A Numerical Study on Effect of Electromagnetic Actuator on Rigid Rotor Supported on Gas Foil Bearing

2017 ◽  
Author(s):  
Kamal Kumar Basumatary ◽  
Gaurav Kumar ◽  
Karuna Kalita ◽  
Sashindra Kumar Kakoty
Keyword(s):  
Numerical Study ◽  
Load Capacity ◽  
Current Trend ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Normal Operation ◽  
Electromagnetic Actuator ◽  
Rigid Rotor ◽  
Magnetic Actuator ◽  
The Stability

Generally, Gas Foil Bearings (GFBs) are used in high speed machineries which are quite prone to instability or wear and tear. The current trend is to develop hybrid bearings which has conventional bearing (GFB) along with active magnetic bearing as an electromagnetic actuator (EMA). The GFBs are used for normal operation and the magnetic actuator can be used for the improvement of the stability and the load capacity of the bearing. In the present work a numerical study has been carried out to study the effects of magnetic actuator on the stability of bump type GFB supported rigid rotor. A rigid rotor supported on two identical GFBs with and without EMA has been investigated. The electromagnetic forces are incorporated in the equation of motion to provide the active control. A PD controller has been used as a controller for the magnetic actuator. It has been observed that the incorporation of EMA to the GFB reduces the sub synchronous vibrations and hence increases the stability.

Nonlinear Dynamics and Control of Rotors Operating Within the Clearance Gaps of Magnetic Bearing Systems

2017 ◽  
Author(s):  
Patrick S. Keogh ◽  
Chris Lusty ◽  
Nicola Y. Bailey
Keyword(s):  
Load Capacity ◽  
Magnetic Bearing ◽  
Contact Dynamics ◽  
Active Magnetic Bearing ◽  
Normal Operation ◽  
External Disturbances ◽  
Contact Conditions ◽  
Control Forces ◽  
Contact Free ◽  
Rotor Dynamic

Under normal operation a rotor spinning within an active magnetic bearing system will be levitated and hence rotor-stator contact conditions do not exist. In such a case, external disturbances and inherent unbalance will cause rotor responses that are maintained by the magnetic bearing control system to be within the clearance gap. However, magnetic bearings have limited dynamic load capacity due to magnetic material field saturation. Hence large external disturbances may be sufficient to cause the clearance gap to become closed and result in rotorstator contact. A touchdown bearing is usually incorporated as a sacrificial stator component to protect the expensive rotor, magnetic bearing and sensor components. Once contact has been made, rotor dynamic conditions may ensue resulting in persistent rotor bouncing or rubbing limit cycle responses. Prolonged exposure to these severe dynamics will cause touchdown bearing degradation and require regular replacement. A clear aim is therefore to restore contact-free levitation through available control capability in an efficient manner. This paper provides an analysis to gain an understanding of the uncontrolled rotor/touchdown contact dynamics. These will then be used to guide the control options that are available to restore contact-free levitation. The use of magnetic bearing control is appropriate if the required control forces are within saturation limits. It is also possible to actuate touchdown bearings and destabilize persistent rotor dynamic contact conditions. For example, piezo-based actuation offers larger control forces than those from magnetic bearing systems.

Surge Vibration-Induced Nonlinear Behavior Regulation of Power Amplifier for Magnetic Bearing in a 315 kW Centrifugal Compressor

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Yin Zhang ◽  
Shiqiang Zheng ◽  
Chen Ma ◽  
Cheng Chen ◽  
Can Wang
Keyword(s):  
Power Amplifier ◽  
Centrifugal Compressor ◽  
Load Capacity ◽  
Stable State ◽  
Magnetic Bearing ◽  
Rotating Stall ◽  
Active Magnetic Bearing ◽  
Stable Region ◽  
Experimental Investigations ◽  
The Stability

The severe vibration induced by surge and rotating stall is an obstacle to the stability of a magnetically suspended centrifugal compressor (MSCC). In order to suppress the severe vibration caused by surge instability, this paper focuses on compressor surge performance improvements enabled by power amplifier control improvements which result in increased dynamic load capacity (DLC) of the systems axial thrust magnetic bearing. A complete discrete-time model of the active magnetic bearing (AMB) power amplifier, composed of three piecewise linear intervals, is developed. A comprehensive view of the dynamic evolution process from stable state to bifurcation for the power amplifier is also analyzed. In order to stabilize the unstable periodic orbits in the power amplifier, a time-delay feedback control (TDFC) method is introduced to enhance the stability of the power amplifier, while the MSCC is subjected to the surge instability. Simulation results show that the stable region of the power amplifier is extended significantly using the TDFC method. Finally, the experimental investigations performed by an MSCC test rig demonstrate the effectiveness of the proposed solution under the conditions of modified surge and mild surge.

