Dynamic characteristics of coupling shaft system in tufting machine based on the Riccati whole transfer matrix method

2016 ◽  
Vol 231 (2) ◽  
pp. 356-371 ◽  
Author(s):  
Shuang Huang ◽  
Xinfu Chi ◽  
Yang Xu ◽  
Yize Sun
Keyword(s):  
Transfer Matrix ◽  
Dynamic Characteristics ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Complex Dynamic ◽  
Rotor Systems ◽  
Machine Type ◽  
Shaft System

Focusing on tufting machine type DHUN801D-400, the complex dynamic model of coupling shaft system is built by using Riccati whole transfer matrix method, and the natural frequencies and mode shapes are analyzed. First, the components of coupling shafts system in tufting machine are introduced. Second, the structures of coupling shafts system are discretized and simplified. Third, the transfer matrix is constructed, the model is solved by using Riccati whole transfer matrix method, and then natural frequencies and mode shapes are obtained. Finally, the experimental results are quoted to demonstrate the applicability of the model. The results indicate that the Riccati whole transfer matrix method is well applicable for modeling the dynamics of complex multi-rotor systems.

Dynamic Analysis of Geared Rotor-Bearing Systems by the Transfer Matrix Method

1995 ◽  
Author(s):  
Siu-Tong Choi ◽  
Sheng-Yang Mau
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Vibration Analysis ◽  
Transmission Error ◽  
Mode Shapes ◽  
Rotor Systems ◽  
Gear Mesh ◽  
Mass Unbalance ◽  
Rotor Bearing

Abstract In this paper, an analytical study of the dynamic characteristics of geared rotor-bearing systems by the transfer matrix method is presented. Rotating shafts are modeled as Timoshenko beam with shear deformation and gyroscopic effects taken into account. The gear mesh is modeled as a pair of rigid disks connected by a spring-damper set and a transmission-error exciter. The transfer matrix of a gear mesh is developed. The coupling motions of the lateral and torsional vibration are studied. In free vibration analysis of geared rotor systems, natural frequencies and corresponding mode shapes, and the whirl frequencies under different spin speeds are determined. Effects of bearing stiffness, isotropic and orthotropic bearings, pressure angle of the gear mesh are studied. In steady-state vibration analysis, responses due to the excitation of mass unbalance and the transmission error are studied. Parametric characteristics of geared rotor systems are discussed.

scholarly journals Improved Riccati Transfer Matrix Method for Free Vibration of Non-Cylindrical Helical Springs Including Warping

2012 ◽  
Vol 19 (6) ◽  
pp. 1167-1180 ◽  
Author(s):  
A.M. Yu ◽  
Y. Hao
Keyword(s):  
Free Vibration ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Axial Deformation ◽  
Cross Sectional ◽  
Helical Springs

Free vibration equations for non-cylindrical (conical, barrel, and hyperboloidal types) helical springs with noncircular cross-sections, which consist of 14 first-order ordinary differential equations with variable coefficients, are theoretically derived using spatially curved beam theory. In the formulation, the warping effect upon natural frequencies and vibrating mode shapes is first studied in addition to including the rotary inertia, the shear and axial deformation influences. The natural frequencies of the springs are determined by the use of improved Riccati transfer matrix method. The element transfer matrix used in the solution is calculated using the Scaling and Squaring method and Pad'e approximations. Three examples are presented for three types of springs with different cross-sectional shapes under clamped-clamped boundary condition. The accuracy of the proposed method has been compared with the FEM results using three-dimensional solid elements (Solid 45) in ANSYS code. Numerical results reveal that the warping effect is more pronounced in the case of non-cylindrical helical springs than that of cylindrical helical springs, which should be taken into consideration in the free vibration analysis of such springs.

