Operational Deflection Shapes Research Articles

Modal parameter estimation using free response measured by a continuously scanning laser Doppler vibrometer system with application to structural damage identification

Spatially dense vibration measurement can be obtained by use of a continuously scanning laser Doppler vibrometer (CSLDV) system that sweeps its laser spot along a scan path. For a linear, time-invariant, viscously damped structure undergoing free vibration, a type of vibration shapes called free response shapes was defined and obtained by the authors using a CSLDV system with the demodulation method. To date, application of free response shapes is limited to structural damage identification, and they cannot be directly used for model validation while mode shapes can be. This paper extends the concept of free response shapes by proposing a new modal parameter estimation (MPE) method using a CSLDV system to estimate modal parameters of the structure undergoing free vibration, including natural frequencies, modal damping ratios, and mode shapes; the MPE method is applicable to linear structures without repeated and closely spaced modes. Advantages of the proposed method are: (1) modal damping ratios and mode shapes can be accurately estimated from obtained free response shapes in the least-square sense, (2) the scanning frequency of the CSLDV system can be relatively low, and (3) estimated mode shapes can be used for structural damage identification as if they were measured by stepped scanning of a scanning laser Doppler vibrometer. A baseline-free method is applied to identify structural damage using mode shapes estimated by the proposed MPE method. The method does not require any baseline information of an undamaged structure, such as its complete geometry, material properties, boundary conditions, modal parameters, and operating deflection shapes. In the proposed MPE method, natural frequencies of the structure are identified from free response of certain fixed points on the structure; its modal damping ratios and mode shapes are simultaneously estimated using free response shapes measured by a CSLDV system. Both numerical and experimental investigations are conducted to study the MPE method and its application to baseline-free damage identification with mode shapes estimated by the MPE method.

Experimental investigation for wheel polygonisation of high-speed trains

The wheel polygonisation is the harmonic wave along the wheel circumference, which has been widely reported in high-speed railway vehicles in China in recent years. The polygonization mechanism has not been fully understood yet, and this work discusses one possible mechanism through several experiments. Firstly, a field test for the CRH3 high-speed train with polygonal wheels is carried out. It is found that the vibration in vertical takes major responsibility, and there are several resonance bands for the train-track system. Another field test shows that the rail is sensitive to the polygonisation characteristic frequency, but the wheel axle is not. Then the rail local vibration modes are analyzed by the operational deflection shape (ODS) test in the laboratory. A loaded bogie is fixed on the tested track to simulate the real working conditions. The result shows that the frequency of one local mode is 591 Hz, which is a typical wheel polygonisation frequency. Besides, the wheel-rail contact point is not on the vibration node of this local mode. Thus, the resonance of this local rail mode can be one possible mechanism for the high-order wheel polygonisation.

High-vibration diagnosis of gas turbines: An experimental investigation

Rotordynamics is a very challenging field because of machine complexities. Many internal and external factors contribute toward change in the structural dynamic characteristics. One of these factors is broad-band high-vibration amplitudes. In this article, a similar high vibration issue on a gas turbine is investigated using bode, orbit, and shaft centerline plots. Data from proximity probes installed on turbine generator system are captured and analyzed against any factor contributing toward high vibration issue. Fish bone diagram was used for root cause investigation. Main components investigated for the root cause of high vibration issue include generator rotor and casing. Rotor behavior has been examined by capturing orbit and shaft centerline diagrams, whereas casing contribution has been investigated by conducting operating deflection shape analysis. A comparison is drawn between a machine suffering from high vibration issue and a normal machine. Resonance was identified as the root cause, and stiffness enhancement was recommended to change the natural frequency of casing. Based on investigations, recommendations are given and a final comparison is drawn after structural modification was done. In addition to early fault finding, reduction in maximum vibration was 38% after implementation of the fix that confirmed the accuracy of the root cause investigation process.

