Jingxiu Ling Haoyu 2023a - Revision history

Rimni: /* 5. Conclusions */

2023-04-28T11:43:21Z

‎5. Conclusions

Rimni: /* References */

2023-04-28T11:37:51Z

‎References

Rimni at 11:20, 28 April 2023

2023-04-28T11:20:37Z

Rimni at 09:05, 28 April 2023

2023-04-28T09:05:30Z

Rimni at 14:38, 27 April 2023

2023-04-27T14:38:23Z

Rimni at 14:06, 27 April 2023

2023-04-27T14:06:30Z

Rimni at 14:05, 27 April 2023

2023-04-27T14:05:53Z

Rimni at 12:34, 27 April 2023

2023-04-27T12:34:22Z

Rimni: /* ORCID iDs */

2023-04-27T11:28:51Z

‎ORCID iDs

Rimni at 11:27, 27 April 2023

2023-04-27T11:27:24Z

@@ Line 979: / Line 979: @@
 :(1) The virtual prototype model is built to obtain the time force history of bearing based on the actual working conditions in the absence of virbration signal measurement equipment. Meanwhile, the accurcy and effectiveness of time force history is vertfied by the convolution neural network.
-:(2) The fatigue of the bearing which occurred at the ball is shown from stress&strain nephogram. Based on the stress&strain nephogram, it is known that the fatigue of the bearing occurred at the ball. The maximum equivalent force is 1361.2Mpa and the equivalent strain becomes 7.40e-3mm/mm.
+:(2) The fatigue of the bearing which occurred at the ball is shown from stress&strain nephogram. Based on the stress&strain nephogram, it is known that the fatigue of the bearing occurred at the ball. The maximum equivalent force is 1361.2 MPa and the equivalent strain becomes 7.40e-3 mm/mm.
 :(3) The stress-strain history at the hazardous location is obtained. A new coordinate system is established through the hazard nodes and the critical plane search is carried out based on the principle of maximum normal strain variation for maximum shear strain. The critical plane of the weights is determined to be  <math display="inline">\phi =100^{\circ }</math>,  <math display="inline">\theta =60^{\circ }</math> according to the Manson-Coffin equation.

@@ Line 1,012: / Line 1,012: @@
 [1] Lundberg G.,  Palmgren A. Dynamic capacity of rolling bearings. Acta Polytechnica Scandinavicai, Mechanical Engineering Series, 1(3):7-53, 1947.
-[2] Ioannidess E., Harris T.A. A new fatigue life model for rolling bearings. ASME J Tribol, 107(3):367-377, 1985.
+[2] Ioannidess E., Harris T.A. A new fatigue life model for rolling bearings. ASME J. Tribol, 107(3):367-377, 1985.
 [3]  Zaretsky E.V.,  Vlcek B.L.,  Hendricks R.C. Effect of silicon nitride balls and rollers on rolling bearing life. Tribology Transactions, 48(3):425-435, 2005.
@@ Line 1,076: / Line 1,076: @@
 [33] Wu Z.R., Li X., Fang L., Song Y.D. Multiaxial fatigue life prediction based on nonlinear continuum damage mechanics and critical plane method. Journal of Materials Engineering and Performance, 27(6):3144-3152, 2018.
-[34] Iftikhar S.H., Albinmousa J. A method for assessing critical plane-based multiaxial fatigue damage models. Fatigue & Fracture of Engineering Materials & Structures. 2018;41(1):235-45.
+[34] Iftikhar S.H., Albinmousa J. A method for assessing critical plane-based multiaxial fatigue damage models. Fatigue & Fracture of Engineering Materials & Structures, 41(1):235-245, 2018.
 [35] Feltner C.E.,  Morrow J.D. Microplastic  strain hysteresis  energy  as  a  criterion  for  fatigue  fracture. Journal of Basic Engineering, 83(1):15-22, 1961.
 [36]  Brown M.W.,  Miller K.J. A theory for fatigue failure under multiaxial sress-strain conditions. Proceedings of the Institution of Mechanical Engineers, 187(65):745-755, 1973.

