Simplified Vibration Model Research Articles

The Influence of Nonlinear High-Intensity Dynamic Processes on the Standing Wave Precession of a Non-Ideal Hemispherical Resonator.

The properties of small size, low noise, high performance and no wear-out have made the hemispherical resonator gyroscope a good choice for high-value space missions. To enhance the precision of the hemispherical resonator gyroscope for use in tasks with large angular velocities and angular accelerations, this paper investigates the standing wave precession of a non-ideal hemispherical resonator under nonlinear high-intensity dynamic conditions. Based on the thin shell theory of elasticity, a dynamic model of a hemispherical resonator is established by using Lagrange's second kind equation. Then, the dynamic model is equivalently transformed into a simple harmonic vibration model of a point mass in two-dimensional space, which is analyzed using a method of averaging that separates the slow variables from the fast variables. The results reveal that taking the nonlinear terms about the square of the angular velocity and the angular acceleration in the dynamic equation into account can weaken the influence of the 4th harmonic component of a mass defect on standing wave drift, and the extent of this weakening effect varies with the dimensions of the mass defects, which is very important for steering the development of the high-precision hemispherical resonator gyroscope.

A study on improving the sound radiation capability of stepped-plate parametric array loudspeakers

It is well known that Parametric Array Loudspeakers (PALs) produce highly directional audible sounds. However, their widespread adoption is hindered by their high cost, which is primarily attributable to the use of an array of ultrasonic radiator units. To address this issue, our research group introduced stepped-plate parametric array loudspeakers (SPPALs) in 2018. SPPALs utilize a single-structure directional ultrasonic radiator, featuring steps of half-wavelength thickness on the radiating plate. This design mitigates the problem of poor directivity, especially at high frequencies, caused by destructive interference resulting from the plate's flexural mode. Moreover, SPPALs can offer cost advantages compared to commercial PALs due to their single structure. However, understanding the vibration characteristics of SPPALs in relation to sound radiation performance is quite challenging due to their various design parameters. In this study, we present an analytical approach that offers a quantitative method for enhanced sound radiation capability. We present a simplified vibration model (SVM), which enables an efficient design process based on a comprehensive analysis of vibration characteristics. By minimizing reliance on finite element method (FEM) simulations, our method expedites the design of various directional speaker systems.

Simplified Method for Vibration Model of Converter Valve in Offshore HVDC Substation Based on Response Surface

To ensure the computational accuracy for the offshore high voltage direct current substation local structure and its large and complex electrical equipment, it is necessary to reduce the modeling complexity and improve the calculation efficiency. Thus, a simplified vibration model with constant key physical parameters was established; the converter valve was used as a test design example and a lower number of samples was used. Finally, the response surface fitting was carried out. Based on the machine learning concept, problems such as the loss of physical meaning of complex system matrices and low iteration efficiency, caused by high-dimensional matrix operations were avoided. In addition, the deterministic screening experiment design greatly reduced the number of samples needed while also ensuring the second-order effect. The fit between the response surface equation and experimental results was good after optimizing the relevant design factors based on the vibration equation. The comparison between the simplified vibration converter valve model and the original complex model has shown that the errors for various physical parameters and the vibration characteristics were below 5% and that the model simplification degree was 95%.

Linear Dynamic Analysis of Free-Piston Stirling Engines on Operable Charge Pressure and Working Frequency along with Experimental Verifications

This paper presents a linear dynamic analysis on operable charge pressure and working frequency of free-piston Stirling engines (FPSE) along with experimental verifications. The equations of motion of the FPSE are formulated as a 2-degree-of-freedom (DOF) vibration system of the power piston (PP) and displacer piston (DP), based on the state equation of ideal gas and the isothermal Stirling cycle model. The dynamic models of FPSE we considered are the 1-DOF simple vibration model of each piston and the 2-DOF root locus model of coupled pistons. We developed a test FPSE for verification of the dynamic models and conducted a series of experiments to measure the dynamic behaviors of PP and DP under varying charge pressures for various masses and stiffnesses of the PP. As a result, both prediction models showed good agreements with experimental results. The 1-DOF vibration model was found to be simple and effective for predicting the operating frequency and charge pressure of FPSE. The root locus method showed reasonable predictions with an operation criterion of the PP–DP phase angle of 90°. In addition, the FPSE was confirmed to operate in resonant oscillations when the DP–PP phase angle is 90°, based on analysis of the force vector diagram of the two pistons.

