Analysis of vibration characteristics of face gear powering-split transmission system. (English) Zbl 1533.70020
Summary: A nonlinear dynamic model of the face gear powering-split transmission system was established, and the nonlinear dynamic characteristics of the face gear powering-split transmission system were studied by considering various factors such as support stiffness, time-varying meshing stiffness, lateral clearance of teeth, comprehensive transmission error and bearing stiffness. The Runge-Kutta integral method is used to solve the differential dynamics of the system. The nonlinear behavior of the system is described by the phase plane diagram, time history diagram, frequency domain diagram, and Poincaré section diagram. The influence of external excitation frequency on the nonlinear behavior of the system is described by the bifurcation diagram. In addition, the multi-scale method is used to analyze the superharmonic resonance of the system and determine the stability conditions of the superharmonic resonance of the system. The influence of meshing damping, time-varying meshing stiffness, and time-delay control parameters on the amplitude-frequency characteristics of the system is studied by numerical analysis of the superharmonic resonance. The results show that the system will show periodic chaotic alternating motion characteristics under external excitation. Selecting meshing damping, meshing stiffness, and time delay control parameters in a reasonable range can effectively reduce the superharmonic co-amplitude and keep the system in a stable state.
MSC:
| 70K30 | Nonlinear resonances for nonlinear problems in mechanics |
| 70K50 | Bifurcations and instability for nonlinear problems in mechanics |
| 70-08 | Computational methods for problems pertaining to mechanics of particles and systems |
Keywords:
superharmonic resonance; support stiffness; bearing stiffness; Runge-Kutta method; frequency domain diagram; Poincaré section diagram; bifurcation diagram; multi-scale methodReferences:
| [1] | Liu, Lu; Zhu, L.; Gou, X., Calculation of line and point contact ratio for orthogonal spur-face gear drive. Int J Mech Sci (2022) |
| [2] | Litvin, F. L.; Fuentes, A.; Howkins, M., Design, generation and TCA of new type of asymmetric face-gear drive with modified geometry. Comput Methods Appl Mech Eng, 43/44, 5837-5865 (2001) · Zbl 0999.70005 |
| [3] | Litvin, F. L., Design, generation, and stress analysis of two versions of geometry of face-gear drives. Mech Mach Theory, 37, 1179-1211 (2002) · Zbl 1062.70571 |
| [4] | Litvin, F. L.; Gonzalez-Perez, I.; Fuentes, A., Design, generation and stress analysis of face-gear drive with helical pinion. Comput Methods Appl Mech Eng, 36/38, 3870-3901 (2005) · Zbl 1131.74323 |
| [5] | Zschippang, H. A.; Weikert, S.; Küçük, K. A.; Wegener, K., Face-gear drive: geometry generation and tooth contact analysis. Mech Mach Theory, 142 (2019) |
| [6] | Mo, S.; Zhang, Y.; Tang, W., Design methods and stress analysis of asymmetric offset face-gear transmission. Proc Inst Mech Eng, Part C: J Mech Eng Sci, 14, 7814-7828 (2022) |
| [7] | Mo, S.; Luo, B.; Song, W.; Zhang, Y.; Cen, G.; Bao, H., Geometry design and tooth contact analysis of non-orthogonal asymmetric helical face gear drives. Mech Mach Theory, 173 (2022) |
| [8] | Mo, S.; Zhang, Y.; Luo, B.; Bao, H.; Cen, G.; Huang, Y., The global behavior evolution of non-orthogonal face gear-bearing transmission system. Mech Mach Theory (2022) |
| [9] | Mo, S.; Yingxin, Z.; Yuling, S., Nonlinear vibration and primary resonance analysis of non-orthogonal face gear-rotor-bearing system. Nonlinear Dyn, 4, 3367-3389 (2022) |
| [10] | Mo, S.; Song, Y.; Feng, Z.; Song, W.; Hou, M., Research on dynamic load sharing characteristics of double input face gear split-parallel transmission system. Proc Inst Mech Eng, Part C: J Mech Eng Sci, 5, 2185-2202 (2022) |
