A generalized multibody dynamic model enabling coupled vibration analysis of dual clutch transmissions (DCT) operating under any duty cycle is proposed. The model includes a new three-dimensional elastic continuum representation of wet clutchsets and predicts both steady state and transient response of DCTs. The coupled dynamic and thermal governing equations with localized, nonlinear multi-axis excitations acting on the clutch disk surface are solved. The nonlinear time-varying wet clutch dynamic model is benchmarked against experimental test results for its dynamic response and pad temperature distribution. Newmark's time-step marching-based integration is used to determine the time-varying dynamic response of a complete transmission system. For the corresponding linear time-invariant version of the model, natural modes are obtained by solving the eigenvalue problem. The proposed model is exercised using a common transmission architecture operating at several different operating conditions and clutch pad schemes. The resulting impact from non-torsional dynamic loads generated due to time-varying clutch pad friction, rotordynamics, gear dynamics, and clutch dynamics is investigated with a specific focus on axial and transverse rotodynamic displacements and bearing dynamic loads.
GkinisTRahmaniRRahnejatH. Effect of clutch lining frictional characteristics on take-up judder. Proc Inst Mech Eng K: J Multi-Body Dyn2017; 231: 493–503.
2.
GoetzMLevesleyMCrollaD. A gearshift controller for twin clutch transmissions. VDI Berichte2004; 1786: 381–400.
3.
GoetzMLevesleyMCrollaD. “Integrated Powertrain Control of Gearshifts On Twin Clutch Transmissions,” SAE Technical Paper 2004-01-1637. 2004.
4.
GoetzMLevesleyMCrollaD. Dynamics and control of gearshifts on twin-clutch transmissions. Proc Inst Mech Eng D: J Automob Eng2005; 219: 951–963.
5.
LeiYWangJGeA. Research on control strategies of double clutch transmission based on system simulation. 2006.
6.
ZhangYZouZChenX, et al.Simulation and analysis of transmission shift dynamics, “. Int J Veh Des2003; 32: 273–289.
7.
KulkarniMShimTZhangY. Shift dynamics and control of dual-clutch transmissions. Mech Mach Theory2007; 42: 168–182.
8.
LiuYQinDJiangH,et al.A systematic model for dynamics and control of dual clutch transmissions. J Mech Des2009; 131(6), 061012 (7 pages).
9.
GalvagnoEVelardocchiaMViglianiA. Dynamic and kinematic model of a dual clutch transmission. Mech Mach Theory2011; 46: 794–805.
10.
GalvagnoEGuercioniGViglianiA. “Sensitivity Analysis of the Design Parameters of a Dual-Clutch Transmission Focused on NVH Performance,” SAE Technical Paper 2016-01-1127. 2016.
11.
BrancatiRPaganoSRoccaE. Dynamic behaviour of an automotive dual clutch transmission during gear shift maneuvers. Appl Sci2023; 13: 4828.
12.
WalkerPDZhangN. Investigation of synchroniser engagement in dual clutch transmission equipped powertrains. J Sound Vib2012; 331: 1398–1412.
13.
WalkerPDZhangN. Modelling of dual clutch transmission equipped powertrains for shift transient simulations. Mech Mach Theory2013; 60: 47–59.
14.
OhJJChoiSBKimJ. Driveline modeling and estimation of individual clutch torque during gear shifts for dual clutch transmission. Mechatronics2014; 24: 449–463.
15.
BeraPSikoraWWędrychowiczD. Non-linear control of a gear shift process in a dual-clutch transmission based on a neural engine model. Control Eng Pract2021; 115.
16.
KimSChoiSB. Cooperative control of drive motor and clutch for gear shift of hybrid electric vehicles with dual-clutch transmission. IEEE/ASME Trans Mechatron2020; 25: 1578–1588.
17.
MrochenAMSawodnyO. Modeling and simulation of a hybrid dual-clutch transmission powertrain. IFAC-PapersOnLine2018; 51: 886–891.
18.
CrowtherAZhangNLiuD,et al.Analysis and simulation of clutch engagement judder and stick-slip in automotive powertrain systems. Proc Inst Mech Eng D: J Automob Eng2004; 218: 1427–1446.
19.
CrowtherAZhangN. Torsional finite elements and nonlinear numerical modelling in vehicle powertrain dynamics. J Sound Vib2005; 284: 825–849.
20.
DowsonD. A generalized Reynolds equation for fluid-film lubrication. Int J Mech Sci1962; 4: 159–170.
21.
PrakashJVijSK. Effect of velocity slip on the squeeze film between rotating porous annular discs. Wear1976; 38: 73–85.
22.
PatirNChengHS. An average flow model for determining effects of three dimensional roughness on partial hydrodynamic lubrication. J Lubr Technol1978; 100: 12–17.
23.
NatsumedaSMiyoshiT. Numerical simulation of engagement of paper based wet clutch facing. J Tribol1994; 116: 232–237.
24.
BergerEJSadeghiFKrousgrillCM. Finite element modeling of engagement of rough and grooved wet clutches. J Tribol1996; 118: 137–146.
