Study On Transfer Matrix Method for the Planar Multibody System with Closed-Loops

2021 ◽  
Author(s):  
Lina Zhang ◽  
Xiaoting Rui ◽  
Jianshu Zhang ◽  
Junjie Gu ◽  
Huaqing Zheng ◽  
...  
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
Multibody System ◽  
Jacobian Matrix ◽  
Global Dynamics ◽  
Closed Loops ◽  
Single Output ◽  
Multiple Input

Abstract The conventional transfer matrix method for multibody systems (MSTMM) with closed-loops (CLs) has superiority of avoiding the global dynamics equations. However, it requires a transfer equation to link Multiple-Input Single-Output (MISO) rigid body with multi-hinge subset and supplement equations caused CLs. In order to simplify the deduction processing and improve the numerical stability, the Riccati transformation is introduced and the Riccati transfer matrix method for multibody systems (RMSTMM) with CL is proposed. In a system with CLs, each CL is cut off at the connection point, and the new unknowns generated at the cut-off point are introduced into the Riccati recurrence relation. The numerical results of the conventional MSTMM and the RMSTMM are compared, and the reliability of the RMSTMM is verified. Meanwhile, the constrained Jacobian matrix is used to eliminate the non-working reactions of the system. The variations of the constraint violation error are compared to validate necessarily of constraints.

Research on the Solver of Riccati Transfer Matrix Method for Linear Multibody Systems

2018 ◽  
Author(s):  
Junjie Gu ◽  
Xiaoting Rui ◽  
Jianshu Zhang ◽  
Gangli Chen
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
Multibody System ◽  
Automatic Generation ◽  
Object Oriented Programming ◽  
Connectivity Matrix ◽  
Closed Loops ◽  
Practical Engineering

Riccati transfer matrix method for multibody systems (RMSTMM) has lower matrix order and better numerical stability than transfer matrix method for multibody systems (MSTMM). In order to make technicians more convenient to apply RMSTMM in practical engineering to improve the computational efficiency of dynamics, in this paper, a linear RMSTMM solver is developed based on the linear RMSTMM theory. A solver input document with good compatibility and extensibility is designed based on extensible markup language (XML); The data structure of multibody system is designed based on object-oriented programming method. The technique of auto selecting the cut hinges of closed-loops of the multibody system is established by introducing the correlation matrix and the dynamic connectivity matrix which depict the connecting state of elements. The automatic generation of the derived tree system by cutting off the closed-loops in the multibody system is realized based on the technique. The automatic regularly numbering of dynamics elements of multibody systems is realized based on the depth first recursive traversal algorithm; Finally, the Riccati transfer matrix recursive technique is implemented based on the regular numbers of dynamics elements of the multibody system. An example is given to verify the effectiveness of the solver which provides a powerful tool for extending the application of RMSTMM in practical engineering.

Implicit Algorithm for Riccati Transfer Matrix Method for Multibody Systems

2018 ◽  
Author(s):  
Tianxiong Tu ◽  
Guoping Wang ◽  
Xiaoting Rui ◽  
Jianshu Zhang ◽  
Xiangzhen Zhou
Keyword(s):  
System Dynamics ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Numerical Stability ◽  
Matrix Method ◽  
Multibody Systems ◽  
Multibody System ◽  
Multibody System Dynamics ◽  
Global Dynamics ◽  
Implicit Algorithm

Rui method, namely the transfer matrix method for multibody systems (MSTMM) is a new and efficient method for multibody system dynamics (MSD) for its features as follows: without global dynamics equations of the system, high programming, low order of system matrix and high computational speed. Riccati transfer matrix method for multibody systems was developed by introducing Riccati transformation in MSTMM, for improving numerical stability of MSTMM. In this paper, based on Riccati MSTMM, applying the thought of direct differentiation method, by differentiation of Riccati transfer equations of rigid bodies and joints, generalized acceleration and its differentiation can be obtained. Combined with Backward Euler algorithm, implicit algorithm for Riccati MSTMM is proposed in this paper. The formulation and computing procedure of the method are presented. The numerical examples show that results obtained by first order accurate implicit algorithm proposed in the paper and the fourth order accurate Runge-Kutta method have good agreement, which indicates that this implicit method is more numerical stability than explicit algorithm with the same order accurate. The implicit algorithm for Riccati MSTMM can be used for improving the computational accuracy of multibody system dynamics.

