A method for fast calculation of modal of automobile brake system
By employing substructure modal synthesis and parameterization, the problem of long computation time in modal analysis of braking systems was solved, enabling fast and accurate modal calculations and improving the efficiency of modal analysis of braking systems.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CONTINENTAL BRAKE SYSTEMS (SHANGHAI) CO LTD
- Filing Date
- 2022-08-25
- Publication Date
- 2026-07-14
AI Technical Summary
Existing technologies have long computation times in modal analysis of braking systems, making it difficult to perform rapid calculations while ensuring accuracy. In particular, when the braking system model is modified, a large number of processes need to be repeated, resulting in low efficiency.
By employing the substructure modal synthesis method and parametric thinking, the parametric model of the braking system assembly model is obtained, a simulation base model is generated, parametric processing is performed, substructure parametric models of different shapes are assembled, the mass and stiffness matrices of the overall model are calculated, and finally, eigenvalues are solved to obtain key modal parameters.
While ensuring computational accuracy, it significantly shortens the analysis cycle, improves computational efficiency, and reduces computation time.
Smart Images
Figure CN116049970B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of braking system technology, specifically a method for rapidly calculating the modes of an automotive braking system. Background Technology
[0002] Modal analysis has long been a mature application in various engineering fields, with experimental modal analysis being the primary method in the early stages of vibration research. In recent years, with the rapid development of computer technology, simulation-based computational modal analysis has been widely used. A large number of general-purpose modal analysis software programs are also available on the market, sharing many commonalities, such as similar analysis workflows that follow a typical process: CAD model, mesh model, material definition, interface interaction definition, load boundary setting, and solution.
[0003] However, the braking system model is a multi-component assembly model, generally quite large, with approximately 1 million degrees of freedom and complex interface relationships. Under certain settings, it can be solved roughly following the above process, but the calculation time per iteration is lengthy. Furthermore, in many stages of braking system simulation analysis, such as early model correction and later scheme research, various modal calculations are required. Each time the basic model is modified, the above process must be repeated, resulting in significant time consumption and hindering the study of the impact of different parameters on the overall model.
[0004] Substructure modal synthesis is a widely used and mature method in the field of modal analysis. It can obtain relatively accurate modal analysis results while reducing model dimensionality. Model parameterization is also a common approach in engineering and a common way to study problems involving parametric variables.
[0005] For complex models like braking systems, applying substructure modal synthesis and parametric thinking to develop a fast calculation method specifically for system modal simulation can significantly reduce the calculation cycle while ensuring calculation accuracy. Summary of the Invention
[0006] To overcome the shortcomings of the prior art, this invention provides a method for rapidly calculating the modes of an automotive braking system. This method can achieve rapid calculation of braking system modes while ensuring calculation accuracy, greatly reducing the analysis cycle and improving efficiency.
[0007] To achieve the above objectives, a method for rapidly calculating the modal characteristics of an automotive braking system is designed, characterized by the following specific method:
[0008] Step 1: Obtain the parametric model of the substructure of the braking system assembly model;
[0009] Step 2: For the parts of the model that need to be modified, generate a simulation base model for parameterization of the modified parts;
[0010] Step 3: Parameterize the simulation base model to obtain models under different shapes, and obtain the substructure parameter models of each different shaped model;
[0011] Step 4: Assemble the parametric models of the braking system assembly substructures from Step 1 and the parametric models of the substructures of various shapes obtained in Step 3 to obtain the mass matrix and stiffness matrix of the overall model under different modification states.
[0012] Step 5: Solve for the eigenvalues of the mass matrix and stiffness matrix of the overall model to obtain the key modal parameters.
[0013] The specific process of step one is as follows:
[0014] S11: Apply hydraulic pressure to the simulation analysis model of the braking system assembly to induce axial contact in the model and obtain the normal relationship between the components of the braking system assembly model.
