Abnormal analysis of wheel hub of a straddle monorail vehicle

Abnormal analysis of wheel hub of a straddle monorail vehicle | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Abnormal analysis of wheel hub of a straddle monorail vehicle Zhao Zengchuang, Wu Pingbo, Ren Lihui This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3842516/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract This article is based on the tire six component force test and wheel hub fatigue test of a certain type of straddle monorail vehicle, and analyzes the reasons for the abnormal phenomenon of the vehicle's wheel hub. Firstly, the vehicle connecting rod was calibrated in the laboratory to obtain the "force strain" coefficient of the connecting rod under tension and compression conditions. The accuracy of this calibration was verified by comparing it with the experimental results; Subsequently, the dynamic displacement of the vehicle and the strain of the connecting rod were obtained by installing displacement sensors at different positions, and the six component force data of the tire was obtained; Finally, based on the IIW standard, the fatigue strength of the wheel hub under AW0 and AW3 operating conditions was evaluated, and the dynamic stress of the wheel hub during emergency braking, the dominant frequency of the dynamic stress of the wheel hub, and the influence of polygonal wear on the dynamic stress of the wheel hub were analyzed. The results show that the maximum dynamic loads of the vertical force of the running wheel, the lateral force of the guide wheel, and the lateral force of the stabilizing wheel are all within the limit load range, and there is a certain safety margin to ensure safe operation; Under the IIW standard, there are 1 point and 3 points on the wheel hub under AW0 and AW3 working conditions that do not meet the fatigue strength criterion requirements, and there are no abnormalities in the other indicators; During emergency braking, there was no abnormal change in the dynamic stress of the wheel hub, and the polygonal wear of the tire shoulder had little effect on the dynamic stress of the wheel hub. This explains the abnormal phenomenon of the vehicle's wheel hub and provides an important reference for subsequent wheel hub design. straddle type monorail vehicle six-component force of tire wheel hub fatigue dynamic stress Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Article Highlights The maximum dynamic load of the six-component force of the running wheel is within the limit load range, which can ensure the safe operation of the vehicle. Under the IIW standard, only a few points of the wheel hub under AW0 and AW3 conditions do not meet the fatigue strength criterion, and the remaining indicators are normal. At the moment of emergency braking, there is no abnormal change in the dynamic stress of the hub, and the wear of the shoulder polygon has little effect on the dynamic stress of the hub. The research in this paper can provide a reference for the design of the continuous wheel hub of monorail vehicles. 0 Introduction Straddle monorail vehicles have the characteristics of low noise, strong climbing ability, strong adaptability of small radius curves, etc.[1],which has significant advantages in the more undulating terrain. For example，it has been mature and widely used in Chongqing[2]. It has significant differences with the traditional steel wheel track rail vehicles, mainly reflected in the bogie structure, guiding mechanism, wheel-rail contact relationship and other aspects[3].The wheels of straddle monorail vehicle generally include running wheels, stabilizing wheels and guide wheels, which are in contact with the rail beams in the form of rubber tyres[4].The frequency of fatigue-induced vehicle breakdowns increases as the vehicle's service time increases. Due to the unique structure of straddle monorail vehicle, fatigue tests are carried out on them using methods slightly different from those used for conventional steel rail vehicles, such as the tire six component force test and wheel hub fatigue test. Domestic and foreign scholars have conducted extensive research on straddle monorail vehicles. For the dynamic performance, Yang et al.[5] established a dynamic model of straddle monorail four-vehicle considering the coupler force, and analyzed the vibration response, ride comfort and dynamic bending behavior. The article points out that the body acceleration vibration response obtained from the single-vehicle model differs significantly from that of the multi-vehicle model, and the ride comfort of the vehicle can be calculated more accurately by using the multi-vehicle model. Du Zi-xue et al.[6] through the force analysis on straddle monorail vehicle bogie and the track beam, the safety performance evaluation indexes of straddle monorail vehicle through curve were studied, combined with railway and vehicle safety performance evaluation index. And it is used to analyze and evaluate the safety performance of straddle monorail vehicle through the S-shaped curve at normal operating speed. Xu Zhou-zhou et al.[7] construct the wheel-track coupling dynamic equation, establish the track beam finite element model and vehicle dynamic model based on iterative method, and verify the convergence and accuracy of the iteration by comparing the calculation results with the vehicle test. For wear grinding, Wen Xiaoxia [8] analyzed the mechanical reason of wheel tire partial wear of monorail vehicles through the establishment of wheel-rail relationship and vehicle coupling dynamics model, revealed the wear mechanism of wheel tire and carried out research on the straddle type monorail wheel tire partial grinding control method. Yao et al.[9] present the design and calibration of a heavy load tire six component force sensor. The authors proved the rationality of the design scheme through "virtual calibration". Although crosstalk exists in the sensors, experiments have proved that a high-accuracy heavy load tire six component force sensor is still obtained with decoupling calculation. Ren Li-hui et al.[10] adopted a linearized tire model and considered the radial rigidity of the running tire, side deflection effect, etc., to establish a dynamics model and analyze the effect of tire pre-pressure on the smoothness of a straddle monorail solo vehicle passing through curves and staggered joints of track girders. Shen Longjiang et al.[11] established the theoretical model and dynamic simulation model of the straddle monorail, focusing on the force analysis of the tire. The results show that by setting a reasonable pre-pressure, we can ensure the vehicle anti-overturning stability and the operation safety, which in turn reduces the wear of tires. From the above study, it can be found that at present, Domestic and foreign scholars on the research of straddle monorail vehicle mainly through theoretical simulation to study the vehicle's various dynamic indexes, for the tire force rarely field test research, and at the same time for the study of wheel fatigue life has not seen public reports. Based on this, this paper analyzes the reasons for the abnormal phenomenon of the wheel hub of a straddle monorail vehicle through the six component force test of the tire and the fatigue test of the wheel hub, which provides an important reference basis for the subsequent design of the wheel hub. 1. Wheel arrangement and calculation method 1.1 Wheel arrangement form The wheel arrangement of a straddle monorail vehicle is shown in Fig. 1 , using the railroad coordinate system, with the forward direction of the vehicle being the x-axis positive direction. Each bogie contains 2 running wheels, 4 guide wheels and 2 stabilizing wheels. 1.2. Equivalent stress amplitude calculation method Fatigue of wheel hubs is a fatigue problem under variable amplitude loads. Stresses below the fatigue limit can also have an effect on the damage of the structure, so the fatigue assessment of structures under variable amplitude loading needs to take into account the contribution of each level of stress to the fatigue damage of the structure. And the standards for the given S-N curves are all S-N curves under symmetric cycling, therefore, the test data were corrected for the average stress, and then the one-dimensional stress spectra of each evaluation point under the test condition were obtained by the rainflow counting algorithm. Finally, to calculate the damage at each measurement point from the corresponding S-N curves. According to the principle of equivalent damage and Miner's cumulative damage theory, the stress amplitude spectrum is equivalent to a constant amplitude stress(Weld seam 2 million times, base metal 10 million times), which is called the equivalent stress amplitude. The procedure for calculating the equivalent stress amplitude is as follows: (1)Based on Miner's cumulative damage theory, the damage value at the time of the test was calculated as : $${\text{D}}_{1}=\sum _{\text{i}=1}^{16}\frac{{\text{n}}_{\text{i}}}{{\text{N}}_{\text{i}}}=\sum _{\text{i}=1}^{16}\frac{{\text{n}}_{\text{i}}{{\sigma }}_{-1\text{a}\text{i}}^{\text{m}}}{{\text{C}}_{1}}$$ 1 Where: \({\text{n}}_{\text{i}}\) is the number of cycles for each level of stress amplitude; \({\text{C}}_{1}\) and \(\text{m}\) are the relevant parameters of the S-N curves, which are taken as 3.0 for the weld and 5 for the base metal. \({{\sigma }}_{\text{a}\text{e}\text{q}}\) is the equivalent stress amplitude corresponding to 3.6 million kilometers (1 million kilometers for the hub) of safe operation of the frame and tie rods. Assume that the damage produced by the equivalent force amplitude acting N times is D, then: $$\text{D}=\frac{\text{N}{{\sigma }}_{\text{a}\text{e}\text{q}}^{\text{m}}}{{\text{C}}_{1}}$$ 2 Where: \(\text{N}\) is generally taken as 2 million times (10 million times for base metal); \({\text{C}}_{1}\) and \(\text{m}\) are the relevant parameters of the S-N curves, which are taken as 3.0 for the weld and 5 for the base metal. The number of kilometers of operation for a measured stress spectrum is known to be \({\text{L}}_{1}\) , and the damage produced by one stress spectrum is \({\text{D}}_{1}\) ; Assuming that the safe operating mileage that produces damage D is L(360/1,000,000km) $$\frac{\text{D}}{\text{L}}=\frac{{\text{D}}_{1}}{{\text{L}}_{1}}$$ 3 Bringing the expressions for D and \({\text{D}}_{1}\) into the above equation and organizing, we have: $${{\sigma }}_{\text{a}\text{e}\text{q}}={\left[\frac{\text{L}}{{\text{L}}_{1}\text{N}}\sum {\text{n}}_{\text{i}}{{\sigma }}_{-1\text{a}\text{i}}^{\text{m}}\right]}^{\frac{1}{\text{m}}}$$ 4 If the equivalent stress amplitude at the measurement point is less than the corresponding fatigue permissible stress, it means that it is able to run for 3.6 (1) million kilometers in this state, and the fatigue limit at the hub (FAT71) can be calculated to be 51.5 Mpa according to the above formula. 