A method for predicting the service life of a sprocket based on an S-N curve

Abstract

This invention belongs to the field of sprocket life prediction, specifically involving a method for predicting sprocket life based on the S-N curve. The method first collects tooth root strain data of the sprocket under two sets of different test loads, logarithmically transforms the S-N power function into a linear equation, substitutes the data to solve for parameters, and then calculates the internal stress under the operating load using stress formulas. Finally, it substitutes this data into the S-N curve to obtain the sprocket life. Simultaneously, the coefficient m can be calculated using relevant formulas to estimate the life enhancement factor of the improved sprocket. The scheme also optimizes the strain gauge arrangement, setting measurement points in the tooth root groove, arranging strain gauges on multiple teeth, and performing data noise reduction. The test loading process is standardized to ensure stable and reliable data. This method is simple to calculate, has high prediction accuracy, and can provide reliable support for sprocket design optimization and maintenance, with strong engineering applicability.

Description

Technical Field

[0001] This invention belongs to the field of sprocket life prediction, specifically relating to a method for predicting sprocket life based on the SN curve. Background Technology

[0002] As a core actuator in continuous transmission systems, sprockets play a crucial role in power transmission in industrial equipment, construction machinery, and transportation. During long-term continuous operation, sprockets are constantly subjected to cyclic loads. The tooth root, as a core area of ​​stress concentration, is highly susceptible to fatigue damage due to repeated alternating stresses. This leads to the gradual formation and propagation of microcracks, ultimately resulting in tooth root fracture and failure. Such failure not only causes sudden shutdowns of the transmission system, leading to production interruptions and equipment damage, but also directly threatens the operational safety of the entire transmission system, significantly shortening its overall service life and causing substantial economic losses and safety hazards to industrial production and equipment maintenance.

[0003] Currently, life assessment of sprocket drive systems in the industry mainly relies on traditional theoretical calculation methods or hypothetical models based on static loads. These assessment methods do not fully reflect the actual working conditions of sprockets, cannot accurately capture the real-time fluctuations of dynamic loads, and are difficult to quantify the local stress concentration effects in key areas such as the tooth root. Since dynamic load changes and meshing impacts during actual transmission significantly affect the stress distribution of sprockets, the neglect of these key influencing factors by traditional methods leads to a large deviation between the life prediction results and the actual service life of the sprockets. This fails to provide reliable theoretical support for sprocket design optimization and maintenance decisions, and also makes it difficult to meet the application requirements of modern industrial fields for high reliability and long service life of transmission systems. Summary of the Invention

[0004] The method for predicting sprocket life based on SN curves provided by this invention can effectively solve the problems existing in the background art.

[0005] This invention provides a method for predicting sprocket life based on SN curves, comprising the following steps:

[0006] Strain data of the sprocket under test were collected under two different test loads.

[0007] Taking the logarithm of both sides of the SN power function for the same material of the sprocket under test, and rearranging it into a linear function, we obtain... ,in For load, The slope The intercept is... ;

[0008] Substitute the two sets of loads and corresponding strain data of the sprocket under test into the linear function equation to solve;

[0009] Substitute the operating load of the sprocket under test into the solved linear function, and then use the stress formula to obtain the internal stress of the operating load. The stress formula is as follows: , of which elastic modulus, is Magnitude of strain This is a correction factor;

[0010] Substituting the obtained stress into the SN curve, the life of the sprocket under test under operating load is obtained.

[0011] As a further optimization of the present invention, the method for collecting strain data of the sprocket under test working under two different test loads includes:

[0012] The strain gauge is attached to the root of the tooth surface of the sprocket to be tested;

[0013] The sprocket to be tested is mounted on the drive shaft or driven shaft of the sprocket-driven lifting test bench;

[0014] Add a test load to the lifting test platform and control the lifting test platform to complete the lifting cycle action;

[0015] Strain data was collected during the lifting and lowering cycle of the test platform using strain gauges.