[0015] S12: Based on step S11, the model is loaded and rotated to make the model tangential contact, thereby obtaining the tangential relationship between the components of the braking system assembly model;
[0016] S13: Obtain friction force data based on tangential and axial contact;
[0017] S14: Based on the friction data, apply friction load to replace the rotational condition in preparation for subsequent matrix extraction;
[0018] S15: Based on step S14, set the modal order according to the modal order range of the project's focus, and perform modal solution of the braking system assembly model;
[0019] S16: Obtain the original mass matrix M0 and original stiffness matrix K0 of the braking system assembly model substructure based on modal solving.
[0020] In step S12, the rotating shaft that is loaded and rotated is the axial direction of the brake disc.
[0021] The modal solution involves calculating the system modes of the braking system assembly model and obtaining the model parameters of the substructures of the braking system assembly model.
[0022] The specific process of step two is as follows:
[0023] S21: A simulation analysis model based on the braking system assembly model, and a spatial domain is established for the parts that need to be modified, that is, each base model corresponds to a spatial domain;
[0024] S22: Set the deformation mode for each spatial domain and perform deformation processing;
[0025] S23: Restore the deformation and export each base model, saving it to the specified path for subsequent use;
[0026] S24: Based on each exported base model, export the key deformation parameters of each base model and store them in the specified path for subsequent use.
[0027] The specific process of step three is as follows:
[0028] S31: Based on the deformation key parameters of each exported base model, set the variation range of the key parameters of each base model;
[0029] S32: Set the range of modal orders for each parameterized base model;
[0030] S33: Based on the parameter ranges in steps S31 and S32, calculate the modes of each parameterized basis model to obtain the mass matrix Mij and stiffness matrix Kij of each parameterized basis model.
[0031] In the mass matrix Mij and stiffness matrix Kij of the parameterized basis model, i belongs to [1,n], n is the number of basis models, j is the number of parameterizations of the i-th basis model, i≥1, j≥1.
[0032] The specific process of step four is as follows:
[0033] S41: Assemble the mass matrix Mij and stiffness matrix Kij of the parameterized basis model of the braking system through different combinations to obtain the mass matrix and stiffness matrix of the parameterized basis model combination under different combined deformation states.
[0034] S42: Reassemble the assembled combined mass matrix and the assembled combined stiffness matrix with the original mass matrix M0 and the original stiffness matrix K0 to obtain the overall mass matrix MT and stiffness matrix KT under different deformation states.
[0035] The overall mass matrix KT = K0 + K1j + K2j + K3j ... + Knj, and the overall stiffness matrix MT = M0 + M1j + M2j + M3j ... + Mnj, where n is the number of base models, j belongs to [1, si], si is the number of parameterizations of the i-th base model, si ≥ 1, i ≥ 1.
[0036] The specific process of step five is as follows:
[0037] S51: Obtain the eigenvalues, i.e. frequencies, of the overall model by solving the characteristic equation MT×[a]+KT×[u]=[0];
[0038] S52: Obtain frequency variation curves under different parameter changes as needed, thereby determining the impact of parameter changes on frequency and indicating the direction for structural modifications.
[0039] The solution to the characteristic equation is MT×[a]+KT×[u]=[0], where [a] is the system acceleration matrix, [u] is the system displacement matrix, and [0] is the zero matrix.
[0040] Compared with the prior art, the present invention provides a method for rapidly calculating the modes of an automotive braking system. This method can achieve rapid calculation of braking system modes while ensuring calculation accuracy, greatly reducing the analysis cycle and improving efficiency. Attached Figure Description
[0041] Figure 1 This is a flowchart of the method of the present invention.
[0042] Figure 2 This is an efficiency comparison chart from an embodiment of the present invention. Detailed Implementation
[0043] The present invention will now be further described with reference to the accompanying drawings.
[0044] like Figure 1 As shown, a method for quickly calculating the modal characteristics of an automotive braking system is as follows:
[0045] Step 1: Obtain the parametric model of the substructure of the braking system assembly model.
[0046] The braking system assembly model substructure is an assembly model with approximately 1 million degrees of freedom. The relationships between components depend on the applied loads and boundary conditions. Axial compressive loads yield the normal relationships between components, while tangential rotational loads yield the tangential relationships. Under specific boundary conditions and loads, the system modes are calculated to obtain the model parameters of the braking system assembly model substructure, including the mass matrix M0 and stiffness matrix K0.
