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2024 | Book

Vibration Engineering and Technology of Machinery, Volume II

Select Proceedings of VETOMAC XVI 2021

Editors: Rajiv Tiwari, Y. S. Ram Mohan, Ashish K. Darpe, V. Arun Kumar, Mayank Tiwari

Publisher: Springer Nature Singapore

Book Series : Mechanisms and Machine Science

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About this book

This book presents the proceedings of the XVI International Conference on Vibration Engineering and Technology of Machinery (VETOMAC 2021). It gathers the latest advances, innovations, and applications in the field of vibration and technology of machinery. Topics include concepts and methods in dynamics, dynamics of mechanical and structural systems, dynamics and control, condition monitoring, machinery and structural dynamics, rotor dynamics, experimental techniques, finite element model updating, industrial case studies, vibration control and energy harvesting, and MEMS. The contributions, which were selected through a rigorous international peer-review process, share exciting ideas that will spur novel research directions and foster new multidisciplinary collaborations. The book is useful for the researchers, engineers and professionals working in the area of vibration engineering and technology of machinery.

Table of Contents

Frontmatter
Delamination Damage Detection in a Composite Beam Using Discrete Wavelet Transform

An expectant attempt to detect delamination damage in a multi-layered composite beam using discrete wavelet transform is proposed. The finite element model of delamination-damaged composite cantilever beam is modeled using ANSYS-APDL software. The first mode of the simulated beam is obtained from the modal analysis. The deflection values of each node in the first mode shape are plotted to get the response of the top-most edge of the delaminated beam. Delamination in the composite beam causes a slope discontinuity in the beam elastic line. The top-most or bottom-most edge of the beam will also get affected due to such slope discontinuity. Detection of slope discontinuity will reveal the presence of delamination in the composite beam. However, it is quite difficult to identify the delamination in the presence of measurement noise. In the current work, a white Gaussian noise is added to the simulated beam responses to mimic the real experimentation. The noisy signal is used as an input signal for wavelet analysis. A dominant spike is observed at the damage position. The effectiveness of the present method is also analyzed with different values of signal-to-noise ratio (SNR).

Ravi Nigam, Niraj K. Saha, Sachin K. Singh
Effect of Input Torque on the Modulation Sidebands of Planetary Gears in a Wind Turbine Gearbox Under Gravity Excitations

Planetary gears are the main components of the wind turbine gearbox (WTG). In the recent investigations of WTG, it has been found that the gravity of planetary gears acts as a fundamental source of external excitation, which considerably changes the planetary gears’ dynamics. In this study, a dynamic model of planetary gears with gravity excitation is developed, and dynamic response is computed using Newmark beta algorithm. Excitations due to time-varying mesh stiffness are also incorporated in the dynamic model, which are inherent in gears and are the primary source of internal excitations. The input torque effect is investigated on planetary gears’ dynamics under gravity excitations for two different mesh phase designs, namely, in-phased meshing and sequentially phased meshing. It is observed that the input torque significantly affects the amplitude of sidebands due to gravity excitations.

Palash Dewangan, Anand Parey
Stochastic Identification of Damped Beams Using Frequency Response Function Data

Stochastic modelling of mass, stiffness as well as damping in structures, is crucial for an accurate prediction of dynamic response and its variability. This is even more challenging for structures with a high level of damping. A new frequency response function-based stochastic FE model updating approach has been proposed to identify the mean and variabilities of parameters related to mass, stiffness and damping matrices. The present work is on the applicability of the proposed method for structures with low, medium, and high level of damping. A simulated study is conducted on beam samples with different damping levels in the presence of noise, incompleteness and modelling errors. Stochastic identification is further demonstrated experimentally on beam samples with low and high level of damping. The efficiency of the proposed method for stochastic updating of damping, mass and stiffness matrices and for prediction of variability in frequency response function (FRFs), modal data, and loss factors is studied.

Asish Kumar Panda, Subodh V. Modak
Study of Vibration and Wear Debris Damage Detection Methods for Mild Wear in Spur Gear System

Mild wear in gear transmission systems accounts for 41% of the gear flank surface failure mechanisms. Vibration detection parameters and wear debris methods are widely used for the condition monitoring of gear transmission systems experiencing mild wear. In this study, an attempt has been made to predict the effectiveness of wear debris damage detection and vibration parameters in estimating the mild wear progressive failure which is a precursor of breakdown. The vibration parameters RMS, kurtosis, crest factor, energy ratio (ER), and FM0 are obtained from the time-averaged vibration data for two sets of run-to-failure experiments for the EN24 steel spur gear system. Each of these experiments is performed at a constant speed (1200 RPM) and load (40 Nm). Wear debris monitoring is performed online. The ER and FM0 have been found to consistently increase after 140 h, indicating initiation of progressive failure. The RMS values are found to be inconsistent in indicating initiation of failure. The kurtosis and crest factor parameters possessed constant behaviour with respect to time. The number of wear debris particles changes at 110 h and 160 h, respectively, showing the initiating and limiting values before the occurrence of severe wear for the first set of the experiment; similarly, 110 h and 140 h for the second set of experiment. Overall, it is found that the wear debris method could effectively predict the failure mechanism much earlier in comparison to parallelly obtained vibration indicators ER and FM0.

