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.

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.

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.

A Numerical Study on the Effect of Unbalance and Misalignment Fault Parameters in a Rigid Rotor Levitated by Active Magnetic Bearings

2019 ◽  
Author(s):  
Prabhat Kumar ◽  
Rajiv Tiwari
Keyword(s):  
Numerical Study ◽  
Equations Of Motion ◽  
Rotor System ◽  
Magnetic Bearings ◽  
Inertia Force ◽  
Dimensional System ◽  
Rigid Rotor ◽  
Active Magnetic Bearings ◽  
Fault Parameters ◽  
Misalignment Fault

Abstract This paper focusses on analysing the vibration behaviour of a rigid rotor levitated by active magnetic bearings (AMB) under the influence of unbalance and misalignment parameters. Unbalance in rotor and misalignment between rotor and both supported AMBs are key fault parameters in the rotor system. To demonstrate this dynamic analysis, an unbalanced rigid rotor with a disc at the middle levitated by two misaligned active magnetic bearings has been mathematically modelled. One of the novel concepts is also described as how the force due to active magnetic bearings on the rigid rotor is modified when the rotor is parallel misaligned with AMBs. With inclusion of inertia force, unbalance force and force due to misaligned AMBs, the equations of motion of the rigid rotor system are derived and converted into dimensionless form in terms of various non-dimensional system and fault parameters. Numerical simulations have been performed to yield the dimensionless rotor displacement and controlling current responses at AMBs. The prime intention of the present paper is to study the effect on the displacement response of the rigid rotor system and the current consumption of AMBs for different ranges of disc eccentricities and rotor-AMB misalignments.

Estimation of Active Magnetic Bearings (AMB) Dynamic Parameters and Residual Mass Imbalance Using FEM With PID Controller and Identification Algorithm of a Flexible Rotor System Fully Levitated on AMB

2019 ◽  
Author(s):  
Bala Murugan S. ◽  
R. K. Behera
Keyword(s):  
Pid Controller ◽  
Rotor System ◽  
Magnetic Bearings ◽  
Identification Algorithm ◽  
Dynamic Parameters ◽  
Active Magnetic Bearings ◽  
Flexible Rotor ◽  
Residual Mass ◽  
Mass Imbalance ◽  
Least Squares Fit

Abstract The dynamic analyses of rotating systems are always a testing task to obtain the definite results. This paper carries the dynamic modelling, analysis and identification of coupled flexible rotor system supported by an auxiliary Active Magnetic Bearings (AMBs). An identification algorithm is used to estimate the dynamic parameters of AMB, and rotor residual mass imbalance. The proposed algorithm is a right method for the analysis of fully levitated rotor on AMBs. Finite element method is used to model the dynamic flexible rotor system with PID controller. A conventional dynamic condensation technique is implemented in the development of identification algorithm to overcome the difficulty in numerical simulation. The least-squares fit technique is deployed to estimate the dynamic parameters in frequency domain. Then the algorithm is extended to find the misalignment forces and moments at the coupling point. Numerical study is carried to check the correctness of the algorithm. The proposed algorithm is yet to be tested to experimental results from a fully levitated rotor test rig supported with AMBs.

Interactions Between Backlash and Bearing Clearance Nonlinearity in Geared Flexible Rotors

2007 ◽  
Author(s):  
N. Ersan Gu¨rkan ◽  
H. Nevzat O¨zgu¨ven
Keyword(s):  
Mathematical Model ◽  
Series Representation ◽  
Calculated Data ◽  
Axial Loading ◽  
Transmission Error ◽  
Gear Mesh ◽  
Bearing Clearance ◽  
Flexible Rotors ◽  
Non Linear ◽  
Clearance Nonlinearity

In this study, the interactions between backlash, bearing clearance and bearing flexibility are studied in geared flexible rotors. For this purpose, the non-linear mathematical model developed in a recent previous study for geared rotors on flexible bearings is extended further to handle clearance nonlinearity in bearings. The model consists of elastic shafts on elastic bearings with clearance, and coupled by a non-linear gear mesh interface. Shafts are modeled by using finite elements. The mathematical model includes the axial loading on shafts, rotary inertia, material damping of shafts, backlash nonlinearity of gear mesh and flexible bearings with clearances nonlinearity. The model considers also the effects of gear errors and profile modifications. The excitation effect of time varying mesh stiffness is indirectly included into the analysis through a periodic displacement representing loaded static transmission error (STE). STE input is modeled by the highest n harmonic terms of the Fourier series representation of the measured or calculated data. The model developed is believed to be one of the most advanced ones: It includes several linear and non-linear effects and capable of handling various different gear-rotor-bearing configurations. Through several case studies, the combined effects of backlash, bearing clearance, and bearing flexibility on dynamic mesh force and bearing loads are studied.

Model-Based Crack Identification Using Full-Spectrum

2013 ◽  
Author(s):  
Shravankumar Chandrasekaran ◽  
Rajiv Tiwari
Keyword(s):  
Equations Of Motion ◽  
Crack Identification ◽  
Force Model ◽  
Identification Algorithm ◽  
Full Spectrum ◽  
Rotor Systems ◽  
Model Based ◽  
Fault Parameters ◽  
Harmonic Components ◽  
Rotor Model

This paper illustrates the application of full-spectrum technique for model-based identification of the crack and unbalance multi-fault parameters in cracked rotor systems. The rotor model chosen is a Laval rotor with disc unbalance and transverse surface crack. The crack force model is a switching crack, which has harmonic components exciting the rotor both in the same and reverse directions of the rotor spin. Development of identification algorithm uses linearized equations of motion in frequency domain. Full-spectrum obtains the complex Fourier coefficients of the force as well as the response. Further usage of these coefficients in the identification algorithm estimates the viscous damping, disc eccentricity, and additive crack stiffness as fault parameters. The accuracy of estimates increases on considering measurements at multiple spin speeds. The algorithm tests reasonably robust for various levels of measurement noise and bias errors in system parameters.

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