Vibration Of Disk Research Articles

Application of Improved Dynamic Substructure Finite Element Model-Based State-Space Techniques in Mistuned Blisks

Aeroengine is a complex mechanical equipment, and it works at high temperature, pressure, rotational-speed, and severe loads. One of the core problems is that the vibration and mistuning of bladed disk lead to failure and affect the safety and reliability of aeroengine. Previously, one sector taken as the research object is not suitable; the integrally mistuned bladed disk (blisk) is taken as the research object is very necessary; however, the computational efficiency of mistuned blisk is very low. Therefore, a reduced-order model approach, i.e., an improved dynamic substructure finite element model-based state-space technique (IDSFEM-SST), is proposed to investigate the mistuned blisk. Firstly, the reduced-order substructure finite element model is established by this method, and then, the modal frequencies and modal strain energy amplitudes are investigated. Secondly, the maximum displacement responses are analyzed. Finally, the computational efficiency and accuracy of mistuned blisk via IDSFEM-SST is compared with that of the classical dynamic substructure finite element model and the high-fidelity finite element model to verify the effectiveness of this approach. This study has significance to the dynamic research and engineering practices for complex mechanical structures.

A comparison of the non-conforming and conforming sector finite element for free vibration of circular discs

A twelve-term non-conforming and a sixteen-term conforming displacement polynomial are obtained from Pascal’s triangle to deduce the shape functions for a sector element. Using the sector element circular disc is discretized. The number of degrees of freedom for the sector element at a given node is three and four. Kirchhoff’s plate theory is the basis for strain energy and kinetic energy because of the transverse motion of the circular plate. Associated stiffness and mass matrices for the sector element are derived in closed form using MATHEMATICA. Using the Lagrange equation, the free vibration equation of motion for the circular disc is derived. A validation study is conducted, and non-dimensional frequencies from the finite element solution are compared with the analytical solutions reported in the literature. Subsequently, the natural frequencies of Al-Al2O3 functionally graded circular disc with gradation in the thickness direction are evaluated for a variety of boundary conditions.

On the vibrations of the imperfect sandwich higher-order disk with a lactic core using generalize differential quadrature method

This article presents the frequency responses of a sandwich disk with a lactic core (honeycomb), two middle layers containing SMA fiber, and two outer layers (multi-scale hybrid nanocomposite (MHC)). The honeycomb core is made of aluminum due to its low weight and high stiffness. The rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the composite layers. By employing Hamilton’s principle, the governing equations of the structure are derived and solved with the aid of the generalized differential quadrature method (GDQM). Compatibility equations are considered for modeling the interface between the layers of the sandwich disk. Afterward, a parametric study is done to present the effects of SMA fiber, boundary conditions, outer to inner radius ratio, honeycomb network angle, thickness to length ratio of the honeycomb, fibers angle, weight fraction of CNTs, honeycomb to face sheet thickness ratio on the frequency of the multi-phase sandwich disk. The results show that employing the honeycomb network as the core of the structure improves the dynamic response of the structure, impressively. Another consequence is that if there are C-C, C-S boundary conditions, by ever-increase in the θh/π, the dynamic response tends to decline.

Optimization of nanostructured/nano sized rice husk ash preparation

The objective of the study is developing a procedure for production and characterization of rice husk ash (RHA). The effects of rice husk (RH) amount, burning/cooling conditions combined with stirring on producing of RHA with amorphous silica, highest SiO2, lowest loss on ignition (LOI), uniform particle shape distribution and nano structured size have been studied. It is concluded that the best amount is 20 g RH in 125 ml evaporating dish Porcelain with burning for 2 h at temperature 700 °C combined with cooling three times during burning to produce RHA with amorphous silica, SiO2 90.78% and LOI 1.73%. On the other hand, cooling and stirring times affect the variation of nano structured size and particle shape distribution. However, no crystalline phases were found in RHA in all cases. Results proved that the Attritor ball mill was more suitable than vibration disk mill for pulverizing nano structured RHA with 50% of particle size (D50) lower than 45 mm and 99 % of particle size (D99) lower than 144 mm to nanosized RHA with D50 lower than 36 nm and D99 lower than 57 nm by grinding time 8.16 min to every 1 g RHA without changes in morphousity of silica.