Dharmender, Ashish K. Darpe, Harish Hirani
Transient Rotor Dynamics Behaviour of Shrink-Fitted Overhung Rotor

The paper aims to predict the transient behaviour of a vertically overhung high-speed rotor bearing system known as a spin test apparatus. The spindle and arbor are shrink-fitted and, hence, at very high-speed conditions are liable to alter the fit condition at the interface. The paper proposes a method to determine the contact stiffness at spindle-arbor assembly—the contact pressure at the interface, obtained through Lame's theorem. The dynamic contact stiffness under the influence of centrifugal force is determined at different spin speeds and modelled as uniformly distributed translational and rotational springs at the interference of spindle and arbor node locations. The contact stiffness is assumed as a function of radial interference and rotational speed and its influence on the stability of the rotor bearing system is investigated. The external damper at the spindle location controls the vibrational amplitude during coast up and affects the system's critical speeds. The predicted transient response agrees well with the experimental response, verifying the proposed identification method of the contact stiffness.

Gyan Setu, A. K. Darpe, B. Premachandran, K. Gupta
Fault Diagnosis of Gear with Multiple Defects in Planetary Gearbox

Continuous and prolonged operation of wind turbine results in fatigue loading on its components and subsequently, the planetary gearbox is one among the most susceptible components subjected to failure. The exposure to continuous loading results in multiple faults in the planetary gearbox, such as pitting, tooth breakage and tooth cracks. A combination of these defects will also occur in the planetary gearbox, which this work has considered. The planetary gearbox dynamic modelling is discussed in this work, which consists of a combination of broken tooth defects and cracked tooth defects occurring on sun gear. The lumped-parameter model consisting of three degrees of freedom for each of the central components, which involve one rotation and two translations in its plane of rotation, is discussed. By considering the Hertzian contact stiffness, tooth pair bending, shearing and axial compression stiffness, the potential energy technique is employed to determine the system's vibration signature from the parametric excitation induced by the variable gear mesh stiffness. The broken tooth and crack cause a fall in a localised region's mean stiffness value. Moreover, a broken tooth can result in the mesh stiffness value to zero during the single tooth contact regime. The vibration spectrum of the faulty system for early fault diagnosis is also discussed in this work.

Hridin Pradeep, Ashish Kamalakar Darpe
Vibration Analysis of Turbine Blade Using Finite Element Method

Analysis of the vibration of a cantilever beam under rotation is performed using the finite element technique. The Hamilton principle is used to derive the coupled dynamic equations of a rotating, tapered, pre-twisted cantilever Timoshenko beam from the nonlinear Von Kármán strain and the related linear stress. To carry out finite element analysis, the equations of motion are discretised using the weighted residual technique. MATLAB Codes are generated. The effect on natural frequencies of dimensionless parameters is studied. 3D blade is designed, and natural frequencies are computed using Finite element method in Ansys and correlation between the two models is analysed.

Kr. Mohd Salman, Ahmad Ali Khan
Analytical Prediction of the Jet Force in Pelton Turbine

Energy generation through hydropower has become increasingly important in our quest for clean, renewable energy. The turbines in the hydropower have to endure harsh working conditions due to the frequent starts and stops to meet the current grid demands and are thus susceptible to structural damage under the action of hydraulic forces. The dynamic response due to these hydraulic forces can create unwanted mechanical vibrations in the system. Pelton Turbines are subjected to strong dynamic forces whenever it is impinged by the jet of water. It is of utmost importance that we avoid the resonance condition when the force due to the jet of water strikes the Pelton buckets. So, the analytical prediction of the jet force of the Pelton turbine is a vital issue. The Pelton buckets are assumed to be rectangular with negligible thickness and the jet of water is assumed to strike centrally on the bucket. The area of the impinging jet is parametrized with the height of the jet. The normal forces acting on the system and buckets are calculated for different bucket positions and the system forces are resolved in the transverse directions. The periodic forces that were obtained were converted into harmonic forces using Fourier series to be used for Forced vibration analysis.

Nishant Bhatta, Hari Bahadur Dura, Janak Kumar Tharu, Mahesh Chandra Luintel
Intelligent Fault Detection Scheme for Rolling Bearing Based on Generative Adversarial Network and AutoEncoders Using Convolutional Neural Network

Fault detection in early operational stages of rolling bearing is crucial for reliable and safe functioning of rotating machinery. Implementation of intelligent fault detection techniques involving deep learning methods enable automatic feature extraction and selection from raw vibration data provides accurate results. The shortage of enough historical data limits the application of deep learning. Therefore, to solve this problem, in this paper data augmentation method is implemented to generate new data that having greater similitude with the real data for better training of deep learning model for fault detection. For this purpose, WGAN (Wasserstein generative adversarial network) is implemented as imbalanced data augmentation method. Also SAE (stacked autoencoder) is implemented to obtain the latent representation of raw vibration data which is used as noise vector to train WGAN. This has greatly improved the quality of data generation from WGAN. The quality assessment of generated samples is quantified by implementing metrics such as KLD (Kullback–Leibler divergence) and NCC (normalized cross-correlation). The comparison with conventional data generation methods such as VAE, and GAN proves the superior quality of data generation by SAE-WGAN. Test rig experiments are used to gather the vibration data, and deep convolutional neural networks are used to classify the faults (DCNN). The ROC curve and performance evaluation metrics like precision, recall, and F1-score amply demonstrated the excellent discriminative power of the suggested methodology for fault detection. Hence the proposed work successfully implemented as condition monitoring tool for early fault detection in rotating machinery.

