Braking interface wear and fatigue crack prediction method based on complete heat-engine coupling

Abstract

The invention discloses a brake interface wear and fatigue crack prediction method based on complete heat-engine coupling, which comprises the following steps: S1, establishing a finite element model, and dispersing total analysis time into a plurality of time periods; s2, starting finite element analysis, and calculating interface node contact pressure and node slip rate; s3, performing transient heat engine coupling analysis; s4, calculating a node wear depth and a wear direction, and updating grid information by using an ALE technology; s5, judging whether the interface contact state is stably converged or not; s6, finishing analysis, unloading the brake load, and obtaining the residual stress of the brake disc; and S7, a crack is preset at the position with the maximum residual stress, the expansion behavior of the crack is simulated, and the stress intensity factor and the fatigue life of the brake disc are calculated. According to the method, tribological behaviors such as contact stress, temperature and abrasion can be simulated, and the fatigue life of the brake disc is predicted by taking residual stress after a heat-engine coupling process as load input.

Description

Technical Field

[0001] The invention relates to the field of friction braking, and in particular to a method for predicting brake interface wear and fatigue cracks based on complete thermal-mechanical coupling. Background Art

[0002] During the friction braking process, the brake pads of vehicles will be severely worn, and the brake interface will accumulate a large amount of friction heat in a short period of time, causing the brake disc to heat up rapidly, thereby generating thermal stress and causing thermal cracks on the surface of the brake disc. These possible failure forms will seriously threaten the safe operation of the braking system. Before designing a product application, it is usually necessary to verify and evaluate it first to determine whether the braking performance is qualified and predict whether the service life meets the standard. Although using experimental methods to test brake friction pairs is the most direct and effective method, since it is necessary to build expensive test equipment and conduct fatigue tests for a long period of time, the experimental verification cycle is long and the cost is high. The finite element simulation method only requires numerical simulation of the braking process, and only the model needs to be modified and the calculation submitted during optimization iteration. Therefore, the use of the finite element method can greatly save costs and improve design efficiency.

[0003] The Chinese patent with application number CN201911411319.2 discloses a friction vibration noise prediction method that takes into account interface uncertainty and time-varying properties. This method proposes a method for predicting friction vibration noise that takes into account the evolution of interface wear, and can simultaneously predict the interface wear and friction vibration noise evolution during the friction process. However, since this method does not take into account the interface friction heat factor, it cannot predict the evolution of temperature during the friction process, as well as the effect of temperature on wear and friction vibration noise. The Chinese patent with application number CN201410457959.8 discloses a simulation method for the sequential coupling of dry sliding friction heat-stress-wear. This method calculates the interface heat flux density through the power equivalent method, and then uses heat conduction analysis to obtain the temperature field of the friction system, and then performs stress analysis to obtain the interface node contact stress and relative slip rate to calculate the node wear. Although this method can accurately obtain information such as temperature and wear of the interface, it is a sequential coupling method. The temperature field is based on the equal power method to obtain the heat flux density, and the system is analyzed for heat conduction by using an external heat source. The generation of temperature does not depend on the stress field of the system. Therefore, this method can only study the effect of the temperature field on wear, and the effect of the change in the stress field after interface wear on the temperature field cannot be reflected. In addition, this method does not consider the effect of thermal-mechanical coupling on the fatigue life of the system. Summary of the invention

[0004] In order to solve the problem that the existing technology cannot accurately predict fatigue life through contact stress, temperature and wear, the present invention proposes a brake interface wear and fatigue crack prediction method based on complete thermal-mechanical coupling to solve the above problem.

