Skip to main content

2015 | Buch

Vibration Engineering and Technology of Machinery

Proceedings of VETOMAC X 2014, held at the University of Manchester, UK, September 9-11, 2014

insite
SUCHEN

Über dieses Buch

The VETOMAC-X Conference covered a holistic plethora of relevant topics in vibration and engineering technology including condition monitoring, machinery and structural dynamics, rotor dynamics, experimental techniques, finite element model updating, industrial case studies, vibration control and energy harvesting, and signal processing.

These proceedings contain not only all of the nearly one-hundred peer-reviewed presentations from authors representing more than twenty countries, but also include six invited lectures from renowned experts: Professor K. Gupta, Mr W. Hahn, Professor A.W. Lees, Professor John Mottershead, Professor J.S. Rao, and Dr P. Russhard.

This work is of interest to researchers and practitioners alike, and is an essential book for most of libraries of higher academic institutes.

Inhaltsverzeichnis

Frontmatter

Keynote Lectures

Frontmatter
Ancient Temple Carts—Modifications for Structure and Steering

Temple carts from ancient times are used to bring out Deities on festival days in a procession. The origin of these carts and their construction is discussed in this paper together with current design practices befitting with changing times.

J. S. Rao, Bigil Kumar
The Rise and Fall of the Rotor Blade Strain Gauge

In any gas turbine the understanding of the way in which the rotor blades vibrate is essential for both the development and production phases. For many years the standard method of obtaining such data has been with the use of strain gauges in conjunction with radio telemetry units or slip rings. With the complexity of the machine increasing and as the operating environment becomes more and more hostile for such systems, new methods are being investigated that will ultimately lead to a non-intrusive technology being developed. Here we review the progress and pioneers of strain gauge measurement dating back to the 1930s and look at a number of technologies that have tried to displace them from their positions as the mainstay of rotor blade vibration measurement.

Peter Russhard
Managing Life Extension for Large Rotating Plant in Power Stations

Risk and reliability management of rotating plant in power stations under life extension have become a major challenge for industry. The increasing numbers of catastrophic failures are calling for a more rigorous regime to address integrity through qualitative as well as quantitative methods. Current condition based assessments as well as condition monitoring techniques need further development into the future to assist power generators manage into unknown territory during life extension.

Wolfgang Hahn
Recent Advances and Prospects in Condition Monitoring

The underlying reason for pursuing Condition Monitoring activities is to enhance the overall performance of plant either by accurately predicting the end of effective life or by diagnosis and location of incipient faults. The achievement of both these objectives requires the use of a combination of measurement, modelling and statistical techniques, but the balance of these three strands varies with the plant under study. Practitioners of these different disciplines sometimes develop rivalries, but in reality all three are essential. The fundamental problem involved is the determination of the physical process within a machine which cannot be measured directly and so must be inferred from external measurements, the most common of which is vibration. This inference from measurement to diagnosis requires some form of model, whether physics or statistics based. The paper describes some work on the monitoring of large turbines and in particular, the ways in which measurements and models can be combined to enhance insight into a machine’s operation. Similarly, our understanding of complex data can be enhanced by the use of Artificial Neural Networks and these can be used to enhance understanding. Combining various approaches leads to some new possibilities which are briefly outlined.

Arthur W. Lees
The Sensitivity Method in Stochastic Model Updating

Probabilistic and interval model updating methods are described, with particular attention paid to variability in nominally identical test structures due, for example, to the effect of accumulated manufacturing tolerances, or degradation of performance caused by wear of engineering components. In such cases the updating parameter distributions are meaningful physically either as PDFs or as intervals. Stochastic model updating is an inverse problem, generally requiring multiple forward solutions, which may be carried out very efficiently by the use of surrogates, in place of full FE models. The procedure is illustrated by experimental examples, including model updating of (i) a frame structure with uncertain locations of two internal beams and (ii) the DLR AIRMOD structure, which displays vibration characteristics very similar to those of a real aircraft.

John E. Mottershead, Michael Link, Tiago A. N. Silva, Yves Govers, Hamed Haddad Khodaparast
Composite Shaft Rotor Dynamics: An Overview

This paper summarizes research on dynamics of composite shafts, with an objective to develop light weight rotor systems. A review of available literature post-1996 is presented here, since a comprehensive review on similar topic was published in 1997 by Singh et al. Specifically the various aspects covered are, theories for dynamic analysis of fiber reinforced composite shaft, their modeling and analysis, experimental work, and design optimization procedures. All these aspects are important for full development of ‘Composite Rotors’ for light weight high performance transmission systems. Directions for future research are outlined.

K. Gupta

Contributed Papers/Chapters

Frontmatter
Investigation of the Synchronous Response in a Back-Back Centrifugal Compressor Due to Imbalance and Seal Distortion

This paper presents a case study on the effect of fouling and damaged long-span labyrinth seals on the rotor dynamics of a high-speed gas centrifugal compressor. This back to back, two stage, nine-impeller compressor is used to compressor natural gas associated with oil production in a particular field within the Sultanate of Oman. The case study investigated involved replicating vibration problems experienced in the field with a rotor-dynamic model so as to understand and demonstrate the influences of seal wear and hydrocarbon fouling on the compressor synchronous vibration.

Mohamed Al Yahyai, David Mba
Comparison of On-Bearing and On-Casing Vibration for Blade Health Monitoring in Rotating Machine

Rotating blades are considered as the most common cause of failures in rotating machinery. In the present research study, the dynamics of the blades both in the healthy and crack conditions are studies on a small experimental rig using the on-bearing and on-casing vibration, which are measured using the accelerometer on bearing pedestals and on casing cover towards on blades. The measured vibration data are analyzed by computing the responses at different engine orders (EOs) related to the blade resonance frequencies and their higher harmonics to understand the blade(s) dynamics behavior. The observations suggest that the on-bearing and on-casing vibration measurements can be extended to the non-intrusive method for the blade health monitoring (BHM). Comparative study between the on-bearing and on-casing vibrations on the simple experimental rig further allow to understand which method is more effective for blade damage detection.

Ahmed A. Gubran, Jyoti K. Sinha
Vibration-Based Condition Monitoring for Rotating Machinery with Different Flexible Supports

In a previous study, a combined vibration and temperature analysis technique for the diagnosis of commonly encountered rotor related faults produced good practicable results even without the use of temperature. This was, however, developed on an experimental rig with relatively rigid supports. The objective of the current study is to investigate the transferability of the said approach on rotating machines with relatively flexible supports. A fault diagnosis (FD) method which compares vibration data acquired from similar machines with different flexible supports is also considered here. The experimental rig used in the previous study was modified to accommodate two different relatively flexible supports. The results of the previously proposed technique showed that diagnosis is insensitive to the support types used. The result of the newly introduced combined FD approach gave improved diagnosis over the previously proposed technique. The observations made are presented in this paper.

Adrian D. Nembhard, Jyoti K. Sinha
Off-Line Crack Detection in Rotors

This paper intends to extend the application of the residual operational deflection shape (R-ODS) to a simplified model of the LP turbine of a steam turbo generator. The numerical model consists of a stepped shaft which accommodates some balance disks to represent the blades at different stages of the LP turbine. The ability of the R-ODS method in detecting cracks in beam-like structures has already been presented. The method removes the effect of the first harmonic component (1x) from the ODSs at higher harmonic components to highlight the non-linear behaviour of cracks. In this paper, single and multiple cracks are introduced at different locations to the finite element model of the rotor. It is assumed the rotor can be taken out from the rig and mounted on a simply supported boundary condition. After carrying out the modal analysis, the rotor is excited at its first resonant frequency and acceleration responses along the rotor are computed to construct the ODSs. The R-ODS method uses the normalised ODSs for the purpose of crack detection. The curvature of R-ODS method is also presented for further improvement in indication of crack locations especially for multiple-crack rotors.

Erfan Asnaashari, Jyoti K. Sinha
Application of Composite Spectrum in Steam Turbo-Generator Set

Composite spectrum and composite bispectrum techniques have been recently developed for identifying fault(s) in rotating machines. The fusion of the measured vibration data at all the machine bearings in the frequency domain is used to construct such a composite spectrum and composite bispectrum for the representation of the entire machine. These techniques are now applied to a Turbo-generator (TG) set which consists of a high pressure (HP) turbine, an intermediate pressure (IP) turbine and 3 low pressure (LP) turbines in addition to an exciter and a generator. Earlier study using the spectrum analysis of the measured vibration acceleration data on the bearings of the TG set during machine normal operation indicates the possibility of the rotating stall in LP turbines and misalignment between the IP and LP rotors. The observations and results of the current study also indicate the presence of localised misalignment and suspected rotating stall in the composite spectrum.

Keri Elbhbah, Jyoti K. Sinha, W. Hahn, G. Tasker
Coherent Composite HOS Analysis of Rotating Machines with Different Support Flexibilities

Earlier studies have shown the possibilities of detecting different faults on a rigidly supported rotating machine through coherent composite spectrum (CCS) and coherent composite bispectrum (CCB) data fusion techniques. The current paper is also related to the use of CS, CB and a newly introduced coherent composite trispectrum (CCT) for faults identification in flexibly supported rotating machines. Six experimentally simulated cases have been considered on two sets of flexibly supported (FS1 and FS2) rotating machines, at 1,200 RPM (20 Hz) speed. Vibration data were then collected from both FS1 and FS2, using only four accelerometers (one per bearing pedestal in the diagonal direction), for the computation of CCS, CCB and CCT. Some combinations of CCB and CCT components were then used to further test the robustness of the techniques in rotating machines’ faults differentiation. The observations and results of the experiments are hereby discussed here.

Akilu Yunusa-Kaltungo, Jyoti K. Sinha
Vibration Behaviour of a Turbo-Generator Set

In situ vibration measurements are carried out on a a typical steam turbo-generator (TG) unit at the West Burton Power Plant UK during the steady state operation. A typical phenomenon of appearance of low frequencies in band of 7–12 Hz is observed mainly related to the vibration measurements on low pressure (LP) turbines bearing pedestals. This band of frequency observed to be modulating with vibration at the machine RPM (50 Hz) and its higher harmonics. The paper summaries the possible causes for such dynamic behaviour.

Wolfgang Hahn, Jyoti K. Sinha
A Comparison Between Hilbert Transform and a New Method for Signal Enveloping

Envelope analysis of vibration signals is a well known tool for amplitude demodulation and diagnosis of a number of vibration problems in machines and structures. The typical application is the fault diagnosis in the anti-friction bearings and gearboxes. Hilbert transformation (HT) is often used to extract the envelope signals (upper and lower) from a time domain signal. However it is observed that the envelope signals obtained by the HT are not always without any error. In this paper, 4 different signals, 3 simulated; sine, amplitude modulated and random, and measured vibration data on anti-friction bearings are analyzed using the HT. The paper compares the accuracy of the envelope data obtained for these different signals using the HT. A new method called three-point moving window (TPMW) method is also developed to generate envelope signals and applied to the 4 different signals that gives better results.

Abdullah Al-Ahmari, Jyoti K. Sinha, Erfan Asnaashari
The Detection of Shaft Misalignments Using Motor Current Signals from a Sensorless Variable Speed Drive

Shaft misalignments are common problems in rotating machines which cause additional dynamic and static loads, and vibrations in the system, leading to early damages and energy loss. It has been shown previously that it is possible to use motor current signature analysis to detect and diagnose this fault in motor drives. However, with a variable speed drive (VSD) system, it becomes difficult to detect faults as the drive compensates for the small changes from fault effects and increased noise in the measured data. In this paper, motor current signatures including dynamic and static data have been investigated for misalignment diagnosis in a VSD system. The study has made a systemic comparison of different control parameters between two common operation modes: open loop and sensorless control. Results show that fault detection features on the motor current from the sensorless mode can be the same as those of the open loop mode, however, the detection and diagnosis is significantly more difficult. In contrast, because of the additional frictional load, features from static data show results of early detection and diagnosis of different degrees of misalignment is as good as that from conventional vibration methods.

