Multi-bond graphs

Simulation of Multi-body Systems Using Multi-bond Graphs... 

Keywords Break variables Differential-algebraic systems Lagrange multipliers Multi-body system Multi-bond graphs Zero-order causal paths... 

Multi-bond graphs are a vectorial extension of one-dimensional bond graphs. The main objective of this chapter is the modeling of multi-body systems using multibond graphs and how to solve the problem that these systems present when zero-order causal paths (ZCPs) appear. 

This section details how a basic bond graph is constructed for defining the movement of a rigid body in space. For modeling MBS, multi-bond graphs will be used. Also explained is how kinematic constraints are set and the section includes how to simplify these models in planar movement. 

Multi-bond graph formulation represents an extension of the single bonds. This way, a multi-bond is formed by a set of single bonds, as Fig. 9.1 shows. The multi-bond elements are represented by a double line arrow. The orientation of the multi-bond indicates the direction of transmission of positive power P > 0) and is represented by a line at the end of the bond like the half arrow of the single bond. 

The multi-bond graph notation, introduced by Breedveld [3,4], has major advantages. First, it enables the bond graph to be viewed in a more compact and concise manner. Second, it enables matrix elements to be inserted, and all the mathematical power implied by such. 

Simulation of Multi-body Systems Using Multi-bond Graphs 9.2.1.1 The Storage Field [C]... 

If elements TF and GY are extended to the multi-bond graph formulation, they become multi-port elements (Fig. 9.5). Their constitutive equations are as follows in (9.5) and (9.6) ... 

Extensions of 0- and 1-Junctions to the Multi-bond Graph Formulation... 

In this section, a standard bond graph will be developed for a free rigid body with three-dimensional movement in which multi-bond graphs will be used. To define... 

Fig. 9.6 Definition of the 0- and 1-junctions in multi-bond graph notation...

In (9.26), the lower the number of break variables, the easier it is to solve this system. The purpose of the following algorithms is to open all the existing causal loops in the bond graph by means of the minimum number of break variables. In a later step, the mathematical model will be automatically obtained based on these break variables. These algorithms have been conceived to deal with one-dimensional and multi-bond graph systems. 

Multi-bond Graph Systems with Topological Loops... 

Various authors have publications about systems modeled with multi-bond graphs [4, 7, 9,18-21], A typical scenario where ZCPs appear in MBG modeling is in multi-body systems [7, 9],... 

The first part of the chapter described how multi-body systems are modeled using multi-bond graphs. 

Breedveld, P.C., 1985, Multi-bond graph elements in physictil systems theory . Joumtil of the... 

Bos, A.M., 1986, Modeling multi-body systems in terms of multi-bond graphs . Ph. D. Thesis, Twente University, Enschede, The Netherlands. 

Cacho, R., Felez, J., Vera, C., 2000, Deriving simulation models from bond graphs with algebraic loops. The extension to multi-bond graph systems . Journal of the Frankhn Institute, Vol. 337, pp. 579-600. 

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