[0047] Step 2: For the parts of the model that need to be modified, generate a simulation base model for parameterization of the modified parts.
[0048] For the modified parts of the system model, different spatial domains are established, and different deformations are implemented for each spatial domain, such as local thickening and thinning, stretching and compression. Through a series of operations, one or more simulation base models S1, S2, S3, ... Sn are constructed, and key deformation parameters are obtained. These key parameters are used for the next step of parameterization.
[0049] Step 3: Parameterize the simulation base model to obtain models under different shapes, and obtain the substructure parameter models of each different shape model.
[0050] Based on a certain automated process, a parameterization program is built to parameterize one or more simulation base models according to requirements, resulting in models under different parameters. These models are generally small, with degrees of freedom typically ranging from 100 to 1000. The modalities of each parameterized model are calculated, and the substructure model parameters of each parameterized model are obtained, including the mass matrices M11, M12, M13…M21, M22, M23…Mn1, Mn2, Mnn; and the stiffness matrices K11, K12, K13…K21, K22, K23…Kn1, Kn2, Knn.
[0051] Step 4: Assemble the parametric models of the braking system assembly substructures from Step 1 and the parametric models of the substructures of various shapes obtained in Step 3 to obtain the mass matrix and stiffness matrix of the overall model under different modification states.
[0052] The braking system assembly substructure (i.e., the main substructure) and the parameterized base model substructure (i.e., the split substructure) are assembled, that is, the stiffness matrix and mass matrix are assembled to obtain the mass matrix MT and stiffness matrix KT of the overall model under different modification states, KT=K0+K1j+K2j+K3j…+Knj, MT=M0+M1j+M2j+M3j…+Mnj.
[0053] Step 5: Solve for the eigenvalues of the mass matrix and stiffness matrix of the overall model to obtain the key modal parameters.
[0054] The eigenvalues of the overall system are solved to obtain key modal parameters, with a focus on modal frequencies. Based on a specific solution program, the equation MT×[a]+KT×[u]=[0] is solved, where [a] is the system acceleration matrix, [u] is the system displacement matrix, and [0] is the zero matrix. This equation has a scale of 100 to 1000, is computationally fast, and has s1*s2…*sn combinations of KT and MT under different configurations, which is equivalent to performing s1*s2…*sn calculations.
[0055] The specific process of this invention is as follows:
[0056] S1: Apply hydraulic pressure to the simulation analysis model of the braking system assembly to make the model axially contacted and obtain the normal relationship between the sub-structural components of the braking system assembly model.
[0057] S2: Based on step S1, the model is loaded and rotated to make the model tangentially contacted, and the tangential relationship between the components of the braking system assembly model is obtained.
[0058] S3: Obtain friction force data based on tangential and axial contact;
[0059] S4: Based on the friction data, apply friction load to replace the rotational condition in preparation for subsequent matrix extraction;
[0060] S5: Based on step S4, set the modal order according to the range of modal orders of interest in the project, and perform modal solving on the braking system assembly model. Typically, braking system modal analysis focuses on lower-order modes, so a range of 50 orders or less is usually sufficient. However, in actual implementation, the range should be determined based on the order of interest required by the project. For example, if you want to see the first 30 orders, set it to 30; for the first 50, set it to 50, and so on.
[0061] S6: Obtain the original mass matrix M0 and original stiffness matrix K0 of the braking system assembly model substructure based on modal solving;
[0062] S7: A simulation analysis model based on the braking system assembly model, and a spatial domain is established for the parts that need to be modified, that is, each base model corresponds to a spatial domain;
[0063] S8: Set the deformation mode for each spatial domain and perform deformation processing; the deformation mode is set according to the project needs. For example, if additional mass needs to be added to a certain position of the braking system, a base model is built at this position. The direction in which the model is stretched and deformed (such as the XYZ axis direction, other vector directions, or special paths) is determined by the actual project requirements. If the model needs to reduce mass, it is compressed at the base model. The direction (such as the XYZ axis direction, other vector directions, or special paths) is also determined by the actual project requirements.
