A full-plate brake temperature rise analysis method

Abstract

The present application belongs to the technical field of heat analysis of vehicle braking system, and discloses a full-disc brake temperature rise analysis method. The method is based on the axisymmetric heat conduction theory, establishes a steady-state temperature prediction model of continuous annular heat source, processes radial heat conduction through variable separation and Hankel transformation, combines the rotation effect and the convection boundary condition, and quickly solves the brake disc temperature distribution. The present application significantly reduces the prediction error and improves the calculation efficiency, is suitable for the thermal performance optimization of various brake materials, supports the extension of non-axisymmetric structure, can not only evaluate the temperature uniformity under steady-state braking, but also guide the brake disc geometric parameters (thickness, radius) and material selection, provides an efficient theoretical tool for brake system design, and has engineering practicability and scientific accuracy.

Description

Technical Field

[0001] This invention belongs to the field of thermal analysis technology of vehicle braking systems, and specifically relates to a method for analyzing the temperature rise of a full disc brake. Background Technology

[0002] With the increasing demands for braking performance in modern transportation equipment, full disc brakes are widely used in special vehicles, high-speed trains, and other fields due to their advantages such as smooth braking and uniform heat dissipation. During continuous braking, the annular heat source formed at the contact interface of the friction pair continuously inputs heat, causing the brake disc temperature to rise sharply, leading to problems such as thermal deformation, friction fade, and material failure.

[0003] Existing research on brake disc thermal analysis mainly focuses on caliper disc brakes, forming two main technical approaches: The first is the moving heat source model, which uses single or dual-point heat sources to discretize and simulate the discontinuous heat flow at local caliper contact. However, this method does not consider the circumferential convection differences caused by brake disc rotation, and the heat source coverage is typically less than 30%. The second is the three-dimensional transient finite element method, which, while enabling refined calculations of the local temperature field, suffers from low computational efficiency and cannot meet the real-time control requirements of engineering. Both methods are based on the assumption of a heat source away from the caliper brake, which is fundamentally incompatible with the continuous annular heat source characteristics of a full-disc brake, making accurate and efficient temperature rise analysis difficult. Summary of the Invention

[0004] The purpose of this invention is to provide a method for analyzing the temperature rise of a full-disc brake, which significantly reduces prediction errors and improves computational efficiency. It is applicable to the thermal performance optimization of various brake materials and supports the extension of non-axisymmetric structures. It can not only evaluate the temperature uniformity under steady-state braking, but also guide the selection of brake disc geometric parameters (thickness, radius) and materials, providing an efficient theoretical tool for brake system design. It combines engineering practicality and scientific accuracy, thereby solving at least one of the technical problems involved in the background art.

[0005] To solve the above-mentioned technical problems, the present invention is implemented as follows: This invention provides a method for analyzing the temperature rise of a full-disc brake, comprising the following steps: Step S1: Establish an axisymmetric analytical model. Based on the steady-state heat conduction equation in cylindrical coordinates, and combining the rotation effect and the distribution of the annular heat source, construct the governing equation. Step S2: Set boundary conditions, including convection heat transfer at the inner and outer edges, insulation of the middle surface, and coupling of surface convection with the heat source; Step S3, Variable Separation and Hankel Transform: Variable separation and dimensionality reduction are performed using Fourier transform and Hankel transform to transform the governing equations into ordinary differential equations. Step S4: Process the annular heat source term, calculate the heat flux density of the annular heat source, and obtain the heat source term through Hankel transformation; Step S5: Solve for the temperature field by solving for the temperature distribution using the method of separation of variables and reconstructing the three-dimensional temperature field using the inverse Hankel transformation. Step S6: Establish a finite element model, set material properties and contact thermal resistance model, combine the multi-cycle braking temperature accumulation formula and Newton's law of cooling to simulate convection heat dissipation, and solve to obtain simulation results.

[0006] Optionally, in step S1, the governing equation is: ; in, This is a correction term for the rotation effect; These are the radial coordinates in the cylindrical coordinate system. For temperature; For the axial coordinates in the cylindrical coordinate system; The angular velocity of the brake disc rotation; Thermal diffusivity; These are the circumferential coordinates in a cylindrical coordinate system. denoted as the thermal conductivity of the material.

[0007] Optionally, in step S2, the boundary conditions include: ; in, The convective heat transfer coefficient; Ambient temperature; This refers to the axial position of the brake disc's center surface.

[0008] Optionally, in step S4, the heat flux density of the annular heat source... Calculated using the following formula: ; in, This refers to the power dissipated during braking; The outer radius of the brake disc; The inner radius of the brake disc.