Maan Singh Rathore, S. P. Harsha
Sparse Frequency Representation Using Autocorrelation of Variational Mode Functions to Detect Compound Fault in Rotating Machines

A gearbox is a torque transmitting unit, in other words, a nonlinear dynamic system, consisting of gear pairs, bearings, and shafts. In a vibration signal, effect of gear tooth faults reflects modulations and appears as sidebands in frequency spectrum. Similarly, bearing faults exhibit modulations too. Thus, when multiple faults termed as compound faults occurring in bearing simultaneously, the sidebands in the resulting vibration signal will be difficult to investigate, due to interference, and hence, specialized techniques are required to solve such problems. An investigation considering the compound fault occurring in a rotating machine is presented in this work. A fault detection approach based on variational mode decomposition and autocorrelation is proposed in this paper for compound faults. VMD demodulates the vibration signal thereby attenuating the effect of spurious noise; however, the low-frequency component related to individual fault is unidentifiable. Therefore, autocorrelation analysis and estimation of correlation coefficient of the extracted variational mode functions (VMFs) was performed followed by the sparsity analysis using Gini Index, Hoyer Index, and $${\mathrm{l}}_{2}/{\mathrm{l}}_{1}$$ l 2 / l 1 norm of the most sensitive VMF to exhibit the fault. It was noted that the proposed approach attempts to solve the problem of complex oscillation characteristics, and mutual interference between multiple bearing faults. The result suggests that the proposed approach is more effective in diagnosing the compound fault.

Vikas Sharma
Estimation of Theoretical and Experimental Natural Frequencies of Rotating Shafts

Whirling is one of the most important things that can cause the shaft to break and the system to fail. It is generally because of the mounting of turbines, compressors, pumps, etc., on the flexible shaft, making it bend in a complicated manner. Dunkerley's empirical relation for transverse vibration of the beam is used to calculate the whirling speed of the shaft due to its self-weight. Silver steel shafts of varying diameters are used for experimental values to determine the critical speed of shafts for the first two modes for fixed–supported end conditions and the first mode for fixed–fixed end conditions. For the above analysis, ANSYS/Workbench has been used to model the same situation and obtain natural frequencies. Also, the variation of diameter on whirling speed is observed.

Abdul Khaliq Ansari, Zain Ahmad Khan, Nazish Khan
Steady-State Nonlinear Forced Vibrational Response of Laminated Sectorial Plates

Annular sectorial plates are versatile mechanical parts that are employed in many different sectors, including aerospace, maritime, and biomedical. During operation, they are exposed to high-amplitude dynamic loads and vibrations. As a linear strain–displacement relation underestimates the vibrational response, accurate design must take geometric nonlinearity into consideration. The time-domain solution of the equations of motion is attained using the modified shooting method and the arc-length/pseudo-arc-length continuation approach in this study to investigate the steady-state nonlinear/linear forced vibrational characteristics of laminated sectorial plates. The nonlinear dynamic behavior of these plates is investigated using frequency response and cyclic stress curves and phase plane plots. Findings reveal that the peak amplitude in the nonlinear analysis is substantially less than in linear analysis, suggesting that the nonlinearity in the plates is becoming harder. The stable and unstable areas of the frequency response curve are also identified by the study.

Ahmad Saood, Mohd. Taha Pervez, Zain Ahmad Khan, Arshad Husain Khan
Data Driven Modeling and Control of Delivery Drone

Data driven dynamic modeling and control of a quadcopter with slung load (i.e., Delivery drone) is developed in this study. The dynamic and controls are studied with both the physics-based mathematical model and data driven modeling methods for comparison purpose. The delivery drone is modeled as 2D nonlinear quadcopter with slung load, based on Lagrangian formulation, from a previous study. Initially, an LQR control is developed with the linearized mathematical model to analyze the performance of delivery drone. For a small disturbance, the oscillations of degrees of freedom associated with quadcopter take a shorter time to reach the equilibrium with LQR control. However, the oscillation of slung load takes longer time to decay than quadcopter oscillations. In the next stage, the data driven model based on feedforward neural network is developed for nonlinear dynamic model of delivery drone. The input data is generated with the numerical simulations of nonlinear model of delivery drone. The simulated response data of slung load oscillation, calculated for small disturbances, is found to be unbounded and unstable. This shows that stability analysis of delivery drone play a crucial role in generating the stable input data. In the next stage, a PID controller is designed with the Data Driven model of the delivery drone. The parameters of the PD controller are found using the trial and error approach. The initial results show the PD controlled system is efficient in controlling the system dynamic oscillations for initial disturbances. These initial results show that the controller design based on Data Driven model can be effectively used in the delivery drones without the necessity of physics-based mathematical models. However, further studies are needed in the data driven-based dynamic modeling and control design with advanced neural network approaches, and experimental validation of results.

Gaurangi Singh, M. Senthil Murugan, Sathiskumar A. Ponnusami
Fault Diagnosis in a Motor Under Variable Speed Conditions: A Survey

The major reason for air pollution is burning a large amount of non-conventional fuel in vehicles. Today the demand for electric vehicles is flourishing. This expedition opens new possibilities in electric vehicle management and maintenance. The efficient condition monitoring of electric vehicles is essential to bring out the best performance and reliability. The majority of failures in electric vehicles occur due to faults in powertrain elements (Vas in Parameter estimation, condition monitoring, and diagnosis for electrical machines. Clarendon, Oxford, U.K., 1999). The induction motor is an essential component of the electric vehicle powertrain. Condition monitoring of the electric motor is essential for the smooth operation of electric vehicles. In the present work, a detailed review of the condition monitoring of induction motors is presented. The current study is devoted to fault diagnosis under variable speed conditions as the motor of an electric motor is subjected to variable speed. At first, the types and root causes of motor faults are described. The mathematical modeling for different fault conditions is discussed. Further, the fault diagnosis techniques based on signal processing and artificial intelligence are illustrated.