Axisymmetric and Non-Axisymmetric Vibration of Thin Growing Viscoelastic Disc

Axisymmetric and non-axisymmetric in-plane vibrations of thin radially growing disc are considered in the frame of the Kelvin–Voigt model of linear viscoelasticity. The main focus of the research is on asymptotic behavior of solutions to the model. Mixed boundary value problems are formulated and converted into standard form by means of time dependent coordinate transformation. The boundary value problems obtained are transformed into infinite systems of ordinary differential equations using the Galerkin-Kantorovich method. It is shown that both axisymmetric and non-axisymmetric problems can be considered in terms of the same mathematical model. The simplified single mode model of the growing disc vibration is formulated and analysed. In the frame of this model the exact solutions are obtained in some interesting special cases. In the general case, solutions are derived using the Wentzel–Kramers–Brillouin (WKB) method. Depending on the exponent of radial growth, the vibration amplitude of the disc demonstrates qualitatively different behavior: if the exponent is less than 0.5 the vibration amplitude decays, if it is more than 0.5 the amplitude increases without bound no matter what size of damping coefficient is assumed. If the exponent equals 0.5 the vibration behavior depends on damping, namely there exist the critical damping coefficient and if the damping coefficient of a particular mode is less than this coefficient, the vibration amplitude grows without bound. Otherwise, if the damping coefficient of the mode is larger than the critical damping coefficient the vibration amplitude decays to zero. In the case where damping coefficient equals to the critical damping one, the amplitude of vibration remains constant. All of the qualitative results obtained for the single mode model are numerically tested and verified using a truncated multimodal system.

차량용 초음파 센서에서 파동유도관에 의한 최소 탐지거리 단축

In this study, a method of shortening the minimum detectable distance of an ultrasonic sensor for the distance measurement of automobiles was developed. It is necessary to overcome the limitations of the minimum detectable distance, which is induced by the residual vibration of an elastic disc in an ultrasonic sensor. The purpose of this study is to design a waveguide to shorten the minimum detectable distance and to improve the performance of proximal measurement by coupling the waveguide with an ultrasonic sensor. We simulated the ultrasound propagation in the designed waveguide through finite element analysis. The analytical results showed clear signals of transmitted and received ultrasound in a wedged-wall waveguide instead of a flat-wall waveguide. Experimental tests were performed to verify the analytical results. The waveguides of the flat and wedged walls were fabricated using a 3D printer and applied during the experiments. The results showed that the ultrasonic sensor coupled with the wedged-wall waveguide measured the proximal distance reasonably.

Vertical-rocking-horizontal vibrations of a rigid disk resting on multi-layered soils with groundwater level

The vertical, rocking and horizontal vibrations of a rigid disk on multi-layered soils are studied by using a coupled approach of stiffness matrix method and “integral equation method”. Considering groundwater level, the layered soils consist of a number of dry layers and saturated layers, and a bedrock at the bottom. To allow the assembly of a global equation of this layered system, the stiffness matrices of the top and bottom saturated layers are modified to match those of adjacent dry layer and bedrock using drainage conditions. Together with the mixed boundary-value conditions at the disk plane, three disk-soil interaction problem, i.e., vertical, rocking and horizontal vibration cases, can be expressed as corresponding dual integral equations for solving. The correctness of the proposed method is verified by existing solutions with good convergence. Parametric studies illustrate the effects of groundwater level, permeability of saturated soil and the hydraulic condition at dry-saturated soil interface on dynamic compliance coefficients of rigid risk and pore pressure in saturated soil layer.

