Dynamic responses of an engine front-end accessory belt drive system with pulley eccentricities via two spatial discretization methods

Abstract

In this study, a generic mathematical model for calculating the natural frequencies and the dynamic responses of a typical front-end accessory drive system with any number of pulleys and arbitrary configurations of the tensioner and pulleys is established. The belt bending stiffness and the pulley eccentricities are considered in this model, and their influences on the natural frequency and the dynamic responses of the front-end accessory drive system are examined. A generic spatial discretization method and a Galerkin discretization method, which uses Lagrange multipliers to enhance the boundary conditions, are presented to discretize the continuous belt spans and to transform the governing partial differential equations into ordinary differential equations. The accuracies of the generic spatial discretization method and the Galerkin discretization method are validated by modal tests, and the advantages of the generic spatial discretization method with respect to the efficiency and the convenience of implementation are assessed by comparing the generic spatial discretization method with the Galerkin discretization method and the two-layer iteration approach. The dynamic responses of the typical front-end accessory drive system at different operational velocities are calculated from the governing ordinary differential equations derived from these two methods. It is shown that large vibration amplitudes occur in certain belt spans owing to the resonance conditions or the beat phenomena in certain operational conditions and that the belt bending stiffness has a negligible influence on the vibrations of the belt drive system because its value is small.

Keywords

Front-end accessory drive system dynamic responses generic spatial discretization method Galerkin discretization method pulley eccentricity

Get full access to this article

View all access options for this article.

References

Cassidy

Fan

MacDonald

Samson

. Serpentine extended life accessory drive. SAE paper 790699, 1979.

Parker

. Efficient eigensolution, dynamic response, and eigensentivity of serpentine belt drives. J Sound Vibr 2004; 270: 15–38.

Nouri

. Dynamic analysis and optimization of tensioner in automotive serpentine belt drive systems. In: ASME 2002 international design engineering technical conferences and computers and information in engineering conference, Vol 2: 28th design automation conference, Montreal, Quebec, Canada, 29 September–2 October 2002, paper DETC2002/DAC-34120, pp. 813–820. New York: ASME.

Hou

Z-C

. Non-linear free oscillations of moving viscoelastic belts. Mech Mach Theory 2002; 37: 925–940.

Huang

RKL

Lee

Chen

. Nonlinear vibration of a curved beam under uniform base harmonic excitation with quadratic and cubic nonlinearities. J Sound Vibr 2011; 280: 5151–5164.

Pellicano

Fregolent

Bertuzzi

Vestroni

. Primary and parametric non-linear resonances of a power transmission belt: experimental and theoretical analysis. J Sound Vibr 2001; 244: 669–684.

Michon

Manin

Remond

. Parametric instability of an axially moving belt subjected to multifrequency excitations: experiments and analytical validation. Trans ASME, J Appl Mech 2008; 75: 041004-1–041004-8.

Scurtu

Clark

. Coupled longitudinal and transverse vibration of automotive belts under longitudinal excitations using analog equation method. J Vibr Control 2012; 18: 1336–1352.

Andrianov

Van Horssen

. On the transversal vibrations of a conveyor belt: applicability of simplified models. J Sound Vibr 2008; 313: 822–829.

10.

Zhang

. Nonlinear vibrations of viscoelastic moving belts, part ii: free vibration analysis. J Sound Vibr 1998; 216: 75–91.

11.

Zhu

. Transverse hysteretic damping characteristics of a serpentine belt: modeling and experimental investigation. J Sound Vibr 2014; 333: 7019–7035.

12.

Hwang

S-J

Perkins

Ulsoy

Meckstroth

. Rotational response and slip prediction of serpentine belt drive systems. Trans ASME, J Vibr Acoust 1994; 116: 71–78.

13.

Leamy

Perkins

. Nonlinear periodic response of engine accessory drives with dry friction tensioners. Trans ASME, J Vibr Acoust 1998; 120: 909–916.

14.