2. Connecting rod calibration The longitudinal force of the running wheel needs to be obtained by calculating the force on the rod, and in order to obtain the force on the rod, the rod needs to be calibrated before testing. By loading the rod on the testing machine, recording the strain values under different loads, with a maximum loading force of 10kN, loading once at an interval of 1kN, a loading time of 10s, a steady loading of 20s, and then to the next cycle. Eventually, we will obtain the variation relationship between the strain and force of the rod, which will provide a calculation basis for the force analysis of the wheel.The connecting rod calibration equipments are shown in Fig. 2 . 2.1. Strain-Force Calibration of Rod When the load on the rod is less than 10kN, the rod is within the elastic deformation range, and the "strain-force" relationship is linearized, and the "force-strain" coefficients of the longitudinal tie rods and lateral connecting rods can be obtained through the test, as shown in Table 1 . Figure 3(a) and Fig. 3(b) show the calibration results of the rod in tenson and compression, respectively. Table 1 'Force-strain' corresponding coefficient Name of rod Force(kN)/Strain (um/m) Longitudinal tie rod 1/4.5 Lateral tie rod 1/17.5 2.2. Comparison of theoretical calculations and test results 2.2.1. Comparison of theoretical calculations and test results As shown in Fig. 4 , which is the vehicle traction device structure diagram, the ratio of the upper tie-rod force to the lower tie-rod force can be obtained by taking moments from the walking surface as 4.2, and we can obtain the ratio of the unilateral longitudinal force to the lateral linkage force by taking moments from the rotating shaft as 1.3. 2.2.2. Measured results When the vehicle undergoes emergency braking, the rod is subjected to the maximum force, at which time the influence of other factors on the force on the rod can be ignored. When the vehicle undergoes emergency braking, the rod is subjected to the maximum force, at which time the influence of other factors on the force on the rod can be ignored. Figure 5 shows the force of the rods when the vehicle undergoes emergency braking, and it can be seen from the figure that when the vehicle undergoes stable deceleration, the stabilized value of the force of the upper tie rod is about 5.6kN, the stabilized value of the force of the lower tie rod is about 1.5kN, and the ratio of the upper tie rod force to the lower tie rod force is about 4:1; the stabilized value of the force of the lateral connecting rod is about 4.9kN, and the ratio of the unilateral longitudinal force to the lateral connecting rod force is 1.44. The measured results are basically consistent with the theoretical calculations. 3. Tire six component force test The wheel six component force consists of the three-directional forces of the road acting at the center of the wheel and the three-directional moments formed by these forces. The analysis of tire force helps to predict the fatigue life of the vehicle structure as well as to analyze the effect of tire force on the wheel hub, it is important for vehicle and wheel development[ 12 , 13 ],and provides an important basis for subsequent wheel hub improvement programs. 3.1. Measuring point arrangement The vertical force of the running wheel and the lateral force of the stabilizing wheel are obtained by testing the dynamic displacement of the tire relative to the track with the laser sensor; the longitudinal force of the running wheel is obtained by testing the longitudinal strain of the calibrated traction tie rod. The laser displacement sensor and tie rod strain measuring point arrangement is shown in Fig. 6. 3.2. Result processing Tire displacement multiplied by the corresponding tire radial rigidity can be directly obtained tire force, each tire radial rigidity and pre-pressure as shown in Table 2 . Tire dynamic force processing to "compression" force is positive, "stretch" force is negative. The following table shows the maximum dynamic compressive force of the tires (without superimposed pre-pressure) with 99.85% confidence level. The maximum tire tensile and compressive forces for each site interval are shown for AW0 and AW3 loading conditions. Table 2 Tire stiffness and preload Running wheel Horizontal wheel Radial rigidity AW0/AW3 (kN/mm) Pre-pressure AW0/AW3 (kN) Radial rigidity (kN/mm) Pre-pressure (kN) 1.466/1.592 37.5/66.9 0.59 5.44 3.3. Test result 3.3.1. Vertical force of the running wheel In this paper, the dynamic vertical force of the running wheel is measured when the vehicle is traveling on the line proper, and due to space limitation, only the interval when the vertical force of the running wheel is at its maximum is listed below. Figures 7 and 8 respectively show the test results in the intervals where the maximum compressive force occurs in the wheels at AW0 and AW3 loads of the vehicle. At AW0 loading, the maximum vertical force on the running wheel is 19.3kN, which occurs at the right running wheel of the 1-position frame; at AW3 loading, the maximum vertical force on the running wheel is 25.9kN, which occurs at the left running wheel of the 1-position frame. The vertical forces on the running wheel at both AW0 load and AW3 load were not exceeded. Meet the design criteria. 3.3.2. Longitudinal force of the running wheel The longitudinal force of the running wheel was calculated by measuring the strain of the frame rods, and Table 3 shows the test results of the corresponding intervals at the maximum value of the longitudinal force of the tires at AW0 and AW3 loads, including the emergency braking condition as well as the normal driving condition on the positive line. It can be seen that the maximum longitudinal force of the running wheel tires during emergency braking is 12.8kN for AW0 load and 8.1kN for normal driving on the positive line, and the maximum longitudinal force of the running wheel tires during emergency braking is 19.5kN for AW3 load and 9.5kN for normal driving on the positive line. The longitudinal forces on the running wheel at both AW0 load and AW3 load were not exceeded. Meet the design criteria. Table 3 Longitudinal force results of running wheel Working condition AW0 tire longitudinal force(maximum tensile force)/kN AW0 tire longitudinal force(maximum compressive force)/kN AW3 tire longitudinal force(maximum tensile force)/kN AW3 tire longitudinal force(maximum compressive force)/kN Emergency braking 12.4 12.8 19.5 12.2 Normal operation 8.1 7 7.9 9.5 3.3.3. The lateral force of guide wheel The lateral force of guide wheel is obtained by testing the dynamic lateral displacement of the tire relative to the track with a laser sensor. Due to space constraints, Figs. 9 and 10 respectively show the test results for the driving intervals corresponding to the maximum values of the lateral force of guide wheel for vehicle loads of AW0 and AW3. The maximum value of the lateral force of guide wheel under AW0 load is 8.3kN, which occurs at the right guide wheel of the 1-position frame; the maximum value of the lateral force of guide wheel under AW3 load is 9.5kN, which occurs at the left guide wheel of the 2-position frame. The lateral forces on the guide wheel were not exceeded for both AW0 and AW3 loads. Meet the design criteria. 3.3.4. Lateral force of stabilizing wheel Like the lateral force of guide wheel, the lateral force of stabilizing wheel is also obtained from the dynamic lateral displacement of the tire relative to the track as measured by the laser sensor. Due to space constraints, only the results of the following driving intervals corresponding to the maximum values of the lateral force of stabilizing wheel are presented, as shown in Figs. 11 and 12 . In particular, the maximum value of the lateral force of the stabilizing wheel under AW0 loading was 7.1kN, which appeared in the left stabilizing wheel of the 1-position frame; the maximum value of the lateral force of the stabilizing wheel under AW3 loading was 7.5kN, which appeared in the left stabilizing wheel of the 1-position frame. The lateral forces on the stabilizing wheel were not exceeded for both AW0 and AW3 loads. Meet the design criteria. 3.3.5. Three-direction torque The three-direction torques are calculated as shown below: the rocking head torque is the product of the difference between the longitudinal force of the left and right side drawbars and half of the transverse span; the slewing torque is the product of the longitudinal force of the tires and the radius of the wheels; and the side-rolling torque is the product of the difference between the vertical force of the left and right side running wheels and half of the transverse span. According to the above calculation method, the following three-direction torque test results were obtained by measuring the relevant indexes, as shown in Table 4 . Table 4 Statistics of maximum three-direction torque Working condition AW0 AW3 Rocking head torque kN.m Slewing torque kN.m Side-rolling torque kN.m Rocking head torque kN.m Slewing torque kN.m Side-rolling torque kN.m Emergency braking 6.9 6 \ 0.9 8.9 \ Normal operation 6.7 2.9 3.7 7.4 4.2 4.4 4. Hub dynamic stress This section respectively test the dynamic stress levels in the wheel hubs of vehicles under AW0 (empty) and AW3 (heavy) loads, to assess the fatigue strength of the hubs according to the relevant guidelines. The rainflow counting and average stress correction were performed on the dynamic stress time course, and the cumulative damage at the corresponding measurement point was analyzed and the equivalent stress amplitude was calculated according to Miner's cumulative damage principle and the type of welded joint corresponding to each measurement point。 4.1. Measuring point arrangement The dynamic stress measurement points of the inner hub are numbered as 3, 4, 5 and 7, and the dynamic stress measurement points of the outer hub are numbered as 3, 4, 5 and 8. Measurement points 3, 4 and 5 of the inner and outer hubs are shown in Fig. 13, and measurement point 7 of the inner hub is located at the back of the inner hub in the figure, symmetrical to the center of the hub with the measurement point 3; and measurement point 8 of the outer hub is located at the back of the outer hub in the figure, corresponding to the position of the measurement point 3. 