• Title/Summary/Keyword: Dynamic Equilibrium Position

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Large displacement Lagrangian mechanics -Part II - Equilibrium principles

  • Underhill, W.R.C.;Dokainish, M.A.;Oravas, G.Ae.
    • Structural Engineering and Mechanics
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    • v.4 no.1
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    • pp.91-107
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    • 1996
  • In Lagrangian mechanics, attention is directed at the body as it moves through space. Each body point is identified by the position it would have if the body were to occupy an arbitrary reference configuration. A result of this approach is that the analyst often describes the body by using quantities that may involve more than one configuration. This is particularly common in incremental calculations and in changes of the choice of reference configuration. With the rise of very powerful computing machinery, the popularity of numerical calculation has become great. Unfortunately, the mechanical theory has been evolved in a piecemeal fashion so that it has become a conglomeration of differently developed patches. The current work presents a unified development of the equilibrium principle. The starting point is the conservation of momentum. All details of configuration are shown. Finally, full dynamic and static forms are presented for total and incremental work.

Position and load-swing control of a 2-dimensional overhead crane (2차원 천정크레인의 위치 및 이송물의 흔들림제어)

  • Lee, Ho-Hoon;Cho, Sung-Kun
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.21 no.10
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    • pp.1683-1693
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    • 1997
  • In this paper, a new nonlinear dynamic model is derived for a 2-dimensional overhead crane based on a new definition of 2-degree-of-freedom swing angle, and a new anti-swing control law is proposed for the crane. The dynamic model and control law take simultaneous travel and traverse motions of the crane into consideration. The model is first linearized for small motions of the crane load about the vertical stable equilibrium. Then the model becomes decoupled and symmetric with respect to the travel and traverse axes of the crane. From this result, a decoupled anti-swing control law is proposed based on the linearized model via the loop shaping and root locus methods. This decoupled method guarantees not only fast damping of load-swing but also zero steady state position error with optimal transient response for the 2-dimensional motion of the crane. Finally, the proposed control method is evaluated by controlling the simultaneous travel and traverse motions of a 2-dimensional prototype overhead crane. The effectiveness of the proposed control method is then proven by the experimental results.

Modeling and Simulation of the 6 DOF Motion of a High Speed Planing Hull Running in Calm Sea (정수중을 활주하는 고속선의 6자유도 운동 모델링 및 시뮬레이션)

  • Yoon, Hyeon Kyu;Kang, Namseon
    • Journal of the Society of Naval Architects of Korea
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    • v.53 no.1
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    • pp.10-17
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    • 2016
  • When a planing hull straightly runs and turns, its floating position and pitch angle are changed depending on its speed, and large transient motion happens. In this paper, six degrees of freedom(6 DOF) equations of motion, which could simulate the motion of a planing hull, are established. Static and dynamic forces in vertical plane are modeled using pre-calculated displacements and metacentric heights depending on various draft, lift under bottom, and vertical damping coefficients which are used to tune the final motion. Hydrodynamic coefficients in horizontal plane at various equilibrium state are calculated by using Lewandowski's empirical formula and the speed-dependent equilibrium state are calculated beforehand by Savitsky's formula. The speed effects are considered by curve-fitting the coefficients at various speed to the polynomials. Accelerating, decelerating and backing, turning, and zig-zag are simulated and compared with the sea trial results, and it is confirmed that the speed reduction, roll, and pitch during such maneuvers of sea trial and simulation are well consistent.

Transient Response Analysis of a Control Valve for CO2 Refrigerant (CO2냉매용 제어밸브의 응답 특성)

  • Kim, Bo Hyun;Jang, Ji Seong
    • Journal of Drive and Control
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    • v.15 no.4
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    • pp.11-16
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    • 2018
  • Pilot operated control valve for $CO_2$ refrigerant is a valve that can perform various functions according to the user's intention by replacing pilot units, widely used for flow rate, pressure, and temperature control of refrigeration and air conditioning systems. In addition, $CO_2$ refrigerant, that requires high pressure and low critical temperature, can be installed and used in all positions of the refrigeration system, regardless of high or low pressure. In this paper, response characteristics are modeled and analyzed based on behavior of the main piston of the pilot-operated control valve. Although various factors influence operation of the main piston, this paper analyzes the effect of equilibrium pressure depending on valve installation position and application, and inlet and outlet orifice size of the load pressure feedback chamber to determine feedback characteristics of the main piston. As a result, it was possible to quantitatively analyze the effect of change in equilibrium and load pressure feedback chamber flow path size on the change in main piston dynamic and static characteristics.

Dynamic Characteristics of HDD Slider by Perturbed Finite Element Method (교란 유한요소법을 이용한 하드 디스크 슬라이더의 동특성 해석)

  • Hwang Pyung;Khan Polina V.
    • Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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    • 2004.11a
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    • pp.143-148
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    • 2004
  • The numerical analysis of the hard disk drive slider is presented. The pressure distribution was calculated using the finite element method. The generalized Reynolds equation was applied in order to include the gas rarefaction effect. The balance of the air bearing force and preload force was considered. The characteristics of the small vibrations near the equilibrium were studied using the perturbation method. Triangular mesh with variable element size was employed to model the two-rail slider. The flying height, pitching angle, rolling angle, stiffness and damping of the two-rail slider were calculated for radial position changing from the inner radius to the outer radius and for a wide range of the slider crown values. It was found that the flying height, pitching angle and rolling angle were increased with radial position while the stiffness and damping coefficients were decreased. The higher values of crown resulted in increased flying height, pitching angle and damping and decreased stiffness.

