• Title/Summary/Keyword: Equation of a Circle

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A Roots Method in GI/PH/1 Queueing Model and Its Application

  • Choi, Kyung Hwan;Yoon, Bong Kyoo
    • Industrial Engineering and Management Systems
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    • v.12 no.3
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    • pp.281-287
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    • 2013
  • In this paper, we introduce a roots method that uses the roots inside the unit circle of the associated characteristics equation to evaluate the steady-state system-length distribution at three epochs (pre-arrival, arbitrary, and post-departure) and sojourn-time distribution in GI/PH/1 queueing model. It is very important for an air base to inspect airplane oil because low-quality oil leads to drop or breakdown of an airplane. Since airplane oil inspection is composed of several inspection steps, it sometimes causes train congestion and delay of inventory replenishments. We analyzed interarrival time and inspection (service) time of oil supply from the actual data which is given from one of the ROKAF's (Republic of Korea Air Force) bases. We found that interarrival time of oil follows a normal distribution with a small deviation, and the service time follows phase-type distribution, which was first introduced by Neuts to deal with the shortfalls of exponential distributions. Finally, we applied the GI/PH/1 queueing model to the oil train congestion problem and analyzed the distributions of the number of customers (oil trains) in the queue and their mean sojourn-time using the roots method suggested by Chaudhry for the model GI/C-MSP/1.

Liquid boundary effect on free vibration of an annular plate coupled with a liquid

  • Kyeong-Hoon Jeong
    • Coupled systems mechanics
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    • v.12 no.2
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    • pp.127-149
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    • 2023
  • A theoretical method is developed to analyze the free vibration of an elastic annular plate in contact with an ideal liquid. The displacement potential functions of the contained liquid are expressed as a combination of the Bessel functions that satisfy the Laplace equation and the liquid boundary conditions. The compatibility condition along the interface between the annular plate and the contained liquid is taken into account to consider the fluid-structure coupling. The dynamic displacement of the wet annular plate is assumed to be a combination of dry eigenfunctions, allowing for prediction of the natural frequencies using the Rayleigh-Ritz method. The study investigates the effect of radial liquid boundary conditions on the natural frequencies of the wet annular plate, considering four types of liquid bounding: outer container bounded, outer and inner bounded, inner bounded, and radially unbounded. The proposed theoretical method is validated by comparing the predicted wet natural frequencies with those obtained from finite element analysis, showing excellent accuracy. The results indicate that the radial liquid bounding effect on the natural frequencies is negligible for the axisymmetric vibrational mode, but relatively significant for the mode with one nodal diameter (n =1) and no nodal circle (m' = 0). Furthermore, the study reveals that the wet natural frequencies are the largest for the plate with an inner bounded cylinder among the radial liquid boundary cases, regardless of the vibration mode.

Estimation of Chinese Cabbage Growth by RapidEye Imagery and Field Investigation Data

  • Na, Sangil;Lee, Kyoungdo;Baek, Shinchul;Hong, Sukyoung
    • Korean Journal of Soil Science and Fertilizer
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    • v.48 no.5
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    • pp.556-563
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    • 2015
  • Chinese cabbage is one of the most important vegetables in Korea and a target crop for market stabilization as well. Remote sensing has long been used as a tool to extract plant growth, cultivated area and yield information for many crops, but little research has been conducted on Chinese cabbage. This study refers to the derivation of simple Chinese cabbage growth prediction equation by using RapidEye derived vegetation index. Daesan-myeon area in Gochang-gun, Jeollabuk-do, Korea is one of main producing district of Chinese cabbage. RapidEye multi-spectral imagery was taken on the Daesan-myeon five times from early September to late October during the Chinese cabbage growing season. Meanwhile, field reflectance spectra and five plant growth parameters, including plant height (P.H.), plant diameter (P.D.), leaf height (L.H.), leaf length (L.L.) and leaf number (L.N.), were measured for about 20 plants (ten plants per plot) for each ground survey. The normalized difference vegetation index (NDVI) for each of the 20 plants was measured using an active plant growth sensor (Crop $Circle^{TM}$) at the same time. The results of correlation analysis between the vegetation indices and Chinese cabbage growth data showed that NDVI was the most suited for monitoring the L.H. (r=0.958~0.978), L.L. (r=0.950~0.971), P.H. (r=0.887~0.982), P.D. (r=0.855~0.932) and L.N. (r=0.718~0.968). Retrieval equations were developed for estimating Chinese cabbage growth parameters using NDVI. These results obtained using the NDVI is effective provided a basis for establishing retrieval algorithm for the biophysical properties of Chinese cabbage. These results will also be useful in determining the RapidEye multi-spectral imagery necessary to estimate parameters of Chinese cabbage.

