scholarly journals Transient Thermoelastic Analysis of Pressurized Rotating Disks Subjected to Arbitrary Boundary and Initial Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Mohammad Zamani Nejad ◽  
Azam Afshin
Keyword(s):  
Thermal Stresses ◽  
Initial Conditions ◽  
Exact Analytical Solution ◽  
Separation Of Variables ◽  
Outer Radius ◽  
Rotating Disks ◽  
Arbitrary Boundary ◽  
Inner Radius ◽  
Transient Thermal

This paper focuses on exact analytical solution of transient thermoelastic behaviors of rotating pressurized disks subjected to arbitrary boundary and initial conditions. The pressure, inner radius, and outer radius are considered constant. The basic thermoelasticity theory under generalized assumptions is used to solve the thermoelastic problem. Using the method of the separation of variables, the relations of temperature and transient thermal stresses in the radial direction are obtained. In the case study, the disk is considered under heat flux. Some useful discussions and numerical examples are presented. The analytical results were compared with those of the finite element method and good agreement was found. The relations obtained in this paper can be applied to any arbitrary boundary and initial conditions.

On the Vibration of a Rotating Disk

1972 ◽  
Vol 39 (4) ◽  
pp. 1143-1144 ◽  
Author(s):  
S. Barasch ◽  
Y. Chen
Keyword(s):  
Approximate Calculation ◽  
Initial Conditions ◽  
Rotating Disk ◽  
Equation Of Motion ◽  
Outer Radius ◽  
Order Equation ◽  
System Of Differential Equations ◽  
Fourth Order Equation ◽  
First Order ◽  
Inner Radius

The equation of motion of a rotating disk, clamped at the inner radius and free at the outer radius, is solved by reducing the fourth-order equation of motion to a set of four first-order equations subject to arbitrary initial conditions. A modified Adams’ method is used to numerically integrate the system of differential equations. Results show that Lamb-Southwell’s approximate calculation of the frequency is justified.

scholarly journals Pengaruh Variasi Radius-Dalam Rim Terhadap Pengurangan Massa dan Momen Inersia Massa Dengan Studi Kasus Benda Putar Berdiameter 10 cm

2018 ◽  
Vol 1 (1) ◽  
Author(s):  
Eka Taufiq Firmansjah
Keyword(s):  
Outer Radius ◽  
Moment Of Inertia ◽  
Mass Reduction ◽  
Inner Radius ◽  
Mass Moment ◽  
Mass Moment Of Inertia ◽  
Machine Elements ◽  
The Moment ◽  
The Masses

ABSTRAK Mesin terdiri dari sekumpulan elemen mesin yang diam dan bergerak. Elemen mesin yang bergerak dengan gerakan berputar disebut benda putar. Pada beberapa kasus seringkali diinginkan pengurangan massa dari benda putar tersebut untuk alasan ekonomis, biasanya untuk elemen mesin yag diproduksi massal. Namun pengurangan massa berakibat pada pengurangan momen inersia massa benda putar bersangkutan. Jika tuntutan perancangan tidak mempermasalahkan perubahan tersebut, maka pengurangan massa tidak menjadi masalah. Namun jika momen inersia massa tidak boleh terlalu rendah, maka harus dicari kompromi dimana pengurangan massa sebesar-besarnya namun penurunan momen inersia massa sekecil-kecilnya. Pada penelitian ini dilakukan studi kasus terhadap benda putar berjari- jari 10 cm jari-jari dalam hub 2 cm dan jari-jari luar hub 4 cm. Jumlah jari-jari ada 4 dengan lebar 1 cm dan tebal benda putar 0,5 cm. Variasi pengurangan massa dilakukan dengan memvariasikan jari-jari- dalam rim. Untuk tiap variasi, dilakukan perhitungan untuk mendapatkan jumlah massa yang dapat dikurangi dan momen inersia massa dari benda putar. Ternyata pada nilai jari-jari dalam tertentu, dapat diperoleh nilai kompromi dari permasalahan diatas. Kata kunci: benda putar, penghematan bahan, momen inersia massa.  ABSTRACT Machine consists of a set of machine elements that still and moving. Machine elements that move in a circular motion called rotary object. In some cases it is often desirable reduction in the mass of the rotating object for economic reasons, usually for a mass production of machine elements. But the mass reduction results in a reduction in moment of inertia of the mass. If the demands of the design allow this decrease of moment of inertia, mass reduction is not a problem. But if the moment of inertia of the masses should not be too low, it must find a compromise in which a mass reduction profusely but the decrease in the mass moment of inertia of the smallest. In this research conducted a case study of rotating element radius of 10 cm, radius of the hub 2 cm and outer radius hub 4 cm. The number of spoke are 4 with a width of 1 cm and uniform thickness 0.5 cm all over rotating element. Variations mass reduction is done by varying the inner radius of the rim. For each variation, calculation is performed to obtain the amount of mass that can be reduced and the mass moment of inertia of the rotating object. It turned out that in the certain value of inner radius of the rim in particular, can compromise the values obtained from the above problem. Keywords: rotating element, reducing material, mass moment of inertia.

