• Journal of the Computational Structural Engineering Institute of Korea
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• v.33 no.1
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• pp.9-16
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• 2020

The objective of this study is to propose closed-form solutions to the free vibration response of single-degree-of-freedom (SDOF) systems, as part of fundamental research on dynamic systems with Coulomb friction. The motion of a dynamic system with Coulomb friction is described by a nonlinear differential equation, and, due to the variation in the sign of friction force term with the direction of motion, it is difficult to obtain the closed-form solution. To solve this problem, the nonlinear differential equation is directly computed by numerical integration, or an approximated solution is indirectly obtained using a linear differential equation wherein the damping effect due to Coulomb friction is replaced by an equivalent viscous damping term. However, these conventional methods do not provide a closed-form solution from a mathematical point of view. In this regard, closed-form solutions to the free vibration response of SDOF systems with Coulomb friction are derived herein by considering that the sign of the friction force term is reversed in each half-cycle of motion and by expanding it to the entire time history using the power series function. In addition, for a given initial condition, both the number of free vibration half-cycles and the response at the instant when free vibration motion stops are predicted under the condition that the motion of free vibration is stopped when the amplitude of the friction force is higher than that of the restoring force due to stiffness.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.4
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• pp.790-796
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• 1990

본 연구에서는 마찰에 의한 기계계의 진동을 단순 쿨롱마찰의 경우와 마찰계 수가 속도의 함수인 일반마찰이 존재하는 기계게의 응답특성을 수치조화균형법을 이용 하여 해석 및 예측하고자 한다.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.36 no.2
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• pp.105-112
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• 2023

In this study, structural analyses were conducted to analyze the performance of a bridge to which friction pendulum systems (FPSs) were applied using different friction models. A Coulomb friction model and a rate dependent friction model were constructed using the friction coefficient of a PVDF/MgO friction material to analyze the effect of different friction analysis models. The Coulomb friction model uses a single friction coefficient regardless of friction velocity, while the rate dependent friction model can reflect the change in the friction coefficient with friction velocity. Nonlinear time history and seismic fragility analyses were conducted to confirm responses of the bridge. The seismic responses of a deck and a column were used to evaluate the performance of the base isolated bridge, and a friction model that can effectively evaluate the performance of isolated bridges was analyzed.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2011.04a
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• pp.516-520
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• 2011

본 논문에서는 먼저 흥인지문에 대해 상시진동실험을 수행하고, 그 데이터를 분석하여 흥인지문의 고유진동수, 모드, 감쇠비의 특성을 분석하였다. 그 결과로부터 흥인지문의 병진모드를 파악하였고, 병진모드에서 측정한 여러 기둥의 모드 상대크기와 위상이 동일함을 확인하였다. 저차 병진모드에서 모든 기둥이 같은 방향으로 강성을 발휘하기 때문에 각층의 강성을 합한 등가의 층강성을 가지는 2자유도의 동적강체해석모델을 제시하였다. 이 해석모델은 선형 범위 내에서 거동한다는 것으로 가정하여 층강성을 산정하였다. 실제 흥인지문의 접합부에는 부재간의 이음과 맞춤에 의한 마찰력이 작용한다. 접합부를 누르는 무거운 지붕하중에 의해 이 마찰력은 증가하게 되고, 이로써 횡하중에 저항하게 된다. 이러한 접합부에 강한 횡하중이 작용하게 되면, 접합부의 이완 및 마찰력의 저하 등으로 인하여 횡강성의 저하가 급격히 일어나는 비선형 특성을 갖게 된다. 이러한 흥인지문의 비선형적인 특성을 파악하기 위해 흥인지문 해석모델에 쿨롱 마찰력을 도입하여 비선형적인 해석모델을 제시하였다.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.2
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• pp.35-42
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• 2004