[0005] The present application discloses a brake interface wear and fatigue crack prediction method based on full thermal-mechanical coupling, comprising the following steps: S1. Establish a finite element model, set the interaction and boundary conditions between the components and perform meshing, and discretize the total analysis time into multiple time periods; S2, start the finite element analysis, first load the braking force, then apply the brake disc speed, and calculate the interface node contact pressure and node slip rate under the initial incremental step; S3, calculate the friction heat according to the contact pressure and slip rate obtained in S2, and perform transient thermal-mechanical coupling analysis; S4, according to the contact pressure and slip rate obtained in S2, call the UMESHMOTION subroutine, calculate the node wear depth and wear direction based on the Archard wear formula, and use the ALE technology to update the mesh information; S5, judging whether the interface contact state is stably converged. If not, return to S1, reduce the initial time step increment and recalculate steps S2-S4 until the interface contact state is stably converged; if stable, increase the time step increment to enter the next analysis cycle; S6, repeat S2-S5, and when the analysis time reaches the simulation time of the braking process, end the thermal-mechanical-wear coupling analysis, unload the braking load, allow the brake disc to cool naturally to room temperature, and obtain the residual stress of the brake disc; S7. Preset cracks at the location where the residual stress is maximum, use the residual stress as the load, use the extended finite element method to simulate the crack propagation behavior, and calculate the stress intensity factor and fatigue life of the brake disc.

[0006] Preferably, the S1 comprises the following steps: Assume the total analysis time is , the total analysis time Discrete time period, where the simulation time of the braking process is recorded as , the initial time is recorded as , the initial increment step is , the maximum incremental step is , the time increment is recorded as , if the current time increment is If it does not converge, reduce the time increment , until convergence; if the current time increment step If convergence is not achieved, increase the time increment ,until After is the time increment, and the total analysis time is ,in For the j The time increment of each incremental step.

[0007] Preferably, the friction heat calculation formula is as follows:

[0008] in, is the energy conversion efficiency, is the friction coefficient, is the interface node contact pressure at the initial incremental step, For Node The distance to the center of the brake disc, For Node The coordinates of is the coordinate of the center of the brake disc, For Node The angular coordinates in the polar coordinate system are: is the brake disc speed.

[0009] Preferably, the Archard wear formula is as follows, assuming that the wear depth is proportional to the contact pressure Proportional to the power:

[0010] in, is the wear coefficient, the wear direction is specified as the normal direction of the wear interface, Is the pressure index.

[0011] Preferably, S6 comprises the following steps: When the analysis time is greater than The thermal-mechanical-wear coupling analysis is completed at this time, and the wear depth of each node on the interface is output. The braking force and the brake disc speed are reduced to 0 within 1 second, so that the braking system dissipates the braking heat under natural convection conditions and cools to room temperature to obtain the brake disc residual stress. The heat convection satisfies the following conditions:

[0012] in, is the heat convection density, is the heat convection coefficient, is the surface temperature of the brake system, is the ambient air temperature; The heat convection coefficient calculation formula is as follows:

[0013] in, is the thermal conductivity of air, is the characteristic length, is the Reynolds coefficient.

[0014] Preferably, the calculation formula of the stress intensity factor is as follows:

[0015]

[0016] The angle of crack extension direction is:

[0017] in, for Type eigenvalue, for Type eigenvalue, is the number of intercepted complex eigenvalues, is the number of real eigenvalues ​​captured, is the crack extension direction angle, is the generalized stress intensity factor, is the intermediate matrix containing the displacement, is the intermediate matrix containing the stress angle distribution function, subscript R represents the real part, subscript I Represents the imaginary part.

[0018] Preferably, the fatigue life of the brake disc is calculated by the following formula: Calculate the stress intensity factor amplitude:

[0019] in, is the largest element in the stress intensity factor matrix, is the minimum element in the stress intensity factor matrix; Prediction of brake disc fatigue life based on Paris formula:

[0020] in, is the crack growth rate, and is a material related constant.

[0021] Beneficial effects of the present invention: (1) The present invention can accurately simulate the tribological behaviors of the brake system, such as contact stress, temperature, and wear, and use the residual stress after the thermal-mechanical coupling process as the load input to analyze the crack growth behavior of the brake disc and predict its fatigue life. This forms a complete damage failure prediction model for the service of the brake friction pair.

[0022] (2) Compared with the traditional sequential coupling method, the simulated temperature field distribution of the present invention is more realistic and can reflect the interaction between contact stress, temperature and wear, and reveal the mechanism of their mutual influence. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 This is a flow chart of a method for predicting brake interface wear and fatigue cracks based on full thermal-mechanical coupling according to an embodiment of the present invention; Figure 2 is a schematic diagram of a finite element model of an embodiment of the present invention; Figure 3 This is a schematic diagram of residual stress distribution of a brake disc according to an embodiment of the present invention; Figure 4 A schematic diagram of a preset crack position according to an embodiment of the present invention; Figure 5 Schematic diagram of crack propagation of a brake disc according to an embodiment of the present invention.

