【正文】 actly match the puted ones, but the indicated frequency range from the finite element modal analysis was similar to that from the impact hammer test. Fig. 4 and Table 1 show the measured natural frequencies and corresponding frequency response function of the 3axis milling machine. It can be seen that the natural frequencies of zaxis stage, which is supposed to be low in stiffness due to its air bearing, locate at a range of 250~390 Hz. The natural frequency of the XY stage shows at about 400 and 710 Hz and, for the back frame, it is around 440 and 640 Hz. It seems that the designed miniaturized 3axis milling machine has higher natural frequencies than conventional machine tools. 3. A CNC System Graphical User Interface Program A PCbased CNC system was developed for the 3axis milling machine. The developed CNC system has two parts, a graphical user interface program in the PC part and a DSP program in the DSP part. The PC part runs on MSWindows and processes user inputs. The DSP part receives thousands timer interrupts per second and interprets mands in realtime for each axis of a machine and executes servo control loops. Two parts share a dual port RAM and municate each other through it. Fig. 5 shows the graphical user interface of the developed CNC system and its brief explanations. One of the major features of the user interface program is a 3D plot window at the bottom right corner in Fig. 5. It displays the tool path described in Gcodes when the user interface program reads in a Gcode file. The current tool position also appears as a small red dot on the screen so that CNCusers can easily identify where the machining process goes in the Gcode file. Users can also use contouring function which merges line segments and arcs which are tangent, or nearly tangent, into a single smooth motion without stopping at each endpoint. Contouring can be turned on and off manually while a program is running, or it can be turned on and off by the program itself using Mcodes M21 and M22. Currently implemented Gcodes and Mcodes are G00 (Rapid Motion), G01 (Linear Motion), G02 (CW Circular Arc), G03 (CCW Circular Arc), G04 (Dwell), G17 (XY Plane Selection), G18 (ZX Plane Selection), G19 (YZ Plane Selection), M21 (Contouring On), M22 (Contouring Off), M30(Program End amp。 用于微型機(jī)械加工系統(tǒng)主要的技術(shù)單元有高速主軸系統(tǒng)、高精度進(jìn)給系統(tǒng)、協(xié)調(diào)運(yùn)動(dòng)控制系統(tǒng)、工裝和 chucking系統(tǒng)、框架設(shè)計(jì)以及基于高剛度優(yōu)化的模塊分配系統(tǒng)。它的尺寸為 200 300 200 mm3，作為我們的測(cè)試機(jī)床。 數(shù)控系統(tǒng)用于操作三軸工作臺(tái)銑床，它包括一個(gè) G指令譯碼器，能實(shí)時(shí)編輯基本的 G指令和 M指令。 本文其余內(nèi)容如下：第二部分介紹了三軸銑床的設(shè)計(jì)。第五部分給出結(jié)論。它的工作臺(tái)體積為 200 300 200 mm3，加工范圍為 20 20 20 mm3。 圖 1 三軸銑床及其參數(shù) 圖 2 三軸銑床圖 本文運(yùn)用了有限元模型對(duì)設(shè)計(jì)的三軸銑床進(jìn)行了有限元分析用以研究其靜態(tài)和動(dòng)態(tài)性能，如圖 3所示。 圖 3 10N力下的有限元模型及靜態(tài)分析 模型揭示了三軸銑床許多的動(dòng)態(tài)特性，我們運(yùn)用沖擊錘測(cè)試證實(shí)計(jì)算的固有頻率。這表明所設(shè)計(jì)的微型三軸銑床擁有比傳統(tǒng)機(jī)床更高的固有頻率。兩部分共享一個(gè)雙向 RAM，并通過它進(jìn)行信息傳遞。成一個(gè)單一的平滑的運(yùn)動(dòng)不間斷地每一個(gè)終端。當(dāng)點(diǎn)擊開啟 G指令按鈕時(shí)，用戶界面程序從內(nèi)存讀取一行，檢查語法，判斷所有有效的記號(hào)。 DPRAM中的。