Analysis method for verifying rationality of empirical tolerance of complex system and application thereof

Abstract

The invention belongs to the field of complex engineering system design and kinetic analysis, and particularly discloses an analysis method for verifying complex system empirical tolerance rationality and application thereof, and the method specifically comprises the following steps: (1) establishing a parameterized model; (2) constructing a multi-physics field dynamics simulation model; (3) importing boundary conditions of operation conditions; (4) operation quality and performance index extraction; (5) data-driven correlation analysis; and (6) verifying and optimizing the reasonability of the empirical tolerance. The method has universality and expandability, can be widely applied to empirical tolerance verification and design optimization of complex systems in the fields of rail transit, aerospace, power transmission, precision manufacturing and the like, and provides a unified theory and calculation framework for tolerance rationality evaluation.

Description

Technical Field

[0001] This invention relates to the field of design and verification of complex systems, and in particular to an analytical method for verifying the rationality of empirical tolerances in complex systems. It is applicable to railway catenary-pantograph systems, overhead transmission lines, vehicle suspension systems, and other mechanical or electromechanical systems with critical geometric tolerances. Background Technology

[0002] In the design and maintenance of complex electromechanical systems, critical geometric tolerances are often determined empirically. For example, in railway catenary-pantograph systems, parameters such as the position of the overhead line, tension, and contact wire height have certain allowable deviations during construction and maintenance to ensure system operability and operational safety. However, existing methods mainly rely on empirical judgment or field tests to verify the rationality of tolerances, which is not only time-consuming and labor-intensive but also makes it difficult to quantify the impact of different tolerance combinations on system performance.

[0003] With the development of railway and electrification system technologies, the dynamic interaction between overhead lines and pantographs has a significant impact on system operation quality. Especially under high-speed operating conditions, the pantograph must be able to track local positional changes of the overhead line to ensure stable contact force and reduce wear and arcing. Existing empirical methods are insufficient for systematically evaluating these dynamic interactions and cannot be generalized to other systems or different operating conditions.

[0004] Currently, the dynamic interaction between overhead lines and pantographs can be modeled and analyzed using the finite element method (FEM) and multibody dynamics (MBD) simulations. For example, Siemens Mobility's Sicat Dynamic software can export overhead line models as text files and study the impact of different tolerance levels on operational quality by modifying model parameters. During the simulation process, adaptation and evaluation tools can be independently developed to systematically analyze indicators such as contact force, lift, and contact path to obtain a quantitative impact of tolerances on operational quality.

[0005] However, existing simulation methods mainly target single systems and lack a unified theoretical analysis framework. They struggle to systematically quantify and verify empirical tolerances and perform sensitivity analysis, and are also difficult to directly extend to other complex systems. Therefore, there is an urgent need for a generalizable analysis method that can quantify the rationality of empirical tolerances in complex systems through modeling, simulation, and performance evaluation. This would provide a basis for system design optimization and standard setting, while simultaneously reducing field testing costs and improving evaluation efficiency. Summary of the Invention

[0006] To address the aforementioned technical problems in the existing technology, this invention provides an analytical method for verifying the rationality of empirical tolerances in complex systems. The specific technical solution is as follows:

[0007] An analytical method for verifying the rationality of empirical tolerances in complex systems is based on multiphysics dynamics modeling and numerical analysis theory. It comprehensively utilizes finite element analysis, multibody dynamics, and sensitivity assessment techniques to establish a quantitative mapping relationship between empirical tolerance parameters and system performance, forming a generalizable quantitative verification and optimization system for empirical tolerances. This achieves systematic theoretical verification and optimization of the rationality of empirical tolerances. The method includes the following steps:

[0008] (1) Establish a parametric model:

[0009] Based on the structural characteristics and operating mechanism of the target complex system, a parameterized model containing geometric parameters, material parameters and boundary constraints is constructed. Key empirical tolerances are embedded in the model as variables, including but not limited to position deviations, structural constraint deviations, material property deviations and assembly errors.