25.
BergerEJSadeghiFKrousgrillCM. Analytical and numerical modeling of engagement of rough, permeable, grooved wet clutches. J Tribol1996; 119: 143–146.
26.
JangJYKhonsariMM. Thermal characteristics of a wet clutch. J Tribol1999; 121: 610–617.
27.
YangL-kLiH-yAhmadianM,et al.Analysis of the influence of engine torque excitation on clutch judder. J Vib Control2017; 23: 645–655.
28.
YuLMaBKimIY,et al.Influences of the uneven contact pressure and the initial temperature on the hot judder behavior in a multi-disc clutch. Proc IMechE, Part J: J Engineering Tribology2020; 234: 500–514.
29.
HuJHouSWeiC. Drag torque modeling at high circumferential speed in open wet clutches considering plate wobble and mechanical contact. Tribol Int2018; 124: 102–116.
30.
WickramarachiPSinghRBaileyG. Analysis of friction-induced vibration leading to Eek Noise in a Dry Friction Clutch. Noise Control Eng J2005; 53: 138–144.
31.
ChenXZhangWWuG. A multi-body dynamic modeling and experimental study of EEK noise during clutch engagement. J Fail Anal Prev2016; 16: 1052–1058.
32.
MinasIMorrisNTheodossiadesS,et al.Noise, vibration and harshness during dry clutch engagement oscillations. Proc IMechE, Part C: J Mechanical Engineering Science2020; 234: 4572–4588.
ÖzgüvenHN. A non-linear mathematical model for dynamic analysis of spur gears including shaft and bearing dynamics. J Sound Vib1991; 145: 239–260.
35.
KahramanAOzguvenHNHouserDR,et al.Dynamic analysis of geared rotors by finite elements. ASME J Mech Des1992; 114: 507–514.
36.
ParkerRVijayakarSImajoT. Non-linear dynamic response of a spur gear pair: modelling and experimental comparisons. J Sound Vib2000; 237: 435–455.
37.
KuburMKahramanAZiniD,et al.Dynamic analysis of a multi-shaft helical gear transmission by finite elements: model and experiment. J Vib Acoust2004; 126: 398–406.
38.
InalpolatMKahramanA. Dynamic modelling of planetary gears of automatic transmissions. Proc IMechE, Part K: J Multi-body Dynamics2008; 222: 229–242.
39.
InalpolatMKahramanA. A theoretical and experimental investigation of modulation sidebands of planetary gear sets. J Sound Vib2009; 323: 677–696.
40.
InalpolatMHandschuhMKahramanA. Influence of indexing errors on dynamic response of Spur Gear Pairs. Mech Syst Signal Process2015; 60–61: 391–405.
41.
EritenelTParkerRG. A static and dynamic model for three-dimensional, multi-mesh gear systems. In: Proc. International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp.945–956.
42.
WalkerPDZhangN. Modelling of dual clutch transmission equipped powertrains for shift transient simulations. Mech Mach Theory2013; 60: 47–59.
43.
RogkasNVasilopoulosLSpitasV. A hybrid transient/quasi-static model for wet clutch engagement. Int J Mech Sci2023; 256.
44.
MindlinRD. Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. J Appl Mech1951; 18: 31–38.
45.
StribeckR. Kugellager fur beliebige Belastungen. Zeitschrift des Vereines deutscher Ingenieure1901; 45: 73–79. (pt I) & 45(4), pp. 118–125 (pt II).
46.
StribeckR. Die wesentlischen Eigenschaften der Gleit- und Rollenlager. Zeitschrift des Vereines deutscher Ingenieure1902; 46: 1341–1348. (pt I) & 46(38), pp. 1432–1438 (pt II) & 46(39), pp. 1463–1470 (pt III).
47.
GreenwoodJAWilliamsonJBP. Contact of nominally flat surfaces. Proc R Soc A: Math Phys Eng Sci1966; 295: 300–319.
48.
FuHFuYJiJ, et al.Influence of short grooves on hydrodynamic lubrication of textured infinitely long sliders.Adv Mech Eng2018; 10(6): 1013–1028.
49.
NeupertTBartelD. Measurement of pressure distribution and hydrodynamic axial forces of wet clutch discs. Tribol Int2021; 163: 107172.
50.
DeurJPetricJAsgariJ,et al.Modeling of wet clutch engagement including a thorough experimental validation. SAE Trans2005; 114: 1013–1028.
51.
SondkarPB. “Dynamic modeling of double-helical planetary gear sets,” Ph.D. Thesis, The Ohio State University. 2012.
52.
MATLAB. MATLAB. 2021a Ed. Natick, MA: The MathWorks, Inc, 2021.
53.
Ansys® Workbench, Release 2022 R2, Help System, ANSYS, In.
54.
VisnapuuANashRWTurnerPC. Damping properties of selected steels and cast irons. U.S. Department of the Interior, Bureau of Mines, 1987.
55.
SAE International, SAE No. 2 Clutch Friction Test Machine Guidelines, SAE Standard J286, Rev. 2012.