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Characteristic Analysis of Rotor System due to the Positioning Angles of HDD Supported by Fluid Dynamic Bearings (유체동압베어링으로 지지되는 HDD 의 장착각도에 따른 회전부의 특성해석)

  • Hwang, Choongman;Jang, Gunhee;Lee, Jihoon;Lee, Minho
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2014.10a
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    • pp.986-992
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    • 2014
  • This research investigates experimentally and numerically the tilting angle, eccentricity ratio, flying height of axial direction, friction torque, and critical mass of the HDD disk-spindle system due to HDD positioning angle. The tilting angle and the eccentricity ratio are the maximum when the HDD positioning angle is $90^{\circ}$ respect to horizontal position because the external force in radial direction and the torque applied to the rotating part are the maximum when the HDD positioning angle is $90^{\circ}$. The flying height increases with the increase of the HDD positioning angle because the direction of gravity applied to the rotating part changes. The friction torque increases with the increase of the HDD positioning angle until it becomes $60^{\circ}$, and decreases with the increase of the HDD positioning angle after it becomes $60^{\circ}$. The stability is the maximum when the HDD positioning angle is $90^{\circ}$.

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A study on the dynamic characteristics of an epicyclic gear trains supported with journal bearing (저널베어링으로 지지된 유성기어열의 동특성에 관한 연구)

  • Lee, Jeong-Han;Ryu, Hyeong-Tae;Cheon, Gil-Jeong
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.22 no.1
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    • pp.198-205
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    • 1998
  • In this paper, the dynamic characteristics of a star type epicyclic gear train have been analyzed. Nonlinear stiffness of a gear pair were obtained considering the bending and shear deformation, Hertz contact deformation, as well as tooth fillet deformation. Nonlinear stiffness coefficients and damping coefficients around the static equilibrium position were obtained by perturbation method. The loci of the planet gears and sun gear were estimated. Tooth meshing forces and bearing reaction forces were calculated. The effects of bearing clearance and oil viscosity on the gear behavior were also analyzed.

Investigation on the Strength and Vibration Safety of the Oxidizer Turbopump (산화제 터보펌프의 구조 강도 및 진동 안전성에 관한 연구)

  • Jeon, Seong-Min;Kim, Jin-han;Yang, Soo-Seok;Lee, Dae-Sung
    • The KSFM Journal of Fluid Machinery
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    • v.5 no.3 s.16
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    • pp.25-32
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    • 2002
  • Structural and dynamic analyses of inducer and impeller for an oxidizer turbopump are peformed to investigate the safety level of strength and vibration at a design point. Due to high rotational speed of turbopump, effects of centrifugal forces are carefully considered in the structural analysis. Hydrodynamic pressure is also considered as an external force applied to inducer and impeller blades. A three-dimensional Finite Element Method (FEM) is used for linear and nonlinear structural analyses with modified Newton-Raphson iteration method. After the nonlinear trim solution is obtained from the structural analysis, dynamic characteristics are obtained as a function of rotational speed from the linearized eigenvalue analysis at an equilibrium position. According to the results of numerical analysis, the safety margins of strength and vibration resonances are sufficient enough for safe operation within the requited life cycle.

Investigation on the Strength and Vibration Safety of the Oxidizer Turbopump (산화제 터보펌프의 구조 강도 및 진동 안전성에 관한 연구)

  • Jeon, Seong Min;Kim, Jinhan;Yang, Soo-Seok;Lee, Dae-Sung
    • 유체기계공업학회:학술대회논문집
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    • 2001.11a
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    • pp.271-278
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    • 2001
  • Structural and dynamic analyses of inducer and impeller for a oxidizer turbopump are peformed to investigate the safety level of strength and vibration at design point. Due to high rotational speed of turbopump, effects of centrifugal forces are carefully considered in the structural analysis. Hydrodynamic pressure is also considered as an external force applied to inducer and impeller blades. A three dimensional finite element method(FEM) is used for linear and nonlinear structural analyses with modified Newton-Raphson iteration method. After the nonlinear trim solution is obtained from the structural analysis, dynamic characteristics are obtained as a function of rotational speed from the linearized eigenvalue analysis at an equilibrium position. According to the results of numerical analysis, the safety margins of strength and vibration resonances m sufficient enough to be operated safely within the required life cycle.

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Stabilization Loop Design Method on Dynamic Platform

  • Kwon, Young-Shin;Kim, Doh-Hyun;Kim, Lee-Han;Hwang, Hong-Yeon
    • 제어로봇시스템학회:학술대회논문집
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    • 2001.10a
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    • pp.156.5-156
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    • 2001
  • Stabilized tracking platform in a missile consisting of a flat planar antenna, pitch/yaw gimbals, gear trains, and current controlled DC drive motors for pitch and yaw gimbal must have a capability to track a target as an inertial sensor in the presence of missile body motion such as maneuvering and vibration. Because of this reason, tracking a target from dynamic platform requires a servo architecture that includes a outer tracking loop(position loop) and inner rate loop that stabilizes the line of sight(LOS). This paper presents a gimbaled platform model including nonlinear phenomena due to viscous and Coulomb friction based on experimental data and torque equilibrium equation, the design concept for the inner tacholoop having P controller structure ...

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