Disk Of Variable Thickness Research Articles

Mathematical model of the gas turbine engine disk for controlling thermal cyclic loading on the stand

A mathematical model of a disk of variable thickness used as an object of temperature control is based on a new approach to solving the problem of approximating differential heat-conduction equations using a finite system of ordinary differential equations.

Stochastic thermal stresses in an FGM annular disc of variable thickness with spatially random heat transfer coefficients

The second-order statistics (i.e. mean and standard deviation) of the temperature and thermal stresses are evaluated in an axisymmetrically heated functionally graded annular disc of variable thickness with spatially random heat transfer coefficients (HTCs) on the major surfaces of the disc. This annular disc is assumed to have arbitrary variations in the HTCs and material composition along the radial direction only. The randomness in the HTCs is considered to be a random field. The stochastic temperature field is analysed by considering the annular disc to be a multilayered one with stepwise thickness variation, where each layer is assumed to have constant deterministic material properties and random HTCs. In order to evaluate the statistics, the Monte Carlo simulation method is applied to analytical solutions for the deterministic temperature and thermal stresses. The analytical solution for the thermal stresses is obtained through the use of a piecewise power function approximation for Young’s modulus. Numerical results demonstrate the effects of the magnitude of the HTC means, volume fraction distributions of the constitutive materials and thickness variation on the statistics of the temperature and thermal stresses.

Elastic stress analysis of non-linear variable thickness rotating disks subjected to thermal load and having variable density along the radius

An analytical procedure for evaluation of elastic stresses and strains in non-linear variable thickness rotating disks, either solid or annular, subjected to thermal load, and having a fictitious density variation along the radius is presented. Thickness variation of disks is described by means of a power of linear function, which can be used to describe a fourfold infinity of actual disk profiles. The procedure is based on two independent integrals of the hypergeometric differential equation describing the displacement field; this theoretical procedure is just general and does not present limitations and drawbacks of the approaches as the one found in technical literature. General unpublished relations of stress state and displacement field in non-linear variable thickness disks subjected, under elastic conditions, to thermal gradient, and featuring a density variation along the radius are defined. Particular consideration is given to some industrial example of turbine rotors carrying hub and rim with buckets on periphery or radial blades on lateral surfaces. The analytical results obtained by using the new general relations perfectly match those obtained by FEA and overlap those concerning the special cases of tapered conical disks found in literature.

Estimation of the fracture front propagation time in structural components

We discuss special features of the fracture front propagation in structural components (variable-thickness disks and plates, internally pressurized thick-walled vessels). The upper and lower bounds of the relative time of the front propagation have been estimated. Some recommendations regarding the application of the results obtained are provided.

Stresses of a rotating circular disk of variable thickness carrying a current and bearing a coaxial viscoelastic coating

In the present work we consider a circular elastic disk (conductor) of variable thickness under the influence of a steady coaxial current and bearing a coaxial viscoelastic coating (insulator). In both conductor and insulator there exist a heat source generation. As a first step, the solution of purely elastic conductor and insulator is obtained. Then the problem of model with viscoelastic coating is solved using the correspondence principle and Ilyushin’s approximation method. A numerical example is given and the results are discussed in order to investigate the influences of time, temperature, and rotation on the stresses and displacements.

The effect of reinforcement structure and profile shape of curved composite disks on their limiting rotational speed

A problem for determination of an upper kinematic limit of load-carrying ability of complex-reinforced flat and curved rotary disks of constant and variable thickness has been stated and solved by the linear-programming technique. Disks with meridional-circumferential fiber arrangement are shown to have the highest limiting angular velocity. Curvature of a disk impairs drastically its load-carrying ability; the maximum safe rotational speeds of disks operating within the elastic deformation of the composite material phases are several-fold lower than the ultimate permissible speeds.

