This investigation is aimed to propose scaling laws for a nonlinear system with connected Geislinger coupling. Different from the scaling laws for rotor systems with linear stiffness that are commonly used, the proposed method has better prediction accuracy for a rotor system with two rotor connected by nonlinear coupling. First, a crankshaft-Geislinger coupling-propeller shaft model is established. On this basis, frequency responses and critical velocities between nonlinear and linear prototype models are compared. Then, the nonlinear stiffness factor is derived based on the system vibration equation and nonlinear stiffness characteristics, and the scaling laws are carried out. Finally, the prediction accuracy is calculated with different scaled models in terms of the modal, frequency response, and transient response respectively. The result shows a better similarity and prediction using the proposed method, which will be powerful in systems with nonlinear stiffness like large flexible structures or nonlinear connections.
HouLChenYChenY.Combination resonances of a dual-rotor system with inter-shaft bearing. Nonlinear Dyn2023; 111(6): 5197–5219.
2.
LiYWenCLuoZ, et al. Dynamic characteristics analysis of a dual-rotor system with bolted-disk joint. Proc IMechE, Part C: J Mechanical Engineering Science2023; 237(3): 534–548.
3.
HouYCaoSKangY, et al. Dynamics analysis of bending–torsional coupling characteristic frequencies in dual-rotor systems. AIAA J2022; 60(10): 6020–6035.
4.
HouSHouLDunS, et al. Vibration characteristics of a dual-rotor system with non-concentricity. Machines2021; 9(11): 251.
5.
ChiangHWDHsuCNTuSH. Rotor-bearing analysis for turbomachinery single- and dual-rotor systems. J Propulsion Power2004; 20(6): 1096–1104.
6.
ZhaoHLiuCSongZ, et al. Analysis and design considerations of a dual-rotor multiple-winding machine. IEEE Trans Ind Electron2022; 69(9): 8727–8738.
7.
GhanbariTSanati MoghadamMDarabiA.Comparison between coreless and slotless kinds of dual rotor discs hysteresis motors. IET Electric Power Appl2016; 10(2): 133–140.
8.
GolovanovDGalassiniAFlanaganL, et al. Dual-rotor permanent magnet motor for electric superbike. In: 2019 IEEE International electric machines & drives conference (IEMDC), 2019, pp.951–956. New York: IEEE.
9.
IkarigaAShimojiHEnokizonoM, et al. Magnetic characteristic analysis of dual-rotor machines. Int J Appl Electromagn Mech2007; 25(1-4): 173–177.
10.
LuJZhangXPanX, et al. Research on unbalanced vibration suppression method for coupled cantilever dual-rotor system. Machines2022; 10(9): 758.
11.
MetallidisPNatsiavasS.Linear and nonlinear dynamics of reciprocating engines. Int J Non Linear Mech2003; 38(5): 723–738.
IijimaKYaoTMoanT.Structural response of a ship in severe seas considering global hydroelastic vibrations. Mar Struct2008; 21(4): 420–445.
14.
BasavanakattimathMSMadhusudanNSureshHN.Effect of vibrations on rotor model assembly due to modifications in coupling design. J Vib Eng Technol2023; 11(1): 119–127.
15.
ChenZXieLShangH, et al. Research on power enhancement of TCD2015V08 diesel engine based on one-dimensional simulation and analysis. In: 2018 International conference on air pollution and environmental engineering (APEE 2018), 2018, p.012009. Bristol: IOP Publishing Ltd.
16.
YiCSYunJHJeongIG, et al. Predicting the oil cooler fan performance of large-sized diesel engines by changing the outlet and torsion angles. J Mech Sci Technol2013; 27(2): 469–475.
17.
RizovV.Non-linear fracture in bi-directional graded shafts in torsion. Multidiscip Model Mater Struct2019; 15(1): 156–169.
18.
HongJChenXWangY, et al. Optimization of dynamics of non-continuous rotor based on model of rotor stiffness. Mech Syst Signal Process2019; 131: 166–182.
