• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.33 no.1
• /
• pp.9-16
• /
• 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 A
• /
• v.34 no.12
• /
• pp.1925-1930
• /
• 2010

For high-speed/high-accuracy position control of a gantry-moving-type linear motor, we propose a nonlinear adaptive controller including a synchronization algorithm. Linear motors are easily affected by force ripple, friction, and parameter variations because there is no mechanical transmission to reduce the effects of model uncertainties and external disturbances. Synchronization error is also caused by skew motion, model uncertainties, and force disturbance on each axis. Nonlinear effects such as friction and ripple force are estimated and compensated for. The synchronization algorithm is used to reduce the synchronous error of the two side pillars. The performance of the controller is evaluated via computer simulations.

• Journal of Power System Engineering
• /
• v.9 no.4
• /
• pp.175-180
• /
• 2005

Incorrections between model and plant are parameter, system order uncertainties and modeling error due to disturbance like friction. Therefore to achieve a good tracking performance, adaptive discrete time sliding mode tracking controller is used under time-varying desired position. Based on the diophantine equation, a new discrete time sliding function is defined and utilized for the control law. Robustness is increased by using both a recursive least-square method and a sliding function-based nonlinear feedback. The effectiveness of the proposed control algorithm is proved by the results of simulation and experiment.

• Journal of Power System Engineering
• /
• v.12 no.1
• /
• pp.80-86
• /
• 2008

A motor cylinder apparatus is used to transfer a load in industrial applications. The apparatus is composed of a motor and power transmission elements such as worm gear and screw. In this case, the nonlinear friction of the transmission elements has a bad influence on the position control performance. To overcome this problem, the position control system consists of a feedback controller to achieve nominal control performance and a disturbance observer to compensate nonlinear friction. Especially the filter of a disturbance observer is designed from viewpoint of robust stability. Finally, the simulation result shows that the proposed control system is effective for the disturbance elimination as well as the friction compensation.

• Journal of the Korean Society for Precision Engineering
• /
• v.17 no.1
• /
• pp.110-119
• /
• 2000

This paper presents simple and effective nonlinear friction compensation methods. When the direction of position command reverses, the integrator output of the PID controller does not change the sign of its output instantaneously, due to friction at zero velocity, i.e. stiction resulting tracking errors, that results in continuous push even though the command direction has been changed. To overcome this problem, we attempt to reverse the sign of the integrator output as the sign of velocity changes. The effectiveness of this approach is demonstrated by experiments on a 3-PRPS (Prismatic-Revolute-Prismatic-Shperical joints) in-parallel 6-D.O.F manipulator. The control strategy has been analyzed for stability. Also discussed are disturbance observer and velocity observer approaches for friction compensation.

• Journal of KSNVE
• /
• v.7 no.1
• /
• pp.6-12
• /
• 1997

물리계에서 일어나는 동적 현상들은 선형해석 만으로 설명하기에는 불충분한 점이 많이 있다. 이는 기계구조물과 같은 실제 계의 진동이 기하학적 비선형성, 강성 의 비선형성 또는 경계조건의 비선형성 등의 영향으로 비선형적인 거동을 하기 때문 이다. 비선형 진동을 하는 기계 계는 우리 주변에서 쉽게 찾아 볼 수 있는데, 그 예로써 진자운동을 포함하여 동흡진기, 회전체계, 공작기계의 절삭운동, 건마찰 (dry friction) 관련 기계장치, 치차 및 기차의 바퀴와 레일 간의 접촉에서 볼수 있는 구분적 선형(piecewise linear) 진동계, 충격 진동계 등을 들 수 있다. 비선형 진동 연구는 limit cycle, 준주기운동(quasiperiodic motion), 점프현상(jump phenomena) 등의 인식에서 시작되어, 과거에는 설명이 안되어 회피되 왔던 랜덤(random) 형태의 비주기운동에 대한 연구로 까지 발전하고 있다. 비선형 진동을 다루는데 있어서 정규모드(normal mode)를 이용하는 방법이 있다. 일반적으로 선형계는 선형 정규모드 (linear normal mode)가 존재하는 것과 같이 비선형계에도 이와 유사한 정규모드가 존재한다는 사실이 연구 보고된 바 있다. 비선형계에 존재하는 정규모드는 계의 매개 변수(system parameters)에 따라 그 안정성이 바뀔 수 있으며, 만일 안정한 정규모드 가 어떤 매개변수에서 그 안정성이 바뀐다면 선형이론으로는 설명될 수 없는 새로운 운동이 일어나고 이러한 운동을 분기모드(bifurcation mode)라고 한다. 안정한 정규 모드 및 분기모드를 포함하여 비선형계를 다류는 것을 "정규모드 동역학(normal mode dynamics)"이라고 한다. 정규모드 동역학은 앞에서 언급된 비선형 현상들의 원인규명, 예측, 안정성해석 및 강제진동 해석을 가능하게 한다. 또한 최근에 활발히 연구되고 있는 혼돈운동(chaotic motion)의 해석도 가능하다. 이 글에서는 비선형 진동해석을 위한 정규모드 동역학에 대한 연구동향 및 기본 이론을 살펴 보았고, 그 적용 예를 통하여 실험결과와 비교 고찰 함으로써 정규모드 동역학의 적용성을 서술하여 보았다. 선형이론으로 이해하기 어려운 현상들에 대하여는 비선형의 관점에서 새롭게 접근하 려는 노력이 필요하며 비선형 이론에 대한 연구가 지속적으로 진행되어야 한다. 진행되어야 한다.

