Stability analysis of rigid rotors supported by gas foil bearings coupled with electromagnetic actuators

2019 ◽  
Vol 234 (2) ◽  
pp. 427-443 ◽  
Author(s):  
Kamal Kumar Basumatary ◽  
Gaurav Kumar ◽  
Karuna Kalita ◽  
Sashindra K Kakoty
Keyword(s):  
Stability Analysis ◽  
Equations Of Motion ◽  
Electromagnetic Actuator ◽  
Electromagnetic Actuators ◽  
Foil Bearings ◽  
Damping Characteristics ◽  
Foil Bearing ◽  
Model Combining ◽  
The Stability ◽  
Rigid Rotors

Rotors supported on gas foil bearings have low damping characteristics, which limits its application. A possible solution could be an integration of a gas foil bearing with an electromagnetic actuator. This paper discusses the effect of electromagnetic actuators on the stability of a rotor supported on gas foil bearings. A coupled dynamic model combining the dynamics of gas foil bearing and electromagnetic actuator has been developed. The fluid film forces from the gas foil bearings and the electromagnetic forces from the electromagnetic actuators are integrated into the equations of motion of the rotor. The sub-synchronous vibration present in case of conventional gas foil bearings is reduced and the stability band of the rotor is increased due to the implementation of electromagnetic actuator.

Experimental Evaluation of the Structure Characterization of a Novel Hybrid Bump-Metal Mesh Foil Bearing

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Kai Feng ◽  
Yuman Liu ◽  
Xueyuan Zhao ◽  
Wanhui Liu
Keyword(s):  
Excitation Frequency ◽  
Structure Characterization ◽  
Viscous Damping ◽  
Metal Mesh ◽  
Equivalent Viscous Damping ◽  
Foil Bearings ◽  
Damping Characteristics ◽  
Foil Bearing ◽  
Mesh Density ◽  
Load Tests

Rotors supported by gas foil bearings (GFBs) experience stability problem caused by subsynchronous vibrations. To obtain a GFB with satisfactory damping characteristics, this study presented a novel hybrid bump-metal mesh foil bearing (HB-MMFB) that consists of a bump foil and metal mesh blocks in an underlying supporting structure, which takes advantage of both bump-type foil bearings (BFBs) and MMFBs. A test rig with a nonrotating shaft was designed to estimate structure characterization. Results from the static load tests show that the proposed HB-MFBs exhibit an excellent damping level compared with the BFBs with a similar size because of the countless microslips in the metal mesh blocks. In the dynamic load tests, the HB-MFB with a metal mesh density of 36% presents a viscous damping coefficient that is approximately twice that of the test BFB. The dynamics structural coefficients of HB-MFBs, including structural stiffness, equivalent viscous damping, and structural loss factor, are all dependent on excitation frequency and motion amplitude. Moreover, they exhibit an obvious decrease with the decline in metal mesh density.

Non-Linear Transient Stability Analysis of a Rigid Rotor Supported on Journal Bearings With Rectangular Dimples

2015 ◽  
Author(s):  
Ram Turaga
Keyword(s):  
Stability Analysis ◽  
Surface Texture ◽  
Transient Stability ◽  
Equations Of Motion ◽  
Journal Bearings ◽  
Pressure Curve ◽  
Rigid Rotor ◽  
Non Linear ◽  
The Stability ◽  
Transient Stability Analysis

The influence of deterministic surface texture on the sub-synchronous whirl stability of a rigid rotor has been studied. Non-linear transient stability analysis has been performed to study the stability of a rigid rotor supported on two symmetric journal bearings with a rectangular dimple of large aspect ratio. The surface texture parameters considered are dimple depth to minimum film thickness ratio and the location of the dimple on the bearing surface. Journal bearings of different Length to diameter ratios have been studied. The governing Reynolds equation for finite journal bearings with incompressible fluid has been solved using the Finite Element Method under isothermal conditions. The trajectories of the journal center have been obtained by solving the equations of motion of the journal center by the fourth-order Runge-Kutta method. When the dimple is located in the raising part of the pressure curve the positive rectangular dimple is seen to decrease the stability whereas the negative rectangular dimple is seen to improve the stability of the rigid rotor.

Vibration Mitigation of Rotors Suspended on Low-Cost Hybrid Gas Foil Bearing

2019 ◽  
Author(s):  
Kamal Kumar Basumatary ◽  
Karuna Kalita ◽  
Sashindra K. Kakoty ◽  
Seamus D. Garvey
Keyword(s):  
High Speed ◽  
Low Cost ◽  
Current Source ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Electromagnetic Actuators ◽  
Manufacturing Method ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Small Series

Abstract The hybrid Gas Foil Bearings combining the Gas Foil Bearing and Active Magnetic Bearing is a possibility for application in high-speed turbomachinery and a few developments have been made in this context. As such, the cost of conventional Gas Foil Bearing increases due to its requirement of precise manufacturing method and the coating material for the top foil and bump foil. In case of Active Magnetic Bearing, the normal electrical arrangement includes a multiplicity of independently controlled current sources usually at least four drives per bearing which increases its cost. Therefore, the hybrid Gas Foil Bearing will have much higher cost. In this work, a new electrical arrangement for the electromagnetic actuators of the hybrid Gas Foil Bearing has been proposed. The new arrangement requires only two drives per bearing and the bias current has been provided (in the same set of windings) through a simple rectifier with small series choke and shunt capacitor. As the number of drives required is less, the proposed bearing will have low cost. Implementing the new approach, the force vectors are achieved using only two current-source drives whereas the usual conventional arrangement requires four such drives. Numerical simulations are performed to explore the capabilities of the low cost bearing.

