A New Approach for Health Monitoring and Detection of Shaft Crack Using an Active Magnetic Actuator During Steady-State Rotor Operation

Author(s):  
M. Kasarda ◽  
T. Bash ◽  
D. Quinn ◽  
G. Mani ◽  
D. Inman ◽  
...  

This work demonstrates the capability of an Active Magnetic Bearing (AMB) to be used as an actuator for interrogating a system by applying multiple forces to a rotating shaft in order to monitor and evaluate the associated responses to these inputs. Similar to modal analysis techniques which apply input signals to static structures in order to monitor responses to those inputs, this approach allows for the measurement of both input and output response in a rotating system for evaluation. However, unlike these techniques, the procedure developed here allows for multiple forms of force inputs to be applied to a rotating structure. This procedure facilitates the development of new improved techniques for diagnosing subtle changes in machinery health or for identifying faults that would potentially go undetected by conventional methods before failure. Although it is expected that this approach can be used in rotors supported in AMBs, the technique developed here uses an AMB on the rotor in conjunction with conventional support bearings. Therefore, this approach has the potential to be used on any rotating machine that can be designed or retrofitted with a single AMB actuator. To demonstrate this approach experimentally, a notched shaft was chosen to represent a shaft crack for identification purposes. Three cases were examined, including a healthy (unnotched) shaft, and three cases of a shaft with a mid-span notch extending to a depth of 10%, 25%, and 40% of shaft diameter, respectively. During testing, excitations up to 1000 Hz were applied via one axis of the AMB actuator to the four rotor cases while the rotor was operating at a steady-state speed of 2400 rpm, and corresponding responses were recorded at the proximity probes. No changes in the 1st or 2nd natural frequencies were detected, but distinct shifts in the 3rd natural frequency were detected from the Frequency Response Function (FRF) data. Since the vast majority of rotating machinery are designed to operate below the 3rd natural frequency, the effect of the notch on the 3rd natural frequency would not have been identified without the application of excitation forces through the AMB actuator. This paper represents an introduction to the new health monitoring approach and results presented here demonstrate the viability of the technique for detecting shaft cracks that might otherwise go undetected in typical steady-state vibration monitoring approaches.

2021 ◽  
Vol 143 (6) ◽  
Author(s):  
Shota Yabui ◽  
Hideyuki Inoue ◽  
Tsuyoshi Inoue

Abstract This study introduces a track-following controller design to measure the rotor dynamics (RD) coefficient of the annular seal using active magnetic bearings. The annular seal is implemented contiguously to prevent leakage of fluid between the rotating shaft and stationary area of a rotating machine. The force caused by the seal at the contact point can cause vibrations, which should be identified for designing rotating machinery. The RD force is coupled with mechanical and fluid dynamics. Moreover, the dynamics depend on the operating conditions of the rotating machine, namely, the rotating speed and orbit of the rotating shaft. This study proposes a control system for the active magnetic bearing to measure the RD force directly at the arbitrary operating condition. The main controller is designed to satisfy a criterion of the frequency characteristics of the rotating system. In addition, the control system employs adaptive feed-forward cancellation (AFC). This can estimate and compensate for the RD force in the control system simultaneously. The experimental results indicate that the control system can achieve an arbitrary operating condition and measure the RD coefficient of the annular seal in real-time. As a result, the RD coefficient is identified based on the equation of motion.


Author(s):  
Shota Yabui ◽  
Tsuyoshi Inoue

In this study, a measurement system is developed to analyze periodic external forces acting on a rotating machinery. The dynamics of a rotating machineries are influenced by various periodic external forces such as unbalanced forces, oil film forces at a journal bearing, and seal contact forces. The characteristics of periodic external forces are dependent on the rotating conditions, rotational speed, and rotating orbit of the rotating shaft. The proposed system employs an active magnetic bearing (AMB), which is implemented using an adaptive feed-forward cancellation (AFC). The use of AFC ensures that the proposed system can realize the desired harmonic orbit assuming actual operations under the periodic external forces. Moreover, AFC can measure the periodic external forces in real-time using an adaptive algorithm. The effectiveness of the proposed system is verified experimentally. Experimental results show that the control system can control the rotating shaft to an accuracy of micrometer order using the implemented AFC. The measurement error of the periodic external forces acting on the rotating system is less than 2%.


Author(s):  
Jerzy T. Sawicki ◽  
Dmitry L. Storozhev ◽  
John D. Lekki

This paper addresses self-diagnostic properties of AMB (active magnetic bearing) supported rotors for on-line detection of the transverse crack on a rotating shaft. In addition to pure levitation, the rotor supporting bearing also serves as an actuator that transforms current signals additionally injected into the control loop into the superimposed specially selected excitation forces into the suspended rotor. These additional excitations induce combination frequencies in the rotor response, providing unique signatures for the presence of crack. The background of theoretical modeling, experimental and computer simulation results for the AMB supported cracked rotor with self-diagnostic excitation forces are presented and discussed.


2009 ◽  
Vol 131 (3) ◽  
Author(s):  
M. Kamel ◽  
H. S. Bauomy

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.


