Multi-friction source dynamics modeling method, system, computer device and storage medium

Abstract

This invention relates to the field of high-speed train braking systems, specifically to a multi-friction source dynamic modeling method, system, computer equipment, and storage medium. The modeling method includes the following steps: based on the wheel-rail-brake coupling effect, the exponential Stribeck friction model, and the uneven distribution of normal forces on each friction block, a multi-level dynamic model of the brake pads under normal operating conditions is constructed; for the typical failure mode of local friction block detachment, a friction block detachment dynamic model is constructed; the effectiveness of the constructed model is verified by comparing it with field test data; nonlinear dynamic simulation is used to analyze the dynamic responses at different levels under normal or abnormal operating conditions, revealing the evolution law of the system from periodic and stick-slip motion to chaotic motion. The embodiments of this invention can effectively reproduce the complex nonlinear behavior in the low-speed friction braking process, which is of great significance for guiding the design and maintenance of high-speed train brake pads.

Description

Technical Field

[0001] This invention relates to a method, system, computer equipment, and storage medium for multi-friction source dynamic modeling, and belongs to the field of high-speed train braking systems. Background Technology

[0002] In recent years, the rapid development of China's high-speed railway has significantly improved travel convenience and operational efficiency. As a core subsystem ensuring the safe operation of trains, friction braking in the braking system is prone to friction-induced stick-slip vibration (FISSV) under low-speed, high-friction conditions, leading to system instability, flutter, and noise, thereby threatening train safety and reducing passenger comfort.

[0003] Existing studies generally employ simplified models, treating brake pads as equivalent to a single mass block, neglecting the spatial distribution characteristics of multiple friction blocks and the triangular support structure. This makes it difficult to accurately characterize the nonlinear dynamic response under the coupled action of multiple friction sources. Furthermore, localized detachment of friction blocks, as a typical failure mode, significantly alters the system's coupling characteristics and load distribution, yet dynamic modeling studies specifically addressing this failure mode are currently lacking.

[0004] Therefore, there is an urgent need to construct a nonlinear dynamic model that can accurately characterize structural features and failure modes, so as to accurately evaluate the dynamic behavior of the system and support the optimal design of the braking system. Summary of the Invention

[0005] In view of this, the present invention provides a multi-friction source dynamic modeling method, system, computer equipment and storage medium, which can effectively reproduce the complex nonlinear behavior in the low-speed friction braking process, and is of great significance for guiding the design and maintenance of high-speed train brake pads.

[0006] The first objective of this invention is to provide a method for dynamic modeling of multiple friction sources.

[0007] The second objective of this invention is to provide a multi-friction source dynamic modeling system.

[0008] A third object of the present invention is to provide a computer device.

[0009] A fourth object of the present invention is to provide a storage medium.

[0010] The first objective of this invention can be achieved by adopting the following technical solution:

[0011] A multi-friction source dynamic modeling method includes: constructing a multi-level dynamic model of the brake pad under normal operating conditions, wherein the multi-level dynamic model includes a first dynamic model, a second dynamic model, and a third dynamic model, wherein: the first dynamic model uses a single friction block as the modeling unit, divides the brake pad into multiple independent friction blocks, and characterizes the torsional stiffness and damping between each friction block and its supporting triangular bracket, as well as the torsional stiffness and damping between each friction block; the second dynamic model uses the triangular bracket-friction block combination as the modeling unit, divides the brake pad into multiple combined units, and describes the torsional stiffness and damping between each combined unit and the steel backing plate, as well as the torsional stiffness and damping between adjacent combined units; the third dynamic model uses the left and right parts of the brake pad as the modeling unit, simplifies the brake pad into two equivalent friction units, and defines the torsional stiffness and damping between the brake pad and the caliper, as well as the torsional stiffness and damping between the left and right units; constructing a failure dynamic model under the condition of friction block detachment, wherein the failure dynamic model uses the remaining effective friction block as the modeling unit, re-establishes the system dynamic equations, thereby simulating the influence of local friction block detachment on the system vibration behavior.

[0012] The second objective of this invention can be achieved by adopting the following technical solution:

[0013] A multi-friction source dynamic modeling system includes: a first building unit for constructing a multi-level dynamic model of a brake pad under normal operating conditions. The multi-level dynamic model includes a first dynamic model, a second dynamic model, and a third dynamic model. The first dynamic model uses a single friction block as the modeling unit, dividing the brake pad into multiple independent friction blocks, and characterizing the torsional stiffness and damping between each friction block and its supporting triangular bracket, as well as the torsional stiffness and damping between the friction blocks. The second dynamic model uses a triangular bracket-friction block combination as the modeling unit, dividing the brake pad into multiple combined units. The torsional stiffness and damping between each combined unit and the steel backing plate, as well as the torsional stiffness and damping between adjacent combined units, are described. The third dynamic model uses the left and right parts of the brake pad as modeling units, simplifies the brake pad into two equivalent friction units, and defines the torsional stiffness and damping between the brake pad and the caliper, as well as the torsional stiffness and damping between the left and right units. The second building unit is used to build a failure dynamic model under the condition of friction block detachment. The failure dynamic model uses the remaining effective friction block as modeling unit and re-establishes the system dynamic equations to simulate the influence of local friction block detachment on the system vibration behavior.

