Technical PaperA digital twin-based approach for the management of geometrical deviations during assembly processes
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 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.
Section snippets
Proposition of a virtual product for the digital twin
The proposed approach consists in updating of the original product's DMU to a hybrid virtual representation, comprising as-built, interface and as-designed components. This section explains how the geometry of such components is modeled and how they interact within the updated virtual product.
Updating as-built components
In the previous section, we defined a direct modeling approach which enables us to model the position and orientation deviations of the as-built components of our digital twin. Updating the virtual model of as-built components is done by updating the surface parameters of its B-Rep model. In this section, we define a method which enables us to relate these parameters to the geometry of the physical product under assembly.
While reconstructing the B-Rep model of a component from one of its
Updating interface components
The previous section detailed the possibility to update as-built components in order to reflect the geometrical deviations of the physical product during its assembly process. Based on the geometry of the as-built components, following assembly operations can be simulated and then optimized in order to ensure that the functional requirements of the final product are eventually met. To do so, the geometry of interface components is also updated.
Once as-built components have been updated, the
Use case and results
The digital twin approach and the hybrid product representation discussed in the previous sections is illustrated through a simple case study.
Conclusion
In this article, we have proposed a hybrid virtual representation to support digital twin implementation. This representation ensures the respect of geometrical functional requirements during assembly processes. The suggested model is based, on the one hand, on a geometrical representation of the components as a set of configurable surfaces and, on the other hand, on a geometrical skeleton. The proposed hybrid representation reflects the product during its assembly process thanks to the update
Conflict of interest
The authors declare that there is no conflict of interest.
Acknowledgments
The presented work was carried out thanks to a partnership between Airbus and the Automated Production Research Laboratory (LURPA) from ENS Paris-Saclay.
The authors would like to thank Arthur Alglave for his work in the development of the D3MO software.
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