[0024] Figure 6 Schematic diagram of comparison between experimental results and numerical simulation results of interface temperature distribution evolution of an embodiment of the present invention; Figure 7 Schematic diagram comparing the experimental results (a) and numerical simulation (b) of the wear distribution of the friction block according to an embodiment of the present invention; schematic diagram comparing the radial normalized wear depth experiment of the friction block and the numerical simulation (c); schematic diagram comparing the tangential normalized wear depth experiment of the friction block and the numerical simulation (d). DETAILED DESCRIPTION

[0025] In order to make the objectives, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below with reference to the accompanying drawings and examples.

[0026] The present application embodiment discloses a brake interface wear and fatigue crack prediction method based on complete thermal-mechanical coupling, the process is as follows: Figure 1 As shown, the following steps are included: S1. Establish a simplified finite element model based on the test device and assign material properties to each component. Set the interaction and boundary conditions between the components and perform meshing to discretize the total analysis time into multiple time periods.

[0027] The finite element model established in this embodiment is as follows Figure 2 As shown in the figure, the finite element model mainly includes a pair of friction blocks and a brake disc. A reference point is established at the center of the brake disc, and the reference point is coupled with the inner surface of the center of the brake disc shaft hole. xThe speed of the shaft drives the brake disc to rotate (the speed in this embodiment is 8r / s); in order to fix the friction block and effectively apply the braking load, it is constrained to move along y Axis and z The translational freedom of the axis is released along x When simulating the braking friction process, a braking pressure of 0.75 MPa is first applied to the friction block, and then a rotation speed of 8 r / s is applied to the brake disc to simulate the braking process.

[0028] Set the contact properties between the friction pad and the brake disc, where the friction pad surface is set to "slave surface", the brake disc surface is set to "master surface", the normal property of the contact interface is set to "hard contact", the tangential friction force property is set to "penalty function", and the friction coefficient Set it to 0.4. And turn on the friction heat generation option in the contact characteristics, which means that the work done by friction during the friction process will be converted into friction heat. The energy conversion coefficient is set to 0.9, which means that 90% of the energy of the work done by friction is converted into heat energy. Set the surface heat distribution coefficient to 0.08, which means that 8% of the heat will be absorbed by the surface of the friction block and 92% of the heat will be absorbed by the surface of the brake disc. At the same time, assuming that the ambient temperature is 25°C, give the entire brake system a predefined temperature field of 25°C.

[0029] In order to effectively simulate the material removal caused by wear, the mesh of the friction pad is specified as an ALE mesh domain so that the mesh in this area can be redrawn in real time during the simulation. At the same time, the nodes on the contact surface of the brake disc and the friction pad are specified as ALE node constraints so that the node coordinates in this domain can be updated according to the wear information, and finally the mesh is redrawn to simulate the wear material removal during the braking process.

[0030] Assume the total analysis time is , the total analysis time Discrete time period, where the simulation time of the braking process is recorded as , the initial time is recorded as , the initial increment step is , the maximum incremental step is The significance of setting the maximum incremental step is to automatically control the convergence of the simulation process. The time increment step is recorded as , if the current time increment is If it does not converge, reduce the time increment , until convergence; if the current time increment step If convergence is not achieved, increase the time increment ,until After is the time increment, and the total analysis time is ,in For the j The time increment of each incremental step.

[0031] S2. Start the finite element analysis, first load the braking force, then apply the brake disc speed, and calculate the interface node contact pressure and node slip rate under the initial incremental step.

[0032] S3. Calculate the friction heat based on the contact pressure and slip rate obtained in S2, and perform transient thermal-mechanical coupling analysis.