Primary accelerometer calibration by scanning laser Doppler vibrometry

A primary calibration system for vibration transducers based on laser Doppler vibrometry was complemented by a commercial scan unit. The data acquisition and analysis were optimized for accuracy and a novel procedure to visualize and compensate parasitic rigid-body motion was developed. Additionally, effects related to drift during the calibration process were explicitly taken into account and compensated, thereby allowing an automated measurement of spatial sensitivity distributions at hundreds of measurement positions with the same accuracy as a single-point primary calibration. The system was applied to study the influence of rocking and deforming motion on the apparent sensitivity of back-to-back vibration transducers during the calibration process. New insights were gained by interpreting the measured spatial sensitivity distributions as operational deflection shapes.

Vibration Analysis of Chenderoh Dam Physical Model Spillway Structure due to the Effect of Water Spilling: Numerical and Experimental Validation

Dam can be defined as a barrier built across the river to restrain and control the flow of water. However, the safety of the dam structure can be threatened by the uncertainties vibration induced from internal and external sources. Thus, in this paper, the vibration analysis in terms of Experimental Modal Analysis (EMA) and Operational Deflection Shapes (ODS) are carried out to determine the reliability of the dam structure. This study only focused on the spillway structure of the Chenderoh Dam that located in Perak, Malaysia. For the simulation, a 3D physical model with 1:20 scale is developed using SolidWorks software and simulated using ANSYS software. Whilst, for validation of the simulation results, EMA and ODS experiment are performed on the physical model of the Chenderoh Dam. The validation will be in terms of mode shape, ODS, natural and operating frequencies. From the results, the first natural frequency of the spillway occurred at 220.87 Hz with the maximum deflection of 1.6 mm and the ODS deformation happened at operating frequency of 45 Hz with the amplitude value of 0.003 m. The operating frequency value is far from the natural frequency of 220.87 Hz; thus, the transient vibration only induces a minimal effect on the spillway structure and the spillway is considered safe for the operation.

Non-Contact Damage Detection under Operational Conditions with Multipoint Laservibrometry.

Scanning laser–Doppler vibrometry (SLDV) can localize and visualize damages in mechanical structures. In order to enable scanning, it is necessary to repeat the vibration. Therefore, this technique is not suited to detect emerging hazards in working machinery that change the vibration behavior. A common technique for such cases is monitoring the vibration excited by machine operation with accelerometers. This technique requires mechanical coupling between sensors and the measurement object, which influences the high-frequency vibration responses. However, in the low-frequency range, local damages do not shift resonances or distort operational deflection shapes (ODS) significantly. These alterations in the vibration behavior are tiny and hard to detect. This paper shows that multipoint laservibrometry (MPV) with laser excitation can measure these effects efficiently, and it further demonstrates that damages influence ODSs at frequencies above 20 kHz much stronger than at frequencies below 20 kHz. In addition, ODS-based damage indices are discussed; these are highly sensitive to minute visible changes of the ODSs. In order to enhance the sensitivity of hazard detection, the response vector assurance criterion value is computed and evaluated during operation. The capabilities and limitations of the methodology on the example of a cantilever with manually emerging damage are demonstrated.

Case study: Identification of brake squeal source mechanism through experimental and computational approaches

In this case study, mechanism leading to squeal noise in an automotive disc brake system is investigated with focus on systematic laboratory experiments and associated computational models. First, experimental modal analyses are conducted on the brake corner assembly components, and the natural frequencies and corresponding mode shapes are obtained. Second, finite element models of same components are developed, updated and validated by comparing predicted modal characteristics with those measured. Third, a controlled laboratory experiment is designed, constructed and operated in a semi-anechoic room. Experiments are conducted at many operational disc speeds and brake line pressures, and acceleration on the caliper and sound pressure are measured. Squeal events at distinct frequencies are successfully identified in the experiments. Fourth, a comprehensive computational model of the brake corner assembly is constructed using validated component models, and squeal investigation is then conducted through complex eigenvalue analyses while mimicking the operational conditions of experiments. The system model yields unstable frequencies at several operational conditions. It is observed that experimentally detected squeal frequencies match well with predicted unstable frequencies. Finally, operational deflection shape measurements on the caliper are also carried out during squeal events, and the predictions are found to be similar to those measured. In conclusion, the squeal generation mechanism of the brake system is understood from the perspective of frictioninduced modal coupling, and an experimentally validated computational model of the brake system is successfully developed that may be used to find solutions to mitigate squeal.