[0064] S9: Restore the deformation and export each base model, storing it in the specified path for subsequent calls; the specified path can be arbitrary, but it is best to use an English path. This method will select the specified path for data retrieval.
[0065] S10: Based on each exported base model, export the key deformation parameters of each base model and store them in the specified path for subsequent use;
[0066] S11: Based on the deformation key parameters of each exported base model, set the variation range of the key parameters of each base model;
[0067] S12: Set the modal order range for each parameterized basis model; this modal order range is quite critical. For parameterized basis models, it needs to be determined according to the shape of the parameterized basis model. Thin shapes need to be set to a higher order, while thick shapes need to be set to a lower order. Generally, the range is 30-100 orders.
[0068] S13: Based on the parameter ranges of steps S11 and S12, calculate the modes of each parameterized basis model to obtain the mass matrix Mij and stiffness matrix Kij of each parameterized basis model;
[0069] S14: Assemble the mass matrix Mij and stiffness matrix Kij of the parameterized basis model of the braking system through different combinations to obtain the mass matrix and stiffness matrix of the parameterized basis model combination under different deformation states. The assembly is similar to permutation and combination, which will include all deformation results. For example, if there are 3 basis models and each basis model is parameterized 4 times, a total of 3*4=12 results will be obtained, that is, 12 Mij and the corresponding 12 Kij.
[0070] S15: Reassemble the assembled combined mass matrix and the assembled combined stiffness matrix with the original mass matrix M0 and the original stiffness matrix K0 to obtain the overall mass matrix MT and stiffness matrix KT under different deformation states.
[0071] S16: Obtain the eigenvalues, i.e. frequencies, of the overall model by solving the characteristic equation MT×[a]+KT×[u]=[0];
[0072] S17: Obtain frequency variation curves under different parameter changes as needed, thereby determining the impact of parameter changes on frequency and indicating the direction for structural modifications.
[0073] In step S2, the rotating shaft that is loaded to rotate is the axial direction of the brake disc.
[0074] Modal solution involves calculating the system modes of the braking system assembly model substructure and obtaining the model parameters of the braking system assembly model substructure.
[0075] In the mass matrix Mij and stiffness matrix Kij of the basis models, i belongs to [1,n], n is the number of basis models, j is the number of parameterizations of the i-th basis model, i≥1, j≥1.
[0076] The overall mass matrix KT = K0 + K1j + K2j + K3j ... + Knj, and the overall stiffness matrix MT = M0 + M1j + M2j + M3j ... + Mnj, where n is the number of basis models, j belongs to [1, si], si is the number of parameterizations of the i-th basis model, si ≥ 1, i ≥ 1.
[0077] Solve the characteristic equation MT×[a]+KT×[u]=[0], where [a] is the system acceleration matrix, [u] is the system displacement matrix, and [0] is the zero matrix.
[0078] This method significantly improves computational efficiency while obtaining accurate results. For example, calculating a braking system assembly model takes approximately 60 minutes, and it involves parameterizing five base models, with each base model requiring three parameterizations. This means that three parameterizations are needed based on the assembly model. 5 This is the second revision.
[0079] The traditional method takes a total calculation time of 60*3. 5 =14580min=243h.
[0080] The method takes approximately 1 minute for each parameterization calculation of the baseline model and approximately 0.1 minutes for each matrix calculation after assembly, for a total computation time of 60 + 1 × 3. 5 +0.1×3 5 =327min = 5.455h. The time ratio is 5.455 / 243 = 2.24%. The more parameters there are, the more obvious the advantage of this method becomes.
[0081] This invention was used in the development of an optimization scheme for the braking NVH project of a certain OEM customer. The development of this scheme involved a total of 11 parametric calculations. Traditional methods require calculating the frequency of the braking system simulation model 11 times (each calculation takes about 1 hour), with a total time of about 1×11=11 hours.