[0014] The third objective of this invention can be achieved by adopting the following technical solution:

[0015] A computer device includes a processor and a memory for storing processor-executable programs, wherein when the processor executes the program stored in the memory, it implements the above-described multi-friction source dynamics modeling method.

[0016] The fourth objective of this invention can be achieved by adopting the following technical solution:

[0017] The storage medium stores a program that, when executed by a processor, implements the aforementioned multi-friction source dynamics modeling method.

[0018] The present invention has the following advantages over the prior art:

[0019] This invention proposes a multi-friction source dynamic modeling method for high-speed train brake pads supported by a triangular support and its application. It comprehensively considers the wheel-rail-brake coupling effect, the exponential Stribeck friction model, and the uneven distribution of the normal force of each friction block, and constructs a hierarchical dynamic model under normal working conditions and under the condition of friction block detachment. This method is of great significance for guiding the design and maintenance of basic braking devices for high-speed trains. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art 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 the structures shown in these drawings without creative effort.

[0021] Figure 1 This is a flowchart of a dynamic modeling method for multiple friction sources.

[0022] Figure 2 This is a simplified dynamic model diagram of a high-speed train wheelset braking system.

[0023] Figure 3 This is a hierarchical nonlinear dynamic model diagram of the basic braking system of a high-speed train under normal braking pad conditions.

[0024] Figure 4 This is a hierarchical nonlinear dynamic model diagram of the basic braking system of a high-speed train under the condition of brake pad detachment.

[0025] Figure 5 The images show the field test results and simulation results of the deceleration process of a trailer bogie for a Chinese high-speed train.

[0026] Figure 6 This paper presents a basic braking device dynamic model for solving the brake pads under normal conditions and the brake pads with friction block detachment, respectively, and obtains the nonlinear dynamic characteristic diagram of the brake pads.

[0027] Figure 7 To obtain the nonlinear dynamic characteristic diagram of the brake pad, we solve the basic braking device dynamic model separately for normal brake pad and friction block detached brake pad.

[0028] Figure 8 This is a structural diagram of a multi-friction source dynamic modeling system. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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 embodiments of the present invention, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0030] To achieve the above objectives, such as Figure 1 As shown, the technical solution of the present invention is as follows: A multi-friction source dynamic modeling method for high-speed train brake pads supported by a triangular support, comprising the following steps:

[0031] S101, based on the wheel-rail-braking coupling effect, the exponential Stribeck friction model, and the uneven distribution of normal forces in each friction block (e.g. Figure 2 As shown, a multi-level dynamic model of the brake pads under normal operating conditions is constructed.

[0032] In this embodiment, according to Figure 2 The demonstration showcased a disc braking system for a Chinese high-speed train, equipped with three macroscopic braking units. It primarily consists of brake calipers, brake pads, and brake discs assembled onto the wheelsets via the axles.

[0033] It should be noted that the following assumptions were made before establishing the dynamic model of the braking system: (1) Since the mass of the brake caliper itself is ignored, the dynamic equation only considers the mass of the brake pad structure itself. (2) All friction blocks are identical, and the braking units rub with the same friction performance. (3) The rigid connection between friction blocks, the rigid connection between triangular supports, and the rigid connection between the left and right ends of the brake pads are replaced by equivalent stiffness and damping. And all stiffness and damping values ​​involved in the model are constants. (4) Friction blocks under the same radius rotate synchronously and have the same smoothing parameters and attenuation factors. (5) Since the vertical motion of the friction blocks is ignored, the normal force applied to the friction blocks is a constant value. (6) Since the vertical motion of the friction blocks is ignored, the normal force applied to the friction blocks is a constant value. (7) Since the influence of the shape of the friction blocks is ignored, the braking radius is taken as the straight-line distance from the center of the braking surface shape of the friction block to the braking center.

[0034] Figure 2 middle, k w and c w These are the torsional stiffness and damping between the brake disc and the wheelset, respectively. F n This represents the normal force applied to the friction block. F f This represents the frictional force generated between the disk and block contact interface. T f This represents the frictional torque acting on the brake pads. T w This represents the frictional torque acting on the wheelset. x This represents the tangential displacement of the brake pads. θ 1 and θ 2. The fluctuation of the torsional angular displacement of the brake disc and wheelset respectively. J d The moment of inertia of a single brake disc. J w This represents the moment of inertia of the wheelset; the moment of inertia of all brake discs mounted on a wheelset is 3. J d . x This represents the tangential displacement of the brake pads.

[0035] Equation 1 gives the relationship between the friction coefficient and relative velocity in the Stribeck model, and its expression is:

[0036] (1)

[0037] In the formula, v r This indicates the relative speed between the brake disc and the brake pads; μ k and μ s These are the coefficients of dynamic friction and static friction, respectively. α The negative slope of the exponential decay factor, which controls the degree of decay; β For smoothing parameters.

