Research Papers: Design of Direct Contact Systems

Optimal Design of an Autotensioner in an Automotive Belt Drive System Via a Dynamic Adaptive PSO-GA

[+] Author and Article Information
Hao Zhu

State Key Laboratory of Mechanical
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

Yumei Hu, Yangjun Pi

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

W. D. Zhu

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

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received August 30, 2016; final manuscript received May 13, 2017; published online July 27, 2017. Assoc. Editor: Massimiliano Gobbi.

J. Mech. Des 139(9), 093302 (Jul 27, 2017) (12 pages) Paper No: MD-16-1603; doi: 10.1115/1.4036997 History: Received August 30, 2016; Revised May 13, 2017

Noise, vibration, and harshness performances are always concerns in design of an automotive belt drive system. The design problem of the automotive belt drive system requires the minimum transverse vibration of each belt span and minimum rotational vibrations of each pulley and the tensioner arm at the same time, with constraints on tension fluctuations in each belt span. The autotensioner is a key component to maintain belt tensions, avoid belt slip, and absorb vibrations in the automotive belt drive system. In this work, a dynamic adaptive particle swarm optimization and genetic algorithm (DAPSO-GA) is proposed to find an optimum design of an autotensioner to solve this design problem and achieve design targets. A dynamic adaptive inertia factor is introduced in the basic particle swarm optimization (PSO) algorithm to balance the convergence rate and global optimum search ability by adaptively adjusting the search velocity during the search process. genetic algorithm (GA)-related operators including a selection operator with time-varying selection probability, crossover operator, and n-point random mutation operator are incorporated in the PSO algorithm to further exploit optimal solutions generated by the PSO algorithm. These operators are used to diversify the swarm and prevent premature convergence. The objective function is established using a weighted-sum method, and the penalty function method is used to deal with constraints. Optimization on an example automotive belt drive system shows that the system vibration is greatly improved after optimization compared with that of its original design.

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Fig. 1

Schematic of a typical automotive belt drive system

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Fig. 2

Flowchart of the crossover operator of the GA-related algorithm

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Fig. 3

Procedure of the n-point random mutation operator

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Fig. 4

Flowchart of the DAPSO-GA

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Fig. 5

Inertia weights versus numbers of iterations: (a) Quadric and (b) Rosenbrock functions

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Fig. 6

Schematic of an example automotive belt drive system: CS—crankshaft pulley, AC—air conditioner pulley, ALT—alternator pulley, Idler—idler pulley, PSP—power steering pump pulley, WP—water pump pulley, and Ten—tensioner pulley

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Fig. 7

Convergence history of the DAPSO-GA for the design problem of the example automotive belt drive system

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Fig. 8

(a) Angular displacements of accessory pulleys and the tensioner arm before optimization, and (b) the enlarged graph of (a) from 0.2 to 0.26 s

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Fig. 9

Angular displacements of accessory pulleys and the tensioner arm after optimization

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Fig. 10

Transverse displacements of the belt span 7 at its end position tangent to the tensioner pulley before and after optimization

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Fig. 11

Transverse displacements of the belt span 8 at its end position tangent to the tensioner pulley before and after optimization

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Fig. 12

Dynamic tensions in belt spans: (a) before optimization and (b) after optimization




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