This article proposes a variation simulation and diagnosis model for ship block assembly processes considering the effects of welding distortion. The welding process and the deformation pattern affecting the final shape of a block assembly are diagnosed. Prior studies on welding distortion mainly focused on mitigation methodologies. In this research, welding distortion is regarded as the main cause of geometric variation in parts. In addition, how geometric variations are accumulated throughout multiple assembly processes is mathematically modeled. The variation simulation model is based on a state space equation, where variations of previous stages are propagated to the current stage. The diagnosis model predicts the quantitative effect of each variation source on the final assembly's geometrical variation, based on a normal equation and designated component analysis. The proposed model is simulated with FEM (Dassault Systèmes Americas Corp., Waltham, MA) and MATLAB (Mathworks (https://www.mathworks.com/), Massachusetts, United States) replicating a realistic block assembly process for validation. The model can effectively simulate the propagation of welding distortion and quantitatively diagnose variation patterns and welding processes.
Analysis, management, and variation diagnostics are some of the important aspects of the production process. These have been mainly studied in mass production processes such as in the automobile industry. Mantripragada and Whitney (1999) and Whitney (2004) proposed a tolerance analysis method for the multistage rigid body assembly using a state space equation. Huang et al. (2006a, 2007) proposed a ship block tolerance model for the single and multiple stage variation propagation of a rigid body model. Liu and Hu (1995,1997) proposed a compliant assembly model using FEM, called the method of influence coefficients (MIC). Govik et al. (2012) proved MIC using an FEM simulation. Variation propagation in a multiple stage process while considering a compliant assembly has been proposed by Camelio et al. (2003, 2002a). Variation propagation models considering the location of data such as in key control characteristics, key product characteristics, and a local coordinate system of parts were proposed by Qu et al. (2016).