Electric wire and cable residual life evaluation method based on Arrhenius model extrapolation
By inversely deriving the initial elongation at break from accelerated aging data of in-service cables and using the Arrhenius model extrapolation method, the problem of obtaining the initial elongation at break in cable life assessment is solved, enabling more accurate prediction of remaining life and improving the safety of locomotive operation.
Patent Information
- Application Number
- CN202511638582.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-10
- Publication Date
- 2026-02-10
AI Technical Summary
In existing technologies, it is difficult to accurately obtain the initial elongation at break of wires and cables that have been in operation for more than twelve years. This leads to inaccurate life assessment results based on the Arrhenius model, which may result in an overestimation of the cable's remaining life and affect locomotive safety.
By using accelerated aging data of in-service cables, the initial elongation at break is derived in reverse. The Arrhenius model extrapolation method is used to correct the life assessment results. This includes sample preparation, initial life endpoint setting, multi-temperature accelerated aging test, initial elongation at break extrapolation, and life correction steps, to establish a more reliable life endpoint.
This enables more accurate and reliable assessment of the remaining life of wires and cables, avoiding optimistic estimates caused by the use of degraded data and improving the safety of locomotive operation.
Smart Images
Figure CN121503040A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of material life prediction technology, and in particular to a method for assessing the remaining life of in-service wires and cables based on Arrhenius model extrapolation. Background Technology
[0002] As the neural network for power transmission and control in locomotives, the insulation condition of electrical wires and cables directly affects driving safety and operational reliability. Typically, the design life of these products is between 20 and 40 years. When a Harmony-type locomotive enters its C6 overhaul, it has accumulated approximately 12 years of operation. Under the combined effects of long-term and complex electrical stress, thermal cycling, mechanical vibration, and environmental factors, the aging effect of the insulation material in the electrical wires and cables continues to accumulate, potentially entering a critical window period where slow degradation is transitioning to accelerated deterioration. At this stage, accurately predicting the remaining service life of the cables has become a core requirement for developing scientific maintenance strategies, preventing operational failures, and ensuring the locomotive's success in the next operating cycle.
[0003] The Arrhenius accelerated thermal aging model, a well-established theory, aims to accurately capture the degradation trajectory of the elongation at break of insulating materials over aging time through laboratory simulation and data extrapolation. This allows for the development of a method for predicting and assessing the remaining life of in-service locomotive wires and cables, thereby enabling a scientific prediction of the remaining life of wires and cables.
[0004] A core prerequisite for the accuracy of life assessment based on the Arrhenius model is the correct determination of the end of the cable's life. Current standards generally use "elongation at break retention rate less than 50% of the initial value" as the criterion, which means that the initial elongation at break of the cable must be accurately known.
[0005] However, obtaining accurate and reliable initial elongation at break (EBF) for C6-grade cables that have been in continuous operation for over twelve years presents significant challenges. First, original data is lacking: due to the long operating period, original factory test data is often unverifiable. Second, inventory samples are difficult to obtain or have degraded performance: unused cables manufactured during the same period twelve years ago are hard to find. Even if unused inventory cables from the same period can be found, their performance has changed due to twelve years of storage, making them unreliable as they could not truly represent the initial state. Third, product iteration differences exist: newly manufactured cables, due to upgraded standards or optimized processes, no longer perform equivalently to products from twelve years ago. Therefore, the true initial EBF of the cable is practically impossible to obtain directly.
[0006] To address this issue, existing technologies typically employ a compromise: using the currently measured elongation at break of the cable already in operation as its initial elongation at break, and calculating the remaining lifespan as 50% of this elongation at break retention rate. However, cables that have been in operation for twelve years typically exhibit performance degradation compared to new cables. Using this degraded value as a benchmark artificially lowers the endpoint of lifespan assessment, leading to an overestimation of remaining lifespan. This optimistic assessment could result in the continued use of degraded cables, posing a potential hazard to the safe operation of locomotives. Summary of the Invention
[0007] The technical problem to be solved by the present invention is to provide a method for assessing the remaining life of wires and cables based on the Arrhenius model extrapolation. Based on the Arrhenius model, the initial elongation at break of the wires and cables is derived through laboratory simulation and data extrapolation. The derived initial elongation at break is used to correct the model, making the life assessment results more reliable.
