• 대한기계학회논문집
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• 제19권6호
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• pp.1545-1553
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• 1995

For general geometry of Coordinate Measuring Machine (CMM), volumetric error equation including 21 systematic error components was showed using vector expression. Different types of CMM listed on an international standard (BS 6808) were classified according to their geometry, and the general volumetric error equation was used for the CMMs. Application of volumetric error equation was also introduced, such as position error compensation, error equation of CNC-machine and parametric error analysis, etc.

• 한국자동차공학회논문집
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• 제5권1호
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• pp.69-78
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• 1997

Main sources of the vibration in gear driving system are transmission error and backlash. Transmission error is the difference of the rotation between driving and driven gear due to tooth deformation and profile error. Vibro-impacts induced by backlash between meshing gears lead to excessive vibration and noise in many geared rotation systems. Nonlinear dynamic characteristics of the gear driving system due to transmi- ssion error and backlash are investigated. Transmission error is calculated for spur gear. Nonlinear equation of motion for the gear driving system is developed with the calculated transmission error and backlash. Numerical analysis of the equation and the experimental results show the existence of meshing frequency, superharmonic compon- ents. Instability of the gear driving motion is found on the basis of Mathieu equation. Rattle vibration due to backlash is also discussed on the basis if nonlinear jump phenomenon.

• 자연과학논문집
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• 제8권1호
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• pp.5-15
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• 1995

IRR 적응 휠터의 공식오차 방식은 지역 최소값에 관계없이 전역 최소값에 수렴하며 안정성이 높다. 그러나 공식오차 방식은 입력 신호에 잡음이 섞여 경우 예측계수가 바이어스 되는 문제가 있다. 본 논문에서는 사전에 잡음에 대한 지식이 없이 바이어스가 없는 예측계수를 얻을 수 있는 새로운 공식 오차 방식을 위한 알고리즘을 제안한다. 이 알고리즘은 공식오차를 스므딩하는 방식을 이용하여 입력에 추가되는 잡음이 백색잡음인 경우 바이어스 없이 계수를 예측할 수 있다. 시뮬레이션을 통해 새로운 알고리즘이 공식오차의 중요한 장점인 빠른 수렴속도와 안정성을 유지하며 바이어스를 효율적으로 제거함을 볼 수 있다.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.113-126
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• 2005

The Cahn-Hilliard equation is modeled to describe the dynamics of phase separation in glass and polymer systems. A priori error estimates for the Cahn-Hilliard equation have been studied by the authors. In order to control accuracy of approximate solutions, a posteriori error estimation of the Cahn-Hilliard equation is obtained by discontinuous Galerkin method.

• 한국항해항만학회지
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• 제29권7호
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• pp.611-614
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• 2005

This paper is to develop the position error equation of in the free-gyro positioning system by using two free gyros. First, the determination of a position is analyzed on the ellipsoid of the Earth and the type of the errors is defined Finally the position error equation is introduced and developed, based on the definition of the type of errors which may be involved in the FPS.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2001년도 제14회 신호처리 합동 학술대회 논문집
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• pp.91-94
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• 2001

Recently a constant-norm constraint equation-error method was proposed to solve the bias problem in adaptive IIR filtering. However, the method adopts a fixed step-size and thus results in slow convergence for a small step-size and significant misadjustment error for a largestep-size. In this paper, we propose a variable step-size (VSS) algorithm that greatly improves convergence properties of the constant-norm constraint equation-error method. The analysis and the simulation results show that the proposed method indeed achieves both fast convergence and small misadjustment error.

• Journal of Power Electronics
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• 제12권5호
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• pp.748-757
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• 2012

In a sensorless control system with a Permanent Magnet Synchronous Motor (PMSM), the angular position of the rotor flux can be estimated by a voltage equation. However, the estimated angle may be inaccurate due to various causes. In this paper, it was comprehensively analyzed how various causes affect the angle error. As a result of the analysis, an error equation intuitively describing these relationships was derived. The parameter errors of a PMSM and the non-ideal properties of the driving system were identified as error-causing factors. To demonstrate the validity of the error equation, PMSMs were tested at various operating points. The variations in angle errors could be well explained with the error equation.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.571-579
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• 2007

Finite difference schemes are considered for a generalization of the Cahn-Hilliard equation with Neumann boundary conditions and the Kuramoto-Sivashinsky equation with a periodic boundary condition, which is of the type $ut+\frac{{\partial}^2} {{\partial}x^2}\;g\;(u,\;u_x,\;u_{xx})=f(u,\;u_x,\;u_{xx})$. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.

• 한국정밀공학회지
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• 제25권5호
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• pp.69-76
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• 2008

Inner diameter of bearing race is automatically measured by complete inspection system after grinding process. Contact type three points supporting method is widely applied to automatic inner diameter measurement because of its excellent stability. However, the geometric consideration regarding three points supporting method is not sufficient. In this study, the error equation from geometric error analysis of three points supporting method is found. The effect of factors in the error equation is also investigated. The error equation is linear for difference of diameter in sample and master on range of tolerance. An error becomes more and more larger, when the distance of two supporting balls or the diameter of supporting ball are increased. In the result, some considerations are proposed for measurement of inner diameter by the three points supporting method.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2004년도 추계학술대회 논문집
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• pp.430-433
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• 2004

The ophthalmic lens manufacturing processes need to extract the aspherical surface equation from the unknown surface since its real profile can be adjusted by the process variables to make the ideal curve without the optical aberration. This paper presents a procedure to get the aspherical surface equation of an aspherical ophthalmic lens. Aspherical form generally consists of the Schulz formula to describe its profile. Therefore, the base curvature, conic constant, and high-order polynomial coefficient should be set to the original design equation. To find an estimated aspherical profile, firstly lens profile is measured by a contact profiler, which has a sub-micrometer measurement resolution. A mathematical tool is based on the minimization of the error function to get the estimated aspherical surface equation from the scanned aspherical profile. Error minimization step uses the Nelder-Mead simplex (direct search) method. The result of the refractive power measurement is compared with the curvature distribution on the estimated aspherical surface equation