@@ Line 1,066: / Line 1,066: @@
 [28] Braccesi C., Morettini G,, Cianetti F,, Palmieri M. Development of a new simple energy method for life prediction in multiaxial fatigue. International Journal of Fatigue, 112:1-8, 2018.
-[29] Wei H, Liu Y. A critical plane-energy model for multiaxial fatigue life prediction. Fatigue & Fracture of Engineering Materials & Structures. 2017;40(12):1973-83.
+[29] Wei H., Liu Y. A critical plane-energy model for multiaxial fatigue life prediction. Fatigue & Fracture of Engineering Materials & Structures, 40(12):1973-1983, 2017.
-[30] Wang YY, Zhang XF, Dong XL, Yao WX. Multiaxial fatigue assessment for outer cylinder of landing gear by critical plane method. Proceedings of the Institution of Mechanical Engineers Part G-Journal of Aerospace Engineering. 2022;236(5):993-1005.
+[30] Wang Y.Y., Zhang X.F., Dong X.L., Yao W.X. Multiaxial fatigue assessment for outer cylinder of landing gear by critical plane method. Proceedings of the Institution of Mechanical Engineers Part G-Journal of Aerospace Engineering, 236(5):993-1005, 2022.
-[31] Luo P, Yao WX, Susmel L. An improved critical plane and cycle counting method to assess damage under variable amplitude multiaxial fatigue loading. Fatigue & Fracture of Engineering Materials & Structures. 2020;43(9):2024-39.
+[31] Luo P., Yao W.X., Susmel L. An improved critical plane and cycle counting method to assess damage under variable amplitude multiaxial fatigue loading. Fatigue & Fracture of Engineering Materials & Structures, 43(9):2024-2039, 2020.
-[32] Liu JH, Zhang Z, Li B, Lang SS. Multiaxial Fatigue Life Prediction of GH4169 Alloy Based on the Critical Plane Method. Metals. 2019;9(2).
+[32] Liu J.H., Zhang Z., Li B., Lang S.S. Multiaxial fatigue life prediction of GH4169 alloy based on the critical plane method. Metals, 9(2), 255, 2019.
-[33] Wu ZR, Li X, Fang L, Song YD. Multiaxial Fatigue Life Prediction Based on Nonlinear Continuum Damage Mechanics and Critical Plane Method. Journal of Materials Engineering and Performance. 2018;27(6):3144-52.
+[33] Wu Z.R., Li X., Fang L., Song Y.D. Multiaxial fatigue life prediction based on nonlinear continuum damage mechanics and critical plane method. Journal of Materials Engineering and Performance, 27(6):3144-3152, 2018.
-[34] Iftikhar SH, Albinmousa J. A method for assessing critical plane-based multiaxial fatigue damage models. Fatigue & Fracture of Engineering Materials & Structures. 2018;41(1):235-45.
+[34] Iftikhar S.H., Albinmousa J. A method for assessing critical plane-based multiaxial fatigue damage models. Fatigue & Fracture of Engineering Materials & Structures. 2018;41(1):235-45.
-[35] C.E.FELTNER,  JD Morrow. Microplastic  strain hysteresis  energy  as  a  criterion  for  fatigue  fracture. Journal of Basic Engineering. 1961;83(1):15-22.
+[35] Feltner C.E.,  Morrow J.D. Microplastic  strain hysteresis  energy  as  a  criterion  for  fatigue  fracture. Journal of Basic Engineering, 83(1):15-22, 1961.
-[36] M. W. Brown, KJ Miller. A Theory for Fatigue Failure under Multiaxial Sress-Strain Conditions. Proceedings of the Institution of Mechanical Engineers. 1973;187(65):745-55.
+[36]  Brown M.W.,  Miller K.J. A theory for fatigue failure under multiaxial sress-strain conditions. Proceedings of the Institution of Mechanical Engineers, 187(65):745-755, 1973.

