Calculation and Analysis of Groove Elastic Support’s Radial Stiffness (RESEARCH NOTE)


1 School of Mechatronics Engineering, Northwestern Polytechnical University, Xi'an, China

2 School of Mechatronics Engineering, Henan University of Science and Technology, Luoyang, China

3 Collaborative Innovation Center of Major Machine Manufacturing in Liaoning, Liaoning, China


In this paper, an analytical formula to calculate the radial stiffness of groove elastic support is presented. The influence of structure parameters on radial stiffness and homogeneity of radial stiffness is investigated as well. The accuracy and calculating speed of the analysis formula are compared to that of finite element method (FEM). Findings are as following: The calculating speed of analysis formula is more efficient than that of finite element method (FEM). When the number of groove is less than 20, the maximum relative error of two methods is less than 10%. The radial stiffness of groove elastic support increases with the groove number, thickness of arc beam and transition angle, but decreases with the groove gap. The radial stiffness changes slightly and periodically with the azimuth angle of radial load, and the greater groove number and the thinner thickness of arc beam, the more homogeneous radial stiffness of groove elastic support.


1.     Xu, W., Wen, Z., Xu, L., Liu, Y. and Shen, X., "High speed rotating test-bed with flexible, squeeze film damped support", Jixie Gongcheng Xuebao(Chinese Journal of Mechanical Engineering)(China),  Vol. 40, No. 9, (2004), 144-147.
2.     Dayi, Z. and Guoxin, M., "Hong jie beijing university of aeronautics and astronautics, beijing 100083, china; rigidity calculation methods for rotor supporting system in gas engine [j]", Tactical Missile Technology,  Vol. 2, (2005), 143-150.
3.     Ahmadi, S.M., Ghazavi, M. and Sheikhzad, M., "Dynamic analysis of a rotor supported on ball bearings with waviness and centralizing springs and squeeze film dampers", International Journal of Engineering-Transactions C: Aspects,  Vol. 28, No. 9, (2015), 1351-1360.
4.     Kirk, R.G. and Gunter, E.J., "The effect of support flexibility and damping on the dynamic response of a single mass flexible rotor in elastic bearings",  (1972).
5.     Mahjouri, S., Shabani, R. and Rezazadeh, G., "Vibration analysis of an air compressor based on a hypocycloidal mechanism: An experimental study", International Journal of Engineering-Transactions B: Applications,  Vol. 28, No. 11, (2015), 1687-1694.
6.     Kang, C., Hsu, W., Lee, E. and Shiau, T., "Dynamic analysis of gear-rotor system with viscoelastic supports under residual shaft bow effect", Mechanism and Machine Theory,  Vol. 46, No. 3, (2011), 264-275.
7.     Ecsedi, I., "Bounds for the torsional rigidity of elastic ring", Mechanics research Communications,  Vol. 26, No. 4, (1999), 445-450.
8.     Liu, J. and Chiu, Y., "Analysis of a thin elastic ring under arbitrary loading", Journal of Engineering for Industry,  Vol. 96, No. 3, (1974), 870-876.
9.     Xingjian, D. and Guangming, W., "Analysis on stiffness of corrugated ring in a rotor-bearing support", Journal of Harbin Institute of Technology,  (1994), 05-13.
10.   CAO, L., GAO, D.-p. and JIANG, H.-f., "Investigation on critical speed characteristics of elastic ring sfd-rotor system [j]", Journal of Propulsion Technology,  Vol. 2, (2008), 20-29.
11.   Cao, L., Gao, D. and Jiang, H., "Damping mechanism of elastic ring squeeze film damper", Journal of Vibration Engineering,  Vol. 6, (2007), 584-589.
12.   Zhang, W. and Ding, Q., "Elastic ring deformation and pedestal contact status analysis of elastic ring squeeze film damper", Journal of Sound and Vibration,  Vol. 346, (2015), 314-327.
13.   Jie, H., Yin, D. and Dayi, Z., "Dynamic design method of elastic ring squeeze film damper", Journal-Beijing University of Aeronautics And Astronautics,  Vol. 32, No. 6, (2006), 649-655.
14.   Zarzour, M.J., "Experimental evaluation of a metal-mesh bearing damper in a high speed test rig", Texas A&M University,  (1999),435-442
15.   Hongwei, M.Y.L. and Haixiong, Z., "Hong jie school of jet propulsion, beihang university, beijing 100191, china; structural stiffness design and experimental evaluation of elastic ring-metal rubber damper [j]", Acta Aeronautica et Astronautica Sinica,  Vol. 6, (2013), 723-730.
16.   Zuo, H., Bai, H. and Feng, Y., "The analysis of stiffness for rubbery metallic material based on mesoscopic features", Materials Sciences and Applications,  Vol. 2, No. 06, (2011), 654-660.
17.   Wang, D., Zhang, W., Wang, Z. and Zhu, J., "Shape optimization of 3d curved slots and its application to the squirrel-cage elastic support design", Science China Physics, Mechanics & Astronomy,  Vol. 53, No. 10, (2010), 1895-1900.
18.   Deng, S.-E., Yan, Y.-C., Wang, Y.-S. and Yang, H.-S., "Vibration analysis of two-piece inner ring angular contact ball bearing with elastic support", Journal of Aerospace Power,  Vol. 28, No. 2, (2013), 241-251.
19.   Carpinteri, A., "Structural mechanics fundamentals, CRC Press,  (2013).