[0010] (2) Constructing a multiphysics dynamics simulation model:

[0011] The parameterized model is solved by finite element analysis (FEM), multibody dynamics analysis or other numerical analysis methods to obtain the response characteristics of the system under different tolerance combinations. The response includes mechanical response and can be extended to electrical response, thermal characteristics and energy transfer characteristics.

[0012] (3) Import operating condition boundary conditions:

[0013] Based on the actual operating scenario, input loads, speeds, environmental parameters, and boundary constraints are used to generate a simulation input dataset that can be used for dynamic analysis.

[0014] (4) Extraction of operational quality and performance indicators:

[0015] Key indicators characterizing the system's performance stability or operational quality are extracted from the simulation results. These performance indicators include operational quality parameters such as contact force, overhead conductor lift, and contact point height, and can be extended to stress distribution, vibration response, or energy transfer characteristics in other complex systems.

[0016] (5) Data-driven correlation analysis:

[0017] The simulation results are post-processed using computer algorithm modules to analyze the variation patterns of system performance indicators under different tolerance parameters. Through statistical analysis and trend identification of simulation sample data, the main influence directions and sensitivity of various factors and their combinations on system performance are revealed, providing data support for the theoretical verification and optimization of the rationality of empirical tolerances.

[0018] (6) Verification and optimization of the rationality of empirical tolerances:

[0019] Based on the allowable limits given in industry standards or design specifications, the performance indicators under different tolerance combinations are compared to evaluate the rationality of the empirical tolerance setting, and optimization suggestions and correction ranges are output based on the analysis results.

[0020] Furthermore, the parametric model in step (1) is automatically generated by a geometric modeling tool and can be exported as an editable text file to enable precise insertion and modification of tolerance parameters.

[0021] Furthermore, in step (2), the finite element method and multibody dynamics are coupled to model the structure, so as to simultaneously consider structural flexibility, nonlinear contact and kinematic constraints.

[0022] Furthermore, the operating conditions described in step (3) can be input based on actual measurements or standard operating conditions, including operating speed, conductor tension, ambient temperature, and structural constraints.

[0023] Furthermore, the performance indicators in step (4) include, but are not limited to, operational quality parameters such as contact force, overhead conductor lift, and contact point height. The distribution characteristics of these performance indicators can be described and compared using statistical visualization methods such as violin plots and box plots to achieve quantitative analysis of system performance under different tolerance conditions.

[0024] Furthermore, the data-driven analysis in step (5) uses computer algorithms to post-process and statistically analyze the simulation results. By identifying the correlation and sensitivity between different tolerance parameters and system performance indicators, it reveals the main influence of parameter changes on system performance, which is used to support the theoretical verification and optimization of the rationality of empirical tolerances.

[0025] Furthermore, the method can be applied to overhead contact line-pantograph systems for rail transit, in which:

[0026] (a) Geometric parameters include contact line height, pull-out value (B-Maβ), and pre-sag.

[0027] (b) Dynamic characteristics include contact forces (including static contact forces), aerodynamic forces, and frictional forces;

[0028] (c) Operational indicators include contact force fluctuation, overhead conductor rise and contact point height fluctuation.

[0029] Furthermore, the method can be extended to empirical tolerance verification and design optimization of mechanical structures, power equipment, aircraft structures, and electromechanical systems.

[0030] Furthermore, the analysis results can output an empirical tolerance rationality report, which includes the ranking of key parameters, performance change trends, rationality assessment conclusions, and optimization suggestions.

[0031] The beneficial effects of this invention are as follows:

[0032] (1) This invention proposes an analytical method for tolerance verification of railway electrification systems. Based on the idea of ​​combining digital simulation and physical measurement, it realizes data interaction and model mutual verification in virtual and real spaces. This method can quantitatively evaluate the performance differences of key components when they are outside or within the tolerance range, thereby verifying the rationality and effectiveness of the empirical tolerance range and providing a scientific basis for system maintenance and repair.

[0033] (2) This invention reveals the comprehensive influence of tolerances on contact force, energy consumption, component wear, and safety by establishing a multi-parameter correlation model in the electrical system. The results show that when some component parameters exceed the empirical tolerance range, the system performance will be affected to a certain extent; while when the parameters of each component are maintained within the reasonable tolerance range, energy efficiency optimization, loss reduction, and operational safety improvement can be achieved, thereby verifying the rationality and applicability of the existing tolerance standards.