[0038] ω , ω 0 represents the instantaneous angular velocity and the average angular velocity of the brake disc, respectively. r Defined as the friction radius, it represents the distance between the geometric center of the brake pad and the rotational center of the friction disc. Then, the disc-pad relative velocity... v r Written as:

[0039] (2)

[0040] F n This represents the normal force applied to the brake pads. Based on this, frictional force... F f and frictional torque T f They are respectively recorded as:

[0041] (3)

[0042] (4)

[0043] During high-speed train operation, the wheel-rail contact interface undergoes slight elastic deformation under the action of normal contact force and tangential creep force, resulting in relative movement between the wheel and rail. This phenomenon is described as creep or wheel-rail adhesion, and the resulting adhesion torque directly affects the traction and braking performance of high-speed trains. When adhesion occurs, the wheel-rail relative velocity (also known as slip velocity) is defined as:

[0044] (5)

[0045] In the formula, V and V 0 represents the instantaneous speed and average speed of the high-speed train, respectively; ω w and ω 0 These are the instantaneous angular velocity and the average angular velocity of the wheel, respectively. R Let be the radius of the wheel. R 0 represents the nominal rolling radius of the wheel.

[0046] Ignoring changes in longitudinal velocity and wheel radius, consider Vx = 0, R1 =0, the slip ratio can be expressed as:

[0047] (6)

[0048] when θ When 2=, the average slip ratio of the wheelset can be defined as:

[0049] (7)

[0050] This embodiment explores the global stability of the system by linearizing the dynamic equations and calculating the bifurcation diagram. Therefore, a wheel-rail adhesion model, which is easy to linearize and reduces computation time, is adopted. At low slip rates, the adhesion coefficient... μ The slope increases with increasing slip ratio, and it is a curve with a positive slope. OA This indicates the adhesive state. Then, when the slip ratio exceeds a critical value, the adhesion coefficient... μ A descending curve with a negative slope. AB This represents the slip state. Therefore, the wheel-rail adhesion coefficient can be represented by a piecewise function:

[0051] (8)

[0052] In the formula, s m The critical slip ratio; μ m The maximum adhesion coefficient corresponding to the critical slip ratio. k μ The negative slope represents the slip state. W This represents the axle load of the high-speed train. Considering that this model does not include the train's vertical motion, the wheel-rail normal contact force... P It has the same value as the axle load. Therefore, the instantaneous adhesion force applied to the wheelset T g It can be described as follows:

[0053] (9)

[0054] Substituting formula (8) into formula (9), we obtain the piecewise function of the instantaneous wheel-rail adhesion torque:

[0055] (10)

[0056] T g From static adhesion torque T g0 and dynamic adhesion torque T w Composition. Substituting the average slip ratio into the formula, the static adhesion torque can be obtained:

[0057] (11)

[0058] According to the formula, the dynamic adhesion torque can be obtained. T w .when s 0 ≤ s m When the wheelset is in an adhesive state, the dynamic adhesive torque is denoted as:

[0059] (12)

[0060] in ω m Defined as:

[0061] (13)

[0062] Similarly, when s 0 > s m When the wheelset is in an adhesive state, the dynamic adhesive torque is denoted as:

[0063] (14)

[0064] Figure 3 (a) A simplified dynamic model of the brake pad at a macroscopic scale is shown. In this view, the entire brake pad is abstracted into two equivalent friction elements, named […]. G -1 and G -2. In the model, k pr and c pr These represent the equivalent torsional stiffness and equivalent torsional damping between the brake pads and the caliper structure, respectively. k p and c p This characterizes the internal torsional stiffness and torsional damping between the left and right parts of the brake pad.

[0065] Figure 3 (b) A more detailed decomposition of the brake pad structure was performed, showcasing a mesoscopic dynamic model. In this model, the original left and right sections were further divided into six independent triangular support-friction block elements (triangular support elements), numbered from... A -1 to A -6 (three on each side). Model parameters k ar and c arThis parameter describes the torsional stiffness and damping characteristics of the connection between each triangular support unit and the steel back plate. k a and c a The torsional coupling stiffness and damping between adjacent triangular support-friction block elements are then defined.

[0066] exist Figure 3 In (c), this model further decomposes each triangular bearing-friction block unit into three independent friction blocks, thus the entire brake pad contains a total of 18 basic friction units, numbered from... B -1 to B -18. At this level... k mr and c mr These represent the torsional stiffness and torsional damping between a single friction block and its supporting triangular bracket, respectively. k m and c m This describes the mutual torsional stiffness and torsional damping between the individual friction blocks.

[0067] S1011. A dynamic model established using a single friction block as the basic unit. This model refines the friction unit into 18 independent friction blocks (B-1 to B-18) and characterizes the torsional stiffness between a single friction block and its supporting triangular bracket. k mr ) and damping ( c mr ), and the mutual torsional stiffness between each independent friction block ( k m ) and damping ( c m ).

[0068] According to Newton's second law, the basic dynamic equations of a braking device with friction blocks as friction units can be constructed. In this work, these dynamic equations are listed independently for each friction block. The dynamic equations B-1 to B-18 can be written in the following forms:

[0069] (15a)

[0070] (15b)

[0071] (15c)

[0072] (15d)

[0073] (15e)

[0074] (15f)

[0075] (15g)

[0076] (15h)

[0077] (15i)

[0078] (15j)

[0079] (15k)

[0080] (15l)

[0081] (15m)

[0082] (15n)

[0083] (15o)

[0084] (15p)

[0085] (15q)

[0086] (15r)

[0087] In the above formula, friction force F f It can be represented as:

[0088] (16)

[0089] The mass of the friction block is expressed as:

[0090] (17)

[0091] In order to reduce the order of the dynamic equations of formula (15a)-(15r), the following assumptions were made:

[0092] (18)

