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1、 Development of a 3-axis Desktop Milling Machine and a CNC System Using Advanced Modern Control Algorithms 1. Introduction As new fields such as IT(Information Technology), BT(Bio Technology) and NT(Nano Technology) emerge as a driving force in the industry, the interests in micro-factory system hav
2、e been growing. The micro-factory is a miniaturized flexiblemanufacturing system which consumes minimal space and energy compared to theconventional one, and it is desired to produce micro/meso size mechanical components necessary for IT, BT and NT applications. Major technical units contributing to
3、 micro mechanical machining systems are,to name a few, high speed spindlesystems, micro high precision feeding systems, control systems to generate coordinated motions, tooling and chucking systems, frame design and module allocationschemes based upon optimization for high stiffness. Researchers hav
4、e been trying to put micro technologies together to build micro-factory systems which make micro/mesosize precision parts to meet the needs from the manufacturing industry.1 In this paper, we present a miniaturized 3-axis milling machine and a dedicated CNC system for the machine. The 3-axis milling
5、 machine is constructed as one of micro-factory module and designed to produce high precision micro parts. It has a desktop size of 200300200 mm3 and is serving as our testbed machine.From finite element analysis and an impact hammer test, we have verified that ithas a good structural stiffness and
6、high natural frequencies. A high speed air turbine spindle on the horizontal z-axis can run at up to 160,000 rpm. This 3-axis milling machine was put under real machining tests and it successfully demonstrated its machining capabilities. A CNC system was developed for operation of the 3-axis desktop
7、 milling machine. The CNC system includes a G-code interpreter which can process a basicset of G-codes and M-codes in real-time. The CNC system consists of two parts.The one is agraphical user interface which runs under Microsoft Windows, andthe other is a DSP program which interpolates commands and
8、 executes a real-time servo control. Two parts communicate each other through a dual port RAM(Random Access Memory). Job assignments for the two parts are discussed in detailin this paper. To improve the performance of the CNC system for the 3-axis milling machine beyond the traditional PID-type con
9、trol, different control schemes have been tested including H control, input shaping control, disturbance observer and cross-coupled control on the 3-axis milling machine. The rest of this paper is organized as follows. Sec. 2 presents the design of the 3-axis milling machine. The results of the fini
10、te element analysis and the natural frequencies obtained from the impact hammer test are given in this section. In Sec 3, a PC-based CNC system developed for the 3-axis milling machine is discussed. Several modern control schemes including H control design, input shaping control, disturbance observe
11、r, and cross-coupled control are discussed with their experimental results to show their effectiveness and drawbacks in Sec 4. The concluding remarks will be given in Sec. 5.2. Design of a 3-axis Milling Machine Micro machine tools are required to have high machining accuracy while providing enough
12、stiffness. To estimate basic machining performance and stiffness of a micro machine tool, a miniaturized 3-axis milling machine was built and used as a testbed. Fig. 1 shows the 3-axis milling machine and its specifications. It has a mini-desktop size of 200300200 mm3 and its cut-ting volume is 2020
13、20 mm3. The vertically installed XY stage is driven by voice-coil motors, and for the z-axis, a magneticallypreloaded air bearing and a linear motor are used. The air spindle runs at up to 160,000 rpm and it is fast enough for high precision machining. A weight balancer using an air bearing cylinder
14、 is installed to counteract the gravity force acting on the XY stage in the y-direction. A small cutting force dynamometer is also installed underneath the work table to monitor the cutting process. Fig. 2 shows a picture of the 3-axis milling machine.2.1 Static and Dynamic Analysis Finite element a
15、nalysis was done to investigate the static and dynamic characteristics of the designed 3-axis milling machine using a finite element model as shown in Fig. 3. The computational results showed that the deflection due to its own weight was negligible. When a 10N force was located at the machining posi
16、tion in z-direction, the numerical results showed that the displacement change at the work table would be about 0.07 ., and the back fame would undergo less than 0.02 . deflection in z-direction. It seems that the 3-axis milling machine has good stiffness due to good frame design and a pair of small
17、 LM guides supporting each x- and y-direction. The modal analysis revealed many important dynamic modes of the 3-axis milling machine. We used the impact hammer test to verify the computed natural frequencies. The measured natural frequencies do not exactly match the computed ones, but the indicated
18、 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 3-axis milling machine. It can be seen that the natural frequencies of z-axis stage,
19、which is supposed to be low in stiffness due to its air bearing, locate at a range of 250390 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 3-axis milling machine has higher natural
20、 frequencies than conventional machine tools.3. A CNC System3.1 Graphical User Interface ProgramA PC-based CNC system was developed for the 3-axis 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
