thickness difference and braking torque fluctuation data with the simulation results, the accuracy and confidence of the model are verified. Using the verified model simulation to replace the bench test for braking torque fluctuation analysis.

2. The analysis method of braking torque fluctuation according to claim 1, characterized in that Establishing the lumped mass-spring mathematical model of the braking system includes the following steps: S1: Establish the differential equation system of the lumped mass-spring mathematical model of the braking system, which includes the mass parameters, stiffness parameters, damping parameters, displacement parameters, and velocity parameters of the brake caliper, brake disc, bracket, inner and outer brake pads, and piston. S2: Determine the simulation parameters. Obtain the stiffness parameters through experimental tests, obtain the mass parameters through design data, and obtain the damping parameters through existing literature queries. S3: Measure the input parameters required for the simulation model through experiments, including the stiffness parameters, brake disc wall thickness difference data, and the initial values of displacement and velocity. The stiffness parameters, mass parameters, and damping parameters are used as the system constraint conditions, the brake disc wall thickness difference data is used as the external excitation, and the initial values of displacement and velocity are used as the initial conditions for solving the differential equation. S4: Using the measured brake disc wall thickness difference data, stiffness parameters, mass parameters, damping parameters, and initial conditions in step S3 as the input, the fourth-fifth order Runge-Kutta method in Matlab is used to solve the differential equation system of the model in step S1, generating simulation calculation data, which includes the brake disc wall thickness difference data. S6: Measure the brake disc wall thickness difference through the brake disc DTV test equipment to obtain the measured brake disc wall thickness difference data. S7: Compare the brake disc wall thickness difference data obtained from the simulation calculation in step S4 with the measured brake disc wall thickness difference data in step S6 to verify the accuracy of the simulation model. S8: Based on the measured brake disc wall thickness difference data in step S5, fit it into a function of displacement and phase through the Fourier function. After converting the function of displacement versus phase into a function of displacement and time according to the settings of the braking process, using this function as the external excitation, combined with the system constraint conditions and initial conditions in step S3, the fourth-fifth order Runge-Kutta method in Matlab is used to solve the differential equation system, generating the simulated braking torque fluctuation curve. S9: Measure the braking torque fluctuation of the brake disc tested in step S5 through a professional BTV test equipment to obtain the measured BTV data. S10: Compare the braking torque fluctuation curve obtained from the simulation calculation in step S7 with the measured BTV data in step S8 to verify the confidence of the simulation model analysis.

3. The analysis method for braking torque fluctuation according to claim 2, characterized in that In step S1, the differential equation system of the lumped mass-spring mathematical model of the braking system is as follows: Where: m C -- Mass of brake caliper; m D -- Mass of brake disc; m P -- Mass of friction pad; m PT -- Mass of piston; -- Brake caliper speed; -- Brake caliper acceleration; x C -- Brake caliper displacement; -- Outer friction block speed; -- Outer friction block acceleration; x PO -- Outer friction block displacement; -- Outer end face velocity of the brake disc; -- Outer end face acceleration of the brake disc; x DO -- Outer end face displacement of the brake disc; -- Inner end face velocity of the brake disc; -- Inner end face acceleration of the brake disc; x DI -- Inner end face displacement of the brake disc; -- Inner friction block speed; -- Inner friction block acceleration; x PI -- Inner friction block displacement; -- Piston speed; -- Piston acceleration; x PT -- Piston displacement; k FP -- Stiffness between the brake caliper jaw part and the outer friction block; k DP -- Stiffness between the friction block and the brake disc; k PP --Stiffness between the inner friction block and the piston; k HS --Equivalent stiffness of the piston including the influence of hydraulics k BC --Sliding stiffness of the brake caliper on the bracket; x B --Displacement of the bracket; c FP --Damping between the brake caliper jaw part and the outer friction block; c DP --Damping between the friction block and the brake disc; c PP --Damping between the inner friction block and the piston; c HS --Equivalent damping of the piston including the hydraulic effect; c bC --Sliding damping of the brake caliper on the bracket; --Speed of the bracket F DO-D -- Generalized force on the outer surface of the brake disc; F DI-D -- Generalized force on the inner surface of the brake disc.

4. The analysis method for braking torque fluctuation according to claim 3, characterized in that: In the lumped mass-spring mathematical model of the braking system, the stiffness parameters k FP , k HS , k DP , k PP , k BC are all obtained through tests. The mass parameters m C , m D , m P , m PT are obtained from the design parameters. The damping parameters c FP , c DP , c PP , c HS , c BC are obtained by querying existing literature.

5. The analysis method for braking torque fluctuation according to claim 4, characterized in that, In step S6, the measured x obtained from the bench test DI and x DO raw data are imported into Matlab, and the Fourier function is used to fit them into functions of displacement versus phase x DI (θ) and x DO (θ). Then the obtained brake disc wall thickness difference function is: DTV(θ) = x DI (θ) - x DO (θ); Compare the brake disc wall thickness difference function obtained by fitting with the brake disc wall thickness difference data obtained by simulation in S4, and correct the model to control the deviation within 5%.

6. The analysis method of braking torque fluctuation according to claim 2, characterized in that In step S7: Let: x1 = x C , x3 = x [O , x5 = x PI , x7 = x [T , The differential equations of the lumped mass-spring mathematical model of the braking system are reduced to: According to the braking process: Where, ω0 is the initial braking speed, a is the braking deceleration, and R is the tire rolling radius; Convert the displacement-versus-phase functions x DI (θ) and x DO (θ) in step S6 into displacement-versus-time functions x DI (t) and x DO (t). Use the fourth-fifth order Runge-Kutta method in Matlab to solve the differential equation system to obtain: Substitute it into the differential equation system of the lumped mass-spring mathematical model of the braking system, and then the force F can be obtained. DO-D and force F DI-D : And, BTV = μ × (F DI-D - F DO-D ) × Reff Where, BTV - braking torque fluctuation; μ - braking friction coefficient; Reff - effective braking radius; Substitute F DO-D and F DI-D to obtain the BTV curve.

7. The analysis method for the braking torque fluctuation according to claim 6, wherein: In step S9, fit the measured BTV data using the Fourier function to obtain the BTV fitting curve, compare the BTV fitting curve with the BTV curve obtained by simulation, and correct the model to control the deviation within 5%.

Images