Stability Analysis of High-Speed Railway Vehicle Based on Multibody Dynamics Analysis

2013 ◽  
Vol 392 ◽  
pp. 156-160
Author(s):  
Ju Seok Kang
Keyword(s):  
Stability Analysis ◽  
Multibody Dynamics ◽  
High Speed ◽  
Equations Of Motion ◽  
Contact Forces ◽  
Design Parameters ◽  
Railway Vehicle ◽  
Dynamics Analysis ◽  
Contact Points ◽  
The Stability

Multibody dynamics analysis is advantageous in that it uses real dimensions and design parameters. In this study, the stability analysis of a railway vehicle based on multibody dynamics analysis is presented. The equations for the contact points and contact forces between the wheel and the rail are derived using a wheelset model. The dynamics equations of the wheelset are combined with the dynamics equations of the other parts of the railway vehicle, which are obtained by general multibody dynamics analysis. The equations of motion of the railway vehicle are linearized by using the perturbation method. The eigenvalues of these linear dynamics equations are calculated and the critical speed is found.

scholarly journals The Dynamic Characteristics of a Turborotor Simulator Supported on Gas-Lubricated Foil Bearings—Part 2: Operation With Heating and Thermal Gradients

1970 ◽  
Vol 92 (4) ◽  
pp. 650-659 ◽  
Author(s):  
L. Licht
Keyword(s):  
Dynamic Characteristics ◽  
High Speed ◽  
Elevated Temperatures ◽  
Load Capacity ◽  
Temperature Gradients ◽  
Thermal Gradients ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Geometrical Imperfections ◽  
The Stability

A high-speed rotor, supported by gas-lubricated foil bearings, is free from self-excited whirl and displays no loss of load capacity when vibrated at frequency equal half the rotational speed [1]. It is demonstrated here that in addition to tolerance of geometrical imperfections, misalignment, and foreign particles [3, 4], the foil bearing performs well at elevated temperatures and accommodates appreciable temperature gradients. The foil bearing is endowed with superior wipe-wear characteristics, and the flexibility of the foil accounts not only for the stability of the foil bearing but also for its forgiveness with respect to distortion, contamination, and contact.

Nonlinear Numerical Prediction of Gas Foil Bearing Stability and Unbalanced Response

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Sébastien Le Lez ◽  
Mihaï Arghir ◽  
Jean Frêne
Keyword(s):  
Dry Friction ◽  
Stability Limit ◽  
Time Step ◽  
Structural Dynamic ◽  
Friction Forces ◽  
Foil Bearings ◽  
Mass Unbalance ◽  
Foil Bearing ◽  
Highly Nonlinear ◽  
The Stability

One of the main interests of gas foil bearings lies in their superior rotordynamic characteristics compared with conventional bearings. A numerical investigation on the stability limit and on the unbalanced response of foil bearings is presented in this paper. The main difficulty in modeling the dynamic behavior of such bearings comes from the dry friction that occurs within the foil structure. Indeed, dry friction is highly nonlinear and is strongly influenced by the dynamic amplitude of the pressure field. To deal with these nonlinearities, a structural dynamic model has been developed in a previous work. This model considers the entire corrugated foil and the interactions between the bumps by describing the foil bearing structure as a multiple degrees of freedom system. It allows the determination of the dynamic friction forces at the top and at the bottom of the bumps by simple integration of ordinary differential equations. The dynamic displacements of the entire corrugated sheet are then easily obtained at each time step. The coupling between this structural model and a gas bearing prediction code is presented in this paper and allows performing full nonlinear analyses of a complete foil bearing. The bearing stability is the first investigated problem. The results show that the structural deflection enhances the stability of compliant surface bearings compared with rigid ones. Moreover, when friction is introduced, a new level of stability is reached, revealing the importance of this dissipation mechanism. The second investigated problem is the unbalanced response of foil bearings. The shaft trajectories depict a nonlinear jump in the response of both rigid and foil bearings when the value of the unbalance increases. Again, it is evidenced that the foil bearing can support higher mass unbalance before this undesirable step occurs.