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

2018 ◽  
Vol 10 (7) ◽  
pp. 168781401878875
Author(s):  
Lu Sun ◽  
Guoping Wang ◽  
Xiaoting Rui ◽  
Xue Rui
Keyword(s):  
System Dynamics ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Transfer Equation ◽  
Matrix Method ◽  
Closed Loop ◽  
Multibody System ◽  
Mixed System ◽  
Global Dynamics ◽  
Mixed Systems

The transfer matrix method for multibody systems has been developed for 20 years and improved constantly. The new version of transfer matrix method for multibody system and the automatic deduction method of overall transfer equation presented in recent years make it more convenient of the method for engineering application. In this article, by first defining branch subsystem, any complex multibody system may be regarded as the assembling of branch subsystems and simple chain subsystems. If there are closed loops in the system, the loops should be “cut off,” thus a pair of “new boundaries” are generated at each “cutting-off” point. The relationship between the state vectors of the pair of “new boundaries” may be described by a supplement equation. Based on above work, the automatic deduction method of overall transfer equation for tree systems as well as closed-loop-and-branch-mixed systems is formed. The results of numerical examples obtained by the automatic deduction method and ADAMS software for tree system dynamics as well as mixed system dynamics have good agreements, which validate the features of proposed method such as high computational speed, more effective for complex systems, no need of the system global dynamics equation, highly programmable, as well as convenient popularization and application in engineering.

Active Vibration Control Design of Multi-Rigid-Flexible-Body Systems Based on Transfer Matrix Method for Multibody Systems

2018 ◽  
Author(s):  
Gangli Chen ◽  
Xiaoting Rui ◽  
Yuanyuan Ding ◽  
Hanjing Lu
Keyword(s):  
Vibration Control ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
Active Vibration Control ◽  
Control Design ◽  
Flexible Body ◽  
Global Dynamics ◽  
Active Vibration

A new approach for active vibration control design of multi-rigid-flexible-body systems based on transfer matrix method for multibody systems (MSTMM) is presented in this paper. The vibration characteristics are computed by solving homogeneous linear algebraic equations. Then, the augmented eigenvector and body dynamics equation are adopted to derive the state space representation by combining modal superposition method. Furthermore, Linear Quadratic Gaussian (LQG) control strategy is employed to design the control law. Compared with the conventional methods, the proposed method has the following features: without system global dynamics equation, high programming, low order of system matrix and high computational speed. Formulations as well as a numerical example are given to validate the proposed method.

Advances in Transfer Matrix Method of Multibody System

2009 ◽  
Author(s):  
Xiaoting Rui ◽  
Guoping Wang ◽  
Laifeng Yun ◽  
Bin He ◽  
Fufeng Yang ◽  
...  
Keyword(s):  
System Dynamics ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
Multibody System ◽  
Engineering Problem ◽  
Multibody System Dynamics ◽  
Integration Scheme ◽  
Linear And Nonlinear

Multibody system dynamics has become important theoretical tool for wide engineering problems analysis in the world. Transfer matrix method of multibody system (MS-TMM) is a new approach for multibody system dynamics, which is developed in 20 years. In this paper, the transfer matrix method for linear and nonlinear multibody systems are introduced respectively. For linear multibody systems, the new concept of body dynamics equation and augmented eigenvector, the construction method of orthogonality, and the computing method of vibration characteristics and dynamic response are introduced; For nonlinear multibody systems, the discrete time transfer matrix method of multibody system (MS-DT-TMM) are presented. The apply of the transfer matrix method for multibody systems with tree, closed loop and network structures are also introduced. The transfer matrix method has good characteristics: 1 It does not require overall dynamics equations of system and simplify the solution procedure. 2 It has high computing speed, because the system matrices are always small irrespective of the size of a system. 3 It avoids the difficulties caused by developing overall dynamic equations of a system and by computing too high order matrices. 4 It provides maximum flexibility in modeling various configurations of multibody systems, by creating library of transfer matrices and assembling them easily, and by introducing any suitable numerical integration scheme. The new method is efficient for linear and nonlinear multi-rigid-flexible-body system, and it has been paid great attention, because many engineering problem of important mechanical system were solved effectively by using this method.