19.
WuJ-J.Prediction of lateral vibration characteristics of a full-size rotor-bearing system by using those of its scale models. Finite Elem Anal Des2007; 43(10): 803–816.
20.
SongYWuJYuG, et al. Dynamic characteristic prediction of a 5-DOF hybrid machine tool by using scale model considering the geometric distortion of bearings. Mech Mach Theory2020; 145: 103679.
21.
De RosaSFrancoF. A scaling procedure for the response of an isolated system with high modal overlap factor. Mech Syst Signal Process2008; 22(7): 1549–1565.
22.
QinZYangZZuJ, et al. Free vibration analysis of rotating cylindrical shells coupled with moderately thick annular plates. Int J Mech Sci2018; 142-143: 127–139.
23.
CoutinhoCPBaptistaAJDias RodrigesJ.Modular approach to structural similitude. Int J Mech Sci2018; 135: 294–312.
24.
FrancoFRobinOCiappiE, et al. Similitude laws for the structural response of flat plates under a turbulent boundary layer excitation. Mech Syst Signal Process2019; 129: 590–613.
25.
YazdiAARezaeepazhandJ.Applicability of small-scale models in prediction flutter pressure of delaminated composite beam-plates. Int J Damage Mech2013; 22(4): 590–601.
26.
PanSDaiQSafaeiB, et al. Damping characteristics of carbon nanotube reinforced epoxy nanocomposite beams. Thin Walled Struct2021; 166: 108127.
27.
AslMENiezreckiCSherwoodJ, et al. Experimental and theoretical similitude analysis for flexural bending of scaled-down laminated I-beams. Compos Struct2017; 176: 812–822.
28.
KasivitamnuayJSinghatanadgidP.Scaling laws for displacement of elastic beam by energy method. Int J Mech Sci2017; 128-129: 361–367.
29.
KasivitamnuayJSinghatanadgidP.Scaling laws for static displacement of linearly elastic cracked beam by energy method. Theor Appl Fract Mech2018; 98: 157–166.
30.
AslMENiezreckiCSherwoodJ, et al. Vibration prediction of thin-walled composite I-beams using scaled models. Thin-Walled Struct2017; 113: 151–161.
31.
De RosaSFrancoFLiX, et al. A similitude for structural acoustic enclosures. Mech Syst Signal Process2012; 30: 330–342.
32.
ŻurKK.Quasi-Green’s function approach to free vibration analysis of elastically supported functionally graded circular plates. Compos Struct2018; 183: 600–610.
33.
WangJLiZLYuW.Structural similitude for the geometric nonlinear buckling of stiffened orthotropic shallow spherical shells by energy approach. Thin-Walled Struct2019; 138: 430–457.
34.
PetroneGManfredoniaMDe RosaS, et al. Structural similitudes of stiffened cylinders. Math Mech Solids2019; 24(3): 527–541.
35.
GhannadiaslAMofidM.Free vibration analysis of general stepped circular plates with internal elastic ring support resting on Winkler foundation by green function method. Mech Based Des Struct Mach2016; 44(3): 212–230.
36.
RezaeepazhandJSimitsesGJRezaeepazhandJ, et al. Use of scaled-down models for predicting vibration response of laminated plates. Compos Struct1995; 30(4): 419–426.
37.
RezaeepazhandJSimitsesGJStarnesJH.Design of scaled down models for predicting shell vibration response. J Sound Vib1996; 195(2): 301–311.
38.
RezaeepazhandJSimitsesGJ.Structural similitude for vibration response of laminated cylindrical shells with double curvature. Compos B Eng1997; 28(3): 195–200.
39.
De RosaSFrancoF. On the use of the asymptotic scaled modal analysis for time-harmonic structural analysis and for the prediction of coupling loss factors for similar systems. Mech Syst Signal Process2010; 24(2): 455–480.
40.
