• Title/Summary/Keyword: system of difference equations

Search Result 362, Processing Time 0.023 seconds

Study on the Travel and Tractive Characteristics of the Two-Wheel Tractor on the General Slope Land(Ⅲ)-Tractive Performance of Power Tiller- (동력경운기의 경사지견인 및 주행특성에 관한 연구 (Ⅲ)-동력경운의 경사지 견인성능-)

  • Song, Hyun Kap;Chung, Chang Joo
    • Journal of Biosystems Engineering
    • /
    • v.3 no.2
    • /
    • pp.34-34
    • /
    • 1978
  • To find out the power tiller's travel and tractive characteristics on the general slope land, the tractive p:nver transmitting system was divided into the internal an,~ external power transmission systems. The performance of power tiller's engine which is the initial unit of internal transmission system was tested. In addition, the mathematical model for the tractive force of driving wheel which is the initial unit of external transmission system, was derived by energy and force balance. An analytical solution of performed for tractive forces was determined by use of the model through the digital computer programme. To justify the reliability of the theoretical value, the draft force was measured by the strain gauge system on the general slope land and compared with theoretical values. The results of the analytical and experimental performance of power tiller on the field may be summarized as follows; (1) The mathematical equation of rolIing resistance was derived as $$Rh=\frac {W_z-AC \[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\] sin\theta_1}} {tan\phi \[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\]+\frac{tan\theta_1}{1}$$ and angle of rolling resistance as $$\theta _1 - tan^1\[ \frac {2T(AcrS_0 - T)+\sqrt (T-AcrS_0)^2(2T)^2-4(T^2-W_2^2r^2)\times (T-AcrS_0)^2 W_z^2r^2S_0^2tan^2\phi} {2(T^2-W_z^2r^2)S_0tan\phi}\] $$and the equation of frft force was derived as$$P=(AC+Rtan\phi)\[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\]cos\phi_1 ? \frac {W_z ?{AC\[ [1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\]sin\phi_1 {tan\phi[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\]+ \frac {tan\phi_1} { 1} ? W_1sin\alpha $$The slip coefficient K in these equations was fitted to approximately 1. 5 on the level lands and 2 on the slope land. (2) The coefficient of rolling resistance Rn was increased with increasing slip percent 5 and did not influenced by the angle of slope land. The angle of rolling resistance Ol was increasing sinkage Z of driving wheel. The value of Ol was found to be within the limits of Ol =2? "'16?. (3) The vertical weight transfered to power tiller on general slope land can be estim ated by use of th~ derived equation: $$R_pz= \frac {\sum_{i=1}^{4}{W_i}} {l_T} { (l_T-l) cos\alpha cos\beta ? \bar(h) sin \alpha - W_1 cos\alpha cos\beta$$The vertical transfer weight $R_pz$ was decreased with increasing the angle of slope land. The ratio of weight difference of right and left driving wheel on slop eland,$\lambda= \frac { {W_L_Z} - {W_R_Z}} {W_Z} $, was increased from ,$\lambda$=0 to$\lambda$=0.4 with increasing the angle of side slope land ($\beta = 0^\circ~20^\circ) (4) In case of no draft resistance, the difference between the travelling velocities on the level and the slope land was very small to give 0.5m/sec, in which the travelling velocity on the general slope land was decreased in curvilinear trend as the draft load increased. The decreasing rate of travelling velocity by the increase of side slope angle was less than that by the increase of hill slope angle a, (5) Rate of side slip by the side slope angle was defined as $ S_r=\frac {S_s}{l_s} \times$ 100( %), and the rate of side slip of the low travelling velocity was larger than that of the high travelling velocity. (6) Draft forces of power tiller did not affect by the angular velocity of driving wheel, and maximum draft coefficient occurred at slip percent of S=60% and the maximum draft power efficiency occurred at slip percent of S=30%. The maximum draft coefficient occurred at slip percent of S=60% on the side slope land, and the draft coefficent was nearly constant regardless of the side slope angle on the hill slope land. The maximum draft coefficient occurred at slip perecent of S=65% and it was decreased with increasing hill slope angle $\alpha$. The maximum draft power efficiency occurred at S=30 % on the general slope land. Therefore, it would be reasonable to have the draft operation at slip percent of S=30% on the general slope land. (7) The portions of the power supplied by the engine of the power tiller which were used as the source of draft power were 46.7% on the concrete road, 26.7% on the level land, and 13~20%; on the general slope land ($\alpha = O~ 15^\circ ,\beta = 0 ~ 10^\circ$) , respectively. Therefore, it may be desirable to develope the new mechanism of the external pO'wer transmitting system for the general slope land to improved its performance.