A Study on the Adequate Radius of Circular Arc in the Involute-Circular Arc Composite Tooth Profile (인벌류우트-원호 합성치형의 적정 원호반경에 대한 연구)

  • 정인승;손지원;윤갑영
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.11 no.2
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    • pp.296-303
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    • 1987
  • The composite gear which is composed of involute curve and circular arc has been studied. In the vicinity of pitch point, its profile is an involute curve, and in the dedenum, a circular arc. The curve in the dedendum is generated by the circular arc of the mating gear. Though the available range between minimum and maximum radius of circular arc can be given by existing tooth profile equation, there was no formulation which relates design parameters to the desired radius. It is attempted to get the formula for the radius of circular arc as a function of design parameters, such as unwounded angle, number of teeth, module, and pressure angle. The radius of circular arc, the chordal tooth thickness at working root circle, nominal bending stress, Hertz stress and contact ratio obtained from derived formula are compared with those of the existing design criteria. And these are compared with those of involute gear.

Prediction of Ship Manoeuvrability in Initial Design Stage Using CFD Based Calculation

  • Cho, Yu-Rim;Yoon, Bum-Sang;Yum, Deuk-Joon;Lee, Myen-Sik
    • Journal of Ship and Ocean Technology
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    • v.11 no.1
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    • pp.11-24
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    • 2007
  • Better prediction of a ship's manouevrabilty in initial design stage is becoming more, important as IMO manoeuvring criteria has been activated in the year of 2004. In the present study, in order to obtain more exact and reliable results for ship manoeuvrability in the initial design stage, numerical simulation is carried out by use of RANS equation based calculation of hydrodynamic forces exerted upon the ship hull. Other forces such as rudder force and propeller force are estimated by one of the empirical models recommended by MMG Group. Calculated hydrodynamic force coefficients are compared with those obtained by empirical models. Standard manoeuvring simulations such as turning circle and zig-zag are also carried out for a medium size Product Carrier and the results are compared with those of pure empirical models and manoeuvring sea trial. Generally good qualitative agreement is obtained in hydrodynamic forces due to steady oblique motion and steady turning motion between the results of CFD calculation and those of MMG model, which is based on empirical formulas. The results of standard manoeuvring simulation also show good agreement with sea trial results.

Measurement and Correction of PCB Alignment Error for Screen Printer Using Machine Vision (2) (머신비전을 이용한 PCB 스크린인쇄기의 정렬오차측정 및 위치보정 (2))

  • 신동원
    • Journal of the Korean Society for Precision Engineering
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    • v.20 no.6
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    • pp.96-104
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    • 2003
  • This paper presents the measurement and correction method of PCB alignment errors for PCB screen printer. Electronic equipment is getting smaller and yet must satisfy high performance standard. Therefore, there is a great demand for PCB with high density. However conventional PCB screen printer doesn't have enough accuracy to accommodate the demand for high-resolution circuit pattern and high-density mounting capacity of electronic chips. It is because the alignment errors of PCB occur when it is loaded to the screen printer. Therefore, this study focuses on the development of the system which is able to measure and correct alignment errors with high-accuracy. An automatic optical inspection part measures the PCB alignment errors using machine vision, and the high-accuracy 3-axis stage makes correction for these errors. This system used two CCD cameras to get images of two fiducial marks of PCB. The centers of fiducial marks are obtained by using moment, gradient method. The first method is calculating the centroid by using first moment of blob, and the latter method is calculating the center of the circle whose equation is obtained by curve-fitting the boundaries of fiducial mark. The operating system used to implement the whole set-up is carried in Window 98 (or NT) environment. Finally we implemented this system to PCB screen printer.

A Study on the Design of Horizontal Traverse Units in an Automatic Object Changer Unit to Establish a Flexible Production System (Part 2) (유연생산 시스템 구축을 위한 공작물 자동교환 유닛의 수평 이송 기구 설계에 관한 연구(파트 2))

  • Park, Hoo-Myung;Sung, Jae-Kyung;Lee, Yong-Joong;Ha, Man-Kyung
    • Journal of the Korean Society of Manufacturing Process Engineers
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    • v.7 no.2
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    • pp.52-59
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    • 2008
  • The objective of this study is to develop an automatic object changer unit to improve processing problems existed in the conventional horizontal machining center. To achieve this goal, this study designed a horizontal transfer as the second project continued to the first project that designed a upward and downward traverse unit. A horizontal traverse unit shows a symmetric structure and consists of frame, which consists of four unit tools, motor and reducer, which are fixed at a frame, operation unit with pinions, first traverse unit, and second traverse unit. Constraint conditions based on the operation mechanism with these elements were configured and obtained following results after modeling a model for a traverse motor. In the kinematic expression of sliding motion with one degree of freedom, the sliding motion is constrained. Also, the rack 3 installed at a frame is used to configure possible kinematic constraint conditions of the rack 2 according to the rolling motion of the pinion 2 in the first traverse unit. In addition, the moment of inertia that is a type of kinetic energy in a converted horizontal traverse unit in the side of the reducer can be applied to introduce the moment of inertia of a converted horizontal traverse unit in the side of the reducer by using the sum of kinetic energy in the rack and pinion, which is a part of the horizontal traverse unit. Also, the equation of motion of the converted upward and downward traverse unit in the side of the motor using the equation of motion of the motor. Furthermore, the horizontal traverse unit predetermines the mass of the first and second traverse unit and applied load including the radius and reduction ratio of the pitch circle in the pinion 1 and applied load to the rack 2. Then, a proper motor can be determined using several parameters in the upward and downward traverse unit in order to verify such predetermined specifications. In future studies later this study, a simulation that verifies the results of the previous two stages of studies using a finite element method.

