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Research Papers

Periodic Response of a Timing Belt Drive System With an Oval Cogged Pulley and Optimal Design of the Pitch Profile for Vibration Reduction

[+] Author and Article Information
Hao Zhu

State Key Laboratory of
Mechanical Transmissions,
School of Automobile Engineering,
Chongqing University,
Chongqing 400044, China;
Department of Mechanical Engineering,
University of Maryland, Baltimore County,
1000 Hilltop Circle,
Baltimore, MD 21250
e-mail: haozu@cqu.edu.cn

Weidong Zhu

Department of Mechanical Engineering,
University of Maryland, Baltimore County,
1000 Hilltop Circle,
Baltimore, MD 21250
e-mail: wzhu@umbc.edu

Yumei Hu

State Key Laboratory of
Mechanical Transmissions,
School of Automobile Engineering,
Chongqing University,
Chongqing 400044, China

XuefengWang

Department of Mechanical Engineering,
University of Maryland, Baltimore County,
1000 Hilltop Circle,
Baltimore, MD 21250

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 17, 2017; final manuscript received July 23, 2017; published online November 17, 2017. Assoc. Editor: Sotirios Natsiavas.

J. Comput. Nonlinear Dynam 13(1), 011014 (Nov 17, 2017) (13 pages) Paper No: CND-17-1122; doi: 10.1115/1.4037764 History: Received March 17, 2017; Revised July 23, 2017

A complete dynamic model of a timing belt drive system with an oval cogged pulley and an auto-tensioner is established in this work. Periodic torsional vibrations of all accessory pulleys and the tensioner arm are calculated using a modified incremental harmonic balance (MIHB) method based on the complete dynamic model. Calculated results from the MIHB method are verified by comparing them with those obtained from Runge–Kutta method. Influences of tensioner parameters and oval pulley parameters on torsional vibrations of camshafts and other accessory pulleys are investigated. A sequence quadratic programing (SQP) method with oval pulley parameters selected as design variables is applied to minimize the overall torsional vibration amplitude of all the accessory pulleys and the tensioner arm in the timing belt drive system at different operational speeds. It is demonstrated that torsional vibrations of the timing belt drive system are significantly reduced by matching belt stretch with speed variations of the crankshaft and fluctuating torque loads on camshafts. The timing belt drive system with optimal oval parameters given in this work has better performance in the overall torsional vibration of the system than that with oval parameters provided by the kinematic model and the simplified dynamic model in previous research.

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References

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Figures

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Fig. 1

Schematic of a typical timing belt drive system

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Fig. 2

Illustration of the position angle and installation angle of the oval C/S at time t

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Fig. 3

Periodic responses of (a) the O/P, (b) the CAM1, and (c) the CAM2 from the MIHB method and Runge–Kutta method with θc0=0 and ε=0 when the rotational speed of the C/S is 800 rpm

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Fig. 4

Torsional vibrations of (a) the CAM1 and (b) the TEN in the timing belt drive systems with the fixed tensioner and the auto-tensioner with different torsional stiffnesses kt and ε=0 when the mean rotational speed of the C/S is 2000 rpm

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Fig. 5

Torsional vibrations of (a) the CAM1 and (b) the TEN in the timing belt drive systems with the fixed tensioner and the auto-tensioner with different arm lengths lt, kt=9.6 Nm/rad, and ε=0 when the mean rotational speed of the C/S is 2000 rpm

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Fig. 6

Torsional vibrations of (a) the camshafts and (b) the O/P from the complete dynamic model (dashed and dash-dotted lines) and the simplified dynamic model [35] (solid lines) with ε=0 when the mean rotational speed of the C/S is 2000 rpm

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Fig. 7

Torsional vibration amplitudes of the CAM2 from (a) the complete dynamic model and (b) the simplified dynamic model [35] with different values of the eccentricity ratio of the oval C/S ε, θc0=−45deg, and cb=1 at different mean rotational speeds of the C/S

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Fig. 8

Torsional vibration amplitudes of the CAM2 with different values of the eccentricity ratio of the oval C/S ε and cb=1 when the mean rotational speed of the C/S is 2000 rpm

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Fig. 9

Torsional vibration amplitudes of the CAM2 with different values of the initial installation angle of the oval C/S θc0, ε=0.02, and cb=1 at different mean rotational speeds of the C/S

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Fig. 10

Torsional vibrations of all the accessory pulleys and the tensioner arm before optimization when the mean rotational speed of the C/S is 2000 rpm

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Fig. 11

Torsional vibrations of all the accessory pulleys and the tensioner arm after optimization when the mean rotational speed of the C/S is 2000 rpm

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Fig. 12

Comparison of the sum of torques exerted on pulleys due to belt stretch that results from the rotation of the noncircular C/S and the STCAM, when the rotational speed of the oval C/S is 2000 rpm

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