@@ Line 1,040: / Line 1,040: @@
 [15] Wu Y., Yuan M., Dong S., Lin L., Liu Y. Remaining useful life estimation of engineered systems using vanilla LSTM neural networks. Neurocomputing, 275:167-79, 2018.
-[16] Tao Z.Q., Zhang M., Zhu Y., Cai T, Zhang ZL, Liu H, et al. Multiaxial notch fatigue life prediction based on the dominated loading control mode under variable amplitude loading. Fatigue & Fracture of Engineering Materials & Structures. 2021;44(1):225-39.
+[16] Tao Z.Q., Zhang M., Zhu Y., Cai T., Zhang Z.L., Liu H., Bai B., Li D.H. Multiaxial notch fatigue life prediction based on the dominated loading control mode under variable amplitude loading. Fatigue & Fracture of Engineering Materials & Structures, 44(1):225-239, 2021.
-[17] Morettini G, Braccesi C, Cianetti F. Experimental multiaxial fatigue tests realized with newly developed geometry specimens. Fatigue & Fracture of Engineering Materials & Structures. 2019;42(4):827-37.
+[17] Morettini G., Braccesi C., Cianetti F. Experimental multiaxial fatigue tests realized with newly developed geometry specimens. Fatigue & Fracture of Engineering Materials & Structures, 42(4):827-837, 2019.
-[18] Sakane M, Itoh T. A synthesis of cracking directions in tension-torsion multiaxial low cycle fatigue at high and room temperatures. Theoretical and Applied Fracture Mechanics. 2018;98:13-22.
+[18] Sakane M, Itoh T. A synthesis of cracking directions in tension-torsion multiaxial low cycle fatigue at high and room temperatures. Theoretical and Applied Fracture Mechanics, 98:13-22, 2018.
-[19] Ottosen NS, Ristinmaa M, Kouhia R. Enhanced multiaxial fatigue criterion that considers stress gradient effects. International Journal of Fatigue. 2018;116:128-39.
+[19] Ottosen N.S., Ristinmaa M., Kouhia R. Enhanced multiaxial fatigue criterion that considers stress gradient effects. International Journal of Fatigue, 116:128-139, 2018.
-[20] Htoo AT, Miyashita Y, Otsuka Y, Mutoh Y, Sakurai S. Notch fatigue behavior of Ti-6A1-4V alloy in transition region between low and high cycle fatigue. International Journal of Fatigue. 2017;95:194-203.
+[20] Htoo A.T., Miyashita Y., Otsuka Y., Mutoh Y., Sakurai S. Notch fatigue behavior of Ti-6A1-4V alloy in transition region between low and high cycle fatigue. International Journal of Fatigue, 95:194-203, 2017.
-[21] Wu CB, Kim JW. Numerical prediction of deformation in thin-plate welded joints using equivalent thermal strain method. Thin-Walled Structures. 2020;157.
+[21] Wu C.B., Kim J.W. Numerical prediction of deformation in thin-plate welded joints using equivalent thermal strain method. Thin-Walled Structures, 157, 107033, 2020.
-[22] Peng YQ, Cai LX, Chen H, Bao C. A Theoretical Model for Predicting Uniaxial Stress-Strain Relations of Ductile Materials by Small Disk Experiments Based on Equivalent Energy Method. Transactions of the Indian Institute of Metals. 2019;72(1):133-41.
+[22] Peng Y.Q., Cai L.X., Chen H., Bao C. A theoretical model for predicting uniaxial stress-strain relations of ductile materials by small disk experiments based on equivalent energy method. Transactions of the Indian Institute of Metals, 72(1):133-141, 2019.
-[23] Kim Y, Kim J, Kang S. A Study on Welding Deformation Prediction for Ship Blocks Using the Equivalent Strain Method Based on Inherent Strain. Applied Sciences-Basel. 2019;9(22).
+[23] Kim Y., Kim J., Kang S. A study on welding deformation prediction for ship blocks using the equivalent strain method based on inherent strain. Applied Sciences-Basel, 9(22), 4906, 2019.
-[24] Li X, Jiang XL, Hopman H. A strain energy-based equivalent layer method for the prediction of critical collapse pressure of flexible risers. Ocean Engineering. 2018;164:248-55.
+[24] Li X., Jiang X.L., Hopman H. A strain energy-based equivalent layer method for the prediction of critical collapse pressure of flexible risers. Ocean Engineering, 164:248-255, 2018.
-[25] Rigon D, Berto F, Meneghetti G. Estimating the multiaxial fatigue behaviour of C45 steel specimens by using the energy dissipation. International Journal of Fatigue. 2021;151.
+[25] Rigon D., Berto F., Meneghetti G. Estimating the multiaxial fatigue behaviour of C45 steel specimens by using the energy dissipation. International Journal of Fatigue, 151, 106381, 2021.
-[26] Gan L, Wu H, Zhong Z. Multiaxial fatigue life prediction based on a simplified energy-based model. International Journal of Fatigue. 2021;144.
+[26] Gan L., Wu H., Zhong Z. Multiaxial fatigue life prediction based on a simplified energy-based model. International Journal of Fatigue, 144, 106036, 2021.
-[27] Feng ES, Wang XG, Jiang C. A new multiaxial fatigue model for life prediction based on energy dissipation evaluation. International Journal of Fatigue. 2019;122:1-8.
+[27] Feng E.S., Wang X.G., Jiang C. A new multiaxial fatigue model for life prediction based on energy dissipation evaluation. International Journal of Fatigue, 122:1-8, 2019.
-[28] Braccesi C, Morettini G, Cianetti F, Palmieri M. Development of a new simple energy method for life prediction in multiaxial fatigue. International Journal of Fatigue. 2018;112:1-8.
+[28] Braccesi C., Morettini G,, Cianetti F,, Palmieri M. Development of a new simple energy method for life prediction in multiaxial fatigue. International Journal of Fatigue, 112:1-8, 2018.
 [29] Wei H, Liu Y. A critical plane-energy model for multiaxial fatigue life prediction. Fatigue & Fracture of Engineering Materials & Structures. 2017;40(12):1973-83.