[0034] (3) The theoretical verification framework proposed in this invention has good universality and scalability, and can be extended to other systems that rely on experience to set tolerances. This method not only provides a theoretical tolerance verification means for railway catenary systems, but also provides a quantitative analysis path for the subsequent formulation or optimization of other engineering tolerance standards, which has high engineering application value and promotion significance.

[0035] This invention addresses the limitations of traditional railway electrification and other complex systems where tolerances rely primarily on empirical judgment, making them ill-suited for high-speed development. It proposes a new paradigm for tolerance rationality verification based on data and model fusion. By establishing a dynamic simulation model of the overhead line and pantograph system and combining it with data analysis methods, system-level response analysis and interpretability assessment of the simulation results are achieved. This method can dynamically evaluate changes in contact force, lift, and energy consumption under different tolerance deviations, revealing the comprehensive impact trend of tolerances on operational quality. This provides a scientific and widely applicable basis for tolerance design and maintenance decisions for overhead lines and other complex engineering systems, significantly improving system safety, reliability, and design accuracy. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the analytical method for verifying the rationality of empirical tolerances in complex systems according to the present invention.

[0037] Figure 2 This is a schematic diagram comparing the changes in contact force, lift, and contact point height of a vehicle under static contact force conditions of 90N and 100N.

[0038] Figure 3 A schematic diagram comparing the lift distribution of a vehicle under static contact forces of 90N and 100N.

[0039] Figure 4 A schematic diagram comparing the contact force distribution of a vehicle under static contact force conditions of 90N and 100N;

[0040] Figure 5 This is a schematic diagram comparing the changes in contact force, lifting amount, and contact point height when the overhead contact line span is within and outside the tolerance range.

[0041] Figure 6 This is a schematic diagram showing the distribution of vehicle lift under varying overhead contact line span conditions.

[0042] Figure 7 This is a schematic diagram of the vehicle contact force distribution under varying overhead contact line span conditions. Detailed Implementation

[0043] The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments. The purpose and effects of the present invention will become clearer. It should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

[0044] like Figure 1 The present invention provides an analytical method for verifying the rationality of empirical tolerances in complex systems. This method is based on multiphysics dynamics modeling and numerical analysis theory, and comprehensively utilizes finite element analysis, multibody dynamics, and sensitivity assessment techniques to establish a quantitative mapping relationship between empirical tolerance parameters and system performance. This forms a generalizable empirical tolerance quantitative verification and optimization system, thereby achieving systematic theoretical verification and optimization of the rationality of empirical tolerances.

[0045] Through the system modeling and simulation calculation module of this invention, the parametric model is automatically generated by the geometric modeling tool and can be exported as an editable text file as shown in Table 1 to enable precise insertion and modification of tolerance parameters. This facilitates the analysis and comparison of system responses under different working conditions. This data is used to verify the correctness of the system model and provides basic data support for subsequent analysis of contact force distribution, contact point lift, and conductor elastic properties.

[0046]

[0047]

[0048] Table 1. System simulation output data table.

[0049] Based on the modeling and simulation results, multiple system models under different operating conditions were established. To explore the influence of various parameters on system performance, this invention compared and analyzed the operating characteristics of different models. Through data processing and visualization techniques, key operating indicators (including contact force, pantograph lifting, contact point height, contact force distribution, and lifting distribution) were systematically analyzed. During the data analysis, software tools based on scientific computing and engineering data visualization were used to statistically process and visualize the model output results, revealing the changing trends of the system's dynamic characteristics under different parameter configurations. The analysis results are as follows: Figures 2 to 7 As shown, the response characteristics and distribution patterns of each key parameter under different model conditions are presented, providing a basis for subsequent system optimization and parameter calibration.

[0050] In the data visualization process, statistical distribution graphs such as violin plots and box plots were used. Violin plots combine the statistical characteristics of box plots with the probability distribution information of kernel density estimation, and can simultaneously show the central tendency and overall distribution pattern of the data; while box plots, by displaying the quartiles, median, and outliers of the data, intuitively reflect the dispersion and distribution range of the data.

