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.

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.

Study on the Dynamics Response of Ultra-Precision Single-Point Diamond Fly-Cutting Machine Tool As Multi-Rigid-Flexible-Body System Based on Transfer Matrix Method for Multibody Systems

2018 ◽  
Author(s):  
Hanjing Lu ◽  
Xiaoting Rui ◽  
Gangli Chen
Keyword(s):  
Machine Tool ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
Flexible Body ◽  
Body System ◽  
Dynamics Model ◽  
Ultra Precision ◽  
Dynamics Response

The dynamics response optimization of an ultra-precision machine tool system is the key to improve machining accuracy. Based on the transfer matrix method for multibody systems (MSTMM), the dynamics model as multi-rigid-flexible-body system is established. The overall transfer equation, overall transfer matrix, eigenfrequency equation and dynamics equation with respect to generalized coordinates are derived in this paper. Considering the environmental micro-vibration, cutting force and spindle centrifugal force during the machining process as external excitations, the vibration characteristics and dynamics response are simulated by using MSTMM. The computational results are in good agreement with test results, which validates the proposed method and dynamics model used in this paper.

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.

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.

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.

Active vibration control of spatial flexible multibody systems

2013 ◽  
Vol 30 (1) ◽  
pp. 13-35 ◽  
Author(s):  
Maria Augusta Neto ◽  
Jorge A. C. Ambrósio ◽  
Luis M. Roseiro ◽  
A. Amaro ◽  
C. M. A. Vasques
Keyword(s):  
Vibration Control ◽  
Multibody Systems ◽  
Active Vibration Control ◽  
Flexible Multibody Systems ◽  
Flexible Multibody ◽  
Active Vibration
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