Samieh Abusaad, Ahmed Benghozzi, Ann Smith, Fengshou Gu, Andrew Ball
Analysis of SGTF Vertical Sodium Pump Using ARMD

In sodium cooled fast breeder reactors (FBR), centrifugal sodium pumps are widely used to circulate the hot sodium in primary as well as in secondary loops. Performance of this critical component is very important in reactor circuits as it affects the load factor and availability of the plant. Operation of the centrifugal sodium pumps, limiting its vibration is a challenge in view of both safety and economy. Various experimental facilities have been set up at IGCAR for testing of FBR components. Vertical centrifugal sodium pumps are used to circulate hot sodium in these facilities. The pump shaft is supported by hydrostatic bearing (HSB) at the bottom and by tapper roller bearing at the top. As the HSB runs with the close tolerance, rotor dynamic analysis was carried out for ensuring its effectiveness and proper functioning of the pump. The results obtained from the analysis are also verified by conducting experiments. This paper discusses the rotor dynamic analysis carried out on a vertical sodium pump used to circulate sodium in steam generator test facility (SGTF) using the rotor dynamic analysis software. In this pump, shaft is supported at the top by tapper roller bearing and hydrostatic bearing at the bottom. Critical speeds and corresponding mode shapes were obtained in the operating range of the rotor speed. Stability analysis was performed for the rotor-bearing system to get the threshold speed of the rotor. Unbalance response of the pump was also carried out to estimate the amplitude of vibration at the bearing locations and compared with experimental results.

Hemant Prakash Agnihotri, V. Prakash, K. K. Rajan
Qualification of Large Structures for Shock Loads

Many critical equipments and components have to withstand shock and vibration during its life time. In defence, space and nuclear industries in particular, it is mandatory to test and analyze such components before acceptance. Analytical and experimental qualification of these components is an important exercise to be fulfilled as per the applicable codes and practices. Test for shock qualification is particularly important for components designed for defence and space applications. When the structure is large, generally an analytical approach is followed and a small scale model is experimentally validated for such qualification and the result is extended to the prototype. This approach may or may not be true always. The paper discusses about the phases of qualifying a large component for a certain level of shock. Achieving the required shock level and the pulse duration experimentally with repeatability is a challenging task. Besides, when the size and shape of the structure is odd, the qualification procedure becomes more complicated and at times difficult to achieve the desired objective. The objective was to achieve the required shock pulse by dropping the test structure from a predetermined height on a target made of commercially available rubber material. The test object is a long stainless steel vessel weighing 805 kg and 2.8 m long. The vessel is housed in a rigid cage with arrangement to lift with a magnetic clutch for instantaneous release for dropping. It was required to subject the vessel to both vertical and horizontal shock of 25 g of 35 ms duration. For dropping the vessel horizontally, the housing cage was dropped on more than one target from a predetermined height. The procedure followed in arriving at the drop height, actual drop height and the achieved shock levels are discussed in the paper.

K. K. Meher, A. Rama Rao
Hybrid Viscous-Structural Damping Identification Method

Damping still remains one of the least well-understood aspects of general vibration analysis. The effects of damping are clear, but the characterization of damping is a puzzle waiting to be solved. A major reason for this is that, in contrast with inertia and stiffness forces, it is not clear which state variables are relevant to determine the damping forces. In this paper, a new hybrid viscous-structural damping identification method is proposed. The proposed method is a direct method and gives explicit structural and viscous damping matrices. The effectiveness of the proposed structural damping identification method is demonstrated by two numerical examples. First, numerical study of lumped mass system is presented which is followed by a numerical study of fixed-fixed beam. The effects of coordinate incompleteness and different level of damping are investigated. The results have shown that the proposed method is able to identify accurately the damping of the system.

Vikas Arora
Effectiveness of Adaptive Filter Algorithms and Spectral Kurtosis in Bearing Faults Detection in a Gearbox

Bearing faults detection at the earliest stages is vital in avoiding future catastrophic failures. Many traditional techniques have been established and utilized in detecting bearing faults, though, these diagnostic techniques are not always successful when the bearing faults take place in gearboxes where the vibration signal is complex; under such circumstances it may be necessary to separate the bearing signal from the complex signal. The objective of this paper is to assess the effectiveness of an adaptive filter algorithms compared to a Spectral Kurtosis (SK) algorithm in diagnosing a bearing defects in a gearbox. Two adaptive filters have been used for the purpose of bearing signal separation, these algorithms were Least Mean Square (LMS) and Fast Block LMS (FBLMS) algorithms. These algorithms were applied to identify a bearing defects in a gearbox employed for an aircraft control system for which endurance tests were performed. The results show that the LMS algorithm is capable of detecting the bearing fault earlier in comparison to the other algorithms.

Faris Elasha, David Mba, Cristobal Ruiz-Carcel
Pitting Detection in Worm Gearboxes with Vibration Analysis

Diagnostics of worm gearboxes are challenged by lack of research in this field; vibration analysis is rarely employed for the condition evaluation of worm gears due to the inherent challenges involved. However, these gears are commonly used in many applications such as escalators, mills and conveyors and significant cost may arise from their maintenance. This paper aims to apply various vibration analysis techniques to identify faults within worm gearboxes. The conditions of three different worm gearboxes were assessed. Various vibration signal analysis techniques including FM4

*

, and spectral kurtosis and enveloping were employed to identify the presence of defects within the worm gearboxes. The analysis techniques applied were able to present fault features which indicated high levels of scratching-induced vibration, confirming profile damage (pitting) of Gearbox A worm wheel teeth. Among the employed techniques; FM4

*

shows high response to the worm gears pitting. In addition the results show sensitivity to the direction of vibration measurement.

Faris Elasha, David Mba, Cristobal Ruiz-Carcel
Impact Vibrations of Ultrasonic Multi-striker Hand Tool

The impact vibrations of the multi-striker ultrasonic hand tool are investigated theoretically and experimentally. The lightweight intermediate strikers are placed into the gap between the end-face of the high-power ultrasonic converter and the specimen being treated. The high-frequency impact force was measured by the calibrated piezoelectric sensor. The dynamical drift of the tool casing was measured by the linear displacement gauge. Both signals were simultaneously recorded with the use of the two-channel digital storage oscilloscope. The scan-pictures allow to determine the duration of the single impact pulse and its peak value, frequency of the pulse sequence, etc. It was observed, that slow oscillations of the tool casing are synchronously accompanied by the periodical changes of impact force. The dynamic model of the high-frequency impact treatment was constructed by the methods of theory of the vibro-impact systems. The induced impact stresses were calculated in the frames of the Hertz contact approximation with the use of experimental data. It is shown that the impact stress value reaches the yield point of material being treated. The ultrasonic impact processing can be interpreted as a cyclic alternation of setting-up and failure of the vibro-impact oscillation of the striker inside the variable gap. The changes in the mechanical properties and texture were analyzed by the metallographic methods. Metal hardening and creation of the profitable residual stresses on the surface of the specimen were observed.

Makhmut Ganiev, Ilshat Gafurov, Ildar Vagapov
Use of the Roving Mass Technique and SWT to Identify and Locate Multiple Cracks in Simply-Supported Beams

The roving mass technique is used to identify and locate multiple cracks in simply-supported beams. The technique involves the traversing of an auxiliary mass along the length of the beams. At each location of the roving mass, the stiffness of the beam is different which, in turn, causes the natural frequencies of the beam to change as the mass is traversed. A plot of the natural frequencies of the beam versus the location of the roving mass results in natural frequency curves (NFCs). If a crack is present in the beam, then the dynamics of the beam is affected because the crack causes a local reduction in the stiffness of the beam. This leads to very slight reductions in the natural frequencies of the beam. However, these slight reductions in the natural frequencies cannot be observed directly from the NFCs. Identification of crack information from the NFCs is achieved by the application of the stationary wavelet transform (SWT) to the NFCs. The presence of a crack is indicated as sharp peaks in the SWT detail coefficients plots. The effects of various roving mass magnitudes on the crack detection method are investigated. It is shown that the technique is efficient in detecting double symmetric cracks about the centre of the beam as well as detecting multiple cracks.

Amirabbas Bahador, S. Olutunde Oyadiji
Single and Multiple Crack Detection in Simply-Supported Beams Using SWT

Any crack in a beam-like structure creates a local reduction in the stiffness which in turn, affects the dynamics of the structure. This local reduction in stiffness generates small discontinuities in the modal displacements of the beam at the crack locations. However, these discontinuities cannot be visually observed in the modal displacement plots. Therefore, the identification of cracks is performed by decomposing the modal displacements using the stationary wavelet transform (SWT). This paper investigates identification of multiple cracks in simply-supported beams using the SWT. The SWT decomposes a signal into two components that are known as the detail and the approximate coefficients. These coefficients can be viewed as the results of passing the signal through low-pass and high-pass filters. The approximate coefficient gives the low frequency components of the signal which in this case is the overall shape of the signal (mode shapes) and the detail coefficient gives the high frequency components of the signal which in this case contains any high frequency noise or effects of small structural discontinuities present in the signal. The detail coefficients of the SWT detect the existence of cracks by showing high values at the crack locations. The method presented can detect both single and multiple symmetric and non-symmetric cracks with high accuracy in beam-like structures. The modal displacement data of the cracked simply supported beams used are obtained from the finite element method. The results are validated experimentally.

Amirabbas Bahador, S. Olutunde Oyadiji
Modal Approach for Optimal Design of Two-Layer Piezoelectric Vibration Energy Harvesters

A modal approach for the development of optimal configurations of two-layer piezoelectric vibration energy harvesters is presented. The harvester comprises a primary cantilevered beam to which a secondary beam is attached via a mass that is located along the length of the primary beam. An additional mass is located along the secondary beam. The two masses are used to tune the natural frequencies of the composite system and one of them also serves as a spacer between the two beams. By varying the dimensions of the beams and masses, and the locations of the masses along the beams, the harvester can produce close resonance frequencies and significant power output. Thus, the frequency bandwidth of significant power generation by the harvester can be extended. To judge the performance of any harvester configuration requires a full analysis, using the coupled electromechanical equations of the piezoelectric harvester, to determine the electrical power output. However, the analysis is lengthy and time consuming. To hasten the process, a modal approach has been developed. The approach determines the modal performance by means of the mass ratio (which represents the influence of modal mechanical behaviour on the power density directly) and the modal electromechanical coupling coefficient. The modal parameters required by the approach are computed numerically by finite element analysis. The modal approach is used to select harvester configurations with optimal or near-optimal performance, which are harvester configurations with close resonances and moderate values of mass ratio. A full analysis is subsequently performed to determine the power outputs of these harvester configurations.

S. Olutunde Oyadiji, Xingyu Xiong
Synthesis of Vibration Gear Continuously Variable Transfer

Drives of machines which are used now do not possess ability to be adapted for extreme working conditions. Such conditions are connected with possible difficulties of motion because of deviations from operation norms (for example, because of long inactivity, deterioration of conditions of lubricant, minor damages, a temperature difference, etc.). In the conditions of impossibility of elimination of minor failures on the move (for example in aeronautical engineering) insignificant discrepancy of operation of service mechanism can serve as a cause of accident. Recently the technological direction of use of adaptive drive of machines is advanced. The adaptive drive mechanism engages the engine and the self-regulated transmission mechanism. The adaptive gear transmission mechanism with two degrees of freedom has ability to actuate an executive working body with a speed back—proportional external load at constant engine power. It means that even in presence of handicap in motion of working body the drive mechanism breakage will not occur. The adaptive vibrating mechanism in the form of the closed gear differential is developed. The vibrating mechanism contains input carrier, output carrier and closed contour located between carriers. The closed contour contains input satellite, external block with two ring (epicycle) wheels, output satellite and internal block with two solar wheels. The wheels in each block are connected by elastic shaft. In an operating time elastic shafts transfer vibrating oscillations to the output carrier. Output carrier transfers vibrating action to working body. The vibrating mechanism provides reliable overcoming of operational overloads. In offered work synthesis of the vibrating mechanism on the set vibrating action is executed. Work is executed on the basis of mechanics laws.

Konstantin S. Ivanov, Roza K. Koilibaeva, Gachip Ualiev, Baurjan Tultaev
Crack Propagation in a 500 MW LP Turbine in Service

A 500 MW turbine generator set that operated through a rigorous two shift regime had developed a crack whilst in service. The shaft line was regularly subjected to multiple starts with oil whirl manifesting on load during certain operational conditions. First observations on generator no. 11 bearing showed an increase in the 1× component over a period of time, with changes through the critical speed during run-down triggering close monitoring. Further observations over time revealed that the Low Pressure turbine three, 1× and 2× components increased during steady state in conjunction with changes in phase angles and critical speed during transient conditions. Early indications showed that the likelihood of a crack in the main turbine shaft was high. Further observations over time revealed that the 1× and 2× steady state trends continued to increase up to the ISO limits set for the turbine generator set. The unit was shut down and qualitative inspections undertaken. The findings revealed that a crack had developed on the main rotor body in the pencil shaft.