[0051] By combining these two types of statistical graphs, this invention enables quantitative and visual analysis of the distribution patterns, central tendency, and abnormal deviations of operating characteristics under different working conditions, providing reliable statistical basis and graphical support for evaluating the impact of tolerance changes on system performance.

[0052] Figure 2 The comparison results are shown for static contact forces of 90N and 100N. The results indicate that the trends of contact force curves, pantograph lifting, and contact point height under different contact forces are basically consistent, with only an overall translational shift. However, this shift can cause some local problems. As the static contact force increases, the contact point height rises significantly, which may cause problems at constrained points (such as turnout areas). In this system, the contact line at the branch rail intersection is designed to be 40mm higher than the main rail contact line. As the static contact force increases, the relative height between the contact line at the branch rail intersection and the main rail shifts, making it difficult to maintain the original 40mm difference. Furthermore, although the elasticity varies in different sections of the track, it remains essentially constant when the contact force changes in a specific section; therefore, the following formula can be used for calculation:

[0053] y stat =F0*e

[0054] Among them, y stat—Static lift, F0—Static contact force, e—Contact line elasticity coefficient.

[0055] In this section, the pantograph lift increases approximately linearly with the increase of contact force. Figure 2 This demonstrates the pattern intuitively and verifies the rationality of the theoretical analysis.

[0056] Figure 3 The two pantograph rise distribution diagrams shown exhibit a consistent overall trend, with only slight deviations. According to the parameter comparison results in Table 2, both rise distributions are within the design tolerance range. With increasing static contact force, the pantograph rise shows a significant upward trend. This additional rise can be adjusted by adjusting the compensation length of the compensation section. However, when the system is simultaneously affected by, for example, significant temperature fluctuations, the requirement for the compensation length will further increase, leading to a significant increase in system risk.

[0057]

[0058] Table 2. Vertical lifting range of contact points in actual lines.

[0059] Furthermore, increased lift also affects the contact wire overlap area. Under otherwise identical conditions, increased lift leads to a longer overlap area, resulting in additional wear between the pantograph contactor and the contact wire, and increased energy loss.

[0060] Figure 4 The two contact force distribution diagrams shown have similar overall trends, with only slight differences in translation. According to the results in Table 3, both sets of contact force distributions are within the tolerance range.

[0061]

[0062]

[0063] Table 3. Requirements for contact force and fluctuation range of railway overhead power transmission network.

[0064] Figure 5 The comparison results show that the pantograph rise fluctuation increases significantly when the contact wire span is within and outside the tolerance range. The results indicate that the pantograph rise fluctuation increases significantly when the span exceeds the tolerance. The elasticity varies in different sections of the line, as shown in the formula:

[0065]

[0066] e—elastic coefficient (mm / N): represents the vertical displacement of the contact line under a unit force, used to characterize the compliance of the system.

[0067] l—Span (m): The horizontal distance between adjacent support points of the contact wire.

[0068] k—Elasticity factor: 4.0 when there is no Y-type auxiliary cable and 3.5 when there is a Y-type auxiliary cable. It is used to calculate the elastic characteristics of the contact wire system.

[0069] H FD —Contact wire tension (kN): The tension of the contact wire.

[0070] H TS — Cable tension (kN): The tension of the supporting cable.

[0071] As the span increases, the elastic coefficient *e* also increases, and vice versa. The contact force distribution is shown in the figure; the overall trends are similar in both cases, therefore the change in contact force can be ignored. According to the formula, the lift increases when elasticity increases, and the lift decreases when elasticity decreases. Figure 5 The curve variation conforms to this theory. When the span exceeds the tolerance, the deviation of the lift curve is greater. The contact point height is too high at some locations, which may cause operational problems in the presence of constraint points; simultaneously, the contact point height is lower than the minimum height within the tolerance range at some locations, but the impact is negligible in this model because the minimum contact point height remains relatively high (>5.58m). The contact force is set to 90N in the model, which is the maximum value within the tolerance range (60N–90N), thus resulting in an overall higher contact line height.