如果 G指令行是關(guān)于圓弧運(yùn)動(dòng)的，用戶界面程序?qū)?huì)計(jì)算圓弧的中心、正方向、起止角。目前，可供執(zhí)行的 G指令和 M指令有 G00（快速移動(dòng) ),G01(直線運(yùn)動(dòng) ),G02(順時(shí)針圓弧運(yùn)動(dòng)）、 G03（逆時(shí)針圓弧運(yùn)動(dòng)）、 G04（暫停）、 G17（選擇 x y平面 ),G18(選擇 ZX平面 ),G19(選擇 YZ平面）、 M21（輪廓開啟）、 M22（輪廓關(guān)閉）、 M30（程序結(jié)束和重置）。用戶界面程序的一個(gè)主要特點(diǎn)是在右下角有一個(gè)三維圖窗口，如圖 5所示。 PC 部分用 MSWindows 和用戶輸入。圖 4和表 1顯 示了測(cè)得的固有頻率和三軸銑床相應(yīng)的頻率響應(yīng)函數(shù)，可以看出而本以為因空氣軸承可能會(huì)有較低的剛度的 Z軸的固有頻率范圍為 250~390Hz。當(dāng)把 10N的力加載到 Z方向的加工位置處時(shí)， 數(shù)值計(jì)算結(jié)果表明 ,工作臺(tái)處位移改變量大約為 ,而背面的 Z方向偏差 小于 。水平工作臺(tái)安裝了運(yùn)用空氣軸承的平衡塊來抵消 Y方向上的重力的作用，工作臺(tái)下邊還安裝了小切削力功率計(jì)用以監(jiān)測(cè)加工過程。為了估計(jì)微型機(jī)床基本的機(jī)械加工性能和剛度 ,我們?cè)O(shè)計(jì)了一個(gè)微型三軸銑床并將其作為測(cè)試機(jī)床。在第三部分中，我們討論了基于 PC的用于三軸 銑床的數(shù)控系統(tǒng)。這兩部分通過一個(gè)雙向 RAM（隨機(jī)讀取存儲(chǔ)器）傳遞信息，兩部分的工作分配在這里進(jìn)行詳細(xì)的討論。水平 Z軸方向上的高速空氣渦輪主軸的轉(zhuǎn)速可達(dá)到 160,000rpm。 本文中 ,我們描述了一種微型三軸銑床及其數(shù)控系統(tǒng)。5 μm over all areas. A feedforward controller such as ZPETC (ZeroPhase Error Tracking Control) takes approximately an inversion of plant dynamics and it requires an accurate plant model. In the yaxis, the feedforward controller was inserted to reduce the error peak at around 0 degree, where the air cylinder counteracting gravity force change its moving direction. It seems that the plant model of yaxis did not capture well the nonlinear characteristics of the air cylinder especially when the yaxis changes direction in motion and that is why the feedforward controller did not show any significant improvement. Effect of Input Shaper The input shaper involves realtime shaping or timedelay filtering of the reference mand to stable systems with the objective of minimizing the residual vibration. It is natural that giving the system an impulse will cause it to vibrate. If a second impulse is given to the system with appropriate amplitude when the system undergoes a half of vibration cycle from the first impulse, it is possible to cancel out the vibration induced by the first impulse with the opposite phase vibration by the second impulse. This is the main idea behind the input shaper. If we have a reasonable estimate of the system’s natural frequency, ω, and damping ratio, ζ, then the residual vibration that results from a sequence of impulses can be described by: If the impulse sequence given at Eq. (8) is convolved with any desired mand signal and the convolution product is then used as the mand to the system, the convolution product will also cause no vibration. The convolution can easily be implemented as an FIR filter designed from Eq. (8) and (9). An H∞ controller was designed for the xaxis similarly as above described. Step responses from an experiment and simulation are pared in Fig. 10. Though the simulation does not show any overshoot, the real system showed 9% overshoot for a step mand with a magnitude of 1 mm. Reflecting that some overshoot may be arguably desirable to get prompt responses from control system, the step response from H∞ control was considered acceptable. When step mands with bigger than 1 mm steps are given, more oscillatory behavior could be obser