428 空間的にランダムな熱伝達率を有する変厚傾斜機能中空円板の確率論的熱応力解析(OS5-1 数理解析,OS5 ものづくりを支える固体の数理解析と関東分野)

428 空間的にランダムな熱伝達率を有する変厚傾斜機能中空円板の確率論的熱応力解析(OS5-1 数理解析,OS5 ものづくりを支える固体の数理解析と関東分野)

A microCT X-ray head model for spectra generation with Monte Carlo simulations

The X-ray spectrum from a small-animal computed tomography (CT) device directly influences the dose delivered to the animal as well as the image quality. For any given imaging task, the spectrum needs to be optimized. The aim of this study is to present a model of a small animal microCT X-ray source and to calculate practical spectra for different anode and filter combinations by using the Monte Carlo method. The GATE simulation package was used for this work. The X-ray source of the MicroCAT II scanner was modeled as a tungsten enclosure containing the X-ray tube with dielectric oil and a thin carbon exit window. The anode was a tungsten or molybdenum cylinder block tilted with respect to the electron-beam axis. Beam filtration was achieved through a disk of variable thickness and composition positioned at the exit window. Photon detection was performed with a thick (1 cm) cylindrical tungsten plate (20 cm diameter). Simulated spectra were compared with spectra measured with a CdTe detector for three beams: 50, 70 and 80 kVp with 2 mm of aluminum filtration. There was a reasonable agreement between measurements and calculations. Identified features of the measured spectra were: K absorption edges of Cd and Te (from the detector itself) and characteristic X-rays from Te (Kα and Kβ) and possibly Sb (Kα). Discrepancies between simulations and measurements can be attributed to elements that have been left out of simulations, imperfect detector alignment, and uncertainty in elemental composition of simulated materials. The Monte Carlo method is a convenient and fast tool allowing the calculation of spectra possessing the essential features of real spectra. These and other spectra will be used in future work to study the influence of X-ray spectrum on dose and image quality for various X-ray CT system configurations.

On the Rotating Fiber-Reinforced Viscoelastic Composite Solid and Annular Disks of Variable Thickness

In this article, analytical solution is developed for the analysis of deformation and stresses in elastic rotating disks with arbitrary cross-sections of continuously variable thickness. The disk may be solid or annular and made of an orthotropic fiber-reinforced viscoelastic composite material with equal or different Young's moduli. Using the method of effective moduli makes the reduction of the problem to that of a homogeneous anisotropic material. Numerical computations were carried out to solve this problem and the results show that the displacement and stresses distributions through the radial direction vary with different parameters. In addition, the dependence of the displacement and stresses on the elastic properties of the material and the variations with constitutive and time parameters are investigated. Due to the effectiveness and efficiency of the present solution, it is especially suitable for the analysis of various rotating anisotropic disks of variable thickness and density.

Elastic–plastic deformations of rotating variable thickness annular disks with free, pressurized and radially constrained boundary conditions

Analytical solutions for the elastic–plastic stress distribution in rotating variable thickness annular disks are obtained under plane stress assumption. The analysis is based on Tresca's yield criterion, its associated flow rule and linear strain hardening material behavior. The thickness of the disk is assumed to vary in parabolic form in radial direction which leads to hypergeometric differential equations for the solution. It is shown that, depending on the boundary conditions used, the plastic core may contain one, two or three different plastic regions governed by different mathematical forms of the yield criterion. The expansion of these plastic regions with increasing angular velocity is obtained together with the distributions of stress, displacement and plastic strain. It is also shown mathematically that in the limiting case the variable thickness disk solution reduces to the solution of rotating uniform thickness disk.

Von mises yield criterion and nonlinearly hardening variable thickness rotating annular disks with rigid inclusion

A computational model is developed to investigate inelastic deformations of variable thickness rotating annular disks mounted on rigid shafts. The von Mises yield condition and its flow rule are combined with Swift’s hardening law to simulate nonlinear hardening material behavior. An efficient numerical solution procedure is designed and used throughout to handle the nonlinearities associated with the von Mises yield condition and the boundary condition at the shaft–annular disk interface. The results of the computations are verified by comparison with an analytical solution employing Tresca’s criterion available in the literature. Inelastic stresses and deformations are calculated for rotating variable thickness disks described by two different commonly used disk profile functions i.e. power and exponential forms. Plastic limit angular velocities for these disks are calculated for different values of the geometric and hardening parameters. These critical angular velocities are found to increase as the edge thickness of the disk reduces. Lower plastic limit angular velocities are obtained for disks made of nonlinearly hardening materials.

Elastic–plastic stresses in linearly hardening rotating solid disks of variable thickness

The distribution of stress, displacement and plastic strain in a rotating elastic–plastic solid disk of variable thickness in a power function form is investigated. The analysis is based on Tresca's yield condition, its associated flow rule and linear strain hardening material behavior. An analytical solution is obtained and numerical results are presented for different values of the geometric parameters. The validity of the solution is demonstrated by comparing the results with those for a uniform thickness disk available in the literature.

