• Journal of the Korean Society for Precision Engineering
• /
• v.12 no.5
• /
• pp.40-45
• /
• 1995

The kinematical relationship of bevel gearsets lies at the root of the gear design. As the demand on precision bevel gears is increased in the related industries, the kinematic analysis of a pair of sperical involute bevel gears needs to be exactly evaluated for the computer aided design. Pitch cone angles of bevel gearsets have been calculated under the assumption that the geared system is equivalent to a coned roller system without slipping. But this kinematical model involves some errors in the value of the ratio of angular velocity. In this paper, the ratio of the angular velocity is exactly derived, based on the perfect involute tooth surface. Four nonlinear equations representing the kinematical relationships are numerically solved to obtain the pitch and base cone angles. The ratios of angular volocities according to pressure and shaft angles are calculated and compared with those of the approximate gear model.

• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 1998.03a
• /
• pp.210-213
• /
• 1998

A kinematically admissible velocity field is developed for the analysis of twisting of extruded products. The twisting of extruded product is caused by the linearly increased rotational velocity from the center on the cross-section of the workpiece at the die exit. In the analysis, the rotational velocity in angular direction is assumed by the multiplication of radial distance and angular velocity. The angular velocity is zero at the die entrance and is increased linearly by axial distance from die entrance. The increase rate of angular velocity is determined by the minimization of plastic work. The results of the analysis show that the angular velocity of the extruded product increase with the die twisting angle and the aspect ratio of product and friction condition and reduction area and show that angular velocity increases with the decreases in die length.

• 한국전산유체공학회:학술대회논문집
• /
• 2007.10a
• /
• pp.127-133
• /
• 2007

This paper represents the numerical study on Taylor flow according to the radius ratio and the angular velocity for flow between tow cylinder. The numerical model is consisted of two cylinder which inner cylinder is rotating and outer cylinder is fix, and the axial direction is used the cyclic condition because of the length for axial direction is assumed infinite. The diameter of inner cylinder is assumed 86.8 mm, the numerical parameters are angular velocity and radius ratio. The numerical method is compared with the experimental results by Wereley, and the results are very good agreement. The critical Taylor number is calculated by theoretical and numerical analysis, and the results is showed the difference about ${\pm}10\;%$. As $Re/Re_c$ is increased, Taylor vortex is changed to wavy vortex, and then the wave number for azimuthal direction is increased. Azimuthal wave according to the radius ratio is showed high amplitude and low frequence in case of small radius ratio, and is showed low amplitude and high frequence in case of large radius ratio.

• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 1997.03a
• /
• pp.130-135
• /
• 1997

A kinematically admissible velocity field is developed for the analysis of twisting of extruded products. The twisting of extruded product is caused by the linearly increased rotational velocity from the center on the cross-section of the workpiece at the die exit. In the analysis, the rotational velocity in angular direction is assumed by the multiplication of radial distance and angular velocity. The angular velocity is zero at the die entrance and is increased linearly by longitudinal distance from die entrance. The increase rate of angular velocity is determined by the minimization of plastic work. The results of the analysis show that the angular velocity of the extruded product changes with the aspect ratio of product and increases with the decreases in die length and in eccentricity of gravity center of the cross-section of workpiece at die entrance from that of the cross-section at the die exit.

• Transactions of Materials Processing
• /
• v.7 no.4
• /
• pp.340-346
• /
• 1998

A kinematically admissible velocity field is developed for the analysis of twisting of the extruded products with elliptical shapes from round billet. The twisting of extruded product is caused by the lin-early increased rotational velocity from the center on the cross-section of the workpiece at the die exit. In the analysis the rotational velocity in angular direction is assumed by the multiplication of radial distance and angular velocity. The angular velocity is zero at the die entrance. The increase rate of angular velocity is determined by the minimization of plastic work. The results of the analysis show that the angular velocity of the extruded product in creases with the die twisting angle, the aspect ratio of product the friction condition, the reduction of area, and decreases with the die length.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.17 no.8
• /
• pp.701-707
• /
• 2007

