Shape variation modelling, analysis and statistical control for assembly system with compliant parts

Modern competitive market demands frequent change in product variety, increased production volume and shorten product/process change over time. These market requirements point towards development of key enabling technologies (KETs) to shorten product and process development cycle, improved production quality and reduced time-to-launch. One of the critical prerequisite to develop the aforementioned KETs is efficient and accurate modelling of product and process dimensional errors. It is especially critical for assembly processes with compliant parts as used in automotive body, appliance or wing and fuselage assemblies. Currently, the assembly process is designed under the assumption of ideal (nominal) products and then check by using variation simulation analysis (VSA). However, the VSA simulations are oversimplified as they are unable to accurately model or predict the effects of geometric and dimensional variations of compliant parts, as well as variations of key characteristics related to fixturing and joining process. This results in product failures and/or reduced quality due to un-modelled interactions in assembly process. Therefore, modelling and prediction of the geometric shape errors of complex sheet metal parts are of tremendous importance for many industrial applications. Further, as production yield and product quality are determined for production volume of real parts, thus not only shape errors but also shape variation model is required for robust assembly system development. Currently, parts shape variation can be measured during production by using recently introduced non-contact gauges which are fast, in-line and can capture entire part surface information. However, current applications of non-contact scanners are limited to single part inspection or reverse engineering applications and cannot be used for monitoring and statistical process control of shape variation. Further, the product shape variation can be reduced through appropriate assembly fixture design. Current approaches for assembly fixture design seldom consider shape variation of production parts during assembly process which result in poor quality and yield. To address the aforementioned challenges, this thesis proposes the following two enablers focused on modelling of shape errors and shape variation of compliant parts applicable during assembly process design phase as well as production phase: (i) modelling and characterisation of shape errors of individual compliant part with capabilities to quantify fabrication errors at part level; and (ii) modelling and characterisation of shape variation of a batch of compliant parts with capabilities to quantify the shape variation at production level. The first enabler focuses on shape errors modelling and characterisation which includes developing a functional data analysis model for identification and characterisation of real part shape errors that can link design (CAD model) with manufacturing (shape errors). A new functional data analysis model, named Geometric Modal Analysis (GMA), is proposed to extract dominant shape error xixmodes from the fabricated part measurement data. This model is used to decompose shape errors of 3D sheet metal part into orthogonal shape error modes which can be used for product and process interactions. Further, the enabler can be used for statistical process control to monitor shape quality; fabrication process mapping and diagnosis; geometric dimensioning and tolerancing simulation with free form shape errors; or compact storage of shape information. The second enabler aims to model and characterise shape variation of a batch of compliant parts by extending the GMA approach. The developed functional model called Statistical Geometric Modal Analysis (SGMA) represents the statistical shape variation through modal characteristics and quantifies shape variation of a batch of sheet metal parts a single or a few composite parts. The composite part(s) represent major error modes induced by the production process. The SGMA model, further, can be utilised for assembly fixture optimisation, tolerance analysis and synthesis. Further, these two enablers can be applied for monitoring and reduction of shape variation from assembly process by developing: (a) efficient statistical process control technique (based on enabler ‘i’) to monitor part shape variation utilising the surface information captured using non-contact scanners; and (b) efficient assembly fixture layout optimisation technique (based on enabler ‘ii’) to obtain improved quality products considering shape variation of production parts. Therefore, this thesis proposes the following two applications: The first application focuses on statistical process control of part shape variation using surface data captured by in-process or off-line scanners as Cloud-of-Points (CoPs). The methodology involves obtaining reduced set of statistically uncorrelated and independent variables from CoPs (utilising GMA method) which are then used to develop integrated single bivariate T2-Q monitoring chart. The joint probability density estimation using non-parametric Kernel Density Estimator (KDE) has enhanced sensitivity to detect part shape variation. The control chart helps speedy detection of part shape errors including global or local shape defects. The second application determines optimal fixture layout considering production batch of compliant sheet metal parts. Fixtures control the position and orientation of parts in an assembly process and thus significantly contribute to process capability that determines production yield and product quality. A new approach is proposed to improve the probability of joining feasibility index by determining an N-2-1 fixture layout optimised for a production batch. The SGMA method has been utilised for fixture layout optimisation considering a batch of compliant sheet metal parts. All the above developed methodologies have been validated and verified with industrial case studies of automotive sheet metal door assembly process. Further, they are compared with state-of-the-art methodologies to highlight the boarder impact of the research work to meet the increasing market requirements such as improved in-line quality and increased productivity