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 Mec ^ anica, Universidade do Minho, Campus de Azur  em, 4800-058 Guimar ~ aes, 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 A Kriging Model for Dynamics of Mechanical Systems With Revolute Joint Clearances 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 rev- olute 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 clear- ance. In the modeling and simulation of the experimental setup and in the followed para- metric 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 hyper- cube 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 mathe- matical 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. [DOI: 10.1115/1.4026233] Keywords: Revolute joint clearance, contact forces, multibody dynamics, Kriging meta- model, genetic algorithms 1 Introduction In the past decade, many researchers have examined the opti- mal dynamical solution of different mechanical systems and mechanisms [1–3]. Additionally, different optimization methods have been implemented to obtain optimal solutions. In the study by Laribi et al. [2], a solution for the path generation problem in mechanisms was presented using the generic algorithm-fuzzy logic method. Selcuk et al. [3] proposed a neural-genetic method to investigate the effects of joints with clearance on its path gener- ation and kinematic transmission quality. In order to reduce the computational complexity, the neural network has been used as a surrogate model in this study. The Genetic algorithm, as a global optimization method, has been widely used in many research ﬁelds, but its associated computational cost dramatically increases, especially for expensive model functions. As a result of manufacturing tolerances, material deformations, and wear after a certain working period, clearances between me- chanical components of mechanical systems occur in most kine- matic joints. Excessive clearance values result in large contact forces at the joints, especially during high-speed mechanical oper- ations. The presence of clearances leads to a decrease in the sys- tem reliability and durability of the system’s components and machines [4,5]. Over the past decades, advances, mainly due to the development of intercross applications between computer- aided analysis of mechanical systems and optimization methodol- ogies, have been achieved. These results could be utilized for the application of different mathematical programming techniques to the parametrical and topological syntheses and analyses of me- chanical systems [6]. The optimization of mechanical system modeling with clearances can be used to bypass the computation- ally intensive simulation of the computer dynamic model. It also helps in the analysis, design, and control of the dynamic perform- ance of a complex mechanical system and in quantifying the inﬂu- ence of clearance parameters. During the past two decades, many studies on the inﬂuence of the joint clearance in planar and spatial multibody mechanical systems have been conducted. Dubowsky and Freudenstein devel- oped the impact ring model, which is a simple model to demon- strate the effects of joint clearance in planar mechanisms [7]. Springs and dashpots were arranged in their model to predict the dynamics response of the mechanical system. Dubowsky and Moening quantiﬁed the interaction between the clearance joints and the mechanical system elasticity using a Scotch–Yoke simula- tion model [8]. Large impact forces developed at the clearance joints caused a failure in the Scotch–Yoke model. Furubashi and Morita presented a four-bar mechanism with multiple clearance revolute joints [9]. They analyzed and compared the results for 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. Journal of Computational and Nonlinear Dynamics JULY 2014, Vol. 9 / 031013-1 Copyright V C 2014 by ASME Downloaded From: http://computationalnonlinear.asmedigitalcollection.asme.org/ on 02/21/2014 Terms of Use: http://asme.org/terms