[0093] Therefore, the dynamic equations for B-1 to B-9 can be written as the following space state equations:

[0094] (19a)

[0095] (19b)

[0096] (19c)

[0097] (19d)

[0098] (19e)

[0099] (19f)

[0100] (19g)

[0101] (19h)

[0102] (19i)

[0103] Therefore, the dynamic equations for B-10 to B-18 can be written as the following space state equations:

[0104] (20a)

[0105] (20b)

[0106] (20c)

[0107] (20d)

[0108] (20e)

[0109] (20f)

[0110] (20g)

[0111] (20h)

[0112] (20i)

[0113] The normal braking force applied to each friction block from B-1 to B-18 is as follows: F n1 , F n2 , F n3 , F n4 , F n5 ,F n6 , F n7 , F n8 , F n9 , F n10 , F n11 , F n12 , F n13 , F n14 , F n15 , F n16 , F n17 , F n18 .

[0114] S1012. A dynamic model established using the "triangular support-friction block" as the basic unit. This model decomposes the brake pad into six independent "triangular support-friction block" units (A-1 to A-6) and describes the torsional stiffness of each unit's connection to the steel backing plate. k ar ) and damping ( c ar ), and the torsional coupling stiffness between adjacent units ( k a ) and damping ( c a ).

[0115] According to Newton's second law, the dynamic equations of a basic braking device with the triangular support as the friction unit can be constructed. In this work, these dynamic equations are listed independently for each triangular support. The dynamic equations A-1 to A-6 can be written in the following forms:

[0116] (21a)

[0117] (21b)

[0118] (21c)

[0119] (21d)

[0120] (21e)

[0121] (21f)

[0122] In the above formula, friction force F fA It can be represented as:

[0123] (twenty two)

[0124] in, m a1 - m a6 It can be represented as:

[0125] (twenty three)

[0126] In order to reduce the order of the dynamic equations of formulas (21a)-(21f), the following assumptions were made:

[0127] (twenty four)

[0128] Therefore, the dynamic equations for A-1 to A-6 can be written as the following spatial state equations:

[0129] (25a)

[0130] (25b)

[0131] (25c)

[0132] (25d)

[0133] (25e)

[0134] (25f)

[0135] S1013. A dynamic model established using the left and right parts of the brake pad as basic units. This model simplifies the entire brake pad into two equivalent friction elements (G-1 and G-2), and defines the equivalent torsional stiffness between the brake pad and the caliper structure. k gr ) and damping ( c gr ), and the internal torsional stiffness between the left and right units of the brake pad ( k p ) and damping ( c p ).

[0136] Based on Newton's second law, a basic dynamic equation for a braking device can be constructed, using the left and right ends of the brake pads as friction units. In this work, these dynamic equations are listed independently for each end. The dynamic equations for G-1 and G-2 can be written as follows:

[0137] (26a)

[0138] (26b)

[0139] In the above formula, friction force F fG It can be represented as:

[0140] (27)

[0141] in, m G1 , m G2 It can be represented as:

[0142] (28)

[0143] In order to reduce the order of the dynamic equations in formulas (26a) and (26b), the following assumptions were made:

[0144] (29)

[0145] Therefore, the dynamic equations of G-1 and G-2 can be written as the following space state equations:

[0146] (30a)

[0147] (30b)

[0148] According to Newton's second law, the basic dynamic equations of a braking device with the brake pads as the friction unit can be constructed. In this work, these dynamic equations are listed in the form of brake pads independent of each other. The dynamic equation of P-1 can be written as:

[0149] (31)

[0150] In the above formula, friction force F fP1 It can be represented as:

[0151] (32)

[0152] in, m P1 It can be represented as:

[0153] (33)

[0154] In order to reduce the order of the dynamic equation of formula (31), the following assumptions were made:

[0155] (34)

[0156] Therefore, the dynamic equation of P-1 can be written as the following spatial state equation:

[0157] (35)

[0158] like Figure 3 According to Newton's second law, the dynamic equations of the brake disc and wheelset can be written as:

[0159] (36)

[0160] (37)

[0161] Among them, frictional torque T fp It can be represented as:

[0162] (38)

[0163] In order to reduce the order of the dynamic equations of formulas (36) and (37), the following assumptions were made:

[0164] (39)

[0165] Therefore, the dynamic equations can be written as the following spatial state equations:

[0166] (40)

[0167] (41)

[0168] S102. For the typical failure mode of local detachment of friction block, construct a dynamic model of brake pad with detached friction block.

[0169] Under low train operating speeds and strong friction at the braking interface, brake pad friction blocks are prone to detachment. To address the nonlinear dynamics problem of the basic braking device arising from this phenomenon, this paper assumes that a triangular support on the brake pad has completely detached, and constructs a hierarchical nonlinear dynamic analysis model of the basic braking device considering friction block detachment, based on the aforementioned modeling approach. Figure 4As shown, this model, through a progressively refined approach, demonstrates the dynamic units and their interconnections of the brake pads at various scales, from the overall system to the local level.

