【正文】 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。它的尺寸為 200 300 200 mm3，作為我們的測(cè)試機(jī)床。 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)。它的工作臺(tái)體積為 200 300 200 mm3，加工范圍為 20 20 20 mm3。 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。兩部分共享一個(gè)雙向 RAM，并通過(guò)它進(jìn)行信息傳遞。當(dāng)點(diǎn)擊開(kāi)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(yǔ)法，判斷所有有效的記號(hào)。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。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。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。水平工作臺(tái)安裝了運(yùn)用空氣軸承的平衡塊來(lái)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(guò)程。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)。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。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 observed as shown in Fig. 11. To cope with the oscillations while radical acceleration, an input shaper was considered being inserted in the inner feedback control loop. After giving large step mands, the xaxis’ damping ratio ζ was estimated to be and natural frequency ω to be rad/sec. From Eq. (8) and (9), an input shaper was constructed as an FIR filter and the designed input shaper was put in the servo loop to preshape the mand before the H∞ controller. The experimental results with a 3 mm step mand are shown in Fig. 11. The input shaper could not cancel out the oscillations pletely but, pared to the H∞ controller only case, it could reduce the oscillations significantly when the xaxis received large step mands. The convolved mand through the input shaper usually increases in length so the overall maneuvering time also increases when an input shaper is used. That is the cost to pay for reducing oscillations. For small step mands including micro steps, the responses with the input shaper were similar to those without the input shaper. It is found that the input shaper can improve the dynamic behavior when acceleration or deceleration is large, but it may hurt vector coordinated motion between multiple axes because it reshapes the spatial reference trajectories which are supposed to be synchronized. Thus, the input shaper may be safely used when an axis is controlled to move with high acceleration but two or more axes are needed to generate a coordinated motion path in synchronization, the input shaper of each axis should be designed to have the same time delays. Disturbance Observer In directdrive systems there are no gear reduction effects to help attenuate disturbance forces at the load, and thus a disturbance observer provides a convenient method for enhancing the disturbance rejection. The a