Transient Thermal Stresses in a Sphere by Local Heating

1974 ◽  
Vol 41 (4) ◽  
pp. 930-934 ◽  
Author(s):  
J. B. Cheung ◽  
T. S. Chen ◽  
K. Thirumalai
Keyword(s):  
Thermal Stresses ◽  
Numerical Solutions ◽  
Integral Transformation ◽  
Separation Of Variables ◽  
Local Heating ◽  
Local Surface ◽  
Displacement Potential ◽  
Heated Zone ◽  
Localized Heating ◽  
Transient Thermal

The problem of transient thermal stresses in a solid, elastic, homogeneous, and isotropic sphere is solved for uniform and nonuniform, local surface heating. The temperature solutions are obtained by using separation of variables and integral transformation. The corresponding thermal stresses are derived by superposing a particular displacement potential function on Boussinesq solutions. Numerical solutions for two particular cases of localized heating of a typical brittle spherical solid have been obtained and presented. The results indicate a tensile stress concentration in the interior of the solid below the heated zone.

Reliability of Thermally Loaded Cylinders

1990 ◽  
Vol 112 (3) ◽  
pp. 303-308 ◽  
Author(s):  
H. S. Zibdeh
Keyword(s):  
Thermal Stresses ◽  
Coefficient Of Thermal Expansion ◽  
Perturbation Technique ◽  
Outer Radius ◽  
Temperature Gradients ◽  
Normal Distributions ◽  
Inner Radius ◽  
Thermal Changes ◽  
Log Normal ◽  
Outer Half

Cylinders often contain fluids at various temperatures. Temperature gradients develop across the cylinder which in turn produce thermal stresses. Using a perturbation technique, expressions for means and standard deviations of thermal stresses in cylinders are presented in this paper. These expressions include the probabilistic effects of changes due to inner and outer radii, modulus of elasticity, Poisson’s ratio, coefficient of thermal expansion, and temperature. It is found out that the cylinder is more sensitive to the geometrical changes than the mechanical and thermal changes. It is also noticed that the effect of variation in the inner radius is more than the outer radius at the inner half of the cylinder. On the other hand, the effect of variation in the outer radius is more than the inner radius at the outer half of the cylinder. Probabilities of failure are calculated for normal and log-normal distributions.

Multiphysics Inverse Analysis Method for Reducing Transient Thermal Stress in a Thick-Walled Pipe

2009 ◽  
Author(s):  
Takuya Ishizaka ◽  
Shiro Kubo ◽  
Seiji Ioka
Keyword(s):  
Thermal Stress ◽  
Temperature Distribution ◽  
Outer Radius ◽  
Temperature History ◽  
Optimum Temperature ◽  
Transient Thermal Stress ◽  
Inner Radius ◽  
Thin Walled Pipe ◽  
Thin Walled ◽  
Transient Thermal

When high temperature fluid flows into a pipe, a temperature distribution in the pipe induces a thermal stress. It is important to reduce the thermal stress for managing and extending the lives of plants. In this problem heat conduction, elastic deformation, heat transfer, liquid flow should be considered, and therefore the problem is of multidisciplinary nature. In a previous paper the present authors proposed an inverse method for determining the optimum thermal load history which reduces the transient thermal stress considering the multidisciplinary physics. The optimum temperature history of inlet fluid may be useful for designing and operating plants. Analytical solutions of the temperature and stress distributions for a thin-walled pipe were used in the analysis. In the present study the reduction of transient thermal stress in a thick-walled pipe is considered. The finite element techniques are employed in the optimization for obtaining the temperature distribution and the thermal stress in the thick-walled pipe. The maximum hoop tensile stress is minimized for the case where inner surface temperature is expressed in terms of a polynomial function of time. The effect of the ratio of inner radius to outer radius on the optimum temperature history is examined. It is found that when the ratio of inner radius to outer radius is larger than 0.8 the optimum temperature history for the thin-walled pipe gives a good estimate. For thicker pipes the optimum temperature history for the thin-walled pipe can be an initial guess for searching the optimum temperature history.

