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.

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.

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.

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.

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.

Dynamic Characteristics of Motorized Spindle With Tandem Duplex Angular Contact Ball Bearings

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Shengye Lin ◽  
Shuyun Jiang
Keyword(s):  
Transfer Matrix ◽  
Dynamic Characteristics ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Ball Bearing ◽  
Ball Bearings ◽  
Motorized Spindle ◽  
Angular Contact Ball Bearing ◽  
Stiffness Coefficients ◽  
Proposed Model

Abstract The purpose of this study is to investigate the dynamics of motorized spindle, in which the tilting effect of tandem duplex angular contact ball bearing is considered. First, the quasi-static model of the duplex angular contact ball bearing is developed based on the Jones's bearing model. Then, the model is numerically solved using the Newton–Raphson method to obtain 16 stiffness coefficients (including the tilting ones). Later, a modified transfer matrix method is used to establish the dynamic model of the motorized spindle system with 16 stiffness coefficients. Finally, experiments have been performed to detect the stiffness of the tandem duplex angular contact ball bearing and the unbalance response of the motorized spindle. Results show that the modified transfer matrix method can be used to analyze the dynamic behavior of the motorized spindle supported on tandem duplex angular contact ball bearings, the tilting effect of the tandem duplex angular contact ball bearing affects the dynamic behaviors of the motorized spindle, and the theoretical dynamic characteristics using the proposed model agree with the experimental ones.

Vibration Analysis of Multi-Disk Multi-Profiled Shaft-Rotor Systems

2014 ◽  
Vol 612 ◽  
pp. 17-22 ◽  
Author(s):  
P.M.G. Bashir Asdaque ◽  
R.K. Behera ◽  
Jakeer Hussain Shaik
Keyword(s):  
Dynamic Characteristics ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Vibration Analysis ◽  
Shear Force ◽  
Bending Moment ◽  
Rotor System ◽  
Step Response ◽  
Rotor Systems

Cantilevered shaft-rotor systems consisting of multi disks and multi profiled shafts are considered. In this paper the procedures for the determination of the deflection, slope, shear force and bending moment at the extremities of the shaft are employed. Critical speeds or whirling frequency conditions are computed using transfer matrix method (TMM). For particular shaft-lengths, rotating speeds and shaft-profiles, the response of the system is determined for the establishment of the dynamic characteristics. A built-in shaft-rotor system consisting of two disks and two different profiled shafts is investigated for illustration purposes. Step response of the multi profiled shaft-rotor system is also found out.

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.

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