Author(s):  
Wei Zhang ◽  
Jean W. Zu

In this two-part paper, we investigate nonlinear dynamics in the rotor-active magnetic bearings (AMB) system with 8-pole legs and the time-varying stiffness. The model of parametrically excited two-degree-of-freedom nonlinear system with the quadratic and cubic nonlinearities is established to explore the periodic and quasiperiodic motions as well as the bifurcations and chaotic dynamics of the system. The method of multiple scales is used to obtain the averaged equations in the case of primary parameter resonance and 1/2 subharmonic resonance. In Part I of the companion paper, numerical approach is applied to the averaged equations to find the periodic, quasiperiodic solutions and local bifurcations. It is found that there exist 2-period, 3-period, 4-period, 5-period, multi-period and quasiperiodic solutions in the rotor-AMB system with 8-pole legs and the time-varying stiffness. The catastrophic phenomena for the amplitude of nonlinear oscillations are first observed in the rotor-AMB system with 8-pole legs and the time-varying stiffness. The procedures of motion from the transient state chaotic motion to the steady state periodic and quasiperiodic motions are also found. The results obtained here show that there exists the ability of autocontrolling transient state chaos to the steady state periodic and quasiperiodic motions in the rotor-AMB system with 8-pole legs and the time-varying stiffness.


Author(s):  
Hiroki Manabe ◽  
Shota Yabui ◽  
Hideyuki Inoue ◽  
Tsuyoshi Inoue

In turbomachinery, seals are used to prevent fluid leakage. At seal part, rotordynamic fluid force (RD fluid force), which causes whirling motion of rotor, is generated. Under certain conditions, the RD fluid force may contribute to instability of the machine. There are several cases that the whirling is accompanied by eccentricity due to the influence of gravity, or the whirling orbit becomes elliptical due to the influence of the bearing support anisotropy. In these cases, mathematical modeling of the RD fluid forces becomes increasingly complex. As a result, the RD fluid force measurement is more preferable. To improve the measurement and evaluation technology of the RD fluid force, a method to arbitrarily control whirling of the orbit is required. In this paper, RD fluid force measurement by controlling the shape of the orbit using an active magnetic bearing (AMB) is proposed. A contact type mechanical seal is used as a test specimen. When the rotating shaft is whirling, the RD fluid force due to hydrodynamics lubrication and the frictional force due to contact occur on the sliding surface. The resultant force of these forces is taken as the reaction force of mechanical seal and the measurement is performed. The measured reaction force of the mechanical seal is compared with simulation results and the validity of the proposed measurement method is confirmed.


Author(s):  
Norihisa Anegawa ◽  
Hiroyuki Fujiwara ◽  
Osami Matsushita

The turbine generator requires sufficient reliability as a major component of the power plant. The rotor dynamics calculates the critical speed of the shaft-bearing system for design to avoid appearance of the critical speed, while the blade dynamics calculates the natural frequency of the blade to avoid nX resonance. For longer blades, however, the lower natural frequency requires that the design of the shaft and blade takes into account the coupling of the blade vibration mode with nodal diameter k = 0 and k = 1 with the vibration of the shaft. The present work analyzes the coupling of the parallel motion of the shaft with the in-plane vibration of the blade within k = 1 modes. More specifically, the existence of an unstable region due to coupling and the coupled resonance in an eight-blade (N = 8) where each blade is assumed to be a 1-DOF mass-spring system were analyzed in detail. Analysis was also made on the forced vibration of a stable damped system. At a rotational speed Ω = |ωs − ωb|, the vibration of the shaft was limited to a relatively small amplitude due to anti-resonance points resulting from the dynamic vibration absorber effect, while the resonance of the blades was relatively big amplitude. A violent coupled resonance resulting from the dynamic absorber effect of the blades and shaft was observed at a rotational speed Ω = ωs + ωb. The resonance in blade vibration at Ω = |ωb − ωs| was experimentally confirmed.


1998 ◽  
Vol 120 (2) ◽  
pp. 596-606 ◽  
Author(s):  
X. Wang ◽  
S. Noah

This study concerns the dynamic response of a rotor landed on auxiliary (catcher) bearings in an Active Magnetic Bearing (AMB) supported rotor, following postulated loss of power or overload of the AMB. An analytical model involving a disk, a shaft and auxiliary bearings on damped flexible supports is constructed and appropriate equations of the nonlinear dynamic system are developed. The equations include a switch function to indicate contact/non-contact events and determine the existence of contact normal forces and tangential friction forces between the shaft and the bearings. Steady state solutions are obtained. An analytical method was formulated and used to yield solutions for cases with well balanced rotors, in absence of any side forces. The Fixed Point Algorithm (FPA) is used to obtain steady state periodic solutions of the unbalanced rotor for various parameters. The FPA is used to determine the stability of the periodic solutions and the type of bifurcation involved. Multiple periodic solutions, quasi-periodic and chaotic responses are detected and discussed. A set of preliminary guidelines for selection of the parameters of the catcher bearings is given.


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