A digital twin-based approach for the management of geometrical deviations during assembly processes

Highlights

• A hybrid representation for the digital twin for assembly processes is proposed.

• This representation includes as-built, as-designed and interface components.

• A geometrical skeleton materializes the structure-functional model of the product and allows to take geometrical deviations into account.

• A method to update this virtual representation from 3D acquisition data using machine-learning is proposed.

• The proposed digital twin is able to simulate and optimize $n+1$ assembly operations by updating the geometry of interface components.

Abstract

The recent transformation in the aeronautical industry gives new prospects in the field of product geometry assurance. These include, in particular the creation of sophisticated virtual models, or digital twins, which can reflect the as-built geometry of physical products and optimize the assembly operations consequently. One of the current obstacles to the implementation of such digital twins is linked to the difficult transition from a conceptual model to a usable virtual representation. In this article, we present the hybrid representation of a product which is capable of integrating the different states of the components at each step of the assembly process. We propose a method to update the virtual representation of already assembled components, in order to include the position and orientation deviations of their surfaces. The B-Rep model of each component is updated from data acquired during the assembly of the product. The various steps of this update, and its associated tools are discussed in the article. Based on the knowledge of the as-built component geometry, the geometry of the yet-to-be-assembled components is adapted so that the final product complies with the functional requirements. To this end, we also discuss a formalism to model the product's functional information and to translate it at a geometrical level thanks to an assembly skeleton.

Introduction

The increasing integration of data processing systems leads to new prospects in the organization of production systems [1]. These prospects include the possibility to optimize manufacturing and assembly operations in real time, using digital twins of the manufactured products. A promising application is the geometrical quality of assembled products [2]. The virtual model of the product is supplemented with inspection data in order to detect and correct non-compliances resulting from geometrical deviations. Geometrical deviations found at component level tend to propagate along the assembly process. Those deviations cause assembly issues and non-compliance with functional requirements, which further leads to an increase in production costs.

Nevertheless, a recent literature review [3], [4] shows that the current developments regarding digital twins in the field of production are mainly conceptual. Thus, key enabling technologies and tools for the implementation of digital twins have become a major research topic [5]. One of the obstacles to this implementation is the transition to a usable virtual representation [6]. One of the major challenges lies in the capacity of this virtual representation to reflect the actual product while being a valid model for simulation and optimization of manufacturing and assembly operations.

In order to answer this problem, some authors [6] suggest to use skin model shapes [7] as virtual representation of digital twins. The skin model shapes, mainly used in the field of tolerancing, are discrete representations of a physical object which can simulate or integrate position, orientation or shape deviations of its surfaces [8]. Simulating the assembly of components thanks to skin model shapes is also possible [9]. The possibility to optimize manufacturing and assembly operations from the understanding of the components deviations (through observation or simulation) is currently limited to the field of tolerancing [10].

In this article we propose a hybrid representation of a product, which can be integrated to the digital twin approach in order to manage geometrical deviations during the assembly process (Fig. 1). Geometrical data about the physical product is transferred to the virtual product using 3D sensors during the observation phase. These data are used to update the as-built components so as to mirror the actual geometry of the product. Based on the knowledge of the as-built components’ geometry, the assembly of remaining components can be simulated and optimized. The resulting information is then transferred back during the prediction stage so that the changes performed on the virtual product can be applied to the physical product.

While current research works are exploring the assembly of components with geometrical deviations, virtual products capable of integrating both as-built components and as-designed components have seldom been studied in the literature. One major difficulty is interfacing as-built components and as-designed components in the virtual product while building an assembly model capable of taking geometrical deviations into account. Once such an assembly model is built, a second difficulty is the optimization of upcoming manufacturing and assembly operations so that the functional requirements of the final product are eventually met. A third and more practical difficulty is finally preserving the continuity of the information linked to the virtual product's geometry during the update phase so that manufacturing and assembly operations can be carried out.

Let us consider the initial virtual product as a Digital Mock-up (DMU). DMUs are extensively used nowadays to support manufacturing and assembly operations. A DMU consists of the as-designed representation of a product, along with some data associated with manufacturing and assembly operations. These data often include geometrical tolerances and functional requirements (Fig. 2b) but also text instructions and machine trajectories. A DMU can be regarded as the static representation of a product. At the step $n$ of the assembly process, geometrical deviations are observed on the physical product (Fig. 2a). One originality of the hybrid representation we propose is that the virtual representation of the product is updated according to the measured deviations of the physical product (Fig. 2c). This includes, on the one hand, as-built components reflecting the actual geometry of the physical product, and on the other hand, to-be-built components. These to-be-built components include as-designed and interface components. The notion of interface components is derived from the field of aeronautics [11] and designates custom-made components whose designs are updated in order to mitigate the effect of geometrical deviations on the functional requirements of the product (Fig. 2d, e). The choice of the components to be used as interface components is based on feasibility and cost criteria [12]. Other to-be-built components remain in their as-designed states and are assumed to be manufactured within their specified tolerance intervals (which may even be enlarged, as the as-built geometrical deviations of the components cannot be considered as random variables anymore). The initial virtual representation of the product, i.e. Digital Mock-up (Fig. 2b), therefore becomes a hybrid representation (Fig. 2c) composed of as-built, interface and as-designed components [13].

In Section 2 of this article, we describe the proposed hybrid representation for the use of digital twins in assembly processes. This description includes both a component representation and a structuro-functional model of the product. We demonstrate that the B-Rep representation, which is widely used to model as-designed component geometry, can be used to model the position, orientation and size deviation of as-built component surfaces as well as interface component geometry. In Section 3, we will explain how the observation stage (Fig. 1) is performed. During this stage, the virtual model is updated according to the measured data, in order to reflect the geometry of the physical product during assembly. In Section 4, we show that the as-built component can be used to simulate and optimize manufacturing and assembly operations through the update of the interface component. The prediction stage (Fig. 1) is performed as well.