Vibration Nodes Research Articles

Fatigue Failure of Steam Turbine Disks—A Centenary Tribute to Wilfred Campbell

Abstract The year 2024 marks one hundred years since Wilfred Campbell published his landmark work on vibrational analysis of rotating disk following a series of disk failures in steam turbines. Despite the absence of advanced engineering analytical tools, Campbell came up with an elegant method to visually demonstrate and capture the mode shapes in rotating disks. The first part of this paper reviews Campbell's life and analytical and experimental work in this area. Regardless of the current advanced engineering capabilities to predict nodal shapes in turbine disks, turbine disks still experience failures related to vibration. The second part of the paper discusses a recent case study where a turbine disk failure occurred as a result of vibration. The discussion includes metallurgical root cause failure analysis and engineering analysis to predict the vibrational characteristics. Metallurgical failure analysis confirmed that the primary mode of failure was fatigue and did not have any issues with the disk material or its mechanical properties. Finite element modeling and analysis were used for the engineering analysis to predict the natural frequencies of the bladed-disk. The engineering analysis showed the evidence of potential resonance, and the failure was related to nodal vibration issues.

Focus control of a concave–convex ultrasonic gel lens in the radial direction

Optical image stabilization (OIS) systems maintain the three-dimensional focal position of a lens through mechanical actuation systems. This paper examines an optical lens for OIS that utilizes ultrasound vibration to alter the focal position, not only in the depth direction but also in the radial direction. The lens has a simple structure with no mechanical moving parts and consists of an ultrasound transducer divided into four pieces, a glass disk, and a transparent viscoelastic gel film that functions as a lens. The acoustic radiation force generated by the resonant flexural vibration of the glass disk can alter the surface profile of the gel film, allowing for a variable-focus function. The concave and convex lenses can be interchanged using two resonant vibration modes: the standing-wave mode, in which the vibration loop appears at the center, and the traveling-wave mode, in which the vibration node appears at the center. The positions of ultrasound vibrations on the lens can be controlled in a two-dimensional plane by adjusting the driving amplitudes of each channel, thereby achieving focus control in the radial direction. The focusing characteristics of the lens are evaluated through ray-tracing simulation.

High sensitivity optical fiber accelerometer based on symmetric hinge structure with dual mass blocks

Abstract An optical fiber Bragg grating accelerometer with symmetric multi-stage flexible hinge and double mass block structure is designed. According to the working principle of the two-degree-of-freedom vibration system, there are vibration nodes in the double mass block during the vibration process, and the vibration nodes can reduce the amplitude of the system and protect the optical fiber; and the multi-stage flexible hinge can reduce the structural rigidity and improve the sensitivity of the accelerometer. The experimental results show that the vibration signal is in the range of 5-90Hz, the acceleration is in the range of 0.1-1G, the sensitivity of the accelerometer is 878.4pm/G, and the linear fit R2=0.991. At the same time, the mechanical structure of the accelerometer is an integrated processing, with high mechanical strength, which can ensure the stability of the work of the accelerometer, and the structure is simple, and easy to package. Changing the length and thickness of the hinge can further expand the measurement range and application scenarios of the accelerometer.

Multi-Objective Optimization of the Ultrasonic Scalpel Rod and Tip with Improved Performance: Vibration Frequency, Amplitude, and Service Life

Ultrasonic scalpel design for minimally invasive surgical procedures is mainly focused on optimizing cutting performance. However, an important issue is the low fatigue life of traditional ultrasonic scalpels, which affects their long-term reliability and effectiveness and creates hidden dangers for surgery. In this study, a multi-objective optimal design for the cutting performance and fatigue life of ultrasonic scalpels was proposed using finite element analysis and fatigue simulation. The optimal design parameters of resonance frequency and amplitude were determined. By setting the transition fillet and keeping the gain structure away from the node position to enable the scalpel to have a high service life with excellent cutting performance. The frequency modulation method of setting the vibration node bosses at the node position and setting the vibration antinode grooves at the antinode position was compared. Then, the mechanism of the influence of various design elements, such as tip, shank, node position, and antinode position, on the resonance frequency, amplitude, and fatigue life of the ultrasonic scalpel was analyzed, and the optimal design principles of the ultrasonic scalpel were obtained. The proposed ultrasonic scalpel design was confirmed by simulations, impedance measurements, and liver tissue cutting experiments, demonstrating its feasibility and enhanced performance. This research introduces innovative design strategies to improve the fatigue life and performance of ultrasonic scalpels to address an important issue in minimally invasive surgery.

