Dynamic Modeling of Belt Drive Systems: Effects of the Shear Deformations

[+] Author and Article Information
Andrea Tonoli

Mechanics Department-Mechatronics Laboratory, Politecnico di Torino, corso Duca degli Abruzzi 24, I-10129 Torino, Italyandrea.tonoli@polito.it

Nicola Amati

Mechanics Department-Mechatronics Laboratory, Politecnico di Torino, corso Duca degli Abruzzi 24, I-10129 Torino, Italy

Enrico Zenerino

Mechatronics Laboratory, Politecnico di Torino, corso Duca degli Abruzzi 24, I-10129 Torino, Italy

J. Vib. Acoust 128(5), 555-567 (Feb 03, 2006) (13 pages) doi:10.1115/1.2202153 History: Received September 02, 2004; Revised February 03, 2006

Multiribbed serpentine belt drive systems are widely adopted in accessory drive automotive applications due to the better performances relative to the flat or V-belt drives. Nevertheless, they can generate unwanted noise and vibration which may affect the correct functionality and the fatigue life of the belt and of the other components of the transmission. The aim of the paper is to analyze the effect of the shear deflection in the rubber layer between the pulley and the belt fibers on the rotational dynamic behavior of the transmission. To this end the Firbank’s model has been extended to cover the case of small amplitude vibrations about mean rotational speeds. The model evidences that the shear deflection can be accounted for by an elastic term reacting to the torsional oscillations in series with a viscous term that dominates at constant speed. In addition, the axial deformation of the belt spans are taken into account. The numerical model has been validated by the comparison with the experimental results obtained on an accessory drive transmission including two pulleys and an automatic tensioner. The results show that the first rotational modes of the system are dominated by the shear deflection of the belt.

Copyright © 2006 by American Society of Mechanical Engineers
Topics: Pulleys , Belts , Engines
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Figure 1

Layout of a three pulley belt transmission including: motor pulley, alternator pulley, and automatic tensioner. The slip arcs are shaded. Mm, Ma: torques on the motor and the alternator; ωpm, ωpa: angular speeds of the motor and alternator pulleys.

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Figure 2

Driving pulley. The angular speed of the pulley ωp is larger than that of the belt tension member ωb. The different angular speed produces a shear deflection γ of the rubber layer of the belt. α arc of contact; φa: adhesion arc; φs slip arc; R radius of the belt fibers (tension member); h thickness of the rubber layer (belt envelope). φ, θ rotation angles of the fiber and the pulley in time interval ζ. FT>FS.

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Figure 3

Bond-like diagram of the simulator. The angular velocities of the three pulleys are input in the belt subsystem that responds with the corresponding torques. The crankshaft angular speed is input in the motor pulley that responds with the torque.

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Figure 4

Lumped parameters model of the transmission. The belt spans are modeled as spring-damper assemblies. The belt/pulley interaction is taken into account by means of the spring damper series Crpm−Krpm and Crpa−Krpa. The arcs of contact of the belt are represented as rotational inertias Jrpm, Jrpa. The free spans are modeled as massless strings with spring-damper parallel assemblies.

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Figure 5

Bond graph model of the belt subsystem. The belt is interfaced by means of power bonds to the alternator, the tensioner, and the motor pulley.

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Figure 6

Tensioner pulley kynematics. vervcr: tangential speeds due to the rotation about the axis; vat: translation speed of the pulley axis; vatc, vate: components of vat tangent to the pulley at points c and e.

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Figure 7

Lumped parameter models of the pulleys. (m) Motor pulley, stiffness Kpm and damping Cpm are used to model the rubber ring integrated in the pulley. (a) Alternator pulley, a one way clutch is used to model the decoupler, the electromechanical interaction in the alternator is modeled as a nonlinear torque to speed characteristic. (at) Automatic tensioner, it is assumed that its motion is a pure translation about the bisector of the arc of contact.

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Figure 8

Bond graph models of the pulleys connected to the belt. The causality and the power flow convention at the interfaces with the belt is the same as Fig. 3.

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Figure 9

Structure of the MATLAB-SIMULINK ® belt transmission model. The belt subsystem interacts with the pulleys in terms of power variables (belt tension and velocity). Each pulley includes the dynamic behavior of the accessory connected to it.

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Figure 10

Angular speed of the alternator pulley. Crankshaft speed: 750rpm; alternator load: minimum load. Experimental values (dotted), simulator results (solid).

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Figure 11

Angular speed of the alternator pulley. Crankshaft speed: 1080rpm; alternator load: minimum load. Experimental values (dotted line), simulator results with compression saturation (solid line); simulator results without compression saturation (dased line); simulator results with no tangential compliance of the arcs of contact (dashdot line).

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Figure 12

Angular speed of the alternator pulley. Crankshaft speed: 1700rpm; alternator load: minimum load. Experimental values (dotted), simulator results (solid).



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