4.2. Test result The sampling frequency of this test was 2400 Hz, and the dynamic stress time course obtained from this test was corrected for rainflow cycle counting and average stress to obtain 32 levels of zero-mean magnitude-frequency stress spectra. Due to the anomalies in individual data points during the test, the data anomaly measurement points were eliminated 4.2.1. IIW Standard Wheel Dynamic Stress Evaluation Results The measurement points were evaluated according to the equivalent stress amplitude calculation method in Section 1.2 and the fatigue strength assessment guidelines in Section 1.3, and the evaluation results are shown in Tables 5 and 6.AW0 condition has 1 point cumulative damage more than 0.5, does not meet the requirements; AW3 condition has 3 measurement points cumulative damage more than 0.5, does not meet the requirements, and one of the inner hub measurement point 3 equivalent stress amplitude up to 51.4MPa, although does not exceed the fatigue limit of 51.5Mpa, but the calculated mileage is only 31,000 kilometers. Table 5 The equivalent stress amplitude and evaluation results of each measuring point under AW0 condition Measurement point location Maximum stress (MPa) Minimum stress (MPa) Stress amplitude (MPa) Equivalent stress amplitude (MPa) Calculating mileage (10 4 km) Cumulative damage Inside Hub 3 29.3 -22.6 25.9 24.5 129 0.77338 Inside Hub 4 24.7 -27.1 25.9 16.6 889 0.11247 Inside Hub 5 8.7 -7.2 8.0 2.1 26256756 0.00000 Inside Hub 7 7.4 -6.9 7.1 1.6 115355112 0.00000 Outer Hub 3 17.2 -13.2 15.2 9.1 18474 0.00541 Outer Hub 4 16.5 -11.5 14.0 7.8 39675 0.00252 Outer Hub 5 16.3 -13.5 14.9 10.1 10897 0.00918 Outer Hub 8 54.7 -32.2 43.4 19.4 417 0.24008 Table 6 The equivalent stress amplitude and evaluation results of each measuring point under AW3 condition Measurement point location Maximum stress (MPa) Minimum stress (MPa) Stress amplitude (MPa) Equivalent stress amplitude (MPa) Calculating mileage (10 4 km) Cumulative damage Inside Hub 3 46.8 -32.5 39.7 51.4 3.1 31.81462 Inside Hub 4 37.0 -27.7 32.3 34.9 22.0 4.54828 Inside Hub 5 9.6 -8.0 8.8 2.9 5140807.5 0.00002 Inside Hub 7 8.1 -8.2 8.2 2.2 19987422.0 0.00001 Outer Hub 3 25.6 -18.1 21.9 18.5 527.2 0.18970 Outer Hub 4 23.2 -17.1 20.2 14.8 1608.6 0.06217 Outer Hub 5 24.0 -20.3 22.1 21.4 252.4 0.39614 Outer Hub 8 33.4 -28.6 31.0 32.2 32.6 3.06624 4.2.2. Wheel dynamic stress during emergency braking Figure 14 shows the variation of dynamic stresses in the wheel hub during emergency braking under AW3 loading, and it can be clearly seen that at the moment of emergency braking, there is no abnormal change in the dynamic stresses in the wheel hub, and the magnitude of the value tends to stabilize。 4.2.3. Wheel dynamic stress principal frequency analysis From Fig. 15(a), it can be seen that the main frequencies of hub dynamic stresses are mainly 6.5 Hz, 13 Hz, and 19.5 Hz, which correspond to the rotational, twofold, and threefold frequencies, respectively, whereas the 35th-order tire shoulder polygon wear frequency is not obvious in the hub dynamic stresses. From Fig. 15(b), it can be seen that the energies below 20 Hz are larger throughout the time period, and the hub dynamic stresses are mainly affected by these frequencies. 4.2.4. Effect of polygon wear on dynamic stresses in hub From section 4.2.3 , it can be seen that the polygon abrasion frequency hub dynamic stress effect is not obvious, in order to further verify, this section of the AW3 load dynamic stress raw data for polygonal frequency bandstop filtering, to remove the effect of polygonal vibration on the dynamic stress of the hub, the comparison results are shown in Table 7 , all the points of the original cumulative damage and the cumulative damage after the bandstop filtering error of not more than 5%, it can be seen that the tire shoulder polygonal It can be seen that the shoulder polygonal abrasion has little effect on the dynamic stress of the wheel hub。 Table 7 The influence of shoulder polygon on dynamic stress of wheel hub under AW3 load Measurement point location Equivalent stress amplitude (MPa) Cumulative damage Initial Bandstop filtering Initial Bandstop filtering Inside Hub 3 51.4 51.4 31.81462 31.72966 Inside Hub 4 34.9 34.8 4.54828 4.50702 Inside Hub 5 2.9 2.9 0.00002 0.00002 Inside Hub 7 2.2 2.2 0.00001 0.00000 Outer Hub 3 18.5 18.5 0.18970 0.18889 Outer Hub 4 14.8 14.7 0.06217 0.06074 Outer Hub 5 21.4 21.4 0.39614 0.39197 Outer Hub 8 32.2 32.0 3.06624 2.94940 5. Conclusion This paper analyzes wheel anomalies occurring in a straddle monorail vehicle, and performs tire six component force tests as well as wheel dynamic stress fatigue strength tests. The results show that the maximum dynamic loads of the vertical force of the running wheel, the lateral force of the guide wheel and the lateral force of the stabilizing wheel are all within the limit load range and have a certain safety margin; In the AW0 condition, there is one measurement point with accumulated damage over 0.5, which does not meet the requirements; in the AW3 condition, there are three measurement points with accumulated damage over 0.5, which does not meet the requirements, of which the equivalent force amplitude of the inner hub measurement point 3 reaches 51.4MPa, although it does not exceed the fatigue limit of 51.5Mpa, but the calculated mileage is only 31,000 kilometers, and the rest of the test indexes do not see any abnormality; at the moment of emergency braking, there is no abnormal change in wheel dynamic stresses, and the tire shoulder polygon wear has little effect on wheel dynamic stresses. This paper analyzes the cause of the wheel hub abnormality of the straddle monorail vehicles through the test, and the tire six component force test and the wheel hub dynamic stress test of the vehicle provides an important reference for the subsequent design of the wheel hub. Declarations Author Contribution Zengchuang Zhao,Pingbo Wu and Lihui Ren wrote the main manuscript text and all of them prepared all figures 1-3. All authors reviewed the manuscript. References Ma, J. Research on Static and Dynamic Behavior of Straddle Monorail Transit System Structure. Southwest Jiaotong University, 2008. He, X. Application and Prospect of Straddle Monorail Transit System in China[J/OL]. Urban Rail Transit, 2015, 1(1): 26–34. DOI: 10.1007/s40864-015-0006-9 . Zhang, J. Research on Dynamics of Straddle Monorail Vehicles. Southwest Jiaotong University, 2009. Zhu, X. Analysis of the Bogie Structure of Straddle Monorail Vehicles. Chongqing Jiaotong University, 2011. Yang, Z., Du, Z., Xu, Z., et al. Research on dynamic behavior of train dynamic model of straddle-type monorail[J/OL]. Noise Vib World, 2020, 51(11): 195–207. Du, Z., Li, Y., Liang, Z., et al. Research on Curve through Safety of Straddle-type Monorail Vehicle. Elec Dr Locomot, 2016 (01): 79–83. Xu, X., Du, Z., Xin, L., et al. Study on Equivalent Calculation of Rigid Flexible Coupling Dynamics of Straddle Monorail. Mach Des Manuf, 2022 (06): 278–281 + 285. Wen, X. Research on the Mechanism and Control Method of Tire Eccentric Wear of Straddle Type Monorail Vehicles. Chongqing Jiaotong University, 2018. Yao, Z., Wei, Y., Lv, J. A heavy load tire six-component force sensor[J/OL]. Int J Front Eng Technol, 2021, 3(3). https://francis-press.com/papers/4102 . Ren, L., Zhou, J., Shen, G. Dynamics Model and Simulation Study of a Straddle Type Monorail Car. China Railway Sci, 2004 (05): 28–34. Shen, L., Zhang, J. Analysis of Mechanical Property of Straddle Monorail Vehicle Based on Tyre. Elec Dr Locomot, 2019 (04): 22–26. Lu, D., Xia, D. Research Progress on Prediction of Force and Moment Characteristics of Automobile Tire. Tire Ind, 20221, 41 (03): 185–189. Ji, Z., Wang, Tie., Li, G. Fatigue Life Analysis of Frame with Measured Six-Component Wheel Force. Mach Des Manuf, 2020,353 (07): 25–28. Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3842516","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":286876427,"identity":"c04c9dae-b2bf-4b9e-b199-98d93e49aa93","order_by":0,"name":"Zhao Zengchuang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA90lEQVRIiWNgGAWjYDACCVSGDQ8/ewNpWtJkJHsOkKblsI3BDQf8OuRnNz98+KPijl3/7B7DzwW/zvMw3GBg/PAxB7cWxjnHjA0kzjxLnnHnjLH0zL7bPIyzG5glZ27DrYVZIsFMwrDtcLKBRI6BNG/PbR5mmQNszLx4tLBJpH+TSPwH1mL8m7fnHA+bRAJ+LTwSOWYSBxsO2wG1mEnz/DjAw0NIi4RETrFhw7HDCRI30sqseRuSeSR4Djbj9Yv8jPSND3/UHLbnn5G8+TbPHzt7++PNBz98xKMFBhIbQCRjG5hsIKweCOwh1B+iFI+CUTAKRsEIAwAFslARUSfT4gAAAABJRU5ErkJggg==","orcid":"","institution":"Tongji University","correspondingAuthor":true,"prefix":"","firstName":"Zhao","middleName":"","lastName":"Zengchuang","suffix":""},{"id":286876428,"identity":"e1e37fce-35f1-4c2c-ba4c-faf752a0e975","order_by":1,"name":"Wu Pingbo","email":"","orcid":"","institution":"Southwest Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Wu","middleName":"","lastName":"Pingbo","suffix":""},{"id":286876429,"identity":"aa271ebd-95d8-48a8-b6b2-d1fe7fe6334f","order_by":2,"name":"Ren Lihui","email":"","orcid":"","institution":"Tongji University","correspondingAuthor":false,"prefix":"","firstName":"Ren","middleName":"","lastName":"Lihui","suffix":""}],"badges":[],"createdAt":"2024-01-07 12:44:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3842516/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3842516/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":54181594,"identity":"c0c4f9d2-04f2-4b83-8f00-e61ca9853305","added_by":"auto","created_at":"2024-04-05 16:36:02","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":32062,"visible":true,"origin":"","legend":"\u003cp\u003eWheel arrangement form\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-3842516/v1/b5f9eec6a9ea73dc850efd38.png"},{"id":54182320,"identity":"686d4b28-fd21-4b2e-aea9-10043344ef81","added_by":"auto","created_at":"2024-04-05 16:44:04","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":676040,"visible":true,"origin":"","legend":"\u003cp\u003eConnecting rod calibration equipment\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-3842516/v1/3deb2061941d784aabcc37da.png"},{"id":54181600,"identity":"2071ae9e-4342-4707-a746-dd71f18e4784","added_by":"auto","created_at":"2024-04-05 16:36:03","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":108704,"visible":true,"origin":"","legend":"\u003cp\u003eRod calibration results\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-3842516/v1/db69352320439ff7a64503c4.png"},{"id":54181588,"identity":"4df8edab-bc46-49e3-bf91-b175a2271eee","added_by":"auto","created_at":"2024-04-05 