Resonant Fatigue Tests on Polished Drill Pipe Specimens

In this study, the fatigue strength of polished drill pipe specimens was investigated and compared with previous test results of corroded and not-corroded pipes. The resonant fatigue test rig, which was designed and implemented by the University of Pisa, is initially presented by providing a detailed description of the set-up of the machine, the calibration of the strain gauges, the control system, and the correct identification of the vibrational node locations. A polishing rig was also designed and put into operation to remove the corrosion pits from the outer surface of almost the entire length of the drill pipe specimens. After the fatigue tests with the resonant rig, and the observation of the fatigue fracture of the specimens, a few samples were extracted from different zones (corroded and not corroded) of the failed drill pipe specimens. This allowed for investigations to be carried out using a scanning electronic microscope. The obtained results were analyzed using the Murakami model, and a discussion is presented about the effect of the corrosion pits on the fatigue strength.

Ultrasonic tool shank with multiple vibration mode for micro-nano drilling: Design, optimization and experiment

The machining effects of hole drilling is limited by merely changing the amplitude. Adjusting ultrasonic vibration frequency to expand the matching range of machining parameters optimization is necessary to improve hole drilling effects. Therefore, the design, optimization, and experiment evaluation for a novel integrated, fined, low-cost dual-frequency ultrasonic tool shank is proposed, which can work in three vibration modes for micro-nano precision drilling. The principle of the dual-frequency ultrasonic transducer is introduced. The electro-mechanical equivalent circuit model with step horn is applied to study the dual-frequency characteristics. The transducer displacement equation model based on the wave equation theory is deduced to find the shared vibration node of the first and third frequency. Sensitivity analysis by equivalent circuit model and Finite element method (FEM) simulation of the key parameter is both conducted to optimize ultrasonic transducer geometry dimension. The vibration node of mounting flange is specified in an identical position for the dual vibration modes. A prototype of ultrasonic tool shank is fabricated and evaluated in experiments. It demonstrates that the dual working frequency of the ultrasonic transducer is 34.9 kHz and 104.5 kHz in the first and third mode resonant vibration, which is benefit to the low and high frequency drilling. Three working modes of the low, high, and coupling frequency vibration is measured by a self-developed ultrasonic generator. When 40 V voltage is excited, the vibration amplitudes of the low and high frequency are 17.8 µm, and 9.3 µm, respectively, which can meet with the drilling requirement. Moreover, the coupling vibration with the low and high mode are excited simultaneously, and the motion trajectory of the coupling vibration is observed in a “M” shape, which is a novel trajectory for the precision micro-nano drilling. Micro drilling experiments show that the 35 kHz ultrasonic vibration drilling can achieve better machining effect than conventional drilling (CD). The 105 kHz ultrasonic drilling outperforms the CD, 35 kHz and coupling ultrasonic drilling at cutting force reduction. The coupling ultrasonic vibration drilling achieves the lowest chipping diameter. It is to be noted that the 105 kHz-8 µm produce the fined smoothly surface. The 35 kHz, 105 kHz and coupling ultrasonic drilling can produce better surface micro morphology with less quantity and size of craters than that of CD.

The Design and Fabrication of an On-Rotor Sensing Wireless Vibration Node for Motor Condition Monitoring

The Design and Fabrication of an On-Rotor Sensing Wireless Vibration Node for Motor Condition Monitoring

Vibration behaviours of multi-debonded sandwich beams with symmetric angle-ply facesheets

Sandwich beams, comprising two stiff facesheets bonded to a core, are light and strong and see widespread application. However, debonded regions between the facesheets and the core can significantly reduce the strength and have an impact on the vibration behaviour. In this study, the previous literature was referred to, and finite element simulations were conducted using ANSYS on debonded sandwich beams with [0°]4, [+45°/−45°]S and [90°]4 carbon fibre reinforced polymer facesheets. The effects of the configurations of the three debonded regions and facesheet stacking orientations were studied. The most important finding is that if debonds cover vibration nodes, the natural frequencies drop more significantly because the stiffness decreases more. It was determined that when there were debonded regions, the natural frequencies of the bending modes of the beams using [0°]4 facesheets decreased more compared to those of the beams using [+45°/−45°]S and [90°]4 facesheets; while the trends are opposite for the natural frequencies of torsion modes of the beams using [+45°/−45°]S facesheets. Reducing the natural frequency can cause a structure to vibrate at the resonance frequency, leading to structural failure. This study contributes to furthering our understanding of how different debonds and facesheet stacking orientations affect the vibrations of sandwich beams.

