As high-speed, heavy-load, and high-power density are realized in hybrid electric vehicle (HEV), the electromechanical coupling inherent vibration of electromechanical composite transmission (EMT) system becomes the bottleneck in this study area. To reduce vibration, the analysis of inherent vibration characteristics of EMT system and parameter influencing law of mechanical-electro-magnetic parameter is key. Here, an electromechanical coupling dynamics model is established considering multi-source excitations, and the inherent vibration model is obtained. Based on this inherent vibration model, firstly, the inherent vibration frequency and mode with and without electromagnetic effect of EMT system are studied and summarized. Secondly, the resonance speed of EMT system is identified based on Campbell diagram and modal energy method. Thirdly, the inherent frequency trajectory and variation law affected by PMSM parameters (inner power factor angle (IPFA), armature current, stator-rotor eccentricity) and the mode mutations phenomenon of inherent frequency trajectory caused by PG parameter (connecting, gear meshing, and bearing support stiffness) are studied. This study results provide a reference for the modeling and analysis of inherent vibration characteristics, as well as the design and optimization of mechanical-electro-magnetic parameter of EMT system.
HuJPengTJiaM, et al. Study on electromechanical coupling characteristics of an integrated electric drive system for electric vehicle. IEEE Access2019; 7: 166493–166508.
2.
ZhouZChenZSpiryaginM, et al. Dynamic response feature of electromechanical coupled drive subsystem in a locomotive excited by wheel flat. Eng Fail Anal2021; 122: 105248.
3.
HuoJWuHSunW, et al. Electromechanical coupling dynamics of TBM main drive system. Nonlinear Dyn2017; 90: 2687–2710.
4.
YiYQinDLiuC.Investigation of electromechanical coupling vibration characteristics of an electric drive multistage gear system. Mech Mach Theory2018; 121: 446–459.
5.
SunLLiuKHuJ, et al. Analysis and mitigation of electromechanical oscillations for DFIG wind turbines involved in fast frequency response. IEEE Trans Power Syst2019; 34(6): 4547–4556.
6.
EhsaniMSinghKVBansalHO, et al. State of the art and trends in electric and hybrid electric vehicles. Proc IEEE2021; 109(6): 967–984.
7.
HanLWangDYangF, et al. Vibration characteristics of the dual electric propulsion system of vessels under electromechanical coupling excitation. Machines2022; 10(6): 449.
8.
LiuHZhanZ.Modal properties of a two-stage planetary gear system with a Timoshenko beam as the intermediate shaft model. Proc IMechE, Part D: J Automobile Engineering2022; 236(2–3): 353–365.
9.
EritenelTParkerRG.An investigation of tooth mesh nonlinearity and partial contact loss in gear pairs using a lumped-parameter model. Mech Mach Theory2012; 56: 28–51.
10.
LiuHYanPGaoP.Effects of temperature on the time-varying mesh stiffness, vibration response, and support force of a multi-stage planetary gear. J Vib Acoust2020; 142(5): 051110.
11.
WangCParkerRG.Nonlinear dynamics of lumped-parameter planetary gears with general mesh phasing. J Sound Vib2022; 523: 116682.
12.
GuangjianWLinCLiY, et al. Research on the dynamic transmission error of a spur gear pair with eccentricities by finite element method. Mech Mach Theory2017; 109: 1–13.
13.
WangZXiangCLiuH, et al. Accuracy and efficiency analysis of the beam elements for nonlinear large deformation. J Vib Eng Technol2023; 11(1): 319–328.
14.
WeiJZhangAQinD, et al. A coupling dynamics analysis method for a multistage planetary gear system. Mech Mach Theory2017; 110: 27–49.
15.
WangZLiuHXiangC, et al. Dynamic responses of electromechanical transmission system based on a nonlinear hybrid model. Proc IMechE, Part D: J Automobile Engineering2023; 237: 1885–1901.
16.
ChenRQinDYiY, et al. Dynamic characteristics of electromechanical coupling of wind turbine drive system under multi-source excitation. Wind Energy2022; 25(3): 391–418.
17.
JiangSLiWWangY, et al. Study on electromechanical coupling torsional resonance characteristics of gear system driven by PMSM: a case on shearer semi-direct drive cutting transmission system. Nonlinear Dyn2021; 104: 1205–1225.
18.
LiuCQinDLiaoY.Electromechanical dynamic analysis for the cutting transmission system of the unmanned long-wall shearer under variable speed process. J Vibroengineering2017; 19(5): 3191–3206.
19.
ZhangKYangJLiuC, et al. Dynamic characteristics of a traction drive system in high-speed train based on electromechanical coupling modeling under variable conditions. Energies2022; 15(3): 1202.
20.
ChenRLiuCQinD, et al. Electromechanical dynamic analysis of the integrated system of switched reluctance motor and planetary gear transmission. J Vib Eng Technol2022; 10: 581–599.
21.