Linear Stability Analysis of a Waveboard Multibody Model With a Minimal Set of Equations

2021 ◽  
Author(s):  
A. G. Agúndez ◽  
D. García-Vallejo ◽  
E. Freire ◽  
A. M. Mikkola
Keyword(s):  
Stability Analysis ◽  
Multibody System ◽  
Equations Of Motion ◽  
Nonholonomic Constraints ◽  
Design Parameters ◽  
Multibody Model ◽  
Aspect Ratios ◽  
Holonomic And Nonholonomic Constraints ◽  
The Stability ◽  
Nonlinear Equations Of Motion

Abstract In this paper, the stability of a waveboard, the skateboard consisting in two articulated platforms, coupled by a torsion bar and supported of two caster wheels, is analysed. The waveboard presents an interesting propelling mechanism, since the rider can achieve a forward motion by means of an oscillatory lateral motion of the platforms. The system is described using a multibody model with holonomic and nonholonomic constraints. To perform the stability analysis, the nonlinear equations of motion are linearized with respect to the forward upright motion with constant speed. The linearization is carried out resorting to a novel numerical linearization procedure, recently validated with a well-acknowledged bicycle benchmark, which allows the maximum possible reduction of the linearized equations of motion of multibody systems with holonomic and nonholonomic constraints. The approach allows the expression of the Jacobian matrix in terms of the main design parameters of the multibody system under study. This paper illustrates the use of this linearization approach with a complex multibody system as the waveboard. Furthermore, a sensitivity analysis of the eigenvalues considering different scenarios is performed, and the influence of the forward speed, the casters’ inclination angle and the tori aspect ratios of the toroidal wheels on the stability of the system is analysed.

Efficient and Robust Approaches to the Stability Analysis of Large Multibody Systems

2007 ◽  
Vol 3 (1) ◽  
Author(s):  
Olivier A. Bauchau ◽  
Jielong Wang
Keyword(s):  
Stability Analysis ◽  
Large Scale ◽  
Equations Of Motion ◽  
Classical Stability ◽  
Linearized Stability ◽  
Signal Synthesis ◽  
Common Framework ◽  
Synthesis Procedure ◽  
The Stability ◽  
Proper Orthogonal

Linearized stability analysis methodologies that are applicable to large scale, multiphysics problems are presented in this paper. Two classes of closely related algorithms based on a partial Floquet and on an autoregressive approach, respectively, are presented in common framework that underlines their similarity and their relationship to other methods. The robustness of the proposed approach is improved by using optimized signals that are derived from the proper orthogonal modes of the system. Finally, a signal synthesis procedure based on the identified frequencies and damping rates is shown to be an important tool for assessing the accuracy of the identified parameters; furthermore, it provides a means of resolving the frequency indeterminacy associated with the eigenvalues of the transition matrix for periodic systems. The proposed approaches are computationally inexpensive and consist of purely post processing steps that can be used with any multiphysics computational tool or with experimental data. Unlike classical stability analysis methodologies, it does not require the linearization of the equations of motion of the system.

Stability of Liquid-Filled Spinning Spheroids Via Liapunov’s Second Method

1979 ◽  
Vol 46 (2) ◽  
pp. 259-262 ◽  
Author(s):  
P. C. Parks
Keyword(s):  
Stability Analysis ◽  
Nonlinear Equations ◽  
Stability Theory ◽  
Equations Of Motion ◽  
Spin Axis ◽  
Liapunov Functions ◽  
The Stability ◽  
Nonlinear Equations Of Motion

In this paper the stability theory of Poincare´ and others, expounded in the last few pages of Sir Horace Lamb’s textbook Hydrodynamics, is extended by a stability analysis using Liapunov functions to cover the full nonlinear equations of motion of spinning liquid-filled spheroids. The linearized criterion is confirmed, that is for stability c/a < 1 or c/a > 3 where the semiaxes of the spheroid are a, a, c, the c-axis being also the spin axis. The unstable motion for 1 < c/a < 3 is examined, and a conjecture that viscosity will destabilize spinning spheroids with c/a > 3 is proposed.

scholarly journals Periodic stability analysis of wind turbines operating in turbulent wind conditions

2016 ◽  
Author(s):  
Riccardo Riva ◽  
Stefano Cacciola ◽  
Carlo Luigi Bottasso
Keyword(s):  
Stability Analysis ◽  
Wind Turbines ◽  
Equations Of Motion ◽  
Reduced Order ◽  
Stochastic Disturbance ◽  
Multibody Model ◽  
Time Histories ◽  
Identification Technique ◽  
Model Independent ◽  
The Stability

Abstract. In this work, a method for the stability analysis of wind turbines is described. A system identification technique, formulated for handling stochastic disturbances, is used to identify a periodic reduced order model from suitable recorded time histories of the system. Afterwards, such reduced model is analyzed according to Floquet theory. The formulation is model-independent, in the sense that it does not require knowledge of the equations of motion of the periodic system being analyzed, and it is applicable to an arbitrary number of blades and to any configuration of the machine. In addition, as wind turbulence can be viewed as a stochastic disturbance, the method is also applicable to real wind turbines operating in the field. The characteristics of the new method are verified first with a simplified analytical model, and then using a high-fidelity multibody model of a multi-MW wind turbine. Results are compared with those obtained by the well known operational modal analysis approach.

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