Annular Disk Research Articles

Transient Thermoelastic Problem of Annular Disc Due to Axisymmetric Heat Supply and Removal of Heat Supply

Transient Thermoelastic Problem of Annular Disc Due to Axisymmetric Heat Supply and Removal of Heat Supply

In-Plane Free Vibration of Circular and Annular FG Disks

The analysis of the in-plane free vibration of the circular and annular FG disks by a meshfree boundary-domain integral equation method is presented in this paper. The material properties of the disks are assumed to vary in the radial direction obeying an exponential law. Based on the two-dimensional linear elastic theory, the motion equations of the FG disks are derived by using the static fundamental solutions. Radial integration method as an efficient tool is adopted to treat the domain integrals which are raised due to the material inhomogeneous and inertial effects. The natural frequencies and associate mode shapes are calculated for the FG disks with combinations of free and clamped boundary conditions. Parametric studies are also conducted to study the effects of the material gradients, radius ratios and boundary conditions on the frequency of the FG disks.

Integrated Forming and Surface Engineering of Disc Springs by Inducing Residual Stresses by Incremental Sheet Forming.

Disc springs are conical annular discs, which are characterized by a high spring force with a small spring travel and good space utilization. In operation, they must meet high demands on the stability of the spring characteristic and the fatigue strength. Under loading, tensile stresses occur which limit the possible applications of disc springs. Compressive stresses can be generated in the stressed areas by means of shot-peening in order to extend the operating limits for a given yield and fatigue strength. Since the spring geometry and characteristics change during shot-peening, the design of the shot-peening treatment is iterative and cumbersome. The present research proposes an incremental forming process for forming and integrated targeted adjustment of residual stresses in disc springs from metastable austenitic stainless steel (MASS), to achieve improved spring properties and high cyclic strength. The main mechanism of residual stress generation is the transformation of metastable austenite into martensite under the action of the forming tool. Different experimental characterization techniques like the hole drilling method, X-ray diffraction, disc compression tests, optical microscopy and cyclic tests are used to correlate the residual stresses and disc spring properties. A numerical model is developed for simulating the martensite transformation in disc springs manufacturing. The results prove that incremental forming enables process-integrated engineering of the desired compressive residual stresses, entailing a higher spring force of metastable austenitic disc springs in comparison to conventional disc springs. Due to martensite formation, the generated residual stresses are stable under cyclic loading, which is not the case for conventionally manufactured springs.

Design and status of the Mu2e crystal calorimeter

The Mu2e experiment at Fermilab searches for the coherent neutrino-less muon to electron conversion in the Coulomb field of an aluminum nucleus. This charged-lepton flavor violating process is characterized by a distinctive signature of a mono-energetic electron (∼ 105 MeV/c) and its observation will be a clear signature of new physics beyond the Standard Model. The Mu2e goal is to improve by four orders of magnitude the search sensitivity with respect to the previous experiments. The Mu2e detector is composed of a tracker, an electromagnetic calorimeter and an external veto for cosmic rays. The calorimeter plays an important role in providing excellent particle identification capabilities, a fast online trigger filter while aiding the track reconstruction capabilities. It consists of 1348 pure CsI crystals divided in two annular disks, each one readout by two large area Silicon Photomultipliers. A large scale prototype has been tested with an electron beam, demonstrating to largely satisfy the Mu2e requirements. At the moment of writing, the crystals and SiPMs production phase is halfway through the completion. An overview of the characterization tests is reported, together with a description of the final mechanical and electronical design.

Interaction of thermal and mechanical waves in axisymmetric generalized thermoelasticity of rotating disk

This study proposes a numerical solution for the coupled thermomechanical response of a rotating annular disk which is subjected to the combined action of thermal and mechanical loads. The annular disk is isotropic and homogeneous with constant thickness. With the aid of the generalized thermoelasticity theory of Lord and Shulman, which includes one relaxation time and avoids the propagation on thermal waves with infinite speed, the energy and motion equations of the disk are extracted. These equations are then transformed to a dimensionless presentation. The developed governing equations are discretized by means of the generalized differential quadrature method. The time-dependent coupled system of equations are traced in time with the aid of the Newmark time marching scheme. Numerical results are given to explore the effect of rotating speed on propagation of temperature, radial displacement and stress waves. It is shown that magnitude of displacement and stress waves is highly dependent to rotation speed, however the magnitude of temperature wave seems to be independent of rotating speed.