Simple vibration model for the design of a vertical axis wind turbine

Wind turbines are widely used these days as one of renewable energy sources. In this paper, a dynamic model of a vertical axis wind turbine is developed by considering coupling effects among shaft bending, shaft torsion, shaft tension, rotor tension and rotor bending. The modal characteristics of the vertical axis wind turbine were obtained by using the dynamic model. The accuracy of the proposed model was first validated by comparing its numerical results to those obtained with a commercial program. Then, the effects of key design parameters such as shaft length, shaft diameter and rotor cross section area on the modal characteristics of the wind turbine were investigated. The natural frequency loci veering phenomena occurred when those parameters varied. The loci veering phenomena were associated with the mode shape switch between shaft bending and rotor bending, which should be carefully examined to improve the vibration quality of the wind turbine. The main contribution of this study is to propose a simple vibration model by which the effects of various design parameters on the modal characteristics of the vertical axis wind turbine can be investigated. Some design guidelines related to the vibration performance are also suggested.

Analysis on vertical steering vibration of drum shearer cutting part

The impact of the load on the shearer is mainly transmitted through cutting part. In this paper, in order to get the vertical steering vibration characteristics of the cutting part of the drum shearer, the working condition of coal mining machine is simplified. A simplified vertical steering model and the simplified vibration model of the whole cutting part of shearer are established. The vertical steering vibration process of the cutting unit is simplified into a single freedom and one forced vibration system under harmonic excitation. The dynamic response of the cutting part under sine excitation is obtained by using Matlab/Simulink for modeling and simulation. The influence of the support rigidity and damping of the high oil cylinder on the vertical steering vibration characteristics of the cutting part is analyzed. The results show that the damping of the cylinder can reduce the vibration of the system and the stability of the swing process of cutting the part is improved.

Dynamic Characteristics of the End-effector of a Drilling Robot for Aviation

This study discusses the dynamic stiffness of the End-effector of a drilling robot for aircraft. In view of the requirements of automatic drilling processing for aircraft parts, based on the analysis of the working process of the automatic drilling End-effector, the End-effector of drilling unit has been employed in precision machine tools, It can provide very smooth motion and good verticality. In the design of the machines, it is necessary to obtain the stiffness of these guideway. Therefore, an identification method of the guideway stiffness is verified in this paper. In this method, the guideway stiffness is identified from the natural frequency of the moving body. First, a virtual prototype of the End-effector of drilling unit flexible is constructed by jointly using both ANSYS, which provides a foundation for further dynamic characteristic simulations. Next, the impact test is carried out for a drilling tool to obtain the vibration mode of its moving body, and simple vibration model is developed based on the obtained vibration mode to identify the natural frequency of the guideways. For further verification, natural frequencies of the moving body are calculated by FEM with the identified natural frequency and compared with the measured natural frequencies. The results shows that : the natural frequencies were calculated almost correctly with the identified equivalent stiffness, and which provides theoretical reference for improving the drilling efficiency and assembly quality of aircraft components.

Analysis of Active Vibration Reduction for Soft Mounted Electrical Machines Based on a Multibody Model

The aim of the paper is to analyze active vibration reduction of soft mounted electrical machines by using actuators between the motor feet and a soft foundation based on a multibody model. The actuator forces are inserted directly in the vibration model without using a feedback control system. The goal is to reduce the forced vibrations, which are caused by typical excitations of electrical motors — eccentricity of rotor mass, bent rotor deflection and magnetic eccentricity. Based on the simplified model, the mathematical coherences are derived and a numerical example is shown, where different vibration reduction concepts are analyzed and the necessary actuator forces are calculated. The aim of the paper is to show the capability of using actuators between motor feet and soft foundation, based on a simplified multibody vibration model. For future work, the multibody model has to be implemented into a feedback control system for active vibration control.

Simplified Vibration Model and analysis of a single-conductor transmission line with dampers

A novel model is developed for a vibrating single-conductor transmission line carrying Stockbridge dampers. Experiments are performed to determine the equivalent viscous damping of the damper. This damper is then reduced to an equivalent discrete mass-spring-mass and viscous damping system. The equations of motion of the model are derived using Hamilton’s principle and explicit expressions are determined for the frequency equation, and mode shapes. The proposed model is verified using experimental and finite element results from the literature. This proposed model excellently captures free vibration characteristics of the system and the vibration level of the conductor, but performs poorly in regard to the vibration of the counterweights.

Modeling of 1-3 piezoelectric composites operating in thickness-stretch vibration mode

For bulk piezoelectric ceramics plates, the fundamental thickness-stretch (TSt) waves are always coupled to the in-plane extension waves and the symmetric thickness-shear waves. The occurrence of these spurious modes in bulk piezoelectric ceramics plates is undesirable as it may interfere with the operation of transducers. 1–3 piezoelectric composites are promising candidates to suppress the spurious modes mentioned above. However, theoretical modelling of multiphase ceramic composite objects is very complex. In this study, a simple analytical TSt vibration model is constructed from three-dimensional equations of linear piezoelectricity. The mechanical damping is considered in the model by introducing a complex elastic constant. The performance of 1–3 piezoelectric composites is analysed and the electrical impedance results from theoretical and experimental analysis are compared. The results show that there is excellent agreement between the experimental electrical impedance and that obtained by the theoretical TSt vibration analysis. This indicates that 1–3 piezoelectric composites can be operated in a nearly pure TSt vibration mode near the fundamental resonance. The analytical model we present is valid for analysing 1–3 piezoelectric composites plates with large aspect ratios quickly and efficiently.

