Skip to main content
SpringerLink
Log in

Dynamics Analysis of Torsional Vibration Induced by Clutch and Gear Set in Automatic Transmission

  • Published:
International Journal of Automotive Technology Aims and scope Submit manuscript

Abstract

The torsional vibration generated during clutch engagement directly affects the shifting quality of automatic transmissions, where the noise source stems from both the clutch and the gear set. To predict the dynamical response and driveline oscillation, a comprehensive mathematical model of the vehicle powertrain equipped with automatic transmission is developed with consideration of nonlinearities in the clutch and the planetary gear set. For the clutch, the dynamics of stickslip is described for the transition between the slipping to locked states. The gear backlash model is used to analyze the rattle noise of the planetary gear set. Based on extensive powertrain simulations for the clutch engagement process, the magnitude of vibration propagation in the driveline are predicted to identify the primary factors of noise generation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

I :

inertia, kg·m2

K :

component stiffness, N·m/rad

k :

component stiffness, N/m

C :

component damping, N·m·s/rad

c :

component damping, N·s/m

r :

component radius, m

θ :

angular displacement, rad

θ :

angular velocity, rad/s

θ :

angular acceleration, rad/s2

δ :

teeth deflections, m

f d :

dynamic coefficient of friction

f s :

static coefficient of friction

f n :

normal load distribution, N/m

F tr :

traction force, N

F n :

normal force, N

F rr :

rolling resistance force, N

g :

function characterizing the road conditions

h :

film thickness of lubrication, m

k Ф :

pressure-sinkage parameter

n :

rolling resistance constant

N f :

number of friction pair

P 0 :

engagement pressure, MPa

T E :

engine torque, N·m

T 0 :

averaged engine torque, N·m

T C :

clutch torque, N·m

T ac :

asperity contact torque of clutch, N·m

T hd :

hydrodynamic torque of clutch, N·m

T INT :

clutch torque at the instant of zero relative speed, N·m

T LT :

lock-up clutch torque, N·m

T b :

braking torque, N·m

u :

internal friction state

v r :

relative velocity, m/s

v s :

Stribeck relative velocity, m/s

V :

vehicle motion velocity, m/s

α 1, α 2 :

pressure angle, rad

ε :

tolerance of velocity calculation, rad/s

φ f, φ fs :

shear stress factors

μ :

traction coefficient

μ c :

Coulomb friction coefficient

μ s :

static friction coefficient

σ 0 :

rubber longitudinal lumped stiffness, N/m

σ 1 :

rubber longitudinal lumped damping, N·s/m

σ 2 :

viscous relative damping, N·s/m

E :

engine

F :

flywheel

CD :

clutch drum

CH :

clutch hub

G :

gear set

S :

sun gear

pi :

planetary gear (i = 1, 2, 3)

P :

planet carrier

R :

ring gear

DS :

drive shaft

D :

differential

W :

wheel

References

  • Bakker, E., Nyborg, L. and Pacejka, H. B. (1987). Tyre modelling for use in vehicle dynamics studies. SAE Paper No. 870421.

    Book  Google Scholar 

  • Berger, E. J., Sadeghi, F. and Krousgrill, C. M. (1996). Finite element modeling of engagement of rough and grooved wet clutches. J. Tribology 118, 1, 137–146.

    Article  Google Scholar 

  • Bodas, A. and Kahraman, A. (2004). Influence of carrier and gear manufacturing errors on the static load sharing behavior of planetary gear sets. JSME Int. J. Series C Mechanical Systems, Machine Elements and Manu-facturing 47, 3, 908–915.

    Article  Google Scholar 

  • Brinkmeier, M., Nackenhorst, U., Petersen, S. and Von Estorff, O. (2008). A finite element approach for the simulation of tire rolling noise. J. Sound and Vibration 309, 1–2, 20-39.

    Article  Google Scholar 

  • Canudas-de-Wit, C., Tsiotras, P., Velenis, E., Basset, M. and Gissinger, G. (2003). Dynamic friction models for road/tire longitudinal interaction. Vehicle System Dynamics 39, 3, 189–226.

    Article  Google Scholar 

  • Centea, D., Rahnejat, H. and Menday, M. T. (1999). The influence of the interface coefficient of friction upon the propensity to judder in automotive clutches. Proc. Institution of Mechanical Engineers, Part D: J. Automobile Engineering 213, 3, 245–258.