Shear-induced buckling of a thin elastic disk undergoing spin-up

The stability of a spinning thin elastic disk has been widely studied due to its central importance in engineering. While the plastic deformation and failure of an annular disk mounted on a rigid and accelerating circular shaft are well understood, shear-induced elastic buckling of the disk due to this ‘spin-up’ is yet to be reported. Here, we calculate this buckling behavior within the framework of the Föppl–von Kármán equations and give numerical results as a function of the disk’s aspect ratio (inner-to-outer radius) and Poisson’s ratio. This shows that shear-induced elastic buckling can dominate plastic failure in many cases of practical interest. When combined with existing theory for plastic failure, the results of the present study provide foundation results for a multitude of applications including the characterization of accelerating compact disks and deployment of space sails by centrifugal forces.

Description of Residual Stress and Strain Fields in FGM Hollow Disc Subject to External Pressure.

Elastic/plastic stress and strain fields are obtained in a functionally graded annular disc of constant thickness subject to external pressure, followed by unloading. The elastic modulus and tensile yield stress of the disc are assumed to vary along the radius whereas the Poisson’s ratio is kept constant. The flow theory of plasticity is employed. However, it is shown that the equations of the associated flow rule, which are originally written in terms of plastic strain rate, can be integrated with respect to the time giving the corresponding equations in terms of plastic strain. This feature of the solution significantly facilitates the solution. The general solution is given for arbitrary variations of the elastic modulus and tensile yield stress along the radial coordinate. However, it is assumed that plastic yielding is initiated at the inner radius of the disc and that no other plastic region appears in the course of deformation. The solution in the plastic region at loading reduces to two ordinary differential equations. These equations are solved one by one. Unloading is assumed to be purely elastic. This assumption should be verified a posteriori. An illustrative example demonstrates the effect of the variation of the elastic modulus and tensile yield stress along the radius on the distribution of stresses and strains at the end of loading and after unloading. In this case, it is assumed that the material properties vary according to power-law functions.

Electron beam test of the large area Mu2e calorimeter prototype

The Mu2e calorimeter consists of 1348 pure CsI crystals coupled to two large area UV-extended Silicon Photomultipliers (SiPMs) organized in two separate annular disks. An intense R&D phase has been pursued to check if this configuration satisfies the Mu2e requirements. In May 2017, a dedicated test has been performed at the Beam Test Facility (BTF) in Frascati (Italy) where the large calorimeter prototype (Module-0) has been exposed to an electron beam in the energy range between 60 and 120 MeV. The prototype consists of 51 crystals, each one readout by two Mu2e SiPMs. We present results for timing and energy resolution both for electrons at normal incidence (0°) and at a grazing impact angle (50°) more similar to the experiment configuration. At 100 MeV, an energy resolution of 5.4% (7.4%) at normal (grazing) incidence has been achieved in good agreement with Monte Carlo expectation. In the same energy range, a time resolution of ∼ XX ps (∼ YY ps) has been measured at normal incidence with 1 GHz (250 MHz) sampling rate. Dependence of time and energy resolutions as a function of beam energy and impinging angle are also presented.