[0009] Optionally, in step S4, the heat source term is obtained through the Hankel transformation: ; in, This is the heat source function after the Hankel transformation; These are the characteristic parameters in the Hankel transform; It is a first-order Bessel function.

[0010] Optionally, in step S5, the temperature distribution is calculated using the following formula: ; in, .

[0011] Optionally, in step S5, the three-dimensional temperature field is reconstructed through the inverse Hankel transformation: ; in, It is a zero-order Bessel function.

[0012] Optionally, in step S6, the contact thermal resistance model is: ; in, For contact thermal resistance; This represents the temperature difference between the two sides of the contact interface.

[0013] Optionally, in step S6, the formula for accumulating the temperature during multi-cycle braking is: ; in, ; For brake pads; For brake disc; The average volumetric temperature of the brake pad or brake disc after the nth braking action; The initial temperature; The heat distribution coefficient of the brake pad or brake disc; This represents the total frictional work performed during a single braking operation. For the quality of the brake pads or brake discs, Specific heat capacity of brake pad or brake disc material; This is the cooling time constant for the brake pad or brake disc; Cooling time after a single braking action; The convective heat transfer coefficient; This refers to the heat dissipation area of ​​the brake pad or brake disc.

[0014] Optionally, in step S6, convective heat dissipation is simulated using Newton's law of cooling: ; in, This refers to the surface temperature of the brake disc.

[0015] Compared with the prior art, the temperature rise analysis method for full-disc brakes provided by this invention has the following significant advantages: (1) Solved the model matching problem: For the first time, a steady-state temperature prediction model suitable for continuous annular heat sources was constructed, overcoming the fundamental defect that the traditional caliper brake heat source model does not match the heat source characteristics of the full disc brake, making the analysis results more in line with engineering practice.

[0016] (2) Improved computational efficiency and accuracy: By using the analytical method of variable separation, Fourier transform and Hankel transform, the complex two-dimensional partial differential equation is reduced to ordinary differential equation for solution. While ensuring scientific accuracy, the computational efficiency is significantly improved and the temperature prediction error is effectively reduced.

[0017] (3) Innovative coupling of key physical effects: By introducing a rotation effect correction term, the coupling effect of circumferential convection and radial heat conduction brought about by the rotation of the brake disc is quantified; the spatial distribution characteristics of the heat source are accurately described by the integral formula of the annular heat source, thereby comprehensively improving the accuracy of temperature field prediction under complex boundary conditions.

[0018] (4) It has both versatility and scalability: This analysis method is not only applicable to the thermal performance evaluation and optimization of various brake materials, but also guides the design and selection of key geometric parameters of brake discs (such as thickness and radius), and supports the extension to non-axisymmetric structures, providing an efficient and universal theoretical tool for the forward design and thermal safety evaluation of braking systems.

[0019] (5) Strong engineering applicability: By combining the analytical model verified by finite element method with the multi-cycle braking temperature accumulation model, it can quickly and accurately predict the steady-state and transient temperature rise characteristics under different working conditions, effectively guide engineering practice, and shorten the product development cycle. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort, wherein: Figure 1 A flowchart of a method for analyzing the temperature rise of a full-disc brake provided by the present invention; Figure 2 Finite element model diagram of the brake provided by this invention; Figure 3 Temperature distribution curve of the rotating disk provided for this invention; Figure 4 The friction plate temperature change curve provided by the present invention; Figure 5 The present invention provides a temperature change curve of the friction pad during a single braking cycle; Figure 6 The brake housing temperature curve provided for this invention; Figure 7 The temperature change curve of the outer casing during a single braking cycle is provided for this invention. Figure 8The convective heat transfer coefficient curve provided by this invention; Figure 9 The present invention provides temperature change curves of the friction plate under two working conditions; Figure 10 The present invention provides a temperature change curve of the friction pad during two braking cycles. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] The terms "first," "second," etc., used in the specification and claims of this invention are used to distinguish similar objects and not to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that embodiments of the invention can be implemented in orders other than those illustrated or described herein, and the objects distinguished by "first," "second," etc., are generally of the same class and the number of objects is not limited; for example, a first object can be one or more. Furthermore, in the specification and claims, "and / or" indicates at least one of the connected objects, and the character " / " generally indicates that the preceding and following objects are in an "or" relationship.