Ramnivas Kumar, Sachin K. Singh
Stability of Cage in Bearings of Reaction Wheels for Satellite Application: A Critical Review

The increased demand for better service in telecommunication, navigation, meteorology, broadcasting, data service, defence and security has made satellite technology one of the most focused areas in recent days. Large numbers of efficient, smaller and cost-effective satellites are being launched to Earth’s orbit for better precision and accuracy. So, in order to provide stability and controlled movement to these, miniature devices, such as reaction-type actuators, are used as wheels. These reaction wheels work on the principle of conservation of angular momentum. These wheels are capable of providing effective attitude control with minimal residual unbalance. The wheels are supported on an angular contact rolling element bearing. Though these bearings are designed and manufactured with strict aerospace procedures, the cage of these bearings often fail at high speeds and extreme atmospheric conditions. So, any defect in these wheels may cause failure to the entire mission. This study summarizes the research outcomes of causes of cage failure and their prevention. The research reveals that the failure of cages of high-speed bearings depends on the size of roller, roller contact force, misalignment, cage asymmetry, cage eccentricity, different loading conditions, radial clearance and cage pocket clearance. Roller bearing test rigs are being used to analyse effect of various parameters, like the bearing unbalance, shaft speed, number of rollers, etc., on cage dynamics as well as on cage slip. This investigation analyses the progress of relevant research, and identifies the shortcomings and future scope for further innovations.

Madhumita Mohanty, Rajiv Tiwari
Fatigue Life Estimation of Pelton Turbine Using Local Strain Approach

This paper studies the fatigue life estimation of the 12 MW Pelton turbine of Khimti Hydropower. The material of turbine is 13Cr–4Ni SS. Pelton turbines are widely used hydraulic machines that efficiently extract energy from high head and low discharge flow. These turbines are subject to repeated load/stress amplitude mainly due to water jet impact from jet nozzles. Finite element analysis indicated that the maximum stress and strain occur at the root of the Pelton bucket. During the long operating hours, these bucket roots initiate micro-cracks which eventually grow to considerable crack size. This paper focuses on fatigue life estimation of Pelton turbines using a local strain approach. Structural analysis of the Pelton runner sector was carried out to determine the maximum local strain value. Modified universal slope and hardness methods were used to obtain strain–life curve for fully reversible load. The Haigh diagram was used to obtain the strain–life curve for pulsating load. The maximum value of local strain was calculated to be 2.38 ×  10–3 mm/mm. For this maximum local strain, fatigue life was calculated as 2.67 × 106 cycles, which falls in the high-cycle fatigue region. This study concluded that the Pelton turbines are designed for infinite life and hence damage tolerance approaches are necessary to investigate the crack growth rates.

Hari Bahadur Dura, Hemanta Dulal, Laxman Motra, Mahesh Chandra Luintel
Rotor Crack Depth Estimation Using Recurrence Quantification Analysis

Condition monitoring of machinery is gaining increasing importance as more and more complicated and interconnected systems are being developed. In such systems, it becomes critically important to forewarn about the impending faults that have developed in the components to ensure robust and safe operation. Faults that develop in rotating machinery are notoriously difficult to detect using conventional methods. These faults can exacerbate very quickly, which can cause irreparable damage, financial loss and potential casualties. Thus, development of robust techniques for damage detection is imperative for improving safety and reliability of machinery. These techniques use signals from widely deployed sensors, and once validated, can be used for continuous monitoring of the machinery systems, thereby aiding further automation. In this paper, we have developed a technique wherein Recurrence Quantification Analysis (RQA) is used in conjunction with Machine Learning to predict the degradation of a crack in a rotating shaft. Recurrence is a phenomenon that is widely exhibited in many nonlinear processes, and recurrence plot is a two-dimensional visualization of the higher dimensional dynamical systems and helps to understand the recurrence of states in phase space. RQA is an objective and quantitative method to analyze recurrence plots and yields features of the dynamical systems which we employ in conjunction with appropriate Machine Learning algorithms in order to develop a robust diagnostics algorithm. To obtain the dynamic response of the system for various fault conditions, a physics-based model of the cracked rotors is used, and in order to map the RQA features to fault space, a multi-layer perceptron neural network is used. The results of this study demonstrate that RQA has outstanding performance in crack depth estimation with minimal need for expert knowledge about the dynamic response of the system.

Utkarsh Andharikar, Amirhassan Abbasi, Foad Nazari, C. Nataraj
Identification of Dominant Source of Vibration in Geared Rotors Using Full-Spectrum Analysis

Torque transfer through gears causes vibration and often leads to irritating tonal noise called gear whine due to micron-level deviations from conjugate gear profile. These profile deviations due to manufacturing as well as tweaked deviations to minimize gear edge contact are quantified in terms of static transmission error (STE). A vast literature is available on STE as the source of vibration and noise at the gear mesh frequency. Another dynamic effect in a loaded geared rotor due to shaft deflection, gear mesh stiffness, gear run-out errors and gear mesh misalignments along the line of action along with STE constitutes the dynamic transmission error (DTE). In this work, a novel gear vibration system model for the low-torque transmission applications with the asymmetric STE assumed in orthogonal transverse directions at the pitch point is presented for identifying dominant source of vibration in geared rotors. In order to avoid nonlinearities due to transverse and torsional vibration couple, the shaft is assumed to be rigid in torsion under low torque. To further reduce complexities in solving resulting EoM, rotor shafts are mounted on rigid supports and gear mesh misalignments have been ignored. The equations of motion are derived with Lagrange dynamics. System model response is calculated by solving EoM in time domain using the RK method. The resulting time domain response is converted into frequency domain using the full spectrum to analyse it. The full-spectrum response splits the response spectrum into backward and forward whirl amplitudes of dominant dynamic effects within the system. With full-spectrum and orbit plots, the gear mesh vibration is analysed by generating response with different shaft speeds and by varying the key gear mesh parameters by loading gear pair with nominal torque to identify the dominant source.