Vibration characteristics investigation of mistuned blisks with receptance substructure component modal synthesis method

To improve the simulation efficiency of mistuned blisk, a method called receptance substructure component modal synthesis method (RSCMSM) is proposed to reduce its degrees of freedom (DOFs). The advantage of this method is that only the interface DOFs need to be solved, which observably enhances the computational efficiency. The modal frequencies, maximum modal shape and frequency response function are calculated via RSCMSM. It is seen that the smooth frequency band is governed by blade vibration and the steep frequency band is governed by disk or bladed-disk coupling vibration. In addition, a peak is observed for the tuned blisk but many peaks appear for the mistuned blisk and many small wave crests are observed near the peak. To verify validity of this method, the computational time of RSCMSM is compared with high fidelity finite element method (HFFEM) and classical substructure component modal synthesis method (CSCMSM), which manifests that the computational efficiency increases by 32.19 %–80.82 % than that of HFFEM when the mistuned level is 0 %~5 %. Moreover, computational efficiency of RSCMSM is increased by 0.85 %–7.56 % than that of CSCMSM. The validity of RSCMSM is verified for calculating the complex mechanical structure.

Vertical vibration of a rigid circular disc embedded in a transversely isotropic and layered poroelastic half-space

Fundamental solution for the time-harmonic vertical vibration of a rigid circular disc embedded in a transversely isotropic and layered poroelastic half-space is developed using a semi-analytical method. First, based on the Green's function of the time-harmonic vertical circular load embedded in the layered half-space, function of the corresponding annular ring load is determined via the method of superposition. Then the disc-medium contact area is discretized into annular ring elements with unknown densities which are determined via an integral least-square approach. Finally, the dynamic vertical compliance is derived by virtue of the equilibrium between the applied load on the disc and the resultant contact stress. Based on the derived fundamental solution, selected numerical examples on the dynamic vertical compliance are presented to investigate the influence of the surface hydraulic condition, fluid saturation, embedment depth of the disc, material anisotropy, material layering, and input frequency.

Physical model for acoustic resonance in annular cavity structure

A physical model for acoustic resonance in the annular cavity structure is developed to represent the typical characteristic when acoustic resonance occurs. Firstly, the measurement of sound pressure in the casing and rotor blades vibration is operated in a multistage high pressure compressor. The sharp peak frequency and discrete multi-tone occur in the frequency spectrum of sound pressure in the compressor, and the vibration of the first stage of rotor blades synchronously presents the high amplitude. The frequencies associated with rotor blades vibration can be calculated with rotating sound source theory. It is also confirmed that acoustic resonance occurs in the multistage compressor. With acoustic similarity principle, an annular cavity model is established to simulate the typical characteristics of acoustic resonance in the compressor based on Large Eddy Simulation (LES) and Lighthill acoustic analogy. The coupling relationship between cavity acoustic mode and disc vibration mode shape is expounded when acoustic resonance occurs in the model. And acoustic resonance will be locked in the certain flow rate range. All these characteristics match well with those occur in the multistage high pressure compressor.

Revisiting the Modeling of the Vibrations of High-Power Piezoceramic Resonators Using an Equivalent Circuit

We estimated different Van Dyke equivalent circuits for low and high power levels. The R, C, L model is compared and matched with AFC of the radial vibrations of a piezoelectric disk. The proposed conception of taking into account only constant (frequency-independent) values of dielectric, elastic, and piezoelectric loss tangents does not conflict with the analytical and experimental results. The additional loss resistor, under high power conditions, has less influence at the resonance than at the antiresonance and must be connected in series with clamped shunting capacity.

Dual-Connected Synchronized Switch Damping for Vibration Control of Bladed Disks in Aero-Engines

An enhanced SSDI (synchronized switch damping on inductor) approach is proposed to suppress the vibration of bladed disks in aero-engines. Different from the authors’ former work (MSSP, 2017; JIMSS, 2018) where a local SSDI circuit is shunted to the piezoelectric materials at each blade sector, in this work two blade sectors are interconnected by a shared SSDI circuit. In this way, the switching action of SSDI is triggered by the relative displacement between two blade sectors. The feasibility of the dual-connected SSDI is numerically examined by a 2-DOF (degree-of-freedom) mechanical system, and further experimentally validated on a single-beam and a double-beam system. Results show that the damping performance increases with the amplitude of relative displacement. This feature is especially favorable for the application of blisks where the blade normally vibrates in different amplitudes and phases. Eventually, we conduct numerical simulation on the forced response of mistuned bladed disk undergoing travelling wave excitation. Results show that the dual-connected configuration can reduce at least half the number of switching shunts while maintain nearly the same performance as the conventional (local) SSDI.