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A Study on 3-Dimensional Near-Field Source Localization Using Interference Pattern Matching in Shallow Water Environments (천해에서 간섭패턴 정합을 이용한 근거리 음원의 3차원 위치추정 기법연구)

  • Kim, Se-Young;Chun, Seung-Yong;Son, Yoon-Jun;Kim, Ki-Man
    • The Journal of the Acoustical Society of Korea
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    • v.28 no.4
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    • pp.318-327
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    • 2009
  • In this paper, we propose a 3-D geometric localization method for near-field broadband source in shallow water environments. According to the waveguide invariant theory, slope of the interference pattern which is seen in a sensor spectrogram directly proportional to a range of the source. The relative ratio of the range between source and sensors was estimated by matching of two interference patterns in spectrogram. Then this ratio is applied to the Apollonius's circle which shows the locus of a source whose range ratio from two sensors is constant. Two Apollonius's circles from three sensors make the intersection point that means the horizontal range and the azimuth angle of the source. And this intersection point is constant with source depth. Therefore the source depth can be estimated using 3-D hyperboloid equation whose range difference from two sensors is constant. To evaluate a performance of the proposed localization algorithm, simulation is performed using acoustic propagation program and analysis of localization error is demonstrated. From simulation results, error estimate for range and depth is described within 50 m and 15 m respectively.

Experimental Evaluation of Levitation and Imbalance Compensation for the Magnetic Bearing System Using Discrete Time Q-Parameterization Control (이산시간 Q 매개변수화 제어를 이용한 자기축수 시스템에 대한 부상과 불평형보정의 실험적 평가)

  • ;Fumio Matsumura
    • Journal of KSNVE
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    • v.8 no.5
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    • pp.964-973
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    • 1998
  • In this paper we propose a levitation and imbalance compensation controller design methodology of magnetic bearing system. In order to achieve levitation and elimination of unbalance vibartion in some operation speed we use the discrete-time Q-parameterization control. When rotor speed p = 0 there are no rotor unbalance, with frequency equals to the rotational speed. So in order to make levitatiom we choose the Q-parameterization controller free parameter Q such that the controller has poles on the unit circle at z = 1. However, when rotor speed p $\neq$ 0 there exist sinusoidal disturbance forces, with frequency equals to the rotational speed. So in order to achieve asymptotic rejection of these disturbance forces, the Q-parameterization controller free parameter Q is chosen such that the controller has poles on the unit circle at z = $exp^{ipTs}$ for a certain speed of rotation p ( $T_s$ is the sampling period). First, we introduce the experimental setup employed in this research. Second, we give a mathematical model for the magnetic bearing in difference equation form. Third, we explain the proposed discrete-time Q-parameterization controller design methodology. The controller free parameter Q is assumed to be a proper stable transfer function. Fourth, we show that the controller free parameter which satisfies the design objectives can be obtained by simply solving a set of linear equations rather than solving a complicated optimization problem. Finally, several simulation and experimental results are obtained to evaluate the proposed controller. The results obtained show the effectiveness of the proposed controller in eliminating the unbalance vibrations at the design speed of rotation.

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The Effect of Corporate Social Responsibility on Corporate Trust and Purchase Intention (기업의 사회적 책임 속성이 기업 신뢰와 구매 의도에 미치는 영향)

  • Nam, Hyun-Dong;Nam, Taewoo
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.43 no.3
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    • pp.243-253
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    • 2020
  • As economic profits and social influences of firms grow with economic development and their organizational expansion, consumers increasingly require firms to have their social responsibility. Because social responsibility strongly influences corporate reliability, consumers' intention to purchase, customer loyalty to the products and the recognition of an ethical firm have gained attention as a concept of strategical importance. The prosperity of society should be proceeded for the sustainable development of a firm and the necessity of social responsibility should be emphasized to achieve virtuous circle structure that promotes growth. Additionally, the social responsibility should be proceeded to form trust on a firm. It is very important to change the recognition of consumers to purchase products and increase the profit of a company. This study aims to analyze how social responsibility properties of firms (economic, ethical, discretionary, and legal aspects as low-level factors of social responsibility which Carroll (1979) defined) affect corporate reliability and purchase intention. The analysis found that consumers trust in firms are positively influenced by ethical responsibility (0.391), economic responsibility (0.293), legal responsibility (0.251), and discretionary responsibility (0.248). The relationship between sub-factor of social responsibility and purchase intention is not significantly influenced by other explanatory variables. Corporate trust exerts a direct influence on purchase Intention (0.456). The social responsibility of a firm didn't influence a direct purchase intention. It was found that it brought positive effect on the purchase intention in the course of forming trust. This study suggests that firms should make efforts to understand the relationship between corporate trust and purchase intention along with the characteristics of social responsibility that consumers recognize and improve management strategies for mutual complementary interests.