[0082] This method requires calculating the frequency of the braking system simulation model once and the frequency of the parameterized model eleven times (each calculation takes approximately 40 seconds), with a total time of approximately 1 + 40 × 11 / 3600 = 1.122 hours. The efficiency improvement is approximately (1.122 - 11) / 11 = 90%. Figure 2 As shown.
[0083] The accuracy comparison between this method and the traditional method is shown in Table 1. As can be seen from the figure, the frequency difference between this method and the traditional method is very small, within 1%, indicating that this method has very high accuracy (accuracy > 99%). Therefore, this method can significantly improve efficiency while meeting the requirements of high accuracy.
[0084] Table 1
[0085] Parameterization [times] 1 2 3 4 5 6 7 8 9 10 11 This method _mode1[Hz] 782.0 782.1 782.2 782.2 782.1 782.0 781.9 781.8 781.6 781.3 781.0 This method _mode2[Hz] 1055.9 1051.9 1047.8 1043.6 1039.3 1035.0 1030.6 1026.1 1021.6 1016.9 1012.2 This method_mode3[Hz] 1859.8 1859.5 1858.9 1858.0 1856.9 1836.6 1809.4 1775.5 1732.6 1679.0 1613.8 This method uses _mode4[Hz] 2108.6 2089.9 2067.5 2043.9 2020.6 1998.4 1977.7 1958.7 1941.7 1926.6 1913.3 This method uses _mode5[Hz] 2974.4 2989.0 2985.2 2973.1 2957.7 2941.1 2922.8 2899.4 2853.4 2725.1 2553.6 This method uses _mode6[Hz] 3797.7 3793.2 3787.6 3780.9 3773.0 3763.7 3752.8 3739.7 3724.0 3704.9 3681.7 This method uses _mode7[Hz] 4505.3 4520.4 4520.9 4509.2 4485.4 4481.1 4475.2 4467.3 4456.5 4441.3 4419.7 This method uses _mode8[Hz] 5648.7 5647.7 5642.1 5525.5 5012.3 4649.3 4574.1 4553.3 4542.7 4535.4 4529.8 Traditional method _mode1[Hz] 781.97 782.11 782.16 782.15 7.82E+02 782.03 781.92 781.77 781.57 781.32 781 Traditional method _mode2[Hz] 1055.8 1051.9 1047.8 1043.6 1.04E+03 1035 1030.6 1026.1 1021.6 1016.9 1012.2 Traditional method _mode3[Hz] 1859.8 1859.5 1858.9 1858 1.86E+03 1836.5 1809.3 1775.4 1732.5 1678.9 1613.8 Traditional method _mode4[Hz] 2108.2 2089.6 2067.2 2043.6 2.02E+03 1998.2 1977.5 1958.5 1941.5 1926.4 1913.2 Traditional method _mode5[Hz] 2973.5 2988.2 2984.4 2972.4 2.96E+03 2940.5 2922.3 2899 2853.1 2725 2553.4 Traditional method _mode6[Hz] 3797.5 3793 3787.3 3780.6 3.77E+03 3763.5 3752.6 3739.5 3723.7 3704.7 3681.5 Traditional method _mode7[Hz] 4504.6 4519.7 4520.3 4508.6 4.49E+03 4480.9 4475 4467.1 4456.2 4441 4419.4 Traditional method _mode8[Hz] 5648.4 5647.5 5641.7 5522.9 5.01E+03 4648.5 4573.4 4552.8 4542.1 4534.9 4529.3
Claims
1. A method for rapidly calculating the modal characteristics of an automotive braking system, characterized in that: The specific method is as follows: Step 1: Obtain the parametric model of the substructure of the braking system assembly model; Step 2: For the parts of the model that need to be modified, generate a simulation base model for parameterization of the modified parts; Step 3: Parameterize the simulation base model to obtain models under different shapes, and obtain the substructure parameter models of each different shaped model; Step 4: Assemble the parametric models of the braking system assembly substructures from Step 1 and the parametric models of the substructures of various shapes obtained in Step 3 to obtain the mass matrix and stiffness matrix of the overall model under different modification states. Step 5: Solve for the eigenvalues of the mass matrix and stiffness matrix of the overall model to obtain the key modal parameters; The specific process for step one is as follows: S11: Apply hydraulic pressure to the simulation analysis model of the braking system assembly to induce axial contact in the model and obtain the normal relationship between the components of the braking system assembly model. S12: Based on step S11, the model is loaded and rotated to make the model tangential contact, thereby obtaining the tangential relationship between the components of the braking system assembly model; S13: Obtain friction force data based on tangential and axial contact; S14: Based on the friction data, apply friction load to replace the rotational condition in preparation for subsequent matrix extraction; S15: Based on step S14, set the modal order according to the modal order range of the project's focus, and perform modal solution of the braking system assembly model; S16: Obtain the original mass matrix M0 and original stiffness matrix K0 of the braking system assembly model substructure based on modal solving; The specific process for step three is as follows: S31: Based on the deformation key parameters of each exported base model, set the variation range of the key parameters of each base model; S32: Set the range of modal orders for each parameterized base model; S33: Based on the parameter ranges in steps S31 and S32, calculate the modes of each parameterized basis model to obtain the mass matrix Mij and stiffness matrix Kij of each parameterized basis model.