Wolfgang Hahn, David Futter
Effect of Ultrasonic Oscillations on the Interaction of al with Ga-In Eutectic Alloy

The development of the compact sources of energy (~10 W) has been advancing during the recent years basing on the use of hydrogen fuel cells. One of the methods of obtaining pure hydrogen is the reaction of water with aluminum activated with Ga-In liquid eutectic alloy. The mechanism of aluminum activation by Ga-In (76 wt% Ga, t

m

= 15.9 °C) eutectic alloy is based on the diffusion of the eutectic components along the grain boundaries of the original aluminum sample. In this paper, we attempted to use ultrasonic action to improve the efficiency of the diffusion process. It has been shown that the activation of aluminum in the ultrasonic field increased the rate of diffusion along the grain boundaries of the starting material by 2 orders of magnitude. The purpose of the work was to study the nature of the acoustic impact on the interaction between Ga-In eutectics and a massive aluminum sample. The heterogeneity of the structure causes corresponding changes in the velocity and direction of acoustic wave propagation in the sample and accordingly affects its resonance characteristics. The product obtained as a result of activation according to the described technique efficiently interacted with water to release hydrogen.

Alexey A. Novikov, Alexandr I. Nizovskii, Mikhail V. Trenikhin, Valerii I. Bukhtiyarov
Nonlinear Control of an Aeroelastic System with a Non-smooth Structural Nonlinearity

Non-smooth nonlinearities such as freeplay, bilinear/piece-wise linear stiffness are among the various types of nonlinearity that have been encountered in aeroelastic systems. Freeplay, for example, may begin to appear as a result of ageing of components such as bolted joints and control surfaces, and has been known to be the cause of flutter-induced limit cycle oscillation (LCO). Therefore, it is evident that effectively controlling these nonlinearities is essential in avoiding the onset of LCO, or indeed any other type of nonlinear response. The present paper addresses the control of systems with non-smooth structural nonlinearities, through application of the feedback linearisation method. In systems with smooth nonlinearities, the required nonlinear feedback is also smooth, and therefore does not give rise to complexities associated with the feedback linearisation method. On the other hand, when controlling systems with non-smooth nonlinearities, the necessary control inputs are also non-smooth, and the applicability of feedback linearisation to such systems is of interest. This task is undertaken in the present work, through the use of numerical simulations on a 3 degree of freedom aeroservoelastic model. An example of a case where the parameterisation of the nonlinearity is uncertain is also addressed.

Shakir Jiffri, John E. Mottershead
A Block Decoupling Control Algorithm for Vibration Suppression of Linear Structures

In this article, a new block decoupling control algorithm is proposed to decouple undamped or damped structures into two independent substructures with desired closed-loop performance. The algorithm is featured by dealing directly with second-order dynamic structural systems. The block decoupling is implemented by imposing appropriate modal nodal constraints on the closed-loop right eigenvectors so that some modes are uncoupled with the others. The decoupling is synthesised into a process of eigenvalue assignment by the use of multi-input multi-output control, which causes no extra increase of constraints on the control gains and makes the block decoupling control problem very straightforward. A necessary solvability condition for the block decoupling problem is given. Two numerical examples are used to illustrate the working of the proposed approach in undamped and damped structural systems respectively.

Xiaojun Wei, John E Mottershead
Measurement and Simulation of the Vibroacoustic Performance of an Electric Motor

Noise and vibration of electrical machines is a major concern. Changes in the machine design to improve its efficiency can lead to unacceptable vibrations. Tools to predict its vibratory and acoustic performance at the design stage need to be developed. An improved finite element model has been developed to analyse the vibration behaviour of a permanent magnet synchronous motor (PMSM) using the finite element software ABAQUS. All components and subsets of the machine have been modelled and validated by experimental modal analysis (EMA) performed on them. Some modelling issues have been overcome so that an accurate enough model has been reached. The laminated stator, as it is formed by a pack of several steel sheets, has been treated as an orthotropic material and windings have been considered a solid orthotropic part as well. The rotor-shaft assembly has also been verified by EMA. The bearings that join the rotor to the assembly of the stator have been represented by radial springs. The electromagnetic forces are applied to the whole machine model in order to obtain the vibration response. These forces are obtained from the magnetic air-gap flux density which has been obtained with a 2D finite element model developed by FLUX. Finally, the vibration response has been used to calculate the radiated noise with an acoustic model developed in LMS Virtual Lab. The results given by the acoustic numerical model are compared with sound power measurements.

Alex McCloskey, Xabier Arrasate, Xabier Hernandez, Oscar Salgado
Forced Vibration of Eight Mistuned Bladed Disks on a Solid Shaft—Excitation of the First Compressor Bladed Disc

Considered here is the effect of multistage coupling on the dynamics of an aircraft engine rotor with eight mistuned bladed discs on a drum-disc shaft. Each disc had a different number of rotor blades. Free and forced vibrations were examined using finite element models of single rotating blades, bladed discs, and an entire rotor. Calculations of the global rotating mode shapes of flexible mistuned bladed discs-shaft assemblies took into account the excitation of the first compressor bladed disc with 0EO, 1EO and 2EO forces. The obtained maximal stress values of all of the rotor blades were carefully examined and compared with a tuned system to discover resonance conditions and coupling effects. Mistuning changes the stress distribution in individual rotor blades and the level of maximum stress increases or decreases as compared to bladed discs which are analyzed without the shaft.

Romuald Rzadkowski, Artur Maurin
Dynamic Analysis of Parametrically Excited Piezoelectric Bimorph Beam for Energy Harvesting

In this work, the dynamics of an energy harvester which is modeled as a base excited cantilever beam with tip mass having piezoelectric patches on both top and bottom surfaces has been investigated. The governing equation of motion of the system is developed using extended Hamilton’s principle and it is solved by using method of multiple scales. Closed form solution has been developed to find out the voltage generated from this nonlinear energy harvester. While in most of the previously considered energy harvesters the system is considered without tip mass and axial load, here putting the additional tip mass and periodic axial load, different resonance conditions have been explored. A parametric study has been carried out to investigate the variation of generated voltage with different system parameters. The study will find application in the generation of voltage for a wide range of frequencies available in ambient vibration.

S. K. Dwivedy, Anvesh K. Reddy, Anshul Garg
About Multi-parametric Analysis of Drill String Vibrations

Coupled flexural-torsional vibrations of drill strings are subject to multi-parametric analysis. A drill string is modelled as a thin elastic beam taking into account the effect of primary static deformation induced by the prescribed compressional force and twisting moment. The appropriately normalized ratio of the two latter quantities along with dimensionless vibration frequency and beam relative thickness are assumed to be the main problem parameters. Three distinct dynamic regimes are determined. Two of them correspond to predominantly torsional or flexural vibrations. The third regime is not widely known. It is specific of the primary static deformation, caused by the aforementioned twisting moment. Simplified limiting equations are formulated for each of the regimes. Associated approximate dispersion relations are compared with the exact dispersion relation corresponding to the original problem. The developed methodology may be useful for qualitative interpretation of numerical and experimental data related to drill string modelling.

Almaz Sergaliyev, Julius Kaplunov, Lelya Khajiyeva
Tuned Mass Damper Inverted Pendulum to Reduce Offshore Wind Turbine Vibrations

Wind energy is in a fast development worldwide and is currently receiving great investments mostly for being a clean energy source. Advances in this area are resulting in increasingly high and slender wind turbines, intensifying vibrations in structures caused by its own operation and, also, by wind force. Searching a better performance leads to offshore devices, i.e. wind turbines installed at the ocean next to coast. These structures take advantage of wind forces generated by more intense and consistent wind with less turbulence in these regions. One of the conceptions for this kind of wind turbine is the floating device. A solution to the problem of excessive vibration, which has been studied by several researchers in recent years, is structural control. One of the structural control devices, already extensively studied and implemented in practice, is the Tuned Mass Damper (TMD). An alternative geometry for TMD is the pendulum absorber. However, previous studies have shown that pendulum TMD installed on floating wind turbines requires an excessive length, therefore a different approach is required. In this work it is proposed an inverted pendulum TMD to improve control performance in an offshore wind turbine modeled as an inverted pendulum. This device may be considered as a linear oscillator only for small vibration amplitudes. Numerical simulations are performed to define TMD parameters that improve the control device performance. Good performance is achieved. However, passive devices only work properly for the design frequency range, and wind forces are random type of excitations. Better results would be achieved if a robust control is developed. This study will serve as a basis for the proposition of a semi-active device.

P. V. B. Guimarães, M. V. G. de Morais, S. M. Avila
Vibration Control of Active Vehicle Suspension System Using Fuzzy Logic Controller

Fuzzy logic control (FLC) algorithm grants a means of converting a linguistic control technique and it is widely used in vehicle applications. This paper demonstrates the application of fuzzy logic technique to design a controller for the active vehicle suspension system to improve the suspension system performance by altering the number and arrangement of the rules set and the universe of discourses. A mathematical model and equations of motion of quarter vehicle active suspension is derived and solved using MATLAB/Simulink software. The proposed fuzzy controllers using 9, 25 and 49 rules set with two different types of membership functions, trapezoidal and triangle, are implemented in a closed loop control system to demonstrate the influence of the numbers of rule set and the type of membership function on the performance of suspension system. Suspension performance criteria were assessed in both time and frequency domains. Performance comparisons between the passive suspension, as a reference, and the proposed controllers of the active suspension were achieved. The simulation results indicate that the proposed active fuzzy controllers can dissipate the energy due to road excitation effectively and improves suspension performance. Among the investigated systems, the 25 rules set with a trapezoidal membership function for the fuzzy controller gives the best performance.

A. Shehata, H. Metered, Walid A. H. Oraby
Two-Stage Data Driven Filtering for Local Damage Detection in Presence of Time Varying Signal to Noise Ratio

Local damage detection in rotating machinery can become a very difficult issue due to time-varying load or presence of another damage reflected in amplitude modulation of the raw vibration signal. In this paper a two-stage filtering method is presented to deal with this problem. The first stage is based on autoregressive (AR) modeling. It is incorporated to suppress high-energy components that mask an informative signal. High-energy amplitudes of mesh harmonics modulated by other damage or load variation can affect selectors of optimal frequency band as well, so they have to be suppressed. The second stage relies on filtering the AR-residual signal using a linear filter based on an informative frequency band selector. Here as a selector we propose to use the average horizontal distance on quantile-quantile plot. We compare the result of the second stage with the spectral kurtosis. The procedure is illustrated by real data analysis of a two-stage gearbox used in a belt conveyor drive system in an open-pit mine.

Jakub Obuchowski, Agnieszka Wylomanska, Radoslaw Zimroz
Energy Harvesting from Near Periodic Structures

In this research energy harvesting from near periodic structure is discussed. The near periodic system consists of two pendulums connected using a common linear spring. Mistuning in the simple coupled pendulum system is achieved by varying the length of one of the pendulums. Effect of this mistuning on amount of energy harvested is developed analytically and numerically. This will be discussed in this paper and at the same time effect of harvesting on mistuning will be presented. It is shown that with a proper electrical damping, optimal power can be obtained and effect of mistuning can be minimized. Same analysis is carried out with energy harvesting from both the pendulums. In case of harvesting from both the pendulums the harvesting bandwidth is increased and electrical damping required to minimize mistuning is more than that in case of harvesting with mistuned pendulum alone.

P. V. Malaji, S. F. Ali
Dynamic Analysis of Multilayered Sandwich Beam with MRE Core

In the present work dynamic analysis of multilayered sandwich beam with MRE core has been carried out. Finite element model has been developed for the multilayered sandwich beam with alternate stiff metallic and soft MRE core materials. Natural frequencies have been determined for 5 and 7 layered beams at different magnetic fields considering three different boundary conditions. Also the effect of increase in number of layers on modal frequencies, time and frequency responses have been studied which show that damping of multilayer beam occurs faster than the 3 layered sandwich beams with equivalent material.

S. K. Dwivedy, S. L. V. N. Avinash
Analysis of Coupled Transverse and Axial Vibrations of Euler Bernoulli and Timoshenko Beams with Longitudinal Crack for Its Detection

This paper presents a method to analyze the vibration of monolithic beams with longitudinal cracks for its detection. Both forward problem of determination of natural frequencies knowing the beam and crack geometry details as well as inverse problem of detection of crack with the knowledge of changes in the beam natural frequencies has been examined. Both long (Euler-Bernoulli) and short (Timoshenko) beams have been studied. For modeling a crack located at the free end of a cantilever, the beam is divided into three segments. For an internal crack located away from the free end of the beam, it is split into four segments. In both cases, two of the segments take care of beam portions above and below the crack. The cracked segments are constrained to have the same transverse displacements but different axial movements. The modeling shows good accuracy for both the forward and inverse problems. The formulation predicts the first five fundamental natural frequencies in the forward problems with a maximum difference of 5 % with reference to finite element solutions for short beams with edge or inner cracks. Further, in the case of inverse problems, edge crack with sizes varying 5 to 50 % of the beam length has been detected with errors less than 3 % in both short as well as long beams. In the case of inner crack located at the mid-span with sizes varying from 5 to 45 % of the beam length has been detected with errors less than 3 % in location and 6 % in size. The results thus show encouraging possibility of exploitation of the proposed method for crack detection in practice.

