In designing any machine element, we need to optimize the design to attain its maximum utilization. Herein, deep-groove ball bearings have been chosen for optimization. Optimization has been done in such a way that the design is robust so that manufacturing tolerances can be considered in the design. Robust design ensures that changes in design variables due to manufacturing tolerances have a minimum effect on the objective function, i.e., its performance. Robustness is achieved by maximizing the mean value of the objective function and minimizing its deviation. For rolling element bearings, its life is one of the most crucial considerations. The rolling bearing rating life depends on dynamic capacity, lubrication conditions, contamination, mounting, manufacturing accuracy, and material quality, and thus, the dynamic capacity and elasto-hydrodynamic minimum film thickness have been taken as objective functions for the current problem. Rolling element bearings have standard boundary dimensions, which include the outer diameter, inner diameter, and bearing width for the case of deep-groove ball bearings. So the performance can be improved by changing internal dimensions, which are the bearing pitch diameter, ball diameter, the inner and outer raceway groove curvature coefficients, and the number of rolling elements. These five internal geometrical parameters are taken as design variables; moreover, five design constraint factors are also included. Thirty-six constraint equations are considered, which are mainly based on geometry and strength considerations. In the present work, the objective functions are optimized individually (i.e., the single-objective optimization) and then simultaneously (i.e., the multi-objective optimization). Nondominated sorting genetic algorithm (NSGA-II) has been used as the optimization tool. Pareto-optimal fronts are obtained for one of the bearings. Of many points on the Pareto-front, only the knee solutions have been presented . This paper shows that geometrically feasible bearings can be designed by optimizing multiple-objective functions simultaneously and by also incorporating the variations in dimensions, which occur due to manufacturing tolerance.

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.

The standard techniques used to detect misalignment in rotor systems are loopy orbits, multiple harmonics with predominant 2X component, and high axial vibration. This paper develops a new approach for the identification of misalignment in coupled rotor systems modeled using two-node Timoshenko beam finite elements. The coupling connecting the turbine and generator rotor systems is modeled by a stiffness matrix, which has both static and additive components. While the magnitude of static stiffness component is fixed during operation, the time-varying additive stiffness component displays a multiharmonic behavior and exists only in the presence of misalignment. To numerically simulate the multiharmonic nature coupling force/moment as observed in experiments, a pulse wave is used as the steering function in the mathematical model of the additive coupling stiffness (ACS). The representative turbogenerator (TG) system has two rotor systems, each having two disks and supported on two flexible bearings—connected by coupling. An active magnetic bearing (AMB) is used as an auxiliary bearing on each rotor for the purposes of vibration suppression and fault identification. The formulation of mathematical model is followed by the development of an identification algorithm based on the model developed, which is an inverse problem. Least-squares linear regression technique is used to identify the unbalances, bearing dynamic parameters, AMB constants, and importantly the coupling static and additive stiffness coefficients. The sensitivity of the identification algorithm to signal noise and bias errors in modeling parameters has been tested. The novelty of paper is the representation and identification of misalignment using the ACS matrix coefficients, which are direct indicators of both type and severity of the misalignment.

Centrifugal pumps (CPs) fail due to anomalies in fluid flow patterns and/or due to failure of mechanical subsystems in them. In this work, a technique built on the multiclass support vector machine (MSVM) is developed to identify multiple faults in the CP. In addition, the complex problem of fault combinations and their classification is dealt with in this work. The combination of features from motor line current sensors and accelerometers is used to train the algorithm. To take into account the transient as well as harmonic components of fault signatures, continuous wavelet transform (CWT) analysis is used. Thereafter, the most important information from the CWT coefficients is selected using the two proposed novel methods CWT-based on energy (BE)-MSVM and CWT-principal component analysis (PCA)-MSVM, which are BE as well as PCA, respectively. It is experimentally observed that faults in the CPs have a very strong association with its operating speed. Thus, in order to make the CP versatile in operation, it is important that the fault diagnosis methodology is also efficient at large speed range of CP operation. This work attempts to develop a fault classification methodology, which is independent of the CP operating speed.

This paper demonstrates the development of a flexible fault diagnosis methodology that can detect up to ten different faults in the induction motor (IM), simultaneously. The major IM electrical faults, such as the broken rotor bar (BRB), phase unbalance (PUF), and stator winding fault (SWF), and mechanical faults, such as bearing fault (BF), unbalanced rotor (UR), bowed rotor (BR), and misaligned rotor (MR), are considered with different fault severities for the diagnosis. The experiments are conducted with three varying loads and seven different speeds, and the frequency domain vibration and current data are acquired at a relatively low sampling rate of 1 kHz. Several statistical features are extracted and then the best feature-set is selected using the wrapper model. Thereafter, a data classification tool based on the support vector machine (SVM) is used for the fault characterization. Initially, a multi-fault diagnosis is performed by training and testing the SVM at the same operating conditions (i.e., load and speed). The performance of the classifier is found to be very good at all IM operating conditions. The main focus of this study lies in overcoming the fault diagnosis, where the data are unavailable at required operating conditions. This is accomplished by employing interpolation and extrapolation strategies for different loads and speeds. The proposed methodology not only solves practical problem of unavailability of data at different operating conditions but also shows good performance and takes low computation time, which are vital requirements of an online intelligent condition monitoring system.