| [11] | Mo, S.; Li, Y.; Luo, B.; Wang, L.; Bao, H.; Cen, G.; Huang, Y., Research on the meshing characteristics of asymmetric gears considering the tooth profile deviation. Mech Mach Theory (2022) |
| [12] | Dong, J.; Tang, J.; Hu, Z., Dynamic characteristics of the face gear transmission system based on a rotor-shaft-bearing model with multiple nodes. Int J Non Linear Mech (2021) |
| [13] | Chang-Jian, C.-W., Strong nonlinearity analysis for gear-bearing system under nonlinear suspension—bifurcation and chaos. Nonlinear Anal: Real World Appl, 11, 1760-1774 (2010) · Zbl 1188.93034 |
| [14] | Li, Z.; Zhu, C.; Liu, H.; Gu, Z., Mesh stiffness and nonlinear dynamic response of a spur gear pair considering tribo-dynamic effect. Mech Mach Theory (2020) |
| [15] | Xiang, L.; Gao, N.; Hu, A., Dynamic analysis of a planetary gear system with multiple nonlinear parameters. J Comput Appl Math, 325-340 (2018) · Zbl 1370.70019 |
| [16] | Sun, T.; Hu, H. Y., Nonlinear dynamics of a planetary gear system with multiple clearances. Mech Mach Theory, 38, 1371-1390 (2003) · Zbl 1062.70577 |
| [17] | Walha, L.; Fakhfakh, T.; Haddar, M., Nonlinear dynamics of a two-stage gear system with mesh stiffness fluctuation, bearing flexibility and backlash. Mech Mach Theory, 44, 1058-1069 (2009) · Zbl 1350.70019 |
| [18] | Wang, J.; Zhang, J.; Yao, Z.; Yang, X.; Sun, R.; Zhao, Y., Nonlinear characteristics of a multi-degree-of-freedom spur gear system with bending-torsional coupling vibration. Mech Syst Signal Process, 810-827 (2019) |
| [19] | Sondkar, P.; Kahraman, A., A dynamic model of a double-helical planetary gear set. Mech Mach Theory, 157-174 (2013) |
| [20] | Hu, J.; Hu, N.; Yang, Yi; Zhang, L.; Shen, G., Nonlinear dynamic modeling and analysis of a helicopter planetary gear set for tooth crack diagnosis. Measurement (2022) |
| [21] | Shi, J.-; Gou, X.-; Jin, Wu-; Feng, R.-, Multi-meshing-state and disengaging-proportion analyses of a gear-bearing system considering deterministic-random excitation based on nonlinear dynamics. J Sound Vib (2023) |
| [22] | Zou, H.; Wang, S.; Li, F.; Liu, L.; Li, L.; Li, Z., Improved algorithm of tooth surface topological modification and nonlinear dynamic analysis of herringbone gears. Mech Mach Theory (2023) |
| [23] | Guo, Yi; Parker, R. G., Dynamic modeling and analysis of a spur planetary gear involving tooth wedging and bearing clearance nonlinearity. Eur J Mech, 29, 1022-1033 (2010) · Zbl 1480.74232 |
| [24] | Zheng, X.; Hu, Y.; He, Z.; Xiao, Y.; Zhang, X., On the extended tooth contact and nonlinear dynamics for spur gears—an analytical model. Mech Mach Theory (2022) |
| [25] | Aihara, T.; Sakamoto, K., Theoretical analysis of nonlinear vibration characteristics of gear pair with shafts. Theor Appl Mech Lett, 2 (2022) |
| [26] | Nadolski, W.; Pielorz, A., Theoretical investigations of nonlinear loads on gear teeth in single gear transmission. Int J Mech Sci, 43, 299-311 (2001) · Zbl 0968.74521 |
| [27] | Wang, J. G.; Lv, B.; Sun, R., Resonance and stability analysis of a cracked gear system for railway locomotive. Appl Math Model, 1, 253-266 (2020) · Zbl 1443.70020 |
| [28] | Alimoradzadeh, M.; Tornabene, F.; Esfarjani, S. M.; Dimitri, R., Finite strain-based theory for the superharmonic and subharmonic resonance of beams resting on a nonlinear viscoelastic foundation in thermal conditions, and subjected to a moving mass loading. Int J Non Linear Mech (2023) |
| [29] | Wang, M.-Q.; Ma, W.-L.; Li, Y.; Chen, E.-L.; Liu, P.-F.; Zhang, M.-Z., Dynamic analysis of piecewise nonlinear systems with fractional differential delay feedback control. Chaos, Solitons Fract (2022) · Zbl 1508.93113 |
| [30] | Peng, J.; Wang, L.; Zhao, Y.; Zhao, Y., Bifurcation analysis in active control system with time delay feedback. Appl Math Comput, 219, 10073-10081 (2013) · Zbl 1294.34072 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