[0008] To solve the above-mentioned technical problems, the technical solution of the present invention is: a method for assessing the remaining life of wires and cables based on Arrhenius model extrapolation, characterized by comprising the following sequential steps: S1. Sample preparation: Obtain in-service wire and cable samples and prepare test specimens for aging tests; S2. Preliminary life end point setting: Measure the current elongation at break ELc6 of the specimen and set it as the temporary initial elongation at break, and set a temporary life end point based on the temporary initial elongation at break; S3. Preliminary test to determine aging temperature: By conducting preliminary accelerated aging tests at one or more temperatures, a set of temperature points for the formal accelerated aging test is determined according to predetermined rules; S4. Accelerated aging test at multiple temperatures: The sample is subjected to accelerated thermal aging at a set of temperature points, and samples are taken periodically to measure the elongation at break, so as to obtain multiple sets of data on the change of elongation at break with aging time at different temperatures. S5. Preliminary lifetime estimation: Based on the provisional lifetime endpoint and the multiple sets of data, the preliminary remaining lifetime at the operating temperature is obtained by extrapolation using the Arrhenius model; S6. Extrapolation of initial elongation at break: Based on the data obtained in the multi-temperature accelerated aging test steps, the theoretical initial elongation at break EL0 of the in-service wire and cable is derived by curve fitting and equivalent aging time calculation. S7. Life correction: The final life endpoint is reset based on the theoretical initial elongation at break EL0, and the final remaining life at the operating temperature is obtained by extrapolation using the multiple sets of data through the Arrhenius model.
[0009] As an improvement, the initial elongation at break extrapolation step specifically includes: a) From the multiple sets of data, select the elongation at break-time data at an accelerated aging temperature that is closest to the actual operating temperature of the cable; b) Perform curve fitting on the selected data to establish a functional relationship between elongation at break and aging time, y=f(t); c) Convert the total operating time of the cable into an equivalent aging time at the temperature selected in step a) using the Arrhenius model; d) Substitute the equivalent aging time into the functional relationship y=f(t) to calculate the theoretical initial elongation at break EL0.
[0010] As an improvement, in step b), the functional relationship y=f(t) is a fitted curve in the form of an exponential function, a logarithmic function, or a power function.
[0011] As an improvement, the functional relationship y=f(t) is: .
[0012] As an improvement, in the preliminary test to determine the aging temperature step, the predetermined rules include: the highest exposure temperature should make the measured endpoint average time greater than 100 hours, the lowest exposure temperature should make the measured endpoint average time greater than 5000 hours, and the extrapolation for determining the heat resistance index should not exceed 25K.
[0013] As an improvement, in the initial life end setting step and the life correction step, the set life end is a 50% retention rate of the corresponding initial elongation at break.
[0014] As an improvement, in the multi-temperature accelerated aging test step, the set of temperature points includes at least three different temperatures.
[0015] As an improvement, in the sample preparation step, the test specimen includes an aging test strip made from the insulation or sheath layer cut from the cable, and a standard dumbbell-shaped specimen cut from the aging test strip.
[0016] As an improvement, the in-service wires and cables are those used in locomotives and rolling stock that have been in operation for more than ten years.
[0017] The beneficial effects of this invention compared to the prior art are: This invention uses the innovative approach of "model extrapolation and inversion" to reverse-engineer the theoretical initial value of in-service cables by utilizing the accelerated aging data of in-service cables themselves, thus fundamentally solving the core pain point of "no benchmark" in the life assessment of in-service equipment. The assessment results are more accurate and reliable: By revising the initial baseline, the optimistic estimates brought about by directly using the degraded data are avoided, making the remaining life prediction more conservative and accurate, and significantly improving the safety margin of locomotive operation. Attached Figure Description
[0018] Figure 1 This is a flowchart of the present invention.
[0019] Figure 2 This is a schematic diagram of the aging test strip.
[0020] Figure 3 The graph shows the relationship between aging time and elongation at break for sample A.
[0021] Figure 4 This is a preliminary remaining lifespan forecast curve.
[0022] Figure 5 This is a fitted curve.
[0023] Figure 6 A schematic diagram to determine the life end point of insulation at various test temperatures.
[0024] Figure 7 Refit the lifetime curve. Detailed Implementation
[0025] The present invention will now be further described with reference to the accompanying drawings.
[0026] like Figure 1 As shown, a method for assessing the remaining life of wires and cables based on Arrhenius model extrapolation includes the following steps:
[0027] (1) Sample preparation like Figure 2 As shown, a C6 repair sample cable was selected. After the sheath and insulation layer were cut from the finished cable, they were cut into aging test strips for aging tests. During the aging test, at different time points, one set of test strips was selected and cut into dumbbell-shaped specimens for elongation at break tests. Usually, each exposure temperature consists of at least 11 aging test strips, and it is appropriate to cut one set of aging test strips into 5 dumbbell specimens. To ensure the test results, generally 7 dumbbell specimens are made for each aging test strip.