Jeslin Thalapil, S. K. Maiti
Detection of Arbitrary Number of New Cracks Appearing in a Beam with Pre-existing Cracks

This paper is concerned with development of a scheme to detect fresh crack(s) in a beam with pre-existing crack(s). The cracks have been modeled by rotational springs. Relationship has been derived through energy method involving natural frequency, mode shape of uncracked beam, crack location(s) and size(s). Natural frequencies of the beam in the two states, before and after development of fresh crack(s), are the basis for the detection. Case studies have been done with uniform and stepped long beam(s). For the case studies, frequencies data have been generated through finite element method. Cantilever beams are examined with crack sizes in the range 15–50 % of section depth. Crack locations are varied within 92 % of the span from the fixed end. In the case of two pre-existing cracks and one fresh crack, the maximum errors in predicting location and size are 1.98 and 4 % respectively. In the case of one pre-existing crack and two fresh cracks the same errors are 6.99 and 8.33 % respectively. In the case of two-stepped cantilever beam with one initial crack and one fresh crack, the errors are 15 and 5.26 % respectively. The accuracy of prediction is thus very encouraging. One advantage of the proposed method is that it gives directly the location and size of the new crack(s).

Dhanjee K. Mahto, Surjya K. Maiti
Acoustic Technique for Diverse Safety Rod Drop Time Measurement in PFBR

Diverse safety rods (DSRs) are used in Prototype Fast Breeder Reactor (PFBR) to shutdown the reactor during emergency conditions (SCRAM). These rods contain neutron absorber materials to reduce the reactivity for the safe shutdown of the reactor. During normal operation of the reactor, DSRs are held above the active core using electromagnets. During a SCRAM the electro-magnets are de-energized and DSR falls into the core. Since it is a safety related action, no active system is used for driving the rods into the core and the rod falls under gravity force. It is required to measure the fall time of DSR during each SCRAM in the reactor to ensure proper insertion of the DSR in the core. Experiments were carried out in various facilities to develop a measurement technique. This paper discusses the details of Diverse Safety Rod Drive Mechanism (DSRDM), acoustic technique used for fall time measurement, experiments carried out, analytical modeling details and its results and conclusion.

V. Prakash, Hemant Prakash Agnihotri, P. Anup Kumar, R. Ramakrishna, K. K. Rajan
Large Amplitude Free Vibration Analysis of Axially Functionally Graded Tapered Rotating Beam by Energy Method

Geometrically nonlinear free vibration behaviour of axially functionally graded non-uniform rotating beams are investigated following variational form of energy method. Nonlinear strain displacement relations are employed to account for geometric nonlinearity present in the system. The static solution of the displacement field of the beam under centrifugal loading is obtained first and then the dynamic problem is formulated as an Eigenvalue problem based on the known static solution. The displacement fields are approximated by linear combination of orthogonally admissible functions and undetermined parameters. The method is validated successfully and results are presented in non-dimensional plane.

Saurabh Kumar, Anirban Mitra
A Frequency-Based Criterion for Automatic Selection of the Optimal Intrinsic Mode Function in Diagnostics of Localized Gear Tooth Faults

To date gearboxes remain one of the most important elements of virtually every power transmission system as far as a continuous operation of the shaft line is concerned. Any failure or breakdown may result in putting the whole production line, supply chain or even peoples life in jeopardy. Endeavours to detect an incipient fault within the system serve multiple purposes from increasing the safety of the people responsible for operating the machines, through to decreasing running and operational costs, allowing time to plan for the inevitable repairs and making sure that the downtime of the machine is kept to an absolute minimum. This, in turn, makes this branch of condition monitoring of rotating machinery one of the most intensively studied. The Empirical Mode Decomposition (EMD) is a relatively new method of signal decomposition, which breaks the original signal up into a number of so-called Intrinsic Mode Functions (IMFs). The decomposition represents a type of adaptive filtering which outputs a number of IMFs which, acquired according to two strict criteria, contain portions of the filtered version of the original signal and so can carry different information about the content of the signal. EMD has already been used in the field of condition monitoring of rotating machinery, but the selection of the optimal IMF for the task often requires the experience of a condition monitoring specialist. This paper proposes a frequency-based tool for automatic selection of the IMF that is best suited for the detection of localized gear tooth faults.

Pawel Rzeszucinski, Michal Juraszek, James R. Ottewill
Vehicle Suspension Performance Analysis Based on Full Vehicle Model for Condition Monitoring Development

The objective of this research is to develop a mathematical model using a seven degree-of-freedom full car. The simulation analyses were conducted to predict the response of the vehicle when driven across speed bumps of different shapes and at range of speeds. Three bump sizes were considered in this study including bump 1 (500 mm × 50 mm), bump 2 (500 mm × 70 mm), and bump 3 (500 mm × 100 mm). These were run through the model at speeds of 8, 16, 24 and 32 km/hr. The model was validated using experimental data, which was collected by driving the vehicle across the bump 1 at a speed of 8 km/h. The performance of the suspension in terms of ride comfort, road handling and stability of the vehicle were analysed and presented. The vibration analysis for different speed levels of 8, 16, 24 and 32 km/hr indicated that, the effect of vehicle speeds on the vibration of the vehicle body increases at lower speeds up to a maximum value after which it began to decrease from the optimum point with increasing vehicle speeds. The model has been used for fault detection of under-inflation of vehicle tyre by 35 %, and also to predict possible future suspension faults.

Moamar Hamed, Belachew Tesfa, Fengshou Gu, Andrew D. Ball
Effects of Monograde and Multigrade Oils on the Friction Force in Four-Stroke Motor Engine: An Experimental and Analytical Approach

In this work computational models with measured friction on a motor of four stroke engine are compared. Fluid Structure Interaction analysis is performed using the Navier Stokes equations in order to calculate the hydrodynamic friction for several engine operational conditions. The piston ring friction was experimentally measured under different conditions on a single-cylinder gasoline engine, using strain gauges along to the cylinder liner. The Hilbert-Huang Transform (HHT) is applied in the experimental signals. A differential deformation fluctuation signal of piston-piston rings and cylinder is adaptively decomposed into Intrinsic Mode Functions (IMFs) through the use of Empirical Mode Decomposition (EMD) methods. Further, the de noised deformation from strain gauges signal is obtained and the friction force can be determined. This method doesn’t require any great engine modification, so the piston ring-cylinder friction reflects the reality. The experimental results for different grade type of oils (SAE 30, SAE 10w40), were compared with the numerical predictions, and presented.

Anastasios Zavos, Pantelis G. Nikolakopoulos
Delamination Detection in a Laminated Composite Beam Based on Changes in Natural Frequencies

This paper presents an analytical method for modelling delamination parallel to beam longitudinal axis that can help in solving both forward and inverse problems. For vibration analysis of a beam with internal delamination, it is divided into four segments. The forward problem of determination of frequencies due to a known delamination is solved analytically using the characteristics equation. Case studies are presented and the frequencies are compared with finite element frequencies which show a very good agreement between the two. To solve the inverse problem of locating damage from measured changes in natural frequencies, the characteristic equation is solved. In this paper a simple method to solve the inverse problem has been proposed. The method is fast and inexpensive and it has been validated using input frequency data generated by finite element method for both cantilever and simply supported beams. The predicted axial locations and sizes agree closely with the actual data. The maximum errors are 5 and 6 % in the prediction of location and size respectively for a known interface.

Kajal Khan, Surjya K. Maiti
Investigation of the Effect of Biodiesel Blends on Fuel Injection Pumps Based on Vibration and Pressure Measurements

Amongst alternative fuels for diesel-engine application, biodiesel is very attractive because it is biodegradable, an environmentally-friendly and sustainable source that can meet future energy demands. However, there are few published studies of the impact of biodiesel fuel and its blends on fuel injection pumps (FIPs). This study will investigate the influence of biodiesels derived from waste cooking oils with incremental blends of B10, B20, B30, B40 and B100. The FIP in this study is a rotary type attached to a four-cylinder, four-stroke direct injection, turbocharged diesel engine. Vibration and pressure measurements were made on the FIP. The results show the peak pressure close to the pump increases slightly the higher the proportion of biodiesel because of increased viscosity, density and bulk modulus of the fuel. Low frequency vibration increased as the proportion of biodiesel increased. These results demonstrate an increase in dynamic load on the pump components. However, high frequency vibration levels are lowest for the blends B10, B20 and B30, which may be helpful for improving the service life of the delivery.

Ali Abruss, Yangchun Guo, Tie Wang, Fengshou Gu, Andrew D. Ball, D. Brown
Robustness Evaluation of Adhesively Bonded Ceramic Quad Flat Chips for Space Applications

Ceramic quad flat packs (CQFP) electronic components have long been used in power devices in the space industry. Soldering CQFPs to a printed circuit board (PCB) is not sufficient and thus the use of adhesives for reinforcement is compulsory. In fact, the risk of failure becomes very high during launch missions due to harsh constant and random accelerations. The paper investigates various distributions of two common thermally conductive and one epoxy adhesives. The intention is to compare the effects of these adhesive bonds on the robustness to vibrations of solder joints. Results are generated from a finite element (FE) model consisting of a CQFP component, an adhesive layer and a PCB. Key outputs such as the maximum deflection of the PCB, the stress in the solder joints and the fatigue lifetime of the assembly are discussed. Recourse to FE simulations allows competitiveness in terms of design cost and delivery time.

Lassaad Ben Fekih, Georges Kouroussis, Christophe De Fruytier, Olivier Verlinden
Coupling Analysis for the Thermo-Acoustic-Vibration Response of a Thin-Walled Box

Monitor and control unit is essential to almost all of the modern aircrafts or spacecrafts, which always places in a relatively closed space and requires a compatible mechanical environment to ensure its normal function. The acoustic, vibration and thermal loads developed in the operation of the aircraft determine a complex environment for its monitor and control unit. In particular, there should be couple effect among the thermal, vibration and acoustic responses. This article presents numerical simulation studies on a thermo-acoustic-vibration response of a typical thin-walled box, to reveal the multi-physics environment of the monitor and control unit. The thermo-structural equations were proposed and solved numerically, following that the vibro-acoustic analysis was implemented. The coupled algorithm was developed to simulate the structure response and sound distribution, and predict the acoustic loss during transmitting through the box shell. The validation cases of the vibration and acoustic response of a plate were performed at first. The outcome provides the multi-physics environment prediction method for designing and optimizing the monitor and control unit.

Yan Yang, Chen-Wu Wu
Chatter Detection in CNC Milling Processes Based on Wiener-SVM Approach and Using Only Motor Current Signals

The CNC milling is one of the most common processes in modern manufacturing, which characterized by highly nonlinear behavior and chatter problems. As other complex processes, Chatter detection in this situation is a crucial step for improving surface quality and reducing both noise and rapid wear of the cutting tool. This paper proposes a new methodology for chatter detection in computer numerical control milling machines. The originality of this method consists for using only motor current signals picked from electrical cabinet of machine and artificial intelligent. The methodology can be decomposed into four general tasks: (1) data acquisition, (2) signal processing, (3), features generation and selection, (4) classification. In signal processing task, electrical signals are resynchronized according to the electrical cycle (60 Hz) by exploiting the cyclostationarity of electrical signals through their cyclic statistics. After that, synchronous average is computed and subtracted from original signals in order to obtain the residual part. Wiener filter is then applied on residual signals by taking as reference the residual electrical signals acquired in spindle free rotation. This procedure allows estimating a signals corresponding to the electrical part and extracting the mechanical part, which linked to a chatter phenomenon and cutting mechanism. The signal processing task is primordial in order to decrease the dynamics of the electrical fundamental component and its harmonics and also to increase the contribution of mechanical parts. Extracted features computed from mechanical parts are then ranked based on theirs entropies in which only best features are selected and presented to the system for classification. At the classification step, the selected features are classified into two classes: stable and unstable utilizing a support vector machine (SVM). The intelligent chatter detection has accuracy above 96 % for the identification of cutting state after being trained by experimental data. The results show that it is possible to monitor chatter behavior in milling process by using motor current signal.

M. Lamraoui, M. El Badaoui, F. Guillet
Dynamics of the Unbalanced Support Centrifuge with Cavity Partially Filled with a Multiphase Liquid Medium

The paper studies dynamics of the statically unbalanced support centrifuge with a cylindrical cavity partially filled with a multiphase liquid medium and mounted on an elastic foundation. The centrifuge is a rotor, installed cantilevered on the shaft. It is fixed at the lower hinged bearing and the upper elastic bearing and rotates with a constant angular velocity. It is easy to pass from the dynamic model of the support centrifuge to the model of the suspended centrifuge. A mathematical model of the system “centrifuge-multiphase liquid-foundation” is developed and solved analytically.