[0016] As a further optimization of the present invention, a groove is provided at the root of the tooth surface of the sprocket to be tested, and the strain gauge is disposed in the groove.

[0017] As a further optimization of the present invention, the sprocket to be tested has several tooth profiles, and strain gauges are provided for each tooth profile.

[0018] As a further optimization of the present invention, a step of noise reduction processing is also included for the data acquired by the strain gauge.

[0019] As a further optimization of the present invention, the two sets of loads on the lifting test platform are applied repeatedly for no less than 3 times, each lasting for no less than 30 seconds. Before changing the load, the load is unloaded to no load and held for no less than 60 seconds.

[0020] As a further optimization of the present invention, the two sets of loads are 250kg and 500kg respectively, and b=1.322 and a=0.2705 are obtained. .

[0021] As a further optimization of the present invention, a method for predicting the improved sprocket life magnification factor is also included, comprising the following steps:

[0022] according to The coefficient m is obtained, where This represents the magnitude of the internal stress of the original sprocket under operating load. The lifespan of the original sprocket, obtained from the SN curve under operating load, is given. This represents the magnitude of the internal stress on the original sprocket under the test load. This is the value taken when the original sprocket has an infinite lifespan under the test load. ;

[0023] Seek .

[0024] This invention combines two sets of load-strain data with logarithmic processing of the SN curve, resulting in simple calculations and high accuracy. The strain gauges attached to the tooth root groove provide stable and reliable data acquisition. The multi-tooth arrangement and noise reduction further improve data accuracy. The standardized loading process ensures test repeatability and can also quickly predict the lifespan improvement, making it highly practical for engineering applications.

[0025] This invention provides a method for predicting sprocket life based on SN curves. By acquiring strain data of the sprocket under two sets of loads and combining the logarithmic processing of the SN curves, the relationship between sprocket stress and life is accurately obtained, and the life of the sprocket under the operating load is predicted.

[0026] This invention also improves measurement accuracy and efficiency by adding grooves to the sprocket, using multiple toothed measuring points, and reducing data noise; it adopts a standardized load loading process, resulting in good repeatability; and it can quickly estimate the lifespan amplification factor after the improvement, providing intuitive data support for sprocket structure optimization and lifespan improvement, making it highly practical. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of the method flow in this embodiment;

[0028] Figure 2 This is a schematic diagram of the strain gauge bonding position in this embodiment.

[0029] Figure 3 It is the SN curve of pa66. Detailed Implementation

[0030] like Figure 1-3 As shown, this embodiment utilizes a comprehensive technical solution encompassing strain acquisition, stress conversion, curve fitting, and life calculation to accurately predict the service life of sprockets. It also allows for a quantitative evaluation of the life-saving effect of structural improvements. This method features strong testing stability and excellent data repeatability, providing a scientifically reliable experimental basis for sprocket optimization design. It can be widely applied to life assessment and structural improvement of sprocket components in industrial transmission systems.

[0031] This embodiment specifically includes the following steps:

[0032] The first step is the measurement point setup, which uses high-precision resistance strain gauges as the core sensing element. During actual service, due to the force characteristics of meshing transmission, the sprocket's fatigue failure mode mainly manifests as bending fatigue. Through finite element simulation analysis and preliminary experimental verification, it was determined that the maximum stress area is concentrated at the tooth root. This area is prone to stress concentration under cyclic loading, making it a key location for the initiation and propagation of fatigue cracks.

[0033] It is particularly important to note that the working principle of strain gauges is based on the deformation sensing of metal foil. If directly subjected to tensile and compressive stress concentration, it can easily lead to damage to the sensing element or distortion of measurement data. Furthermore, relative sliding friction will occur on the tooth surfaces during meshing, which cannot meet the requirements for proper adhesion and installation of the strain gauge. Therefore, in this embodiment, the strain gauge is precisely attached to the root of the tooth surface of the sprocket to be measured. Figure 2 As shown, the red dashed box indicates the attachment position of the strain gauge in the actual test. The strain gauge is strictly located on the center line of the tooth to be tested. This position can capture the real strain signal of the tooth root bending deformation to the greatest extent, while avoiding mechanical interference during the meshing process.