Shangguan

W-B

Zeng

X-K

. Modeling and validation of rotational vibration responses for accessory drive systems – Part II: simulations and analyses. Trans ASME, J Vibr Acoust 2013; 135: 031003-1–031003-13.

15.

Beikmann

Perkins

Ulsoy

. Free vibration of serpentine belt drive systems. Trans ASME, J Vibr Acoust 1996; 118: 406–413.

16.

Kong

Parker

. Equilibrium and belt-pulley vibration coupling in serpentine belt drives. Trans ASME, J Appl Mech 2003; 70: 739–749.

17.

Kong

Parker

. Vibration of an axially moving beam wrapping on fixed pulleys. J Sound Vibr 2005; 280: 1066–1074.

18.

Dukkipati

Qie

Zhu

Qatu

. Vibrations and instability in automotive front end accessory drive belt system. SAE paper 2009-01-1417, 2009.

19.

Pakdemirli

Ulsoy

. Stability analysis of an axially accelerating string. J Sound Vibr 1997; 203: 815–832.

20.

Parker

Lin

. Parametric instability of axially moving media subjected to multi-frequency tension and speed fluctuations. Trans ASME, J Appl Mech 2001; 68: 49–57.

21.

Cheng

. Nonstick and stick–slip motion of a Coulomb-damped belt drive system subjected to multi-frequency excitations. Trans ASME, J Appl Mech 2003; 70: 871–884.

22.

Sandhu

Wehrly

Resh

Rose

. An investigation of rotational response of accessory drive serpentine belt system. SAE paper 2001-01-1425, 2001.

23.

Ulsoy

Whitesell

Hooven

. Design of belt-tensioner systems for dynamic stability. Trans ASME, J Vibr Acoust 1985; 107(3): 282–290.

24.

Beikmann

Perkins

Ulsoy

. Nonlinear coupled vibration responses of serpentine belt drive systems. Trans ASME, J Vibr Acoust 1996; 118: 567–574.

25.

Zhang

. Modal analysis of serpentine belt drive systems. J Sound Vibr 1999; 222: 259–279.

26.

Hou

Z-C

Lao

Y-X

Q-H

. Sensitivity analysis and parameter optimization for vibration reduction of undamped multi-ribbed belt drive systems. J Sound Vibr 2008; 317: 591–607.

27.

Ding

D-P

. Static and dynamic behaviors of belt-drive dynamic systems with one-way clutch. Nonlinear Dynamics 2014; 78: 1553–1575.

28.

Pellicano

Catellani

Fregolent

. Parametric instability of belts: theory and experiments. Comput Struct 2004; 82: 81–91.

29.

Chen

L-Q

Zhao

. Simulations of transverse vibrations of an axially moving string: a modified difference approach. Appl Math Comput 2005; 166(3): 596–607.

30.

Zhu

Parker

. Non-linear dynamics of a one-way clutch in belt–pulley systems. J Sound Vibr 2005; 279(1): 285–308.

31.

Dufva

Kerkkanen

Maqueda

Shabana

. Nonlinear dynamics of three-dimensional belt drives using the finite-element method. Nonlinear Dynamics 2007; 48(4): 449–466.

32.

Kerkkänen

Vallejo

Mikkola

. Modeling of belt-drives using a large deformation finite element formulation. Nonlinear Dynamics 2006; 43: 239–256.

33.

Čepon

Manin

Boltežar

. Validation of a flexible multibody belt-drive model. Strojniški Vest – J Mech Engng 2011; 57(7–8): 539–546.

34.

Jia

Song

. Elastic dynamic analysis of synchronous belt drive system using absolute nodal coordinate formulation. Nonlinear Dynamics 2015; 81(3): 1393–1410.

35.

Zhu

Ren

. An accurate spatial discretization and substructure method with application to moving elevator cable-car systems – Part I: methodology. Trans ASME, J Vibr Acoust 2013; 135(5): 051036-1–051036-10.

36.

Zhu

Ren

. An accurate spatial discretization and substructure method with application to moving elevator cable-car systems – Part II: application. Trans ASME, J Vibr Acoust 2013; 135(5): 051037-1–051037-21.