Almatbek Kydyrbekuly, Lelya Khajiyeva
Design and Test of a Piezoelectric Inertial Mass Actuator for Active Vibration Control

Active control of vibrations can outperform passive systems in certain applications, e.g. when broadband damping is requested or when several orders of a periodic disturbance have to be cancelled. To generate dynamic forces for the active control system, inertial mass actuators are frequently used. Mainly, they comprise a force generating element driving a single-degree-of-freedom oscillator which is coupled to the structure to be controlled. Thus, those actuators can also be used for retrofitting of existing structures or for prototyping purposes. In this paper, a design for an inertial mass actuator utilizing piezoceramic actuators is studied. Since those actuators integrate both stiffness and force generation into one element, this enables more compact and mechanically robust designs. With respect to the future integration into industrial applications, standard multilayer piezoelectric actuators are considered to decrease the costs of the system and allow for a high reliability. Usually, an inertial mass actuator should possess a low resonance frequency in order to enable operation over a broad frequency range. Since the stiffness of piezoelectric multilayer actuators is rather high, a lever mechanism is designed which transforms the stiffness of the piezoelectric element into the desired range. An analytical model of the inertial mass actuator is derived and parameter studies are performed to investigate the characteristics of the design. A prototype is set up and the main parameters like resonance and block force are experimentally validated. Finally, the integration of the actuator into an active vibration control system for a lightweight structure is described.

Sven Herold, Dirk Mayer, Tobias Melz, Tobias Röglin
Heat Transfer and Thermoelastic Dynamics of a Rotating Flexible Disc in a Hard Disc Drive

Multi-field dynamic coupling takes place in computer hard disc drives, involving air flow, heat transfer and thermoelastic vibration of a rotating flexible disc in an enclosure filled with air. Air velocities and pressure induced by disc rotation in the enclosure are obtained by using penalty finite element method. Temperature increments in the rotating disc, driving shaft, enclosure and air flow are determined interactively by including the external heat sources from the shaft driving motor and enclosure circuit board, the internal heat source from aerodynamic heating due to viscous fluid dissipation, the heat convection in air flow, and the free convection heat loss at enclosure’s outside surfaces. Natural frequencies of the rotating disc under the thermal stresses induced by the disc’s temperature increment and centrifugal force are determined. Effects of air flow, heat convection and aerodynamic heating induced by disc rotation on heat balance in the enclosure and natural frequencies of the rotating flexible disc are investigated. This investigation is useful to hard drive design.

Yong-Chen Pei, Huajiang Ouyang
A New Direct Method for Updating Mass and Stiffness Matrices with No Spillover

A direct method for model updating of mass and stiffness matrices of structures without spillover is presented, which requires the knowledge of only the few eigenpairs to be updated of the original undamped model. Upon a necessary and sufficient condition, proposed previously by authors, for the incremental mass and stiffness matrices that modify some eigenpairs while keeping other eigenpairs unchanged, the finite element model updating problem that preserves symmetry and avoids spillover is formulated as a semi-definite programming problem, which can be efficiently solved by existing semi-definite programming algorithms. Numerical examples are given to demonstrate the accuracy and effectiveness of the presented updating method.

Jiafan Zhang, Huajiang Ouyang, Jun Yang
Wave Propagation in a Honeycomb Composite Sandwich Structure in the Presence of High-Density Core Using Bonded PZT-Sensors

“Honeycomb Composite Sandwich Structure” (HCSS), is one of the novel materials that has been adopted universally to form major structural components of aerospace, marine and automotive vehicles due to its high strength to weight ratio and high energy-absorption capabilities. In this research paper, the scope to study the general characteristics of guided wave (GW) propagation in an HCSS plate with the presence of a high-density (HD) core subjected to time-dependent transient surface excitations is presented numerically and experimentally. Significant effects are detected due to the presence of HD core in terms of decay in amplitude and reduction in group velocity of the output GW signals. A two-dimensional (2D) numerical model is made in ABAQUS. An effective non-reflecting boundary condition (NRBC) is modeled in ABAQUS in order to mitigate the undesirable boundary reflections during numerical simulation. Good agreements between the numerical and experimental results are noticed for all the cases studied.

Shirsendu Sikdar, Sauvik Banerjee
Health Monitoring of Stiffened Metallic Plates Using Nonlinear Wave Interaction and Embedded PZT Transducers

The ultimate strength of a structural component can be limited in the presence of microscopic imperfections, which serve as the origin of damage process. These micro imperfections are considerably shorter than the acoustic wavelength of the frequencies normally used in ultrasonic nondestructive technique. As a result, the sensitivity of the linear acoustic characteristics (attenuation, velocity etc.) is not sufficient enough to detect the microscopic imperfections of a structure. But, these micro imperfections produce local excess nonlinearity, which is higher than the intrinsic nonlinearity of the intact structure. On the other hand, weakly or incompletely bonded interfaces (e.g., contact-type defects, cracks, debondings, delaminations and loosening in bolted joints) also exhibit highly nonlinear behavior as the contact area changes frequently when elastic waves propagate through the interface. The various nonlinear techniques for damage detection developed in the recent years are: non-linear resonant ultrasound spectroscopy (NRUS) and non-linear wave modulation spectroscopy (NWMS).The later consists of two methods, namely harmonics generation and sidebands generation. In this work a simulation study has been carried out using ANSYS Finite Element (FE) software, where the NWMS methodology is adopted for the case of a stiffened aluminum plate for different degrees of damage in the form of different delamination lengths. A damage index (DI) is defined by taking into account the relative amplitude of the harmonics or the side-bands with respect to the carrier frequency amplitude. It is found that the DI increases with the increase in delamination length.

Deba Datta Mandal, Debashis Wadadar, Sauvik Banerjee
Using Roving Disc and Natural Frequency Curves for Crack Detection in Rotors

In this work, a simple crack identification and localisation approach, which is based on a finite element model of a cracked rotor, is proposed. The model simulates the behaviour of a cracked rotor to provide data to be used to identify the location and depth ratios of a crack in stationary rotor systems. The cracked region, which is an open crack type, is modelled as time-varying stiffness. The rotor is considered as a simply-supported beam carrying a roving disc as an auxiliary mass which transverses along the shaft from one end to the other. A new technique, which is called frequency curve product (FCP) method, is presented to identify and locate a crack clearly in rotor systems. The proposed technique is based on the normalised natural frequency curves (NNFCs) of cracked and intact rotors using the principle of roving masses and natural frequency curves. This technique is developed in order to firstly, solve the disappearance of a crack effect from NNFCs when the crack is close to or exactly at a node of a mode shape. Secondly, FCP curves combine the first four NNFCs in a single plot to identify the crack location clearly. Different pairs of the normalised natural frequencies of different modes of vibration are multiplied together in order to enhance the identification and location of cracks. It is shown that this technique identifies the exact crack location through unifying all the first four natural frequency curves at the maximum positive value in the plot.

Zyad N. Haji, S. O. Oyadiji
Vibration Based Diagnosis of Distributed Bearing Faults

Bearings are vital components in rotating machinery, being the only one that separate stationary and rotating elements of the machines. Bearings are subjected to degradation in various manners, e.g. scuffing, pitting, brinelling, electro erosion. In the early stage of degradation, faults emerge on the rolling surface locally. These tiny surface defects are hardly visible but do not cause problems in system operation. As time progresses, the process further deteriorates the rolling surface. The damage on the rolling surface widens in size and becomes distributed fault. The aim of this paper is to propose an approach for detection of distributed bearing faults. It is based on assumption that these faults excite particular vibrational pattern that can make them distinguishable from local faults. For this purpose, a lumped parameter model capable of simulating vibrational response of damaged bearing was adopted. The model was extended by incorporating fluctuations in ball diameter. By analyzing envelope spectra of simulated and measured vibrations we show that vibrational patterns produced by localized and distributed faults differ. The main contribution of the paper is a new feature which combines BPFO (ball pass frequency outer) and FTF (fundamental train frequency) component of the envelope spectrum. A simulation study dealing with broad range of damage propagation scenario is performed in order to assess performance of the proposed features. Finally, validation is performed on the set of damaged bearings.

Boštjan Dolenc, Pavle Boškoski, Jurij Pfajfar, Đani Juričić
Freight Car Roller Bearing Fault Detection Using Artificial Neural Networks and Support Vector Machines

This paper deals with fault detection and diagnostics of freight rail tapered roller bearings using statistical features and auto-regressive m.odel parameters extracted from bearing vibration signals. Two classifiers are used to distinguish cup, cone, and roller defects, namely, artificial neural networks (ANNs) and support vector machines (SVMs). Time domain vibration data is collected from normal bearings, and defective bearings with combinations of cup, cone, and roller defects. Features are used to train both ANNs and SVMs, and performance is compared for both classifiers. Mutual information between time domain features and target classes is computed in order to rank features with the highest relevance. Excellent performance was observed using laboratory data and the trained ANNs and SVMs, with testing accuracy as high as 100 % in some cases.

Daniel Maraini, C. Nataraj
Light Rotor-Stator Partial Rub Characterization Using Instantaneous Angular Speed Measurement

Instantaneous angular speed (IAS) measurement is recently recognized as a promising technique for condition monitoring of various rotating machines and their subsystems. There are various approaches considering counting techniques and processing of signal. This paper considers application of analog signals from toothed wheel encoder or zebra tape encoder and acquisition at low to moderate sampling rates. Such a system can experience problems with non-uniformity of encoder segments geometry, thus correction of encoder segment non-uniformity was performed. The rubbing often occurs in rotating machinery at position with small clearances and can sometimes cause catastrophic breakdown of machine. So it is important to develop reliable tools for rub diagnosis. As the rubbing process is nonlinear this paper beside conventional Fourier transform also considered potential of sifting operation of Empirical mode decomposition (EMD) method. EMD was employed to produce intrinsic mode functions (IMFs) and to further improve the detection capabilities of Fourier transform. Developed procedure for IAS measurement was successfully tested on laboratory test rig for rotor to stator contact dynamics investigation at speed transition from no rub to light rotor to stator partial rub condition.

Sanjin Braut, Roberto Zigulic, Goranka Stimac, Ante Skoblar
Sequential Recurrence Analysis of Experimental Time Series of a Rotor Response with Bearing Outer Race Faults

Rolling elements bearings are one of the most common components used in expensive, high precision and critical machines such as gas turbines, rolling mills and gyroscopes. They can be subjected to various defects which could lead to catastrophic results. This includes inner and outer race defects and hence it is of interest to analyze the system response under such defects. A better understanding of the system performance under such defects can be beneficial when performing system diagnostics and system design. In this paper we are focused on the outer race defect and perform a comparative nonlinear time series analysis of a healthy system and a defective system. We consider various levels of outer race defects. The analysis is based on the recurrence properties of the system in its reconstructed state space. After determining the appropriate time lags through the average mutual information technique and the corresponding embedding dimensions through the false neighbor technique, we perform a sequential analysis of the system by subdividing the time series into bins and investigating the system response through recurrence quantification analysis parameters along with the entropy. This contributes to the enhancement of the science of diagnostics of outer race defects by analyzing the signature of various recurrence quantification analysis parameters as the system goes from a healthy state to a severely defective state.

C. A. Kitio Kwuimy, M. Samadani, K. Kappaganthu, C. Nataraj
Adhesive Layer Influence on Compressive and Tension Stiffness of Thin-Layer Rubber-Metal Elements

The technique of “force–displacement” stiffness characteristics calculation for thin-layer rubber-metal damping devices is presented in this work. It is proposed to take into account adhesive layers and deformation of non-elastomeric layers working under tension and compression. A variational method of linear theory of elasticity for weakly compressible materials is used for calculations. The received dependences allow explaining nonlinearity of “force–displacement” stiffness characteristics and various behavior of glued rubber-metal device under tension and compression, observed in experimental investigations.

Vladimirs Gonca, Svetlana Polukoshko, Galina Hilkevica
Multi Speed Model Updating of Rotor Systems

Accurate Finite Element (FE) models of rotor systems are required for predicting its dynamic behavior, in dynamic design and fault identification purposes. In inverse eigen-sensitivity method of finite element model updating, the limited number of measured eigenvalues available at any spin speed restricts the maximum number of parameters that can be updated. This paper proposes a multi speed model updating method based on inverse eigenvalue sensitivities to update parameters of a rotor system. The method uses eigenvalues obtained at more than one spin speed to update the model. Such an approach allows not only to update more number of parameters but also helps in obtaining a more consistent estimate of updating parameters.