[0034] To further improve measurement stability and strain gauge fit, this embodiment pre-machines a special groove at the root of the sprocket teeth. The size of the groove precisely matches the shape of the strain gauge, ensuring that the strain gauge is completely embedded in the groove, avoiding frictional damage during meshing, and ensuring that the structural mechanical properties of the tooth root area are not significantly affected. After the strain gauge is installed in the groove, it is fixed using a special strain gauge adhesive. During the bonding process, the coating thickness is strictly controlled to ensure uniformity and avoid air bubbles. After bonding, a 24-hour constant temperature curing treatment is performed to ensure a strong mechanical bond between the strain gauge and the tooth root surface, reducing interference from environmental vibration and temperature changes on the measurement signal. The sprocket under test in this embodiment is made of nylon.

[0035] To improve testing efficiency and shorten the cycle of multi-tooth profile comparison tests, this embodiment innovatively designs two different tooth profile structures on the same sprocket under test. The two tooth profiles differ in key structural dimensions such as tooth root fillet radius and tooth profile curve parameters, while maintaining the same other structural parameters. This allows for simultaneous data acquisition and lifespan prediction of both tooth profiles under identical test conditions, enabling comparative analysis of the impact of structural parameters on lifespan. In other embodiments, depending on actual testing needs, only one tooth profile can be verified using a single variable, or three or more tooth profiles can be set up for multi-parameter optimization tests. The testing scheme is highly flexible and can adapt to different requirements.

[0036] After the strain gauges are installed, the sprocket to be tested needs to be assembled onto the drive shaft of the sprocket-driven lifting test bench. During assembly, a torque wrench is used to tighten the mounting bolts according to the set torque value to ensure that there is no relative slippage between the sprocket to be tested and the drive shaft. At the same time, the radial runout of the sprocket is detected by a dial indicator to control its error and ensure the smoothness of the transmission process.

[0037] After assembly, a no-load test run is conducted to observe the rotation status of the sprocket under test. Once it is confirmed that there are no abnormalities such as jamming or unusual noises, the formal testing phase can begin. In other embodiments, an installation-then-deployment approach can be adopted. That is, the sprocket under test is first fixed to the lifting test platform, and then the strain gauges are attached and wired using specialized tooling. This method reduces the risk of damage to the strain gauges during assembly. Furthermore, depending on the structural design of the test platform and testing requirements, the sprocket under test can also be assembled onto the driven shaft of the lifting test platform. By adjusting the loading method and measurement parameters, equivalent force simulation and strain acquisition can also be achieved.

[0038] During the loading phase of the test, after applying the test load to the lifting test platform, the PLC control system controls the test platform to perform lifting cycle actions, accurately simulating the alternating stress state of the sprocket under test in actual working conditions. This embodiment uses multi-group graded loads for loading tests, with each load group applied repeatedly, and each loading duration set. The graded loading design is based on the testing principle of material fatigue characteristics. By gradually increasing the load level, the strain response law of the sprocket under test under different stress levels can be comprehensively captured, providing richer data support for subsequent curve fitting and life calculation.

[0039] During the experiment, because manual adjustment of the motor's meshing state was required, each load was applied repeatedly to eliminate systematic errors caused by human factors. By observing the changes in stress and strain amplitudes in the multiple test results, if the signal fluctuation amplitude was small and the strain change trend remained consistent, it could be determined that the human systematic error in the experiment was small, and the test data had high reliability. This method of repeated testing can effectively offset the influence of random errors and improve the rigor of the test conclusions. At the same time, in order to eliminate the interference of residual stress that may be generated under the previous load on subsequent tests and to ensure the consistency of test data under each load level, this embodiment first unloads the test bench to an unloaded state and maintains it for a set time before changing the load, so that the stress state of the sprocket under test can be completely restored to the initial level.