Numerical solution of thermal elastic-plastic functionally graded thin rotating disk with exponentially variable thickness and variable density

Thermal elastic-plastic stresses and strains have been obtained for rotating annular disk by using finite difference method with Von-Mises? yield criterion and non-linear strain hardening measure. The compressibility of the disk is assumed to be varying in the radial direction. From the numerical results, we can conclude that thermal rotating disk made of functionally graded material whose thickness decreases exponentially and density increases exponentially with non-linear strain hardening measure (m = 0.2) is on the safe side of the design as compared to disk made of homogenous material. This is because of the reason that circumferential stress is less for functionally graded disk as compared to homogenous disk. Also, plastic strains are high for functionally graded disk as compared to homogenous disk. It means that disk made of functionally graded material reduces the possibility of fracture at the bore as compared to the disk made of homogeneous material which leads to the idea of stress saving.

Elasto-plastic instability of autoclamped rotating annular disk

Possible loss of stability of an autoclamped rotating annular thin disk of finite constant thickness is investigated with the help of the small parameter method. The relationship between rotational velocity and radius of the plastic zone was established. Based on the Saint-Venant yield condition a characteristic equation is obtained in a first approximation with respect to the small parameter. Cite as: D. M. Lila, “Elasto-plastic instability of autoclamped rotating annular disk,” Prykl. Probl. Mekh. Mat. , Issue 16, 82–90 (2018) (in Russian), http://doi.org/10.15407/apmm2018.16.82-90

Thermoelastic stresses in functionally graded rotating annular disks with variable thickness

This article presents semi-analytical solutions for stress distributions in exponentially and functionally graded rotating annular disks with arbitrary thickness variations. The disk is under pressure on its boundary surfaces and exposed to temperature distribution varying linearly across thickness. Material properties are supposed to be graded in the radial di- rection of the disk and obeying to two different forms of distribution of volume fraction of constituents. Different conditions at boundaries for stresses and displacement are discus- sed. Accurate and efficient solutions for displacement and stresses in rotating annular disks are determined using infinitesimal theory. Numerical results are carried out and discussed for different cases. It can be deduced that the gradient of material properties and thick- ness variation as well as the change of temperature sources have a specific effect in modern applications.

Ferrofluid-based annular squeeze film bearing with the effects of roughness and micromodel patterns of porous structures

ABSTRACTBased on the ferrohydrodynamic theory by R.E. Rosensweig and roughness effects by Christensen’s stochastic theory, a mathematical model of ferrofluid lubricated flat (parallel) annular disks (plates or surfaces) squeeze film bearing, is developed with the effects of porosity at the upper disk, circumferential or radial roughness at the lower disk and radially variable magnetic field. The validity of the Darcy’s law is assumed for the porous matrix. The resultant modified Reynolds-Darcy equation is solved in terms of Bessel function. Expressions for dimensionless load-carrying capacity are obtained and computed. The results for circumferential roughness pattern show that dimensionless load-carrying capacity increases when thickness & permeability of the porous matrix decreases, and effect of surface roughness & width of the annular part increases. The effects of micromodel patterns of two different porous structures are also discussed. Slightly better performances of the bearing are observed for globular sphere permeability model. A comparative study is also made when lower disk is circumferentially rough or radially rough or smooth for globular sphere model.

Effect of Plastic Anisotropy on the Distribution of Residual Stresses and Strains in Rotating Annular Disks

Hill’s quadratic orthotropic yield criterion is used for revealing the effect of plastic anisotropy on the distribution of stresses and strains within rotating annular polar orthotropic disks of constant thickness under plane stress. The associated flow rule is adopted for connecting the stresses and strain rates. Assuming that unloading is purely elastic, the distribution of residual stresses and strains is determined as well. The solution for strain rates reduces to one nonlinear ordinary differential equation and two linear ordinary differential equations, even though the boundary value problem involves two independent variables. The aforementioned differential equations can be solved one by one. This significantly simplifies the numerical treatment of the general boundary value problem and increases the accuracy of its solution. In particular, comparison with a finite difference solution is made. It is shown that the finite difference solution is not accurate enough for some applications.

