Investigation of Magnitude and Position of Maximum von Mises Stress in The Cylindrical Contact Problems
الموضوعات :
Hasan Heirani
1
,
Reza Naseri
2
1 - Department of Mechanical Engineering, Faculty of Engineering, Bozorgmehr University of Qaenat, Qaen, Iran.
2 - Department of Mechanical Engineering, Technical and Vocational University (TVU), Tehran, Iran.
تاريخ الإرسال : 17 الثلاثاء , صفر, 1444
تاريخ التأكيد : 01 الثلاثاء , شعبان, 1444
تاريخ الإصدار : 16 الجمعة , صفر, 1445
الکلمات المفتاحية:
Maximum von Mises stress,
Contact mechanics,
Depth prediction,
Hertzian stresses,
ملخص المقالة :
In the analysis of contact mechanics problems, determination of stress field in mechanical elements is essential. Between the stress components the von Mises stress is more important, because it is used in the investigation of yield criteria and fatigue fracture of elements. The aim of this study is to present formulas for determining the magnitude and position of maximum von Mises stress. For this purpose, the effect of various material properties, element geometries and loading conditions on these two parameters are investigated. By applying Hertzian contact stress and von Mises relations, the magnitude and position of maximum von Mises stress are determined. The von Mises stress is assumed to be a function of material properties, geometry of the element and loading conditions and finally two formulas are presented for the calculation of the magnitude and position of maximum von Mises stress. The results of these presented formulas are in close agreement with the literature. The error is less than 1% for depth prediction and less than 6% for stress value prediction, which confirms the accuracy of the presented formulas.
المصادر:
Boresi, A. P., Schmidt, R. J., and Sidebottom, O. M., Advanced Mechanics of Materials, 5th ed, John Wiley and Sons, New York, USA, 1993, Chap. 18.
Beer, F. P., Johnston, E. R., DeWolf, J. T., and Mazurek, D. F., Mechanics of Materials, 7th ed, McGraw-Hill, New York, USA, 2014, Chap. 7.
Heirani, H., Farhangdoost, K., Effect of Friction Coefficient and Maximum Contact Pressure on The Spalling Depth of Gear Teeth Flank, Proceedings of the 7th International Conference on Fracture Fatigue and Wear, 2018, pp. 63-68, DOI: 10.1007/978-981-13-0411-8_6.
Johnson, K. L., Contact Mechanics, Cambridge University Press, Cambridge, UK, 1985, Chap. 4.
Glodez, S., Winter, H., and Stuwe, H. P., A Fracture Mechanics Model for The Wear of Gear Flanks by Pitting, Wear, Vol. 208, No. 1-2, 1997, pp. 177-183, DOI: 1016/S0043-1648(97)00008-2.
Glodez, S., Ren, Z., Modelling of Crack Growth Under Cyclic Contact Loading, Theoretical and Applied Fracture Mechanics, Vol. 30, No. 2, 1998, pp. 159-173, DOI: 1016/S0167-8442(98)00053-6.
Glodez, S., Ren, Z., and Flasker, J., Simulation of Surface Pitting Due to Contact Loading, International Journal for Numerical Method in Engineering, Vol. 43, No. 1, 1998, pp. 33-50, DOI: 1002/(SICI)10970207(19980915)43:1<33::AID-NME410>3.0.CO;2-Z.
Glodez, S., Abersek, B., Flasker, J., and Ren, Z., Evaluation of the Service Life of Gears in Regard to Surface Pitting, Engineering Fracture Mechanics, Vol. 71, No. 4-6, 2004, pp. 429-438, DOI: 1016/S0013-7944(03)00049-3.
Aslantas, K., Tasgetiren, S., A Study of Spur Gear Pitting Formation and Life Prediction, Wear, Vol. 257, No. 11, 2004, pp. 1167-1175, DOI: 1016/j.wear.2004.08.005.
Fajdiga, G., Glodez, S., and Kramar, J., Pitting Formation Due to Surface and Subsurface Initiated Fatigue Crack Growth in Contacting Mechanical Elements, Wear, Vol. 262, No. 9-10, 2007, pp. 1217-1224, DOI: 1016/j.wear.2006.11.016.
Francois, H., Gilbert, H., Damien, H., Mikael, G., and Thomas, B., CDM Approach Applied to Fatigue Crack Propagation on Airframe Structural Alloys, Procedia Engineering , Vol. 2, No. 1, 2010, pp. 1403-1412, DOI: 1016/j.proeng.2010.03.152.
Wei, P., Zhou, H., Liu, H., Zhu, C., Wang, and W., Deng, G., Modeling of Contact Fatigue Damage Behavior of A Wind Turbine Carburized Gear Considering Its Mechanical Properties and Microstructure Gradients, International Journal of Mechanical Sciences, Vol. 156, 2019, pp. 283-296, DOI: 1016/j.ijmecsci.2019.04.004.
Liu, H., Wang, W., Zhu, C., Jiang, C., Wu, W., and Parker, R. G., A Microstructure Sensitive Contact Fatigue Model of A Carburized Gear, Wear, Vol. 436, 2019, pp. 203035, DOI: 1016/j.wear.2019.203035.
He, H., Liu, H., Zhu, C., and Tang, J., Study on the Gear Fatigue Behavior Considering the Effect of Residual Stress Based on The Continuum Damage Approach, Engineering Failure Analysis, Vol. 104, 2019, pp. 531-544, DOI: 1016/j.engfailanal.2019.06.027.
Li, W., Deng, S., and Liu, B., Experimental Study on The Influence of Different Carburized Layer Depth on Gear Contact Fatigue Strength, Engineering Failure Analysis, Vol. 107, 2020, pp. 104225, DOI: 1016/j.engfailanal.2019.104225.
Guan, J., Wang, L., Zhang, C., and Ma, X., Effects of Non-Metallic Inclusions on The Crack Propagation in Bearing Steel, Tribology International, Vol. 106, 2017, pp. 123-131, DOI: 1016/j.triboint.2016.10.030.
Heirani, H., Farhangdoost, K., Predicting Depth and Path of Subsurface Crack Propagation at Gear Tooth Flank Under Cyclic Contact Loading, Journal of Solid Mechanics, Vol. 9, No. 3, 2017, pp. 587-598, DOI: 1001.1.20083505.2017.9.3.10.9.
Sun, P., An, Z., and Jiang, W., Analysis of Non-Hertz Contact Stress and Bearing Capacity on Meshing Pairs in a Real-Time Non-Clearance Precision Ball Transmission, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 40, No. 6, 2018, pp. 1-11, DOI: 1007/s40430-018-1197-2.
Kohn, A. O., Silva, F. A., A Numerical and Analytical Study of The Stress Field Generated by The Contact Between a Rail and a Wheel, SN Applied Sciences, Vol. 2, No. 7, 2020, pp. 1-8, DOI: 10.1007/s42452-020-3044-1.
Budynas, R., Nisbett, K., Shigley's Mechanical Engineering Design, 10th ed, McGraw-Hill, New York, USA, 2015, Chap. 3.
Qin, W. J., Guan, C. Y., An Investigation of Contact Stresses and Crack Initiation in Spur Gears Based on Finite Element Dynamics Analysis, International Journal of Mechanical Sciences, Vol. 83, 2014, pp. 96-103, DOI: 1016/j.ijmecsci.2014.03.035.
