• Tribology and Lubricants
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• v.16 no.6
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• pp.432-439
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• 2000

The present work is an attempt to calculate the steady state pressure and perturbed pressure of herringbone grooved journal bearings. A generalized coordinate system is introduced to handle the complex bearing geometry. The coordinates are fitted to the groove boundary and the Reynold's equation is transformed to be fitted to this coordinate system using the Gauss divergence theorem. This method makes it possible to deal with an arbitrary configuration of a lubricated surface. The caharacteristics of finite herringbone groove journal bearing are well calculated using this method.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.126-127
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• 2003

In the generalized characteristic coordinate system (GCCS) proposed by Wu and Shi [1], the frame moves at a speed which is a linear combination of the convective speed and the sound speed, thus unifying the classical Eulerian approach, Lagrangian approach, and the unified coordinate system (UCS) of Hui and his co-workers [2]. Here some properties of Euler equations in the GCCS are studied and the advantages of GCCS in capturing expansion fans and shock waves are demonstrated by the results of numerical tests.

• Journal of the Society of Naval Architects of Korea
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• v.58 no.6
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• pp.348-357
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• 2021

In this paper, the generalized hydrodynamic force and response of a flexible body are calculated at different reference coordinate systems. We generalize the equation of motion for a flexible body by using the conservation of momentum (Mei et al., 2005). To obtain the equations in the generalized mode, two different reference coordinates are adopted. The first is the body-fixed coordinate system by a rigid body motion. The other is the inertial coordinate system which has been adopted for the analysis. Using the perturbation scheme in the weakly-nonlinear assumption, the equations of motion are expanded up to second-order quantities and several second-order forces are obtained. Numerical tests are conducted for the flexible barge model in head waves and the vertical bending is only considered in the hydroelastic responses. The results show that the linear response does not have the difference between the two formulations. On the other hand, second-order quantities have different values for which the rigid body motion is relatively large. However, the total summation of second-order quantities has not shown a large difference at each reference coordinate system.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 1999.06a
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• pp.317-324
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• 1999

The present work is an attempt to calculate the steady state pressure and perturbed pressure of herringbone grooved journal bearings. A generalized coordinate system is introduced to handle the complex bearing geometry. The coordinates are fitted to the groove boundary and the Reynold's equation is transformed to be fitted to this coordinates system using the Gauss divergence theorem. This method makes it possible to deal with an arbitrary configuration of a lubricated surface. The characteristics of finite herringbone grooved journal are well calculated using this method.

• KSTLE International Journal
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• v.3 no.2
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• pp.110-113
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• 2002

The lubricative characteristics of negative pressure slider were performed by using coordinate transform method. Governing equation is derived by applying generalized coordinate system to the divergence formulation method. This method makes it possible to deal with an arbitrary configuration of a lubricated surface. The pressure profile of the slider is calculated. These results are compared to that from direct numerical method. The steady-state, including minimum film thickness, pitching and rolling angle are calculated by multi-dimensional Newton-Rapshon method. The stiffness and damping characteristics are also calculated.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.3
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• pp.1015-1027
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• 1996

In this paper, a numerical procedure for the calculation of the incompressible Navier-Stokes equations in a generalized nonorthogonal body fitted coordinate system is proposed and is validated through three test problems. Present numerical procedure derives the pressure equation by using the pressure substitution method on the regular grid system, and discretized momentum equations are based on the covariant velocity components. Cavity flow, backward facing step flow, and two dimensional channel flow with a sinusoidal wavy wall are chosen as three test problems. Numerical solutions obtained by present procedure shows a good agreement with previous numerical and/or experimental results. Convergence rate is also satisfactory.

• Transactions of the Korean Society of Automotive Engineers
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• v.5 no.1
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• pp.154-161
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• 1997

This paper presents the method to eliminate the constraint reaction in the Lagrange multiplier form equation of motion by using a generalized coordinate driveder from the velocity constraint equation. This method introduces a matrix method by considering the m dimensional space spanned by the rows of the constraint jacobian matrix. The orthogonal vectors defining the constraint manifold are projected to null vectors by the tangential vectors defined on the constraint manifold. Therefore the orthogonal projection matrix is defined by the tangential vectors. For correcting the generalized position coordinate, the optimization problem is formulated. And this correction process is analyzed by the quasi Newton method. Finally this method is verified through 3 dimensional vehicle model.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.8 s.239
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• pp.1123-1131
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• 2005

In this paper, a formulation for a spatial sliding joint, which a general multibody can move along a very flexible cable, is derived using absolute nodal coordinates and non-generalized coordinate. The large deformable motion of a spatial cable is presented using absolute nodal coordinate formulation, which is based on the finite element procedures and the general continuum mechanics theory to represent the elastic forces. And the non-generalized coordinate, which is neither related to the inertia forces nor external forces, is used to describe an arbitrary position along the centerline of a very flexible cable. In the constraint equation for the sliding joint, since three constraint equations are imposed and one non-generalized coordinate is introduced, one constraint equation is systematically eliminated. Therefore, there are two independent Lagrange multipliers in the final system equations of motion associated with the sliding joint. The development of this sliding joint is important to analyze many mechanical systems such as pulley systems and pantograph/catenary systems for high speed-trains.

• Tribology and Lubricants
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• v.27 no.2
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• pp.71-76
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• 2011

In this study, the nondimensional load capacity of water hydrodynamic journal bearings is calculated. A generalized coordinate formulation is applied to handle the complexity of bearing geometry. A window-based analysis program is developed to analysis the cylindrical hydrostatic bearings. Load capacities are calculated according to some design parameters such as clearance, diameter of orifice, size of recesses and temperature. The results are presented and discussed.

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.567-581
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• 2014

Over the years, there has been much research conducted on quadratic curves and the set of points with the generalized notion of eccentricity in a plane with metrics such as taxicab distance or Chinese-checker distance. On the other hand, polar taxicab distance has been newly proposed on the polar coordinate system, a type of curvilinear coordinate system, to overcome the limitation of pre-existing metrics in terms of describing curved routes. Previous study has looked into the fundamental properties of this metric. From this point of view, we study the quadratic curves and the set of points with the generalized notion of eccentricity in a plane with polar taxicab distance.