On the Stability Analysis of Active Magnetic Bearing With Parametric Uncertainty and Position Tracking Control

2016 ◽  
Author(s):  
Junya Kato ◽  
Kentaro Takagi ◽  
Tsuyoshi Inoue
Keyword(s):  
Tracking Control ◽  
Feedback Linearization ◽  
Disturbance Observer ◽  
Parametric Uncertainty ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Uncertain Parameters ◽  
Rigid Rotor ◽  
Pd Control ◽  
The Stability

This paper considers effect of the parametric uncertainty of an active magnetic bearing which is used to control a rigid rotor. In the feedback control law, PD control and feedback linearization is used. Firstly, this paper shows that one of the two uncertain parameters in the electromagnet model significantly affects the stability of the system. Moreover, this paper analytically shows a method to select the nominal value of the critical parameter affecting the stability. Next, while the shaft is rotating, this paper considers reducing vibration due to rotating unbalance by inversion-based disturbance observer and controlling position by feedforward control, besides PD control and feedback linearization. Based on the linearized model, this paper shows the performance degradation caused by the parametric error and investigates the tracking error experimentally. Finally, in order to improve the tracking performance under the existence of the uncertain parameters, this paper proposes to employ an inversion-based feedforward controller designed from the augmented control object, which includes the controlled object (rigid rotor and magnetic bearing), the disturbance observer and the feedback linearization. The experiment of tracking control of the rotor position is carried out to demonstrate the effectiveness of the proposed method.

An Evaluation of Stability Indices Using Sensitivity Functions for Active Magnetic Bearing Supported High-Speed Rotor

2006 ◽  
Vol 129 (2) ◽  
pp. 230-238 ◽  
Author(s):  
Naohiko Takahashi ◽  
Hiroyuki Fujiwara ◽  
Osami Matsushita ◽  
Makoto Ito ◽  
Yasuo Fukushima
Keyword(s):  
High Speed ◽  
Transfer Functions ◽  
Mimo System ◽  
Magnetic Bearing ◽  
Singular Value ◽  
Active Magnetic Bearing ◽  
Sensitivity Functions ◽  
Phase Lags ◽  
The Stability ◽  
Stability Indices

In active magnetic bearing (AMB) systems, stability is the most important factor for reliable operation. Rotor positions in radial direction are regulated by four-axis control in AMB, i.e., a radial system is to be treated as a multi-input multioutput (MIMO) system. One of the general indices representing the stability of a MIMO system is “maximum singular value” of a sensitivity function matrix, which needs full matrix elements for calculation. On the other hand, ISO 14839-3 employs “maximum gain” of the diagonal elements. In this concept, each control axis is considered as an independent single-input single-output (SISO) system and thus the stability indices can be determined with just four sensitivity functions. This paper discusses the stability indices using sensitivity functions as SISO systems with parallel/conical mode treatment and/or side-by-side treatment, and as a MIMO system with using maximum singular value; the paper also highlights the differences among these approaches. In addition, a conversion from usual x∕y axis form to forward/backward form is proposed, and the stability is evaluated in its converted form. For experimental demonstration, a test rig diverted from a high-speed compressor was used. The transfer functions were measured by exciting the control circuits with swept signals at rotor standstill and at its 30,000 revolutions/min rotational speed. For stability limit evaluation, the control loop gains were increased in one case, and in another case phase lags were inserted in the controller to lead the system close to unstable intentionally. In this experiment, the side-by-side assessment, which conforms to the ISO standard, indicates the least sensitive results, but the difference from the other assessments are not so great as to lead to inadequate evaluations. Converting the transfer functions to the forward/backward form decouples the mixed peaks due to gyroscopic effect in bode plot at rotation and gives much closer assessment to maximum singular value assessment. If large phase lags are inserted into the controller, the second bending mode is destabilized, but the sensitivity functions do not catch this instability. The ISO standard can be used practically in determining the stability of the AMB system, nevertheless it must be borne in mind that the sensitivity functions do not always highlight the instability in bending modes.

scholarly journals Development and Experimental Validation of Auxiliary Rolling Bearing Models for Active Magnetic Bearings (AMBs) Applications

