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.

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.

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.

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

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.

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