[0023] Please see Figure 1 As shown, this invention provides a method for analyzing the temperature rise of a full-disc brake. Its core lies in using a combination of analytical and finite element methods to efficiently and accurately predict the temperature field distribution of the full-disc brake during braking. Specifically, it includes the following steps: Step S1: Establish an axisymmetric analytical model and construct the governing equations. Based on a cylindrical coordinate system ( , , Based on the steady-state heat conduction theory under the condition of fully considering the circumferential convection effect caused by the rotation of the brake disc and the characteristics of the continuous annular heat source formed by the friction pair, the governing equations are constructed as follows: ; in, This is a correction term for the rotation effect; These are the radial coordinates in the cylindrical coordinate system. For temperature; For the axial coordinates in the cylindrical coordinate system; The angular velocity of the brake disc rotation; Thermal diffusivity; These are the circumferential coordinates in a cylindrical coordinate system. is the thermal conductivity of the material.

[0024] Step S2: Set boundary conditions, which include: 1. Convective heat transfer boundaries at the inner and outer cylindrical edges of the brake disc: ; 2. The middle surface of the brake disc ( The adiabatic boundary of ) ; 3. Brake disc friction surface ( The convection and heat flux coupling boundary: ; in, The convective heat transfer coefficient; Ambient temperature; This refers to the axial position of the brake disc's center surface.

[0025] Step S3: Solve the governing equations by dimensionality reduction using integral transform. Fourier transform is used to process the circumferential (…) ) coordinates, using Hankel transformation to process radial ( The coordinates transform the partial differential governing equations into those relating to the axial direction ( Ordinary differential equations for coordinates: ; in, This is the transformed temperature function; The heat source function after the Hankel transformation. These are the characteristic parameters in the Hankel transform; It is the imaginary unit.

[0026] Step S4: Process the annular heat source term. The heat flux density of the annular heat source is calculated from the braking dissipation power: ; in, This refers to the power dissipated during braking; The outer radius of the brake disc; The inner radius of the brake disc; Then, the heat source function in the transform domain is obtained through the Hankel transform: ; in, This is the heat source function after the Hankel transformation; These are the characteristic parameters in the Hankel transform; It is a first-order Bessel function.

[0027] Step S5: Solve for the temperature field in the transformed domain and perform an inverse transformation. Solve the ordinary differential equations to obtain the temperature distribution along the z-axis in the transformed domain: ; Finally, the three-dimensional temperature field distribution in physical space is reconstructed using the inverse Hankel transform: ; in, It is a zero-order Bessel function.

[0028] Step S6: Establish a finite element model for verification and transient analysis. A detailed three-dimensional model of the brake is established using commercial finite element software (such as ABAQUS or ANSYS) (as shown in Example 1). Figure 2 The four dry-plate brake models shown are configured. Material properties for each component are set (see Table 2), and a contact thermal resistance model is introduced between the friction contact pairs. To quantify the barrier to heat transfer at the interface, among which, For contact thermal resistance; This represents the temperature difference across the contact interface. To simulate continuous braking conditions, the volumetric average temperature after each braking cycle is calculated using a multi-cycle braking temperature accumulation formula: ; in, ; For brake pads; For brake disc; The average volumetric temperature of the brake pad or brake disc after the nth braking action; The initial temperature; The heat distribution coefficient of the brake pad or brake disc; This represents the total frictional work performed during a single braking operation. For the quality of the brake pads or brake discs, Specific heat capacity of brake pad or brake disc material; This is the cooling time constant for the brake pad or brake disc; Cooling time after a single braking action; The convective heat transfer coefficient; This refers to the heat dissipation area of ​​the brake pad or brake disc.

[0029] Meanwhile, surface convection cooling during braking is governed by Newton's law of cooling. A simulation was conducted, in which, The temperature is the surface temperature of the brake disc. Transient thermal analysis is used to obtain the temperature distribution, maximum temperature point, and cooling process of the brake under different operating conditions (such as high-frequency braking and emergency braking). The results are compared and verified with the analytical model results to correct model parameters and ensure prediction accuracy.

[0030] The following detailed description of the temperature rise analysis method for full-disc brakes provided by the present invention is based on a specific embodiment 1.

[0031] Example 1 This analysis takes a certain type of four-pair dry disc brake as an example. The initial temperature of the brake and the ambient temperature are set to 25°C. The parameters for high-frequency braking are shown in Table 1, and the material property parameters are shown in Table 2.