On the Limits of Applicability of the Theory of String Vibrations in Assessing the Configuration of Wires of a Power Transmission Line in the Process of One-half-wave «Dance»

When studying the «dance», some authors assume that the configuration (shape) of the wire during a onehalf-wave dance corresponds to a sinusoid and the sinusoidal law is used as a coordinate function. With such fluctuations, all sections of the wire within the half-waves have the same direction of movement, simultaneously pass the neutral position and reach the extreme upper and lower positions. However, observations of the oscillatory processes of wires on the anchor spans of a power transmission line showed that at low mechanical stresses of the wire, the nature of the oscillation with one half-wave differs significantly from the above. The difference lies in the fact that additional vibration nodes appear within the span. Between the nodes, the wires move in antiphase, resembling three-half-wave oscillations, only with different half-wave lengths (edge effects). The coordinates of the moving nodes, as observations show, depend on the initial mechanical stress of the wire. In this regard, the question arises about the limits of applicability of the theory of string vibrations in describing the configuration of wires in the process of a one-half-wave dance. The results of experimental data on the identification of wire configurations for single-half-wave oscillations are presented. The calculation formula for the critical voltage of the wire, at which edge effects are observed, is obtained. The relevant conclusions are presented at the end.

Feasibility study on multifrequency excitation of the melt pool during ultrasonic-assisted laser beam welding

The constantly increasing demands on components and their resource-efficient production require new strategies in modern process chains. The Collaborative Research Centre (CRC) 1153 “Tailored Forming” is working on the production of hybrid solid components made from joined semi-finished products with subsequent forming. Laser beam welding with ultrasonic assistance has proven to be advantageous in the production of semi-finished products due to the active influence on the microstructure as a result of the excitation. In this work, the feasibility of extending the monofrequency excitation of the melt pool used so far during welding to a multifrequency excitation is investigated. Results from simulations and experiments show that a multi-frequency excitation of the weld pool can be effectively realised. Furthermore, it is shown that a combination of previously separately used excitation methods (positioning of the melt pool in the vibration node and in the vibration antinode, respectively) with two different frequencies is successful and leads to a combination of effects as desired, what can be seen from micrographs.

Research on Inherent Frequency and Vibration Characteristics of Sandwich Piezoelectric Ceramic Transducer

Great progress has been made in the field of ultrasonic processing in recent years, and piezoelectric ceramic transducers have been widely used as drive sources. In this paper, a sandwich piezoelectric ceramic transducer is designed, and the vibration of each part of the transducer is analyzed by elastic mechanics and piezoelectric theory. According to its mechanical and electrical boundary conditions, the vibration model of the piezoelectric transducer was established. Based on the equivalent elastic modulus method for simplifying the pre-stressed bolts into a one-dimensional transducer vibration model, the relationship between the one-dimensional axial response frequency of the transducer and the length of each component was obtained. Based on the half wavelength theory, a transducer with the vibration node in the crystal stack and an inherent frequency of 15 kHz was designed and fabricated. In order to verify the natural frequency and vibration characteristics of the piezoelectric transducer, a laser vibration measurement system was built in this study. The vibration characteristics of the transducer under different parameters such as voltage and frequency were analyzed, and the accuracy of the vibration model was verified. The vibration states of the end surface of the transducer and the radial surface were evaluated at the first-order inherent frequency and second-order inherent frequency. The results show that the equivalent simplified model established in this study can effectively design the inherent frequency of the transducer, and the operation at the first-order inherent frequency meets the one-dimensional assumptions of this study. The transducer operating conditions measured in this study also provide a more detailed reference for ultrasonic processing applications.

Dynamic and sound radiation characteristics of a non-uniformly heated isotropic plate

The influence of non-uniform heating on the anisotropic plate’s dynamic and acoustic response characteristics is investigated numerically. The effect of non-uniform heating on the plate is accounted in the form of pre-stress developed on the plate due to non-uniform heating of the plate. The influence of structural boundary conditions, nature of temperature variation, and level of temperature on vibration and acoustic response characteristics are investigated in detail. Thermal buckling strength and fundamental buckling mode are highly sensitive to the nature of temperature variation across the plate. Free vibration mode shapes of the plates with high aspect ratio and free edges are changing their pattern with an increase in temperature. The resonant amplitude of sound power radiated associated with a particular mode is dominated by vibration nodes and anti-nodes shifting relative to the excitation location. Further, an increase in sound power level with an increase in temperature is observed clearly in the lower octave frequency bands.