[0170] Figure 4 This paper presents a refined dynamic model of a high-speed train's basic brake pad under conditions of partial detachment of specific friction blocks (specifically, the A-1 triangular support unit and its constituent B-1, B-2, and B-3 friction blocks, resulting in functional loss). The model is constructed using the remaining independent friction blocks in the system that still possess frictional function as the basic dynamic units. This figure aims to provide a deeper understanding and quantitative analysis of brake pads under non-ideal conditions involving the detachment of friction blocks in specific areas (such as…). Figure 4 (a) The brake pads are partially missing in the upper left corner area (but the material properties are not changed), which provides a key theoretical framework for understanding the overall dynamic behavior, the redistribution of internal loads, and the possible abnormal vibration characteristics. Figure 4 (b) specifically demonstrates the dynamic connection between the remaining effective friction blocks in the system (B-4 to B-18 in this model) under this specific friction block detachment state, as well as their complex interactions with their respective load-bearing structures (such as triangular supports) and with external constraints (such as brake calipers) through higher-level structures (such as steel backing).

[0171] After the brake pad friction blocks detach, the normal braking forces applied to each friction block are as follows: F nd1 , F nd2 , F nd3 , F nd4 , F nd5 , F nd6 , F nd7 , F nd8 , F nd9 , F nd10 , F nd11 , F nd12 , F nd13 , F nd14 , F nd15 , F nd16 , F nd17 , F nd18 .

[0172] According to Newton's second law, the basic dynamic equations of the braking device, which uses friction blocks as friction units, after the brake pads have disengaged, can be constructed. In this work, these dynamic equations are listed independently for each friction block. The dynamic equations B-1 to B-18 can be written in the following forms:

[0173] (42a)

[0174] (42b)

[0175] (42c)

[0176] (42d)

[0177] (42e)

[0178] (42f)

[0179] (42g)

[0180] (42h)

[0181] (42i)

[0182] (42j)

[0183] (42k)

[0184] (42l)

[0185] (42m)

[0186] (42n)

[0187] (42o)

[0188] Among them, friction F f It can be represented as:

[0189] (43)

[0190] in:

[0191] (44)

[0192] In order to reduce the order of the dynamic equations of formulas (44a)-(44o), the following assumptions were made:

[0193] (45)

[0194] Therefore, the dynamic equations of B-4 to B-9 can be written as the following space state equations:

[0195] (46a)

[0196] (46b)

[0197] (46c)

[0198] (46d)

[0199] (46e)

[0200] (46f)

[0201] (46g)

[0202] (46h)

[0203] (46i)

[0204] Therefore, the dynamic equations for B-10 to B-18 can be written as the following space state equations:

[0205] (47a)

[0206] (47b)

[0207] (47c)

[0208] (47d)

[0209] (47e)

[0210] (47f)

[0211] (47g)

[0212] (47h)

[0213] (47i)

[0214] According to Newton's second law, the basic dynamic equations of the braking device, specifically the brake pad after the friction block detaches (using the triangular support as the friction unit), can be constructed. In this work, these dynamic equations are presented independently for each triangular support. The dynamic equations A-2 to A-6 can be written in the following forms:

[0215] (48a)

[0216] (48b)

[0217] (48c)

[0218] (48d)

[0219] (48e)

[0220] In the above formula, friction force F fAd It can be represented as:

[0221] (49)

[0222] in, m a1 - m a6 It can be represented as:

[0223] (50)

[0224] In order to reduce the order of the dynamic equations (48a)-(48e), the following assumptions were made:

[0225] (51)

[0226] Therefore, the dynamic equations for A-2 to A-6 can be written as the following space state equations:

[0227] (52a)

[0228] (52b)

[0229] (52c)

[0230] (52d)

[0231] (52e)

[0232] (52f)

[0233] Based on Newton's second law, a basic dynamic equation for a braking device can be constructed, taking the left and right ends of the brake pad after the friction block has disengaged as friction units. In this work, these dynamic equations are listed independently for each end. The dynamic equations for G-1 and G-2 can be written as:

[0234] (53a)

[0235] (53b)

[0236] In the above formula, friction force F fG It can be represented as:

[0237] (54)

[0238] in, m G1 , m G2 It can be represented as:

[0239] (55)

[0240] In order to reduce the order of the dynamic equations of formulas (53a) and (53b), the following assumptions were made:

[0241] (56)

[0242] Therefore, the dynamic equations of G-1 and G-2 can be written as the following space state equations:

[0243] (57a)

[0244] (57b)

[0245] According to Newton's second law, the basic dynamic equations of a braking device can be constructed, with the brake pads after the friction block has disengaged as the friction unit. In this work, these dynamic equations are presented in the form of the brake pads after the friction block has disengaged, acting independently. The dynamic equation for P-1 can be written as:

[0246] (58)

[0247] In the above formula, friction force F fdP1 It can be represented as:

[0248] (59)

[0249] in, m P1 It can be represented as:

[0250] (60)

[0251] In order to reduce the order of the dynamic equation of formula (58), the following assumptions were made:

[0252] (61)

[0253] Therefore, the dynamic equation of P-1 can be written as the following spatial state equation:

[0254] (62)

[0255] like Figure 3 According to Newton's second law, the dynamic equations of the brake disc and wheelset can be written as:

[0256] (63)

[0257] (64)

[0258] Among them, frictional torque T fp It can be represented as:

[0259] (65)

[0260] In order to reduce the order of the dynamic equations of formulas (63) and (64), the following assumptions were made:

[0261] (66)

[0262] Therefore, the dynamic equations can be written as the following spatial state equations:

[0263] (67)

[0264] (68)

[0265] S103. Verify the effectiveness of the established model by comparing it with field test data.