Kinetic Behavior of Immobilized Tyrosinase on Carbon in a Simulated Packed-Bed Reactor (충전층에서 탄소에 고정시킨 Tyrosinase의 반응속도에 관한 연구)

  • Shin, Sun Kyoung;Kim, Kyeo-Keun
    • Analytical Science and Technology
    • /
    • v.10 no.1
    • /
    • pp.66-74
    • /
    • 1997
  • Influence of the axial dispersion on immobilized enzyme catalytic bed was investigated in order to examine the kinetic behavior of the biocatalysis. The enzyme employed in this study was the tyrosinase(EC 1.14.18.1) immobilized on carbon support : this system requires two substrates of phenol and oxygen. This enzyme has potential application for phenol degradation in waste water. A simulated reactor was a packed-bed reactor of 2.54cm in diameter and 10cm long, loaded with the immobilized carbon particle with an average diameter of $550{\mu}m$. A phenol feed in the strength of 55.5mM(5220ppm) was used to observe the behavior of the immobilized enzyme column at three different dissolved oxygen levels of 0.08445mM(2.7ppm), 0.1689mM(5.4ppm) and 0.3378mM(9.5ppm) with the flow rates in the range of 60(1mL/s) to 180mL/min(3mL/s). Examination of the Biot number and Damkolher numbers of the immobilized system enables us to eliminate the contribution of external mass transfer to set of differential equations derived from the dispersion model. Solution of the equation was finally obtained numerically with the application of the Danckwert boundary conditions and the assumed zero-and first order rates on the non-linear two substrate enzyme kinetics. Higher conversion of phenol was observed at the low flow rates and at the higher oxygen concentration. Comparison of axial dispersion and plug flow model showed that no detectable difference was observed in the column outlet conversion between the axial and the plug flow models which was in complete agreement with the previous studies.

  • PDF

Development of a Model for Predicting Modulus on Asphalt Pavements Using FWD Deflection Basins (FWD 처짐곡선을 이용한 아스팔트 포장구조체의 탄성계수 추정 모형 개발)

  • Park, Seong Wan;Hwang, Jung Joon;Hwang, Kyu Young;Park, Hee Mun
    • KSCE Journal of Civil and Environmental Engineering Research
    • /
    • v.26 no.5D
    • /
    • pp.797-804
    • /
    • 2006
  • A development of regression model for asphalt concrete pavements using Falling Weight Deflectometer deflections is presented in this paper. A backcalculation program based on layered elastic theory was used to generate the synthetic modulus database, which was used to generate 95% confidence intervals of modulus in each layer. Using deflection basins of FWD data used in developing this procedure were collected from Pavement Management System in flexible pavements. Assumptions of back-calculation are that one is 3 layered flexible pavement structure and another is depth to bedrock is finite. It is found that difference of between 95% confidence intervals and modulus ranges of other papers does not exist. So, the data of 95% confidence intervals in each layer was used to develop multiple regression models. Multiple regression equations of each layer were established by SPSS, package of Statics analysis. These models were proved by regression diagnostics, which include case analysis, multi-collinearity analysis, influence diagnostics and analysis of variance. And these models have higher degree of coefficient of determination than 0.75. So this models were applied to predict modulus of domestic asphalt concrete pavement at FWD field test.

An experimental study for estimation of head loss coefficients at surcharged four-way combining manholes (과부하 4방향 합류맨홀에서의 손실계수 산정을 위한 실험 연구)