[0072] Figure 6 The study demonstrates the difference in uplift distribution between spans within and outside the tolerance range. The average uplift is essentially the same in both groups, but the uplift distribution is more concentrated within the tolerance range, consistent with theoretical expectations. According to Table 2, both uplift distributions are within the allowable tolerance range. The results indicate that uplift increases significantly with increasing system elasticity, and its influencing mechanism is related to… Figure 3 Similar to the description above. For this model, due to the large statistical value of the contact force, the effect of reduced lift is not significant; however, under conditions of low contact force, reduced lift may have a negative impact on the system. Specifically, reduced lift leads to a smaller overlap area between the pantograph and the contact wire, thereby reducing the transition zone length. An excessively small overlap area may result in insufficient contact between the pantograph and the contact wire, causing current interruption or train power supply interruption. The overlap area plays a crucial role in maintaining a stable electrical connection; too small an overlap area can cause voltage fluctuations, affecting the reliability of the electrical system. Furthermore, a reduction in lift may cause the chain structure to sink, especially in bridge sections, as bridge structures are more sensitive to vertical movement. Chain sinking will impose additional loads on the bridge structure, increase component wear, and affect structural integrity.

[0073] Figure 7The two contact force distribution diagrams shown exhibit similar overall trends. According to the results in Table 3, both sets of contact force distributions are within the allowable tolerance range. Variations in the longitudinal span have almost no effect on the contact force.

[0074] Using the methods described above, the influence characteristics of changes in other parameters (such as pull-out value B-Maβ, pre-sag, and contact wire wear) can also be analyzed, which will not be listed here. Furthermore, the coupling effect of various factors and their comprehensive impact on system performance can be studied through multi-parameter linkage adjustment. The results of this study further verify the rationality and importance of tolerance range setting. Almost all system components, when exceeding tolerance ranges, negatively impact the mechanical stability and power supply performance of the electrification system. The introduction of tolerance design has significant advantages: it not only simplifies maintenance and repair processes but also effectively reduces energy loss, improves transmission efficiency, and enhances operational safety. It is worth noting that the study found that even if a single or a small number of component parameters exceed tolerance ranges, the train can still maintain normal operation in the short term, and the main operating indicators remain within the allowable range, but energy loss and structural wear will increase. When multiple factors deviate simultaneously (e.g., when contact wire wear is large and static contact force is small), even if each remains within tolerance range, the cumulative effect on system operation often exceeds the effect of a single factor exceeding tolerance range.

[0075] For example, in the modeling and analysis of this system, the static contact force is set to 90N, which is the upper limit of the tolerance range (60N to 90N). This setting amplifies the effects of some components (such as contact line wear), and even if the wear rate is within the tolerance range of 10% to 20%, the contact point height still shows a significant upward trend. At the same time, this setting also partially offsets the adverse effects of deviations in other parameters (such as longitudinal span). Figure 5 As shown, even when the longitudinal span exceeds the tolerance range, the minimum height of the contact point remains above 5.50m. Based on different input models and parameter sensitivity analysis results, machine learning methods can be used to establish mathematical models to quantitatively describe the influence of each component parameter on mechanical response and energy consumption performance. Therefore, tolerance distribution and design standards can be adaptively optimized for different line conditions and operating environments. Furthermore, the various statistical characteristic value calculation methods shown in Table 4 can also be extended to other electromechanical systems for verifying the tolerance rationality and robustness of complex systems, providing theoretical support for the design and maintenance of highly reliable electromechanical equipment.

[0076]

[0077] Table 4. Statistical characteristics of contact force distribution under different static contact force conditions.