Ride Comfort Performance of Active Vehicle Suspension with Seat Actuator Based on Non-Fragile H∞ Controller

The purpose of this paper is to investigate an active seat suspension system with two active actuators using a non-fragile robust control strategy. A simple deterministic vibration model of human body is added to the seat suspension dynamical model in order to make the modeling more accurate. Desired controller is obtained by solving a linear matrix inequality formulation by considering the vertical body acceleration as measurement signal. Finally, the effect of the seat actuator and controller gain variations on the closed-loop system performance is investigated numerically for two deterministic external excitations: bump and a realization of Gaussian white noise. Simulations show that the seat actuator has a noticeable effect on the seat suspension performance especially under random disturbances.

Budgeting and control of the mechanical noise in the International Linear Collider final focus system

In this paper, we present a simplified vibration model of the silicon detector (SiD), where the final doublet (QD0) is captured inside the detector and the penultimate magnet (QF1) is inside the machine tunnel. Ground motion spectra measured at the detector hall at SLAC have been used together with a spectrum of the technical noise on the detector. The model predicts that the maximum level of rms (root mean square) vibration seen by QD0 is well below the capture range of the interaction point (IP) feedback system available in the ILC. With the addition of an active stabilization system on QD0, it is also possible to get closer to the stability requirements of the compact linear collider (CLIC). These results can have important implications for CLIC.

헬멧의 충격응답 분석을 위한 단순진동 모델

Abstract - In this study, to analyze the impulsive response of a helmet, a simple vibration model is presented. Based upon the experimental data and the simulation results, an equivalent one degree of freedom vibrational system is adapted, and transient impulsive responses are analysed to investigate the influence of en-gineering parameters such as damping, natural frequency, and impact velocity on the impulsive response of the helmet. Maximum gravitational acceleration reduces as the damping factor value increases. When the damping factor value is around 0.6 or larger, the maximum acceleration does not change. With respect to the natural fre-quency and the impact velocity, it increases linearly. The relationship between head injury criterion(HIC) and maximum gravitational acceleration is also presented. The scheme of this study is expected to be utilized to economize the design process of high quality helmets.Key words : Helmet, Impulse, HIC, Head Injury Criterion, G-Acceleration 1)

Modeling of Axial Spring Stiffness in Active Vibration Controlled Drilling

During drilling process, substantial amount of vibration and shock are induced to the drill string. Active vibration controlled drilling is introduced to reduce the vibration and increase the efficiency of drilling process. In this system, two main components that determine the damping coefficient are magnetorheological (MR) damper and spring assembly. Performance of vibration damping system is depending on the viscosity of MR fluid in the damper and spring constant of spring assembly. One of the key issues that are unclear from the design is the correlation between the axial spring stiffness configuration and the damping force which needs to be tuned actively. There has been lack of studies on how the viscosity of MR fluid on the active vibration damper affects the damping stiffness of the whole system. The objective of the project is to extract the correlations for the viscous damping coefficient, equivalent spring stiffness and power input to the system. Simplified vibration model is thus created using Simulink, together with experimental data fed from APS Technology’s in-house team. Inputs of the simulation such as force exerted, mass of mandrel, spring constant and step time are based on the experimental data and can be adjusted to suit different experiments. By having the model, behavior of the system can be studied and analyzed. From the simulation, it is also observed that the relationship between damping coefficient and power input of the system is linear.

Dynamic Characteristics of Ultra-Precision Machine Tools (Evaluation for Stiffness of Guideways by Impact Test)

This study discuss the dynamic stiffness of guideways of a ultra-precision machine tools. V-V roller guideways have been employed in ultra-precision machine tools, as they can provide very smooth motion and good straightness. Recently, general linear ball guideways are also employed in ultra-precision machine tools. In the design of the machines, it is necessary to obtain the stiffness of these guideways. Therefore an identification method of the guideway stiffness is verified in this paper. In this method, the guideway stiffness is identified from the natural frequency of the moving body. First, the impact test is carried out for an ultra-precision machine tool to obtain the vibration mode of its moving body. Next, a simple vibration model is developed based on the obtained vibration mode to identify the equivalent stiffness of the guideways. Then, the static stiffness of the guideways is measured for the verification of the identified equivalent stiffness. For further verification, natural frequencies of the moving body are calculated by FEM with the identified equivalent stiffness and compared with the measured natural frequencies. The identified equivalent stiffness agreed well with the measured static stiffness. Furthermore, the natural frequencies were calculated almost correctly with the identified equivalent stiffness.

