Study on automatic deduction method of overall transfer equation for branch multibody system

Abstract

The transfer matrix method for multibody system is a new method developed in recent 20 years for studying multibody system dynamics. The new version of transfer matrix method for multibody system and automatic deduction theorem of system overall transfer equation have been formed in 2012. The overall transfer equation plays one of the key roles for transfer matrix method for multibody system. In order to study branch system dynamics with new version of transfer matrix method for multibody system, the automatic deduction theorem of overall transfer equation has been expanded in this article, which made it practicable to deduce automatically the overall transfer equation for branch system with new version of transfer matrix method for multibody system. The transfer equations and transfer matrices of typical elements are developed for the automatic deduction theorem of overall transfer equation. Thereby new version of transfer matrix method for multibody system owns the following features: there is no need to establish the global dynamics equation of system, by which the study on multibody system dynamics will be simplified greatly; the automatic deduction of overall transfer equation for multibody system is realized, consequently the algorithm is simple and highly programmable; moreover, the order of system matrix is always low, which result in high computational speed. The branch multibody system dynamics has been computed with the automatic deduction theorem of overall transfer equation as well as ordinary multibody system dynamics method. The computational results obtained by the two methods have good agreements, which validate the automatic deduction theorem of overall transfer equation for branch multibody system.

Study on automatic deduction method of overall transfer equation for tree systems as well as closed-loop-and-branch-mixed systems

“…In general, any multibody system, according to its topology graph, may always be categorized into one of the following systems: chain systems, closed-loop systems, branch systems, tree systems, or closed-loop-and-branch-mixed systems. Automatic deduction theorem of overall transfer equation has been given for chain systems and closed-loop systems of new version of MSTMM in Rui et al 19 and for branch systems of new version of MSTMM has been given in Rui et al 20 Hence, automatic deduction theorems of overall transfer equation for general systems are composed by and Rui et al 19,20 , and this paper together.…”

“…The automatic deduction theorem of overall transfer equation of chain systems and closed-loop systems 19 for the new version of MSTMM was presented in 2014. Subsequently, this theorem was extended for branch systems 20 in 2015. The salient contributions of this article are as follows:…”

A new version of the Riccati transfer matrix method for multibody systems consisting of chain and branch bodies

“…The corresponding topology in Fig. 1(b) provides the transfer relationship among state vectors, element numbers, and transfer directions [7], where body elements are represented by circles, with inside numbers indicating the bodies' sequence numbers, whereas arrows and numbers beside indicate hinge elements and hinge sequence numbers; the arrowhead shows the transfer direction of state vectors. Especially, the number 0 represents system boundaries.…”

“…Multibody system methods are important for design and analysis of modern complex mechanical systems [1][2][3][4], where improving computational speed and stability of algorithms has always been one of the key research directions. In order to increase computation speed and simplify modeling, one of the authors and his co-workers presented and perfected constantly the transfer matrix method for multibody systems (MSTMM) [4][5][6][7]. Especially, the Riccati transformation was introduced to deal with long body chains.…”

“…Recently, the form of B X. Rui state vector has been changed from displacements and angles to translational and angular accelerations to allow for arbitrary integration algorithms [6], and the automatic deduction theorem was presented to obtain the overall transfer equation more easily [7], which now calls for an adaption of the Riccati approach to this new transfer matrix method.…”