The paper presents a lumped-parameter dynamic model of an electromechanically actuated wet clutch found in an active limited slip differential. The bond graph modelling technique is used to describe the multi-physical clutch system including the clutch actuator dynamics, the axial dynamics with the fluid film squeeze effect, the thermal dynamics, and the torque development dynamics with a multi-functional clutch friction coefficient static characteristic. Different variants of the individual subsystem models are considered, ranging from first-principle models to simplified and numerically more efficient models. The proposed models are parameterized and thoroughly validated on the basis of the experimental data collected by using an active differential and clutch test rig. The modelling results are used for the purpose of analysis of the clutch steady state and transient behaviour under various operating modes.
HrovatD.AsgariJ.FodorM.Automotive mechatronic systems, techniques and applications, vol. 2 – transportations and vehicle systems (Ed. LeondesC. T.), 2000, pp. 1–98 (Gordon and Breach, New York).
2.
AssadianF.Mechatronics and its role in the automotive domain. In Proceedings of the UKACC International Conference on Control, Coventry, UK, 7–10 October 2010.
3.
SawaseK.UshirodaY.MiuraT.Left–right torque vectoring technology as the core of super all wheel drive control S-AWC. Mitsubishi Motors Tech. Rev., 2006, 18, 16–23.
4.
DeurJ.IvanovićV.HancockM.AssadianF.Modeling and analysis of active differential dynamics. Trans. ASME, J. Dynamic Systems, Measmt, Control, 2010, 132(6), 061501/1–061501/13.
5.
SawaseK.SanoY.Application of active yaw control to vehicle dynamics by utilizing driving/braking force. JSAE Rev., 1999, 20, 289–295.
6.
HancockM.Vehicle handling control using active differentials. PhD Thesis, University of Loughborough, Loughborough, Leicestershire, UK, 2006.
7.
PiyabongkarnD.LewJ.GroggJ.KyleR.Stability-enhanced traction and yaw control using electronic limited slip differential. SAE paper 2006-01-1016, 2006.
8.
BilligC.BoedrichH.BrackJ.HollB.HolleM.KimmichF.The dynamic performance control from BMW. Automobiltechnische Z., 2008, 110, 19–25.
9.
GassmannT.BarlageJ. A.Electronic torque manager (ETM): an adaptive driveline torque management system. SAE paper 2004-01-0866, 2004.
10.
WestR. S.HaseltonD.Approaches to achieving AWD torque accuracy. SAE paper 2008-01-0303, 2008.
11.
FrancisP.HaseltonD.PritchardL.Pre-emptive Torque Management™ (PTM)™. SAE paper 2006-01-0817, 2006.
12.
WhealsJ. C.DeaneM.DruryS.GriffithG.HarmanP.ParkinsonR.ShepherdS.TurnerA.Design and simulation of a Torque Vectoring™ rear axle. SAE paper 2006-01-0818, 2006.
WhealsJ. C.McMickingJ.ShepherdS.BonnetB.JacksonN.HallO.Proven high efficiency actuation and clutch technologies for eAMT™ and eDCT™. SAE paper 2009-01-0513, 2009.
17.
RobertsR.SchauttM.HartmannH.GombertB.Modelling and validation of the mechatronic wedge brake. SAE paper 2003-01-3331, 2003.
18.
HeroldP.ThalhammerT.GietiS.Integral active steering: the new steering system from BMW. Automobiltechnische Z. ATZextra, 2008, BMW 7, 104–107.
19.
JacobsonB.Engagement of oil immersed multi-disc clutches. In Proceedings of the ASME International Power Transmission and Gearing Conference, 1992, DE-Vol. 43-2, pp. 567–574 (ASME, New York).
20.
SandaS.NagasawaY.SuzukiA.IlayashiK.ItohH.Mechanism of friction of wet clutch with paper based facings: observations and modeling of facing surface during engagement. In Proceedings of the International Tribology Conference, Yokohama, Japan, 29 October–2 November 1995, pp. 1519–1524 (Japanese Society of Tribologists, Tokyo).
21.
BergerE. J.SadeghiF.KrousgrillC. M.Finite element modeling of engagement of rough and grooved wet clutches. Trans. ASME, J. Tribol., 1996, 118, 137–155.
22.
BergerE. J.SadeghiF.KrousgrillC. M.Analytical and numerical modeling of engagement of rough, permeable, grooved wet clutches. Trans. ASME, J. Tribol., 1997, 119, 143–148.