Bhyri Rajeswara Rao, Rajiv Tiwari
Influence of Geometric Parameters on the Dynamic Performance of Spiral Bevel Gear

Spiral bevel gears are ubiquitous in numerous power transmission systems. The exigent demands such as high performance, more strength and less noise in helicopter drives can be met by selecting the optimal geometrical design parameters. However, a comprehensive study on the influences of geometric parameters on the transmission system dynamics is not found in the literature. Therefore, in this study, the effects of geometric design parameters such as spiral angle, pressure angle and pitch cone angle on the spiral bevel gear set dynamic characteristics for various boundary conditions are studied. Firstly, the analytical modeling of coupled lateral–axial–torsional vibrations of the spiral bevel gear set is derived theoretically under a few assumptions. Then the emphasis on the effects of geometric parameters on the dynamic characteristics such as critical speeds, coupled mode shapes and unbalance vibration response of the gear pair supported by flexible and rigid boundary conditions are investigated numerically. Under rigid support conditions, it is observed that there is no remarkable influence of geometric parameters on the critical speeds. However, the unbalance response amplitudes at and around the resonance peaks are notably affected. Whereas the critical speeds and unbalance responses are essentially affected by the variation of axial and torsional stiffness at the supports. Meanwhile, the influence of geometric parameters on the critical speeds corresponding to torsional and axial modes is remarkable for the flexible support conditions. Furthermore, the steady state response due to combined torsional and unbalance excitations is also studied, and the results show that the geometric parameters influence the axial, lateral and torsional responses. The results obtained through this study are useful in the design of the spiral bevel gear set.

Anuradha Gollapudi, Sagi Rathna Prasad, Piyush Shakya, A. Seshadri Sekhar
Finite Element Modelling and Dynamic Stability Analysis of a Functionally Graded Rotor Shaft-Bearing System

The extensive analyses of rotor-bearing-disk systems are inevitably a challenging problem to get the exact results. In the development of the current industries, based on the specific applications the functionally graded (FG) rotating shafts are used extensively. It is observed that very few studies were reported on FG rotor-bearing-disk systems on stability issues. The current study carries the finite element (FE) dynamic modelling approach, and the stability study of a rotating FG rotor-disk-bearing system. The FG rotor shaft model is considered to be based on Timoshenko beam theory by accounting for the gyroscopic effects, rotary and translational inertia, shear deformation, bending and material (viscous and hysteretic) damping. The governing equations are obtained by implementing Hamilton’s principle. In the present study, stainless steel (SUS304) and Zirconia (ZrO2) are typically treated as main components which are radially categorized FG shaft. Five-noded beam elements are considered by taking into account of four degrees of freedom per node. The results from Campbell diagram, stability threshold, time histories and damping ratio for FG shaft are compared with the regular standard steel shaft. It is observed that the results obtained for FG rotating shaft are notably controlled by the constituents of the radially classified FG shaft. This result leads to the importance of FG shaft over the standard steel shaft.

S. Bala Murugan, R. K. Behera
Moment Independent Sensitivity Analysis of Porous Functionally Graded Plates Subjected to Free Vibrations

This paper presents a moment-independent sensitivity analysis of porous functionally graded plates subjected to random free vibrations. This study intends to identify the parameters that have significant impacts on the output. The FE formulation employs eight-noded isoperimetric quadratic elements. Monte Carlo simulation technique is adopted with a standard Eigenvalue problem to evaluate random natural frequencies. Power law is used to describe the distribution of material properties in these structures. The study considers elastic modulus, Poisson ratio, shear modulus, and mass density as the various random input parameters, while the outputs obtained are the first three natural frequencies. To reduce evaluation time and cost, PCE model is used as a surrogate, which is also validated to demonstrate its prediction accuracy with the MCS results. The first three probabilistic natural frequencies are depicted using statistical analyses. The outcomes obtained in this study are the first known results, and can be applied in the optimal designing of structures constructed from hybrids.

Himanshu Prasad Raturi, Vaishali, Subrata Kushari, Pradeep Kumar Karsh, Sudip Dey
Effect of Misalignment in a Geared-Rotor System Integrated with Active Magnetic Bearings

Gears are key components in any industrial rotary machine, therefore the study of vibration in a geared-rotor system is considered vital. In such a geared system, assembly fault, like misalignment, is very common. Such fault gives external excitation forces on the mating gears. Moreover, the force distribution among the meshing teeth of a gear pair also gets changed due to misalignment. In this work, an experimental study has been made on a geared-rotor setup equipped with active magnetic bearings (AMB). The AMB is used for active vibration control of the geared-rotor system. The control law that has been applied to the AMBs is based on the PID controller. Shaft misalignment faults are deliberately induced in the system to study their effect on the dynamics of the test setup. The experiment is carried out by varying the intensity of misalignment in the input shaft near the pinion. Through the experiments, the dynamic response of the geared system in the frequency domain has been studied and explained.

Pantha Pradip Das, Rajiv Tiwari, Dhrubajyoti Bordoloi
Coupled Vibration Suppression and Energy Harvesting System from Laminated Composite Structure

The demand for smart structures and smart devices has increased in the last decade. This is due to their wide range of applications in data collection, health monitoring, vibration controlling and energy harvesting. These applications can be accomplished by attaching sensors and actuators to the structures. Using conventional battery sources is a costly affair to power these sensors in terms of both financial and environmental aspects. Furthermore, the life and power of the battery sources drop quickly, which leads to a significant decrease in their efficiency and cost-effectiveness. Non-conventional energy sources like solar, thermal, wind and vibration energy can be used to overcome this problem. Among these, vibrational energy harvesting gained large attention due to its abundant availability in nature. Laminated composite structures are now used in wind turbines, automobiles, etc. In the present paper, vibrations from the laminated composite structure are to be minimized by piezoelectric surface actuators. The electromechanical equations of the vibration actuator with energy harvester system are solved and the vibration control, power harvester efficiency charts are illustrated.