Experimental Study on Application of Tuned Mass Dampers for Chatter in Turning of a Thin-Walled Cylinder

Chatter is more likely to occur during the turning process of a thin-walled cylindrical workpiece owing to the low rigidity of such workpieces. Chatter causes intensive vibration, deterioration of the surface finish accuracy, tool damage, and tool wear. Tuned mass dampers (TMD) are usually applied as a passive damping technique to induce a large damping effect using a small mass. This study experimentally investigated the effect of the mounting arrangement and tuning parameters of the TMDs on the production of chatter during the turning process of a thin-walled cylinder, wherein multiple TMDs with extremely small mass ratios were attached to the rotating workpiece. The results of the cutting tests performed by varying the circumferential and axial mounting positions of the TMDs exhibited different characteristics of the chatter suppression effect. Conclusively, the TMDs could suppress the chatter generated by the vibration mode with circumferential nodes if they were mounted on the workpiece to avoid the coincidence of the circumferential arrangement with the pitch of the vibration nodes, regardless of the extremely small mass of the TMDs.

Using sound in the very near field of vibrating plates for determination of their mechanical properties

During the evaluation of Young’s modulus by vibroacoustic methods, it is usually assumed that the Poisson's ratio is known. This assumption is based on a reasonable tolerance of the vibroacoustic methods to an inadequate estimate of Poisson's ratio. However, most studies do not consider the influence of the Poisson's ratio error in the estimation of the Young's modulus error. Moreover, the evaluation of the total error typically does not include any parametric analysis at all. Therefore, a new vibroacoustic method is proposed that provides a simple and reciprocal determination of the Young's modulus and Poisson's ratio. The method is based on measurements of the natural vibration modes of elongated plates using a scanning microphone in the very near field. The results of the sound pressure scanning are interpolated with a quadratic harmonic function to improve the spatial resolution in locating the vibration nodes. The advantage of this method is that the Poisson's ratio can be calculated directly by measuring the wavelength of the bending wave. Poisson's ratio is otherwise much more difficult to measure than Young's modulus. Therefore, this method can be used to determine the Poisson's ratio of various polymers, wood, and composites. The parametric analysis of the proposed method is compared with the parametric analysis of the standardised ASTM 1875 method “Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Sonic Resonance”. The results show that the accuracy of the Poisson's ratio determination is mainly influenced by the accuracy of the material density and the accuracy of the measured sample thickness. The accuracy of these two parameters also has a dominant influence on the accuracy of the determination of the Young's modulus. The proposed method and its accuracy are demonstrated on three different plates: aluminium, steel and soft plexiglass. The results of the proposed method for aluminium were compared with those obtained by the standardised ASTM method. The proposed method provides smaller error for given experimental conditions.

A Vibration Suppression Method for the Multistage Rotor of an Aero-Engine Based on Assembly Optimization

The assembly quality of the multistage rotor is an essential factor affecting its vibration level. The existing optimization methods for the assembly angles of the rotors at each stage can ensure the concentricity and unbalance meet the requirements, but it cannot directly ensure its vibration responses meet the indexes. Therefore, in this study, we first derived the excitation formulas of the geometric and mass eccentricities on the multistage rotor and introduced it into the dynamics model of the multistage rotor system. Then, the coordinate transfer model of the geometric and mass eccentricities errors, including assembly angles of the rotors at all stages, was established. Moreover, the mathematical relationship between the assembly angles of the rotors at all stages and the nodal vibration responses was established by combining the error transfer model with the dynamics model of the multistage rotor system. Furthermore, an optimization function was developed, which takes the assembly angles as the optimization variables and the maximum vibration velocity at the bearings as the optimization objective. Finally, a simplified four-stage high-pressure rotor system was assembled according to the optimal assembly angles calculated in the simulations. The experimental results showed that the maximum vibration velocity at the bearings under the optimal assembly was reduced by 69.6% and 45.5% compared with that under the worst assembly and default assembly. The assembly optimization method proposed in this study has a significant effect on the vibration suppression of the multistage rotor of an aero-engine.

