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Research Papers

A Kriging Model for Dynamics of Mechanical Systems With Revolute Joint Clearances

[+] Author and Article Information
Zhenhua Zhang

Department of Mechanical Engineering,
Wichita State University,
Wichita, KS 67260
e-mail: zxzhang1@wichita.edu

Liang Xu

Department of Mechanical Engineering,
Wichita State University,
Wichita, KS 67260
e-mail: lxxu3@wichita.edu

Paulo Flores

Departamento de Engenharia Mecânica,
Universidade do Minho,
Campus de Azurém,
Guimarães 4800-058, Portugal
e-mail: pflores@dem.uminho.pt

Hamid M. Lankarani

Department of Mechanical Engineering,
Wichita State University,
Wichita, KS 67260
e-mail: hamid.lankarani@wichita.edu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received August 1, 2013; final manuscript received December 10, 2013; published online February 13, 2014. Assoc. Editor: Ahmet S. Yigit.

J. Comput. Nonlinear Dynam 9(3), 031013 (Feb 13, 2014) (13 pages) Paper No: CND-13-1195; doi: 10.1115/1.4026233 History: Received August 01, 2013; Revised December 10, 2013

Over the past two decades, extensive work has been conducted on the dynamic effect of joint clearances in multibody mechanical systems. In contrast, little work has been devoted to optimizing the performance of these systems. In this study, the analysis of revolute joint clearance is formulated in terms of a Hertzian-based contact force model. For illustration, the classical slider-crank mechanism with a revolute clearance joint at the piston pin is presented and a simulation model is developed using the analysis/design software MSC.ADAMS. The clearance is modeled as a pin-in-a-hole surface-to-surface dry contact, with an appropriate contact force model between the joint and bearing surfaces. Different simulations are performed to demonstrate the influence of the joint clearance size and the input crank speed on the dynamic behavior of the system with the joint clearance. In the modeling and simulation of the experimental setup and in the followed parametric study with a slightly revised system, both the Hertzian normal contact force model and a Coulomb-type friction force model were utilized. The kinetic coefficient of friction was chosen as constant throughout the study. An innovative design-of-experiment (DOE)-based method for optimizing the performance of a mechanical system with the revolute joint clearance for different ranges of design parameters is then proposed. Based on the simulation model results from sample points, which are selected by a Latin hypercube sampling (LHS) method, a polynomial function Kriging meta-model is established instead of the actual simulation model. The reason for the development and use of the meta-model is to bypass computationally intensive simulations of a computer model for different design parameter values in place of a more efficient and cost-effective mathematical model. Finally, numerical results obtained from two application examples with different design parameters, including the joint clearance size, crank speed, and contact stiffness, are presented for the further analysis of the dynamics of the revolute clearance joint in a mechanical system. This allows for predicting the influence of design parameter changes, in order to minimize contact forces, accelerations, and power requirements due to the existence of joint clearance.

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Figures

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Fig. 1

Revolute joint with clearance (clearance exaggerated for clarity)

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Fig. 2

Slider-crank mechanism with clearance joint

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Fig. 3

(a) Model of the slider-crank mechanism developed in MSC. ADAMS, and (b) exaggerated joint clearance at the piston pin

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Fig. 4

Dynamic response of the slider-crank from MCS.ADAMS modeling with a crank speed of 200 rpm: (a) slider position for a clearance of 0.25 mm, and (b) slider acceleration for a clearance of 0.25 mm

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Fig. 5

Dynamic response of the experimental slider-crank from Ref. [22] with a crank speed of 200 rpm: (a) slider position for a clearance of 0.25 mm, and (b) slider acceleration for a clearance of 0.25 mm

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Fig. 6

Slider acceleration for different clearance sizes: (a) 0.05 mm, (b) 0.1 mm, (c) 0.2 mm, and (d) 0.5 mm

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Fig. 7

Contact force for different clearance sizes: (a) 0.05 mm, (b) 0.1 mm, (c) 0.2 mm, and (d) 0.5 mm

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Fig. 8

Crank moment for different clearance sizes: (a) 0.05 mm, (b) 0.1 mm, (c) 0.2 mm, and (d) 0.5 mm

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Fig. 9

Slider acceleration for different crank speeds: (a) 200 rpm, (b) 1000 rpm, (c) 2000 rpm, and (d) 5000 rpm

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Fig. 10

Contact force for different crank speeds: (a) 200 rpm, (b) 1000 rpm, (c) 2000 rpm, and (d) 5000 rpm

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Fig. 11

Crank moment for different crank speeds: (a) 200 rpm, (b) 1000 rpm, (c) 2000 rpm, and (d) 5000 rpm

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Fig. 12

Flow chart for implementation of the DOE and Kriging-based optimization model

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Fig. 13

Design points selected by the LHS

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Fig. 14

(a) Exact model of the Branin function, and (b) surrogate model predicted by the Kriging model

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Fig. 15

(a) Surface plot for joint contact force, (b) surface plot for slider acceleration, and (c) surface plot for crank power consumption

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Fig. 16

Surface plots for contact forces: (a) low-speed input, (b) medium-speed input, and (c) high-speed input

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Fig. 17

Dynamic response in terms of contact force with constant stiffness coefficient

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