Study on the Natural Vibration Characteristics of Flexible Missile With Thrust by Using Riccati Transfer Matrix Method

2015 ◽  
Vol 83 (3) ◽  
Author(s):  
Gangli Chen ◽  
Xiaoting Rui ◽  
Fufeng Yang ◽  
Jianshu Zhang
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Compressive Force ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Engine Thrust ◽  
Natural Vibration Characteristics

Due to the mass consumption and engine thrust of a flexible missile during the powered phase flight, its natural vibration characteristics may be changed significantly. The calculation of natural frequencies and mode shapes plays an important role in the structural design of the missile. Aiming at calculating the natural vibration characteristics of the missile rapidly and accurately, a nonuniform beam subjected to an engine thrust is used to model the free vibration of the missile and Riccati transfer matrix method (RTMM) is adopted in this paper. Numerical results show that the natural frequencies of a typical single stage flexible missile are increased unceasingly in its powered phase, and its mode shapes are changed a lot. When the presented methodology is used to study the natural vibration characteristics of flexible missiles, not only the mass, stiffness, and axial compressive force distributions are described realistically but also numerical stability, high computation speed, and accuracy are achieved.

scholarly journals Transfer Matrix Method for Dynamic Characteristics Analysis of Missile-Canister System in Silo

2020 ◽  
Vol 319 ◽  
pp. 01001
Author(s):  
Anfeng Zhou ◽  
Daokui Li ◽  
Shiming Zhou ◽  
Da Cui ◽  
Xuan Zhou
Keyword(s):  
Transfer Matrix ◽  
Dynamic Characteristics ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Discrete Distribution ◽  
Mode Shapes ◽  
Beam Model ◽  
Radial Vibration ◽  
Single Beam ◽  
Double Beam

In order to ensure the safety of the missile-canister system in silo during the earthquake, a modified transfer matrix method is provided to study the dynamic characteristics of the system. Firstly, a discrete viscoelastic connected double-beam model is developed taking account of the structural nonuniformity and the discrete distribution of the adapters. Secondly, the transfer matrix method of a single beam is modified to solve the problem of discrete connection between the two beams of the double-beam model. Then the natural circular frequencies and mode shapes are calculated by the proposed method, comparing with the finite element method (FEM). Finally, the influence of the stiffness of radial vibration isolators and adapters on the dynamic characteristics of the system is analysed. The comparison shows that the results of the proposed method are well consistent with the FEM calculations and the proposed method is validated. The variations of the first six natural circular frequencies with radial vibration isolator stiffness and adapter stiffness are obtained, which provides a basis for the seismic-relieving design.

An Investigation on Dynamic Characteristics of a Gas Turbine Rotor Using an Improved Transfer Matrix Method

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
Cheng Meng ◽  
Ming Su ◽  
Shaobo Wang
Keyword(s):  
Gas Turbine ◽  
Dynamic Model ◽  
Transfer Matrix ◽  
Dynamic Characteristics ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Mode Shapes ◽  
Correction Coefficient ◽  
Critical Speeds ◽  
Contact Effects

This paper presents an investigation on dynamic characteristics of a rod-fastened rotor. Based on the framework of a traditional Riccati transfer matrix method (TMM), an improved Riccati TMM considering contact effects brought by a face tooth is developed. A correction coefficient for equivalent stiffness imported from a three-dimensional (3D) finite element contact case analysis is defined to evaluate the contact effects, and then the dynamic model of the rod-fastened rotor including bearing support is established. A computer program is further developed to obtain the dynamic characteristics such as critical speeds of lateral vibration, mode shapes, and an unbalance response. The improved TMM is applied to investigate the dynamic characteristics of a real central tie rod rotor of the class-F gas turbine for verification of its effectiveness, and the calculated critical speeds are in good agreement with test measurement results, implying that the method is accurate and the dynamic model is reliable. This approach can also be applied to analyze other combined rotors with a homogeneous structure.

An Improved Extended Transfer Matrix Method for a Damped System

1991 ◽  
Author(s):  
Yuan Mao Huang
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Good Method ◽  
Mode Shapes ◽  
Vibration Effect ◽  
Damped System ◽  
Matrix Products ◽  
The Matrix

Abstract Installation of a damper is a good method to reduce the torsional vibration effect and to prolong the life of a system. However, consideration of the damping effect results in a complicated system. This study derives a mathematical model for the analysis of a single branch damped system. The extended transfer matrix method is used with Newton-Raphson iterative technique. The procedures automatically eliminate the complicated operations of the matrix inversion and reduce the multiplication of the matrix products. The natural frequencies, both real and imaginary parts of the state vectors and mode shapes of the system can be determined.

scholarly journals Dynamic Characteristics of Magnetic Suspended Dual-Rotor System by Riccati Transfer Matrix Method