[0266] like Figure 5(a) An acceleration sensor installed on the end of the rotating frame is used to acquire acceleration signals to monitor the vibration transmitted from the braking unit during braking. Comparative analysis of the experimental and simulation results shows that the vibration acceleration at the experimental monitoring location and the simulated brake pad vibration velocity exhibit similar evolution patterns. This indicates that the established nonlinear dynamic model of the basic braking device can well simulate the frictional self-excited vibration characteristics generated during the train's friction braking process.

[0267] S104. Using nonlinear dynamic simulation, the dynamic response at different levels under normal and friction block detachment conditions is analyzed to reveal the evolution law of the system from periodic and stick-slip motion to chaotic motion.

[0268] Figure 6 The diagram shows and compares the brake pads of a high-speed train in their normal state (a) and in the state after partial detachment of the friction blocks (b), defining their left and right ends as follows: Figure 3 (a) The relative speeds between macroscopic friction units G-1 and G-2 and the brake disc. v r and related dynamic characteristics.

[0269] according to Figure 7 As shown in the bifurcation diagrams (a) and (b), for both normal and brake pads with detached friction blocks, the chaotic vibration region of the system mainly occurs in the lower speed range. With increasing ω, the tangential motion of the brake pad transitions from complex chaotic vibration to stable periodic vibration. However, compared to normal brake pads, the chaotic band of brake pads with partially detached friction blocks is more pronounced. v r The dispersion width on the shaft is significantly reduced. This indicates that due to the absence of some friction sources, the instantaneous amplitude at low speeds is suppressed, and the vibration state moves more rapidly towards periodic motion. Furthermore, regarding... Figure 7 (a) and Figure 7 (b) Relative speed between the brake pads and the brake disc v r Perform statistical analysis, Figure 7 (c) The relative velocity of the brake pads whose middle friction blocks have detached. v r The median and IQR of the brake pads are both lower than those of normal brake pads. This is consistent with the phenomenon observed in the bifurcation diagram, that is, the vibration behavior of the brake pads is more stable after the friction block falls off.

[0270] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware, and the corresponding program can be stored in a computer-readable storage medium.

[0271] It should be noted that although the method operations of the above embodiments are described in a specific order in the accompanying drawings, this does not require or imply that these operations must be performed in that specific order, or that all the operations shown must be performed to achieve the desired result. On the contrary, the order of execution of the described steps may be changed. Additionally or alternatively, certain steps may be omitted, multiple steps may be combined into one step, and / or one step may be broken down into multiple steps.

[0272] Figure 8 This is a structural diagram of a multi-friction source dynamic modeling system. (Example:) Figure 8 As shown, the multi-friction source dynamics modeling system includes:

[0273] The first building unit 801 is used to build a multi-level dynamic model of the brake pad under normal operating conditions. The multi-level dynamic model includes a first dynamic model, a second dynamic model, and a third dynamic model. The first dynamic model uses a single friction block as the modeling unit, divides the brake pad into multiple independent friction blocks, and characterizes the torsional stiffness and damping between each friction block and its supporting triangular bracket, as well as the torsional stiffness and damping between each friction block. The second dynamic model uses the triangular bracket-friction block combination as the modeling unit, divides the brake pad into multiple combined units, and describes the torsional stiffness and damping between each combined unit and the steel backing plate, as well as the torsional stiffness and damping between adjacent combined units. The third dynamic model uses the left and right parts of the brake pad as the modeling unit, simplifies the brake pad into two equivalent friction units, and defines the torsional stiffness and damping between the brake pad and the caliper, as well as the torsional stiffness and damping between the left and right units.

[0274] The second building unit 802 is used to build a failure dynamics model under the condition of friction block detachment. The failure dynamics model uses the remaining effective friction block as the modeling unit to re-establish the system dynamics equations, thereby simulating the influence of local friction block detachment on the vibration behavior of the system.

[0275] The verification unit 803 is used to verify the effectiveness of the established model by comparing it with field test data.

[0276] The simulation analysis unit 804 is used to analyze the dynamic response at different levels under normal and friction block detachment conditions using nonlinear dynamic simulation, revealing the evolution law of the system from periodic and stick-slip motion to chaotic motion.

[0277] This embodiment provides a computer device, including a processor, a memory, an input device, a display device, and a network interface connected via a system bus. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. When the computer program is executed by the processor, it implements the multi-friction source dynamics modeling method of the above embodiment, including the following steps:

[0278] Step 1: Based on the wheel-rail-brake coupling effect, the exponential Stribeck friction model, and the uneven distribution of normal forces in each friction block, a multi-level dynamic model of the brake pads under normal operating conditions is constructed:

[0279] Step 11: A dynamic model is established using a single friction block as the basic unit. This model refines the friction unit into 18 independent friction blocks (B-1 to B-18) and characterizes the torsional stiffness between a single friction block and its supporting triangular bracket. k mr ) and damping ( c mr ), and the mutual torsional stiffness between each independent friction block ( k m ) and damping ( c m );

[0280] Step 12: A dynamic model is established using the "triangular support-friction block" as the basic unit. This model decomposes the brake pad into six independent "triangular support-friction block" units (A-1 to A-6) and describes the torsional stiffness of each unit's connection to the steel backing plate. k ar ) and damping ( c ar ), and the torsional coupling stiffness between adjacent units ( k a ) and damping ( c a );

[0281] Step 13: Establish a dynamic model using the left and right parts of the brake pad as basic units. This model simplifies the entire brake pad into two equivalent friction elements (G-1 and G-2), and defines the equivalent torsional stiffness between the brake pad and the caliper structure. k gr ) and damping ( c gr ), and the internal torsional stiffness between the left and right units of the brake pad ( k p ) and damping ( cp ).