  • Ryu, Taek Hee;Kim, Jung Soo;Yoon, Sei Eui
    • Journal of Korea Water Resources Association
    • /
    • v.49 no.12
    • /
    • pp.1015-1025
    • /
    • 2016
  • In general, manholes installed as urban drainage facilities are a variety forms such as straight path manholes, 90 degree bend manhole, three-way combining manhole, and four-way combining manhole. In particular, the surcharged flow at a four-way manholes installed in the downstream of urban sewer system is the main cause of the urban inundation caused by the energy loss. Therefore, it is necessary to analyze the flow characteristics and estimate the head loss coefficients at surcharged four-way combining manholes. The hydraulic experimental apparatus which can change the manhole shapes (square, circle) and flow ratios were installed to estimate the head loss coefficients. In the experiments, two inflows ($Q_m$, $Q_{lat}$) were varied from 0 to $4.8{\ell}/sec$ and 24 combinations were tested in total. The flow ratios $Q_{lat}/Q_{out}$ were varied from 0 to 1 for a total flow $Q_{out}$ ($Q_{out}=Q_m+2Q_{lat}$) of 2, 3, 4, and $4.8{\ell}/sec$, respectively. The variation of head losses were strongly influenced by the lateral inflow because the head loss coefficient increases as the flow ratios $Q_{lat}/Q_{out}$ increases. It was estimated head loss coefficients of the circular manhole is slightly lower than those of the square manhole. However, there was no significant difference of head loss as discharges change. The range of head loss coefficients at four-way combining manhole according to the change of the lateral inflow ratio was estimated to be 0.4 to 0.8. Also, the relation equations between the head loss coefficients (K) and the lateral inflow ratios ($Q_{lat}/Q_{out}$) were suggested in this paper.

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
    • /
    • v.8 no.5
    • /
    • pp.964-973
    • /
    • 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.

  • PDF

A Study on the Design of Ship′s Bow Form using Surface Panel Method (판요소법을 이용한 선수형상 설계에 관한 연구[1])

  • Jae-Hoon Yoo;Hyo-Chul Kim
    • Journal of the Society of Naval Architects of Korea
    • /
    • v.33 no.3
    • /
    • pp.35-47
    • /
    • 1996
  • A surface panel method treating a boundary-value problem of the Dirichlet type is presented to design a three dimensional body with free surface corresponding to a prescribed pressure distribution. An integral equation is derived from Green's theorem, giving a relation between total potential of known strength and the unknown local flux. Upon discretization, a system of linear simultaneous equations is formed including free surface boundary condition and is solved for an assumed geometry. The pseudo local flux, present due to the incorrect positioning of the assumed geometry, plays a role f the geometry corrector, with which the new geometry is computed for the next iteration. Sample designs for submerged spheroids and Wigley hull and carried out to demonstrate the stable convergence, the effectiveness and the robustness of the method. For the calculation of the wave resistance, normal dipoles and Rankine sources are distributed on the body surface and Rankine sources on the free surface. The free surface boundary condition is linearized with respect to the oncoming flow. Four-points upwind finite difference scheme is used to compute the free surface boundary condition. A hyperboloidal panel is adopted to represent the hull surface, which can compensate the defects of the low-order panel method. The design of a 5500TEU container carrier is performed with respect to reduction of the wave resistance. To reduce the wave resistance, calculated pressure on the hull surface is modified to have the lower fluctuation, and is applied as a Dirichlet type dynamic boundary condition on the hull surface. The designed hull form is verified to have the lower wave resistance than the initial one not only by computation but by experiment.

  • PDF

An Experimental Study for Estimation of Head Loss Coefficients at Surcharged Combining Junction Manholes (과부하 합류맨홀에서의 손실계수 산정을 위한 실험적 연구)

  • Kim, Jung-Soo;Choi, Hyun-Soo;Yoon, Sei-Eui
    • Journal of Korea Water Resources Association
    • /
    • v.43 no.5
    • /
    • pp.445-453
    • /
    • 2010
  • Energy loss at manholes, often exceeding friction loss of pipes under surcharged flow, is considered as one of the major causes of inundation in urban area. Therefore, it is necessary to analyze head losses at manholes, especially in case of surcharged flow. Hydraulic experimental apparatus which can change the manhole shape (square, circular) were installed for this study. In the experiments, two inflows ($Q_1,\;Q_2$) were varied from 0 to $4{\ell}$/sec and 15 combinations were tested in total. The flow ratios $Q_2/Q_3$ were varied from 0 to 1 for a total flow $Q_3$ ($Q_3=Q_1+Q_3$) of 2, 3, and $4{\ell}$/sec, respectively. The variation of head losses were strongly influenced by the lateral inflow because the head loss coefficient increases as the flow ratio $Q_2/Q_3$ increases. There was no significant difference of head loss between square manhole and circular one, and also no large variation of head loss as discharges change. The relation equations between K and $Q_2/Q_3$ were suggested in this paper.

