International Journal of Rotating Machinery

Volume 2018, Article ID 5159189, 18 pages

https://doi.org/10.1155/2018/5159189

## Investigation on the Effects of Structural Dynamics on Rolling Bearing Fault Diagnosis by Means of Multibody Simulation

Faculty of Mechanical Engineering, Institute for Machine Elements and Systems Engineering (MSE), RWTH Aachen University, Schinkelstr. 10, 52062 Aachen, Germany

Correspondence should be addressed to Reza Golafshan; ed.nehcaa-htwr.esmi@nahsfalog.azer

Received 23 October 2017; Accepted 22 January 2018; Published 13 March 2018

Academic Editor: Paolo Pennacchi

Copyright © 2018 Reza Golafshan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The present study aims to combine the fields modal analysis and signal processing and to show the use of Frequency Response Function (FRF), as a vibration transfer path, in enhancing reliability and abilities of the next generation vibration-based rolling bearing condition monitoring (CM) systems in complex mechanical systems. In line with this purpose, the hereby-presented paper employs an appropriate numerical model, that is, Multibody Simulation (MBS) of a vehicle’s drivetrain as a manner for numerical modal and structural analyses. For this, first, the principles of vibration-based bearing fault detection are reviewed and presented. Following that, a summary of MBS modelling and validating strategies are given. Then, the validated MBS model is used as a case study for further investigations. The results can confirm existence of challenges in fault detection of rolling bearings, in particular in complex mechanical systems. In further discussions, the capability of FRFs in fault localization and determination of ideal sensor positions is discussed in some detail. Finally, concluding remarks and suggestions for future works are summarized.

#### 1. Introduction

In a vibration-based fault detection and fault diagnosis system, mechanical damage is referred to changes on geometric properties of the analyzed machine. These sudden changes may generate additional dynamical forces acting in the system. Then, based on the system responses, damage/faults can be detected and localized. Since all machines vibrates even in their good operational condition due to interactions between machine components, the captured vibrations signals are required to analyze using signal postprocessing techniques. Many diagnostic procedures assume a linear behavior, and thus each individual spectral component (or a group of them) is supposed to relate to a specific dynamic force in the corresponding machine [1]. Therefore, captured time domain vibration signals need to be transformed to the frequency domain to distinguish the various sources and to detect the probable faults, accordingly [2]. However, due to the mechanical complexities and varying operating conditions, it is not always possible to capture, separate, process, and identify the faulty signals, and this could be the case in many complex systems; hence, an overview of dynamics of the analyzed structure/machine may be needed for the reliable and next generation vibration-based fault detection systems [3, 4]. It is known that the captured vibration signals contain structural properties (i.e., vibration transfer path) of the system being analyzed and they are assumed to remain same under varying operating conditions (e.g., torque loads and rotating speeds). Thus, a prestudy on dynamics of the analyzed structure/machine may be necessary to develop suitable and reliable condition monitoring (CM) and detection techniques to detect and diagnose various failures and achieve cost savings to the industry. The modal behavior of a system can be a useful insight to gain beneficial information on the system response to various possible faults and failures. According to the findings in the literature, modal domain features (i.e., natural frequencies, mode shapes, and damping ratios) are widely used in the field Structural Health Monitoring (SHM), in particular for composite and large civil structures [5]. By tracking and analyzing changes over time the presence of a failure, from crack propagation to unbalance localization, can be approved. However, for mechanical and rotating systems, it is assumed that modal features remain more or less constant in case of presence of a mechanical fault, for example, pitting in bearings. This mentioned assumption is the basis for some of the recent and nonstationary signal processing techniques [6]. By eliminating the estimated structural response characteristics, a less sensitive signal to speed and load changes can be obtained [7]. These methods are based on removing the estimated vibration transfer path effects and modal characteristics of the system from measured signals. Note that the dynamical analysis of a structure/machine can be performed using the well-known Experimental Modal Analysis (EMA) techniques to extract the exact vibration transfer path in its frequency domain. In this regard, dynamic analysis can also be performed using continuous (permanent) measurements. For example, Operational Modal Analysis (OMA), as one of the most common techniques for dynamic analyses of running machines, is used for CM of wind turbines, for example, for tower and blades [8, 9], where some important modal info and parameters can be extracted, tracked, and analyzed for a specific application.

In addition to the traditional use of modal testing for design, Noise Vibration Harshness (NVH), and fault localization purposes, the Frequency Response Function (FRF) in modal analysis, as a vibration transfer path function, can be used in other applications such as fault isolation and ideal sensor placement. However, it should be pointed out that the modal analysis on a real structure/machine may not be feasible due to test environment restrictions or due to the lack of reliable mount data. It can therefore be shown that, with a reliable numerical model in hand, the corresponding dynamical analysis can be carried out numerically and reliably. The Multibody Simulation (MBS) approach has approved its usability in identification of system dynamic (modal) characteristics, as a reliable alternative for the real machine [10]. The MBS models can be used for assessments of load interactions between various components in a mechanical system [11]. These models can also represent a testing manner [12], in case there are some restrictions to performing measurements on the real machine. Recently, it is shown that the online or up-to-minute condition monitoring is also a growing application field for the so-called Digital Twin concept using MBS modelling [13, 14]. Only relying on sensor data is sometimes not sufficient. In this situation the simulation (i.e., MBS) models, provided by the Digital Twin, can regularly be modified through measured data and reused after these modifications. By using the simulation models, it is also possible to interpret the measurements in a different way, rather than just detecting deviations from the norm.