    Google Scholar 

  • Crowther, A., Zhang, N., Liu, D. K. and Jeyakumaran, J. K. (2004). Analysis and simulation of clutch engagement judder and stick-slip in automotive powertrain systems. Proc. Institution of Mechanical Engineers, Part D: J. Automobile Engineering 218, 12, 1427–1446.

    Google Scholar 

  • Derevjanik, T. S. (2001). Detergent and friction modifier effects on metal/metal and clutch material/metal frictional performance. SAE Paper No. 2001-01-1993.

    Book  Google Scholar 

  • Deur, J., Petric, J. and Hrovat, D. (2006). Recent advances in control-oriented modeling of automotive power train dynamics. IEEE/ASME Trans. Mechatronics 11, 5, 513–523.

    Article  Google Scholar 

  • Duan, C. and Singh, R. (2005). Stick-slip behavior of torque converter clutch. SAE Paper No. 2005-01-2456.

    Book  Google Scholar 

  • Fakhfakh, T., Walha, L., Louati, J. and Haddar, M. (2006). Effect of manufacturing and assembly defects on twostage gear systems vibration. Int. J. Advanced Manufacturing Technology 29, 9–10, 1008-1018.

    Article  Google Scholar 

  • Guzzella, L. and Onder, C. (2009). Introduction to Modeling and Control of Internal Combustion Engine Systems. Springer-Verlag Berlin Heidelberg, Heidelberg, Germany.

    Google Scholar 

  • Isermann, R. (2014). Engine Modeling and Control. Spriger-Verlag Berlin Heidelberg. Heidelberg, Germany.

    Book  Google Scholar 

  • Jang, J. Y. and Khonsari, M. M. (1999). Thermal characteristics of a wet clutch. J. Tribology 121, 3, 610–617.

    Article  Google Scholar 

  • Jang, J. Y. and Khonsari, M. M. (2013). Wet clutch friction material: The surfaced groove effect. Encyclopedia of Tribology, 4102–4108.

    Chapter  Google Scholar 

  • Jazar, R. N. (2008). Vehicle Dynamics: Theory and Application. Springer. New York, USA.

    Book  Google Scholar 

  • Kamoulakos, A. and Kao, B. G. (1998). Transient dynamics of a tire rolling over small obstacles -A finite element approach with PAM-SHOCK. Tire Science and Technology 26, 2, 84–108.

    Article  Google Scholar 

  • Kahraman, A. and Singh, R. (1991). Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system. J. Sound and Vibration 146, 1, 135–156.

    Article  Google Scholar 

  • Karnopp, D. (1985). Computer simulation of stick-slip friction in mechanical dynamic systems. J. Dynamic Systems, Measurement, and Control 107, 1, 100–103.

    Article  Google Scholar 

  • Kiekbusch, T., Sappok, D., Sauer, B. and Howard, I. (2011). Calculation of the combined torsional mesh stiffness of spur gears with two-and three-dimensional parametrical FE models. Strojniški Vestnik–J. Mechanical Engineering 57, 11, 810–818.

    Article  Google Scholar 

  • Kim, Y. W., Rizzoni, G. and Utkin, V. (1998). Automotive engine diagnosis and control via nonlinear estimation. IEEE Control Systems 18, 5, 84–99.

    Article  Google Scholar 

  • Kugimiya, T., Yoshimura, N., Kuribayashi, T., Mitsui, J. I., Ueda, F., Ando, Y., Nakada, T. and Ohira, H. (1997). Next generation high performance ATF for slip-controlled automatic transmission. SAE Paper No. 972927.

    Book  Google Scholar 

  • Leine, R. I., Van Campen, D. H., De Kraker, A. and Van Den Steen, L. (1998). Stick-slip vibrations induced by alternate friction models. Nonlinear Dynamics 16, 1, 41–54.

    Article  MATH  Google Scholar 

  • Li, M., Khonsari, M. M., McCarthy, D. M. C. and Lundin, J. (2014). Parametric analysis for a paper-based wet clutch with groove consideration. Tribology International, 80, 222–233.

    Article  Google Scholar 

  • Li, M., Khonsari, M. M., McCarthy, D. M. C. and Lundin, J. (2015). On the wear prediction of the paper-based friction materialin a wet clutch. Wear, 334-335, 56–66.