2019 ◽  
Vol 2019 ◽  
pp. 1-19 ◽  
Author(s):  
Anna Tangredi ◽  
Enrico Meli ◽  
Andrea Rindi ◽  
Alessandro Ridolfi ◽  
Pierluca D’Adamio ◽  
...  
Keyword(s):  
Load Capacity ◽  
Critical Phenomenon ◽  
Magnetic Bearing ◽  
Design Tool ◽  
Magnetic Bearings ◽  
Active Magnetic Bearing ◽  
Active Magnetic Bearings ◽  
Short Period ◽  
Auxiliary Bearing ◽  
Bearing System

Nowadays, the search for increasing performances in turbomachinery applications has led to a growing utilization of active magnetic bearings (AMBs), which can bring a series of advantages thanks to their features: AMBs allow the machine components to reach higher peripheral speeds; in fact there are no wear and lubrication problems as the contact between bearing surfaces is absent. Furthermore, AMBs characteristic parameters can be controlled via software, optimizing machine dynamics performances. However, active magnetic bearings present some peculiarities, as they have lower load capacity than the most commonly used rolling and hydrodynamic bearings, and they need an energy source; for these reasons, in case of AMBs overload or breakdown, an auxiliary bearing system is required to support the rotor during such landing events. During the turbomachine design process, it is fundamental to appropriately choose the auxiliary bearing type and characteristics, because such components have to resist to the rotor impact; so, a supporting design tool based on accurate and efficient models of auxiliary bearings is very useful for the design integration of the Active Magnetic Bearing System into the machine. This paper presents an innovative model to accurately describe the mechanical behavior of a complete rotor-dynamic system composed of a rotor equipped with two auxiliary rolling bearings. The model, developed and experimentally validated in collaboration with Baker Hughes a GE company (providing the test case and the experimental data), is able to reproduce the key physical phenomena experimentally observed; in particular, the most critical phenomenon noted during repeated experimental combined landing tests is the rotor forward whirl, which occurs in case of high friction conditions and greatly influences the whole system behavior. In order to carefully study some special phenomena like rotor coast down on landing bearings (which requires long period of time to evolve and involves many bodies and degrees of freedom) or other particular events like impacts (which occur in a short period of time), a compromise between accuracy of the results and numerical efficiency has been pursued. Some of the elements of the proposed model have been previously introduced in literature; however the present work proposes some new features of interest. For example, the lateral and the axial models have been properly coupled in order to correctly reproduce the effects observed during the experimental tests and a very important system element, the landing bearing compliant suspension, has been properly modelled to more accurately describe its elastic and damping effects on the system. Furthermore, the model is also useful to characterize the frequencies related to the rotor forward whirl motion.

scholarly journals Research on Automatic Balance Control of Active Magnetic Bearing-Rigid Rotor System

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Yang Liu ◽  
Shuaishuai Ming ◽  
Siyao Zhao ◽  
Jiyuan Han ◽  
Yaxin Ma
Keyword(s):  
Vibration Control ◽  
Rotational Speed ◽  
Notch Filter ◽  
Magnetic Bearing ◽  
Rotor System ◽  
Vibration Response ◽  
Active Magnetic Bearing ◽  
Rigid Rotor ◽  
Phase Compensation ◽  
Synchronous Control

In this paper, in order to solve the problem of unbalance vibration of rigid rotor system supported by the active magnetic bearing (AMB), automatic balancing method is applied to suppress the unbalance vibration of the rotor system. Firstly, considering the dynamic and static imbalance of the rotor, the detailed dynamic equations of the AMB-rigid rotor system are established according to Newton’s second law. Then, in order to rotate the rotor around the inertia axis, the notch filter with phase compensation is used to eliminate the synchronous control current. Finally, the variable-step fourth-order Runge–Kutta iteration method is used to solve the unbalanced vibration response of the rotor system in MATLAB simulation. The effects of the rotational speed and phase compensation angle on the unbalanced vibration control are analysed in detail. It is found that the synchronous control currents would increase rapidly with the increase of rotational speed if the unbalance vibration cannot be controlled. When the notch filter with phase shift is used to balance the rotor system automatically, the control current is reduced significantly. It avoids the saturation of the power amplifier and reduces the vibration response of the rotor system. The rotor system can be stabilized over the entire operating speed range by adjusting the compensation phase of the notch filter. The method in the paper is easy to implement, and the research result can provide theoretical support for the unbalance vibration control of AMB-rotor systems.