16:36:01","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":115797,"visible":true,"origin":"","legend":"\u003cp\u003eTraction device structure diagram\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-3842516/v1/7abffa7560379927f4ed59c5.png"},{"id":54181587,"identity":"a58e7362-614c-4b15-91a9-9f93802f99eb","added_by":"auto","created_at":"2024-04-05 16:36:01","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":59894,"visible":true,"origin":"","legend":"\u003cp\u003eAW3 load emergency braking condition\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-3842516/v1/b9269e78c2948c72541b12b1.png"},{"id":54181585,"identity":"7c30e8ee-6009-44bf-b748-94081976305f","added_by":"auto","created_at":"2024-04-05 16:36:00","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":558751,"visible":true,"origin":"","legend":"\u003cp\u003eSensor layout diagram\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-3842516/v1/fae4028c169550bd73f14050.png"},{"id":54181589,"identity":"9097f090-7689-4125-865e-361269cde133","added_by":"auto","created_at":"2024-04-05 16:36:01","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":66424,"visible":true,"origin":"","legend":"\u003cp\u003eVertical force of running wheel under AW0 load ( 1-position frame )\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-3842516/v1/b3e72be4c6cf364f9c9fdb5e.png"},{"id":54181596,"identity":"038949d1-2d71-4f7e-9780-93dbd3c72c5f","added_by":"auto","created_at":"2024-04-05 16:36:02","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":80856,"visible":true,"origin":"","legend":"\u003cp\u003eVertical force of running wheel under AW3 load ( 1-position frame )\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-3842516/v1/f722e5f7598a30788546716a.png"},{"id":54181591,"identity":"ce743539-ebc5-4ad9-99d6-3ffef1ad4130","added_by":"auto","created_at":"2024-04-05 16:36:02","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":63878,"visible":true,"origin":"","legend":"\u003cp\u003eLateral force of guide wheel under AW0 load (1-position frame)\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-3842516/v1/9410ce41edd44e20ac1799ec.png"},{"id":54181590,"identity":"dca0351a-814a-4e46-b78c-6f89fc1b5faa","added_by":"auto","created_at":"2024-04-05 16:36:02","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":63148,"visible":true,"origin":"","legend":"\u003cp\u003eLateral force of guide wheel under AW3 load (2-position frame\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-3842516/v1/9c3a3740b2d746ef38dd5f70.png"},{"id":54182319,"identity":"74c24d05-12fb-4f71-b81f-63e23bb81dd6","added_by":"auto","created_at":"2024-04-05 16:44:02","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":87071,"visible":true,"origin":"","legend":"\u003cp\u003eLateral force of stabilizing wheel under AW0 load (1-position frame)\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-3842516/v1/4d7d5453e1105d5e64a547e1.png"},{"id":54181586,"identity":"2b9c951c-44ee-4b38-a044-6a6a8216d816","added_by":"auto","created_at":"2024-04-05 16:36:01","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":90506,"visible":true,"origin":"","legend":"\u003cp\u003eLateral force of stabilizing wheel under AW3 load (1-position frame)\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-3842516/v1/5408c845026a940ab2b5ff00.png"},{"id":54181604,"identity":"f593f96a-bb2c-4d31-b8a4-87eef4c6853c","added_by":"auto","created_at":"2024-04-05 16:36:04","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":368654,"visible":true,"origin":"","legend":"\u003cp\u003eDynamic stress measuring point layout of hub\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-3842516/v1/d0b4b6b8a2178b6cc082d388.png"},{"id":54181593,"identity":"41af51be-9fdb-4ffd-ad68-2ebe28df4c1e","added_by":"auto","created_at":"2024-04-05 16:36:02","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":233578,"visible":true,"origin":"","legend":"\u003cp\u003eDynamic stress of hub during emergency braking under AW3 load\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-3842516/v1/385963801ddb935aa20158f6.png"},{"id":54181597,"identity":"6d83ec9a-ab83-45b4-aea8-2d3199609983","added_by":"auto","created_at":"2024-04-05 16:36:02","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":191044,"visible":true,"origin":"","legend":"\u003cp\u003eDynamic stress spectrum analysis of hub under AW3 load\u003c/p\u003e","description":"","filename":"15.png","url":"https://assets-eu.researchsquare.com/files/rs-3842516/v1/2b2a18e0e0a5aca0c8ba2616.png"},{"id":54182744,"identity":"60c987c0-31ae-4b16-816e-f827444d99fd","added_by":"auto","created_at":"2024-04-05 16:52:11","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3917131,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3842516/v1/3bf56692-494a-4032-b1c4-cdd31573cff3.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Abnormal analysis of wheel hub of a straddle monorail vehicle","fulltext":[{"header":"Article Highlights","content":"\u003cp\u003eThe maximum dynamic load of the six-component force of the running wheel is within the limit load range, which can ensure the safe operation of the vehicle. Under the IIW standard, only a few points of the wheel hub under AW0 and AW3 conditions do not meet the fatigue strength criterion, and the remaining indicators are normal. At the moment of emergency braking, there is no abnormal change in the dynamic stress of the hub, and the wear of the shoulder polygon has little effect on the dynamic stress of the hub. The research in this paper can provide a reference for the design of the continuous wheel hub of monorail vehicles.\u003c/p\u003e"},{"header":"0 Introduction","content":"\u003cp\u003eStraddle monorail vehicles have the characteristics of low noise, strong climbing ability, strong adaptability of small radius curves, etc.[1],which has significant advantages in the more undulating terrain. For example，it has been mature and widely used in Chongqing[2]. It has significant differences with the traditional steel wheel track rail vehicles, mainly reflected in the bogie structure, guiding mechanism, wheel-rail contact relationship and other aspects[3].The wheels of straddle monorail vehicle generally include running wheels, stabilizing wheels and guide wheels, which are in contact with the rail beams in the form of rubber tyres[4].The frequency of fatigue-induced vehicle breakdowns increases as the vehicle\u0026apos;s service time increases. Due to the unique structure of straddle monorail vehicle, fatigue tests are carried out on them using methods slightly different from those used for conventional steel rail vehicles, such as the tire six component force test and wheel hub fatigue test.\u003c/p\u003e\n\u003cp\u003eDomestic and foreign scholars have conducted extensive research on straddle monorail vehicles. For the dynamic performance, Yang et al.[5] established a dynamic model of straddle monorail four-vehicle considering the coupler force, and analyzed the vibration response, ride comfort and dynamic bending behavior. The article points out that the body acceleration vibration response obtained from the single-vehicle model differs significantly from that of the multi-vehicle model, and the ride comfort of the vehicle can be calculated more accurately by using the multi-vehicle model. Du Zi-xue et al.[6] through the force analysis on straddle monorail vehicle bogie and the track beam, the safety performance evaluation indexes of straddle monorail vehicle through curve were studied, combined with railway and vehicle safety performance evaluation index. And it is used to analyze and evaluate the safety performance of straddle monorail vehicle through the S-shaped curve at normal operating speed. Xu Zhou-zhou et al.[7] construct the wheel-track coupling dynamic equation, establish the track beam finite element model and vehicle dynamic model based on iterative method, and verify the convergence and accuracy of the iteration by comparing the calculation results with the vehicle test.\u003c/p\u003e\n\u003cp\u003eFor wear grinding, Wen Xiaoxia [8] analyzed the mechanical reason of wheel tire partial wear of monorail vehicles through the establishment of wheel-rail relationship and vehicle coupling dynamics model, revealed the wear mechanism of wheel tire and carried out research on the straddle type monorail wheel tire partial grinding control method. Yao et al.[9] present the design and calibration of a heavy load tire six component force sensor. The authors proved the rationality of the design scheme through \u0026quot;virtual calibration\u0026quot;. Although crosstalk exists in the sensors, experiments have proved that a high-accuracy heavy load tire six component force sensor is still obtained with decoupling calculation. Ren Li-hui et al.[10] adopted a linearized tire model and considered the radial rigidity of the running tire, side deflection effect, etc., to establish a dynamics model and analyze the effect of tire pre-pressure on the smoothness of a straddle monorail solo vehicle passing through curves and staggered joints of track girders. Shen Longjiang et al.[11] established the theoretical model and dynamic simulation model of the straddle monorail, focusing on the force analysis of the tire. The results show that by setting a reasonable pre-pressure, we can ensure the vehicle anti-overturning stability and the operation safety, which in turn reduces the wear of tires.\u003c/p\u003e\n\u003cp\u003eFrom the above study, it can be found that at present, Domestic and foreign scholars on the research of straddle monorail vehicle mainly through theoretical simulation to study the vehicle\u0026apos;s various dynamic indexes, for the tire force rarely field test research, and at the same time for the study of wheel fatigue life has not seen public reports. Based on this, this paper analyzes the reasons for the abnormal phenomenon of the wheel hub of a straddle monorail vehicle through the six component force test of the tire and the fatigue test of the wheel hub, which provides an important reference basis for the subsequent design of the wheel hub.\u003c/p\u003e"},{"header":"1. Wheel arrangement and calculation method","content":"\u003ch2\u003e1.1 Wheel arrangement form\u003c/h2\u003e\u003cp\u003eThe wheel arrangement of a straddle monorail vehicle is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, using the railroad coordinate system, with the forward direction of the vehicle being the x-axis positive direction. Each bogie contains 2 running wheels, 4 guide wheels and 2 stabilizing wheels.