@@ Line 1,009: / Line 1,009: @@
 <div class="auto" style="text-align: left;width: auto; margin-left: auto; margin-right: auto;font-size: 85%;">
 [1] Lundberg G.,  Palmgren A. Dynamic capacity of rolling bearings. Acta Polytechnica Scandinavicai, Mechanical Engineering Series, 1(3):7-53, 1947.
@@ Line 1,035: / Line 1,034: @@
 [12] Zhai X., Wei X., Yang J. A comparative study on the data-driven based prognostic approaches for RUL of rolling bearings. 2019 IEEE Symposium Series on Computational Intelligence (SSCI), Xiamen, China, pp. 1751-1755, 2019.
-[13] Cao L., Qian Z., Zareipour H., Wood D., Mollasalehi E., Tian S., et al. Prediction of remaining useful life of wind turbine bearings under non-stationary operating conditions. 2018;11(12):3318.
+[13] Cao L., Qian Z., Zareipour H., Wood D., Mollasalehi E., Tian S., Pei Y. Prediction of remaining useful life of wind turbine bearings under non-stationary operating conditions. Energies, 11(12):3318, 2018.
-[14] Gao TH, Li YX, Huang XZ, Wang CL. Data-Driven Method for Predicting Remaining Useful Life of Bearing Based on Bayesian Theory. Sensors. 2021;21(1).
+[14] Gao T.H., Li Y.X., Huang X.Z., Wang C.L. Data-driven method for predicting remaining useful life of bearing based on Bayesian theory. Sensors, 21(1):182, 2021.
-[15] Wu Y, Yuan M, Dong S, Lin L, Liu Y. Remaining useful life estimation of engineered systems using vanilla LSTM neural networks. Neurocomputing. 2018;275:167-79.
+[15] Wu Y., Yuan M., Dong S., Lin L., Liu Y. Remaining useful life estimation of engineered systems using vanilla LSTM neural networks. Neurocomputing, 275:167-79, 2018.
-[16] Tao ZQ, Zhang M, Zhu Y, Cai T, Zhang ZL, Liu H, et al. Multiaxial notch fatigue life prediction based on the dominated loading control mode under variable amplitude loading. Fatigue & Fracture of Engineering Materials & Structures. 2021;44(1):225-39.
+[16] Tao Z.Q., Zhang M., Zhu Y., Cai T, Zhang ZL, Liu H, et al. Multiaxial notch fatigue life prediction based on the dominated loading control mode under variable amplitude loading. Fatigue & Fracture of Engineering Materials & Structures. 2021;44(1):225-39.
 [17] Morettini G, Braccesi C, Cianetti F. Experimental multiaxial fatigue tests realized with newly developed geometry specimens. Fatigue & Fracture of Engineering Materials & Structures. 2019;42(4):827-37.