De RosaSFrancoFPolitoT. Partial scaling of finite element models for the analysis of the coupling between short and long structural wavelengths. Mech Syst Signal Process2015; 52-53: 722–740.
41.
De RosaSFrancoFMeruaneV. Similitudes for the structural response of flexural plates. Proc IMechE, Part C: J Mechanical Engineering Science2016; 230(2): 174–188.
42.
FrancoFBerryAPetroneG, et al. Structural response of stiffened plates in similitude under a turbulent boundary layer excitation. J Fluid Struct2020; 98: 103119.
43.
WuJJ.Prediction of the torsional vibration characteristics of a rotor-shaft system using its scale model and scaling laws. Int J Mech Eng Mechatron2015; 9(09): 229–234.
44.
ZhangWLuoZLiY, et al. A novel method to determine the coupling scaling laws of vibration characteristics for rotor-bearing systems. J Vib Control2021; 27(21–22): 2630–2641.
45.
LiLLuoZHeF, et al. A partial similitude method considering variable powers in scaling laws and applied to rotor-bearing systems. Int J Mech Sci2020; 186: 105892.
46.
LiLLuoZHeF, et al. An improved partial similitude method for dynamic characteristic of rotor systems based on Levenberg–Marquardt method. Mech Syst Signal Process2022; 165: 108405.
47.
LiLLuoZHeF, et al. Experimental and numerical investigations on an unbalance identification method for full-size rotor system based on scaled model. J Sound Vib2022; 527: 116868.
48.
FuSLuoNHuangH, et al. Torsional vibration attenuation characteristics and stiffness identification of flexible coupling in vehicle power train. Shock Vib2020; 2020: 8851581–8851613.
49.
LiY. Dynamic analysis of torsional vibration of reed damper of diesel engine. In: 3rd International conference on fluid mechanics and industrial applications, 2019, p.012050. Bristol: IOP Publishing Ltd.
50.
LingSXiangTLinL. The simulation and experiment research on the influence of crankshaft flexible torsion to diesel instantaneous speed. In: LiuHWangGZhangG (eds) Material Science, Civil Engineering and Architecture Science, Mechanical Engineering and Manufacturing Technology ii, 2014, pp.924–927, Stafa-Zurich: Trans Tech Publications Ltd.
51.
LuanYGuanZ-QChengG-D, et al. A simplified nonlinear dynamic model for the analysis of pipe structures with bolted flange joints. J Sound Vib2012; 331(2): 325–344.
52.
QinZHanQChuF.Analytical model of bolted disk–drum joints and its application to dynamic analysis of jointed rotor. Proc IMechE, Part C: J Mechanical Engineering Science2014; 228(4): 646–663.
53.
WangMHanQWenB, et al. Modal characteristics and unbalance responses of fan rotor system with flexible support structures in aero-engine. Proc IMechE, Part G: J Aerospace Engineering2017; 231(9): 1686–1705.
54.
YuPZhangDMaY, et al. Dynamic modeling and vibration characteristics analysis of the aero-engine dual-rotor system with fan blade out. Mech Syst Signal Process2018; 106: 158–175.
55.
LuoZLiLHeF, et al. Partial similitude for dynamic characteristics of rotor systems considering gravitational acceleration. Mech Mach Theory2021; 156: 104142.
56.
LiLLuoZLiY, et al. Structural similitude for a scaled rotor system considering stiffness characteristics of bolted joints. Proc IMechE, Part C: J Mechanical Engineering Science2022; 236(10): 5192–5207.
57.
ZhuYWangYLuoZ, et al. Similitude design for the vibration problems of plates and shells: a review. Front Mech Eng2017; 12(2): 253–264.
58.
ZhouL.A new structural similitude method for laminated composite cylinders. Thin Walled Struct2021; 164: 107920.
DasPPSatpathySBhattacharyaS. A voltage injection-based current harmonics suppression strategy for six-phase PMSM with nonsinusoidal back EMF[J]. IEEE J Emerg Sel Top Power Electron, 2024; 5(1): 285–297.