Development of a 3-DOF Mobile Positioning Mechanism with 6 Contact Points (Input Voltages by Dynamic Analysis under Conditions of Quasi-Constant Internal Forces)

In this paper, we describe a design and input voltage waveforms for a 3-DOF precise inchworm mechanism with 6 contact points. In those ten years, we have developed an omnidirectional and holonomic inchworm mechanism to provide a flexible, compact, and precise microscopic processing. In previous mechanism, a pair of U-shaped electromagnets arranged to cross each other are connected by four piezoelectric actuators so that the mechanism can move in any direction. However, microscopic operations are still difficult because of vibrations caused by inclination of the U-shape electromagnets. In this paper, we have proposed newly developed mechanism composed of a pair of Y-shaped electromagnets and six piezoelectric actuators to prevent the inclination of the electromagnets. We have analyzed a 3-DOF simple vibration model to get the dynamical response of the mechanism. We have also solved quasi-constant conditions of internal forces between a pair of the Y-shaped-electromagnets. Finally, we develop the expression for input voltage waveforms which represents holonomic and omnidirectional motion. We have checked the validity of the theoretical input voltages by orthogonal and rotational experimental results.

Research on on-line automatic diagnostic technology for scratch defect of rolling element bearings

An on-line automatic diagnostic technology is presented in this paper, based on the simplified vibration model of early scratch defects of rolling element bearings and the analysis of vibration characteristics of early scratch defects. According to characteristics of periodic high frequency natural vibration excited by early scratch defects of the bearing, high frequency resonance technique (HFRT) is adopted for on-line diagnosing in the paper. An algorithm on peak detection of the vibrational energy is used to catch the main frequency of high frequency resonance automatically, denoising technology to improve the signal-to-noise ratio, and automatic identification technology to evaluate defect site of the tested bearing. An on-line automatic diagnostic system for early scratch defects of rolling element bearings, developed based on the above principles, can effectively identify early scratches on outer race, inner race and ball.

Numerical Simulation of Subway Train Vertical Random Vibration Load in Time Domain

It is of importance to identify the subway train random vibration load correctly. On the basis of the in-situ dynamic response measurement, the deterministic data for vertical acceleration of rail were obtained. The problem of identifying the random vibration load of subway train was solved in Matlab, according to the simplified vibration model of vehicle system, and in Newmark-β method. Then the time curve and the amplitude spectrum curve of the vertical random vibration train load were obtained. Compared with Fast Fourier Transform method, Newmark-β method is more simple and practical to simulate the train vertical random vibration load directly in the time domain.

Derivation of a plane vibration model for electrical machines on soft machine foundations

The paper shows the derivation of a plane vibration model for natural vibration analysis of electrical machines mounted on soft machine foundations. The model represents a simplified single mass system, which can be used to calculate the natural vibrations, which occur in the transversal plane of a soft mounted electrical machine. After the mathematical description of the analytical vibration model and the necessary boundary conditions have been derived, an example of an electrical machine mounted on a steel frame foundation is shown. The natural frequencies are calculated and a comparison between the analytical vibration model and a finite-element vibration model is deduced, showing satisfying correlations. Additionally, it is shown in the example that the size of the contact area between machine feet and foundation may significantly influence the natural vibrations, by stiffening the foundation. On one hand, the aim of the paper is to derive a simplified plane vibration model to calculate the natural vibrations in the transversal plane of soft mounted electrical machines. On the other hand, the aim is to describe the derivation of the plane vibration model and to derive the necessarily boundary conditions for the calculation of the substitute foundation stiffness data.

Wear Prediction of Steam Generator Tubes due to Shell Side Foreign Objects

A method to evaluate tube wear due to foreign objects on a steam generator tube sheet is introduced. In order to produce the database for the evaluation, a simplified vibration model based on the zonal approach concept and dissected tube model is introduced in this paper. The entire tube sheet region of the steam generator is divided into 30 zones. The data of a representative tube is used in a zone that includes hundreds of tubes. Therefore, the number of tubes analyzed to produce the database is dramatically reduced by the zonal approach concept. The dissected tube model simplifies the mode analysis by adopting a single-span beam instead of a multispan beam idealizing the full-length U-tube of a steam generator. It is shown that the natural frequencies obtained from the dissected model are about 4 to 5% lower than those of the dominant modes between the tube sheet and the first tube support structure obtained from the analysis of the full-length U-tubes. If the concerned region is between the tube sheet and the first tube support structure of the steam generator, using the zonal approach concept and the dissected tube model is very effective to save time and efforts to calculate the vibration data. In this paper, a method to predict the wear depth of the tubes due to the fixed foreign objects on the tube sheet in the secondary side of a steam generator with the simplified vibration model is introduced.