[0033] According to the law of energy conversion, the friction heat converted at each node is:

[0034] in, The energy conversion efficiency is set to 0.9 in this embodiment, which means that 90% of the work done by friction is converted into heat of the system. is the friction coefficient, is the interface node contact pressure at the initial incremental step, For Node The distance to the center of the brake disc, For Node The coordinates of is the coordinate of the center of the brake disc, For Node The angular coordinates in the polar coordinate system are: is the brake disc speed.

[0035] S4. Based on the contact pressure and slip rate obtained in S2, the UMESHMOTION subroutine is called. The contact stress and temperature of the friction block contact node are called by the subroutine UMESHMOTION. The node wear depth and wear direction are calculated based on the Archard wear formula: The Archard wear formula is as follows: Assume that the wear depth is proportional to the contact pressure. Proportional to the power:

[0036] in, is the wear coefficient, which is related to temperature and can be expressed as a temperature-dependent polynomial: , are the polynomial coefficients, is the node temperature, the wear direction is specified as the normal direction of the wear interface, is the pressure index. Since the hardness of the brake disc material is much greater than that of the friction pad, its wear can be ignored compared to the friction pad, so this process only considers the wear of the friction pad.

[0037] After the wear calculation is completed, the ALE technology is used to redraw and update the mesh of the friction block to simulate the material removal process caused by wear, and the mesh is redrawn once in each incremental step.

[0038] S5. Determine whether the interface contact state is stably converged. If not, return to S1, reduce the initial time step increment and recalculate steps S2-S4 until the interface contact state is stably converged; if stable, increase the time step increment to enter the next analysis cycle.

[0039] S6, repeat S2-S5, when the analysis time is longer than The thermal-mechanical-wear coupling analysis is completed at (preset braking process simulation time), and then the braking load is unloaded to allow the brake disc to cool naturally to room temperature and obtain the brake disc residual stress. The brake disc residual stress distribution is shown in Figure 3 As shown in Figure 2, the residual stress distribution of the brake disc is similar to the temperature distribution, and is mainly located on the annular zone where the friction block passes.

[0040] When the analysis time is greater than The thermal-mechanical-wear coupling analysis is completed at this time, and the wear depth of each node on the interface is output. Then the braking force and the brake disc speed are reduced to 0 within 1 second, and the brake system is cooled to room temperature under natural convection conditions to obtain the brake disc residual stress.

[0041] The heat convection satisfies the following conditions:

[0042] in, is the heat convection density, is the heat convection coefficient, in this implementation The value is about 80W / (m℃), is the surface temperature of the brake system, is the air environment temperature, and in this embodiment the air environment temperature is 25°C.

[0043] The heat convection coefficient calculation formula is as follows:

[0044] in, is the thermal conductivity of air, is the characteristic length, is the Reynolds coefficient.

[0045] S7. Preset a crack at the point where the residual stress is maximum, use the residual stress as the load, use the extended finite element method (XFEM) to simulate the crack propagation behavior, and calculate the stress intensity factor and fatigue life of the brake disc.

[0046] After obtaining the residual stress of the brake disc, find the location of its maximum residual stress, then create a new brake disc crack growth analysis model, and preset cracks at the corresponding maximum residual stress. The cracks are generally semi-elliptical, and the ratio of crack depth to crack length is 1:4, such as Figure 4 As shown in the figure, the crack center is located at the maximum position of residual stress. A static analysis step is established to create an XFEM crack, and the residual stress obtained in the fully coupled thermal-mechanical-wear analysis is applied as a predefined field to the newly created brake disc crack growth model.

[0047] To simulate the expansion behavior of the brake disc crack under the action of residual stress, the stress threshold required for crack expansion needs to be set in the material parameters of the brake disc. In this embodiment, the threshold is set to 140MPa, that is, when the maximum principal stress at the tip of the brake disc crack exceeds 140MPa, the crack will expand, and the crack expansion follows the principle of maximum energy release. Figure 5 As shown by Figure 5 It can be seen that the crack extends along the radial direction of the brake disc. This is because the residual stress of the brake disc mainly manifests as circumferential tensile stress.