Manoj Chouksey, Jayanta K. Dutt, Subodh V. Modak
Vibration Control of Semi-active MR Seat Suspension for Commercial Vehicles Using Genetic PID Controller

Nowadays, proportional integral derivative (PID) controller is the most popular control algorithm applied in engineering systems and has been generally accepted in industrial control. Recent developments in commercial vehicles have heightened the need for improving the ride comfort. The application of magnetorheological (MR) dampers in a seat suspension has been shown to provide significant benefits in this area. In most research on seat MR dampers the control application was not quite suitable for the semi-active and nonlinear hysteretic nature of MR dampers. This paper introduces an investigation into the use of a controlled MR damper for a semi-active seat suspension for commercial vehicle, enabling more suitable control. The proposed control system comprises a system controller that computes the desired damping force using a PID controller tuned using genetic algorithm (GA), and a continuous state damper controller that provides a direct estimation of the command voltage that is required to track the desired damping force. A mathematical model of a six degree-of-freedom semi-active seat suspension with human body model using an MR damper is derived. The proposed semi-active seat suspension is compared to a passive seat suspension for prescribed base displacements. These inputs are representative of the vibration of the body (sprung) mass of a passive quarter–vehicle suspension under bump and random-profile road excitation. Control performance criteria such as seat travel distance and head acceleration are evaluated in both time and frequency domains, in order to quantify the effectiveness of the proposed semi-active control technique. The simulated results indicate that the proposed genetic PID of the semi-active MR seat suspension provides a significant improvement in ride comfort.

S. Gad, H. Metered, A. Bassuiny, A. M. Abdel Ghany
Identification of Hysteretic Behavior of Magnetorheological Dampers Using NLARX Model

Magnetorheological (MR) dampers are the most promising devices for vibration control applications because it has many advantages such as mechanical simplicity, high dynamic range, low power requirements, large force capacity and robustness. In this paper, a new approach for studying the forward and inverse dynamical behavior of an MR damper using Non-Linear Autoregressive Models with Exogenous Inputs (NLARX) is presented. NLARX is a built-in function related to the identification toolbox, MATLAB/Simulink software, used to identify the nonlinear behavior of dynamic and engineering systems. The training and validation of the proposed model are done theoretically using the data generated from the modified Bouc–Wen model. Validation data sets representing a wide range of working conditions of the damper show that the use of the NLARX model to predict the forward and inverse dynamical behavior of MR dampers is reasonably accurate.

A. Shehata, H. Metered, W. Oraby
Online Roundness Error Identification and Model-Based Monitoring for Rotors

Condition monitoring is vital for operating rotors safely. The application of model-based approaches allows a more detailed diagnosis than signal-based methods. Yet, model-based methods require identifying the properties of the undamaged rotor accurately. Measurements at single parts and modal analysis help to verify the rotor model. When monitoring rotor displacements with eddy-current sensors, also roundness errors must be considered. For roundness identification at operation speed, a method based on three non-orthogonal eddy-current sensors is presented. Several experiments show that the measurement data can be split into the contents rotor orbit and roundness error. The extracted orbit is evaluated by an academic model-based monitoring system developed for our test rig. Currently, it can evaluate unbalance, bow, misalignments and/or stator contact.

Markus Rossner, Thomas Thuemmel, Heinz Ulbrich
Study on Dynamic Load Sharing Characteristics of Double-Row Planetary Gear Train

The non-linear transverse-torsional coupled model of double-row planetary gear train is established, and planet’s eccentricity error and time-varying meshing stiffness are taken into consideration. The solution of differential governing equation of motion is determined by applying the Fourier series method. The behavior of dynamic load sharing characteristics affected by the system parameters including gear eccentricity error, torsional stiffness of first stage carrier and input rate are investigated. Some theoretical results are summarized as guidelines for further research and design of double-row planetary gear train at last.

Rupeng Zhu, Dongping Sheng, Guanghu Jin, Fengxia Lu, Heyun Bao, Miaomiao Li
A Novel Method to Improve the Resolution of Envelope Spectrum for Bearing Fault Diagnosis Based on a Wireless Sensor Node

In this paper, an accurate envelope analysis algorithm is developed for a wireless sensor node. Since envelope signals employed in condition monitoring often have narrow frequency bandwidth, the proposed algorithm down-samples and cascades the analyzed envelope signals to construct a relatively long one. Thus, a relatively higher frequency resolution can be obtained by calculating the spectrum of the cascaded signal. In addition, a 50 % overlapping scheme is applied to avoid the distortions caused by Hilbert transform based envelope calculation. The proposed method is implemented on a wireless sensor node and tested successfully for detecting an outer race fault of a rolling bearing. The results show that the frequency resolution of the envelope spectrum is improved by 8 times while the data transmission remains at a low rate.

Guojin Feng, Dong Zhen, Xiange Tian, Fengshou Gu, Andrew D. Ball
Vibrational Characteristics of a Cracked Rotor Subjected to Periodic Auxiliary Axial Excitation

Rotor failure due to cracks can be catastrophic with large costs in down time, damage to equipment and injury to personnel. Prevention of such problems is only attained by developing reliable methods for crack detection and diagnosis. In this paper, the vibratory response of a cracked rotor to an auxiliary axial excitation is investigated experimentally for the purpose of crack detection. An open crack (slot) is artificially created in the rotor-shaft of the experimental rig. The effects of running speed, crack depth and crack-unbalance angle variations on the vibratory response are investigated experimentally. It is shown that the auxiliary excitation method can be efficiently used in crack detection as an online condition monitoring technique. By properly choosing the frequency of the periodic axial excitation and the running speed, the presence of a crack in the excited shaft can be ruled out and the crack growth can be monitored. The crack-unbalance angle can influence the identification process negatively by masking the crack effect on the vibratory response. However, an unbalance trial mass test can help in finding out the unknown crack angle.

Heba H. El-Mongy, Younes K. Younes, Mohamed S. El-Morsy
Parametric Modeling of Main Excitation Sources on Board Vessels

Efficient analysis methods for predicting the vibro-acoustic behavior of vessels are important, especially during the early design stages. A prediction software tool can help to identify critical points in the ship design and to avoid costly rework subsequent to sea trials. Therefore, an approach based on numerical system-level simulation, to estimate noise, vibration and harshness performance during each step of the design process is proposed. This paper is focused on the development of numerical models of main excitation sources on board. Parametric excitation models for main engines and pumps as well as structural models for power trains and foundations are built up. The sources introduce excitation forces into the foundations or torsional moments into the power train. The overall simulation model is built up modular and contains structural submodels as well as excitation submodels. System-level simulations using

Matlab/Simulink

are performed and both stationary operational conditions and transient excitations, e.g. engine run-ups and misfiring, are simulated. The numerical results are presented and the accuracy of the model is evaluated by comparing numerical and experimental data.

Christoph Tamm, Georg Stoll, Sven Herold
Investigation of Motor Current Signature Analysis in Detecting Unbalanced Motor Windings of an Induction Motor with Sensorless Vector Control Drive

Maintaining the efficiency of AC motors in site equipment is important, given the increasing cost of energy. Reduction of motor efficiency from baseline manufacturer data can go undetected until total failure of the equipment is experienced. This paper introduces motor current signature analysis methods used to detect the early onset of motor efficiency reduction in AC motors controlled by modern Sensorless-Vector Variable Speed Control inverters. A step increase in the resistance of one stator winding is simulated in stages. Off-line processing of motor current data signals using data analysis methods developed for the MATLAB platform is used to identify imbalances caused by subtle stator resistance increases. Initial results indicate that small increases in stator resistances can be observed in the motor current signals received after data processing techniques have been used on the measured signals. The test results are presented herein along with details on the research work to be continued.

M. Lane, D. Ashari, F. Gu, A. D. Ball
Analysis of Locally Nonlinear Two Dimensional Periodic Structures Using NOFRFs

The analysis of locally nonlinear two dimensional (2D) periodic structures is studied using the concept of nonlinear output frequency response functions (NOFRFs). NOFRFs are a series of one-dimensional functions of frequency, which allow the analysis of nonlinear systems to be implemented in a manner similar to the analysis of linear system in the frequency domain. By inspecting the relationships between the NOFRFs of unit cell in the locally nonlinear two dimensional periodic structures, a series of properties about the NOFRFs of the nonlinear system are derived. The correctness of these properties is demonstrated by numerical studies. These properties obtained in this paper are of significance to the frequency response analysis for nonlinear 2D periodic structures. One important potential application of these properties is the location of damage in 2D periodic structures, which make system behave locally nonlinearity.

C. M. Cheng, Z. K. Peng, W. M. Zhang, G. Meng
Research on Multi-correlative Subsystems Analysis for Vibration Source Identification

The complex vibration source identification of structure in the vibration analysis and control is an important aspect that people pay more attention. First, the complex vibration system of structure is divided to several related subsystem each other in the paper. The model of subsystem-input/single-output system is established. The correlations between inputs and the model after average process in multi subsystem-input system are developed. The value changes of correlated input matrix and the affecting to the output in various relevant condition of subsystem-inputs are analyzed. According to coherence analysis, the method to estimate the contribution of inputs to the output is obtained. And the accuracies of method are verified by simulation. Finally, the vibration data are given by an automobile test. After the data analysis, the usefulness of new method provided in the paper is verified.

S. M. Li, X. X. Jiang, C. W. Lim
A Nut-Type Ultrasonic Motor Driven with Single Phase Signal

Most travelling wave ultrasonic motors use two phase signal with a 90° time phase difference to generate a traveling wave, this paper propose a novel nut-type travelling wave ultrasonic motor which uses only a single phase driving signal to excite two bending modes in r − θ plane of a nut-type stator simultaneously. Thus, both the motor structure and the driving circuit will be simplified. The working principle of the new single phase drive traveling wave nut-type ultrasonic motor was described. The working modes are observed with a finite element method software. A prototype nut-type ultrasonic motor was fabricated, and its electrical impedance was tested to observe the two working modes. The prototype motor worked at frequencies between two resonance frequencies under single phase drive as expected, and it also rotated bi-directional successfully.

Zhuzi Chen, Yu Chen, Tieying Zhou, Deyong Fu
Theoretical and Experimental Investigation into ‘Efficient Modal Control Strategies’ as Applied on a Plate Structure

In this work some efficient modal control strategies for ‘active vibration control’ are theoretically simulated and experimentally implemented. Experimentation is done on a cantilevered test plate instrumented with one piezoelectric sensor and two piezoelectric actuators. Test system is modelled using finite element procedures. Finite element model is reduced to first three modes using modal reduction technique. Experiments are performed using modal space control (no weighting), modal space control (displacement weighting), modified independent modal space control, modal space control (energy weighting) and modal space control (fuzzy logic based weighting). It has been observed that, efficient modal control strategies conserve energy without sacrificing much on performance.

Manu Sharma, S. P. Singh
Smart Machines with Flexible Rotors

The concept of smart machinery is of current interest. Several technologies are relevant in this quest including magnetic bearings, shape memory alloys (SMA) and piezoelectric activation. Recently a smart bearing pedestal was proposed based on SMAs and elastomeric O-rings. However, such a device is clearly relevant only for the control of rigid rotors; for flexible rotors there is a need for some modification on the rotor itself. In this paper, equations of motion are developed to describe a rotor with a force generator (for example, a piezoelectric element) mounted on it. It is shown that such a system may be used to compensate for imbalance by inducing a rotor bend. This leads to some questions as to the optimum control strategies, and the paper discusses some of the possibilities.

Arthur W. Lees, Michael I. Friswell
Vibration Localization of Rotationally Periodic Structures

Structures with uniform periodic spacing and repeated geometry are found in complex engineering systems. Examples include turbine blades, ship hull, aircraft fuselage and oil pipelines with periodic supports. The vibration characteristics of these periodic structures are highly sensitive to its mass distribution, stiffness distribution and geometrical properties. Parametric uncertainties in structures which arise out of material defects, structural damage or variations in material properties can break the symmetry of periodic structures. These uncertainties can drastically change and localize the vibration modes. Identification of severe mode localization in the design process can help prevent failure due to high cycle fatigue in periodic structures such as turbine blades. A 2-DOF system is used to demonstrate the effect of parametric uncertainties on eigenvalue veering and mode localization phenomenon. The Finite Element Method (FEM) was developed to study the free vibrations of two linearly un-damped systems, namely, two cantilever beams coupled system and an idealized turbine blade. The effect of parametric uncertainties on eigenvalue veering and mode localization is demonstrated and a novel numerical method using the Modal Assurance Criterion (MAC) to quantify mode localization in complex systems is proposed.

