切削力을 利用한 채터 檢出 및 프랙탈 모델링에 關한 硏究

Abstract

엔드밀 가공에서의 진동은 절삭공구와 공작물 사이의 주기적인 상대진동이 주된 원인이 되고 있다. 이 진동이 어느 정도 커지면 치수 정밀도가 저하하고 가공물의 표면이 악화될 뿐 아니라 공구의 마멸을 촉진하여 공구 수명이 감소되고, 공작기계 성능에도 좋지 못한 영향을 미쳐서 생산성능의 저하와 원가 상승의 원인이 된다. 본 논문은 채터 연구를 위하여 엔드밀 가공에 있어서 여러 절삭 조건에서 발생하는 채터 현상을 시계열 모델링 알고리즘 및 웨이브렛 변환을 이용하여 채터를 분석하였다. 또한 프랙탈 해석을 엔드밀 가공 한 공작물에 적용하여 프랙탈 보간과 프랙탈 차원 해석을 통하여 다양한 형상의 특성을 분석하여 제시하고자 하였으며 세 가지 방법으로 엔드밀 절삭력을 분석하였다. 첫째로 시계열 모델링을 이용한 고유 모드 분석을 하였고 둘째로 웨이브렛 변환을 이용하여 채터를 분석하는 방법을 연구하였으며 셋째로 엔드밀 가공시 샘플링 된 절삭력의 고정 데이터를 이용하여 프랙탈 보간을 하여 전체적인 절삭력을 생성해 내는 프랙탈 방법을 적용하였다. 이 세 가지 방법들로 구성된 채터 검출 및 특성 분석 시스템 프로그램 개발로 현장의 사용자가 이 시스템을 이용하여 채터에 관한 사전 데이터 베이스를 구축 할 수 있으며 이 예비 데이터를 이용하여 가공 시에 일어날 수 있는 채터와 같은 이상 현상을 사전에 예측 확인하여 가공 조건을 변경하여 가공하면 채터 발생을 줄여 정밀도를 향상 시킬 수 있다.

The chatter phenomenon shows the dynamic characteristics of tool vibration in endmilling process and it changes according to the irregular dynamic characteristics of tool vibration. Also, this chatter causes an undesirable effect on the tool life, machining integrity, surface quality of the workpiece and other geometric accuracy. A chatter behavior in endmilling is a complex and nonlinear phenomenon and it is very difficult to detect and diagnose this phenomenon. So it is necessary to develop new method for analyzing the chatter mechanics. Even if there are many chatter analysis method in endmilling, it has some limitation. In this study, three methods were introduced for the analysis of chatter. Firstly, the static and dynamic characteristics of endmilling was modelled and studied using time series. Also, several time series such as AR (burg, fb, least square, yule walker, geometric lattice, instrument variable), ARMA, ARMAX, ARX (ls, iv4), Box Jenkins, Output error algorithms were compared with one another. As a result, this study shows that the ARMAX, ARX(iv4) and ARMA are generally reliable algorithms for the calculation of the modal parameters such as natural frequency and damping ratio in endmilling. Also the calculated mode of ARMAX model using eq(3.8) and eq(3.9) was about = 610 Hz for cutting froce Fx and Fy. However, because of its weak stiffness in z-direction force, chatter frequencies, , of cutting force Fz was calculated about 560 Hz and 650 Hz. Also, time series power spectrum was compared with one and another. To verify the reality of time series spectrum, the FFT(Fast Fourier Transform) was used for comparing the spectrum analysis and monitoring of a machining process. Time series spectrum shows a good consistency with the real FFT spectrum. Furthermore the chatter mode can be calculated exactly using the mathematical eq.(3.8) and eq.(3.9). Secondly, this paper presents new method for the detection of chatter in endmilling operation based on the wavelet transform. This wavelet transform method provides various behaviors of chatter characteristics. The fundamental detail coefficient properties of the wavelet transform were reviewed. The reliability of this parameter, which was wavelet transformed, was verified by comparing the spectra of detail coefficient in each level using FFT. The behavior of detail coefficient obtained by wavelet transform reveals the possibility of detecting and analyzing chatter and other malfunction states using endmilling force. Because the wavelet transforms are closely related to filtering effect, the presented method can be applied to the other real-time cutting force monitoring and analysis in a various range of machining condition. Also, the standard deviation of detail coefficient in each level was discussed. In standard deviation analysis, it was proved that if there is a chatter in the machining, then the standard deviation ratio ranges from 2 to 2.2 in level 3 or level 4, which are optimal level. Finally, there are some force modelling methods in endmilling. For this purpose, the fractal interpolation method was used to estimate and analyze the endmilling force in this study. Due to the chaotic behavior of dynamic property in endmilling force, a desirable method must be introduced to represent this property well. As a result, it was proved that the fractal interpolation is one method to analyze the endmilling force prediction well. The fractal analysis discussed in this study is within the scope of the fractal interpolation and its dimension. Also, in analyzing the fractal dimension, two methods have been introduced. Using these two methods, the fractal dimensions in the endmilling force were analyzed. In real measured force, there are many factors that affects on the behaviors of endmilling force characteristics. In this sense, a fractal dynamic force modelling was investigated in several stage of endmilling using fractal methods.