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec2\" class=\"Section2\"\u003e \u003ch2\u003e1.2. Equivalent stress amplitude calculation method\u003c/h2\u003e \u003cp\u003eFatigue of wheel hubs is a fatigue problem under variable amplitude loads. Stresses below the fatigue limit can also have an effect on the damage of the structure, so the fatigue assessment of structures under variable amplitude loading needs to take into account the contribution of each level of stress to the fatigue damage of the structure. And the standards for the given S-N curves are all S-N curves under symmetric cycling, therefore, the test data were corrected for the average stress, and then the one-dimensional stress spectra of each evaluation point under the test condition were obtained by the rainflow counting algorithm. Finally, to calculate the damage at each measurement point from the corresponding S-N curves.\u003c/p\u003e \u003cp\u003eAccording to the principle of equivalent damage and Miner's cumulative damage theory, the stress amplitude spectrum is equivalent to a constant amplitude stress(Weld seam 2\u0026nbsp;million times, base metal 10\u0026nbsp;million times), which is called the equivalent stress amplitude.\u003c/p\u003e \u003cp\u003eThe procedure for calculating the equivalent stress amplitude is as follows:\u003c/p\u003e \u003cp\u003e(1)Based on Miner's cumulative damage theory, the damage value at the time of the test was calculated as :\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$${\\text{D}}_{1}=\\sum _{\\text{i}=1}^{16}\\frac{{\\text{n}}_{\\text{i}}}{{\\text{N}}_{\\text{i}}}=\\sum _{\\text{i}=1}^{16}\\frac{{\\text{n}}_{\\text{i}}{{\\sigma }}_{-1\\text{a}\\text{i}}^{\\text{m}}}{{\\text{C}}_{1}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({\\text{n}}_{\\text{i}}\\)\u003c/span\u003e \u003c/span\u003e is the number of cycles for each level of stress amplitude;\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({\\text{C}}_{1}\\)\u003c/span\u003e \u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{m}\\)\u003c/span\u003e\u003c/span\u003e are the relevant parameters of the S-N curves, which are taken as 3.0 for the weld and 5 for the base metal.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({{\\sigma }}_{\\text{a}\\text{e}\\text{q}}\\)\u003c/span\u003e \u003c/span\u003eis the equivalent stress amplitude corresponding to 3.6\u0026nbsp;million kilometers (1\u0026nbsp;million kilometers for the hub) of safe operation of the frame and tie rods. Assume that the damage produced by the equivalent force amplitude acting N times is D, then:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\text{D}=\\frac{\\text{N}{{\\sigma }}_{\\text{a}\\text{e}\\text{q}}^{\\text{m}}}{{\\text{C}}_{1}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\text{N}\\)\u003c/span\u003e \u003c/span\u003e is generally taken as 2\u0026nbsp;million times (10\u0026nbsp;million times for base metal);\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({\\text{C}}_{1}\\)\u003c/span\u003e \u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{m}\\)\u003c/span\u003e\u003c/span\u003eare the relevant parameters of the S-N curves, which are taken as 3.0 for the weld and 5 for the base metal.\u003c/p\u003e \u003cp\u003eThe number of kilometers of operation for a measured stress spectrum is known to be \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{L}}_{1}\\)\u003c/span\u003e\u003c/span\u003e, and the damage produced by one stress spectrum is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{D}}_{1}\\)\u003c/span\u003e\u003c/span\u003e; Assuming that the safe operating mileage that produces damage D is L(360/1,000,000km)\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\frac{\\text{D}}{\\text{L}}=\\frac{{\\text{D}}_{1}}{{\\text{L}}_{1}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eBringing the expressions for D and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{D}}_{1}\\)\u003c/span\u003e\u003c/span\u003e into the above equation and organizing, we have:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$${{\\sigma }}_{\\text{a}\\text{e}\\text{q}}={\\left[\\frac{\\text{L}}{{\\text{L}}_{1}\\text{N}}\\sum {\\text{n}}_{\\text{i}}{{\\sigma }}_{-1\\text{a}\\text{i}}^{\\text{m}}\\right]}^{\\frac{1}{\\text{m}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIf the equivalent stress amplitude at the measurement point is less than the corresponding fatigue permissible stress, it means that it is able to run for 3.6 (1) million kilometers in this state, and the fatigue limit at the hub (FAT71) can be calculated to be 51.5 Mpa according to the above formula.\u003c/p\u003e \u003c/div\u003e"},{"header":"2. Connecting rod calibration","content":"\u003cp\u003eThe longitudinal force of the running wheel needs to be obtained by calculating the force on the rod, and in order to obtain the force on the rod, the rod needs to be calibrated before testing. By loading the rod on the testing machine, recording the strain values under different loads, with a maximum loading force of 10kN, loading once at an interval of 1kN, a loading time of 10s, a steady loading of 20s, and then to the next cycle. Eventually, we will obtain the variation relationship between the strain and force of the rod, which will provide a calculation basis for the force analysis of the wheel.The connecting rod calibration equipments are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Strain-Force Calibration of Rod\u003c/h2\u003e \u003cp\u003eWhen the load on the rod is less than 10kN, the rod is within the elastic deformation range, and the \"strain-force\" relationship is linearized, and the \"force-strain\" coefficients of the longitudinal tie rods and lateral connecting rods can be obtained through the test, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Figure\u0026nbsp;3(a) and Fig.\u0026nbsp;3(b) show the calibration results of the rod in tenson and compression, respectively.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e'Force-strain' corresponding coefficient\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eName of rod\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eForce(kN)/Strain (um/m)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLongitudinal tie rod\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1/4.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLateral tie rod\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1/17.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Comparison of theoretical calculations and test results\u003c/h2\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e2.2.1. Comparison of theoretical calculations and test results\u003c/h2\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e, which is the vehicle traction device structure diagram, the ratio of the upper tie-rod force to the lower tie-rod force can be obtained by taking moments from the walking surface as 4.2, and we can obtain the ratio of the unilateral longitudinal force to the lateral linkage force by taking moments from the rotating shaft as 1.3.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e2.2.2. Measured results\u003c/h2\u003e \u003cp\u003eWhen the vehicle undergoes emergency braking, the rod is subjected to the maximum force, at which time the influence of other factors on the force on the rod can be ignored. When the vehicle undergoes emergency braking, the rod is subjected to the maximum force, at which time the influence of other factors on the force on the rod can be ignored. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows the force of the rods when the vehicle undergoes emergency braking, and it can be seen from the figure that when the vehicle undergoes stable deceleration, the stabilized value of the force of the upper tie rod is about 5.6kN, the stabilized value of the force of the lower tie rod is about 1.5kN, and the ratio of the upper tie rod force to the lower tie rod force is about 4:1; the stabilized value of the force of the lateral connecting rod is about 4.9kN, and the ratio of the unilateral longitudinal force to the lateral connecting rod force is 1.44. The measured results are basically consistent with the theoretical calculations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"3. Tire six component force test","content":"\u003cp\u003eThe wheel six component force consists of the three-directional forces of the road acting at the center of the wheel and the three-directional moments formed by these forces. The analysis of tire force helps to predict the fatigue life of the vehicle structure as well as to analyze the effect of tire force on the wheel hub, it is important for vehicle and wheel development[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e],and provides an important basis for subsequent wheel hub improvement programs.\u003c/p\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Measuring point arrangement\u003c/h2\u003e \u003cp\u003eThe vertical force of the running wheel and the lateral force of the stabilizing wheel are obtained by testing the dynamic displacement of the tire relative to the track with the laser sensor; the longitudinal force of the running wheel is obtained by testing the longitudinal strain of the calibrated traction tie rod. The laser displacement sensor and tie rod strain measuring point arrangement is shown in Fig.\u0026nbsp;6.\u003c/p\u003e\u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Result processing\u003c/h2\u003e \u003cp\u003eTire displacement multiplied by the corresponding tire radial rigidity can be directly obtained tire force, each tire radial rigidity and pre-pressure as shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Tire dynamic force processing to \"compression\" force is positive, \"stretch\" force is negative. The following table shows the maximum dynamic compressive force of the tires (without superimposed pre-pressure) with 99.85% confidence level. The maximum tire tensile and compressive forces for each site interval are shown for AW0 and AW3 loading conditions.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eTire stiffness and preload\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eRunning wheel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eHorizontal wheel\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRadial rigidity AW0/AW3 (kN/mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePre-pressure AW0/AW3 (kN)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRadial rigidity (kN/mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePre-pressure (kN)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1.466/1.592\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e37.5/66.