Research Progress and Development Tendency of Transfer Matrix Method for Multibody Systems (Rui Method)

2019 ◽  
Author(s):  
Xiaoting Rui ◽  
Xun Wang ◽  
Jianshu Zhang ◽  
Junjie Gu ◽  
Shujun Zhang
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
Research Progress ◽  
Global Dynamics ◽  
Computational Stability ◽  
Research Fields ◽  
Complex Mechanical Systems ◽  
Development Tendency

Abstract The transfer matrix method for multibody systems, known as the “Rui method”, is a new method for dealing with multibody system dynamics, which does not need the global dynamics equations of the system, keeps high computational speed, and is highly formalized programming. This method has been widely applied to scientific research and key engineering of many complex mechanical systems in more than 50 research fields. The following aspects regarding the transfer matrix method for multibody systems are reviewed in this paper: history, basic principles, formulas, algorithm, and applications in engineering. Some hot topics in this field are also reviewed and prospected, mainly regarding to the improvement of the computational stability and efficiency.

Riccati Transfer Matrix Method for Linear Tree Multibody Systems

2016 ◽  
Vol 84 (1) ◽  
Author(s):  
Junjie Gu ◽  
Xiaoting Rui ◽  
Jianshu Zhang ◽  
Gangli Chen ◽  
Qinbo Zhou
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Numerical Stability ◽  
Matrix Method ◽  
Multibody Systems ◽  
Method Comparison ◽  
Harmonic Excitation ◽  
State Response ◽  
Multiple Input ◽  
Transfer Equations

The Riccati transfer matrix method (RTMM) improves the numerical stability of analyzing chain multibody systems with the transfer matrix method for multibody systems (MSTMM). However, for linear tree multibody systems, the recursive relations of the Riccati transfer matrices, especially those for elements with multiple input ends, have not been established yet. Thus, an RTMM formulism for general linear tree multibody systems is formulated based on the transformation of transfer equations and geometrical equations of such elements. The steady-state response under harmonic excitation of a linear tree multibody system is taken as an example and obtained by the proposed method. Comparison with the finite-element method (FEM) validates the proposed method and a numerical example demonstrates that the proposed method has a better numerical stability than the normal MSTMM.

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

2019 ◽  
Vol 49 (3) ◽  
pp. 337-354 ◽  
Author(s):  
Xue Rui ◽  
Dieter Bestle ◽  
Guoping Wang ◽  
Jiangshu Zhang ◽  
Xiaoting Rui ◽  
...  
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Multibody System ◽  
Branch System ◽  
Computational Speed ◽  
Speed Accuracy

Abstract Computational speed and stability are two important aspects in the dynamics analysis of large-scale complex multibody systems. In order to improve both in the context of the multibody system transfer matrix method, a new version of the Riccati transfer matrix method is presented. Based on the new version of the general transfer matrix method for multibody system simulation, recursive formulae are developed which not only retain all advantages of the transfer matrix method, but also reduce the truncation error. As a result, the computational speed, accuracy and efficiency are improved. Numerical computation results obtained by the proposed method and an ordinary multibody system formulation show good agreement. The successful computation for a spatial branch system with more than 100000 degrees of freedom validates that the proposed method is also working for huge systems.

scholarly journals Riccati transfer matrix method for linear multibody systems with closed loops

AIP Advances ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 115307
Author(s):  
J. J. Gu ◽  
X. T. Rui ◽  
J. S. Zhang
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
Closed Loops

Developments in Transfer Matrix Method for Multibody Systems (Rui Method) and its Applications

2018 ◽  
Author(s):  
Xiaoting Rui ◽  
Xun Wang ◽  
Qinbo Zhou ◽  
Jianshu Zhang
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
Classical Mechanics ◽  
Science Research ◽  
Future Research ◽  
Global Dynamics ◽  
Research Directions ◽  
Novel Approach

Compared to classical mechanics, the transfer matrix method for multibody systems is a rather novel approach for analyzing multibody system dynamics. For its features that it avoids the global dynamics equation of the system, keeps a high computational speed and allows highly formalized programming, this method has been widely used in science research as well as design of dynamics performance and experiments for various complicated mechanical systems. Up to now, there have been more than 50 research directions in science research and key engineering applications based on this method. In this paper, the following aspects are systematically reviewed: history, basic principles, formulas, algorithm, automatic deduction theorem of overall transfer equation, visualized simulation and design software, comparison with other dynamics methods, tendency, and future research directions.

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