[0032] Table 1 Parameters for High-Frequency Braking Table 2 Material property parameters Analysis using the aforementioned method reveals that after 20 cycles of braking, the highest temperature, approximately 436°C, is located at the contact surface between the mating disc and the friction pad; the lowest temperature, approximately 168°C, is located at the inner edge of the contact area between the moving disc and the heat insulation plate. The overall temperature trend of the brake is from low to high from the upper surface of the stationary disc to the friction pad, and from high to low from the edge of the base to the upper surface of the support body, then to the rotating disc and finally the moving disc. This is because the friction pad and mating disc are constantly in a state of friction during braking, hence the highest temperature. The heat from the moving disc can only be transferred from the base upwards or from the outer teeth of the stationary disc to the outer shell, then from the outer shell through the rolling balls to the rotating disc, and finally from the rotating disc through the ball bearings to the moving disc. Due to the extremely low thermal conductivity of the heat insulation plate, very little heat is transferred from the heat insulation plate to the moving disc, thus the rotating disc has the lowest temperature.

[0033] Depend on Figure 3 It can be seen that after 20 cycles of cyclic braking, the highest temperature of the brake disc reached 159 degrees Celsius. This is because, within a single braking cycle of 81 seconds, the brake friction pads and mating pads only experience friction and heat flow for 3.3 seconds. For the remaining time, the brake is in an idling state, during which no heat is generated; heat is only dissipated through heat conduction to other components and convection with the air. Therefore, the highest temperature of the brake does not continue to rise. Figure 4 It can be seen that under cyclic braking conditions, the temperature of the brake friction pads rises in a sawtooth pattern. Figure 5 The figure shows the temperature change of the friction pad during one braking cycle. In the first 3.3 seconds, the brake friction pad generates a large amount of heat flow due to friction, and its temperature rises rapidly from 25 degrees to 180 degrees. During the subsequent idling time, since there is no friction, there is no heat flow input to the surface of the friction pad. Its heat is transferred to other areas through thermal conduction and dissipated into the air through thermal convection.

[0034] Depend on Figure 6It can be seen that the temperature of the brake housing gradually increases during braking and is always in the rising stage. This is because the temperature of the housing is mainly transferred through contact with the base and the outer teeth of the stationary disc. The reason why there is no falling stage is mainly because the heat input by heat conduction is greater than the heat lost by heat convection. Figure 7 The figure shows the temperature change curve of the outer casing during a single braking cycle. In the initial stage, there is a slight decreasing trend due to natural convection, but the overall temperature of the casing is still in an upward phase. The reason why the rate of temperature increase gradually slows down is that as the casing temperature rises, the temperature difference between it and the surrounding air gradually increases, and the temperature gradient with the contact surfaces gradually decreases. Therefore, the heat absorbed through heat conduction decreases while the heat dissipated through convection increases, hence the rate of temperature increase gradually slows down.

[0035] To investigate the impact of forced convection cooling on temperature distribution during brake braking, the relationship between forced convection and temperature change was simulated during brake idling. The brake does not have a dedicated air-cooled structure; the convective exchange with air mainly relies on the rotation of the friction plates driving the surrounding airflow. This is essentially the same as forced convection cooling, but obtaining the convective heat transfer coefficient is more complex and generally requires computational fluid dynamics analysis. Through CFD analysis, the convective heat transfer coefficient curves of the brake friction pairs under forced air cooling were obtained (e.g., ...). Figure 8 (As shown in the figure). This curve indicates that the convective heat transfer coefficient increases slightly with increasing friction pair temperature, but increases significantly with increasing air velocity, exhibiting a non-linear change. Based on the vehicle speed under high-frequency braking conditions, the flow field velocity driven by the brake disc can be obtained. An appropriate value is then selected based on the curve's variation. Forced convection cooling only reduces the numerical value of the temperature; it does not affect the distribution areas of the highest and lowest temperatures. The highest temperature remains on the contact surface between the mating plates and the friction plates, at approximately 157 degrees Celsius, while the lowest temperature is located at the inner edge of the contact surface between the moving disc and the heat shield, at approximately 92 degrees Celsius. After the brake is subjected to forced convection cooling, the temperature values ​​of each component drop significantly. The highest and lowest temperatures with and without forced convection cooling are shown in Table 3. Table 3 Temperature of various components of the brake Figure 9 , Figure 10The diagram shows the temperature change at the same node on the friction pads with and without forced convection. During braking, convective cooling has little impact on temperature because a large amount of heat is input during braking. Therefore, within the same braking cycle, the temperature change during the braking phase is almost equal for both conditions. Convective cooling mainly occurs during the brake idling phase, when there is no heat input. Therefore, under forced convection, the brake temperature drops significantly. The starting temperature of the next braking cycle is the ending temperature of the previous cycle's cooling. Thus, after continuous high-frequency braking, due to the forced convection generated by the rotation of the brake pads, the temperature will not rise significantly. The vehicle's own cooling boundary conditions can achieve a balance between brake energy input and heat dissipation.