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.44\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.3. Test result\u003c/h2\u003e \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e \u003ch2\u003e3.3.1. Vertical force of the running wheel\u003c/h2\u003e \u003cp\u003eIn this paper, the dynamic vertical force of the running wheel is measured when the vehicle is traveling on the line proper, and due to space limitation, only the interval when the vertical force of the running wheel is at its maximum is listed below. Figures\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e7\u003c/span\u003e and \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e8\u003c/span\u003e respectively show the test results in the intervals where the maximum compressive force occurs in the wheels at AW0 and AW3 loads of the vehicle. At AW0 loading, the maximum vertical force on the running wheel is 19.3kN, which occurs at the right running wheel of the 1-position frame; at AW3 loading, the maximum vertical force on the running wheel is 25.9kN, which occurs at the left running wheel of the 1-position frame. The vertical forces on the running wheel at both AW0 load and AW3 load were not exceeded. Meet the design criteria.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section3\"\u003e \u003ch2\u003e3.3.2. Longitudinal force of the running wheel\u003c/h2\u003e \u003cp\u003eThe longitudinal force of the running wheel was calculated by measuring the strain of the frame rods, and Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the test results of the corresponding intervals at the maximum value of the longitudinal force of the tires at AW0 and AW3 loads, including the emergency braking condition as well as the normal driving condition on the positive line. It can be seen that the maximum longitudinal force of the running wheel tires during emergency braking is 12.8kN for AW0 load and 8.1kN for normal driving on the positive line, and the maximum longitudinal force of the running wheel tires during emergency braking is 19.5kN for AW3 load and 9.5kN for normal driving on the positive line. The longitudinal forces on the running wheel at both AW0 load and AW3 load were not exceeded. Meet the design criteria.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eLongitudinal force results of running wheel\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWorking condition\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAW0 tire longitudinal force(maximum tensile force)/kN\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAW0 tire longitudinal force(maximum compressive force)/kN\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAW3 tire longitudinal force(maximum tensile force)/kN\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eAW3 tire longitudinal force(maximum compressive force)/kN\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEmergency braking\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e12.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e12.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e19.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e12.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNormal operation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e9.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section3\"\u003e \u003ch2\u003e3.3.3. The lateral force of guide wheel\u003c/h2\u003e \u003cp\u003eThe lateral force of guide wheel is obtained by testing the dynamic lateral displacement of the tire relative to the track with a laser sensor. Due to space constraints, Figs.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e9\u003c/span\u003e and \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e10\u003c/span\u003e respectively show the test results for the driving intervals corresponding to the maximum values of the lateral force of guide wheel for vehicle loads of AW0 and AW3. The maximum value of the lateral force of guide wheel under AW0 load is 8.3kN, which occurs at the right guide wheel of the 1-position frame; the maximum value of the lateral force of guide wheel under AW3 load is 9.5kN, which occurs at the left guide wheel of the 2-position frame. The lateral forces on the guide wheel were not exceeded for both AW0 and AW3 loads. Meet the design criteria.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section3\"\u003e \u003ch2\u003e3.3.4. Lateral force of stabilizing wheel\u003c/h2\u003e \u003cp\u003eLike the lateral force of guide wheel, the lateral force of stabilizing wheel is also obtained from the dynamic lateral displacement of the tire relative to the track as measured by the laser sensor. Due to space constraints, only the results of the following driving intervals corresponding to the maximum values of the lateral force of stabilizing wheel are presented, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e11\u003c/span\u003e and \u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e12\u003c/span\u003e. In particular, the maximum value of the lateral force of the stabilizing wheel under AW0 loading was 7.1kN, which appeared in the left stabilizing wheel of the 1-position frame; the maximum value of the lateral force of the stabilizing wheel under AW3 loading was 7.5kN, which appeared in the left stabilizing wheel of the 1-position frame. The lateral forces on the stabilizing wheel were not exceeded for both AW0 and AW3 loads. Meet the design criteria.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section3\"\u003e \u003ch2\u003e3.3.5. Three-direction torque\u003c/h2\u003e \u003cp\u003eThe three-direction torques are calculated as shown below: the rocking head torque is the product of the difference between the longitudinal force of the left and right side drawbars and half of the transverse span; the slewing torque is the product of the longitudinal force of the tires and the radius of the wheels; and the side-rolling torque is the product of the difference between the vertical force of the left and right side running wheels and half of the transverse span. According to the above calculation method, the following three-direction torque test results were obtained by measuring the relevant indexes, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eStatistics of maximum three-direction torque\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eWorking condition\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eAW0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e \u003cp\u003eAW3\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRocking head torque kN.m\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSlewing torque kN.m\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSide-rolling torque kN.m\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRocking head torque kN.m\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eSlewing torque kN.m\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eSide-rolling torque kN.m\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEmergency braking\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\\\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e8.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\\\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNormal operation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e4.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e4.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"4. Hub dynamic stress","content":"\u003cp\u003eThis section respectively test the dynamic stress levels in the wheel hubs of vehicles under AW0 (empty) and AW3 (heavy) loads, to assess the fatigue strength of the hubs according to the relevant guidelines. The rainflow counting and average stress correction were performed on the dynamic stress time course, and the cumulative damage at the corresponding measurement point was analyzed and the equivalent stress amplitude was calculated according to Miner's cumulative damage principle and the type of welded joint corresponding to each measurement point。\u003c/p\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003e4.1. Measuring point arrangement\u003c/h2\u003e \u003cp\u003eThe dynamic stress measurement points of the inner hub are numbered as 3, 4, 5 and 7, and the dynamic stress measurement points of the outer hub are numbered as 3, 4, 5 and 8. Measurement points 3, 4 and 5 of the inner and outer hubs are shown in Fig.\u0026nbsp;13, and measurement point 7 of the inner hub is located at the back of the inner hub in the figure, symmetrical to the center of the hub with the measurement point 3; and measurement point 8 of the outer hub is located at the back of the outer hub in the figure, corresponding to the position of the measurement point 3.\u003c/p\u003e \u003cdiv id=\"Sec19\" class=\"Section2\"\u003e \u003ch2\u003e4.2. Test result\u003c/h2\u003e \u003cp\u003eThe sampling frequency of this test was 2400 Hz, and the dynamic stress time course obtained from this test was corrected for rainflow cycle counting and average stress to obtain 32 levels of zero-mean magnitude-frequency stress spectra. Due to the anomalies in individual data points during the test, the data anomaly measurement points were eliminated\u003c/p\u003e \u003cdiv id=\"Sec20\" class=\"Section3\"\u003e \u003ch2\u003e4.2.1. IIW Standard Wheel Dynamic Stress Evaluation Results\u003c/h2\u003e \u003cp\u003eThe measurement points were evaluated according to the equivalent stress amplitude calculation method in Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e1.2\u003c/span\u003e and the fatigue strength assessment guidelines in Section 1.3, and the evaluation results are shown in Tables\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and 6.AW0 condition has 1 point cumulative damage more than 0.5, does not meet the requirements; AW3 condition has 3 measurement points cumulative damage more than 0.5, does not meet the requirements, and one of the inner hub measurement point 3 equivalent stress amplitude up to 51.4MPa, although does not exceed the fatigue limit of 51.5Mpa, but the calculated mileage is only 31,000 kilometers.