[0282] Step 2: For the typical failure mode of local detachment of friction blocks, construct a dynamic model of brake pads with detached friction blocks.

[0283] Step 3: Verify the effectiveness of the established model by comparing it with field test data.

[0284] Step 4: Using nonlinear dynamic simulation, analyze the dynamic response at different levels under normal and friction block detachment conditions, and reveal the evolution law of the system from periodic and stick-slip motion to chaotic motion.

[0285] In some embodiments, the friction block detachment dynamic model in step 2 establishes new dynamic equations by removing the friction source of the detached friction block, adjusting the system coupling and load distribution.

[0286] In some embodiments, the verification in step 3 is achieved by comparing the simulation results under emergency braking conditions with the test data of the line to confirm the accuracy of the model.

[0287] In some embodiments, the nonlinear dynamic simulation in step 4 uses bifurcation diagrams, phase plane diagrams, and statistical box plots to analyze the influence of friction radius and triangular support arrangement on vibration stability and intensity.

[0288] This embodiment provides a storage medium, which is a computer-readable storage medium, storing a computer program. When the computer program is executed by a processor, it implements the multi-friction source dynamics modeling method of the above embodiment, including the following steps:

[0289] Step 1: Based on the wheel-rail-brake coupling effect, the exponential Stribeck friction model, and the uneven distribution of normal forces in each friction block, a multi-level dynamic model of the brake pads under normal operating conditions is constructed:

[0290] Step 11: A dynamic model is established using a single friction block as the basic unit. This model refines the friction unit into 18 independent friction blocks (B-1 to B-18) and characterizes the torsional stiffness between a single friction block and its supporting triangular bracket. k mr ) and damping ( c mr ), and the mutual torsional stiffness between each independent friction block ( k m ) and damping ( c m );

[0291] Step 12: A dynamic model is established using the "triangular support-friction block" as the basic unit. This model decomposes the brake pad into six independent "triangular support-friction block" units (A-1 to A-6) and describes the torsional stiffness of each unit's connection to the steel backing plate. k ar ) and damping ( c ar ), and the torsional coupling stiffness between adjacent units ( k a ) and damping ( c a );

[0292] Step 13: Establish a dynamic model using the left and right parts of the brake pad as basic units. This model simplifies the entire brake pad into two equivalent friction elements (G-1 and G-2), and defines the equivalent torsional stiffness between the brake pad and the caliper structure. k gr ) and damping ( c gr ), and the internal torsional stiffness between the left and right units of the brake pad ( k p ) and damping ( c p ).

[0293] Step 2: For the typical failure mode of local detachment of friction blocks, construct a dynamic model of brake pads with detached friction blocks.

[0294] Step 3: Verify the effectiveness of the established model by comparing it with field test data.

[0295] Step 4: Using nonlinear dynamic simulation, analyze the dynamic response at different levels under normal and friction block detachment conditions, and reveal the evolution law of the system from periodic and stick-slip motion to chaotic motion.

[0296] In some embodiments, the friction block detachment dynamic model in step 2 establishes new dynamic equations by removing the friction source of the detached friction block, adjusting the system coupling and load distribution.

[0297] In some embodiments, the verification in step 3 is achieved by comparing the simulation results under emergency braking conditions with the test data of the line to confirm the accuracy of the model.

[0298] In some embodiments, the nonlinear dynamic simulation in step 4 uses bifurcation diagrams, phase plane diagrams, and statistical box plots to analyze the influence of friction radius and triangular support arrangement on vibration stability and intensity.

[0299] It should be noted that the computer-readable storage medium in this embodiment can be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof.

[0300] In this embodiment, the computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in connection with an instruction execution system, apparatus, or device. In this embodiment, the computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, carrying a computer-readable program. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. The computer-readable signal medium can also be any computer-readable storage medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The computer program contained on the computer-readable storage medium can be transmitted using any suitable medium, including but not limited to: wires, optical cables, RF (radio frequency), etc., or any suitable combination thereof.

[0301] The computer-readable storage medium described above can be used to write computer programs for executing this embodiment in one or more programming languages ​​or combinations thereof. These programming languages ​​include object-oriented programming languages—such as Java, Python, and C++—and conventional procedural programming languages—such as C or similar programming languages. The program can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0302] In summary, this invention proposes a multi-friction source dynamic modeling method for high-speed train brake pads with triangular support and its application. It comprehensively considers the wheel-rail-brake coupling effect, the exponential Stribeck friction model, and the uneven distribution of normal forces of each friction block, and constructs a hierarchical dynamic model under normal working conditions and friction block detachment conditions. This method is of great significance for guiding the design and maintenance of basic braking devices for high-speed trains.

[0303] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope disclosed in the present invention, based on the technical solution and inventive concept of the present invention, shall fall within the scope of protection of the present invention.