Electromechanical properties and actuation capability of an extension mode piezoelectric fiber composite actuator with cylindrically periodic microstructure

An extension mode piezoelectric fiber composite (PFC) actuator with cylindrically periodic microstructure is presented in this work especially for directional actuation of plane structures of revolution. The PFC actuator is designed in the form of a thin annular disk where the continuous piezoelectric fibers are periodically distributed along the circumferential direction to yield the directional actuation along the radial direction in the cylindrical principal material coordinate system. This kind of microstructure of the annular PFC actuator yields its radially varying electromechanical properties that are determined through the asymptotic segmentation of its (PFC) volume into a large number of microvolumes of different fiber volume fractions. The closed-form expressions for the effective electromechanical coefficients of the microvolumes are derived, and the corresponding verification is carried out through the numerical homogenization using finite element procedure. The results reveal the indicative magnitude of an effective piezoelectric coefficient ( $$e_{31})$$ that quantifies the directional actuation along the radial direction. But, the magnitude of this coefficient ( $$e_{31})$$ decreases indicatively with the increasing radius, and thus the annular PFC actuator is redesigned in a special manner for the improved magnitude of the coefficient ( $$e_{31})$$ at any radius. With these improved properties of the annular PFC actuator, its indicative actuation capability in control of vibration of an annular plate is observed, and thus this annular PFC actuator may be recommended for active control of plane structures of revolution specifically where the actuation along the radial direction is the major requirement.

On the qualitative dynamics of rotating disks: Thermal shocks and structural integrity

Within engineering circles, overriding breakthroughs have allowed rotating mechanisms to be safely embedded under severe operational circumstances as well as harsh loads. Meanwhile, a literature survey reflects that the implementation of functionally graded materials (FGMs) has revolutionized the characteristics of rotating disks in industrial segments. One of the most challenging situations for FG rotating disks is exposure to multi-dimensional thermal shocks during heating (ascendant) and cooling (descendant), when even materials with high fracture resistance may become deficient. In this paper, a general picture is drawn of a transient thermoelastic design of FG rotating disks to mitigate failure issues stemming from ascendant/descendant thermal gradients and body forces. Contrary to the majority of reports, thermal and displacement fields of the rotating system are affected in both radial and circumferential paths in the polar system, indicating the need for two-dimensional analysis of transient heat transfer. Material properties of the geometry can be judiciously chosen in the r and θ directions, underpinning a practical recipe in the load-bearing capacity of the model for in-situ applications. Transient numerical simulations of deflections, stresses, and thermal fields of a circular annular disk are graphically elaborated using the Fourier and polynomial differential quadrature approaches. On the basis of awareness of the nature of the applied loads, it is found that an appropriate selection criterion of the variation of the material properties from among all available candidates noticeably ameliorates the impact of temperature shocks on the centrifugal force of the rotary system. With regard to the yielding criteria of the structures, the outcomes of the proposed study extend the boundaries of current traditional designs, demonstrating parallel progress in theories and viable materials.

3D-CFD Simulation of Liquid–Liquid Two-Phase Flow in A Pilot-Plant Scale Annular Pulsed Disc and Doughnut Column

ABSTRACTA three-dimensional (3D) computational fluid dynamics (CFD) simulation of liquid–liquid two-phase flow is performed on a pilot-plant scale annular pulsed disc and doughnut column (APDDC). Two-fluid Euler–Euler method augmented with k-ε model is used. The two-phase hydraulic performance are investigated and compared with experimental results under various operation conditions. Favorable agreements are obtained, corroborating the ability of the simulation model to predict hydrodynamic parameters of pilot-plant scale APDDC. As a novel result, it is discovered that circumferential fluctuations of continuous phase velocity and dispersed phase volume fraction exist in the pilot-plant scale APDDC, which might be due to the large-scale structure of turbulence. Effects of operation conditions on the hydrodynamic performance and flow profiles in APDDC are studied based on simulation results and correlated regarding to operation parameters. The studied hydrodynamic parameters include turbulent kinetic energy dissipation, swirling strength, and pressure drop.