\u003c/p\u003e \u003ctable id=\"Tab5\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eThe equivalent stress amplitude and evaluation results of each measuring point under AW0 condition\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"7\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMeasurement point location\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMaximum stress (MPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMinimum stress\u003c/p\u003e\n \u003cp\u003e(MPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eStress amplitude\u003c/p\u003e\n \u003cp\u003e(MPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eEquivalent stress amplitude\u003c/p\u003e\n \u003cp\u003e(MPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCalculating mileage (10\u003csup\u003e4\u003c/sup\u003ekm)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCumulative damage\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eInside Hub 3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e29.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-22.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e25.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e24.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e129\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.77338\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eInside Hub 4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e24.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-27.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e25.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e16.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e889\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.11247\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eInside Hub 5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-7.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e26256756\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.00000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eInside Hub 7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-6.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e115355112\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.00000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eOuter Hub 3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e17.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-13.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e15.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e18474\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.00541\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eOuter Hub 4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e16.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-11.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e14.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e39675\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.00252\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eOuter Hub 5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e16.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-13.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e14.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10897\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.00918\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eOuter Hub 8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e54.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-32.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e43.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e19.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e417\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.24008\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\u003ctable id=\"Tab6\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eThe equivalent stress amplitude and evaluation results of each measuring point under AW3 condition\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"11\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eMeasurement point location\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eMaximum stress (MPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eMinimum stress\u003c/p\u003e\n \u003cp\u003e(MPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eStress amplitude\u003c/p\u003e\n \u003cp\u003e(MPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eEquivalent stress amplitude\u003c/p\u003e\n \u003cp\u003e(MPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCalculating mileage (10\u003csup\u003e4\u003c/sup\u003ekm)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCumulative damage\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eInside Hub 3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e46.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e-32.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e39.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e51.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e31.81462\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eInside Hub 4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e37.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e-27.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e32.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e34.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e22.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.54828\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eInside Hub 5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e9.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e-8.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e8.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5140807.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00002\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eInside Hub 7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e8.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e-8.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e8.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19987422.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00001\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eOuter Hub 3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e25.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e-18.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e21.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e18.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e527.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.18970\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eOuter Hub 4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e23.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e-17.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e20.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1608.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.06217\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eOuter Hub 5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e24.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e-20.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e22.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e21.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e252.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.39614\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eOuter Hub 8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e33.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e-28.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e31.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e32.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e32.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.06624\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e \u003c/div\u003e \u003cdiv id=\"Sec21\" class=\"Section3\"\u003e \u003ch2\u003e4.2.2. Wheel dynamic stress during emergency braking\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e14\u003c/span\u003e shows the variation of dynamic stresses in the wheel hub during emergency braking under AW3 loading, and it can be clearly seen that at the moment of emergency braking, there is no abnormal change in the dynamic stresses in the wheel hub, and the magnitude of the value tends to stabilize。\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec22\" class=\"Section3\"\u003e \u003ch2\u003e4.2.3. Wheel dynamic stress principal frequency analysis\u003c/h2\u003e \u003cp\u003eFrom Fig.\u0026nbsp;15(a), it can be seen that the main frequencies of hub dynamic stresses are mainly 6.5 Hz, 13 Hz, and 19.5 Hz, which correspond to the rotational, twofold, and threefold frequencies, respectively, whereas the 35th-order tire shoulder polygon wear frequency is not obvious in the hub dynamic stresses. From Fig.\u0026nbsp;15(b), it can be seen that the energies below 20 Hz are larger throughout the time period, and the hub dynamic stresses are mainly affected by these frequencies.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec23\" class=\"Section3\"\u003e \u003ch2\u003e4.2.4. Effect of polygon wear on dynamic stresses in hub\u003c/h2\u003e \u003cp\u003eFrom section \u003cspan refid=\"Sec22\" class=\"InternalRef\"\u003e4.2.3\u003c/span\u003e, it can be seen that the polygon abrasion frequency hub dynamic stress effect is not obvious, in order to further verify, this section of the AW3 load dynamic stress raw data for polygonal frequency bandstop filtering, to remove the effect of polygonal vibration on the dynamic stress of the hub, the comparison results are shown in Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e, all the points of the original cumulative damage and the cumulative damage after the bandstop filtering error of not more than 5%, it can be seen that the tire shoulder polygonal It can be seen that the shoulder polygonal abrasion has little effect on the dynamic stress of the wheel hub。\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe influence of shoulder polygon on dynamic stress of wheel hub under AW3 load\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eMeasurement point location\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eEquivalent stress amplitude (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eCumulative damage\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInitial\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBandstop filtering\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eInitial\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBandstop filtering\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInside Hub 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e51.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e51.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e31.81462\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e31.72966\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInside Hub 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e34.