Vibration Control of Spur Geared Rotor Systems With Transmission Errors by Active Magnetic Bearings

2019 ◽  
Author(s):  
Gargi Majumder ◽  
Rajiv Tiwari
Keyword(s):  
Vibration Control ◽  
Transmission Error ◽  
Magnetic Bearings ◽  
Physical Contact ◽  
Vibration Measurement ◽  
Mesh Deformation ◽  
Control Force ◽  
Active Magnetic Bearings ◽  
Full Spectrum ◽  
Gear Mesh

Abstract Dynamic forces between the mating gears are generated due to the mesh deformation, gear eccentricities, transmission error, and gear run-out, which cause excessive vibration and noise. Study and control of these forced vibrations in gear box are vital to prevent any adverse effects on the gears and its supporting structures. Hence, this work presents a novel concept of active vibration control by introducing Active Magnetic Bearings (AMBs) on the shaft of a spur gearbox having conventional bearings as well. The AMB suppresses the response of the system by generating controlled electromagnetic forces based on the gear shaft vibration measurement. The AMB force is applied without any physical contact as opposed to mechanical forces in conventional bearings. A coupled torsional-lateral vibration analysis has been simulated with the effects of mesh deformation, gear eccentricities, transmission error, and gear run-out. The electromagnetic actuator is designed in such a way that a resultant radial control force can be developed with the help of forces in two mutually perpendicular directions. With a feedforward PID controller, the transverse vibration amplitude is observed to be suppressed to a considerable level. The frequency domain analysis is done using a full spectrum, which shows that multiple harmonics of gear mesh frequency is minimized simultaneously.

Transverse Vibration of Geared-Rotor Integrated With Active Magnetic Bearings in Identification of Multiple Faults

2021 ◽  
Vol 143 (9) ◽  
Author(s):  
Gargi Majumder ◽  
Rajiv Tiwari
Keyword(s):  
Mathematical Model ◽  
Transverse Vibration ◽  
Transmission Error ◽  
Magnetic Bearings ◽  
Mesh Deformation ◽  
Identification Algorithm ◽  
Active Magnetic Bearings ◽  
Full Spectrum ◽  
Gear Mesh ◽  
Fault Parameters

Abstract This paper presents a novel concept of the modeling, active control of transverse vibration responses, and identification of fault parameters in a geared-rotor system integrated with active magnetic bearings (AMBs). The sources of error in gears while in the operation are the gear mesh deformation, transmission error, and runout, resulting in dynamic forces, excessive vibration, and noise. To avoid any undesirable effect on the gear-pair and other supporting structures, it is essential to investigate these forced vibrations in time and frequency domain. Hence, an approach to monitor and control the transverse vibration of mating gears is presented with the help of AMBs. The AMBs are capable of suppressing the vibration of the system (transients as well as steady-state) by controlled electromagnetic forces considering the rotor vibrational displacement with a closed-loop feedback system. A mathematical model has been developed with geared rotor faults, like the mesh deformation, gear run-out, and asymmetric transmission error. The transmission error has been modeled as the sum of mean and varying components of error in two orthogonal transverse directions. Based on the mathematical model, an identification algorithm has been developed. Considering full spectrum analysis of the rotor vibration and AMB current information, estimation of system parameters, i.e., the equivalent mesh stiffness, mesh damping, gear runouts, the mean and varying transmission error magnitude and phase angles, and the current and displacement constants of AMBs has been performed. Gaussian noise in responses and modeling errors in mathematical models have been added to test the robustness of the proposed algorithm to comply with the experimental settings.

Characteristic Parameters Estimation of Active Magnetic Bearings in a Coupled Rotor System

2019 ◽  
Vol 4 (3) ◽  
Author(s):  
Sampath Kumar Kuppa ◽  
Mohit Lal
Keyword(s):  
Numerical Technique ◽  
Forced Response ◽  
Rotor System ◽  
Parameters Estimation ◽  
Magnetic Bearings ◽  
Fast Fourier Transformation ◽  
Active Magnetic Bearings ◽  
Least Squares Regression ◽  
Characteristic Parameters ◽  
Full Spectrum

Abstract Present research inspects the performance of rotor–bearing–coupling system in the presence of active magnetic bearings (AMBs). A methodology is suggested to quantify various fault characteristics along with AMB characteristic parameters of a coupled turbine generator system. A simplest possible turbogenerator system is modeled to analyze coupling misalignment. Conventional methodology to estimate dynamic system parameters based on forced response information is not enough for AMB-integrated rotor system because it requires current information along with displacement information. The controlling current of AMB is tuned and controlled with a controller of proportional–integral–derivative (PID) type. A numerical technique (Lagrange's equation) is applied to get equations of motion (EOM). Runge–Kutta technique is used to obtain EOM to acquire the time domain responses. The fast Fourier transformation (FFT) is applied on obtained responses to acquire responses in the frequency domain, and full spectrum technique is applied to propose the methodology. A methodology that depends on the least squares regression approach is proposed to evaluate the multifault parameters of AMB-integrated rotor system. The robustness of the algorithm is checked against various levels of noise and modeling error and observed efficient. An appreciable reduction in misalignment forces and moments is observed by using AMBs.

The Oil-Free Shaft Line

1988 ◽  
Author(s):  
Bruno Wagner
Keyword(s):  
Vibration Control ◽  
Magnetic Bearing ◽  
Magnetic Bearings ◽  
Active Magnetic Bearing ◽  
Active Magnetic Bearings ◽  
Present Stage ◽  
Shaft Line ◽  
Process Gas ◽  
Gas Seals ◽  
Length Reduction

This paper recalls the principles and main features of the active magnetic bearings and especially the advantages for turbomachines. Oil-free working and vibration control are part of them. Field experiences are described for different shaft line configurations. Step by step we are going to get totally rid of oil with the introduction of active magnetic bearings together with dry gas seals and gearless drive. Future machines will take the benefit of all this field experience. The trend of the design optimization is the active magnetic bearings in the process gas itself, for a length reduction of shafts. But at the present stage, the active magnetic bearing is a proven technology today.