An experimental study of the feasibility of phase‐based video magnification for damage detection and localisation in operational deflection shapes

AbstractOptical measurements from high‐speed, high‐definition video recordings can be used to define the full‐field dynamics of a structure. By comparing the dynamic responses resulting from both damaged and undamaged elements, structural health monitoring can be carried out, similarly as with mounted transducers. Unlike the physical sensors, which provide point‐wise measurements and a limited number of output channels, high‐quality video recording allows very spatially dense information. Moreover, video acquisition is a noncontact technique. This guarantees that any anomaly in the dynamic behaviour can be more easily correlated to damage and not to added mass or stiffness due to the installed sensors.However, in real‐life scenarios, the vibrations due to environmental input are often so small that they are indistinguishable from measurement noise if conventional image‐based techniques are applied. In order to improve the signal‐to‐noise ratio in low‐amplitude measurements, phase‐based motion magnification has been recently proposed.This study intends to show that model‐based structural health monitoring can be performed on modal data and time histories processed with phase‐based motion magnification, whereas unamplified vibrations would be too small for being successfully exploited. All the experiments were performed on a multidamaged box beam with different damage sizes and angles.

Dynamic Performance Analysis of the micro-hole EDM Machine Tool

The EDM machine is special processing machine using the principle of EDM process of conductive materials. By means of modal analysis, ODS (Operational, Deflection, Shapes) analysis and order analysis, the static and dynamic performance parameters of the EDM machine tool are studied. According to the processing requirements, the structure of the machine tool is optimized, and the weak links are strengthened so as to reduce the aperture dispersion of the machined holes. Through the modal test this experiment firstly analyzes the natural frequency, damping ratio and modal shape in each mode of machine tool structure to understanding the characteristics of each order machine main mode. Then, through ODS (Operational Deflection Shapes) test, it analyzes the vibration characteristics of machine tool structure in operation condition. And it also analyzes the relation-shape between the vibration of rotating machinery and the speed of the machine through the order analysis to predict the vibration of actual machine tool structure in a certain band external or internal variety of vibration response. Finally, it makes a comprehensive study on the static and dynamic performance of machine tools, and provides a reference for the design and optimization of structure dynamic strength.

An experimental investigation of resonance sources and vibration transmission for a pure electric bus

Electric vehicles generally have a better noise, vibration, and harshness quality than traditional vehicles due to the relatively quiet electric motors. By contrast, the noise, vibration, and harshness issues of the driveline system become more outstanding and significant in the absence of the “masking effect” by the engine. The electrification of the powertrain has also brought many changes in the sources or transmission of vibration, which has led to some new noise, vibration, and harshness issues. Specifically, the intense vibration of the prototype bus appears when driving in third gear, which makes the passengers uncomfortable. This paper presents an efficient analytical strategy for identifying the resonance sources and vibration transmission for a pure electric bus. The strategy incorporates order analysis, operating deflection shape, and transfer path analysis. Order analysis shows that the resonance is primarily caused by the second-order excitation associated with the driveline, and the vibration sources are further identified using operating deflection shape analysis. Moreover, the vibration transfer paths from the driveline to the bus floor are quantitatively determined by the transfer path analysis method. The results show that the coupling vibration of the powertrain and the rear drive axle, which amplifies the resonance of the whole driveline, is transmitted to the bus floor primarily through powertrain mounts and V rods. Based on the results, the design and structure modifications of the driveline and transfer paths are recommended to handle this issue. The proposed identification strategy would be beneficial for accurate and efficient engineering troubleshooting on the vibration issues.