Claims

1. A method of multi-friction source dynamics modeling, characterized by, include: A multi-level dynamic model of the brake pads under normal operating conditions is constructed. This multi-level dynamic model includes a first dynamic model, a second dynamic model, and a third dynamic model, wherein: The third dynamic model is a macroscopic dynamic model that abstracts the brake pad into two equivalent friction units, left and right, and defines the torsional stiffness and damping between the brake pad and the caliper structure, as well as the torsional stiffness and damping between the left and right parts of the brake pad. The second dynamic model is a mesoscopic dynamic model, which divides the brake pad into six independent triangular support-friction block units, three on the left and three on the right. It defines the torsional stiffness and damping between each triangular support-friction block unit and the steel backing plate, as well as the torsional stiffness and damping between adjacent triangular support-friction block units. The first dynamic model uses a single friction block as the modeling unit, further dividing each triangular support-friction block unit into three independent friction blocks, and characterizing the torsional stiffness and damping between each friction block and its supporting triangular support, as well as the torsional stiffness and damping between each friction block. A failure dynamics model is constructed under the condition of friction block detachment. The failure dynamics model uses the remaining effective friction block as the modeling unit and re-establishes the system dynamics equations to simulate the influence of local friction block detachment on the vibration behavior of the system. The multi-level dynamic model is constructed based on the wheel-rail-braking coupling effect, the exponential Stribeck friction model, and the non-uniform distribution of the normal force of each friction block. Ignoring variations in longitudinal velocity and wheel radius, a wheel-rail adhesion model is adopted, which is based on a piecewise functional relationship between slip ratio and adhesion coefficient, as shown in the following equation: ； in, μ Coefficient of adhesion ，s slip ratio ，s m The critical slip ratio, μ m The maximum adhesion coefficient corresponding to the critical slip ratio. k μ The negative slope represents the slip state.

2. The multi-friction source dynamic modeling method according to claim 1, characterized in that, In the exponential Stribeck friction model, the relationship between the friction coefficient and the relative velocity is as follows: ； in, v r This indicates the relative speed between the brake disc and the brake pads. μ k and μ s These are the coefficients of dynamic friction and static friction, respectively. α To control the negative slope of the exponential decay factor, β For smoothing parameters.

3. The multi-friction source dynamic modeling method according to any one of claims 1-2, characterized in that, The brake pad is a high-speed train brake pad supported by a triangular support. The brake pad is divided into six independent triangular support-friction block units, three on each side; each triangular support-friction block unit is further subdivided into three independent friction blocks.

4. The multi-friction source dynamic modeling method according to any one of claims 1-2, characterized in that, In the failure dynamics model, the detached area is regarded as a functional loss unit, and its mass, stiffness and damping parameters are set to zero. The coupling relationship between the remaining friction blocks and their connection relationship with the triangular bracket and the steel back plate are reconstructed.

5. The multi-friction source dynamic modeling method according to any one of claims 1-2, characterized in that, Also includes: The effectiveness of the established model was verified by comparing it with field test data; Nonlinear dynamic simulation was used to analyze the dynamic response at different levels under normal and friction block detachment conditions, revealing the evolution law of the system from periodic and stick-slip motion to chaotic motion.

6. A multi-friction source dynamics modeling system, characterized in that, include: The first construction unit is used to construct a multi-level dynamic model of the brake pads under normal operating conditions. The multi-level dynamic model includes a first dynamic model, a second dynamic model, and a third dynamic model, wherein: The third dynamic model is a macroscopic dynamic model that abstracts the brake pad into two equivalent friction units, left and right, and defines the torsional stiffness and damping between the brake pad and the caliper structure, as well as the torsional stiffness and damping between the left and right parts of the brake pad. The second dynamic model is a mesoscopic dynamic model, which divides the brake pad into six independent triangular support-friction block units, three on the left and three on the right. It defines the torsional stiffness and damping between each triangular support-friction block unit and the steel backing plate, as well as the torsional stiffness and damping between adjacent triangular support-friction block units. The first dynamic model uses a single friction block as the modeling unit, further dividing each triangular support-friction block unit into three independent friction blocks, and characterizing the torsional stiffness and damping between each friction block and its supporting triangular support, as well as the torsional stiffness and damping between each friction block. The second building unit is used to build a failure dynamics model under the condition of friction block detachment. The failure dynamics model uses the remaining effective friction block as the modeling unit to re-establish the system dynamics equations, thereby simulating the impact of local friction block detachment on the vibration behavior of the system. The multi-level dynamic model is constructed based on the wheel-rail-braking coupling effect, the exponential Stribeck friction model, and the non-uniform distribution of the normal force of each friction block. Ignoring variations in longitudinal velocity and wheel radius, a wheel-rail adhesion model is adopted, which is based on a piecewise functional relationship between slip ratio and adhesion coefficient, as shown in the following equation: ； in, μ Coefficient of adhesion ，s slip ratio ，s m The critical slip ratio, μ m The maximum adhesion coefficient corresponding to the critical slip ratio. k μ The negative slope represents the slip state.

7. A computer device, comprising a processor and a memory for storing a processor-executable program, characterized in that, When the processor executes the program stored in the memory, it implements the multi-friction source dynamic modeling method according to any one of claims 1-5.

8. A storage medium storing a program, characterized in that, When the program is executed by the processor, it implements the multi-friction source dynamic modeling method according to any one of claims 1-5.

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