Subhransu Kumar Panda, J. Srinivas
Development of Flexible Rotor Balancing Procedure Using Response Matching Technique

The two main methods used for flexible rotor balancing are Influence Coefficient Method (ICM) and Modal Balancing Method (MBM). ICM relies on experimental trial data with several trial masses installed sequentially on all balancing plains to compute response changes per unit mass, called influence coefficients. MBM requires prior knowledge of mode shape and critical speeds of the rotor to compute orthogonal set of balancing masses for each mode. The objective of this paper is to develop a flexible rotor balancing procedure, wherein FEM model rotor response is matched to the actual rotor response using iterative technique. Unbalance masses, moments, and shaft stiffness are iterated on the model to match experimental response data at three distinct speeds that are below the rotor flexible critical speed. The model rotor is virtually balanced at its flexible critical speed by adding optimized balancing masses iteratively using gradient decent approach. Suitable constraints are placed on the level of residual vibrations. Rotor bow parameters are also incorporated in the model. A parameter called bending parameter is introduced to balance flexible rotor. Experimental rotor mounted on flexible supports is used for the validation of the proposed balancing method.

Shubham Saxena, M. B. Deepthi Kumar, Karimulla Shaik, A. S. Patil
Vibration Control and Energy Harvesting Using Coupled Pendulum Absorbers

This paper analyzes the dynamics and energy harvesting of a resonantly excited single-degree-of-freedom linear system with an array of pendulums coupled by springs as absorbers. Energy generation along with vibration reduction gives added advantage of generating sufficient electrical energy to powerup portable electronics. Energy harvesting converts vibration into useful electrical energy using a suitable transduction method. The mathematical model is developed for the proposed model. The numerical method will be used to obtain the response of the system. The effect of multiple pendulums with and without coupling on frequency bandgap of the primary mass and bandwidth of harvested energy will be analyzed. The effect of various parameters on the performance will also be reported.

P. V. Malaji, Grezgorz Litak, Vikram Pakrashi, Abdessattar Abdelkefi, R. S. Kattimani, L. N. Karadi
Spindle Bearing Vibration Characteristics of Surface Grinding Machine Tool

Machine tool, one among many resources in a machine shop of engineering manufacturing sector, takes maximum share in work done and hence it becomes mandate to maintain and ensure the availability of machine tool in good working condition. The decision on machine tool condition is made based on several criteria such as vibration, lubricant contamination and surface finish. In the present study, an experimental approach was developed to investigate the spindle bearing vibration characteristics of surface grinding machine to aid the decision-making process. The vibration data from the spindle bearing was acquired using tri-axial accelerometer and multi-channel FFT analyser under different operating conditions. The vibration behaviour of the spindle bearing of the machine tool was analysed to determine the most influencing combination of material hardness and grit size of the grinding wheel. Prediction analysis was also carried out by building the relationship between vibration and surface roughness using quadratic regression model. An empirical formula was developed to establish the surface roughness and multi-input parameters. The empirical formula was validated with Chi-square test to determine the variation between the empirically computed and experimental values. The experimental investigation reveals that the hardness of the workpiece material is the most influencing parameters on surface roughness and tangential vibration, whereas the combination of grinding wheel grit size and depth of cut is the most influencing parameter on radial and axial vibrations.

K. Lokesha, P. B. Nagaraj, Gururaj Lalagi, P. A. Dinesh
Fault Prediction in Induction Motor Using Artificial Neural Network Algorithms

The paper reflects on the investigation of current signals and vibration signals monitoring for induction motor (IM) effective fault prediction using artificial neural network (ANN) algorithms. Failures in induction motor may occur due to the propagation of various mechanical and electrical faults. In this study, vibration and current signals were acquired after multiple experiments of varying rotational speeds from the experimental test rig and converted into the frequency domain. In this study, ten different fault conditions which are frequently encountered in IM, i.e., four mechanical fault conditions, five electrical fault conditions, and one no defect condition, have been considered. Fault prediction has been done using vibration and current signals concurrently. Three statistical parameters, i.e., standard deviation, skewness, and kurtosis have been considered for extracting features from the signal dataset. F1-score, which is a combination of precision and recall of the classifier into a single metric which is done by taking the harmonic mean, has been used as a metric for evaluating the prediction accuracies of each fault. On the other hand, accuracy has been used for evaluating the overall performance of the ANN model. The results showed that the proposed methodology achieves a very good accuracy and F1-score for the standard deviation data at all speeds while for skewness and kurtosis extracted data, it gives an average prediction accuracy. Owing to this, standard deviation turns out to be the best statistical feature for feature extraction, followed by skewness and kurtosis for the fault prediction of IM.

Ayushi Rai, Rajiv Tiwari, D. J. Bordoloi
Novel Method for Selective and Controlled Online Mass Removal Using Laser Beam for In Situ Balancing of Flexible Rotor Bearing System

Balancing flexible rotors is a tedious process as compared to rigid rotor bearing systems due to shaft bending. Flexible rotors are allowed to run near their bending critical speeds and (stops) prevent the system from balancing from correction planes. Prediction of unbalance accurately has been the topic of research for a long time. To avoid the difficulties of present time-consuming balancing procedures, a new methodology was developed to balance rigid and flexible rotors. This paper presents a new methodology where in situ balancing is possible to perform by removal of mass from the rotor which is running in vacuum using a LASER beam. An experimental test setup was developed to demonstrate the mass removal from an overhung flexible rotor, which is running in vacuum. An electronics system for the measurement of position and synchronization of the LASER beam with the rotor speed is demonstrated. The method of generation of synchronization pulse and desired arc so as to fire the LASER beam in synchrony with the rotating disc is also explained. The system trial with various operating speeds is conducted and the quantity of mass removal and resolution is calculated. The experimental results are also presented with the identification of critical issues to be addressed for application in actual rotor systems for in situ balancing.

