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

Solving basic problems of compliant tolerance analysis by static analogy

Predicting the geometric variation of sheet metal assemblies is a complex task, because deformation during joining operations influences the propagation of initial part deviations. To consider this effect, the paper proposes a method that formulates tolerance analysis as an equivalent problem of static analysis. Previously proposed for rigid parts, the static analogy is extended to compliant parts and applied to two-dimensional problems modeled with straight beams under the assumptions of small displacements and normal distributions of errors. For such simple cases, the method solves the problem by linearization, avoiding the use of Monte Carlo simulation and the related computational burden. Compared to existing linearization methods, the static analogy is less efficient in the integration with a finite element solver. However, it features an especially simple procedure that does not require the calculation of deflections, thus allowing a streamlined solution and even manual calculations. The comparison with alternative methods provides a first verification of the feasibility of the method, in view of further developments with the aim of dealing with cases of realistic complexity

3D convolutional neural networks to estimate assembly process parameters using 3D point-clouds

Closed loop dimensional quality control for an assembly system entails controlling process parameters based on dimensional quality measurement data to ensure that products conform to quality requirements. Effective closed-loop quality control reduces machine downtime and increases productivity, as well as enables efficient predictive maintenance and continuous improvement of product quality. Accurate estimation of dimensional variations on the final part is a key requirement, in order to detect and correct process faults, for effective closed-loop quality control. Nowadays, this is often done by experienced process engineers, using a trial-and-error approach, which is time-consuming and can be unreliable. In this paper, a novel model to estimate process parameters error variations using high-density cloud-of-point measurement data captured by 3D optical scanners is proposed. The proposed model termed as PointDevNet uses 3D convolutional neural networks (CNN) that leverage the deviations of key nodes and their local neighbourhood to estimate the process parameter variations. These process parameters variation estimates are leveraged for root cause isolation as a necessary but currently missing step needed for the development of closed-loop quality control framework. The proposed model is compared with an existing state-of-the-art linear model under different scenarios such as a single and multiple root causes, and the presence of measurement noise. The state-of-the-art model is evaluated under different point selections and results are compared to the proposed model with consideration to an industrial case study involving a sheet metal part, i.e. window reinforcement panel

Parametric variational analysis of compliant sheet metal assemblies with shell elements

One of most demanding tasks in the manufacturing field is controlling the variability of parts as it may affect strongly the deliverability of key characteristics defined at the final (product) assembly level. Current CAT systems offer a good solution to the tolerance analysis/synthesis task, but to handle flexible objects with shape errors more effort is needed to include methods able to capture the elastic behaviour of parts that adds more variability on the final assembly. Usually, sheet metal assemblies require dedicated fixtures and clamps layout to control the gap between parts in the specific location where a join must be placed. Due to the variability of parts the position of clamps can also be varied. The paper describes a FEM-based method able take into account part flexibility and shape error to parametrically analyse sheet metal assemblies by acting on some key parameters to look for the optimal clamp layout that guarantee the gap between parts to be under control after joining parts together. This method offers, with respect to commercial solutions, the ability to model fixtures, clamps and different joint types with no matter on the mesh nodes’ position. Locations of such elements are based on the shape functions defined at element (shell) mesh level and modelled as local constraints. So the user can generate a mesh without a previous knowledge of the exact positions of clamps, for example. This allows to conduit a faster parametric analysis without remeshing the surfaces and with no need to physically model the clamps. An aeronautic case study is described with a four-part assembly riveted on a quite complex fixture by using several clamps

Fixture capability optimisation for early-stage design of assembly system with compliant parts using nested polynomial chaos expansion

AbstractThis paper introduces the novel concept of fixture capability measure to determine fixture layout for the best assembly process yield by optimizing position of locators and reference clamps to compensate stochastic product variations and part deformation. This allows reducing the risk of product failures caused by product and process variation. The method is based on three main steps: (i) physics-based modelling of parts and fixtures, (ii) stochastic polynomial chaos expansion to calculate fixture capability, and (iii) fixture capability optimisation using surrogate modelling. The methodology is demonstrated and validated using the results of an aerospace wing sub-assembly joined by riveting technique

Integrated Tolerance and Fixture Layout Design for Compliant Sheet Metal Assemblies

Part tolerances and fixture layouts are two pivotal factors in the geometrical quality of\ua0a compliant assembly. The independent design and optimization of these factors for compliant\ua0assemblies have been thoroughly studied. However, this paper presents the dependency of these\ua0factors and, consequently, the demand for an integrated design of them. A method is developed\ua0in order to address this issue by utilizing compliant variation simulation tools and evolutionary\ua0optimization algorithms. Thereby, integrated and non-integrated optimization of the tolerances and\ua0fixture layouts are conducted for an industrial sample case. The objective of this optimization is\ua0defined as minimizing the production cost while fulfilling the geometrical requirements. The results\ua0evidence the superiority of the integrated approach to the non-integrated in terms of the production\ua0cost and geometrical quality of the assemblies

Shape error modelling and analysis by conditional simulations of Gaussian random fields for compliant non-ideal sheet metal parts

Accurate modelling of geometric and dimensional errors of sheet metal parts is crucial in designing correct GD&T and preventing unnecessary design changes during the development and launch of a new assembly process. A novel conditional simulation based methodology to probabilistically model and generate non-ideal sheet metal part geometric variations is developed. The methodology generates part geometric variations, which accurately emulate part fabrication process in terms of covariance of generated deviations. The methodology uses as inputs one or more of the following: measurement data of current parts, historical measurements of similar parts or FEM-based simulations. The proposed methodology emulates real processes and products accurately by generating non-ideal part representatives based on the aforementioned input data. Results provide an easy engineering interpretation to the designer. The methodology is demonstrated using automotive door hinge reinforcement

Variation Analysis of Three Dimensional non-rigid Assemblies

Variation analysis methods are, currently, more widely used during new product development to greatly reduce downstream rework and/or design changes. This is significantly important when considering large, built up sheet or thin plate flexible" assemblies as those currently used in automotive or aerospace industries. Whereas methods to take flexibility into account can be found in literature, there are few addressing detailed process for three-dimensional assembly of industrial complexity. This paper presents a streamlined procedure for variation analysis of a complex assembly that integrates Datum Flow Chain analysis, a commercial three-dimensional variation analysis and FEA. The procedure is applied to a realistic industry case, a commercial airplane's wing-box assembly to determine the effect of part variation and flexibility on the assembly's variation. The case study shows that a structural enclosure such as the wing-box assembly is robust against pull-up forces applied during assembly operations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87278/4/Saitou64.pd