An Asymptotic Solution for Laminar Flow of an Incompressible Fluid Between Rotating Disks

1968 ◽  
Vol 35 (1) ◽  
pp. 155-159 ◽  
Author(s):  
L. Matsch ◽  
W. Rice
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Radial Velocity ◽  
Velocity Component ◽  
Tangential Velocity ◽  
Outer Radius ◽  
Creeping Flow ◽  
Arbitrary Distribution ◽  
Rotating Disks ◽  
Inner Radius

Laminar flow is considered between parallel rotating disks having a circular exhaust hole at an inner radius and supplied with fluid at the outer radius with pressure higher than the available sink pressure. The problem statement for asymptotic (fully developed) flow is formulated. A procedure for perturbing a creeping flow solution and an iteration scheme are developed to produce a solution for higher Reynolds numbers. The solution depends on two parameters, a Reynolds number and a mass flow parameter, and is asymptotic in the sense that a third parameter would be necessary for a solution with an arbitrary tangential velocity component specified at the outer radius of the disks and/or an arbitrary distribution of the radial velocity component between the disks. From computations conducted by digital computer, the region having uninflected radial velocity profiles is delineated. Typical results are presented for the velocity components as functions of Reynolds number, the average radial component of velocity at the entrance, and the inner radius of the disks.

Correlation of Theoretical and Photothermoelastic Results on Thermal Stresses in Idealized Wing Structures

1960 ◽  
Vol 27 (1) ◽  
pp. 79-86 ◽  
Author(s):  
Herbert Tramposch ◽  
George Gerard
Keyword(s):  
Thermal Stress ◽  
Thermal Behavior ◽  
Experimental Evaluation ◽  
High Speed ◽  
Thermal Stresses ◽  
Initial Conditions ◽  
Temperature Distributions ◽  
Wing Structures ◽  
Simplifying Assumptions ◽  
Transient Thermal

After a rather complete exploratory program described in previous papers, the photothermoelastic method was applied to the experimental evaluation of thermal-stress theories. The new technique was correlated with several theories which analyzed the transient thermal stresses in idealized wing structures of high-speed aircraft. Various theories were investigated which represented the same idealized wing models and differed from each other only in the simplifying assumptions regarding the temperature distributions in skin and webs. The theories were evaluated by duplicating the boundary and initial conditions on plastic models and then by correlating the theories with the observed fringe orders in nondimensional form. A significant general conclusion was reached after correlating the available theories and experimental results. Owing to simplifying assumptions concerning the thermal behavior in the flanges, thermal stresses predicted by the available theories are all higher than the experimental observation. In some cases the discrepancy is as great as 30 per cent.

scholarly journals Extended and Unscented Kalman Filtering Applied to a Flexible-Joint Robot with Jerk Estimation

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Mohammad Ali Badamchizadeh ◽  
Iraj Hassanzadeh ◽  
Mehdi Abedinpour Fallah
Keyword(s):  
Initial Conditions ◽  
Covariance Matrices ◽  
Flexible Joints ◽  
Velocity Measurements ◽  
Lagrange Equations ◽  
Robust Nonlinear Control ◽  
Flexible Joint ◽  
Flexible Joint Robots ◽  
Simulation Results

Robust nonlinear control of flexible-joint robots requires that the link position, velocity, acceleration, and jerk be available. In this paper, we derive the dynamic model of a nonlinear flexible-joint robot based on the governing Euler-Lagrange equations and propose extended and unscented Kalman filters to estimate the link acceleration and jerk from position and velocity measurements. Both observers are designed for the same model and run with the same covariance matrices under the same initial conditions. A five-bar linkage robot with revolute flexible joints is considered as a case study. Simulation results verify the effectiveness of the proposed filters.

Improved Diffuser/Volute Combinations for Centrifugal Compressors

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
T. Steglich ◽  
J. Kitzinger ◽  
J. R. Seume ◽  
R. A. Van den Braembussche ◽  
J. Prinsier
Keyword(s):  
Cross Sections ◽  
Pressure Ratio ◽  
Pressure Rise ◽  
Outer Radius ◽  
Inner Radius ◽  
Pressure Pipeline ◽  
The Cross ◽  
Improved Performance ◽  
High Pressure Pipeline ◽  
Original Configuration

Internal volutes have a constant outer radius, slightly larger than the diffuser exit radius, and the circumferential increase of the cross section is accommodated by a decrease of the inner radius. They allow the design of compact radial compressors and hence are very attractive for turbochargers and high-pressure pipeline compressors, where small housing diameters have a favorable impact on weight and cost. Internal volutes, however, have higher losses and lower pressure rise than external ones, in which the center of the cross sections is located at a larger radius than the diffuser exit. This paper focuses on the improvement of the internal volute performance by taking into account the interaction between the diffuser and the volute. Two alternative configurations with enhanced aerodynamic performance are presented. The first one features a novel, nonaxisymmetric diffuser̸internal volute combination. It demonstrates an increased pressure ratio and lower loss over most of the operating range at all rotational speeds compared with a symmetric diffuser̸internal volute combination. The circumferential pressure distortion at off design operation is slightly larger than in the original configuration with a concentric vaneless diffuser. Alternatively, a parallel-walled diffuser with low-solidity vanes and an internal volute allows a reduction of the unsteady load on the impeller and an improved performance, approaching that of a vaneless concentric diffuser with a large external volute.

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