A. K. Wankhede, Karimulla Shaik, Munendra Singh, Archana Sharma, B. G. Fernandis
Optimum Design of Intershaft Squeeze Film Damper (ISSFD) Ring for Vibration Attenuation

Squeeze film dampers (SFDs) have become an inevitable feature in aircraft gas turbines which usually get introduced on one of the bearings supporting the HP spool. There are no practical attempts being made to introduce external damping in the other bearing supporting the HP spool, which usually is an intershaft bearing. This work essentially attempts to optimize the design of Intershaft Squeeze Film Damper (ISSFD) ring that could be introduced in the intershaft bearing plane satisfying the space constraint to attenuate vibration. The work involves the fabrication and testing of ISSFD rings for the optimum design by evaluating their static stiffness and damping potential on specially built instrumented test facilities. The static stiffness value of ISSFD rings is evaluated using a static test rig, and the damping potential of rings is evaluated on a single spool dynamic test rig in terms of vibration attenuation capability and also by quantifying the damping factor. ISSFD rings each having three, four and six grooves were tested, and the percentage reduction of vibration amplitude normalized with bearing support stiffness was evaluated. The introduction of oil in the grooves of ISSFD rings resulted in increased bearing plane stiffness and damping thus resulting in increased critical speed and vibration attenuation. Six grooved rings demonstrated relatively a high level of performance defined in terms of vibration reduction levels. Critical speed analysis is carried out on the FE model of the rotor bearing system and the critical speed values obtained correlate well with experimental values.

H. M. Shivaprasad, G. Giridhara, Raghu Yogaraju, P. P. Yathish Muddappa, R. N. Ravi Kumar, V. Arun Kumar
Friction Analysis of an Unbalanced Disk with Recurrence Plot by Using Simpson Integration and Empirical Mode Decomposition

The most common failures that raise vibration levels in rotating machines are friction and unbalanced faults of their components. This kind of fault affects severely the reliability of the equipment and the service life of machines. There are numerous publications on the various techniques used to diagnose friction and unbalanced faults, and some of them are focused on resolving the problem to transform the vibration taken by an accelerometer into velocity and displacement to completely characterize the movement of rotating components. In this paper, the Recurrence Plot (RP) is proposed to analyze dry friction on mechanical rotating systems, and Simpson’s rule with Empirical Mode Decomposition (EMD) is implemented to integrate the acceleration to compute the velocity and displacement which are needed for RP construction. To analyze dry friction an experiment is implemented with an unbalanced disk mounted on a flexible shaft and a friction point on its outer diameter. Vibrations are obtained by an accelerometer fixed on one support and with a vibrometer pointed near the contact surface point of the disk. This work aimed to address the suitability of RP for the analysis of a typical nonlinear friction phenomenon of an unbalanced disk. The RP was computed and compared at different speeds by using both instruments while keeping the unbalanced test mass constant. The results indicated that the RP patterns show significant differences when the friction load is applied but only some of the quantification parameters reflect these differences.

Ignacio Torres-Contreras, Juan Carlos Jauregui-Correa, Salvador Echeverria-Villagomez, Juan Primo Benitez-Rangel
Improving Wideband Sound Absorption of Single Layer Micro-perforated Panel Absorber: A Finite Element and Experimental Approach

Traditional porous sound absorbers were the only mode to attenuate excessive sound nearly two decades ago. But due to their degrading acoustic performance at low-frequency range and other practical issues like hygiene, high pressure surrounding, fiber-free feature, etc., micro-perforated panel (MPP) absorbers gradually replaced them. Though MPP absorbers significantly improve over porous sound absorbers, the acoustic absorption is limited to one to two octaves only. In this paper, a 3D-printed MPP absorber is coupled with a thin layer of a natural absorber, such as a jute felt at a rigid wall, to improve the sound absorption characteristics in the desired frequency band. Maa’s theoretical model is employed along with the transfer matrix method to determine the sound absorption of the proposed model. Both finite element and experimental methods were used to validate the results obtained from the theoretical model. Two microphone impedance tube is the main constituent of the experimental setup subjected to random harmonic excitation. Significant improvement is observed in the wideband sound absorption of the above-proposed sound absorber compared to the single-layered MPP absorber.

D. K. Agarwalla, A. R. Mohanty
Influence of Auxetic Structure Parameters on Dynamic Impact Energy Absorption

This paper focuses on the compressive response of two-dimensional re-entrant auxetic structures under dynamic loads. Classical analysis of cellular structures is adapted in order to include all the geometrical characteristics of the unit cell. For constant velocities of loading, an analytical model (based on shock propagation in a RPPL material) of the successive collapse of the cells is presented. It provides the dynamic plateau stress $${{\varvec{\sigma}}}_{\varvec{dyn}}$$ σ dyn until densification occurs. The stress $${{\varvec{\sigma}}}_{\varvec{dyn}}$$ σ dyn depends on the unit cell data and on the velocity of loading. We also demonstrate the convergence of the analytical model with a more complex Finite Element model implemented in the time explicit solver RADIOSS™. Simulations of the compressive response at a constant velocity or under an initial impact velocity are presented. Both cases show a satisfying correlation between the analytic and numerical approaches. The Finite Element simulations enable to relate the local (at cell scale) to the global (structural) responses. The results obtained through this methodology make it possible to assess the impact mitigation capacity of the auxetic structure.