FuXLiuGMaS, et al. An efficient method for the dynamic analysis of planetary roller screw mechanism. Mech Mach Theory2020; 150: 103851.
22.
YanPLiuHGaoP, et al. Optimization of distributed axial dynamic modification based on the dynamic characteristics of a helical gear pair and a test verification. Mech Mach Theory2021; 163: 104371.
23.
SongJYLeeJHKimDW, et al. Analysis and modeling of permanent magnet variable flux memory motors using magnetic equivalent circuit method. IEEE Trans Magn2017; 53(11): 1–5.
24.
YangXLiuHLuD, et al. Investigation of the dynamic electromechanical coupling due to the thrust harmonics in the linear motor feed system. Mech Syst Signal Process2018; 111: 492–508.
25.
BaiWQinDWangY, et al. Dynamic characteristic of electromechanical coupling effects in motor-gear system. J Sound Vib2018; 423: 50–64.
26.
ChenXHuJPengZ, et al. Bifurcation and chaos analysis of torsional vibration in a PMSM-based driven system considering electromechanically coupled effect. Nonlinear Dyn2017; 88: 277–292.
27.
LongYDuJYangK, et al. Modelling of a direct-driven electromechanical actuation system based on the Lagrange–Maxwell equation. IET Electric Power Appl2021; 15(11): 1438–1451.
28.
LinJParkerRG.Analytical characterization of the unique properties of planetary gear free vibration. J Vib Acoust1999; 121: 316–321.
29.
GuoYParkerRG.Purely rotational model and vibration modes of compound planetary gears. Mech Mach Theory2010; 45(3): 365–377.
30.
MbarekAHammamiAFernandez Del RinconA, et al. Effect of load and meshing stiffness variation on modal properties of planetary gear. Appl Acoust2019; 147: 32–43.
31.
BotmanM.Epicyclic gear vibrations. J Eng Ind1976; 98(3): 811–815.
32.
CooleyCGParkerRG.Eigenvalue sensitivity and veering in gyroscopic systems with application to high-speed planetary gears. Eur J Mech A Solids2018; 67: 123–136.
33.
ZhangQHeRZhangY, et al. Analysis of the relationship between the meshing stiffness and the inherent characteristics of planetary gear transmission mechanism. J BIT2019; 28(4): 811–818.
34.
ChenXWeiHDengT, et al. Investigation of electromechanical coupling torsional vibration and stability in a high-speed permanent magnet synchronous motor driven system. Appl Math Model2018; 64: 235–248.
35.
MendesASMeirellesPSZampieriDE.Analysis of torsional vibration in internal combustion engines: modelling and experimental validation. Proc IMechE, Part K: J Multi-body Dynamics2008; 222(2): 155–178.
36.
ChenXHuJPengZ, et al. Nonlinear torsional vibration characteristics of PMSM for HEV considering electromagnetic excitation. Int J Appl Electromagn Mech2015; 49(1): 9–21.
37.
ChenXHuJChenK, et al. Modeling of electromagnetic torque considering saturation and magnetic field harmonics in permanent magnet synchronous motor for HEV. Simul Model Pract Theory2016; 66: 212–225.
38.
LiuFXiangCLiuH, et al. Nonlinear vibration of permanent magnet synchronous motors in electric vehicles influenced by static angle eccentricity. Nonlinear Dyn2017; 90: 1851–1872.
39.
LiuHWuYWangX, et al. Nonlinear normal modes and primary resonance for permanent magnet synchronous motors with a nonlinear restoring force and an unbalanced magnetic pull. Nonlinear Dyn2019; 97: 1197–1213.
40.
ÖzşahinOÖzgüvenHNBudakE.Analytical modeling of asymmetric multi-segment rotor – bearing systems with Timoshenko beam model including gyroscopic moments. Comput Struct2014; 144: 119–126.
41.
CraigRRJrTaleffEM.Mechanics of materials. Hoboken, NJ: John Wiley & Sons, 2020.
42.
ZhanZLiuHFeenyBF, et al. Prognostics of gear manufacturing errors for planetary gear systems based on power flow theory. J Vib Acoust2022; 144(4): 041010.
43.
ShiJLMaXGXuCL, et al. Meshing stiffness analysis of gear using the Ishikawa method. Appl Mech Mater2013; 401–403: 203–206.
44.
LinHHHoustonRLCoyJJ.On dynamic loads in parallel shaft transmissions. 1: modelling and analysis. NASA, 1987.
45.
ZhuCChenSSongC, et al. Dynamic analysis of a megawatt wind turbine drive train. J Mech Sci Technol2015; 29: 1913–1919.
46.
LloydGHamburgG.Guideline for the certification of wind turbines. 2010.
47.
ChenXYuanSPengZ.Nonlinear vibration for PMSM used in HEV considering mechanical and magnetic coupling effects. Nonlinear Dyn2015; 80: 541–552.
48.
LinJParkerRG.Sensitivity of planetary gear natural frequencies and vibration modes to model parameters. J Sound Vib1999; 228(1): 109–128.