For improving the performance of the machine monitoring and fault detection procedures, it can be shown that, as a complementary investigation in the scope of ideal sensing positions as well as estimation of the fault location, a model-oriented approach using MBS modelling may be a useful strategy. In addition to this, the model-oriented designing approach for CM and fault diagnosis algorithms may offer a new degree-of-freedom, in particular in the context of Blind Source Separation (BSS) family methods. The core of BSS-based signal processing method may be optimized according to insights from a comprehensive MBS model, where the excitation sources can be specified numerically and reliably. This becomes even more critical for those systems having many subsystems (i.e., components) running in varying operating conditions.

Rolling bearings, as one of the most common and important components in many mechanical engineering applications (e.g., drivetrains), are always considered as a part with potentially high-risk against the failures. Bearings have very significant impact on the global vibrations of a rotary mechanical system. Furthermore, in electrified vehicles, a bearing failure may lead to increasing the rotational friction of the rotor, and thus a decrease in the performance of the electric motor. Therefore, vibration-based fault detection and diagnosis of the rolling bearings have become a vigorous area of work and have attracted more and more attention in the literature [15, 16]. These studies in condition monitoring are mainly focused on finding the best signal processing technique to detect an incipient failure. Since rolling element bearings are subjected to moving distributed radial and axial loads, any probable fault can excite the system resonances in a specific frequency range depending on neighboring components. It can be concluded that the captured bearing vibration signals carry the information about the system structure in a comparatively high frequency range, which can be interpreted as the transmission path(s) of the vibration. It is also known that the inherent frequency of a bearing is fixed resonance frequency/frequencies even if the fault repetition frequencies (bearing fundamental frequencies) tend to change with shaft speed. This can be a key factor in localizing the similar faulty bearing(s) rotating at the same speed.

Many research studies are dedicated to the field of vibration-based condition monitoring (CM), diagnosis, and fault detection, mostly in oil and gas, wind energy, and railway, including tracks and vehicles, sectors, yet fewer ones are focused on specific requirements and demands for a similar system in the field of automotive engineering. Although numerous general-purpose fault detection and diagnosis algorithms and methods using signal processing techniques are reported in the literature, implementation, applicability, reliability, and ideal (optimal) sensing positions for both offline and online CM systems are still a challenge due to the involved computational complexity and expensive hardware. On-Board Diagnostic (OBD) systems in automotive engineering applications are recently employed and used for various purposes (e.g., Co_{2} emission and electronic components). In order to achieve a reliable and cost-effective an OBD CM and fault detection system for the drivetrain of a vehicle, the diagnostic algorithm should be simple, robust, and beneficial from ideally located sensors. Since thousands of data points are captured and need to be processed during the monitoring process, characteristics of the captured signals, number and locations of the sensor(s), and the detection algorithm itself have become critical parameters for a precision monitoring.

The present study therefore aims to address and investigate some challenges and complexities in vibration-based fault detection and diagnosis for rolling bearings in automotive sector for a drivetrain of an electrified vehicle. In line with this purpose, an experimentally validated MBS model is used for the investigations. Note that a large number of manufacturers, in particular in automotive and wind energy sectors, already have and use numerical models for NVH and testing purposes, so that the modelling step in the development and design procedure of a dedicated and/or implemented condition monitoring systems would not be a time consuming step in designing the next generation monitoring and testing systems. It is worth stating here that this study should be considered as a basis for future works in combination of the fields vibration-based fault detection and numerical modelling.

In the present study, the use of structural dynamics in condition monitoring and fault detection of the complex mechanical systems are studied. The MBS model of a drivetrain for an electrified vehicle created and validated in a previous study is used in numerical analyses as a case study. First, a comprehensive theoretical basis of the vibration-based fault detection for rolling bearings is given. Then, a summary of the modelling strategy as well as subsequent revisions applied to the model to create faulty components (i.e., bearings) is described. Three artificially created faulty cases using the MBS model are then used for numerical investigations on bearing fault diagnosis. In further discussions, the role of Frequency Response Function (FRF), as the transfer path function, in faulty bearing(s) localization and also in finding the ideal sensor location is studied. Finally, some concluding remarks are made about the reliability and applicability of the approach used in this study for bearing fault diagnosis and sensor placement.