[0036] This embodiment analyzes the temperature rise pattern of the brake power compartment under high-frequency braking and emergency braking conditions, and studies the effect of forced convection cooling on temperature distribution under high-frequency braking conditions, thus obtaining the temperature distribution of the brake.

[0037] High-frequency braking of vehicles leads to a stepwise increase in temperature, with the temperature rise increasing more pronounced at higher braking frequencies. The highest accumulated temperature rise reaches 430 degrees Celsius for the friction pair core plate, 436 degrees Celsius for the friction layer surface, and 380 degrees Celsius for the support structure. The airflow generated by the rotation of the brake disc promotes convective cooling, reducing the maximum accumulated temperature rise: approximately 64.4% for the friction pair core plate, approximately 63.8% for the friction layer surface, and approximately 63.7% for the support structure. Clearly, the friction pair core plate has the greatest impact.

[0038] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0039] Furthermore, it should be noted that the scope of the methods and systems in the embodiments of the present invention is not limited to performing functions in the order shown or discussed, but may also include performing functions substantially simultaneously or in the reverse order, depending on the functions involved. For example, the described methods may be performed in a different order than described, and various steps may be added, omitted, or combined. In addition, features described with reference to certain examples may be combined in other examples.

[0040] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of the present invention.

Claims

1. A method for analyzing the temperature rise of a full-disc brake, characterized in that, Includes the following steps: Step S1: Establish an axisymmetric analytical model. Based on the steady-state heat conduction equation in cylindrical coordinates, and combining the rotational effect with the continuous annular heat source distribution, construct the governing equations: The governing equation is: ； in, This is a correction term for the rotation effect; These are the radial coordinates in the cylindrical coordinate system; For temperature; For the axial coordinates in the cylindrical coordinate system; The angular velocity of the brake disc rotation; Thermal diffusivity; These are the circumferential coordinates in a cylindrical coordinate system. The thermal conductivity of the material; The heat flux density of a continuous annular heat source; Step S2: Set boundary conditions, including convection heat transfer at the inner and outer edges, insulation of the middle surface, and coupling of surface convection with the heat source; Step S3, Variable Separation and Hankel Transform: Variable separation and dimensionality reduction are performed using Fourier transform and Hankel transform to transform the governing equations into ordinary differential equations. Step S4: Process the annular heat source term, calculate the heat flux density of the annular heat source, and obtain the heat source term through Hankel transformation; Step S5: Solve for the temperature field by solving for the temperature distribution using the method of separation of variables and reconstructing the three-dimensional temperature field using the inverse Hankel transformation. Step S6: Establish a finite element model, set material properties and contact thermal resistance model, combine the multi-cycle braking temperature accumulation formula and Newton's law of cooling to simulate convection heat dissipation, and solve to obtain simulation results.

2. The method according to claim 1, characterized in that, In step S2, the boundary conditions include: ； in, The convective heat transfer coefficient; The ambient temperature; This refers to the axial position of the brake disc's center surface.

3. The method according to claim 1, characterized in that, In step S4, the heat flux density of the annular heat source Calculated using the following formula: ； in, This refers to the power dissipated during braking; The outer radius of the brake disc; The inner radius of the brake disc.

4. The method according to claim 3, characterized in that, In step S4, the heat source term is obtained through Hankel transformation: ； in, This is the heat source function after the Hankel transformation; These are the characteristic parameters in the Hankel transform; It is a first-order Bessel function.

5. The method according to claim 1, characterized in that, In step S5, the temperature distribution is calculated using the following formula: ； in, .

6. The method according to claim 1, characterized in that, In step S5, the three-dimensional temperature field is reconstructed through the inverse Hankel transformation: ； in, It is a zero-order Bessel function.

7. The method according to claim 1, characterized in that, In step S6, the contact thermal resistance model is: ； in, For contact thermal resistance; This represents the temperature difference between the two sides of the contact interface.

8. The method according to claim 1, characterized in that, In step S6, the formula for accumulating temperature during multi-cycle braking is: ； in, ; For brake pads; For brake disc; The average volumetric temperature of the brake pad or brake disc after the nth braking action; The initial temperature; The heat distribution coefficient of the brake pad or brake disc; This represents the total frictional work performed during a single braking operation. For the quality of the brake pads or brake discs, Specific heat capacity of brake pad or brake disc material; This is the cooling time constant for the brake pad or brake disc; Cooling time after a single braking action; The convective heat transfer coefficient; This refers to the heat dissipation area of ​​the brake pad or brake disc.

9. The method according to claim 1, characterized in that, In step S6, convective heat dissipation is simulated using Newton's law of cooling: ； in, This refers to the surface temperature of the brake disc.

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