@@ Line 838: / Line 838: @@
 {| class="wikitable" style="margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;width:auto;"
 |-style="text-align:center"
-! style ="font-size:100%;| <math display="inline">\varepsilon</math> !! <math display="inline">\gamma</math> !! <math display="inline">\sigma</math>
+!  <math display="inline">\varepsilon</math> !! <math display="inline">\gamma</math> !! <math display="inline">\sigma</math>
 |-
 |  style="text-align: center;vertical-align: top;"|-1.28E-02

@@ Line 994: / Line 994: @@
 This work was supported by the China Postdoctoral Science Foundation (Granted No. 2020M671956), Natural Science Foundation of Fujian (Granted No. 2020J01871), Scientific Research Foundation of Fujian University of Technology (Granted No.GY-Z160048) and Fujian Province Foreign Cooperation Industrialization Project (Grant No.2021I1006).
 <!--==ORCID iDs==
@@ Line 1,001: / Line 1,000: @@
 Haoyu Li: [https://orcid.org/0000-0003-3586-7483 https://orcid.org/0000-0003-3586-7483]
 -->
 ==Acknowledges==
@@ Line 1,010: / Line 1,008: @@
 ==References==
-[1] Gustaf Lundberg, Arvid Palmgren. Dynamic Capacity of Rolling Bearings. Acta Polytechnica Scandinavicai, Mechanical Engineering Series. 1947;1(3):pp 7-53.
+<div class="auto" style="text-align: left;width: auto; margin-left: auto; margin-right: auto;font-size: 85%;">
-[2] E.  loannides  TAH. A New Fatigue Life Model for Rolling Bearings. J Tribol—T ASME. 1985;107(3):367-78.
+[2] Ioannidess E., Harris T.A. A new fatigue life model for rolling bearings. ASME J Tribol, 107(3):367-377, 1985.
-[3] ERWIN V. ZARETSKY BLVRCH. Effect of Silicon Nitride Balls and Rollers on Rolling Bearing Life. Tribology Transactions. 2005;48:3:425-35.
+[3]  Zaretsky E.V.,  Vlcek B.L.,  Hendricks R.C. Effect of silicon nitride balls and rollers on rolling bearing life. Tribology Transactions, 48(3):425-435, 2005.
-[4] Yakout M, Elkhatib A, Nassef MGA. Rolling element bearings absolute life prediction using modal analysis. Journal of Mechanical Science and Technology. 2018;32(1):91-9.
+[4] Yakout M., Elkhatib A., Nassef, M.G.A. Rolling element bearings absolute life prediction using modal analysis. Journal of Mechanical Science and Technology, 32(1):91-99, 2018.
-[5] Gupta PK, Oswald FB, Zaretsky EV. Comparison of Models for Ball Bearing Dynamic Capacity and Life. Tribology Transactions. 2015;58(6):1039-53.
+[5] Gupta P.K., Oswald F.B., Zaretsky E.V. Comparison of models for ball bearing dynamic capacity and life. Tribology Transactions, 58(6):1039-1053, 2015.
-[6] Klebanov IM, Murashkin VV, Danilchenko AI. Validity of the Bearing Life Models at Rolling Contact Fatigue. Journal of Friction and Wear. 2021;42(3):199-203.
+[6] Klebanov I.M., Murashkin V.V., Danilchenko A.I. Validity of the bearing life models at rolling contact fatigue. Journal of Friction and Wear, 42(3):199-203, 2021.