A Semi-analytic Stress Solution for Elastic/Plastic FGM Discs Subject to External Pressure

A new semi-analytic plane stress solution for the elastic/plastic distribution of stress in a thin annular disc subject to pressure over its outer radius is presented. The yield stress varies along the radius of the disc and is a monotonically decreasing function of the radius. It is shown that the general solution consists of several stages and the general structure of the solution depends on material and geometric parameters. An example illustrating the general solution is provided.

Experimental study on the vortex structure and path instability of freely falling annular disks

Bodies freely falling in steady water or air are common scenes encountered in various scientific and engineering fields, including the flapping flight of birds and the reentry of a space shuttle. In this work, the freely falling annular thin disks with small dimensionless moments of inertia I* and Reynolds number Re are investigated experimentally in a water tank. We use stereoscopic vision to record the position and orientation of the disks. The flow structure behind the disks is studied by applying fluorescent dye visualization and PIV method. Varying the geometry dimensionless parameter (the inner to outer diameter ratio η and I*) of the disks reveals two new falling patterns. When ηcrit1=0.6 0.8, the circular vortex loops shed frequently from the disk, which causes a lengthways vibration superimposed onto straight vertical motion. We also observe another two falling patterns reported previously: hula-hoop and helical motion. By comparing the wake structure of the two motions, we find that the vortex layer twists more violently in the hula-hoop motion, which is the reason for the different trajectory between them. Further research on flow field reveals that the torque on the disk that causes the vibration is due to the formation, elongation and shedding of the vortex.

Progressive failure behavior of composite flywheels stacked from annular plain profiling woven fabric for energy storage

Annular disk flywheels made of plain profiling woven carbon-fiber-reinforced composites possess favorable biaxial strength along radial and circumferential directions to get higher rotation speed and higher energy density in flywheel energy storage system. Each preform disk layer of fabric stacked for the new composite flywheel in our case study was profiling woven with a continuous fill yarn and radial arranged warp yarns in plain woven style. The progressive failure numerical algorithm was applied to reveal the failure phenomenon in fan-shaped representative volume unit of the plain woven fabric composite flywheel under centrifugal load in high speed running. In the numerical simulation of progressive failure, the analytical iterations were compiled with ANSYS-APDL based on 3D Tsai-Wu failure criterion and Reddy’s sudden material property degradation model. The analysis results indicated that the orthogonal plain profiling fabrics enhanced flywheel’s damage tolerance while the radial fiber yarns delayed transvers cracks. Spin experiments of the test flywheels were carried out on the one-point supporting shaft system driven by high speed motor in a vacuum chamber. All eight flywheel samples reached the tangential speed beyond 850 m/s in spin test, exhibiting a good consistency in material performance. The maximum speed was 898 m/s and the corresponding energy storage density was 64.5 W h/kg in the damage limitation spin test of the plain woven composite flywheel. The spin test verified the validity of the biaxial reinforcement using plain fabric by profiling woven method for composite flywheels with thick radial size. Progressive failure analysis simulation was useful in predicting the burst speed of woven fabric composite flywheels.

Axial dispersion and pressure drop for single-phase flow in annular pulsed disc and doughnut columns: A CFD study

Computational Fluid Dynamics (CFD) simulations have been performed to understand the effects of different operating and geometric parameters on axial dispersion and pressure drop for single-phase flow in annular pulsed disc and doughnut columns (APDDCs) which are relevant for spent nuclear fuel reprocessing. The first step of the two-step computational approach involves solution of Reynolds Averaged Navier-Stokes (RANS) equations with standard k-ε model of turbulence in 2D axisymmetric computational domain to obtain velocity and pressure fields. In the next step, dilute species transport equation is additionally solved to obtain residence time distribution (RTD) and axial dispersion coefficient. The computational approach has been validated by using experimental data of pulsed disc and doughnut columns (PDDCs) reported in literature. The validated computational approach has been used to perform parametric analysis to understand the effects of flow velocity, amplitude of pulsing, disc spacing, percen open area, the ratio of outer diameter and inner diameter of the annulus and flow cross-sectional area on pressure drop and axial dispersion coefficient.