2. The method for rapidly calculating the modal characteristics of an automotive braking system according to claim 1, characterized in that: In step S12, the rotating shaft that is loaded and rotated is the axial direction of the brake disc.
3. The method for rapidly calculating the modal characteristics of an automotive braking system according to claim 1, characterized in that: The modal solution involves calculating the system modes of the braking system assembly model and obtaining the model parameters of the substructures of the braking system assembly model.
4. The method for rapidly calculating the modal characteristics of an automotive braking system according to claim 1, characterized in that: The specific process of step two is as follows: S21: A simulation analysis model based on the braking system assembly model, and a spatial domain is established for the parts that need to be modified, that is, each base model corresponds to a spatial domain; S22: Set the deformation mode for each spatial domain and perform deformation processing; S23: Restore the deformation and export each base model, saving it to the specified path for subsequent use; S24: Based on each exported base model, export the key deformation parameters of each base model and store them in the specified path for subsequent use.
5. The method for rapidly calculating the modal characteristics of an automotive braking system according to claim 1, characterized in that: In the mass matrix Mij and stiffness matrix Kij of the parameterized basis model, i belongs to [1,n], n is the number of basis models, j is the number of parameterizations of the i-th basis model, i≥1, j≥1.
6. The method for rapidly calculating the modal characteristics of an automotive braking system according to claim 1, characterized in that: The specific process of step four is as follows: S41: Assemble the mass matrix Mij and stiffness matrix Kij of the parameterized basis model of the braking system through different combinations to obtain the mass matrix and stiffness matrix of the parameterized basis model combination under different combined deformation states. S42: Reassemble the assembled combined mass matrix and the assembled combined stiffness matrix with the original mass matrix M0 and the original stiffness matrix K0 to obtain the overall mass matrix MT and stiffness matrix KT under different deformation states.
7. The method for rapidly calculating the modal characteristics of an automotive braking system according to claim 6, characterized in that: The overall mass matrix KT = K0 + K1j + K2j + K3j … + Knj, and the overall stiffness matrix MT = M0 + M1j + M2j + M3j … + Mnj, where n is the number of base models, j belongs to [1, si], si is the number of parameterizations of the i-th base model, si ≥ 1, i ≥ 1.
8. The method for rapidly calculating the modal characteristics of an automotive braking system according to claim 1, characterized in that: The specific process of step five is as follows: S51: Obtain the eigenvalues, i.e. frequencies, of the overall model by solving the characteristic equation MT×[a]+KT×[u]=[0]; S52: Obtain frequency variation curves under different parameter changes as needed, thereby determining the impact of parameter changes on frequency and indicating the direction for structural modifications.
9. The method for rapidly calculating the modal characteristics of an automotive braking system according to claim 8, characterized in that: The solution to the characteristic equation is MT×[a]+KT×[u]=[0], where [a] is the system acceleration matrix, [u] is the system displacement matrix, and [0] is the zero matrix.