Identification of unbalance in a rotor bearing system

Abstract

Model based methods for fault identification in rotating systems are gaining importance for the last three decades due to their ability to identify both location and severity of the fault. Model based methods are of different types. Among them, equivalent loads minimization method is one method. In this method, fault is identified in a rotor bearing system by minimizing difference between equivalent loads estimated in the system due to the fault and theoretical fault model loads. This method has a limitation that the error in identified fault parameters increases with decrease in number of measured vibrations. Thus a comprehensive methodology for fault identification with minimum error even in case of fewer measured vibrations is attempted in the present work. Two different approaches: equivalent loads minimization and vibration minimization method are applied for the identification of unbalance fault in a rotor system. Unbalance fault is identified using proposed methods by measuring transverse vibrations at only one location.

Introduction

Rotating machinery is a basic part in any industry. In real systems, faults are inevitable due to the errors in manufacturing, provision of tolerances on mating parts, errors while assembling different parts of the system and if they are not significant in magnitude initially, faults may develop in the system due to the operating conditions such as heat generation, looseness, wear, etc. Failure of the rotor system has safety implications along with economical considerations. Hence, rotating machinery needs to be monitored continuously for the faults. Greatest challenge in the area of condition monitoring is the diagnosis of a fault before it becomes critical.

Any defect in rotors will affect vibration behaviour and nature of this effect is different for different faults. Hence condition monitoring based on vibration measurements can be used to identify those defects qualitatively. Vibration signals give early indication of mechanical failures. Many researchers studied these faults based on their effect on vibrations only. Vibration in any rotating machinery is caused by faults like unbalance, misalignment, crack, etc. Model and signal based methods are usually used to identify these faults in rotor systems. With the advancement in signal processing techniques such as wavelet transforms, Hilbert–Huang transforms, faults are identified even at their early stage of occurrence in the system and also can be distinguished from one another. After identifying type of fault, its location and amount (severity) have to be identified for completely describing the state of damaged system.

Model based methods are used to identify location and magnitude of the fault. Model based methods are of different types. Many researchers have successfully identified rotor faults using model based methods. Markert et al. [1] and Platz et al. [2], [3] identified rotor faults using model based methods that use virtual loads generated in the system due to the faults. Sekhar [4] used this approach for the identification of unbalance and crack acting simultaneously in a rotor bearing system. Jain and Kundra [5] identified unbalance and crack using model based methods, but validated unbalance identification experimentally on a test rig. Bachschmid et al. work group [6], [7], [8], [9], [10] has done extensive research and contributed to a great extent on the model based methods for rotor faults identification. Pennacchi and Vania [6] identified coupling misalignment using model based method. Bachschmid et al. [7] identified multiple faults by means of minimization of a multidimensional residual between vibrations in some measuring planes on the machine and calculated vibrations due to the acting faults. Pennacchi et al. [8] used a modal foundation to model supporting structure of the machine and it is then introduced in least squares fault identification technique in frequency domain. Bachschmid and Pennacchi [9] experimentally validated model based methods to locate the fault, to evaluate its severity and to discriminate among the faults that have similar symptoms. They introduced a new qualitative index, called residual to evaluate accuracy of the performed identification.

Vania and Pennacchi [10] developed methods to measure accuracy of the results obtained with model based techniques to identify faults in rotating machines. They also tested those methods using both machine response simulated with mathematical models and experimental data on a real machine. Sinha et al. [11] estimated unbalance and misalignment of a flexible rotating machine from a single run-down. They demonstrated their method using experimental data. Based on different symptoms fault diagnosis procedures follow; faults can be determined by applying classical or inference methods [12]. Lees et al. [13] gave a detailed review on the use of model based identification of rotating machines. They discussed different approaches for the derivation of foundation models from operational data and then model updating. They also elaborated different models derived for the rotor faults and their application in fault identification. Recently, Jalan and Mohanty [14] identified unbalance and misalignment experimentally in a rotor bearing system using model based method.

In model based methods, generally rotor system is modelled using finite beam elements and faults are modelled as equivalent loads that will be generated in the system if they are present. In equivalent loads minimization method, difference between equivalent loads generated in real systems due to the fault and theoretical fault model loads are minimized using least squares algorithm to identify fault parameters. Equivalent loads generated in the system are estimated using measured vibration response at all the degrees of freedom (dof). These loads are significant in magnitude at fault location. It is not economical and also not feasible to measure vibration response at all the dof. Thus only at fewer dof the vibration response is measured and mode shapes are used to approximate vibrations at unmeasured degrees of freedom using modal expansion or any other shape expansion methods. This method has a limitation that the error in identified fault parameters increases with decrease in number of measured vibrations. Thus a refined methodology for fault identification with minimum error even in case of fewer measured vibrations is attempted here.

In the present work, theoretical fault models used in the least squares algorithm of equivalent loads minimization method are modified to reduce error in identified fault parameters. Also, another method based on vibration minimization is applied for fault identification where difference between measured vibrations and calculated vibrations (obtained by adding theoretical fault model loads at the fault location on undamaged system) are minimized to identify fault parameters. Both methods are simulated for unbalance fault identification in a rotor system. Also, unbalance fault is experimentally identified using these methods in a SPECTRAQUEST MFS rotor system successfully by measuring transverse vibrations at one location (i.e., 2 dof) only.