[0048] Accurately solving the fracture parameters at the crack tip is the key to predicting crack propagation behavior. In order to avoid the shortcomings of relying on a fine crack tip mesh with or without conventional quarter-node singular elements, this embodiment uses a novel method to calculate stress intensity factors (SIFs). The calculation derivation process is as follows: The asymptotic displacement and stress near the crack tip are expressed as:

[0049]

[0050] in, is the number of intercepted complex eigenvalues, is the number of real eigenvalues ​​captured, is the crack extension direction angle, is the generalized stress intensity factor, and is the intermediate matrix containing the displacement and stress angle distribution functions, subscript represents the real part, Represents the imaginary part.

[0051] in and The solution method adopts a special one-dimensional finite element eigenanalysis method. Using this method, the numerical characteristic solution of the singular displacement field and stress field can be obtained by the following numerical characteristic equation:

[0052] in, is the variation symbol, is the feature vector, is the characteristic value, is the mass matrix, is the damping matrix, is the stiffness matrix.

[0053] According to the Hellinger-Reissner variational principle, a functional is defined in the crack tip unit region:

[0054] in, is the matrix consisting of unit external normal vectors, is the boundary displacement vector, is the unit volume near the crack tip, and is the displacement component in the rectangular coordinate system, , and is the stress component in the rectangular coordinate system, represents the boundary surface near the crack tip, represents the volume element, Represents a microelement of area.

[0055] To avoid The singular terms in the inner integral are difficult to solve. The divergence theorem can be used to transform the volume integral in equation (8) into the following surface integral:

[0056] in, is the outer surface of the unit near the crack tip, is the stress matrix.

[0057] Element boundary displacement Can be displaced by two adjacent nodes and Interpolation means:

[0058] in, is the interpolation function matrix obtained according to the one-dimensional Lagrange interpolation method, which automatically satisfies the continuity of node displacements between adjacent units. , , Bring-in get:

[0059] in, , and They are:

[0060]

[0061] in, , denote the element intermediate matrices containing displacement and stress angle distribution functions, respectively. is the element stress matrix.

[0062] According to the functional condition ,available:

[0063] in, is the node displacement.

[0064] General Bring-in available:

[0065] Crack tip stiffness matrix It can be expressed as:

[0066] By performing a finite element analysis on the cracked geometry, the nodal displacements can be directly extracted from the solution of the overall finite element equations. , and then by - The numerical solution of the singular stress field around the crack tip is obtained. Finally, the stress intensity factor at the crack tip is obtained through the numerical solution of the singular stress field:

[0067]

[0068] in, for Type eigenvalue, for Type characteristic value.

[0069] The angle of crack extension direction is:

[0070] Calculate the stress intensity factor amplitude:

[0071] in, is the largest element in the stress intensity factor matrix, is the smallest element in the stress intensity factor matrix.

[0072] Prediction of brake disc fatigue life based on Paris formula:

[0073] in, is the crack growth rate, and is a material related constant.

[0074] In a specific embodiment, the experimental results of interface temperature distribution and interface wear distribution are compared with the simulation results. Figure 6 The figure shows the comparison between the experimental and simulation results of the interface temperature distribution evolution, which shows that the numerical simulation simulates the evolution of the temperature field distribution of the brake disc very well, and the simulated temperature distribution and size are basically consistent with the experimental results. Figure 7 The figure shows the comparison of interface wear distribution results. The results show that the wear distribution of the friction block obtained by simulation is basically consistent with the experimental observation, which fully proves the reliability of the simulation method.

[0075] In summary, this application discloses a brake interface wear and fatigue crack prediction method based on full thermomechanical coupling, which can accurately simulate the friction behaviors of the brake system such as contact stress, temperature and wear, and use the residual stress after the thermomechanical coupling process as the load input to analyze the thermal crack propagation behavior of the brake disc and realize its fatigue life prediction. Compared with the traditional sequential coupling method, the temperature field distribution simulated by the method proposed in this application is more realistic, and can reflect the interaction relationship between contact stress, temperature and wear, and can reveal the mechanism of their mutual influence.

