scholarly journals Modelling and Simulation of Nonlinear Jump Phenomena of a Non-ideal Rotor Involving Fractional Order PD Controller

2021 ◽  
Vol 2115 (1) ◽  
pp. 012029
Author(s):  
Gaurav Ghosh ◽  
Abhishek Kumar Jha ◽  
Sovan Sundar Dasgupta
Keyword(s):  
High Speed ◽  
Transient Analysis ◽  
Input Power ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Pd Controller ◽  
Sommerfeld Effect ◽  
Locus Method ◽  
Novel Approach ◽  
Jump Phenomena

Abstract Rotating machinery with high speed powered by industrial motors frequently suffers from instability by exhibiting non-linear jump phenomena, formally known as Sommerfeld effect. The drives whose excitation is a function of the system responses, referred to as non-ideal. The system dynamics of such systems exhibit a couple of complex and interesting features when the input power exceeds a critical value. The present research suggests a novel approach to study the efficacy of active magnetic bearing with fractional PD controller to suppress the instability caused by the Sommerfeld effect. The steady-state results obtained by solving the system characteristic equation numerically is compared with the transient analysis. Finally, root locus method is introduced to obtain the bifurcation points at which this kind of instability completely disappears.

An Improved Catcher Bearing Model and an Explanation of the Forward Whirl/Whip Phenomenon Observed in Active Magnetic Bearing Transient Drop Experiments

2013 ◽  
Author(s):  
Jason Wilkes ◽  
Giuseppe Vannini ◽  
Jeff Moore ◽  
David Ransom
Keyword(s):  
High Speed ◽  
Experimental Tests ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Constant Frequency ◽  
Axial Thrust ◽  
Novel Approach ◽  
Transient Simulations ◽  
The Coefficient Of Friction ◽  
Reaction Forces

Though many approaches have been proposed in the literature to model the reaction forces in a catcher bearing (CB), there are still phenomena observed in experimental tests that cannot be explained by existing models. The following paper presents a novel approach to model a CB system. Some of the elements in the model have been previously introduced in the literature; however, there are other elements in the proposed model that are new, providing an explanation for the forward whirling phenomena that has been observed repeatedly in the literature. The proposed CB model is implemented in a finite element rotordynamic package, and nonlinear time-transient simulations are performed to predict published experimental results of a high speed vertical sub-scale compressor; with no other forces present in the model, the agreement between simulations and experimental data is favorable. The results presented herein show that friction between the journal and axial face of the catcher bearing results in a forward cross-coupled force that pushes the rotor in the direction of rotation. This force is proportional to the coefficient of friction between the axial face of the rotor and catcher bearing and the axial thrust on the rotor. This force results in synchronous whirl when the running speed is below a combined natural frequency of the rotor-stator system, and constant frequency whip when the speed is above a whip frequency.

An Improved Catcher Bearing Model and an Explanation of the Forward Whirl/Whip Phenomenon Observed in Active Magnetic Bearing Transient Drop Experiments

2013 ◽  
Vol 136 (4) ◽  
Author(s):  
Jason Wilkes ◽  
Jeff Moore ◽  
David Ransom ◽  
Giuseppe Vannini
Keyword(s):  
High Speed ◽  
Experimental Tests ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Constant Frequency ◽  
Axial Thrust ◽  
Novel Approach ◽  
Transient Simulations ◽  
The Coefficient Of Friction ◽  
Reaction Forces

Though many approaches have been proposed in the literature to model the reaction forces in a catcher bearing (CB), there are still phenomena observed in experimental tests that cannot be explained by existing models. The following paper presents a novel approach to model a CB system. Some of the elements in the model have been previously introduced in the literature; however, there are other elements in the proposed model that are new, providing an explanation for the forward whirling phenomena that has been observed repeatedly in the literature. The proposed CB model is implemented in a finite-element rotordynamic package, and nonlinear time-transient simulations are performed to predict published experimental results of a high-speed vertical subscale compressor; with no other forces present in the model, the agreement between simulations and experimental data is favorable. The results presented herein show that friction between the journal and axial face of the catcher bearing results in a forward cross-coupled force that pushes the rotor in the direction of rotation. This force is proportional to the coefficient of friction between the axial face of the rotor and catcher bearing and the axial thrust on the rotor. This force results in synchronous whirl when the running speed is below a combined natural frequency of the rotor-stator system and constant frequency whip when the speed is above a whip frequency.

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.

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.

Controlling Journal Bearing Instability Using Active Magnetic Bearings

2007 ◽  
Author(s):  
A. El-Shafei ◽  
A. S. Dimitri
Keyword(s):  
Journal Bearing ◽  
Magnetic Bearing ◽  
Journal Bearings ◽  
Active Magnetic Bearing ◽  
Rotating Speed ◽  
Damping Characteristics ◽  
Oil Whip ◽  
Novel Approach ◽  
Oil Whirl ◽  
Load Carrying

Journal Bearings are excellent bearings due to their large load carrying capacity and favorable damping characteristics. However, Journal bearings are known to be prone to instabilities. The oil whirl and oil whip instabilities limit the rotor maximum rotating speed. In this paper, a novel approach is used to control the Journal bearing (JB) instability. An Active Magnetic Bearing (AMB) is used to overcome the JB instability and to increase its range of operation. The concept is quite simple: rather than using the AMB as a load carrying element, the AMB is used as a controller only, resulting in a much smaller and more efficient AMB. The load carrying is done by the Journal bearings, exploiting their excellent load carrying capabilities, and the JB instability is overcome with the AMB. This results in a combined AMB/JB that exploits the advantages of each device, and eliminates the deficiencies of each bearing. Different controllers for the AMB to control the JB instability are examined and compared theoretically and numerically. The possibility of collocating the JB and the AMB is also examined. The results illustrate the effectiveness of the concept.