Two-Level Control Structure of Magnetic Bearings

1993 ◽  
Vol 5 (5) ◽  
pp. 438-442 ◽  
Author(s):  
Nobuyoshi Taguchi ◽  
◽  
Takakazu Ishimatsu ◽  
Takashi Shimomachi ◽  
◽  
...  
Keyword(s):  
Control System ◽  
Vibration Control ◽  
Control Structure ◽  
Active Vibration Control ◽  
Experimental Results ◽  
Magnetic Bearings ◽  
Active Magnetic Bearings ◽  
Level Control ◽  
Whirling Motion ◽  
Active Vibration

Active magnetic bearings have several advantages over conventional mechanical and fluid bearings. However, when the magnetic bearings are used at high rotational speeds, whirling motions and vibrations synchronized with the rotation of the rotor should be considered. In order to suppress these unfavorable vibrations of rotor which is supported by magnetic bearings, we have developed an active vibration control system with a two-level control structure. Experimental results show that our active bearings system effectively suppresses the whirling motion.

20420 Modeling and Stabilization of levitation and vibration control on active magnetic bearings system with flexible rotor

2015 ◽  
Vol 2015.21 (0) ◽  
pp. _20420-1_-_20420-2_
Author(s):  
Hirokazu Tomono ◽  
Tasuku Kamekawa ◽  
Hiroyuki Fujisaki ◽  
Masamitsu Shiga ◽  
Toru Watanabe ◽  
...  
Keyword(s):  
Vibration Control ◽  
Magnetic Bearings ◽  
Active Magnetic Bearings ◽  
Flexible Rotor

Multiharmonic Adaptive Vibration Control of Misaligned Driveline via Active Magnetic Bearings

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Hans A. DeSmidt ◽  
K. W. Wang ◽  
Edward C. Smith
Keyword(s):  
Vibration Control ◽  
Closed Loop ◽  
Explicit Knowledge ◽  
Operating Conditions ◽  
Magnetic Bearings ◽  
Active Magnetic Bearings ◽  
Load Torque ◽  
Stability Robustness ◽  
Adaptive Vibration Control ◽  
Loop Stability

Active magnetic bearings (AMBs) have been proposed by many researchers and engineers as an alternative to replace traditional contact bearings in rotor and driveshaft systems. Such active, noncontact bearings do not have frictional wear and can be used to suppress vibration in sub- and supercritical rotor-dynamic applications. One important issue that has not yet been addressed by previous AMB-driveline control studies is the effect of driveline misalignment. Previous research has shown that misalignment causes periodic parametric and forcing actions, which greatly impact both driveline stability and vibration levels. Therefore, in order to ensure closed-loop stability and acceptable performance of any AMB controlled driveline subjected to misalignment, these effects must be accounted for in the control system design. In this paper, a hybrid proportional derivative (PD) feedback/multiharmonic adaptive vibration control (MHAVC) feedforward law is developed for an AMB/U-joint-driveline system, which is subjected to parallel-offset misalignments, imbalance, and load-torque operating conditions. Conceptually, the PD feedback ensures closed-loop stability while the MHAVC feedforward suppresses steady-state vibration. It is found that there is a range of P and D feedback gains that ensures both MHAVC convergence and closed-loop stability robustness with respect to shaft internal damping induced whirl and misalignment effects. Finally, it is analytically and experimentally demonstrated that the hybrid PD-MHAVC law effectively adapts to and suppresses multiharmonic vibration induced by imbalance, misalignment, and load-torque effects at multiple operating speeds without explicit knowledge of the disturbance conditions.

Adaptive Control of Active Magnetic Bearings to Prevent Rotor-Bearing Contact

2006 ◽  
Author(s):  
Abdul-Hadi G. Abulrub ◽  
M. Necip Sahinkaya ◽  
Clifford R. Burrows ◽  
Patrick S. Keogh
Keyword(s):  
Adaptive Control ◽  
Sudden Change ◽  
Experimental System ◽  
Magnetic Bearing ◽  
Open Loop ◽  
Contact Dynamics ◽  
Magnetic Bearings ◽  
Control Force ◽  
Active Magnetic Bearings ◽  
The Impact

Active Magnetic Bearing (AMB) systems offer various advantages over conventional bearings but due to their limited force capacity, with high levels of vibrations the rotor may come into contact with retainer bearings. Under conventional PID control, when a rotor comes into contact with its retainer bearings it remains in contact, until the rotor is run down and the system shut down. This may not be acceptable in some applications, such as aerospace and automotive applications. In this paper, a recursive open-loop adaptive control (ROLAC) algorithm is presented, as an extension of the existing open loop adaptive controller (OLAC), that updates the control force amplitude and phase at each sampling period for rapid response to changes in external excitations. The effectiveness of the algorithm in counteracting a sudden change of rotor unbalance is demonstrated by simulation and experimental results. The experimental system consists of a flexible 2 m long rotor with a mass of 100 kg supported by two radial active magnetic bearings. A simulation model of the system, including the contact dynamics, was used to assess the feasibility of the suggested controller before applying it to the experimental system. Depending on excitation levels, it is shown that the proposed controller is fast enough to prevent contact in most cases. If contact does occur the impact is minimized, and the method is able to recover the rotor position quickly. The proposed controller is implemented in real time and applied to the experimental system. It is shown that the controller works efficiently as predicted by the simulation studies.

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