Flow-Induced Vibration Response of the Chenderoh Dam Bottom Outlet Section Due to the Effects of Water Spilling

Hydropower-type dam can generate an electricity to the surrounding areas during the release of water from the upstream to the downstream. However, in some cases, the flow-induced vibration during the water spilling might induced significant vibration effects to the dam structure. This is a common phenomenon that happened in any of dam structures during the operating condition. In this study, the flow-induced vibration response at the bottom outlet section of the real scale Malaysian Chenderoh Dam model is investigated using ANSYS software. The results of frequency domain response and operational deflection shapes (ODS) from the flow-induced vibration are compared with the natural frequencies and mode shapes of the bottom outlet section. From the study, the transient vibration responses induced from the flow of water occurred at the operating frequency of 23.14 Hz while the natural frequency of the bottom outlet section is located at 9 Hz of frequency. This indicates that for the normal case of water spilling at the bottom outlet section, there is no resonance phenomenon happened. However, this result is useful for the dam operation section in order to avoid any disaster of the dam structure in the future.

Electronic speckle pattern interferometry: applications to the structural acoustics of percussion instruments

Electronic speckle pattern interferometry provides real-time images of operating deflection shapes of acoustically driven structures. This technique is particularly useful in the study of musical percussion instruments containing bars, plates, and membranes. Musically relevant examples involving drumheads, crotales, and the musical saw are presented. Imaging through water is described as well as methods for studying coupled vibrations between the two heads of a drum.

A multi-view optical technique to extract the operating deflection shapes of a full vehicle using digital image correlation

Abstract The automotive and aerospace industries are increasingly using light-weight material to improve vehicle performance while reducing fuel consumption. However, using light-weight material can increase the air-borne and structure-borne noise. Thus, special attention needs to be paid in designing the vehicle body structure and evaluating its dynamics. In order to accomplish this, modal analysis is conventionally used. In this technique, the structure is excited using an impulse hammer or a mechanical shaker, and the response is measured using accelerometers. However, using contact-based transducers can mass-load the structure and can only provide data at a few discrete points. In the last decade, stereo-photogrammetry and three-dimensional digital-image correlation have received special attention in collecting operating data for structural analysis. These non-contact optical techniques provide a wealth of distributed data over the entire structure. However, the stereo-camera system is limited by the field of views of the cameras and can only measure the response on the parts of a structure for which cameras have lines of sight. Therefore, a single pair of DIC cameras may not be able to provide deformation data for an entire structure. A multi-view 3D DIC approach, however, can be used to predict the vibrational characteristics of a full vehicle. A pair of DIC cameras is passed over the entire vehicle to capture the deformation data of each field of view. The measured data includes the geometry and displacement data, which is mapped into a global coordinate system using 3D transformation matrices. The obtained data in the time domain for each field of view is transformed to the frequency domain using a Fast Fourier Transformation (FFT) to extract the operational deflection shapes and resonant frequencies for each field of view. The obtained deflection shapes are scaled and stitched in the frequency domain to extract the operating deflection shapes of the entire vehicle.

Study for the Identification of Dominant Frequencies and Sensitive Structure on Machine Tools Using Modal Decoupling and Structural Sensitivity Analysis

The research on machine tool vibration has significant impact to improve the processing quality of the processed parts. The vibration response on the surface quality is quite different based on different modes of vibration. Current study proposed a new approach of modes decoupling based on Operational Deflection Shape (ODS) and structural sensitivity analysis, which used to identify the structural vibrations on surface topography in manufacturing process. Method According to the modes decoupling based on the ODS method, the dominant vibration frequencies of machine tool are identified in a wide range of frequency band. Furthermore, the modal mass distribution matrix analysis is used to determine the sensitive structures that cause greater machining errors. A milling process is used to conduct experiments. The experimental and theoretical results indicate that (i) the contribution of dominant vibration frequency to the vibration of machine tool is larger than weak modes vibration and (ii) the sensitive structure has higher vibration energy than the insensitive structures. The multimode vibration at dominant frequencies of the sensitive structures (MVDFSS) directly can determine the surface topography of the products.