Dynamic Analysis for the Rotor Drop Process and Its Application to a Vertically Levitated Rotor/Active Magnetic Bearing System

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Yulan Zhao ◽  
Guojun Yang ◽  
Patrick Keogh ◽  
Lei Zhao
Keyword(s):  
High Speed ◽  
Sliding Friction ◽  
Engineering Application ◽  
Magnetic Bearing ◽  
Contact Forces ◽  
Active Magnetic Bearing ◽  
Detailed Model ◽  
Vertical Rotor ◽  
Auxiliary Bearing ◽  
Rotor Dynamic

Active magnetic bearings (AMBs) have been utilized widely to support high-speed rotors. However, in the case of AMB failure, emergencies, or overload conditions, the auxiliary bearing is chosen as the backup protector to provide mechanical supports and displacement constraints for the rotor. With lack of support, the auxiliary bearing will catch the dropping rotor. Accordingly, high contact forces and corresponding thermal generation due to mechanical rub are applied on the dynamic contact area. Rapid deterioration may be brought about by excessive dynamic and thermal shocks. Therefore, the auxiliary bearing must be sufficiently robust to guarantee the safety of the AMB system. Many approaches have been put forward in the literature to estimate the rotor dynamic motion, nonetheless most of them focus on the horizontal rotor drop and few consider the inclination around the horizontal plane for the vertical rotor. The main purpose of this paper is to predict the rotor dynamic behavior accurately for the vertical rotor drop case. A detailed model for the vertical rotor drop process with consideration of the rotating inclination around x- and y-axes is proposed in this paper. Additionally, rolling and sliding friction are distinguished in the simulation scenario. This model has been applied to estimate the rotor drop process in a helium circulator system equipped with AMBs for the 10 MW high-temperature gas-cooled reactor (HTR-10). The HTR-10 has been designed and researched by the Institute of Nuclear and New Energy Technology (INET) of Tsinghua University. The auxiliary bearing is utilized to support the rotor in the helium circulator. The validity of this model is verified by the results obtained in this paper as well. This paper also provides suggestions for the further improvement of auxiliary bearing design and engineering application.

A Contribution on the Investigation of the Dynamic Behaviour of Rotating Shafts With a Hybrid Magnetic Bearing Concept (HMBC) for Blower Application

2008 ◽  
Author(s):  
Martin Gronek ◽  
Torsten Rottenbach ◽  
Frank Worlitz
Keyword(s):  
Energy Supply ◽  
High Speed ◽  
Experimental Tests ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Analytical Models ◽  
Test Facility ◽  
Reactor Technology ◽  
Rotating Shafts ◽  
Technical Features

Within a subproject of the RAPHAEL-Program, which is part of the 6th EURATOM Framework Program supervised by the European Commission it was investigated whether the use of a Hybrid Magnetic Bearing Concept (HMBC) will be beneficial for a blower application. As in the RAPHAEL program the subproject “Component Development” deals with R&D on components of High Temperature Reactor Technology (HTR), a major focus is on safety- and reliability-related issues. That implies special requirements for the support of high speed rotating shafts in HTR-Applications that only can be satisfied by using Active Magnetic Bearings (AMB). Regarding safety and competitiveness, AMBs are considered key components for the support of rotating HTR-components due to their technical features. AMBs are characterized by an electromagnetic actuator that is generating the bearing force depending on the clearance between stator and rotor, in which the rotor is levitated. Therefore an active control of the coil current is necessary. Furthermore, Touch Down Bearings (TDB) are needed to avoid damages in case of an emergency shut down or in case of energy supply losses. This contribution provides an internal insight on the advantages of a Hybrid Magnetic Bearing Concept that is characterized by a completely Active Magnetic Bearing-supported vertical arranged rotor and an additional permanent magnetic Radial Bearing. One benefit of the HMBC is an additional radial guidance of the shaft that may reduce the loads while dropping into the Touch Down Bearings e.g. in case of energy supply losses of the AMBs. Reduced loads on the TDBs will increase their life cycle and the availability of the AMB supported component. The Scope of this R&D-Project, which will be described more detailed in this contribution, includes the analytical modeling and simulation of the dynamic behavior of the Hybrid Magnetic Bearing System, the modification of the completely AMB-supported test facility FLP500 with a radial PMB and the experimental tests and validation of the analytical models to provide recommendations for the investigated blower application as an HTR-component. Furthermore, the effects occurring during the modification of the test facility and the approach that was necessary to solve unexpected problems will be described.

High-Precision Cutting Tool Tracking With a Magnetic Bearing Spindle

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Alexander Smirnov ◽  
Alexander H. Pesch ◽  
Olli Pyrhönen ◽  
Jerzy T. Sawicki
Keyword(s):  
Pid Control ◽  
Disturbance Rejection ◽  
High Speed ◽  
Cutting Tool ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
External Loading ◽  
Reference Tracking ◽  
Tool Position ◽  
Tool Tracking

A method is presented for tool tracking in active magnetic bearing (AMB) spindle applications. The method uses control of the AMB air gap to achieve the desired tool position. The reference tracking problem is transformed from the tool coordinates into the AMB control axes by bearing deflection optimization. Therefore, tool tracking can be achieved by an off-the-shelf AMB controller. The method is demonstrated on a high-speed AMB boring spindle with a proportional integral derivative (PID) control. The hypothetical part geometries are traced in the range of 30 μm. Static external loading is applied to the tool to confirm disturbance rejection. Finally, a numerical simulation is performed to verify the ability to control the tool during high-speed machining.

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