[0040] Regarding specific parameter settings, this embodiment uses two sets of loads on the lifting test bench: 250kg and 500kg. Each load is applied repeatedly at least three times, with each loading lasting 30 seconds. This duration ensures that the strain signal reaches a stable state while avoiding thermal strain interference caused by prolonged loading leading to an increase in the temperature of the sprocket under test. Before changing the load, the load is unloaded to no load and held for 60 seconds to ensure complete release of residual stress. In other embodiments, the number of load repetitions, the duration of each loading, and the no-load holding time can be adjusted to be greater than 30 seconds, or greater than 60 seconds, depending on the material characteristics, structural dimensions, and actual working conditions of the sprocket under test. For example, for sprockets made of high-strength alloy steel, the load level and the number of repetitions can be appropriately increased to more accurately reflect their fatigue life characteristics.

[0041] During the data acquisition process, the strain gauge simultaneously records key parameters such as loading time, load magnitude, and strain value. Real-time monitoring and preliminary processing are performed using data acquisition software to eliminate obviously abnormal data points. After strain data acquisition, the strain signal is converted into the corresponding stress value using the stress-strain conversion formula. Curve fitting is then performed using the material's S-N curve, and finally, the predicted service life of the tested sprocket under set operating conditions is calculated using this model.

[0042] Given the presence of multi-source coupled disturbances at the test site, such as electromagnetic interference, mechanical vibration, temperature drift, and power frequency noise, high-frequency random noise and low-frequency trend terms are superimposed on the original strain signal, resulting in a significant reduction in the signal-to-noise ratio (SNR), making it difficult to directly use for quantitative analysis of stress-load relationships. Therefore, this embodiment also adds a systematic noise reduction process to improve data quality and ensure the reliability of subsequent mechanical parameter extraction.

[0043] To address the broadband random noise and power frequency interference present in the measured strain signals, this embodiment employs two time-domain noise reduction strategies—Moving Average (MA) and Savitzky-Golay (SG) filters—in the post-processing stage of strain gauge data acquisition, balancing algorithm real-time performance and signal fidelity. MA is used to initially suppress high-frequency random components, while the SG filter further smooths noise while preserving signal peak-valley characteristics to the greatest extent possible. The relevant algorithms are implemented using Python 3.12 as the development environment.

[0044] Then, based on the strain data acquired by the strain gauges... Combined with the elastic modulus of the material With correction factor The stress at the root of the sprocket tooth under test is calculated. When no stress concentration occurs, Take 1.

[0045] Based on strain data, an SN curve model is used for fitting to construct a functional relationship between strain and test load.

[0046] Select at least two different loads, measure the corresponding tooth root strain data, and fit them using the SN curve model; convert the fitting results into a linear relationship by taking the logarithm, and solve for the slope and intercept of the fitted curve to complete the SN curve calibration.

[0047] Specifically, two sets of loads, 250kg and 500kg, were set, and the tooth root strain data under these loads were obtained. The strain data were then fitted using an SN curve model, and the logarithm of the fitted data was taken to convert it into a linear relationship, yielding the function. ,in For the load on the lifting test platform, the slope b = 1.322, the intercept A = lna = -0.614, and a = 0.2705 are obtained. .

[0048] For the structurally improved sprocket, its stress-strain data are obtained through the same testing procedure. This data is then substituted into the model to calculate the improved lifespan value. Comparing this improved lifespan with the original structure's lifespan allows for a quantitative assessment of the lifespan improvement effect. Therefore, this embodiment also provides a method for predicting the lifespan amplification factor of the improved sprocket, including the following steps:

[0049] according to The coefficient m is obtained, where This represents the magnitude of the internal stress of the original sprocket under operating load. The lifespan of the original sprocket, obtained from the SN curve under operating load, is given. This represents the magnitude of the internal stress on the original sprocket under the test load. This represents the lifespan of the original sprocket under the test load. The strain data obtained under the test load has an almost infinite duration on the SN curve, so we take [the value here]. .

