Dynamic and Vibration Analysis for Geometrical Structures of Planetary Gears
الموضوعات :
A Shahabi
1
(
Department of Mechanical Engineering, University of Sistan and Baluchestan, Zahedan , Iran
)
A.H Kazemian
2
(
Department of Mechanical Engineering, University of Sistan and Baluchestan, Zahedan , Iran
)
الکلمات المفتاحية: Vibration, Time–varying mesh stiffness, Dynamic Model, Planetary gear,
ملخص المقالة :
In industry applications, planetary gear systems are widely used in power transmission systems. In planetary gears, dynamic loads, noise and reduction the structural life are produced by system vibrations. For gear transmission systems, the parametric excitation which introduced by the periodically time–varying mesh stiffness of each gear oscillation is the main source of vibration. Generally, there are two methods to evaluate the gear mesh stiffnesses, the finite element method and the analytical method. In this wok, the periodically time–varying mesh stiffness of planetary gears is investigated. The influence of pressure angles on mesh stiffness of meshing gears is shown and the dynamic model of planetary gear sets is studied. When planets of the single–stage spur planetary gear system are meshed by new planets, the system is converted to special type of system with meshed planets. Vibration for geometrical structures (symmetric and anti–symmetric) of planetary system with meshed planets is investigated. Mesh stiffness of meshing gears by estimation function is obtained and numerical results of natural frequencies and vibration modes are derived.
[1] Li S., Wu Q., Zhang Z., 2014, Bifurcation and chaos analysis of multistage planetary gear train, Nonlinear Dynamics 75(1-2): 217-233.
[2] Sekar R.P., 2020, A Comparative study of tooth wear, mechanical power losses and efficiency in normal and high contact ratio asymmetric spur gears, Journal of Solid Mechanics 12(1): 148-164.
[3] Camacho-Gutiérrez S., Jáuregui-Correa J.C., Dominguez A., 2019, Optimization of excitation frequencies of a gearbox using algorithms inspired by nature, Journal of Vibration Engineering & Technologies 7: 551-563.
[4] Chen Z., Shao Y., 2013, Dynamic simulation of planetary gear with tooth root crack in ring gear Engineering Failure Analysis 31: 8-18.
[5] Sun T., Hu H., 2003, Nonlinear dynamics of a planetary gear system with multiple clearances, Mechanism and Machine Theory 38(12): 1371-1390.
[6] Hao Z., Xianghe Y., Qingkai H., Hai H., 2019, Dynamic behaviors of geared rotor system in integrally centrifugal compressor, Journal of Vibration Engineering & Technologies 7: 241-249.
[7] Inalpolat M., Kahraman A., 2010, A dynamic model to predict modulation sidebands of a planetary gear set having manufacturing errors, Journal of Sound and Vibration 329: 371-393.
[8] Iglesias M., Fernández A., De-Juan A., Sancibrián R., García P., 2013, Planet position errors in planetary transmission: Effect on load sharing and transmission error, Frontiers of Mechanical Engineering 8(1): 80-87.
[9] Jiang H., Liu F., 2019, Analytical models of mesh stiffness for cracked spur gears considering gear body deflection and dynamic simulation, Meccanica 54: 1889-1909.
[10] Lin J., Parker R.G., 1999, Analytical characterization of the unique properties of planetary gear free vibration, Journal of vibration and acoustics 121: 316-321.
[11] Kahraman A., 1994, Load sharing characteristics of planetary transmissions, Mechanism and Machine Theory 29: 1151-1165.
[12] Kahraman A., 1994, Natural modes of planetary gear trains, Journal of Sound Vibration 173: 125-130.
[13] Kazaz L., Pfister C., Ziegler P., Eberhard P., 2020, Transient gear contact simulations using a floating frame of reference approach and higher-order ansatz functions, Acta Mechanica 231: 1337-1350.
[14] Ambarisha V.K., Parker R.G., 2007, Nonlinear dynamics of planetary gears using analytical and finite element models, Journal of Sound and Vibration 302(3): 577-595.
[15] Li C.H., Chiou H.S., Hung C., Chang Y.Y., Yen C.C., 2002, Integration of finite element analysis and optimum design on gear systems, Finite Elements in Analysis and Design 38(3): 179-192.
[16] Chen Z.G., Shao Y.M., Lim T.C., 2012, Non-linear dynamic simulation of gear response under the idling condition, International Journal of Automotive Technology 13(4): 541-552.
[17] Lin J., Parker R.G., 2001, Natural frequency veering in planetary gears, Mechanics of Structures and Machines 29: 411-429.
[18] Liu L., Niu J., Li X., 2018, Dynamic analysis of gear system under fractional-order PID control with the feedback of meshing error change rate, Acta Mechanica 229: 3833-3851.
[19] Mandol S., Bhattacharjee D., Dan P.K., 2016, Robust optimization in determining failure criteria of a planetary gear assembly considering fatigue condition, Structural and Multidisciplinary Optimization 53: 291-302.
[20] Masoumi A., Pellicano F., Samani F.S., Barbieri M., 2015, Symmetry breaking and chaos-induced imbalance in planetary gears, Nonlinear Dynamics 80: 561-582.
[21] Parker R.G., 2000, A physical explanation for the effectiveness of planet phasing to suppress planetary gear vibration, Journal of Sound and Vibration 236: 561-573.
[22] Phadatare H.P., Pratiher B., 2020, Nonlinear modeling, dynamics, and chaos in a large deflection model of a rotor–disk–bearing system under geometric eccentricity and mass unbalance, Acta Mechanica 231: 1-22.
[23] Shu R., Wei J., Qin D., Lim T.C., Zhang A., 2018, Global sensitivity analysis and dynamic optimization of multi-motor driving transmission system, Structural and Multidisciplinary Optimization 58: 797-816.
[24] Tatar A., Schwingshackl C.W., Friswell M.I., 2019, Dynamic behaviour of three-dimensional planetary geared rotor systems, Mechanism and Machine Theory 134: 39-56.
[25] Wang J., Li S., Xin Y., An Z., 2019, Gear fault intelligent diagnosis based on frequency-domain feature extraction, Journal of Vibration Engineering & Technologies 7: 159-166.
[26] Shen Y., Yang S., Liu X., 2006, Nonlinear dynamics of a spur gear pair with time-varying stiffness and backlash based on incremental harmonic balance method, International Journal of Mechanical Sciences 48(11): 1256-1263.
[27] Wei S., Han Q.K., Dong X.J., Peng Z.K., Chu F.L., 2017, Dynamic response of a single-mesh gear system with periodic mesh stiffness and backlash nonlinearity under uncertainty, Nonlinear Dynamics 89(1): 49-60.
[28] Zheng H., Cheng G., Li Y., Liu C., 2019, A new fault diagnosis method for planetary gear based on image feature extraction and bag-of-words model, Measurement 145:1-13.
[29] Erdin E., Tuc B., Tunalioglu M., 2017, Effect of coating materials on wear in internal Gears, International Journal of Engineering 30(11): 1792-1799.
[30] Lei Y., Hu J., Fu Y., Liu Z., Yan B., 2019, Simulation and experimental study of vibration and noise of pure electric bus transmission based on finite element and boundary element methods, International Journal of Engineering 32(7): 1023-1030.
[31] Zhu H., Chen W., Zhu R., Gao J., Liao M., 2020, Study on the dynamic characteristics of a rotor bearing system with damping rings subjected to base vibration, Journal of Vibration Engineering & Technologies 8: 121-132.
