• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.161-185
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• 2016

We consider a mathematical model which describes the quasistatic frictional contact between a piezoelectric body and an electrically conductive obstacle, the so-called foundation. A nonlinear electro-viscoelastic constitutive law is used to model the piezoelectric material. Contact is described with Signorini's conditions and a version of Coulomb's law of dry friction in which the adhesion of contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation. We derive a variational formulation for the model, in the form of a system for the displacements, the electric potential and the adhesion. Under a smallness assumption which involves only the electrical data of the problem, we prove the existence of a unique weak solution of the model. The proof is based on arguments of time-dependent quasi-variational inequalities, differential equations and Banach's fixed point theorem.

• Journal of Industrial Technology
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• v.24 no.B
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• pp.207-214
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• 2004

An active stick which supplies force feedback to the operator is developed in this study. A mathematical model of the active stick is derived, and compared with the experimental result. It turns out that the frictional torque due to the mechanical contacts of several parts of the stick is one of the major barriers to achieve high precision operation of the stick. The frictional effect of the stick is cancelled out by using a friction observer. The efficacy of the friction observer is verified through the numerical simulation. Because of the observer dynamics, there are some limitations in exact recovering the static friction and Stribeck effect. However, the friction observer follows the real friction on the average. It's anticipated that the application of the friction observer to the closed loop control of the active stick improves the performance of the displacement versus force characteristics, which will be proved experimentally in the further study.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.1 no.1
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• pp.8-14
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• 1989

A mathematical model for computing the bed friction of combined wave-current flow has been developed based on the Prandtl's mixing length theory. Using various approximate expressions, solutions are obtained explicitly. The computational results are compared and found in reasonable agreements with the data of field measurements.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.55 no.5
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• pp.245-249
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• 2006

This study tries to test and analyze the static friction torque generated by an electromagnetic clutch. Then the torque is improved by optimizing the shape of armature. For the purpose of design change and optimization of the electromagnetic clutch, the static friction torque prediction is very important. We construct an axi symmetric FEM model for analyzing the static friction torque and used a torque tester for evaluating the real torque. For a test, predicted static friction torque is compared with the experimental one to discuss the rationality of torque analysis process. The analytical result agrees well with experimental data, explaining the validity of the mathematical process and FEM model. After confirming the torque analysis process, the optimization process is investigated. The optimization result shows that the static torque is improved by changing the armature shape.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.9 s.90
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• pp.837-845
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• 2004

A variable friction damper for vehicle driveline has been proposed. This new torsional damper system uses a solenoid as an actuator to vary friction force of the damper. To verify the idea of using a solenoid in a variable damper system, the test fixture and the dampers are made and tested. Also, to find out the range of damper friction forces that influence the vehicle driveline vibration, a mathematical model of the driveline had been developed and simulated. Test and simulation results show that, within electric current used in the vehicle electric system, the solenoid can develop enough friction force that will surpass resonance in the driveline of 1.5 L Gasoline engine vehicle during acceleration.

• Transactions of the Korean Society of Automotive Engineers
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• v.12 no.2
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• pp.160-167
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• 2004

A two degree-of-freedom mathematical model is presented to investigate the friction mechanism of a disc brake system. A contact parameter is introduced to describe the coupling between the in-plane and the out-of-plane motions. The model with the contact parameter is considered under the assumption that the out-of-plane motion depends on the friction force along the in-plane motion. In order to describe the relationship between the friction force and the out-of plane motion, the dynamic friction coefficient is considered as a function of both relative velocity and normal farce. Using this friction law, a contact stiffness matrix along the normal direction can be obtained. The out-of-plane motion is then investigated by both the stability analysis and the numerical analysis for various parametric conditions. The results show that the stiffness parameters of the pad and the disc must be controlled at the same time. Also, the numerical analysis shows the existence of limit cycle caused by the effect of intermittent contact stiffness.

• International Journal of Fluid Machinery and Systems
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• v.4 no.4
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• pp.396-409
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• 2011

Water turbines have been used in electricity generation for well over a century. Hydroelectricity now supplies 19% of world electricity. Many hydro power plants are operated with Pelton turbines, which is an impulse turbine. The main reasons for using impulse turbines are that they are very simple and relatively cheap. As the stream flow varies, water flow to the turbine can be easily controlled by changing the number of nozzles or by using adjustable nozzles. Scientific investigation and design of turbines saw rapid advancement during last century. Most of the research that had been done on turbines were focused on improving the performance with particular reference to turbine components such as shaft seals, speed increasers and bearings. There is not much information available on effects of blade friction on the performance of turbine. The main focus in this paper is to analyze the performance of Pelton turbine particularly with respect to their blade friction.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.40 no.2
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• pp.199-206
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• 2016

Linear motion (LM) ball guides with rolling contact are core units of feed-drive systems. They are widely applied for precision machinery such as machine tools, semiconductor fabrication machines and robots. However, the friction force induced from LM ball guides generates heat, which deteriorates positioning accuracy and incurs changes of stiffness and preload. To accurately analyze the effects and apply the results to precision machine design, mathematical modeling of the friction force is required. In this paper, accurate formulation of the friction force due to rolling, viscous, and slip frictions is conducted for LM ball guides. To verify the reliability of the developed friction model, experiments are performed under various assembly, load and velocity conditions. Effects of frictional components are analyzed through the formulated friction model.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.811-814
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• 2002

Using a mathematical theory, we show that the optimality condition of a turbulent diffuser with maximum pressure recovery at the exit is zero shear stress along the wall. The optimal diffuser shape is designed through iterative procedures by using the $k-{\varepsilon}-{\nu}^{2}-f$ turbulence model for flow simulation. The Reynolds number based on the bulk mean velocity and the channel height at the diffuser entrance is 18,000. We also perform large eddy simulation to validate the shape design results and investigate the flow characteristics near the zero-skin friction wall. Results from large eddy simulation show that the skin friction is slightly higher than zero but is still very small as compared to that of the flat plate boundary layer flow Although the time-averaged wall shear stress is slightly above zero along the diffuser wall, instantaneous flow reversals occur intermittently. The streamwise mein velocity shows an asymptotic behavior of the half-power-law near the wall where the skin friction is close to zero.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.16 no.2
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• pp.63-68
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• 2017

Friction occurs when surfaces that are in contact move relatively between solid surfaces, fluid layers, and materials slide against one another. This friction force causes wear on the contact surface, generates unwanted heat and leads to performance degradation. Thus, much research has been performed to avoid friction reduction. Among these studies, a textured surface that has micro patterns on the surface has drawn attention for its ability to reduce friction. A mathematical model is developed in this study to examine friction reduction due to the texture of a surface. Numerical simulations are carried out with respect to various factors such as the shape aspect ratio and texture depth of a diamond-shaped texture in the hydrodynamic lubrication regime. As a result, a shape aspect ratio of 1 is best for friction reduction.