23.
YangY.LamR. C.FujiiT.Prediction of torque response during the engagement of wet friction clutch. SAE paper 981097, 1998.
24.
DeurJ.PetrićJ.AsgariJ.HrovatD.Modeling of wet clutch engagement including a thorough experimental validation. SAE paper 2005-01-0877, 2005.
25.
FujiiY.ToblerW. E.SnyderT. D.Prediction of wet band brake dynamic engagement behaviour. Part 1: mathematical model development. Proc. IMechE, Part D: J. Automobile Engineering, 2001, 215(4), 479–492.
26.
FujiiY.ToblerW. E.SnyderT. D.Prediction of wet band brake dynamic engagement behaviour. Part 2: experimental model validation. Proc. IMechE, Part D: J. Automobile Engineering, 2001, 215(5), 603–611.
27.
Ye-BenL.HanZ.-P.Simulation of the interfacial thermohydrodynamics and thermomechanical phenomena of wet clutch discs by 3-D FEM analysis. SAE paper 922096, 1992.
28.
ZhaoS.HilmasG. E.DharaniL. R.Behavior of a composite multidisk clutch subjected to mechanical and frictionally excited thermal load. Wear, 2008, 264, 1059–1068.
29.
YangY.LamR. C.ChenY. F.YabeH.Modeling of heat transfer and fluid hydrodynamics for a multidisc wet clutch. SAE paper 950898, 1995.
30.
WangC.-H.SoomA.DargushG. F.Transient thermoelastic contact of sliding rings with axisymmetric surface roughness. Trans. ASME, J. Tribol., 2004, 126, 217–224.
31.
MäkiR.PärN.OlssonR.GanemiB.Measurement and characterization of anti-shudder properties in wet clutch applications. SAE paper 2005-01-0878, 2005.
32.
MarklundP.MäkiR.LarssonR.HöglundE.KhonsariM. M.JangJ.Thermal influence on torque transfer of wet clutches in limited slip differential applications. Tribol. Int., 2007, 40(5), 876–884.
33.
MarklundP.LarssonR.Wet clutch friction characteristics obtained from simplified pin on disc test. Tribol. Int., 2008, 41(9–10), 824–830.
34.
KraussC.SchwekutschM.A method for controlling a twin-clutch transmission. US Pat. 2006/0236798 A1, 2006.
35.
MorselliR.ZanasiR.CirsoneR.SereniE.BedogniE.SedoniE.Dynamic modeling and control of electro-hydraulic wet clutches. IEEE Trans. Intell. Transpn Systems, 2004, 1, 660–665.
36.
BalauA.-E.CaruntuC.-F.LazarC.Simulation and control of an electro-hydraulic actuated clutch. Mech. Systems Signal Processing, 2011, 25(6), 1911–1922.
37.
TrederM.WoernleC.Simulation and experimental validation of the dynamic behavior of an electromechanically actuated multiple-disk clutch. PAMM, Proc. Appl. Math. Mech., 2004, 4, 171–172.
38.
HusseinM.KobM. S. C.TawiK. B.SupriyoB.AriyonoS.Electro-mechanical friction clutch (EMFC) controller development for automotive application. In Proceedings of the World Congress on Engineering (WCE 2010), London, UK, 30 June–2 July 2010, vol. II, pp. 1642–1647 (International Association of Engineers, Hong Kong).
39.
KarnoppD.MargolisD. L.RosenbergR. C.System dynamics: a unified approach, 2nd edition, 1990 (Wiley–Interscience, New York).
40.
WincklerP. S.Improved carbon-based friction material for an automotive continuous slip service. US Pat. 525486, 1996.
41.
IvanovićV.HeroldZ.DeurJ.HancockM.AssadianF.Experimental setups for active limited slip differential dynamics research. SAE paper 2008-01-0302, 2008.
42.
Armstrong-HélouvryB.DupontP.Canudas de WitC.A survey of models, analysis tools and compensation methods for the control of machines with friction. Automatica, 1994, 40, 419–425.
43.
HaessigD. A.FriedlandB.On the modeling and simulation of friction. Trans. ASME, J. Dynamic Systems, Measmt, Control, 1991, 113, 354–346.
44.
KarnoppD. C.Computer simulation of stick–slip friction in mechanical dynamic systems. Trans. ASME, J. Dynamics Systems, Measmt, Control, 1985, 107, 100–103.