2019 ◽  
Vol 2019 ◽  
pp. 1-22
Author(s):  
Dongxiong Wang ◽  
Nianxian Wang ◽  
Kuisheng Chen ◽  
Chun Ye
Keyword(s):  
Dynamic Model ◽  
Transfer Matrix ◽  
Dynamic Characteristics ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Weight Ratio ◽  
Rotor System ◽  
Mode Shapes ◽  
Outer Rotor ◽  
The Relationship

The magnetic suspended dual-rotor system (MSDS) can effectively increase the thrust weight ratio of aeroengines. However, the MSDS dynamic characteristics have rarely been investigated. In this research, a MSDS with the outer rotor supported by two active magnetic bearings (AMBs) is designed, and the PID control is employed. The Riccati transfer matrix method using complex variables is adopted to establish the MSDS dynamic model. Subsequently, the influences of AMBs’ control parameters on the MSDS dynamic characteristics are explored. According to the analysis, two rigid mode shapes remain unchanged with the variation of the relationship between their corresponding damped critical speeds (DCSs). Moreover, the rigid DCSs disappear with large derivative coefficient. Eventually, the validity of the dynamic model and the appearance of rigid DCSs are verified.

A Transfer Matrix Technique for Evaluating the Natural Frequencies and Critical Speeds of a Rotor With Multiple Flexible Disks

1992 ◽  
Vol 114 (2) ◽  
pp. 242-248 ◽  
Author(s):  
F. Wu ◽  
G. T. Flowers
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Research Effort ◽  
Dynamical Behavior ◽  
Rotor System ◽  
Matrix Formulation ◽  
Critical Speeds ◽  
Rotor Systems

The influence of disk flexibility on the rotordynamical behavior of turbomachinery is a topic that is of some concern to designers and analysts of such equipment. Research in this area has indicated that disk flexibility may significantly alter the dynamical behavior of a rotor system. This research effort is concerned with developing a procedure to account for disk flexibility which can readily be used for investigating how such effects might influence the natural frequencies and critical speeds of practical rotor systems. A transfer matrix procedure is developed in this work in which the disk flexibility effects are accounted for by means of additional terms included in the transfer matrix formulation. In this way the efficiency and practicality of the transfer matrix method is retained. To demonstrate this technique, a simple rotor system is studied for the effect of disk flexibility and the results discussed.

Generalized Solutions of Piezoelectric Vibration-Based Energy Harvesting Structures Using an Electromechanical Transfer Matrix Method

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Timothy Reissman ◽  
Adam Wickenheiser ◽  
Ephrahim Garcia
Keyword(s):  
Energy Harvesting ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Generalized Solutions ◽  
Mode Shapes ◽  
Transition Matrices ◽  
Tip Mass ◽  
Piezoelectric Vibration

Piezoelectric vibration-based energy harvesting (pVEH) offers much potential as renewable energy structures. Within the literature, often geometry-specific models are developed, making designs of new structures difficult. In this work, a generalized linear algebraic method is developed. The method incorporates the transfer matrix method (TMM) into the well-accepted distributed parameter electromechanical model for a composite-piezoelectric, Euler–Bernoulli beam. The result is an electromechanical TMM which is highly accurate at predicting both structural and energy harvesting performances for a wide variety of designs which have chainlike topologies. A simplification is made within the method to model structures which operate solely within bending modes, reducing the computation to analyses of only four-by-four state transition matrices, regardless of structural complexity. As many applications aim to optimize the large bending mode piezoelectric effect, this simplification does not limit the versatility of the method. To demonstrate the validity of this statement, comparisons were performed to evaluate the accuracy of the method's predictions for six piezoelectric topologies, including a unimorph without a tip mass, a bimorph with a tip mass, several partial-length bimorphs without a tip mass, and three different multibeam bimorph structures with inline and folded-back designs. The results show differences no greater than 2.24% for the first and second natural frequencies of the structures. Likewise, the method yields excellent predictions for the mode shapes, their slopes, and the voltage frequency responses, especially within the ±10% bounds of the natural frequencies. Thus, the future design of new structures is shown to be simplified using this generalizable method.

Sign in / Sign up

Export Citation Format

Share Document