Elastic–plastic deformation of a rotating solid disk of exponentially varying thickness

The elastic–plastic deformation of a rotating solid disk of variable thickness in exponential form is investigated using Tresca's yield criterion, its associated flow rule and linear strain hardening. An analytical solution is obtained and numerical results are presented for different values of the geometric parameters. In the limiting case of uniform thickness the solution reduces to Gamer's solution.

Limit angular velocities of variable thickness rotating disks

Elastic and plastic limit angular velocities are calculated for rotating disks of variable thickness in power function form. Analytical solution is obtained and used to calculate elastic limit angular velocities of variable thickness rotating annular disks and annular disks with rigid inclusion. An efficient numerical solution procedure is designed and used to obtain the elastic limit angular velocities of variable thickness rotating solid disks. Von Mises yield criterion and its flow rule is used to estimate plastic limit angular velocities. Both linear and nonlinear hardening material behaviors are treated numerically. The results are verified by comparing with those of uniform thickness rotating solid disks available in the literature. Elastic and plastic limit angular velocities are found to increase with the reduction of the disk thickness at the edge as well as the reduction in the disk mass due to the shape of the profile.

On the rotating elastic–plastic solid disks of variable thickness having concave profiles

In this paper, an analytical solution for the elastic–plastic stress distribution in rotating variable thickness solid disks is presented. The analysis is based on Tresca's yield criterion, its associated flow rule and linear strain hardening material behavior. It is shown that depending on the shape of the disk profile, the radial stress in the central region may exceed the circumferential stress. The plastic zone which develops away from the axis of the disk consists of three annular regions governed by different mathematical forms of the yield criterion. The propagation of these plastic regions with increasing angular velocity is obtained together with the distributions of stresses and deformations in nondimensional forms.

On the modeling of narrow gaps using the standard boundary element method.

Numerical methods based on the Helmholtz integral equation are well suited for solving acoustic scattering and diffraction problems at relatively low frequencies. However, it is well known that the standard method becomes degenerate if the objects that disturb the sound field are very thin. This paper makes use of a standard axisymmetric Helmholtz integral equation formulation and its boundary element method (BEM) implementation to study the behavior of the method on two test cases: a thin rigid disk of variable thickness and two rigid cylinders separated by a gap of variable width. Both problems give rise to the same kind of degeneracy in the method, and modified formulations have been proposed to overcome this difficulty. However, such techniques are better suited for the so-called thin-body problem than for the reciprocal narrow-gap problem, and only the first is usually dealt with in the literature. A simple integration technique that can extend the range of thicknesses/widths tractable by the otherwise unmodified standard formulation is presented and tested. This technique is valid for both cases. The modeling of acoustic transducers like sound intensity probes and condenser microphones has motivated this work, although the proposed technique has a wider range of applications.

103 傾斜機能材料からなる変厚回転円板の熱応力緩和最適設計(材料力学I)

103 傾斜機能材料からなる変厚回転円板の熱応力緩和最適設計(材料力学I)

Stress distribution in a linear hardening annular disk of variable thickness subjected to external pressure

The subject of investigation is a linear hardening annular disk of variable thickness subjected to external pressure. The variation of thickness is considered for two different cases: (1) h = h o (1 − tr) k and (2) h = h o (1 − tr k ), where h 0, t and k are real constants. The analysis is based on Tresca's yield condition and its associated flow rule. The governing differential equations are presented in terms of radial displacement. Exact elastic—plastic solutions are obtained in terms of hypergeometric functions for the radial displacement and stress distributions. Numerical results showing the influence of the thickness variation on the stress distribution for different values of the hardening parameter are presented graphically. It can be seen from the present analysis that the thickness variation influences the radial stress and displacement distributions significantly. The present investigation may provide useful information for structural designers and engineers working in these scopes.

Tresca's Yield Condition and the Linear Hardening Rotating Solid Disk of Variable Thickness

Tresca's Yield Condition and the Linear Hardening Rotating Solid Disk of Variable Thickness

On the Applicability of Tresca's Yield Condition to the Linear Hardening Rotating Solid Disk of Variable Thickness

On the Applicability of Tresca's Yield Condition to the Linear Hardening Rotating Solid Disk of Variable Thickness