• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2009.04a
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• pp.573-578
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• 2009

Starting from the rotating beam finite element in which the interpolating shape functions satisfies the governing static homogeneous differential equation of Euler-Bernoulli rotating beams, we derived new shape functions that satisfies the governing differential equation which contains the terms of hub radius and setting angle. The shape functions are rational functions which depend on hub radius, setting angle, rotational speed and element position. Numerical results for uniform and tapered cantilever beams with and without hub radius and setting angle are compared with the available results. It is shown that the present element offers an accurate method for solving the free vibration problems of rotating beam.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.9 s.114
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• pp.912-918
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• 2006

A modeling method for the vibration analysis of rotating multi-blade systems considering the coupling stiffness effect is presented in this paper. Blades are assumed as cantilever beams and the coupling stiffness effect originates from disc or shroud between blades. As the angular speed, hub radius ratio, and the coupling stiffness vary, the natural frequencies of the system vary. Numerical results show that the coupling stiffness is very important to estimate the natural frequencies. Along with the natural frequencies, associated mode shapes, critical angular speed, and critical hub radius ratio are obtained through the analysis.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1354-1359
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• 2006

A modeling method for the vibration analysis of rotating multi-blade systems considering the coupling stiffness effect is presented in this paper. Blades are assumed as cantilever beams and the coupling stiffness effect originates from disc or shroud between blades. As the angular speed, hub radius ratio, and the coupling stiffness vary, the natural frequencies of the system vary. Numerical results show that the coupling stiffness is very important to estimate the natural frequencies. Along with the natural frequencies, associated mode shapes, critical angular speed, and critical hub radius ratio are obtained through the analysis.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.6
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• pp.591-598
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• 2009

Starting from the rotating beam finite element in which the interpolating shape functions satisfy the governing static homogeneous differential equation of Euler-Bernoulli rotating beams, we derived new shape functions that satisfy the governing differential equation which contains the terms of hub radius and setting angle. The shape functions are rational functions which depend on hub radius, setting angle, rotational speed and element position. Numerical results for uniform and tapered cantilever beams with and without hub radius and setting angle are compared with the available results. It is shown that the present element offers an accurate method for solving the free vibration problems of rotating beams.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.8
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• pp.2516-2523
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• 1996

The equations of motion for rotating contilever beams with a concentrated mass loated in an arbitrary position are derived. For the modeling of the concentrated mass the Dirac delta function is used for the mass density function. Parametric studies are performed with five dimensionless variables ; natural frequencies, angular velocity, hub radius, concentrated mass, and the mass location. The concentrated mass, whereverit may locate, lowers the natural frequencies of a stationaly beam. However, when the beam rotates, the natural frequencies(if they increase or decrease) are dictated by the location of the concentrated mass.

• Steel and Composite Structures
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• v.19 no.5
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• pp.1279-1298
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• 2015

In this paper, free vibration characteristics of a rotating double tapered functionally graded beam is investigated. Material properties of the beam vary continuously through thickness direction according to the power-law distribution of the volume fraction of the constituents. The governing differential equations of motion are derived using the Hamilton's principle and solved utilizing an efficient and semi-analytical technique called the Differential Transform Method (DTM). Several important aspects such as taper ratios, rotational speed, hub radius, as well as the material volume fraction index which have impacts on natural frequencies of such beams are investigated and discussed in detail. Numerical results are tabulated in several tables and figures. In order to demonstrate the validity and accuracy of the current analysis, some of present results are compared with previous results in the literature and an excellent agreement is observed. It is showed that the natural frequencies of an FG rotating double tapered beam can be obtained with high accuracy by using DTM. It is also observed that nondimensional rotational speed, height taper ratio, power-law exponent significantly affect the natural frequencies of the FG double tapered beam while the effects of hub radius and breadth taper ratio are negligible.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.6
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• pp.1598-1603
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• 1994

A preliminary design procedure for a multi-stage axial compressor is developed, which is based on the stage-stacking method. It determines the flow coefficient which gives rise to the design conditions required such as pressure ratio, mass flow rate and rotational speed for a given specific mass flow rate at inlet to a compressor. With this flow coefficient, blade radii, every stage and compressor performance characterics such as stage pressure ratio, adiabatic efficiency etc. are calculated by stacking each stage performance characteristics. It is shown that there is an optimum number of stage which results in the maximum of compressor overall efficiency for a given specific mass flow rate at inlet to a compressor. A test design was tried for three different geometric design constraints, and comparison with a previous study shows that present procedure could be used reliably in determining the number of compressor stage in preliminary design stage.

• Transactions of the Korean Society of Automotive Engineers
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• v.24 no.1
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• pp.74-81
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• 2016

The aim of this study was to find the initial design value of turbine blade for electrical type turbocompound system generating 10 kW. Turbocompound is one of the waste heat recovery system applying to internal combustion engine to recover exhaust gas energy that was about 30 % of total input energy. To design the turbine blade, 1-D mean line flow model was used. Exhaust gas temperature, pressure, flow rate and turbine rotating speed was fixed as primary boundary conditions. The velocity triangles was defined and used to determine the rotor inlet radius and width, the rotor outlet radius at shroud and radius at hub, the rotor flow angles and the number of blades.

• Transactions of Materials Processing
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• v.8 no.6
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• pp.604-611
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• 1999

This paper is concerned with the family of parts that generally feature a central hub with radial protrusions. As opposed to conventional forward and backward extrusion, in which the material flows in a direction parallel to that of the punch or die motion, the material flows perpendicular to the punch motion in radial extrusion. Three variants of radial extrusion of a collar or flange are investigated. Case I involves forcing a cylindrical billet against a flat die, Case II involves deformation against a stationary punch recessed in the lower die, and Case III involves both the upper and lower punches moving together toward the center of the billet. Extensive simulational work is performed with each case to see the process conditions in terms of forging load, balanced and symmetrical flow in the flange. Also, the effect of the gap size and die corner radii to the material flow are investigated. In this study, the forming characteristics of radial extrusion will be considered by comparing the forces, shapes etc. The design factors during radial extrusion are investigated by the rigid-plastic FEM simulation.

• Structural Engineering and Mechanics
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• v.22 no.2
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• pp.151-167
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• 2006

A p-version of the finite element method in conjunction with the modeling dynamic method using the arc-length stretch deformation is considered to determine the bending natural frequencies of a cantilever flexible plate mounted on the periphery of a rotating hub. The plate Fourier p-element is used to set up the linear equations of motion. The transverse displacements are formulated in terms of cubic polynomials functions used generally in FEM plus a variable number of trigonometric shapes functions representing the internals DOF for the plate element. Trigonometric enriched stiffness, mass and centrifugal stiffness matrices are derived using symbolic computation. The convergence properties of the rotating plate Fourier p-element proposed and the results are in good agreement with the work of other investigators. From the results of the computation, the influences of rotating speed, aspect ratio, Poisson's ratio and the hub radius on the natural frequencies are investigated.