Review on the Three-Dimensional Magnetotelluric Modeling (MT 법의 3차원 모델링 개관)

  • Kim, Hee-Joon;Nam, Myung-Jin;Song, Yoon-Ho;Suh, Jung-Hee
    • Geophysics and Geophysical Exploration
    • /
    • v.7 no.2
    • /
    • pp.148-154
    • /
    • 2004
  • This article reviews the development of three-dimensional (3-D) magnetotelluric (MT) modeling. The 3-D modeling of electromagnetic fields is essential in understanding the physics of MT soundings, and in implementing an inversion method to reconstruct a 3-D resistivity image. Although various numerical schemes have been developed over the last two decades, practical methods have been quite limited. However, the recent rapid improvement in computer speed and memory, as well as the advance in iterative solution algorithms for a large system of equations, makes it possible to model the MT responses of complex 3-D structures, which have been very difficult to simulate before. The use of staggered grids in finite difference method has become popular, conserving a magnetic flux and an electric current and allowing for realistic discontinuous fields. The convergence of numerical solutions has been greatly accelerated by adopting Krylov subspace methods, proper preconditioning techniques, and static divergence corrections. The vector finite-element method using edge elements is also free from the discontinuity problem, and seems a natural choice for modeling complex structures including irregular topography because its flexibility allows one to capture full geometric complexity.

Arch Forms & Dimensions after Orthodontic Treatment by Premolar Extraction (소구치 발치에 의한 교정치료후의 치열궁 형태 및 크기에 관한 연구)

  • Lee, Seung-Mi;Yoon, Young-Jooh;Kim, Kwang-Won
    • The korean journal of orthodontics
    • /
    • v.28 no.5 s.70
    • /
    • pp.717-729
    • /
    • 1998
  • This study was done to estimate arch forms and dimensions at the bracket level where archwire was placed in Angle's Class I first premolars extraction cases. 60 post-treatment dental casts which had attained good orthodontic treatment results were used in this study Many landmarks and linear measurement items to describe arch forms and dimensions were determined and measured. With a computer system and digitizer, arch forms were described and linear measurement items were statistically analysed. The following results were obtained. 1. The average labial and lingual arch forms at the bracket level were obtained. 2. Arch forms were expressed by parabolic equations and coefficients of determination. 3. Arch widths were larger in male than in female. 4. There were statistical significances in upper intercanine width, upper interfirst molar width, upper intersecond molar height, lower intercanine width and lower interfirst molar width between both sexes (p<0.05, p<0.01). 5. Interfirst molar width differences between maxilla and mandible were 6.43mm in male and 6.05mm in female.

  • PDF

Comparisons of Soil Water Retention Characteristics and FDR Sensor Calibration of Field Soils in Korean Orchards (노지 과수원 토성별 수분보유 특성 및 FDR 센서 보정계수 비교)

  • Lee, Kiram;Kim, Jongkyun;Lee, Jaebeom;Kim, Jongyun
    • Journal of Bio-Environment Control
    • /
    • v.31 no.4
    • /
    • pp.401-408
    • /
    • 2022
  • As research on a controlled environment system based on crop growth environment sensing for sustainable production of horticultural crops and its industrial use has been important, research on how to properly utilize soil moisture sensors for outdoor cultivation is being actively conducted. This experiment was conducted to suggest the proper method of utilizing the TEROS 12, an FDR (frequency domain reflectometry) sensor, which is frequently used in industry and research fields, for each orchard soil in three regions in Korea. We collected soils from each orchard where fruit trees were grown, investigated the soil characteristics and soil water retention curve, and compared TEROS 12 sensor calibration equations to correlate the sensor output to the corresponding soil volumetric water content through linear and cubic regressions for each soil sample. The estimated value from the calibration equation provided by the manufacturer was also compared. The soil collected from all three orchards showed different soil characteristics and volumetric water content values by each soil water retention level across the soil samples. In addition, the cubic calibration equation for TEROS 12 sensor showed the highest coefficient of determination higher than 0.95, and the lowest RMSE for all soil samples. When estimating volumetric water contents from TEROS 12 sensor output using the calibration equation provided by the manufacturer, their calculated volumetric water contents were lower than the actual volumetric water contents, with the difference up to 0.09-0.17 m3·m-3 depending on the soil samples, indicating an appropriate calibration for each soil should be preceded before FDR sensor utilization. Also, there was a difference in the range of soil volumetric water content corresponding to the soil water retention levels across the soil samples, suggesting that the soil water retention information should be required to properly interpret the volumetric water content value of the soil. Moreover, soil with a high content of sand had a relatively narrow range of volumetric water contents for irrigation, thus reducing the accuracy of an FDR sensor measurement. In conclusion, analyzing soil water retention characteristics of the target soil and the soil-specific calibration would be necessary to properly quantify the soil water status and determine their adequate irrigation point using an FDR sensor.