Arun Chandrashaker, Sondipon Adhikari
Forward and Backward Whirling of a Rotor with Gyroscopic Effect

The determination of whirling frequencies of high speed turbines is always challenging in rotor dynamics. The natural frequencies of a Jeffcott rotor are split in the presence of gyroscopic effect. It is quite well known that the lower branch corresponds to the backward whirl and the upper branch corresponds to forward whirl. The forward whirl mode of the rotor has been observed experimentally, however, the backward whirl has not been observed. In this study it is shown that the backward whirl can be observed when the rotor is coasting down to rest from above the critical speed corresponding to the backward whirl. In order to illustrate the forward and the backward critical speeds of a simple Jeffcott rotor, the natural frequencies are obtained analytically for the second natural frequency of the system because of the large gyroscopic effect present in that mode. An experimental set up was used to verify the presence of backward whirl while the rotor is coasting down to rest. The rotor is also simulated using finite element method by ANSYS, and Campbell diagram is plotted. The analytical, experimental and ANSYS simulations confirm the existence of the backward whirl when the rotor is coasting down.

Ali Fellah Jahromi, Rama B. Bhat, Wen-Fang Xie
Analysis of Nonlinear Dynamic Second-Order Effect of a Large-Scale Container Crane Under Seismic Excitations

Under seismic excitations, the second-order effect (P-Delta effect) exists in deformed structure under vertical loading even in linear-elastic system. For the vulnerability of the large-scale container crane, the effect is particularly remarkable in the slender structure, especially under large deformations. The current research on the rule of the static P-Delta effect has gained tremendous achievements, through systematic, reliable and simplified calculation methods. This paper however proposes the nonlinear dynamic second-order effect of the large-scale container crane. The aim of this paper is to analyze the influence of P-Delta effect on nonlinear dynamic seismic responses owing to different seismic conditions and seismic excitations. Meanwhile, by comparing with the methods of numerical FEM simulations, the simplified theoretical calculation conclusions of the dynamic second-order effect for the bending-type structure on portal frame can be verified. This research reveals clearly the regular pattern of P-Delta effect and influencing factors. The results have great significance on the seismic design of large-scale container crane. The main

-

findings are presented in the paper.

Dong Wang, Gongxian Wang, Yeping Xiong, Jiquan Hu
Predictive Coefficient Method for Establishing Similarity Model of Jumbo Container Cranes

Shaking table similar model test is an important and frequently-used research technique in dynamic response analysis of large structures. Similar conditions derived from dynamic similarity theory usually cannot be fully implemented on scale model, which causes model distorted. Moreover, the test results obtained from distorted similar model cannot be accurately inverted to predict the dynamic behaviors of the prototype structure. This research proposes Predictive Coefficient Method for establishing similarity model of Jumbo container cranes. In the case of container gantry cranes model test, Prediction Coefficient of dynamic response is obtained from distortion model and prototype in the method of Finite element prediction coefficient firstly; then Hammer modal test and seismic shaking table test of a container crane model and get its dynamic properties are carried out; thus the Predictive Coefficient can be amended and achieved by compare the numerical results and experimental results. The analysis results show that the distortion model test results according to the Prediction Coefficient Method can accurately predict the prototype structure dynamic characteristics and this method also can improve the reliability of similarity model test results.

Zhe Li, Gongxian Wang, Jiquan Hu
Stability and Bifurcation Analysis of an Axially Accelerating Beam

The present work deals with nonlinear transverse vibration of a beam moving with a harmonically fluctuating velocity and subjected to parametric excitation at a frequency close to twice the natural frequency in presence of internal resonance. The geometric cubic nonlinearity in the equation of motion is due to stretching effect of the beam. The analysis is carried out using the method of multiple scales (MMS) by directly attacking the governing nonlinear integral-partial-differential equations and the associated boundary conditions. The resulting set of first- order ordinary differential equations governing the modulation of amplitude and phase of the first two modes are analyzed numerically to obtain steady state and dynamic bevaviour along with stability as well as bifurcation of the travelling system. The system exhibits trivial, single mode and two mode solutions with pitchfork, saddle-node and Hopf bifurcations. The sensitivity of the system towards the variation in frequency and amplitude of fluctuating velocity component, variation in damping, flexural stiffness and initial points are studied.

Bamadev Sahoo, L. N. Panda, Goutam Pohit
Analysis of Indirect Measurement of Cutting Forces Turning Metal Cylindrical Shells

Cutting forces measurement is an important component of the machining processes development and control. The use of conventional direct measurement systems is often impossible as they interfere in the process’s dynamics. This work proposes a method of cutting force indirect estimation during turning thin-walled cylindrical shells. Calculation of the flexibility matrix has enabled us to relate measured displacements of certain workpiece’s points to the cutting force. An optimization approach for choosing the measurement points location has been proposed, based on the best conditioning of the flexibility matrix.

Kirill Kondratenko, Alexandre Gouskov, Mikhail Guskov, Philippe Lorong, Grigory Panovko
Hybrid Permanent Magnet and Foil Bearing System for Complete Passive Levitation of Rotor

This paper deals with the complete passive levitation for a typical Jeffcott rotor and rotation of the same at the speeds around 40,000 rpm. The passive levitation is achieved by supporting the rotor axially by a permanent magnet bearing and discrete bump foil bearings for the radial support. The permanent magnet bearing is made up of three pairs of ring magnets arranged in Halbach pattern. Bump foil bearings are designed for rotor weight to provide the radial support to the rotor system. The proposed rotor-bearing configuration is analysed using Finite Element Analysis (FEA) software (ANSYS) for rotor dynamic characteristics. The designed rotor bearing system is fabricated and tested up to the speeds of 40,000 rpm. The system response is acquired using advanced rotor-dynamic data acquisition system. The experimental results show that the rotor is completely airborne and stable at the desired speed.

Siddappa Iranna Bekinal, Tumkur Ramakrishna rao Anil, Sadanand Subhas Kulkarni, Soumendu Jana
Amplitude Demodulation of Instantaneous Angular Speed for Fault Detection in Multistage Gearbox

Traditional fault detection processes in gearbox are mostly based on vibration signal analysis. However, many a times extraction of fault features by the vibration signal analysis becomes difficult as the signal carries structure-borne noise. Moreover, position of the vibration sensor affects the signal to noise ratio of the signal. The presence of a fault in a gearbox changes the rotating dynamics of the system which varies the speed of the output shaft. Therefore, aim of this paper is to analyse the varying speed of the output shaft for detection of fault in a multistage automobile gearbox. Here, the varying speed is measured as instantaneous angular speed (IAS). Besides carrying information related to the fault, this IAS signal carries less structure borne noise due to direct response of rotating dynamics. Furthermore, in presence of fault, this varying speed signal or IAS signal is frequency modulated signal. Besides frequency modulation, the IAS signal becomes amplitude modulated under the application of load. Demodulation is a well known technique in the area of signal processing, which extracts the modulating part from a signal. Hence, the amplitude demodulation technique has been applied to the IAS signal which reveals various important frequencies related to the gearbox. Thus the technique helps to detect the fault in a multistage automobile gearbox under different load conditions.

Sankar K. Roy, A. R. Mohanty, C. S. Kumar
Experimental Grey Box Model Identification and Control of an Active Gas Bearing

Gas bearings have inherent dynamics that gives rise to low damping and potential instability at certain rotational speeds. Required damping and stabilization properties can be achieved by active flow control if bearing parameters are known. This paper deals with identification of parameters in a dynamic model of an active gas bearing and subsequent control loop design. A grey box model is determined based on experiments where piezo actuated valves are used to perturb the journal and hence excite the rotor-bearing system. Such modelling from actuator to output is shown to efficiently support controller design, in contrast to impact models that focus on resonance dynamics. The identified model is able to accurately reproduce the lateral dynamics of the rotor-bearing system in a desired operating range, in this case around the first two natural frequencies. The identified models are validated and used to design a model-based controller capable of improving the damping of the gas bearing. Experimental impact responses show an increase in damping by a factor nine for the investigated conditions.

Lukas Roy Svane Theisen, Fabián G. Pierart, Henrik Niemann, Ilmar F. Santos, Mogens Blanke
Monitoring of the Damage in Rolling Element Bearings

Envelope Analysis of vibration signal is the most used and simplest method for the diagnostics of rolling element bearings. This method is based on the identification of bearing damage frequency components in the so-called Envelope Spectrum. If the recognition of the damage type is quite a simple task, the monitoring and the evaluation of the trend of a suitable damage index are complex tasks to be performed in an automatic way. The damage index must be robust against variations of system operating conditions and external vibration sources to avoid misleading results. In the paper, the case of a rolling element bearing in which the defect develops until a permanent failure is described as well as the algorithm implemented for alarm signaling.

Steven Chatterton, Pietro Borghesani, Paolo Pennacchi, Andrea Vania
Effect of Structural Dynamics on the Shaft Line Rotor Response in Turbomachines

The accurate model of the complicated dynamic phenomena characterizing rotors and support structure represents a critical issue in the rotor dynamic field. A correct prediction of the whole system behavior is fundamental to identify safe operating conditions and to avoid instability operating range that may lead to erroneous project solutions or possible unwanted consequences for the plant. Although a generic rotating machinery is mainly composed by four components (rotors, bearings, stator and supporting structure), many research activities are often more focused on the single components rather than on the whole system. The importance of a combined analysis of rotors and elastic supporting structures arises with the continuous development of turbomachinery applications, in particular in the Oil and Gas field where a wide variety of solutions, such as off-shore installations or modularized turbo-compression and turbo-generator trains, requires a more complete analysis not only limited to the rotor-bearing system. Complex elastic systems such as rotating machinery supporting structures and steel foundations might, in some situations, strongly dominate the entire shaft line rotor dynamic response (mode shapes, resonance frequencies and unbalance response). They give birth to transfer functions which will introduce coupling phenomena between machines bearings, becoming enablers of a new shaft line dynamic. Since FEM theory offers a number of different solutions to represent the rotor and the rotating machine support system (beam models, solid models, transfer function, etc.), in this paper a great emphasis is given to the results of an experimental campaign done on a centrifugal compressor as validation of the new rotor dynamic approach.

E. Meli, G. Pallini, A. Rindi, F. Capanni, S. Rossin
Nonstationary Processes Studying Based on “Caterpillar”—SSA Method

This paper deals with “Caterpillar”-SSA method—a new powerful model-free method of time series analysis and forecasting. It allows to decompose the nonstationary time series into trend, periodic components (sum of elementary harmonic), noise (random components) and to forecast subsequent behavior of system, if separability condition of time series and possibility of reverse synthesis of individual elements are fulfilled. This paper shows application of this method for random and nonlinear vibrations study on the example of building element vibration under seismic action.

Svetlana Polukoshko, Galina Hilkevica, Vladimirs Gonca
Vibration Measurements on PFBR Fuel Subassemblies

Prototype Fast Breeder Reactor (PFBR) is a 500 MWe liquid metal cooled fast breeder reactor, which is in the final stage of construction. The core of PFBR consists of 1,758 subassemblies supported at the bottom on the grid plate sleeves. Liquid sodium is used as the coolant and flow through the maximum rated fuel subassembly is 36 kg/s. The coolant flows axially from the bottom of the subassembly to top and it is in highly turbulent regime. This turbulent flow can excite flow-induced vibration of fuel subassembly which can cause failure of the fuel pin clad tubes from fatigue, wear and vibration induced fretting. Excessive vibration of fuel subassembly can also results in reactivity noise, fatigue or rattling. Flow induced vibration studies of dummy fuel subassemblies in water were conducted in subassembly test facility and the design was qualified for PFBR. However it is planned to measure the amplitude and frequency of vibration during pre-commissioning tests of PFBR. Measurements are planned during the isothermal run of PFBR at 200 °C with dummy subassemblies loaded in the core. Since measurement has to be carried out in high temperature sodium environment, conventional contact type sensors such as accelerometers, strain gages etc. cannot be employed for vibration measurement. Non-contact measurement technique using ultrasound waves was planned to be developed for vibration measurement. Extensive experiments were carried out in various test facilities and ultrasonic vibration measurement technique was established and demonstrated. Based on the experimental results, a device named SONAR was designed and developed for PFBR. The SONAR device is equipped with ultrasonic sensors, which focuses on subassembly crown region, and is capable of movement in Z-axis (up and down) and in Theta-axis (rotation). The movement of the subassembly is detected from the train of ultrasonic pulses and echoes from the target subassembly. Time signal and frequency spectra of vibration are extracted from the ultrasonic signals using signal processing technique implemented in LabVIEW platform. This paper discusses the details of the FIV measurements on PFBR fuel subassemblies, details of ultrasonic technique and SONAR device, its testing and results and conclusion.