Effect of turbine rotor disc vibration on hot gas ingestion and rotor-stator cavity flow

Gas ingestion numerical model and rotor-stator (RS) cavity model with rotor vibration are proposed to investigate the effect of rotor disc vibration on the flow characteristics in the RS cavity and gas ingestion. Results show that the sealing effectiveness at the rim seal clearance is increased due to the rotor disc vibration, and the amplitudes of the pressure fluctuation and the radial velocity of the gas ingestion flow at rim seal clearance are reduced. The speed of the Kelvin-Helmholtz vortex is approximately 82.28% of that without rotor vibration. Numerical results reveal that the effect of the rotor vibration on the RS cavity flow covers the whole cavity, the unsteady flow at the low radius region in RS cavity is caused by the vibration rotor disc. The frequency of the pressure oscillation at the low radius region is approximately equal to the vibration frequency of the rotor disc as the periodic variation of the tip clearance shape in the horizontal intake section of sealing air and the induced periodic mass flow rate of inlet sealing air. The flow characteristics in RS cavity are together determined by the rotor vibration parameters and the Kelvin-Helmholtz vortices in rim seal region.

Multi-Wave Vibration Caused by Flutter Instability and Nonlinear Tip-Shroud Friction

Abstract Measurements revealed the contribution of multiple traveling waves to the flutter vibrations of bladed disks. Saturated flutter vibration, whether in this multi-wave or in its better-understood single-wave form, is a nonlinear phenomenon. However, it is still not understood of what physical origin the relevant nonlinearities are, and under what conditions single-wave or multi-wave flutter vibration occurs. Recent theoretical work suggests that multi-wave flutter vibration can be explained by strongly nonlinear frictional interblade coupling. The verity of this hypothesis is strictly limited by the simplicity of the considered model, namely, a cyclic chain of seven oscillators with frictional coupling and rather unrealistic aeroelastic behavior. In this work, it is demonstrated that nonlinear dynamical contact interactions at tip-shrouds are a likely cause for the observed multi-wave flutter vibration. To this end, a more realistic structural turbine blade row model with a more realistic aeroelastic behavior is considered. Some insight into its intriguing dynamics, dependence of limit states on initial conditions, and eigenvalue placement is provided. For instance, it is shown that there is an intimate relation between internal combination resonance conditions of certain traveling wave modes and the spectral content of single- and multi-wave flutter oscillations.

Effects of couple stresses on the in-plane vibration of micro-rotating disks

Micro-rotating disks are extensively used in micro-electromechanical systems such as micro-gyroscopes and micro-rotors. Because of the sensitivity of these elements, enough knowledge about the mechanical behavior of these structures is an essential matter for designers and fabricators. The small-scale effects on the in-plane free vibration of such micro-disks present an important aspect of the mechanical behavior of these elements. The small-scale effects on the in-plane free vibration of these micro-disks are investigated in this study using the modified couple stress theory. By using the Hamilton principle, the partial differential equations governing the coupled radial and tangential motion of the disk particles with their corresponding boundary conditions are derived. Then, the solution for the boundary value problem is analytically presented. The effects of the angular speed of the micro-disks and the length scale parameter of the modified couple stress theory on the steady radial and tangential displacements, and on the natural frequencies are investigated. Those results are compared with the ones previously obtained from the classical continuum mechanics analysis.

Numerical Simulation of the Perforated Shell’s Oscillations in a Vibrational Priller

The widespread catalysts and nuclear fuel production are the sol-gel technology, including several stages, namely, the raw materials preparation, dispersing it into drops, the granules formation in gas and then in liquid media, granules removal with liquid separation. The vibration granulator is proposed to use on the dispersion stage. One of the problems in their development is determining the vibrational characteristics of a perforated bucket filled with liquid to a certain level. Considering that vibrations are transmitted from the emitter disk through the liquid melt and cause vibrations of the perforated shell, in research, it was decided to use the Fluent Flow and the Transient Structural modules of the ANSYS Workbench software. As a result, numerical simulation results of the emitter disk vibration effect on the cylindrical body are presented. Also, parameters of a discrete mathematical model are evaluated by the bucket vibrations characteristics. The corresponding model considers the inertial, stiffness, and damping properties of functional elements. Additionally, according to the modal analysis results of the priller body, it was determined the eigenfrequencies of the hydromechanical system. Finally, based on the numerical simulation results and their analysis using Fourier transformations, it was determined that the oscillations of the lower part of the bucket, consisting of two harmonic oscillations that equal 230 Hz and 520 Hz.