Estimating residual unbalances of a flexible rotor that is fully levitated on active magnetic bearings (AMBs) are challenging tasks due to the modeling error of AMB rotordynamic parameters. In this work, an identification algorithm has been developed for the estimation of dynamic parameters of speed-dependent AMBs and residual unbalances in a high-speed flexible rotor-bearing system. Parameters are identified during an estimation process with the help of displacement and current information at AMB locations only. For reducing the finite element model to suit the measurement availability, an improved dynamic reduction scheme has been proposed, which considers the gyroscopic matrix also in the transformation matrix. For a numerical testing of the developed identification algorithm, a multidisk flexible-shaft rotor is considered, which is fully levitated on AMBs. Speed-dependent AMB parameters have been modeled by a cubic function. Proportional–integral–derivative (PID) controllers are used to control the supply current to AMBs. Displacements and currents are generated using the finite element method of the rotor-AMB numerical model. These responses have been used in the identification algorithm for the estimation of the AMB displacement and current stiffness as well as of residual unbalances, concurrently. The algorithm with the proposed reduction scheme has shown an excellent estimation agreement in the presence of noisy responses and bias errors in rotor model parameters.

This paper proposes advancement in the fault diagnosis of induction motors (IMs) based on the wavelet packet transform (WPT) and the support vector machine (SVM). The aim of this work is to develop and perform the fault diagnosis of IMs at intermediate operating conditions (i.e., the speed and the load) to take care of situations where the data are limited or difficult to obtain at required speeds and loads. In order to check the capability of proposed fault diagnosis, ten different IM fault (mechanical and electrical) conditions are considered simultaneously. In order to obtain the useful information from raw time series data that can characterize each of the fault classes at various operating conditions, the wavelet packet is applied to decompose the data of vibration and current signals from the experimental test rig. Fault features are then obtained using the decomposed data and further used for the diagnosis. In this work, five different wavelet functions (i.e., the Haar, Daubechies, Symlet, Coiflet, and Discrete Meyer) are considered in order to analyze the impact of different wavelets on the IM fault diagnosis. The proposed fault diagnosis has been initially attempted for the same speed and load cases and then extended innovatively to the intermediate speed and load cases. In order to check the robustness of the proposed methodology, the diagnosis is performed for a wide range of motor operating conditions. The results show the feasibility of the proposed fault diagnosis for the successful detection and isolation of various faults of IM, even with limited data or information at some motor operating conditions.

When the hydraulic flow path is incompatible with the physical contours of the centrifugal pump (CP), flow instabilities occur. A prolonged operation in the flow-instability region may result in severe damages of the CP system. Hence, two of the major causes of flow instabilities such as the suction blockage (with five levels of increasing severity) and impeller defects are studied in the present work. Thereafter, an attempt is made to classify these faults and differentiate the physics behind the flow instabilities caused due to them. The tri-axial CP vibration data in time domain are employed for the fault classification. Multidistinct and multicoexisting fault classifications have been performed with different combinations of these faults using support vector machine (SVM) algorithm with radial basis function (RBF) kernel. Prediction results from the experiments and the developed methodology help to segregate the faults into appropriate class, identify the severity of the suction blockage, and substantiate the practical applicability of this study.

Vibration characteristics of a cracked Jeffcott rotor with an offset disk under the action of an active magnetic bearing (AMB), implemented to improve the radial positioning of the rotor, has been studied. Presence of the AMB suppresses the vibration induced due to the crack and unbalance; identification of the crack could be made by utilizing the vibration signal in conjunction with the controller current of the AMB. A four degrees-of-freedom (DOF) cracked rotor is modeled considering the gyroscopic effect due to the offset disk and a switching crack excitation function (SCEF) to introduce the breathing of crack. The dynamic condensation is applied to eliminate rotational displacements, which would pose practical difficulty in accurate measurement, from the system equations of motion (EOM) to develop an identification algorithm. Frequency domain transformation of the EOM is made with the help of the full spectrum analysis. An algorithm developed with the purpose of crack identification in the form of additive crack stiffness estimates the viscous damping, disk unbalance, and AMB constants as well. The algorithm has been tested for the measurement noise (in the displacement and the current) and bias errors in system parameters, and found to be robust.

In the design of cylindrical roller bearings (CRBs), a long life is one of the most essential criteria. However, the life of bearings depends on the multitude of factors that includes the fatigue, lubrication, and thermal characteristics in bearings. In the present work, three primary objectives namely, the dynamic capacity, the elastohydrodynamic lubrication (EHL) minimum film-thickness, and the maximum temperature have been optimized, sequentially. Some of these objectives may be contradicting to each other. The optimum bearing design has been attempted by first deriving a constrained nonlinear formulation and then optimizing it with an evolutionary algorithm. Constraint violations study has been performed to have assessment of the effectiveness of each of the constraints. A convergence study has been carried out to ensure the near global optimum point in the design. In terms of the basic dynamic capacity of the bearing, there is an excellent conformity among the optimized and customary bearings. A sensitivity study of various geometric design variables has been performed to see changes in objective functions and results show that geometric variables have hardly any undesirable influence.