[0028] (2) Performance testing and selection of preliminary life end point Sample C6 was selected, and its elongation at break was tested according to EN 60811-501 "Cables and optical fibers—Test methods for nonmetallic materials—Part 501: Mechanical tests—Measurement of mechanical properties of insulation and sheath compounds" and GB / T 2951.11 "General test methods for insulation and sheath materials of cables and optical fibers—Part 11: General test methods—Measurement of thickness and dimensions—Mechanical properties tests". Since the initial elongation at break of the cable was unknown, the elongation at break measured for sample C6 was temporarily taken as the initial elongation at break, and a retention rate of less than 50% of the elongation at break was set as the end point for subsequent accelerated aging tests. Taking sample A of cable C6 as an example, its directly measured elongation at break ELc6 = 150%, the initial elongation at break EL0, and the end point for the lifespan 0.5EL0. When EL0 was unknown, EL0 = ELc6 = 150%, and the end point for the lifespan 0.5ELc6 = 75% was set for accelerated aging tests.
[0029]
[0030] (3) Preliminary test According to the temperature determination requirements of GB / T 11026.1 "Heat Resistance of Electrical Insulation Materials - Part 1: Aging Procedure and Evaluation of Test Results", and considering the types of raw materials for various wire and cable models, as well as practical experience, preliminary aging test temperature points were selected for a preliminary test lasting approximately one week. Through analysis of at least four sets of data, four temperature values for the accelerated aging test were determined. According to GB / T 11026.1 "Heat Resistance of Electrical Insulation Materials - Part 1: Aging Procedure and Evaluation of Test Results", to reduce uncertainties in calculating the corresponding heat resistance characteristic parameters, the following requirements should be noted: a) When determining the temperature in Celsius (TI) at which the heat resistance relationship is derived over a time of 20,000 h (or other specified time), the minimum exposure temperature should be such that the average or median time to the measured endpoint is greater than 5,000 h. b) Extrapolations performed to determine TI should not exceed 25K; c) The highest exposure temperature should be the average or median of the measurable endpoints greater than 100 h (or less than 500 h if possible). d) If the time is shorter than the specified time, the corresponding time may need to be reduced by the same proportion if necessary.
[0031] Taking cable A as an example, its insulation material is irradiated with cross-linked polyolefin. Based on material properties and experience, a preliminary test was conducted at 180℃. The test results are as follows:
[0032] As can be seen, in the initial preliminary test, the elongation at break retention rate was only 32% after 72 hours, and dropped to 0% after 96 hours, failing to meet requirement c) above. A second preliminary test was conducted by lowering the temperature by 5℃. The test results are as follows:
[0033] The second preliminary test met the requirements, and based on this, the four temperature groups were determined as follows:
[0034] (4) Accelerated aging test and tensile test The prepared aging test strips were placed in four aging test chambers at different temperatures. According to GB / T 11026.1 "Heat Resistance of Electrical Insulation Materials - Part 1: Aging Procedures and Evaluation of Test Results", at regular intervals, one set of aging test strips was taken out and cut into dumbbell specimens for tensile testing, and the elongation at break of the specimens was measured.
[0035] The test results for sample A are as follows:
[0036] (5) Initial lifetime estimation like Figure 3 As shown, a graph showing the relationship between aging time and elongation at break is plotted based on the test results of sample A.
[0037] The Arrhenius model is a chemical reaction kinetics model in which the relationship between temperature and chemical reaction rate can be expressed by the Arrhenius equation: (1)
[0038] In the formula: K—Reaction rate constant; A0 — is the pre-exponential factor; Ea – Activation energy, measured in kJ / mol; R—gas constant; T—Thermodynamic temperature, measured in K.
[0039] After a series of mathematical transformations, it finally becomes: (2)
[0040] In the formula: τ—Expected lifespan of cable insulation material under thermal aging; T—the aging temperature of the cable insulation material; a — a constant related to the failure performance; b is a constant related to the activation energy.
[0041] like Figure 4 As shown, when the elongation at break retention rate is 50%, the endpoint time at each temperature is determined, and the life curve is fitted with four endpoint times. Finally, the remaining life at 90℃ is 21.3 years.
[0042] (6) Extrapolation of initial elongation at break Because using the elongation at break measured from the C6 sample as the initial elongation at break introduces a certain bias, model extrapolation is used here to determine the initial elongation at break to correct for remaining life. Typically, remaining life estimation assesses the cable's remaining life at 90℃. Accelerated life tests are conducted at four temperature points: 175℃, 165℃, 150℃, and 135℃, measuring the elongation at break. To minimize the impact of additional aging mechanisms introduced by high temperatures, the accelerated aging data closest to 90℃ (i.e., the accelerated aging data at 135℃) is selected as the extrapolation benchmark. Figure 5 As shown, by curve fitting the elongation at break measured at 135℃, the fitted curve equation is obtained as follows: .
