Elsevier

Journal of Manufacturing Systems

Volume 45, October 2017, Pages 201-211
Journal of Manufacturing Systems

Technical Paper
Assembly simulation of multi-branch cables

https://doi.org/10.1016/j.jmsy.2017.09.007Get rights and content

Highlights

  • A physically based deformation model of multi-branch cables is proposed.

  • An assembly simulation module of multi-branch cables is integrated into DELMIA.

  • Interactive simulation is realized through GPU acceleration technique.

Abstract

Cable assembly simulation is a key issue in the computer-aided design (CAD) of products with complex electrical components. In this study, an assembly simulation method is developed to simulate the assembly process of multi-branch cables. First, based on the Cosserat theory of elastic rods, a novel scheme is introduced to model the joints of multi-branch cables. The potential energy of joints is calculated by taking the topology and anatomical features into consideration. Various physical properties are considered. Various constraints, including connectors, collars, and handles are analyzed, based on which the initial conditions of assembly simulation are determined. The configuration of the cable is then calculated by minimizing its potential energy. To increase computational efficiency, GPU acceleration is introduced, which makes the simulation run at interactive rates even for a cable with resolution up to 1000 discrete points. Finally, the proposed algorithm is integrated into the commercial assembly simulation system, DELMIA. Several simulations were performed with our system. It was demonstrated that the proposed method is able to handle cables with complex topologies. In addition, the proposed method is about four times as efficient as a previous method, and it is able to generate realistic configurations of multi-branch cables at interactive rates. Thus, the proposed method is helpful in the assembly process planning of cables.

Introduction

Cables are widely used to transport electrical power and signals in many mechatronic products. For these products, assembly of cables is an important issue that should be taken into account from the initial design stage. For example, in modern airplanes, a large number of cables with different roles must be installed in a densely packed space. This makes the assembly of cables a very difficult task. In recent decades, assembly simulation in virtual environment has shown great advantages in assembly planning [1], verification [2] and training [3] comparing with traditional ways. In particular, in order to facilitate the assembly of cables, much research effort has been devoted to the physically based assembly simulation of cables [4], [5], [6]. Since no real prototypes need to be built and the potential problems can be predicted at early stages, it is able to increase the efficiency and decrease the cost of manufacture.

To obtain a visually satisfying object behavior with low computational cost and simulate the deformation of cables in interactive rates, mass spring model [7], inverse kinematics [8] and elastic rod model [9] have been introduced. Robinson et al. [10] conducted the assembly simulation of cables in a virtual reality environment and the results showed that the route design and assembly planning of cables can effectively benefit from the simulation work. Roussel et al. [11] explored the automatic manipulation planning of cables, by which the assembly paths of cables can be automatically determined. Mikchevitch et al. [12] discussed the input data (such as CAD models, material properties of cables and input data defined by operators) required for realistic simulations of cables. Despite the remarkable progress that has been made, existing studies were mostly limited to unbranched cables, and the assembly simulation of multi-branch cables has not been well addressed. Most of the commercial computer-aided design (CAD) systems for assembly simulation are incapable of depicting the physical properties of multi-branch cables. As one of the popular systems for assembly simulation, DELMIA, could only simulate the configuration of multi-branch cables based on geometric curves without considering any physical properties.

In this study, we sought to simulate the assembly of multi-branch cables using a physically based model which can ensure the fidelity of simulation. Specifically, a novel scheme is introduced to model the joints of multi-branch cables, considering their topology and anatomical features. Thus, the proposed model can provide realistic simulations of the deformation of multi-branch cables. To support the simulation of assembly processes, several constraints are analyzed to generate initial conditions for solving the cable’s configuration. Because the cable typically moves at a slow speed during the assembly process, the dynamic behavior of the cable is negligible and a quasi-static simulation is sufficient. The cable’s static configuration is finally obtained by minimizing its potential energy. In this study, we also sought to increase the computational efficiency to realize an interactive simulation. Specifically, a GPU acceleration technique is applied to obtain the real-time solution for complex assembly cases.

The remainder of this article is organized as follows. Section 2 briefly surveys prior research on approaches for modeling flexible objects that have common features with multi-branch cables: that is, deformable linear objects and branched structures. In Section 3, we provide some geometry descriptions, based on which the configuration and strains of a cable can be described effectively. In Section 4, we develop a model for simulating the deformation of multi-branch cables. Specifically, we briefly introduce the concepts of the Cosserat theory of elastic rods, then extend the model to enable the modeling of joints. The effects of various constraints are also discussed to support the assembly simulation. In Section 5, the potential energy is calculated and an energy minimizing algorithm is applied to obtain the static configuration of a cable. GPU acceleration is used to assist in the calculation, increasing the efficiency of computation tremendously. Finally, the effectiveness and efficiency of the proposed method are demonstrated in several examples in Section 6.

Section snippets

Related work

As the foundation of assembly simulation, the physically based deformation model of multi-branch cables is an important issue. Since the multi-branch cable is a type of branched structure and each branch can be regarded as one deformable linear object. Thus, it is helpful to briefly review related research work on the physically based models of deformable linear objects and branched structures.

Geometry description

Geometry description is the first step in modeling the deformation of a cable, which includes descriptions of the configuration and strains. The geometry description should be accurate in terms of describing the shape, stretching, bending, and torsion of a cable, and convenient for subsequent modeling and calculations.

Deformation model for a multi-branch cable

The modeling procedure is shown in Fig. 2. First, the deformation model of multi-branch cables is established based on an extension of the elastic rod model of Cosserat theory. Then, various constraints are analyzed to obtain the initial conditions for assembly simulation. At last, the assembly simulation can be conducted based on the constraint information and deformation model.

Calculation of the equilibrium of a multi-branched cable

In most cases, the cable is static or moves at a slow speed during an assembly process, so the quasi-static assumption is reasonable. It is assumed that the cable is in static equilibrium at every moment. Then, solving the static configuration of a cable becomes the key part of assembly simulation of the cable.

Results

Several simulations were performed to demonstrate the performance of the proposed model. By integrating the proposed model into the commercial assembly simulation system, DELMIA, the efficiency and reliability of the model was demonstrated. The assembly simulations of multi-branch cables were conducted based on the Assembly Process Simulation module of DELMIA. These simulations were run on an Intel i5-2300 and GTX 960. The computational efficiency was increased by using GPU acceleration of the

Conclusions and future work

We described a physically based deformation model of multi-branch cables. Our deformation model overcomes the limitation of existing CAD systems where the deformation of multi-branch cables in an assembly simulation cannot be handled. In the proposed model, various deformations, such as stretching, bending, and torsion, were taken into account based on the Cosserat theory of elastic rods. A novel scheme for modeling the joints was proposed, considering the topologies and anatomical features.

Acknowledgments

The authors are grateful for support by the National Natural Science Foundation of China (Grant No. 51605030) and the National Defense Fundamental Research Foundation of China (Grant No. JCKY2016204B201).

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