[0076] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for predicting brake interface wear and fatigue cracks based on full thermal-mechanical coupling, characterized in that: The following steps are involved: S1. Establish a finite element model, set the interaction and boundary conditions between the components and perform meshing, and discretize the total analysis time into multiple time periods; S2, start the finite element analysis, first load the braking force, then apply the brake disc speed, and calculate the interface node contact pressure and node slip rate under the initial incremental step; S3, calculate the friction heat according to the contact pressure and slip rate obtained in S2, and perform transient thermal-mechanical coupling analysis; S4, according to the contact pressure and slip rate obtained in S2, call the UMESHMOTION subroutine, calculate the node wear depth and wear direction based on the Archard wear formula, and use the ALE technology to update the mesh information; S5, judging whether the interface contact state is stably converged. If not, return to S1, reduce the initial time step increment and recalculate steps S2-S4 until the interface contact state is stably converged; if stable, increase the time step increment to enter the next analysis cycle; S6, repeat S2-S5, and when the analysis time reaches the simulation time of the braking process, end the thermal-mechanical-wear coupling analysis, unload the braking load, allow the brake disc to cool naturally to room temperature, and obtain the residual stress of the brake disc; S7. Preset cracks at the location where the residual stress is maximum, use the residual stress as the load, and use the extended finite element method to simulate the expansion behavior of the brake disc crack, and calculate the stress intensity factor and the fatigue life of the brake disc.

2. The brake interface wear and fatigue crack prediction method based on full thermal-mechanical coupling according to claim 1 is characterized in that: The S1 comprises the following steps: Assume the total analysis time is , the total analysis time Discrete time period, where the simulation time of the braking process is recorded as , the initial time is recorded as , the initial increment step is , the maximum incremental step is , the time increment is recorded as , if the current time increment is If it does not converge, reduce the time increment , until convergence; if the current time increment step If convergence is not achieved, increase the time increment ,until After is the time increment, and the total analysis time is ,in For the j The time increment of each incremental step.

3. The brake interface wear and fatigue crack prediction method based on full thermal-mechanical coupling according to claim 2 is characterized in that: The friction heat calculation formula is as follows: in, is the energy conversion efficiency, is the friction coefficient, is the interface node contact pressure at the initial incremental step, For Node The distance to the center of the brake disc, For Node The coordinates of is the coordinate of the center of the brake disc, For Node The angular coordinates in the polar coordinate system are: is the brake disc speed.

4. The brake interface wear and fatigue crack prediction method based on full thermal-mechanical coupling according to claim 3 is characterized in that: The Archard wear formula is as follows, assuming that the wear depth is proportional to the contact pressure. Proportional to the power: in, is the wear coefficient, the wear direction is specified as the normal direction of the wear interface, Is the pressure index.

5. The method for predicting brake interface wear and fatigue cracks based on full thermal-mechanical coupling according to claim 4 is characterized in that: The S6 comprises the following steps: When the analysis time is greater than The thermal-mechanical-wear coupling analysis is completed at this time, and the wear depth of each node on the interface is output. The braking force and the brake disc speed are reduced to 0 within 1 second, so that the braking system dissipates the braking heat under natural convection conditions and cools to room temperature to obtain the brake disc residual stress. The heat convection satisfies the following conditions: in, is the heat convection density, is the heat convection coefficient, is the surface temperature of the brake system, is the ambient air temperature; The heat convection coefficient calculation formula is as follows: in, is the thermal conductivity of air, is the characteristic length, is the Reynolds coefficient.

6. The brake interface wear and fatigue crack prediction method based on full thermal-mechanical coupling according to claim 5 is characterized in that: The calculation formula of the stress intensity factor is as follows: The angle of crack extension direction is: in, for Type eigenvalue, for Type eigenvalue, is the number of complex eigenvalues ​​intercepted, is the number of real eigenvalues ​​captured, is the crack extension direction angle, is the generalized stress intensity factor, is the intermediate matrix containing the displacement, is the intermediate matrix containing the stress angle distribution function, subscript R represents the real part, subscript I Represents the imaginary part.

7. The method for predicting brake interface wear and fatigue cracks based on full thermal-mechanical coupling according to claim 6 is characterized in that: The brake disc fatigue life is calculated by the following formula: Calculate the stress intensity factor amplitude: in, is the largest element in the stress intensity factor matrix, is the minimum element in the stress intensity factor matrix; Prediction of brake disc fatigue life based on Paris formula: in, is the crack growth rate, and is a material related constant.

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