[0043] Under normal circumstances, the operating temperature of high-voltage cables is between 50-70℃. Assuming the operating temperature is 60℃, the aging time of twelve years is equivalent to 135℃ using the Arrhenius model, which is 1190.4 days. Substituting this into the above formula, the initial elongation at break is 299.42%.
[0044] (7) Lifetime correction like Figure 6 As shown, 50% of this initial elongation at break is equivalent to the elongation at break of C6, and the life end is calculated to be 53.4% of the original model.
[0045] like Figure 7 As shown, based on this end of the lifespan, the lifespan curve was refitted, and the final remaining lifespan was 12.4 years.
Claims
1. A method for assessing the remaining life of wires and cables based on Arrhenius model extrapolation, characterized in that, Includes the following sequential steps: S1. Sample preparation: Obtain in-service wire and cable samples and prepare test specimens for aging tests; S2. Preliminary life end point setting: Measure the current elongation at break ELc6 of the specimen and set it as the temporary initial elongation at break, and set a temporary life end point based on the temporary initial elongation at break; S3. Preliminary test to determine aging temperature: By conducting preliminary accelerated aging tests at one or more temperatures, a set of temperature points for the formal accelerated aging test is determined according to predetermined rules; S4. Accelerated aging test at multiple temperatures: The sample is subjected to accelerated thermal aging at a set of temperature points, and samples are taken periodically to measure the elongation at break, so as to obtain multiple sets of data on the change of elongation at break with aging time at different temperatures. S5. Preliminary lifetime estimation: Based on the provisional lifetime endpoint and the multiple sets of data, the preliminary remaining lifetime at the operating temperature is obtained by extrapolation using the Arrhenius model; S6. Extrapolation of initial elongation at break: Based on the data obtained in the multi-temperature accelerated aging test steps, the theoretical initial elongation at break EL0 of the in-service wire and cable is derived by curve fitting and equivalent aging time calculation. S7. Life correction: The final life endpoint is reset based on the theoretical initial elongation at break EL0, and the final remaining life at the operating temperature is obtained by extrapolation using the multiple sets of data through the Arrhenius model.
2. The method for assessing the remaining life of wires and cables based on Arrhenius model extrapolation according to claim 1, characterized in that, The initial elongation at break extrapolation step specifically includes: a) From the multiple sets of data, select the elongation at break-time data at an accelerated aging temperature that is closest to the actual operating temperature of the cable; b) Perform curve fitting on the selected data to establish a functional relationship between elongation at break and aging time, y=f(t); c) Convert the total operating time of the cable into an equivalent aging time at the temperature selected in step a) using the Arrhenius model; d) Substitute the equivalent aging time into the functional relationship y=f(t) to calculate the theoretical initial elongation at break EL0.
3. The method for assessing the remaining life of wires and cables based on Arrhenius model extrapolation according to claim 2, characterized in that, In step b), the functional relationship y=f(t) is a fitted curve in the form of an exponential function, a logarithmic function, or a power function.
4. The method for assessing the remaining life of wires and cables based on Arrhenius model extrapolation according to claim 3, characterized in that, The functional relationship y=f(t) is: 。 5. The method for assessing the remaining life of wires and cables based on Arrhenius model extrapolation according to claim 1, characterized in that, In the preliminary test to determine the aging temperature step, the predetermined rules include: the highest exposure temperature should make the measured average time to the endpoint greater than 100 hours, the lowest exposure temperature should make the measured average time to the endpoint greater than 5000 hours, and the extrapolation made to determine the heat resistance index should not be greater than 25K.
6. The method for assessing the remaining life of wires and cables based on Arrhenius model extrapolation according to claim 1, characterized in that, In both the initial life end setting step and the life correction step, the set life end is a 50% retention rate of the corresponding initial elongation at break.
7. The method for assessing the remaining life of wires and cables based on Arrhenius model extrapolation according to claim 1, characterized in that, In the multi-temperature accelerated aging test step, the set of temperature points includes at least three different temperatures.
8. The method for assessing the remaining life of wires and cables based on Arrhenius model extrapolation according to claim 1, characterized in that, In the sample preparation step, the test specimen includes an aging test strip made from the insulation or sheath layer cut from the cable, and a standard dumbbell-shaped specimen cut from the aging test strip.
9. The method for assessing the remaining life of wires and cables based on Arrhenius model extrapolation according to claim 1, characterized in that, The in-service wires and cables are those used in locomotives and rolling stock that have been in operation for more than ten years.