-[7] Cheenady AA, Arakere NK, Londhe ND. Accounting for microstructure sensitivity and plasticity in life prediction of heavily loaded contacts under rolling contact fatigue. Fatigue & Fracture of Engineering Materials & Structures. 2020;43(3):539-49.
+[7] Cheenady A.A., Arakere N.K., Londhe N.D. Accounting for microstructure sensitivity and plasticity in life prediction of heavily loaded contacts under rolling contact fatigue. Fatigue & Fracture of Engineering Materials & Structures, 43(3):539-549, 2020.
-[8] Lei Y, Li N, Lin JJIToI, Measurement. A new method based on stochastic process models for machine remaining useful life prediction. IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT. 2016;65(12):2671-84.
+[8] Lei Y., Li N., Lin J. A new method based on stochastic process models for machine remaining useful life prediction. IEEE Transactions on Instrumentation and Measurement, 65(12):2671-2684, 2016.
-[9] Ding N, Li HL, Yin ZW, Jiang FM. A novel method for journal bearing degradation evaluation and remaining useful life prediction under different working conditions. Measurement. 2021;177.
+[9] Ding N., Li H.L., Yin Z.W., Jiang F.M. A novel method for journal bearing degradation evaluation and remaining useful life prediction under different working conditions. Measurement, 177, 109273, 2021.
-[10] Wang H, Chen JH, Qu JM, Ni GX. A new approach for safety life prediction of industrial rolling bearing based on state recognition and similarity analysis. Safety Science. 2020;122.
+[10] Wang H., Chen J.H., Qu J.M., Ni G.X. A new approach for safety life prediction of industrial rolling bearing based on state recognition and similarity analysis. Safety Science, 122, 104530, 2020.
-[11] Chen YH, Peng GL, Zhu ZY, Li SJ. A novel deep learning method based on attention mechanism for bearing remaining useful life prediction. Applied Soft Computing. 2020;86.
+[11] Chen Y.H., Peng G.L., Zhu Z.Y., Li S.J. A novel deep learning method based on attention mechanism for bearing remaining useful life prediction. Applied Soft Computing, 86, 105919, 2020.
-[12] Zhai XJ, Wei XK, Yang JH, Ieee, editors. A Comparative Study on the Data-driven Based Prognostic Approaches for RUL of Rolling Bearings. IEEE Symposium Series on Computational Intelligence (SSCI); 2019 Dec 06-09; Xiamen, PEOPLES R CHINA2019.
+[12] Zhai X., Wei X., Yang J. A comparative study on the data-driven based prognostic approaches for RUL of rolling bearings. 2019 IEEE Symposium Series on Computational Intelligence (SSCI), Xiamen, China, pp. 1751-1755, 2019.
-[13] Cao L, Qian Z, Zareipour H, Wood D, Mollasalehi E, Tian S, et al. Prediction of Remaining Useful Life of Wind Turbine Bearings under Non-Stationary Operating Conditions. 2018;11(12):3318.
+[13] Cao L., Qian Z., Zareipour H., Wood D., Mollasalehi E., Tian S., et al. Prediction of remaining useful life of wind turbine bearings under non-stationary operating conditions. 2018;11(12):3318.
 [14] Gao TH, Li YX, Huang XZ, Wang CL. Data-Driven Method for Predicting Remaining Useful Life of Bearing Based on Bayesian Theory. Sensors. 2021;21(1).