In this paper the vibration system is composed of a rotating cantilever pipe conveying fluid. The equation of motion is derived by using the Lagrange's equation. Generally, the system of pipe conveying fluid becomes unstable by flutter. Therefore, the influence of the rotating angular velocity, mass ratio and the velocity of fluid flow on the stability of a cantilever pipe by the numerical method are studied. The influence of mass ratio, the velocity of fluid, the angular velocity of a cantilever pipe and the coupling of these factors on the stability of a cantilever pipe are analytically clarified. The critical fluid velocity ($u_{cr}$) is proportional to the angular velocity of the cantilever pipe. In this paper Flutter(instability) is always occurred in the second mode of the system.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2007.05a
• /
• pp.1185-1190
• /
• 2007

In this paper the vibration system is consisted of a rotating cantilever pipe conveying fluid. The equation of motion is derived by using the Lagrange's equation. Also, the equation of motion is derived applying a modeling method that employs hybrid deformation variables. Generally, the system of pipe conveying fluid becomes unstable by flutter. So, we studied about the influences of the rotating angular velocity, mass ratio and the velocity of fluid flow on the stability of a cantilever pipe by the numerical method. The influences of mass ratio, the velocity of fluid, the angular velocity of a cantilever pipe and the coupling of these factors on the stability of a cantilever pipe are analytically clarified. The critical fluid velocity$(u_{cr})$ is proportional to the angular velocity of the cantilever pipe. In this paper Flutter(instability) always occur in the second mode of the system.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.18 no.1
• /
• pp.101-109
• /
• 2008

The stability of a rotating cantilever pipe conveying fluid with a crack and tip mass is investigated by the numerical method. That is, the effects of the rotating angular velocity, mass ratio, crack severity and tip mass on the critical flow velocity for flutter instability of system are studied. The equations of motion of rotating pipe are derived by using the Euler-Bernoulli beam theory and the extended Hamilton's principle. The crack section of pipe is represented by a local flexibility matrix connecting two undamaged pipe segments. Also, the crack is assumed to be in the first mode of fracture and always opened during the vibrations. When the tip mass and crack are constant, the critical flow velocity for flutter is proportional to the rotating angular velocity of pipe. In addition, the stability maps of the rotating pipe system as a rotating angular velocity and mass ratio ${\beta}$ are presented.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.16 no.2
• /
• pp.369-381
• /
• 1992

Characteristics of flow and heat transfer have been studied numerically in a square duct with a periodic pressure gradient. The flow in a duct was assumed to be fully developed and constant heat flux was imposed at the surfaces of a square duct. The distributions of axial velocity and time-space averaged temperature are investigated with angular velocity and amplitude ratio at a given Reynolds number 1000. When the periodic pressure gradient was imposed axially in a duct, the reverse flow may be occurred near the duct wall. The magnitude of this reverse flow increases as the amplitude ratio increases or as the angular frequency decreases. In the ranges of the amplitude ratio and the angular velocity in present investigation, the ratio of the periodic time space averaged temperature to the nonperiodic space averaged temperature has been found to be greater than one. This means that the cooling effect at the duct walls deteriorates with a periodic situation compared with nonperiodic one.

• 유체기계공업학회:학술대회논문집
• /
• 2006.08a
• /
• pp.323-326
• /
• 2006

Numerical solutions for spin-up problem of a thermally stratified fluid in a cylinder with an insulating sidewall and time-dependent rotation rate are presented. Detailed results are given for aspect ratio of O(1), fixed Ekman number $10-^{4}$, Rossby number 0.05 and Prandtl number O(1). Angular velocity of a cylinder wall changes with following formula, $\Omega_f=\Omega_i+\Delta\Omega[1-\exp(-t/t_c)]$. Here, this $t_c$, value, which is very significant in present study, represents that how fast/slow the angular velocity of the cylinder wall reaches final angular velocity. The normalized azimuthal velocity and meridional flow plots for several tc value which cover ranges of the stratification parameter S(1 ~ 10) are presented. The role of viscous-diffusion and Coriolis term in present study is examined by diagnostic analysis of the azimuthal velocity equation.