Robust Active Chatter Control in Milling Processes With Variable Pitch Cutters

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
Tao Huang ◽  
Lijun Zhu ◽  
Shengli Du ◽  
Zhiyong Chen ◽  
Han Ding
Keyword(s):  
Nonlinear Differential Equations ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Linear Matrix ◽  
Variable Pitch ◽  
Stability Lobe ◽  
Milling Operations ◽  
Controller Gain ◽  
Chatter Control ◽  
The Stability

Milling chatters caused by the regenerative effect is one of the major limitations in increasing the machining efficiency and accuracy of milling operations. This paper studies robust active chatter control for milling processes with variable pitch cutters whose dynamics are governed by multidelay nonlinear differential equations. We propose a state feedback controller based on linear matrix inequality (LMI) approach that can enlarge multiple stability domains in the stability lobe diagram (SLD) while the controller gain is minimized. Numerical simulations of active magnetic bearing systems demonstrate the effectiveness of the proposed method.

Nonlinear Oscillation of a Rotor-AMB System With Time Varying Stiffness and Multi-External Excitations

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
M. Kamel ◽  
H. S. Bauomy
Keyword(s):  
Steady State ◽  
Order Approximation ◽  
Nonlinear Differential Equations ◽  
Steady State Solution ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Multiple Time ◽  
Time Varying ◽  
The Stability ◽  
Amb System

The rotor-active magnetic bearing system subjected to a periodically time-varying stiffness having quadratic and cubic nonlinearities is studied and solved. The multiple time scale technique is applied to solve the nonlinear differential equations governing the system up to the second order approximation. All possible resonance cases are deduced at this approximation and some of them are confirmed by applying the Rung–Kutta method. The main attention is focused on the stability of the steady-state solution near the simultaneous principal resonance and the effects of different parameters on the steady-state response. A comparison is made with the available published work.

Non-Linear Behaviors in the Motion of a Magnetically Supported Rotor on the Catcher Bearing During Levitation Loss: An Experimental Description

2002 ◽  
Author(s):  
E. N. Cuesta ◽  
V. R. Rastelli ◽  
L. U. Medina ◽  
N. I. Montbrun ◽  
S. E. Diaz
Keyword(s):  
Load Capacity ◽  
Magnetic Bearing ◽  
Normal Operation ◽  
Practical Implementation ◽  
Power Failure ◽  
Linear Behavior ◽  
Non Linear ◽  
Recent Developments ◽  
Emergency Stop ◽  
Industrial Level

Recent developments improving load capacity foretell the practical implementation of Active Magnetic Bearings (AMB) on industrial level, pushed by the advantages of reduced wear and higher speeds that they make available. However, the possibility of an eventual power failure forces the use of back-up (catcher) bearings, which usually are of the ball bearing type. The back-up bearings present a clearance between the shaft and the inner race, such that there is not contact during normal operation. On a power failure or an emergency stop, the rotor is only supported by the catcher bearings. Thus, the rotor motion within the clearance results on a succession of impacts, contact and non-contact intervals producing a non-linear behavior of the system. The complexity of this non-linear behavior prevents the use of traditional methods for the design of the catcher bearings, calling for the need of extensive experimentation and previous experience in their dimensioning process. Here, the response of a rigid rotor, supported by a pivot on the drive side and a magnetic bearing on the other side, is measured during the emergency stop from several operating speeds. Non-linear analysis tools, such as Poincare´ Maps and Bifurcation Diagrams, are employed to demonstrate the non-linear characteristics of the motion, which in some conditions is shown to become chaotic with a vibration limit cycle. The rotor motion on the catcher bearings (with the magnetic bearing deactivated) is measured at constant running speeds. The limit cycles and chaotic attractors are described, showing the relation of the non-linear effects to the rotational speed.

Nonlinear Vibration in a Vertical Rigid Rotor Supported by the Magnetic Bearing: Case Considering the Delays of Both Electric Current and Magnetic Flux

2007 ◽  
Author(s):  
Tsuyoshi Inoue ◽  
Motoki Sugiyama ◽  
Yasuhiko Sugawara ◽  
Yukio Ishida
Keyword(s):  
Magnetic Flux ◽  
Electric Current ◽  
Magnetic Force ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Nonlinear Phenomena ◽  
Control Force ◽  
Rigid Rotor ◽  
Rotating Speed ◽  
First Order

Active magnetic bearing (AMB) becomes to be widely used in various kinds of rotating machinery. However, as the magnetic force is nonlinear, nonlinear phenomena may occur when the rotating speed becomes higher and delay of control force increases. In this paper, the magnetic force is modeled by considering both the second order delay of the electric current and the first order delay of the magnetic flux, and the AMB force is represented by a power series function of the electric current and shaft displacement. The nonlinear theoretical analysis of the vertical rigid rotor supported by AMB is demonstrated. The effects of the delays and other AMB parameters on the nonlinear phenomena are clarified theoretically and experimentally.

Sign in / Sign up

Export Citation Format

Share Document