Adeline Petit, Aravind Rajan Ayagara, André Langlet, Rémi Delille, Yves Parmantier
Vibration Analysis of Functionally Graded Folded Plate

This research work aims to present numerical solutions for free vibration analysis of moderately thick-folded plate structures made of functionally graded materials. First-order shear deformation theory has been applied in this finite element analysis. Nine-noded isoparametric Lagrangian plate bending elements are used. Young’s modulus and density are assumed to vary continuously through the plate thickness according to the power-law distribution. A transformation matrix of order 6 × 6 has been used to combine the system matrices. Several parametric studies have been performed for different folded configurations of the structure, varying its thickness, power-law index, material and boundary constraints. It is observed that the geometry of the fold along with other parameters significantly affects the natural frequency of the folded plate structure.

Debalina Basu Dutta, Sreyashi Das, Arup Guha Niyogi
Mitigation of Plate Vibrations Using Inerter Based Vibration Absorber

The present investigation depicts the dynamic response of a steel plate attached with an inerter based passive vibration absorber when it is subjected to a uniformly distributed pulse loading. An inerter is a passive mechanical element with the characteristic that the applied force at its nodes is proportional to the relative acceleration between these nodes. Herein, the modal analysis of steel plate is performed using the finite element method. The equivalent single degree of freedom (SDOF) system for steel plate is developed by evaluating equivalent mass, stiffness, and load by incorporating the highest participating modes. The parameters for the equivalent SDOF system are also obtained using transformation factors based on the assumed deflected shape of the plate. The displacement response of the central point of plate obtained from FE simulation is compared with the response of the equivalent SDOF system for the validation. Furthermore, mitigation of vibrations of the plate is attempted by incorporating inerter based passive vibration absorber. The vibration absorber’s parameters, i.e., inertance, damping coefficient, and stiffness are varied to investigate their influence on the response of the system.

Lekhani Gaur, Ashish K. Darpe, Tanusree Chakraborty
Updation of Structural Dynamic Response Simulation Using Measured Data for a Typical Naval Aircraft Arrested Landing

Field-measured data form a reliable and accurate means to validate and update simulation. In the present study, vibratory responses in the form of acceleration time data measured during the arrested landing of a typical naval fighter have been used to validate and update dynamic response computations. Naval aircraft operate from an aircraft carrier deck wherein landing recovery is done by the engagement of an aircraft arrestor hook by cables running across the deck. The aircraft usually approaches at a high rate of descent and forward speed and is brought to rest in a short duration and distance. This causes the airframe and equipment mounted inside to experience an initial shock followed by a transient vibration. In order to ensure that the landing shock does not result in unduly high responses of the airframe and installation of critical equipment mounted inside, it is necessary to predict the likely shock response levels experienced by the Airframe. The methodology adopted is to carry out dynamic response computations on a global aircraft FE model. The Shock Response Spectra (SRS) of computed acceleration responses are then compared with measured accelerometer data during arrested landing and the analysis model is updated based on this. This was implemented for a naval fighter application. For reasons of confidentiality, this methodology is illustrated here using a simplified 2D FEM of a naval fighter. These studies have helped to improve simulations and give greater confidence in the predictions. The updated simulations are used to predict responses for test points yet to be evaluated and also for conditions where actual flight tests may be risky or impractical.

Gourav Kumar Dutta, E. Hemalatha
Damage Due to Stress Wave Propagation in Composite Fan Blades of Aircraft Engine Subjected to Bird Strike Loading

It has been observed that when the rotating composite fan blade in an aircraft engine is subjected to high-velocity bird strike, the damage is generally seen on/near the trailing edge even though the impact is happening on the leading edge. This behavior of the blade is tentatively attributed to the stress wave propagation, but there is a strong need for deep understanding to be developed on this. This report talks about the efforts to understand the reasons for trailing edge strain hot spots happening due to bird strike impact on the leading edge. In this context, fundamental plate-level bird impact and simple wavelet excitation studies were performed along with the stress wave propagation studies. The studies show that the stress wave propagation could be attributed up to some extent to the high strain spots appearing on/near the trailing edge. The studies also showed that these strain hot spots can be avoided by applying some innovative techniques.

Prakash Jadhav
Vibration and Stability Response of Laminated Composite Panels with Elliptical Cutout Under Hygrothermal Conditions

The purpose of this paper is to discuss the vibration and buckling responses of laminated composite panels with a central elliptical hole in a hygrothermal (HTL) environment. This work is an extension of previous work on Hygrothermomechanical vibration and buckling analysis of composite laminates with elliptical cutout (EC) under localized edge loads. By considering the effect of transverse shear deformation and rotational inertia, a nine-noded heterosis plate element had been used to discretize the plate. Geometric non-linearity is being used to evaluate the HTL response to free vibration. The dynamic method was utilized to address the buckling issues since the stress distribution in the plate element is non-uniform. A finite element code has been developed to evaluate the outcomes of environmental effects with various parameters such as ply angle orientation, EC orientation, various EC dimensions and sizes, thickness, and boundary conditions to examine the vibration and buckling responses under hygrothermomechanical conditions.

K. S. Subash Chandra, T. Rajanna, K. Venkata Rao
Backmatter
Metadata
Title
Vibration Engineering and Technology of Machinery, Volume II
Editors
Rajiv Tiwari
Y. S. Ram Mohan
Ashish K. Darpe
V. Arun Kumar
Mayank Tiwari
Copyright Year
2024
Publisher
Springer Nature Singapore
Electronic ISBN
978-981-9989-86-7
Print ISBN
978-981-9989-85-0
DOI
https://doi.org/10.1007/978-981-99-8986-7

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