A Comprehensive Study on Detection of Hidden Delamination Damage in a Composite Plate Using Curvatures of Operating Deflection Shapes

The aim of this work is to investigate the accuracy and sensitivity of a continuously scanning laser Doppler vibrometer (CSLDV) for detection of hidden delamination damage in composite plates. Some work on using a CSLDV for detection of damage in aluminum beams and plates has been done by the authors. The current work is related to a worldwide round robin study sponsored by the Society of Experimental Mechanics. The main difference between the current work and previous work is that the damaged composite plate was provided by the organizer of the round robin study instead of being made by the authors. Hence, the authors have no information about locations of the damage, which means this is more like a blind test. The most significant advantage of using a CSLDV for vibration measurement of a structure is that a spatially dense operating deflection shape (ODS) of the structure can be obtained and further used to calculate the curvature of the ODS (CODS). A comprehensive study to detect the hidden damage in the composite plate by using the first seven CODSs from the corresponding ODSs of the plate is conducted. The study shows that different CODSs have different sensitivities to local anomaly induced by the damage and only two of the seven CODSs can be used to detect the locations of the hidden damage.

A novel investigation into the application of non-destructive evaluation for vibration assessment and analysis of in-service pipes

ABSTRACTFlow-induced vibrations are a major problem in all oil and gas processing industries, so all piping systems which work non-stop for 24/7 require regular condition monitoring and inspection to assess changes in their dynamic characteristics and structural integrity in order to prevent catastrophic failures. A novel method of non-destructive testing and evaluation of these pipes, while in service, is proposed in this paper. The method enables early detection of the root causes and pinpoints the location of the impending failure due to excess vibration as a result of cyclic force induced by the flow prior to condition-based maintenance procedures. The technique relies on the combined application of Operating Deflection Shapes (ODS) analysis and computational mechanics utilizing Finite Element Analysis (FEA), i.e. linear elastic stress analysis. The effect on vibration levels on the in-service pipes is assessed and verified. The effect of any change in the forces corresponding to changes in the Differential Pressure (DP) at a constant flow rate through the pipes can then be estimated. It was concluded that maintaining the differential pressure above some “critical” threshold ensures the pipe operates under the allowable dynamic stress for a theoretically “indefinite” life cycle.

The potential of stop band material in multi-frequency ultrasonic transducers

Ultrasonic transducers play a major role in surround sensing for automotive and industrial applications. The development of autonomous driving functions is one of the top challenges for mobility solutions of the 21st century. In this context, surround sensing systems with high performance serve as a key enabler. This leads to an increasing number of sensors which are desired to operate in parallel or in shorter intervals. Hence, measurements should be conducted with two different frequencies to discriminate the sensor signals. Known multi-frequency ultrasonic transducers mostly employ multiple electro-mechanical coupling elements which require more complex sensor electronics.To overcome this issue, the authors present a study on multi-frequency ultrasonic transducers using only one electro-mechanical coupling element. In order to achieve suitable sound radiation properties at two well separated operating frequencies, spatially distributed stop band material is employed. As a result, the operational deflection shape can be controlled at a certain frequency. In finite element simulation, the relation between spatially distributed stop band material and the resulting operational deflection shapes is investigated. The sound radiation behavior is estimated using the numerical results from a harmonic analysis as input for the Rayleigh integral. In experimental investigations, the presented approach is validated. Finite element simulation and experimental testing show good accordance. Based on the results of the presented study, it is possible to realize a multi-frequency ultrasonic sensor with one electro-mechanical transducer element only and suitable sound radiation behavior at multiple operating frequencies.

An optical-based technique to obtain operating deflection shapes of structures with complex geometries