#### 2. Vibration-Based Rolling Bearing Fault Diagnosis: Theoretical Background

In general, a mechanical system’s dynamic characteristics (i.e., vibration response) are specified by the corresponding transfer path and excitation sources, as governed by the mathematics of convolution. According to the previous findings in the literature [2], a typical captured vibration signal by a sensor, , of a machine consists of shaft(s), electric motor, rolling bearing(s), gear stage(s), coupling(s), and so on in its operating condition with an individual focus on rolling bearing vibrations can be considered aswhere , , and correspond to the bearing, the transfer path which modulates the fault(s) response to a higher frequency range (i.e., system resonances), and noise originating from measurement system, numerical errors, and/or incidental and transient excitations, and so on, respectively. While both and are related to uncontaminated periodic responses of all other machine parts (due to electric motor, gears, shaft misalignment and unbalances, etc.), represents the unmodulated part and represents the modulated part of periodic responses with the bearing signal. Also, stands for the convolution operator. Eq. (1) can then be extended aswhere , , and , respectively, are the number of fault(s) existing in the bearing (varying from 1 up to = 4, as there are generally 4 types of faults in a rolling bearing), the amplitude of the vibration response to the th fault which reflects the strength of the fault, and Dirac delta function, where denotes the time period between impulses (i.e., 1/BPFO or 1/BPFI). Note that the maximum amplitude of can be assumed to be constant over time for outer race defects due to its stationary condition [17]. The amplitude spectrum of the vibration signal model in (2) for a system having a bearing with a single fault can therefore be derived using Fourier Transform asIn case the signal energy distribution is desired, the energy spectral density of can also be obtained aswhere denotes the complex conjugate of .

It is well-known that the amplitude spectrum of vibration signals may not detect and display the bearing fault frequencies. In such cases, envelope spectrum is the most common method for the fault frequency detection. Nevertheless, in harsh operating conditions, the calculated envelope spectrums are not capable of displaying the fault diagnostic information (i.e., bearing fault frequencies) due to heavy background noise and/or existence other excitation sources. As a result, some preprocessing steps, prior to the envelope analysis, are strongly recommended in the literature.

Recall from convolution propertiesand Nyquist sampling theoremUsing the convolution and Nyquist sampling properties, the right-hand side of (3) can be expanded as follows:Then,

Eq. (8) reveals that contains various and crucial information regarding current status of the test machine (i.e., bearing system). These three constituents can be categorized as (I) uncontaminated period components, (II) modulated impulsive components, and (III) noise. From rolling bearing fault detection point of view, the diagnostic info is associated with the term .

A wide range of studies available in the literature are dedicated to signals containing multiple sources [6, 18]. Source separation techniques are proposed in order to separate and eliminate (if needed) the nonrelated periodic components. Perhaps the most common prewhitening technique for eliminating the nonrelated periodic components in rolling bearing vibration signals is autoregressive (AR) filtering, documented and suggested in [2]. Prior to further postprocessing, the other component needs to be eliminated is the noise, , representing the random and unwanted signals. This can be carried out using denoising algorithms, such as SVD-based denoising method presented in [19]. As a result, after the prewhitening and denoising processes, the denoised version of , called , can be estimated as

In order to extract the modulating component, , in (9), demodulation should be performed. For this, an appropriate estimation of is required in order to extract the fault diagnostic info. One method to estimate in the desired frequency range (i.e., system resonance) is the spectral kurtosis (SK) [20]. Using the same property of convolution theorem given earlier, demodulating in the frequency domain can then be formulated aswhere is an estimation of . Again, here represents, for example, shaft-related components originating from unbalances, torsional vibrations, and eccentric faults. In some cases, in particular in complex mechanical systems, estimation of can be a complex and time consuming step.

Back to the present theoretical formulation in (9), in practice, however, demodulation on the bearing signal, , is carried out by a bandpass filtering (e.g., SK-based optimized filter) with a central-frequency at the system resonance, and then Hilbert Transform in the time domain aswhere is also known as the envelope signal and is the Hilbert Transform of asThe so-called envelope spectrum is then be obtained by Fourier Transform of the envelope signal, , as

As is being shown, the transfer path function, , plays a major role in diagnostic vibration signals captured from a mechanical system. In the following sections in the present study it is shown that the transfer path can be analyzed in more detail in order to estimate fault location and ideal sensing positions. This function can be represented by Frequency Response Function.

#### 3. Summary of Numerical Modelling

In this section, a brief summary of numerical modelling is presented. In addition, some details of the model revision for fault detection purposes are described.

In general, the dynamical systems can be presented in terms of their equation of motion (E.o.M.) aswhere , , , , and stand for the displacement vector, the force vector (including external and internal torques and moments), inertia (mass), damping, and stiffness matrices of the involved bodies, respectively. In Elastic Multibody Simulation (EMBS), the E.o.M. may be solved in an iterative way, either in time domain or frequency domain. For this, the system matrices and the force (e.g., containing the excitations) vector need to be formed first. However, prior to assemblies of the machine parts by implementation of the masses, stiffness, and the external excitations, EMA is employed in order to validate the modal properties of each elastic parts used in the model. Following this bottom-up process, the entire dynamical system (i.e., drivetrain) consisting of all validated subsystems is validated against the experiments. Some details of the numerical modelling and validation process are readily available in [21]. The previously created EMBS model of a test Battery Electric Vehicle (BEV) for which the numerical investigations are performed is shown in Figure 1.