Journal of Manufacturing Systems 27 (2008) 36–44 Contents lists available at ScienceDirect Journal of Manufacturing Systems journal homepage: www.elsevier.com/locate/jmansys Technical paper Simulation and integration of geometric and rigid body kinematics errors for assembly variation analysis Wenzhen Huang a,∗ , Zhenyu Kong b a Department of Mechanical Engineering, University of Massachusetts Dartmouth, North Dartmouth, MA, USA b School of Industrial Engineering and Management, Oklahoma State University, Stillwater, OK, USA article info Article history: Received 26 February 2007 Received in revised form 26 May 2008 Accepted 27 June 2008 abstract Rigid and compliant models have been developed in parallel in the literature for variation analysis of different assembly processes. For a complex assembly system, it is desirable to balance accuracy and simplicity by introducing a rigid-compliant hybrid model. This paper develops a new method aimed at providing an interface between rigid and compliant assembly models. Part geometric errors (PGE) and rigid body kinematics stackup error (RE) are simulated and integrated in rigid assembly processes. A covariance matrix of PGE and RE is then constructed, providing input to subsequent compliant assembly models. Algorithms are developed (1) to predict RE by using the stream of variation (SOVA) model; (2) to simulate PGE based on statistical modal analysis (SMA) and specified tolerances; and (3) to integrate RE and PGE in rigid assembly processes for covariance matrix construction. This is an initial step toward the development of a rigid-compliant hybrid assembly model for variation analysis in multistation manufacturing systems (MMS). © 2008 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved. 1. Introduction Dimensional variation significantly affects the quality and func- tion of product and production system performance. For instance, poor dimensional quality may cause severe problems of wind noise, water leakage, and door closing effort in automotive man- ufacturing. It is also a main factor of production delay in both au- tomotive and aerospace industries and has recently become a key issue in stack-assembly quality control in fuel cell manufacturing. In the last decade, rigid and compliant assembly variation models have been developed in parallel. Rigid models, assumed part rigidity for simplicity, are valid for open assembly processes that produce open structures (static determined systems). Open assembly structures are open chains of a series of assembled parts, such as automotive underbody, apertures, and so on, and most mechanical assemblies [11]. To create a sturdy structural component, a closure is usually assembled, creating a closed loop of parts and forming a static undetermined structure. Examples include automotive cabs, engine compartments, aircraft fuselages, etc. The imperfection in parts manufacturing and upstream assembly results in gaps that must be closed in an assembly process with force. This gap-closing operation is defined as a ∗ Corresponding author. Tel.: +1 508 910 6568. E-mail addresses: whuang@umassd.edu (W. Huang), james.kong@okstate.edu (Z. Kong). closing process. Deformation and lock-in stress are produced in the closing process. The compliant model was developed to analyze the deformation in the gap-closing processes. On the rigid-model side, the relationships of product/process factors or key control characteristics (KCCs) and dimensional quality indices or key product characteristics (KPCs) are modeled by kinematics principles [5,6,8]. A state-space model [14,7] was developed for multistation manufacturing systems that facilitate variation analysis and diagnosis with state-transition and observation equations. Comprehensive reviews were given in Ceglarek et al. [4] and Shi [18]. Stream of variation models (SOVA) have recently been extended to 3D rigid assembly [12,13]. The rigid model analyzes only kinematics error stackup effects from fixtures and part mating features, overlooking the part geometric errors for simplicity. The rigid assembly analysis is largely a model-driven technique, relying on tolerance input. On the compliant-model side, all of the components in an assembly were modeled as deformable parts by FEM-based mechanistic methods [1–3,11,15–17]. The deformation of an assembly is analyzed by a linear FEA model, taking a gap between parts as input. Current methods either assume a user-defined gap for ad hoc deterministic analyses (e.g., CATIA) or directly assume a known gap covariance matrix for statistical analysis [17, 3,1]. Statistical modal analysis (SMA), a data-driven alternative [9, 10], was also developed to characterize part error (PGE) patterns for diagnosis. However, the data-driven covariance approach and SMA are neither available from the measurement data 0278-6125/$ – see front matter © 2008 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.jmsy.2008.06.004