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e34.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4.54828\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4.50702\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInside Hub 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.00002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.00002\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInside Hub 7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.00001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.00000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOuter Hub 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e18.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e18.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.18970\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.18889\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOuter Hub 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e14.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e14.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.06217\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.06074\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOuter Hub 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e21.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e21.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.39614\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.39197\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOuter Hub 8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e32.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e32.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.06624\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.94940\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eThis paper analyzes wheel anomalies occurring in a straddle monorail vehicle, and performs tire six component force tests as well as wheel dynamic stress fatigue strength tests. The results show that the maximum dynamic loads of the vertical force of the running wheel, the lateral force of the guide wheel and the lateral force of the stabilizing wheel are all within the limit load range and have a certain safety margin; In the AW0 condition, there is one measurement point with accumulated damage over 0.5, which does not meet the requirements; in the AW3 condition, there are three measurement points with accumulated damage over 0.5, which does not meet the requirements, of which the equivalent force amplitude of the inner hub measurement point 3 reaches 51.4MPa, although it does not exceed the fatigue limit of 51.5Mpa, but the calculated mileage is only 31,000 kilometers, and the rest of the test indexes do not see any abnormality; at the moment of emergency braking, there is no abnormal change in wheel dynamic stresses, and the tire shoulder polygon wear has little effect on wheel dynamic stresses. This paper analyzes the cause of the wheel hub abnormality of the straddle monorail vehicles through the test, and the tire six component force test and the wheel hub dynamic stress test of the vehicle provides an important reference for the subsequent design of the wheel hub.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eZengchuang Zhao,Pingbo Wu and Lihui Ren wrote the main manuscript text and all of them prepared all figures 1-3. All authors reviewed the manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eMa, J. Research on Static and Dynamic Behavior of Straddle Monorail Transit System Structure. Southwest Jiaotong University, 2008.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHe, X. Application and Prospect of Straddle Monorail Transit System in China[J/OL]. Urban Rail Transit, 2015, 1(1): 26\u0026ndash;34. DOI:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1007/s40864-015-0006-9\u003c/span\u003e\u003cspan address=\"10.1007/s40864-015-0006-9\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang, J. Research on Dynamics of Straddle Monorail Vehicles. Southwest Jiaotong University, 2009.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhu, X. Analysis of the Bogie Structure of Straddle Monorail Vehicles. Chongqing Jiaotong University, 2011.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYang, Z., Du, Z., Xu, Z., et al. Research on dynamic behavior of train dynamic model of straddle-type monorail[J/OL]. Noise Vib World, 2020, 51(11): 195\u0026ndash;207.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDu, Z., Li, Y., Liang, Z., et al. Research on Curve through Safety of Straddle-type Monorail Vehicle. Elec Dr Locomot, 2016 (01): 79\u0026ndash;83.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eXu, X., Du, Z., Xin, L., et al. Study on Equivalent Calculation of Rigid Flexible Coupling Dynamics of Straddle Monorail. Mach Des Manuf, 2022 (06): 278\u0026ndash;281\u0026thinsp;+\u0026thinsp;285.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWen, X. Research on the Mechanism and Control Method of Tire Eccentric Wear of Straddle Type Monorail Vehicles. Chongqing Jiaotong University, 2018.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYao, Z., Wei, Y., Lv, J. A heavy load tire six-component force sensor[J/OL]. Int J Front Eng Technol, 2021, 3(3). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://francis-press.com/papers/4102\u003c/span\u003e\u003cspan address=\"https://francis-press.com/papers/4102\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRen, L., Zhou, J., Shen, G. Dynamics Model and Simulation Study of a Straddle Type Monorail Car. China Railway Sci, 2004 (05): 28\u0026ndash;34.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShen, L., Zhang, J. Analysis of Mechanical Property of Straddle Monorail Vehicle Based on Tyre. Elec Dr Locomot, 2019 (04): 22\u0026ndash;26.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLu, D., Xia, D. Research Progress on Prediction of Force and Moment Characteristics of Automobile Tire. Tire Ind, 20221, 41 (03): 185\u0026ndash;189.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJi, Z., Wang, Tie., Li, G. Fatigue Life Analysis of Frame with Measured Six-Component Wheel Force. Mach Des Manuf, 2020,353 (07): 25\u0026ndash;28.\u003c/span\u003e\u003c/li\u003e \u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"discover-applied-sciences","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Applied Sciences](https://link.springer.com/journal/42452)","snPcode":"42452","submissionUrl":"https://submission.springernature.com/new-submission/42452/3","title":"Discover Applied Sciences","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"straddle type monorail vehicle, six-component force of tire, wheel hub fatigue, dynamic stress","lastPublishedDoi":"10.21203/rs.3.rs-3842516/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3842516/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis article is based on the tire six component force test and wheel hub fatigue test of a certain type of straddle monorail vehicle, and analyzes the reasons for the abnormal phenomenon of the vehicle's wheel hub. Firstly, the vehicle connecting rod was calibrated in the laboratory to obtain the \"force strain\" coefficient of the connecting rod under tension and compression conditions. The accuracy of this calibration was verified by comparing it with the experimental results; Subsequently, the dynamic displacement of the vehicle and the strain of the connecting rod were obtained by installing displacement sensors at different positions, and the six component force data of the tire was obtained; Finally, based on the IIW standard, the fatigue strength of the wheel hub under AW0 and AW3 operating conditions was evaluated, and the dynamic stress of the wheel hub during emergency braking, the dominant frequency of the dynamic stress of the wheel hub, and the influence of polygonal wear on the dynamic stress of the wheel hub were analyzed. The results show that the maximum dynamic loads of the vertical force of the running wheel, the lateral force of the guide wheel, and the lateral force of the stabilizing wheel are all within the limit load range, and there is a certain safety margin to ensure safe operation; Under the IIW standard, there are 1 point and 3 points on the wheel hub under AW0 and AW3 working conditions that do not meet the fatigue strength criterion requirements, and there are no abnormalities in the other indicators; During emergency braking, there was no abnormal change in the dynamic stress of the wheel hub, and the polygonal wear of the tire shoulder had little effect on the dynamic stress of the wheel hub. This explains the abnormal phenomenon of the vehicle's wheel hub and provides an important reference for subsequent wheel hub design.\u003c/p\u003e","manuscriptTitle":"Abnormal analysis of wheel hub of a straddle monorail vehicle","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-04-05 16:35:45","doi":"10.21203/rs.3.rs-3842516/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-05-05T13:47:11+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-05-05T13:38:51+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-04-29T13:53:04+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"331776077308236623205451479445235448811","date":"2024-04-27T07:52:01+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"48d5072b-b043-4431-ba37-68acf534dffc","date":"2024-04-24T03:22:05+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"d723e9d3-4e9a-426b-bea2-6781f92a1745","date":"2024-04-08T15:47:46+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-04-03T02:55:55+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-04-02T12:08:12+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-04-02T12:06:12+00:00","index":"","fulltext":""},{"type":"submitted","content":"Discover Applied Sciences","date":"2024-01-07T12:39:44+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"discover-applied-sciences","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Applied Sciences](https://link.springer.com/journal/42452)","snPcode":"42452","submissionUrl":"https://submission.springernature.com/new-submission/42452/3","title":"Discover Applied Sciences","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"2f5dd868-de2a-4e4b-8145-98bf867eaae1","owner":[],"postedDate":"April 5th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2024-10-03T10:08:26+00:00","versionOfRecord":[],"versionCreatedAt":"2024-04-05 16:35:45","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3842516","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3842516","identity":"rs-3842516","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}