Claims

1. An analytical method for verifying the rationality of empirical tolerances in complex systems, characterized in that, Based on multiphysics dynamics modeling and numerical analysis theory, and by comprehensively utilizing finite element analysis, multibody dynamics, and sensitivity assessment techniques, the correlation between empirical tolerance parameters and system performance is established. This includes the following steps: (1) Establish a parametric model: Based on the structural characteristics and operating mechanism of the target complex system, a parametric model containing geometric parameters, material parameters and boundary constraints is constructed, and key empirical tolerances are embedded into the model as variables. (2) Construct a multiphysics dynamics simulation model: The parameterized model is solved by finite element analysis or multibody dynamics analysis to obtain the response characteristics of the complex system under different tolerance combinations. (3) Import operating condition boundary conditions: Based on the actual operating scenario, input loads, speeds, environmental parameters, and boundary constraints are used to generate a simulation input dataset that can be used for dynamic analysis. (4) Extraction of operational quality and performance indicators: Extract key indicators characterizing system performance stability or operational quality from simulation results; (5) Data-driven correlation analysis: Post-processing of simulation results is performed to analyze the variation patterns of system performance indicators under different tolerance parameters; statistical analysis and trend identification of simulation sample data are used to reveal the main influence direction and sensitivity of various factors and their combinations on system performance. (6) Verification and optimization of the rationality of empirical tolerances: Based on the allowable limits given in industry standards or design specifications, the performance indicators under different tolerance combinations are compared to evaluate the rationality of the empirical tolerance setting, and optimization suggestions and correction ranges are output based on the analysis results.

2. The analytical method for verifying the rationality of empirical tolerances in complex systems according to claim 1, characterized in that, In step (1), the key empirical tolerances include positional deviations, structural constraint deviations, material property deviations, or assembly errors.

3. The analytical method for verifying the rationality of empirical tolerances in complex systems according to claim 1, characterized in that, The parametric model in step (1) is automatically generated by a geometric modeling tool and can be exported as an editable text file to enable precise insertion and modification of tolerance parameters.

4. The analytical method for verifying the rationality of empirical tolerances in complex systems according to claim 1, characterized in that, In step (2), the response characteristics include mechanical response and can be extended to electrical response, thermal characteristics and energy transfer characteristics.

5. The analytical method for verifying the rationality of empirical tolerances in complex systems according to claim 1, characterized in that, In step (2), when using the finite element method coupled with multibody dynamics for modeling, structural flexibility, nonlinear contact and kinematic constraints are considered simultaneously.

6. The analytical method for verifying the rationality of empirical tolerances in complex systems according to claim 1, characterized in that, The operating conditions described in step (3) are input based on actual measurements or standard operating conditions, including operating speed, conductor tension, ambient temperature and structural constraints.

7. The analytical method for verifying the rationality of empirical tolerances in complex systems according to claim 1, characterized in that, In step (4), the performance indicators include contact force, the lifting amount of the overhead conductor and the height of the contact point, and can be extended to stress distribution, vibration response or energy transfer characteristics in other complex systems. The distribution characteristics of the performance indicators are described and compared by statistical visualization through violin diagrams or box plots, so as to achieve quantitative analysis of system performance under different tolerance conditions.

8. The analytical method for verifying the rationality of empirical tolerances in complex systems according to claim 1, characterized in that, The data-driven analysis in step (5) uses computer algorithms to post-process and statistically analyze the simulation results. By identifying the correlation and sensitivity between different tolerance parameters and system performance indicators, it reveals the main influence of parameter changes on system performance, which is used to support the theoretical verification and optimization of the rationality of empirical tolerances.

9. The analytical method for verifying the rationality of empirical tolerances in complex systems according to claim 1, characterized in that, The analysis results can output an empirical tolerance rationality report, which includes the ranking of key parameters, performance change trends, rationality assessment conclusions, and optimization suggestions.

10. The application of the analytical method for verifying the rationality of empirical tolerances in complex systems according to any one of claims 1-9, characterized in that, Applications in overhead contact line-pantograph systems for rail transit (a) Geometric parameters include contact line height, pull-out value (B-Maß), and pre-sag; (b) Dynamic characteristics include contact forces (including static contact forces), aerodynamic forces, and frictional forces; (c) Operational indicators include contact force fluctuation, overhead conductor uplift, and contact point height fluctuation; It can be extended to the verification of empirical tolerances and design optimization of mechanical structures, power equipment, aircraft structures and electromechanical systems.

Images