@@ Line 417: / Line 417: @@
 <div class="center" style="font-size: 75%;">'''Table 3'''. Output torque scaling factor vs. actual dynamic ring thrust value (partial)</div>
-<div id='tab-1'></div>
+<div id='tab-3'></div>
 {| class="wikitable" style="margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;width:auto;"
 |-style="text-align:center"
@@ Line 502: / Line 502: @@
 <div class="center" style="font-size: 75%;">'''Table 4'''. 61918 bearing parameters</div>
-<div id='tab-1'></div>
+<div id='tab-4'></div>
 {| class="wikitable" style="margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;width:auto;"
 |-style="text-align:center"
@@ Line 543: / Line 543: @@
-The load time history of the bearing is loaded and the bearing is restrained according to the actual working conditions. The bearing is loaded as shown in [[#img-11|Figure 11]]. The bearing as a support component does not rotate during the clamping of the tire by the tire unloader and during the 90° flip. Therefore, the bearing is set to be fully fixed on the outer ring and fully constrained on the bottom surface of the inner ring, and the cage action on it is simulated by constraining the direction of rotation of the ball using the column coordinate system. The simulation time step is set to 0.005s and the results of the equivalent force and deformation of the bearing are shown in [[#img-12|Figure 12]] to [[#img-15|Figure 15]]. The maximum equivalent force appears on the bearing ball, with a value of 1361.2MPa, and the maximum equivalent effect becomes 7.40e-3mm/mm, as well as its position is close to the maximum equivalent force. This can be assumed that the bearing ball will be the first to suffer fatigue damage.
+The load time history of the bearing is loaded and the bearing is restrained according to the actual working conditions. The bearing is loaded as shown in [[#img-11|Figure 11]]. The bearing as a support component does not rotate during the clamping of the tire by the tire unloader and during the 90° flip. Therefore, the bearing is set to be fully fixed on the outer ring and fully constrained on the bottom surface of the inner ring, and the cage action on it is simulated by constraining the direction of rotation of the ball using the column coordinate system. The simulation time step is set to 0.005s and the results of the equivalent force and deformation of the bearing are shown in [[#img-12|Figure 12]] to [[#img-15|Figure 15]]. The maximum equivalent force appears on the bearing ball, with a value of 1361.2 MPa, and the maximum equivalent effect becomes 7.40e-3 mm/mm, as well as its position is close to the maximum equivalent force. This can be assumed that the bearing ball will be the first to suffer fatigue damage.
 <div id='img-11'></div>
@@ Line 973: / Line 973: @@
 Based on the results of the damage calculation in different directions, the maximum damage direction was found to be in the direction of <math display="inline">\omega =160^\circ</math> on the critical plane. The mechanical parameters in the <math display="inline">\omega =160^\circ</math> direction were multiaxial cycle counted and the amount of damage was calculated for each cycle. The resulting cumulative damage <math display="inline">D</math> was found to be 3.73E-06. The damage was converted to 268303 cycles according to the Miner criterion, which translates into a time duration of 1490.58 h in cycles.
-==5. Conclusion==
+==5. Conclusions==
 A detailed review of the life prediction models and methods of bearing has been presented in this paper. The development of life prediction models and life prediction methods was reviewed, and their advantages and disadvantages were discussed. The bearing which is used in rocker arm of mining unloader machine is investigated. Based on the results and discussion, the following conclusion can be drawn:
@@ Line 981: / Line 981: @@
 :(2) The fatigue of the bearing which occurred at the ball is shown from stress&strain nephogram. Based on the stress&strain nephogram, it is known that the fatigue of the bearing occurred at the ball. The maximum equivalent force is 1361.2Mpa and the equivalent strain becomes 7.40e-3mm/mm.
-:(3) The stress-strain history at the hazardous location is obtained. A new coordinate system is established through the hazard nodes and the critical plane search is carried out based on the principle of maximum normal strain variation for maximum shear strain. The critical plane of the weights is determined to be  <math display="inline">\phi {\mbox{=100}}^{\circ }</math> ,  <math display="inline">\theta {\mbox{=60}}^{\circ }</math> according to the Manson-Coffin equation.
+:(3) The stress-strain history at the hazardous location is obtained. A new coordinate system is established through the hazard nodes and the critical plane search is carried out based on the principle of maximum normal strain variation for maximum shear strain. The critical plane of the weights is determined to be  <math display="inline">\phi =100^{\circ }</math>,  <math display="inline">\theta =60^{\circ }</math> according to the Manson-Coffin equation.
-:(4) The amount of damage is calculated for different directions on the critical plane, and the direction that produces the maximum damage is  <math display="inline">\omega {\mbox{=160}}^{\circ }</math> . The maximum amount of damage to the bearing is 3.73E-06 for one operation of the tire unloader. The Miner theory calculates the number of cycles the bearing can make to be 268,303, which translates into a time duration of 1490.58h.
+:(4) The amount of damage is calculated for different directions on the critical plane, and the direction that produces the maximum damage is  <math display="inline">\omega =160^{\circ }</math>. The maximum amount of damage to the bearing is 3.73E-06 for one operation of the tire unloader. The Miner theory calculates the number of cycles the bearing can make to be 268,303, which translates into a time duration of 1490.58h.
 This article has important reference and practical significance for life prediction of bearing. It provides methods and technical support for life prediction which is used under multiaxial random loading.