Magnetic Bearing Sizing for Flexible Rotors

1992 ◽  
Vol 114 (2) ◽  
pp. 223-229 ◽  
Author(s):  
E. H. Maslen ◽  
P. E. Allaire
Keyword(s):  
Critical Speed ◽  
Load Capacity ◽  
Magnetic Bearing ◽  
Flexible Rotor ◽  
Rotor Systems ◽  
Motion Constraints ◽  
Mass Unbalance ◽  
Flexible Rotors ◽  
Bearing Load ◽  
External Loads

Magnetic bearing load capacity in flexible rotor systems must be adequate to accommodate external loads acting on the rotor. The first part of this paper develops the theoretical basis for computing the bearing load capacity requirements of flexible rotors subject to bounded external harmonic loads and strict motion constraints. The second part of this work illustrates the application of the theory to a specific example: a fairly simple three disk flexible rotor subject to mass unbalance loads. Load capacity requirements are computed for the example shaft at its first three free-free forward whirl critical speeds. Based on the bounds obtained, two bearing design cases are examined: one with 45 N load capacity and the other with 223 N load capacity. The performance of the rotor is not improved with the higher capacity bearing and neither is capable of adequately constraining the rotor at its second critical speed. It is concluded that this shaft cannot be operated above its second free-free critical speed without a midspan bearing.

Rotor vibration with auxiliary bearing contact in magnetic bearing systems Part 1: Synchronous dynamics

2003 ◽  
Vol 217 (4) ◽  
pp. 377-392 ◽  
Author(s):  
P S Keogh ◽  
M O T Cole
Keyword(s):  
Position Control ◽  
Magnetic Bearing ◽  
Physical Interaction ◽  
Flexible Rotor ◽  
Rotor Vibration ◽  
Full Control ◽  
Flexible Rotors ◽  
Bearing Contact ◽  
Auxiliary Bearing ◽  
Control Capability

Magnetic bearing systems incorporate auxiliary bearings to prevent physical interaction between rotor and stator laminations. Rotor/auxiliary bearing contacts may occur when a magnetic bearing still retains a full control capability. To actively return the rotor to a non-contacting state it is essential to determine the manner in which contact events affect the rotor vibration signals used for position control. An analytical procedure is used to assess the nature of rotor contact modes under idealized contacts. Non-linearities arising from contact and magnetic bearing forces are then included in simulation studies involving rigid and flexible rotors to predict rotor response and evaluate rotor synchronous vibration components. An experimental flexible rotor/magnetic bearing facility is also used to validate the predictions. It is shown that changes in synchronous vibration amplitude and phase induced by contact events causes existing controllers to be ineffective in attenuating rotor displacements. These findings are used in Part 2 of the paper as a foundation for the design of new controllers that are able to recover rotor position control under a range of contact cases.

Aseismic Vibration Control of Flexible Rotors Using Active Magnetic Bearing

2001 ◽  
Vol 124 (1) ◽  
pp. 49-57 ◽  
Author(s):  
Osami Matsushita ◽  
Toshio Imashima ◽  
Yoshitaka Hisanaga ◽  
Hiroki Okubo
Keyword(s):  
Seismic Waves ◽  
Control Method ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Flexible Rotor ◽  
Feed Forward Control ◽  
Kobe Earthquake ◽  
Flexible Rotors ◽  
Additional Control ◽  
Modal Model

The wide application of active magnetic bearing (AMB) requires an aseismic evaluation with respect to AMB rotor vibrations caused by actual earthquakes. A flexible rotor supported by AMB is selected for this purpose. A shaking simulation obtained using the quasi-modal model and the actual Kobe earthquake was completed. A corresponding test rotor was excited by seismic waves and the resulting vibration was measured for the vibration evaluation. In order to reduce the response severity against earthquakes, we propose an additional feed forward control method which is proportional to the signal detected by the accelerometers attached to the bearing housings. Since this additional control can cancel rotor vibration generated by the earthquakes, AMB rotor vibrations are successfully suppressed at a low level.