The control systems with friction cause the steady state error and slow response, because friction is a sensitive to the change of system condition and has highly nonlinear characteristics. To overcome these problems and do precise position control for a ball-screw system, we use Coulomb friction estimator and the sliding mode control(SMC) to compensate its negative effect. The applied SMC for tracking position has a characteristics of robust stability and reducing chattering, and is derived from the Lyapunov stability theorem and reaching condition. Compensating the estimated friction torque to the bounded disturbance term of the SMC's equivalent control input, it has a tracking performance better than the PID from the experimental results.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.4
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• pp.866-875
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• 1994

The problem of a rigid rod sliding on a rough horizontal surface in the plane is analyzed, which is commonly cited as an example of the inconsistency of rigid body frictional mechanics. The inconsistency is demonstrated by analyzing the normal reaction force at the contact point with the surface, and the concept of tangential collision is derived to resolve the inconsistency. Using the Poisson's hypothesis for the coefficient of restitution and Coulomb's law for the friction, the general methodology for solving the tangential collision is presented. The problem of the inconsistency generated in the sliding rod is completely resolved, building the concept of the tangential collision and adopting the theory of frictional impact. The result presented in this paper will obviate a generic obstacle to the development of simulation packages for planar rigid body mechanical systems with temporary contacts, and planning efficient motion strategies for robot manipulators.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1993.04a
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• pp.57-61
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• 1993

본 연구목적은 선형부분구조물과 그 부분구조물들을 결합하는 비선형연결부 로 이루어진 구조물을 해석하기 위해 비선형 연결부의 모델변화를 효과적으 로 규명하는데 있다. 제안된 방법은 시간영역에서만 계산이 가능하였던 힘- 상태 사상법을 주파수영역으로 확장함으로써, 전체구조물에서 선형부분구조 물들은 분리 해석이 가능하고, 시간영역의 많은 데이터를 줄일 수 있는 장점 이 있다. 제안된 방법의 타당성 및 장점을 검증하기 위해서 쿨롱마찰 비선형 특성을 갖는 두 가지의 구조물에 대하여 각각 실험적으로 연결부의 매개변 수를 규명하였다.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.401-405
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• 1996

A new method of nonlinear robust controller synthesis is introduced which is an extension of linear mixed $H_2/H_{\infty}$ control. This method guarantees robust stability fur hard nonlinearity and uncertainty of the plant. The method is applied to the control of a flexible link of robot with Coulomb friction. Simulation shows good performances with respect to the response and the robustness.

• Journal of the Korean Society for Precision Engineering
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• v.9 no.2
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• pp.92-100
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• 1992

플렉시블한 관절을 가지고 있는 로보트에 대하여 계단(step) 혹은 경사(ramp) 함수로 기준입력이 주어졌을 때, 모델의 불확실성이나 외란 아래에서 추적오차가 없는 디지찰 제어기법을 제시하고 실제로 실험을 통하여 제어기를 MC 68000으로 구현함으로써 제안한 제어 알고리즘의 유용성을 보였다. 제어기 설계에 있 어서 고려한 사항들은 비선형 마찰력, 중력에 의한 외란, 구동기와 부하사이의 뒤틀림 스프링 효과, 구리고 측 정할 수 없는 상태변수들이다. 또한 미분불가능한 쿨롱마찰로 인하여 전체 시스템이 이산/연속 혼성 시스템이 되어 출력에서 나타나는 리미트 싸이클을 해석/추정하기 위하여 혼성 시스템에서의 기술함수(Describing Function) 법을 제시하였다.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.893-898
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• 2003

Coulomb friction is an important factor for precise position tracking control systems. The control systems with friction causes the steady state error because of being sensitive to the change of system condition and highly nonlinear characteristics. To overcome these problems, we use an estimation scheme of Coulomb friction to experiment for it's compensating. The estimated factor for Coulomb friction is used as a feed-forward compensator to improve the tracking performance of ball-screw systems. The tracking performance was improved by compensating the estimated friction torque in the feed-forward term. And, the sliding mode control which is derived from the Lyapunov stability theorem is applied for robust stability and reducing chattering. The experimental results show that the sliding mode controller with adaptive friction compensator has a good tracking performance compared with the friction uncompensated controller.