Computer-aided design system for vibration-frequency density meters

The article is devoted to the description of the developed automated design system for vibration-frequency density meters with a demonstration of the wide functionality of the program and interface settings. The development solves the problem of designing vibration-frequency density meters, calculating the quality factor and sensitivity of resonators, which provide the dependence of the frequency of self-oscillations on the controlled density. The lack of clear methodological recommendations for calibration, correction techniques for different methods of mounting the resonator significantly limits the use of vibration-frequency density meters, since the tasks set require special skills, competencies of both developers and personnel during operation.
 The algorithm of the developed software package is based on the calculation of the amplitude-frequency characteristics of a tubular resonator using a differential equation to determine the frequencies and forms of bending vibrations of a tubular resonator. The software implementation of the developed calculation model makes it possible not only to visualize the shapes, frequency, antinodes and vibration nodes of a tubular resonator of any design and a wide range of materials, but also takes into account the type of fastening, the numerical value of the support stiffness, makes it possible to adjust the placement of supports that meets the operating conditions while visualizing the shapes oscillations, simulate the distribution of sensitivity along the entire measurement range. The developed computer-aided design system has a simple and clear interface, and the absence of the necessary software installation and settings makes the product more accessible in the industrial environment of small enterprises.
 When using a subroutine for the numerical solution of the equation of free vibrations of a string, the software complex can be used to design string mechanical resonators of vibration-frequency sensors.
 
 Keywords: vibration-frequency density meter; resonator; amplitude and frequency of oscillations; fixing conditions; antinode; sensitivity

IWSHM 2019: Perturbation-based Bayesian damage identification using responses at vibration nodes

One important topic for structural health monitoring is to achieve accurate damage detection with a small number of noisy sensors and without the requirement of a high-fidelity finite element model. This article adopts the Bayesian probabilistic approach combined with a perturbation model using responses at a few vibration nodes for damage monitoring. First, the node displacement, or the response at vibration node, is adopted in this study for real-time damage assessment with a relatively small number of sensors. Then, the construction method of the node displacement response curves based on the perturbation model is proposed to replace the expensive finite element model. After that, a Bayesian framework integrated the node displacement measurement and the response curves are adopted to acquire the probability distribution of the damage parameter. In this article, the accuracy of the node displacement–based Bayesian framework with the perturbation method is evaluated. The proposed method is applied to a supporting structure of a sailplane under different noise levels.

Simulation and Experiment of New Ultrasonic Vibration Network

A reasonable ultrasonic vibration network can improve the casting quality of aluminum alloy. Ultrasonic vibration network based on a honeycomb structure has been designed, referred to as a new vibration network. The new vibration network can solve the problems of nonuniform distribution of power ultrasonic wave, small working area and low volume of ultrasonic vibration network, low efficiency of the frequency spectrum and power spectrum, and poor quality of aluminum alloy casting. The number of vibration nodes can be determined based on the number of layers of the vibration source nodes. The edge length of regular hexagonal honeycomb cells can be determined based on the size of the casting ingot. The output power and resonant frequency of the ultrasonic vibration network can be adjusted in real time according to the status of aluminum alloy melt. A seven-node new ultrasonic network and a four-node ultrasonic network with a traditional structure were selected and used in the experiment and simulation of a 500 mm diameter 2219 aluminum alloy ingot. In comparison with the traditional four-node ultrasonic network, the effective volume and area, frequency spectrum efficiency, and comprehensive coverage probability of the seven-node new ultrasonic vibration network increased by 34.06%, 23.12%, 17.25%, and 0.308, respectively. The difference between the desired value and average efficiency of the power spectrum was 0.292 W/cm2, and the average grain size of aluminum alloy decreased by 34.98 microns. These results indicate that the efficiency of ultrasonic-vibration-assisted casting system and the quality of aluminum alloy casting can be improved using the new ultrasonic vibration network.

A Bayesian probabilistic approach for damage identification in plate structures using responses at vibration nodes

Structural health monitoring for plate structures is important since they are essential structural components in many applications. One interesting topic for structural health monitoring methods is to achieve accurate damage detection with a small number of sensors and without the requirement of a high-fidelity finite element model. Traditional damage detection techniques for plates need many sensors to be distributed on the surface of the plate. This paper adopts dynamic responses at a few vibration nodal points combined with a Bayesian probabilistic approach for damage identification in plate structures. Vibrational amplitudes at nodal points, also referred as node displacement or NODIS, have the potential to achieve real-time damage assessment with a relatively small number of sensors. Thus, they can serve as efficient structural damage indicators. Despite these advantages, this method has not been applied to plate-type structures. This paper proposes a vibration-based SHM method for plates that is suitable for real-time monitoring, requires a small number of industrial sensors, does not rely on a high-fidelity FE model and can be applied for damage assessment of location and severity. In the Bayesian framework, an efficient perturbation-based surrogate model is derived for plate structures to replace the expensive FE model. The accuracy of the perturbation-based surrogate model is investigated and compared with FE results. Then, this paper evaluates the performance of the NODIS-based Bayesian framework with the perturbation method by comparing it with FE results. At last, the proposed method is applied to a carbon fiber reinforced polymer sandwich structure with different grinding depths.

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.