Abstract The dynamic characteristics of structures are conventionally obtained by exciting the structure using an impulse hammer or a mechanical shaker and measuring the response using uniaxial or multi-axial accelerometers. However, contact-based sensors can mass-load the structure and do not provide full-field data. Hence, obtaining the true dynamics of the structure using conventional sensors can be challenging. That makes test engineers seek different non-contact techniques that can provide full-field data without mass-loading the structure. Recently, stereo-photogrammetry and three-dimensional digital image correlation (3D DIC) have been adopted to collect operating data for structural analysis. These non-contact optical techniques provide a wealth of distributed data over the entire structure. However, the stereo-camera system is limited by the field-of-view of the cameras; a single pair of DIC cameras may not be able to provide deformation data for the entire structure. Hence, it is challenging to obtain the vibration characteristics of the entire structure. In the current work, a multi-view 3D DIC approach is used and validated to predict the vibrational characteristics of an automotive muffler with a complex structure. A pair of DIC cameras travels over the entire structure to capture the deformation of each field of view. The measured data includes the geometry and displacement data, which is later mapped into a global coordinate system. The measured data in the time domain for each field-of-view is transformed to the frequency domain to extract the operational deflection shapes and resonant frequencies for each field of view. The obtained deflection shapes are stitched together in the frequency domain to extract the operating deflection shapes and resonant frequencies of the automotive body panel with a complex structure.

A Novel Approach for 3D-Structural Identification through Video Recording: Magnified Tracking.

Advancements in optical imaging devices and computer vision algorithms allow the exploration of novel diagnostic techniques for use within engineering systems. A recent field of application lies in the adoption of such devices for non-contact vibrational response recordings of structures, allowing high spatial density measurements without the burden of heavy cabling associated with conventional technologies. This, however, is not a straightforward task due to the typically low-amplitude displacement response of structures under ambient operational conditions. A novel framework, namely Magnified Tracking (MT), is proposed herein to overcome this limitation through the synergistic use of two computer vision techniques. The recently proposed phase-based motion magnification (PBMM) framework, for amplifying motion in a video within a defined frequency band, is coupled with motion tracking by means of particle tracking velocimetry (PTV). An experimental campaign was conducted to validate a proof-of-concept, where the dynamic response of a shear frame was measured both by conventional sensors as well as a video camera setup, and cross-compared to prove the feasibility of the proposed non-contact approach. The methodology was explored both in 2D and 3D configurations, with PTV revealing a powerful tool for the measurement of perceptible motion. When MT is utilized for tracking “imperceptible” structural responses (i.e., below PTV sensitivity), via the use of PBMM around the resonant frequencies of the structure, the amplified motion reveals the operational deflection shapes, which are otherwise intractable. The modal results extracted from the magnified videos, using PTV, demonstrate MT to be a viable non-contact alternative for 3D modal identification with the benefit of a spatially dense measurement grid.

Full-field strain prediction using mode shapes measured with digital image correlation

Health and condition monitoring of composite structures are critical in engineering especially in the wind, civil, aviation, and auto industries. However, considering the geometry and size of the structures, analyzing critical locations can become challenging. Traditional sensors such as strain-gauges are widely used to collect operating data, but these conventional methods cannot present full-field data and only show the measurement data at a few discrete locations. Baqersad and Bharadwaj have recently developed a Strain Expansion-Reduction Approach (SERA) to bridge this gap and to expand a limited set of measurements and obtain full-field strain data. This approach uses the strain mode shapes from Finite Element Analysis (FEA) to develop a transformation matrix that expands the limited strain data measured using strain-gauges and predicts full-field strain over the entire structure. However, for many structures, it is challenging to accurately model the geometry or material properties for finite element analysis. Many of these structures are made of composite materials and material modes for these structures might not be readily available. In this paper, we use the strain mode shapes extracted using Digital Image Correlation (DIC) in the expansion process. These mode shapes represent actual properties of the structures. The strain mode shapes for a sample structure of a product can be extracted in a test facility using this approach (e.g., a wind turbine blade or a suspension A-arm). An in situ limited set of measurement can be performed using strain-gauges or fiber optic sensors on the structure. Then, the limited data can be expanded using the strain mode shapes to extract full-field strain results. To demonstrate the merit of the approach, we applied the proposed technique to expand real-time operating data measured using a few strain-gauges mounted to a composite spoiler. Using a transformation matrix generated using the DIC operating deflection shapes, the expansion technique predicted the full field strain on the spoiler. It was shown that the proposed methodology could effectively expand the strain data at limited locations to accurately predict the strain at locations where no sensors were placed.