Research on cold mechanical vibration of air-cooled disc brake

Cold mechanical vibration of air-cooled brake disc is mainly caused by the non-uniform geometry, including disk thickness variation (DTV) and side face run-out (SFR). A mathematical model consisting of the non-uniform geometry is constructed, which is imported into the dynamic brake model established by Lagrange equation as initial parameters. The braking moment fluctuation during braking process is obtained by MATLAB software. The experimental verification is realized based on Link3900 NVH test platform, where result shows that the calculated brake pressure is quite consistent with the test value. By single variable method, the key influence factor that affected braking moment fluctuation is analyzed, including DTV, SFR, friction coefficient, contact stiffness coefficient and damping coefficient. The conclusion shows that reducing these parameters within a certain range can significantly reduce the amplitude of cold vibration, except for the contact damping coefficient.

Study of Resonance Phenomena During Thin-Film Perforation upon the Passage of Multicharged Ions

The process of the perforation of a nanometer-thick film during passage of the wave packet of a multicharged ion is studied. It is shown that the resonant behavior of vibrations of the disk released from the film has a significant effect on the perforation process. The resonance mechanism is based on the “push-pull” process. A model of the strength of the polarization interaction between the film and the wave packet of the particle is proposed. The model makes it possible to estimate the threshold value of the force required to form a pore during the passage of a multicharged ion through the film.

Extended stiffness matrix method for horizontal vibration of a rigid disk embedded in stratified soils

• Horizontal vibration of a rigid disk embedded in stratified soils is studied. • Potential function method is applied to obtained the general solutions of a poroleastic medium and an elastic medium. • An extended stiffness matrix method is proposed for solution of the stratified soils. • The mixed boundary value problem of soils–disk interaction is represented as four coupled integral equations. • Examples are carried out to illustrate the influences of groundwater, embedment position of the disk. In this paper, an extended stiffness matrix method is proposed for horizontal vibration of a rigid disk embedded in stratified soils. Considering the influence of groundwater level, the soils are modeled as a layered system composed of elastic and poroelastic media. The potential functions, Fourier series and Hankel transform are applied to obtain the displacement and stress solutions of the elastic medium and poroelastic medium. Conventional stiffness matrix method is generally used to solve a single-medium layered system with high efficiency and computational stability, but cannot be directly applied to the present layered model. The principle of the extended stiffness matrix method is to make the displacement and stress and stiffness matrix dimensions of the poroelastic layer match those of adjacent elastic layers, allowing the assembly of a global equation. the problem of imcompatibility between an elastic medium and a poroelastic medium at interface is addressed by the extended stiffness matrix method which also provides a new idea for solution of layered systems consisting of different media. Subsquently, the mixed boundary value problem of the soils–disk interaction is represented as four coupled integral equations which can be reduced to a pair of Fredholm integral equations of the second kind to solve. The accuracy of the present method is verified by the existing solutions, and then several numerical examples are presented to illustrate the effects of groundwater level and permeability of saturated soil layer as well as the embedded depth of the rigid disk on the dynamic interaction between the disk and the stratified soils.

Dynamic response of guided spline circular saws vs. collared circular saws, subjected to external loads

ABSTRACT While collared saws are no longer widely used in North America for primary breakdown of logs to boards, these are common in most of European sawmills. In North America, guided spline circular saws are used for sawing of boards of varying dimensions. This paper presents a stability analysis of spinning disk, an idealized representation of circular saw, for collared and splined arbor saws, when subjected to radial and tangential in-plane forces. The governing linear equations of transverse motion of a spinning disk, subjected to edge-loads, are used in evaluation of the energy transfer from the applied loads to the disk vibrations. This analysis is used to examine the role of critical system components in the development of instability. Unique experimental results of dynamic behavior of both saw types are presented in calculation of critical and flutter instability speeds of the system.