Modelling of Magnetic Fields with the Finite Element Method in Machine Diagnostic Systems

2009 ◽  
Vol 147-149 ◽  
pp. 155-160 ◽  
Author(s):  
Jakub Łagodziński
Keyword(s):  
Load Capacity ◽  
Active Vibration Control ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
The Finite Element Method ◽  
Diagnostic Systems ◽  
Bearing Load ◽  
Switch System ◽  
Active Vibration ◽  
The Magnetic Field

Two issues are discussed in the paper. The first one concerns the FEM modelling of the magnetic field enclosing the permanent magnet – reed switch system. The system works as the motion detection device of the hydraulic servoactuator distributor to improve the helicopter steering reliability and flight safety. The second one describes optimization of the active magnetic bearing (AMB) design with the FEM. The optimization has two goals: weight reduction and bearing load capacity. The bearing is applied to active vibration control of helicopter flexible tail rotor shaft.

Measured and Predicted Force and Stiffness Characteristics of Industrial Magnetic Bearings

1991 ◽  
Vol 113 (4) ◽  
pp. 784-788 ◽  
Author(s):  
J. Imlach ◽  
B. J. Blair ◽  
P. E. Allaire
Keyword(s):  
Critical Speed ◽  
Closed Loop ◽  
Load Capacity ◽  
Magnetic Bearing ◽  
Magnetic Bearings ◽  
Dynamic Loadings ◽  
On Line ◽  
Stiffness Characteristics ◽  
Canned Motor ◽  
Displacement Information

Closed-loop stiffness and load capacity (force) equations have been developed for industrial magnetic bearings. Two sets of magnetic bearings have been constructed using these equations as a design basis. These bearings have been installed in two canned motor pumps. The predicted force and stiffness values from the equations are compared to experimental measurements to determine their validity. When obvious sources of error were eliminated, agreement within 10 percent was obtained for development pump’s magnetic bearings. Agreement was generally better for this pump than for the demonstration pump. By employing these equations, along with easily measured current and displacement information from magnetic bearing equipped machinery, actual stiffness’ and bearing loadings can be determined for operating equipment. Thus, the range of information available from magnetic bearings is extended to include static and dynamic loadings as well as shaft orbits and critical speed and damping information (Humphris et al., 1989). This enhances their use as diagnostic and preventative maintenance tools which are built into machinery and can be used on line.

Balancing of Flexible Rotors Having Arbitrary Mass and Stiffness Distribution

1966 ◽  
Vol 88 (2) ◽  
pp. 217-223 ◽  
Author(s):  
M. S. Hundal ◽  
R. J. Harker
Keyword(s):  
Dynamic Response ◽  
Normal Modes ◽  
Flexible Rotor ◽  
Arbitrary Mass ◽  
Suggested Procedure ◽  
Mass Unbalance ◽  
Flexible Rotors ◽  
Balance Corrections ◽  
Stiffness Distribution ◽  
Rotor Axis

A method for balancing a flexible rotor is developed which is based upon the dynamic response of the rotor in its normal modes as excited by the distributed mass unbalance. The balance corrections are determined by equating the modal components of the corrections to the modal components of the unbalance of the rotor. Methods of balancing individual modes as well as simultaneous balancing in any number of modes are presented. The suggested procedure requires calculation of the normal modes and critical speeds, and measurement of the dynamic amplitude at selected points along the rotor axis.

Should a Flexible Rotor Be Balanced in N or (N + 2) Planes?

1972 ◽  
Vol 94 (2) ◽  
pp. 548-558 ◽  
Author(s):  
W. Kellenberger
Keyword(s):  
Critical Speed ◽  
System Of Equations ◽  
Flexible Rotor ◽  
Orthogonal Functions ◽  
Linear System Of Equations ◽  
Flexible Rotors ◽  
Speed Range ◽  
Set Up ◽  
Limiting Case ◽  
Analytical Expressions