45.
DeurJ.AsgariJ.HrovatD.Modeling of and automotive planetary gear set based on Karnopp model for clutch friction. In Proceedings of the ASME International Mechanical Engineering Congress and Exposition (IMECE 2003), Washington, DC, USA, 2003, vol. 72, no. 2, pp. 903–910 (ASME, New York).
46.
Al-BenderF.SweversJ.Characterization of friction force dynamics. IEEE Control Systems Mag., 2008, 6, 64–81.
47.
ÅströmJ. K.Canudas de WitC.Revisiting the LuGre friction model. IEEE Control Systems Mag., 2008, 28(6), 101–114.
48.
DahlP. R.A solid friction model. Technical Report TOR-0158(3107-18)-1, The Aerospace Corporation, El Segundo, California, USA, 1968.
49.
Canudas de WitC.OlssonH.ÅströmK. J.LischinskyP.A new model for control of systems with friction. IEEE Autom. Control, 1995, 40(3), 419–425.
50.
DeurJ.AsgariJ.HrovatD.A 3D brush-type dynamic tire friction model. Veh. System Dynamics, 2004, 42, 133–173.
51.
Canudas de WitC.LischinskyP.Adaptive friction compensation with partially known dynamic friction model. Int. J. Adaptive Control Signal Processing, 1997, 11, 65–68.
52.
DahlP. R.Measurement of solid friction parameters of ball bearings. In Proceedings of the Sixth Annual Symposium on Incremental motion, control systems and devices, Urbana–Champaign, Illinois, USA, 1977, pp. 49–60 (University of Illinois Press, Champaign).
53.
IvanovićV.Modeling and control of vehicle powetrain components with emphasized friction effects (in Croatian). PhD Thesis, University of Zagreb, Croatia, 2010.
54.
IvanovićV.DeurJ.HeroldZ.HancockM.AssadianF.Modeling and experimental validation of active limited slip differential clutch dynamics. In Proceedings of the ASME International Mechanical Engineering Congress and Exposition (IMECE 2008), Boston, Massachusetts, USA, 31 October–6 November 2008, vol. 17, pp. 295–304, available on CD-ROM (ASME, New York).
55.
EschmannP.HasbargenI.WeigandK.Ball and roller bearings: theory, design, and application, 1985 (John Wiley, New York).
56.
WahlA. M.Mechanical springs, 2nd edition, 1963 (McGraw-Hill, New York).
57.
OrthweinW. C.Clutches and brakes: design and selection, 2nd edition, 2004 (Marcel Dekker, New York).
58.
IvanovićV.DeurJ.HeroldZ.HancockM.AssadianF.Experimental characterization of wet clutch friction behaviors including thermal dynamics. SAE Int. J. Engines, 2009, 2(1), 1211–1220.
59.
HamrockB. J.SchmidW. R.JacobsonB. O.Fundamentals of fluid film lubrication, 2nd edition, 2004 (Marcel Dekker, New York).
60.
Ali JafriF.FußM.BaileyG.KaoC.-K.RazzackiS. T.AvnyE.Shudder durability of a wet launch clutch. Part II – durability study. SAE paper 2009-01-0330, 2009.
61.
CrowtherA.ZhangN.LiuD. K.JeyakumaranJ. K.Analysis and simulation of clutch engagement judder and stick–slip in automotive powertrain systems. Proc. IMechE, Part D: J. Automobile Engineering, 2004, 218(12), 1427–1446.
62.
Calculations page, the SKF Group, 2011, available from www.skf.com.
63.
CameronT. M.McCombsT.TersigniS.JaoT.-C.Flash temperatures in clutches. SAE paper 2005-01-3890, 2005.
64.
Ali JafriF.FußM.BaileyG.KaoC.-K.RazzackiS. T.AvnyE.Shudder durability of a wet launch clutch. Part I – thermal study and development of durability test profile. SAE paper 2009-01-0329, 2009.
65.
VelardocchiaM.AmisanoF.FloraR.A linear thermal model for an automotive clutch. SAE paper 2000-01-0834, 2000.
66.
IvanovićV.DeurJ.HancockM.AssadianF.A closed-loop strategy of active differential clutch control. In Proceedings of the ASME Dynamic systems and control conference (DSCC 2009), Hollywood, California, USA, 12–14 October 2009, part B, pp. 1523–1530 (ASME, New York).