P. Anup Kumar, R. Vidhyalakshmi, H. P. Agnihotri, Sudheer Patri, S. Chandramouli, V. Prakash, K. K. Rajan
Multiple Fault Classification Using Support Vector Machine in a Machinery Fault Simulator

The classification of various faults using a fault simulator and support vector machines (SVMs) has been studied. A database is created for number of faults by measuring vibration signals using seven accelerometers mounted on a machinery fault simulator (MFS). Statistical features are extracted in time domain from the vibration signals. Then, the sensitive features are selected using compensation distance evaluation technique. Multi-class SVMs ensemble algorithm is implemented for classification of the various faults by considering SVMs created by the possible combinations of sensitive features for each class of the fault. The effect of distance evaluation criterion for selection of sensitive features amongst the extracted twelve statistical features has been addressed. By using the developed algorithm, the effective location of accelerometer among seven accelerometers for better classification of the faults has been investigated. Measurements are done at five different rotational speeds. The robustness of the developed algorithm has been tested at different speeds.

S. Fatima, A. R. Mohanty, V. N. A. Naikan
A Method for Vibro-Acoustic FE Model Updating of Cavities Using Frequency Response

Interior noise due to structure-borne sources has always been a cause of concern in the cavities encountered in aerospace, automotive and other applications. In the design of such cavities, the coupled vibro-acoustic model is the key to evaluate its structural and acoustic design. It can also be used as a diagnostic tool to identify the potential noise sources and to assess the effectiveness of the proposed design modifications. However effectiveness of this model greatly depends on the accuracy of predictions made by these models. It is however seen that often there are inaccuracies in the modeling of structural and acoustic domain of a cavity. Methods to deal with structural and acoustic modeling inaccuracies have been developed in the past through FE model updating for uncoupled FE model, while the same have not been addressed in the context of a coupled vibro-acoustic FE model. This issue forms the topic of this paper. This paper proposes a method for updating vibro-acoustic FE model using frequency response function with the aim of identifying the material property of flexible surface of cavity. The updating problem is formed as constrained optimization. The method requires measured vibro-acoustic frequency responses of the system. Updating parameters related to the material property and the stiffness of joint between the plate and rectangular cavity are used. The effectiveness of the proposed method is validated through numerical studies on a 3D rectangular box cavity. The robustness of the method under presence of noise is also investigated. The proposed method is found to work satisfactorily to correctly estimate the updating parameters and yield an updated model that correlates well with the measured frequency response.

D. V. Nehete, S. V. Modak, K. Gupta
Experimental and Numerical Study of Friction-Induced Noise of Brake Pad Materials Having Grooved Surface

An experimental and numerical study was performed in this work to predict the squeal instability when pad specimens having different surfaces rotating on a brake disc specimen. The numerical results were consequently compared with the experimental results to investigate the effect of surface modification of pad materials on squeal generation. It was shown that surface modification of pad materials had a significant influence on the squeal instability. Diagonal grooved surface was found to be able to efficiently reduce squeal generation, which can be mainly attributed to its relatively smaller contact pressure distribution area compared to that of the smooth surface.

X. C. Wang, J. L. Mo, D. W. Wang, H. Ouyang, J. Zhao, G. X. Chen, M. H. Zhu
Neural Network Modeling of Submarine Shell

Submarine propeller operating in unsteady wake flow often results in dynamic fluctuating force which is transmitted through rotator-raft system and leads to shell structure vibration and structure-borne noise transmission. Even though methods like Flügge’s equations of motion or FEM can be used to model cylinder shell, as for submarine equipped with devices the vibration behaviour of shell will not agree with that acquired from model developed with those methods. In this paper, Neural Network is used to analyse vibration of the submarine shell structure consisting of conical shell, hull and hemisphere shell. Firstly, a finite element model for the combined shell structure is developed for numerical simulations, whose aim is to acquire shell’s vibration information so as to represent the actual output of sensors arranged on submarine shell. Then actuating force is applied on this model based on the prior knowledge of typical blade passing frequency and fluctuating force. The vibration characteristics and responses at the interested positions on the shell are analyzed numerically. These data are used in Neural Network as training and testing data respectively to further develop a non-linear submarine shell model. Vibration responses at the same points acquired from finite element model are compared with the Neural Network model respectively. Results show that Neural Network can be used to model the complex submarine shell structure for effective vibration analysis. Future research will be concentrated on applying Neural Network with the testing data that acquired from actual submarine to develop a controlled plant.

Fei Wang, Yeping Xiong, Zhenping Weng
Novel Approach for Structural Dynamic Topology Optimizations Based on Power Flow Mode Theory

The generalized damping based power flow mode theory [

1

] reveals natural power flow behaviours of a dynamic system based on the inherent characteristics of the system’s damping distribution, which provides insight into energy dissipation mechanisms of the dynamic system. In this paper, a new Power Flow Mode dynamic Topology OPtimization (PFMTOP) approach is proposed based on the developed power flow mode theory to achieve topologically optimised systems’ damping material distributions with enhanced vibration suppression capability. Conventional method of topology optimization focuses on minimizing the structural frequency response or dynamic compliance without considering structural damping. The new approach developed herein uses the trace of system’s characteristic damping matrix as design objective to find an optimal damping material layout that maximize the energy dissipation for a given volume of the material to achieve minimum power flow response. Topology optimal design of damping distributions of two-phase structures subject to dynamic loading is studied. Example presented demonstrates the applicability and efficiency of the new PFMTOP approach. The obtained results reveal that the proposed approach can significantly enhance vibration energy dissipation and provides an effective method for optimised systems’ damping material distributions with enhanced vibration suppression capability and reduced material usages. This new method can be readily extended to more complex structures to optimize the topology of damping material layer for improved vibrational power flow control.

Ye-Ping Xiong
Accurate Calculation of the Phase Shift Angle of Sinusoidal Signals Using Trapezoidal Rule

In this work, the phase shift angle of a signal is obtained following a procedure that involves carrying out trapezoid rule numerical integration. The two required numerical integrations in this procedure define the tangent function of the phase shift angle. Accurate results (up to the 14th significant figures) are obtained using four equally spaced points (at 0°, 120°, 240° and 360°) on a periodic signal. But the procedure presented here has no limit in the amount of data points that can be used in the numerical integrations. Thus, this procedure can be used to estimate the phase shift angle when data includes noise, using as many points on a period as necessary.

Luis E. Monterrubio
Effect of the Rail Support Stiffness on the Occurrence Propensity of Rail Corrugation Based on the Self-excited Vibration of a Wheel-Rail System

From the viewpoint of friction-induced vibration, a self-excited vibration of a railway wheel-rail system is found to easily occur when the creep force between the wheel and rail is saturated. This self-excited vibration is probably responsible for rail corrugation. In this paper, a self-excited vibration model is established, which consists of a wheel, a rail and a series of sleepers. The model is used to study the effect of the rail support stiffness on the occurrence propensity of rail corrugation. Results show that the occurrence propensity of rail corrugation decreases with increasing rail support stiffness.

G. X. Chen, W. J. Qian, J. L. Mo, M. H. Zhu
Modeling and Dynamic Force Simulation for Detection of Profile Error in Spur Gear Pair

This paper describes modeling and simulation of spur gear pair in Adams–View. Initially, virtual model of an ideal gear pair is created in Adams and variation of the dynamic force is obtained by considering the tooth mesh stiffness and mesh damping coefficient. The magnitude of force variation thus obtained is confirmed with the design calculations. The dynamic force magnitudes thus obtained and those found in Adams are closely matching. Later on, tooth profile error is introduced in the gear pair by removing part of involute surface from one of the gears making one tooth surface as flat. Dynamic force variation is now obtained for the defective gear pair. After comparing the dynamic forces for defect free and defective gear pairs, it is found that change in dynamic force pattern is a good indicator of tooth profile error in spur gears.

Atul B. Andhare, Manish Kumar Verma
Availability Improvement by Early Detection of Motor Bearing Failure Using Comprehensive Condition Monitoring Techniques at DTPS

This paper shares a success story out of the Implementation of Co-ordinated Condition Monitoring techniques at DTPS, wherein imminent Motor bearing failure of one of the most critical HT auxiliary used during coal bunkering system i.e. Belt Conveyor-4B was diagnosed. On 15/01/2014, Motor NDE and DE bearing acceleration value deviated from 1.3 and 1.2 g to 2.2 and 4.9 g (Peak) respectively. Suspecting deterioration in Motor bearings and to confirm the same a Ultrasonic Monitoring carried out and observed that Ultrasonic level also increased from 4 to 8 LEDs. In view of Steep increasing trend of Motor bearings Acceleration value and Ultrasonic level, it was decided to replace the Motor with spare one. During inspection of motor, it was observed that Motor bearing clearances were found increased than the normal value and bearings rollers found damaged. Thorough inspection of Motor winding and Stator Rotor also done and found intact.No Scoring marks observed on both ends of Motor shaft. Vibration Analysis and Ultrasonic Monitoring helped in diagnosing the exact root cause of abnormity of deterioration of Motor bearings at early stage and thus avoided the catastrophic failure. The application saved the plant from huge losses in terms of power generation, down time, associated maintenance and spares costs which could have caused total cost of £58,854.3.

Hemant M. Bari, Atul A. Deshpande, Suhas S. Patil
Base Isolator of Vertical Seismic Vibration Using a Negative Stiffness Mechanism

A model of a base isolator for vertical seismic vibration is considered. It consists of a mass and two springs, one of which is a linear type and the other is of varying stiffness. It is assumed that the varying stiffness spring can be changed from positive to negative stiffness. The varying stiffness is accomplished by the horizontally placed springs which are also connected the vertical spring by rigid links providing geometric stiffness which is negative due to compression in the spring and the axial stiffness from the inclined links which decrease as their orientation approaches the horizontal direction. The numerical investigation shows that the force induced in the vertical spring becomes constant regardless of the displacement around half of the maximum contraction. The experiment also confirmed this force-displacement relationship. In the range of displacement, the force transmitted to an object supported by the isolator due to the ground motion can be limited. This mechanism offers a possible way to prevent an object from being damaged by excessive force during earthquakes.

Yusuke Mochida, Naohiro Kida, Sinniah Ilanko
A Novel Piezoelectric Rotational Speed Meter

A novel piezoelectric rotational speed meter which is within the family of solid-state wave gyroscope based on direct and inverse piezoelectric effect is proposed in the paper. The hard core of the speed meter is a vibratory ring with circular inner surface and octagonal outer surface. First, the paper presents the principle introduction and structure design of the rotational speed meter. Second, simulation results and mode test results show appropriate working modal frequency and modal shape. We found that the working frequencies of active and sense mode are nearly equal. In addition, coriolis test are done to validate the working principle. Finally, the data from the experiment are analyzed to obtain the equation between output signals and angular velocity. We conclude two equations which can be used to work out the angular velocity input and the scale factors of the equations are 16.4 mV/min/r and the correlation coefficient is 0.998 and 0.995 respectively. These results are more accurate when the angular velocities range from 5 to 700 RPM.

Weiqing Huang, Meng-xin Sun, Jian-hui Zhang, Qing-jun Ding, Yin Wang
A New Linear Motor with Two Piezoelectric Stacks Based on Differential Friction Effects

The existing resonant linear piezoelectric motors must operate with high working voltage in resonant condition, resulting that their operating frequency range is narrow and their running stability is poor. So a kind of linear piezoelectric stepping motor with broad frequency domain was proposed based on friction difference. First, the friction difference driven principle of motor is proposed by analyzing the continuous stepping motion in a period. Then the pizoelectric actuator unit is designed with flexible structure and the motor was constructed with two piezoelectric actuator units in two perpendicular direction. further, both the displacement characteristics of mover and the amplitude charateristics of the actuator were tested with keyence laser displacement sensor (LDS). Finally, the stepping charateristics of the motor were reserched on by analyzing the displacement testing data with mathematical software. The experimental results shows that the motor can operate stably within the scope of 350–750 Hz. When excitation voltage is 30 V and pre-load is 3 or 10 N, the lateral amplitude of the drive foot is approximately 4 μm and the stable average steplength ranges from 3.1 to 3.2 μm with the error rate about 5–7.5 %.

Weiqing Huang, Xifu Chen, Jianhui Zhang
Metadaten
Titel
Vibration Engineering and Technology of Machinery
herausgegeben von
Jyoti K. Sinha
Copyright-Jahr
2015
Electronic ISBN
978-3-319-09918-7
Print ISBN
978-3-319-09917-0
DOI
https://doi.org/10.1007/978-3-319-09918-7

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.