The problem of balancing flexible rotors consists mainly of eliminating rotating bearing forces. Analytical expressions are derived for the deformation and the rotating bearing forces of a rotor, using orthogonal functions. With this kind of representation it is possible to set up simple conditions for the vanishing rotating bearing forces. They lead to a linear system of equations giving the compensating unbalances in each of a set number of balancing planes. Two methods used in practice are theoretically explained and compared. The “N” method employs N planes for balancing a speed range up to, and including, the Nth critical speed and can be characterized by the condition A = 0, see equation (13). The “(N + 2)” method requires two more planes for the same speed range and is characterized by A = 0 and B = 0. It is proved that limlimN→∞B=0, so that in the limiting case of an infinite number of balancing planes (speed range from zero to infinity) both methods are of equal value. The two methods differ for finite N in their accuracy and the amount of calculation. Considering simple examples with known unbalance distribution it will be shown that the main error of the N method is the result of treating B as equal to 0, which it is not, thus accounting for the greater accuracy of the N + 2 method. The additional effort needed for the latter method is justified in those cases where greater accuracy is demanded.

scholarly journals Chaos of flexible rotor system with critical speed in magnetic bearing based on the improved precise Runge–Kutta hybrid integration

2018 ◽  
Vol 10 (9) ◽  
pp. 168781401880085 ◽  
Author(s):  
Xi Fang ◽  
Dongbo Zhang ◽  
Xiaoyu Zhang ◽  
Huachun Wu ◽  
Fei Gao ◽  
...  
Keyword(s):  
Critical Speed ◽  
Integration Method ◽  
Magnetic Bearing ◽  
Rotor System ◽  
Kutta Method ◽  
Hybrid Integration ◽  
Flexible Rotor ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Bearing System

Magnetic rotor-bearing system has drawn great attention because of its several advantages compared to existent rotor-bearing system, and explicit Runge–Kutta method has achieved good results in solving dynamic equation. However, research on flexible rotor of magnetic bearing is relatively less. Moreover, explicit Runge–Kutta needs a smaller integral step to ensure the stability of the calculation. In this article, we propose a nonlinear dynamic analysis of flexible rotor of active magnetic bearing established by using the finite element method. The precise Runge–Kutta hybrid integration method and the largest Lyapunov exponent are used to analyze the chaos of the rotor system at the first- and second-order critical speed of the rotor. Experiment on chaos analysis has shown that compared with the explicit Runge–Kutta method, the precise Runge–Kutta hybrid integration method can improve the convergence step of calculation significantly while avoiding iterative solution and maintain high accuracy which is four times the increase of the integral step.

scholarly journals Unbalance Estimation for a Large Flexible Rotor Using Force and Displacement Minimization

Machines ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 39
Author(s):  
Tuhin Choudhury ◽  
Risto Viitala ◽  
Emil Kurvinen ◽  
Raine Viitala ◽  
Jussi Sopanen
Keyword(s):  
Industrial Applications ◽  
Estimation Accuracy ◽  
Test Case ◽  
Paper Machine ◽  
Flexible Rotor ◽  
Modal Expansion ◽  
Mass Unbalance ◽  
Flexible Rotors ◽  
Paper Machines ◽  
Equivalent Load

Mass unbalance is one of the most prominent faults that occurs in rotating machines. The identification of unbalance in the case of large flexible rotors is crucial because in industrial applications such as paper machines and roll grinders, high vibrations can adversely affect the quality of the end product. The objective of this research is to determine the unbalance location, magnitude and phase for a large flexible rotor with few measured coordinates. To this end, an established force-based method comprising of modal expansion and equivalent load minimization is applied. Due to the anisotropic behavior of the test rotor, the force method required at least six measured coordinates to predict the unbalance with an error of 4 to 36%. To overcome this limitation, an alternate method, eliminating the use of modal expansion, is proposed. Here, displacements generated by varying the location of a reference unbalance along the rotor axis, are compared to measured displacements to detect the unbalance location. Furthermore, instead of force-based fault models, the minimization of displacements at measured locations determines the unbalance parameters. The test case in this study is the guiding roll of a paper machine and its different unbalance states. The algorithm is tested initially with a simulation-based model and then validated with an experimental set up. The results show that the displacement method can locate the unbalance close to the actual location and it can predict the unbalance magnitude and phase with only two measured coordinates. Lastly, using measured data from 15 measurement points across the tube section of the test rotor, a comparison shows how the selection of the two measured locations affects the estimation accuracy.

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