• Tunnel and Underground Space
• /
• v.23 no.3
• /
• pp.219-227
• /
• 2013

Although Mohr-Coulomb failure criterion has limitations in that it is a linear criterion and the effect of the intermediate principal stress on failure is ignored, this criterion has been widely accepted in rock mechanics design. In order to overcome these shortcomings, the Hoek-Brown failure criterion was introduced and recently a number of 3-D failure criteria incorporating the effect of the intermediate principal stress on failure have been proposed. However, in many rock mechanics designs, the possible failure of rock mass is still evaluated based on Mohr-Coulomb criterion and most of practitioners are accustomed to understanding the strength of rock mass in terms of the internal friction angle and cohesion. Therefore, if the equivalent Mohr-Coulomb strength parameters of the advanced failure criteria are calculated, it is possible to take advantage of the advanced failure criteria in the framework of the Mohr-Coulomb criterion. In this study, a method expressing the tangential Mohr-Coulomb strength parameters in terms of the stress invariant is proposed and it is applied to the generalized Hoek-Brown criterion and the HB-WW criterion. In addition, a new approach describing the geometric meaning of the ${\sigma}_2$-dependency of failure criteria in 3-D principal stress space is proposed. Implementation examples of the proposed method show that the influence of the intermediate principal stress on the tangential friction angle and cohesion of the HB-WW criterion is considerable, which is not the case for the 2-D failure criterion.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.23 no.6
• /
• pp.429-441
• /
• 2011

In the southeast coastal zone of Yellow Sea, the tide characteristics showing ebb-dominant tide and tidal flow were confirmed by analysis of observed tide and tidal currents. Physical factors generating asymmetric tide were reviewed. Influence of bottom shear stress, tidal flat, and nonlinear terms in shallow water equations was investigated by two-dimensional tide modeling. The model results gave good agreements with observed tides, but the amplitude of simulated $M_4$ tide was less than that of observed tide. The tidal flats existing in the study area widely have great effect on the generation of nonlinear tide. The M4 tide is mainly generated near the tidal flats. The deletion of tidal flats prevents the production of the M4 tide. We can conclude that the wide tidal flats is a primary cause of tide asymmetry in the study area.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2014.04a
• /
• pp.223-224
• /
• 2014

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.34 no.3
• /
• pp.369-374
• /
• 2010

Linear motors are easily affected by load disturbances, force ripples, friction, and parameter variations because there are no mechanical transmissions that can reduce the effects of model uncertainties and external disturbance. In this study, a nonlinear adaptive controller to achieve high-speed/high-accuracy position control of a two-axis linear motor is designed. The operation of this controller is based on a cross-coupling algorithm. Nonlinear effects such as friction and force ripples are estimated and compensated for. An enhanced cross-coupling algorithm is proposed for effectively improving the biaxial contour accuracy while achieving closed-loop stability. The proposed controller is evaluated by performing computer simulations.