[0050] Seek .

[0051] In this embodiment, the actual load of the original sprocket is 1500 kg, and the test load is 500 kg, calculated using the formula... The strain calculated under a 1500kg load is 4274. The SN curve shows that the actual lifespan of a 1500kg load is 200,000 cycles, while a 500kg load corresponds to an infinite lifespan. (The infinite lifespan is taken as...) The strain of the original sprocket under a 500kg load was measured to be 1000 through the test in this embodiment.

[0052] Substituting the data into the above formula, we get:

[0053]

[0054] The value of m is 2.217.

[0055] Multiply the obtained lifespan magnification factor by the obtained lifespan of the original sprocket under operating load to obtain the lifespan of the improved sprocket under operating load.

[0056] It should be understood that the descriptions of directions or positional relationships such as up, down, left, right, front, back, top, bottom, tail, horizontal and vertical in this application are all based on the accompanying drawings in the specification and are only used to express the technical solution more clearly and simplify the description, rather than indicating or implying that the device or component referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as limiting the scope of protection of this application.

[0057] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the essence and scope of the technical solutions of the present invention.

Claims

1. A method for predicting sprocket life based on SN curves, characterized in that, Includes the following steps: Strain data of the sprocket under test were collected under two different test loads. Taking the logarithm of both sides of the SN power function for the same material of the sprocket under test, and rearranging it into a linear function, we obtain... ,in For load, The slope The intercept is... ; Substitute the two sets of loads and corresponding strain data of the sprocket under test into the linear function equation to solve; Substitute the operating load of the sprocket under test into the solved linear function, and then use the stress formula to obtain the internal stress of the operating load. The stress formula is as follows: , of which elastic modulus, is Magnitude of strain This is a correction factor; Substituting the obtained stress into the SN curve, the life of the sprocket under test under operating load is obtained.

2. The method for predicting sprocket life based on SN curves according to claim 1, characterized in that, Methods for collecting strain data of the sprocket under test under two different test loads include: The strain gauge is attached to the root of the tooth surface of the sprocket to be tested; The sprocket to be tested is mounted on the drive shaft or driven shaft of the sprocket-driven lifting test bench; Add a test load to the lifting test platform and control the lifting test platform to complete the lifting cycle action; Strain data was collected during the lifting and lowering cycle of the test platform using strain gauges.

3. The method for predicting sprocket life based on SN curves according to claim 2, characterized in that, A groove is provided at the root of the tooth surface of the sprocket to be tested, and the strain gauge is placed in the groove.

4. The method for predicting sprocket life based on SN curves according to claim 2, characterized in that, The sprocket under test has several tooth profiles, and strain gauges are provided for each tooth profile.

5. The method for predicting sprocket life based on SN curves according to claim 2, characterized in that, It also includes a step of noise reduction processing for the data acquired by strain gauges.

6. The method for predicting sprocket life based on SN curves according to claim 2, characterized in that, The two sets of loads on the lifting test bench are applied repeatedly for no less than 3 times, each lasting for no less than 30 seconds. Before changing the load, the load is unloaded to no load and held for no less than 60 seconds.

7. The method for predicting sprocket life based on SN curves according to claim 1, characterized in that, With two loads of 250 kg and 500 kg respectively, we obtain b = 1.322 and a = 0.2705. .

8. The method for predicting sprocket life based on SN curves according to claim 1, characterized in that, It also includes a method for predicting the improved sprocket life magnification factor, comprising the following steps: according to The coefficient m is obtained, where This represents the magnitude of the internal stress of the original sprocket under operating load. The lifespan of the original sprocket, obtained from the SN curve under operating load, is given. This represents the magnitude of the internal stress on the original sprocket under the test load. This is the value taken when the original sprocket has an infinite lifespan under the test load. ; Seek .

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