    Article  Google Scholar 

  • Lin, J. and Parker, R. G. (2002). Planetary gear parametric instability caused by mesh stiffness variation. J. Sound and Vibration 249, 1, 129–145.

    Article  Google Scholar 

  • Moskwa, J. J. (1988). Automotive Engine Modeling for Real Time Control. Ph. D. Disssertation. Massachusetts Institute of Technology. Cambridge, Massachusetts, USA.

    Google Scholar 

  • Newingham, T. D. (1963). Automatic transmission fluidcomponent effects on friction. SAE Paper No. 630442.

    Book  Google Scholar 

  • Oldfield, R. C. and Watts, R. F. (2006). Impact of lubricant formulation on the friction properties of carbon fiber clutch plates. Lubrication Science 18, 1, 37–48.

    Article  Google Scholar 

  • Özgüven, H. N. and Houser, D. R. (1988). Mathematical models used in gear dynamics -A review. J. Sound and Vibration 121, 3, 383–411.

    Article  Google Scholar 

  • Pacejka, H. (2005). Tire and Vehicle Dynamics. Elsevier. New York, USA.

    Google Scholar 

  • Pacejka, H. B. and Sharp, R. S. (1991). Shear force development by pneumatic tyres in steady state conditions: A review of modelling aspects. Vehicle System Dynamics 20, 3-4, 121–175.

    Article  Google Scholar 

  • Rodgers, J. J. and Haviland, M. L. (1960). Friction of transmission clutch materials as affected by fluids, additives, and oxidation. SAE Paper No. 600178.

    Book  Google Scholar 

  • Shiao, Y. and Moskwa, J. J. (1995). Cylinder pressure and combustion heat release estimation for SI engine diagnostics using nonlinear sliding observers. IEEE Trans. Control Systems Technology 3, 1, 70–78.

    Article  Google Scholar 

  • Shiraishi, M., Yoshinaga, H., Miyori, A. and Takahashi, E. (2000). Simulation of dynamically rolling tire. Tire Science and Technology 28, 4, 264–276.

    Article  Google Scholar 

  • Sun, T. and Hu, H. (2003). Nonlinear dynamics of a planetary gear system with multiple clearances. Mechanism and Machine Theory 38, 12, 1371–1390.

    Article  MATH  Google Scholar 

  • Theodossiades, S. and Natisavas, S. (2000). Non-linear dynamics of gear-pair systems with periodic stiffness and backlash. J. Sound and Vibration 229, 2, 287–310.

    Article  Google Scholar 

  • Walker, P. D. and Zhang, N. (2015). Numerical investigations into shift transients of a dual clutch transmission equipped powertrains with multiple nonlinearities. J. Vibration and Control 21, 8, 1473–1486.

    Article  Google Scholar 

  • Weeks, R. W. and Moskwa, J. J. (1995). Automotive engine modeling for real-time control using matlab/ simulink. SAE Paper No. 950417.

    Book  Google Scholar 

  • Willermet, P. A., Gupta, G. K., Honkanen, D., Sprys, J. W. and Mcwatt, D. G. (1998). ATF bulk oxidative degradation and its effects on LVFA friction and the performance of a modulated torque converter clutch. SAE Paper No. 982668.

    Book  Google Scholar 

  • Wong, J. Y. (2008). Theory of Ground Vehicles. John Wiley & Sons. New Jersey, USA.

    Google Scholar 

  • Zhang, N., Liu, D. K., Jeyakumaran, J. M. and Villanueva, L. (2002). Modelling of dynamic characteristics of an automatic transmission during shift changes. Proc. Institution of Mechanical Engineers, Part I: J. Systems and Control Engineering 216, 4, 331–341.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, Louisiana State University, Baton Rouge, 70803, USA

    Meng Li, Michael Khonsari & Ruzhou Yang

Authors
  1. Meng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael Khonsari
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ruzhou Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michael Khonsari.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, M., Khonsari, M. & Yang, R. Dynamics Analysis of Torsional Vibration Induced by Clutch and Gear Set in Automatic Transmission. Int.J Automot. Technol. 19, 473–488 (2018). https://doi.org/10.1007/s12239-018-0046-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12239-018-0046-8

Key words

Search

Navigation