21、 runs on MS-Windows and processes user inputs. The DSP part receives thousands timer interrupts per second and interprets commands in real-time for each axis of a machine and executes servo control loops. Two parts share a dual port RAM and communicate each other through it. Fig. 5 shows the graphic
22、al 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 G-codes when the user interface program reads in a G-code file. The curre
23、nt 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 G-code file. Users can also use contouring function which merges line segments and arcs which are tangent, or nearly tangent, into a single smooth motion withou
24、t stopping at each end-point. 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 M-codes M21 and M22. Currently implemented G-codes and Mcodes are G00 (Rapid Motion), G01 (Linear Motion), G02 (CW Circular Arc), G03 (CCW
25、 Circular Arc), G04 (Dwell), G17 (X-Y Plane Selection), G18 (Z-X Plane Selection), G19 (Y-Z Plane Selection), M21 (Contouring On), M22 (Contouring Off), M30(Program End & Reset). When a user click the Open G-code button, a whole G-code file is read in and saved in a memory area, and then the G-codes
26、 appear at the bottom left list box. When the Start G-code button is clicked, the user interface program takes out a line from the memory and checks its syntax and identifies all the meaningful tokens. During preprocessing a G-code line, the user interface program is supposed to compute, a motion pl
27、ane, a driving axis, maximum allowable velocity and acceleration, the starting position of the deceleration, directional cosines. If the G-code line is about circular motion, the center point of the arc, the normal direction of the arc, and start and end angles are also computed by the user interfac
28、e program. All the preprocessed information is entered in the DPRAM and handed to the DSP program. A circular buffer in the DPRAM has rooms for only 4 lines of G-codes, so the user interface program needs to keep monitoring the circular buffer usage. When the user interface program finds that the DS
29、P program finishes carrying out a G-code line and empties its space, it fills in the empty space in the circular buffer with a new preprocessed G-code line in the order in which they occur.3.2 DSP Program The DSP program interpolates the preprocessed G-codes in real-time and generates position comma
30、nds for multiple axes to follow. It also closes servo control loops. Generally a sampling rate is set to be ten times larger than the bandwidth of a plant to be controlled. The developed CNC system adopted a sampling rate of 2,000 Hz for the servo loops. The DSP program takes out a G-code line from
31、the circularbuffer and computes the angle between two successive G-code lines. If the angle is less than a certain (predefined) degree and the contouring is on, it sets a flag so that the tool path does not reduce its velocity when it enters into the next segment. When a timer interrupt occurs, the
32、DSP program computes the desired velocity and position of each axis and generates commands for the servo control loop. The computed velocity should be less than the maximum allowable velocity computed by the user interface program and start decreasing when the position reaches the position of decele
33、ration to make a complete stop at the end point if contouring function is not used. If the current motion is linear, all the computations are for the driving axis and commands for the other axes are calculated from straight-line equations related to the driving axis. If the current motion is circula
34、r, angular velocity and angular acceleration are similarly used as in the linear motion and the final commands are made from the polar coordinate to the Cartesian coordinate transformation. After generating real-time commands for each axis the DSP program drives the servo control loops of the 3-axis
35、. The errors which are differences between the commands and the actual feedback positions are fed into a control algorithm such as PID and the control signals for the motor drives are computed.4. Control System Design To improve the performance of servo control for the 3-axis milling machine, severa
36、l control algorithms have been tested on the 3-axis milling machine. They include PID, H control, input shaping control, disturbance observer, and cross-coupled control. These control schemes were digitally implemented on a Daytona DSP board from Spectrumsignal Co. The DSP board has two TI320C6701 c
37、hips on it and a sampling rate of 2,000 Hz has been used. The design procedure and experimental results from each control are described as follows.4.1 H Optimal Control Design Using a conventional PID controller for the z-axis which has a linear motor and air-bearing, it seemed that high gain PID ea
38、sily started oscillations. As an alternative, an H controller was designed and applied to the z-axis and performance of hand tuned PID and H control is compared. An open-loop plant model for control design was obtained from experimental frequency response data. The frequency responses were measured
39、with a dynamic signal analyzer using a swept sine method that generates fixed-amplitude sine waves of varying frequencies. From the frequency responses for different input amplitudes, an averaged frequency response wascomputed and a nominal continuous-time plant model was fitted.Fig. 6 shows the ave
40、raged frequency response and a nominal open-loop plant model. A second order plant model was obtained from the curve fit. The identified open-loop plant model G(s) forthe z-axis wasWe can see that the z-axis has a complex pole pair at around 4.5Hz. When a PID-type controller in a typical digital for
41、m ofwhere u(k) is controller output, e(k) is error signal, T is samplingperiod, and z is a delay, is applied to the plant, it turns out that a high gain PID can easily excite the oscillatory mode of the plant. To avoid so-called derivative kick, the derivative gain Kd was forced to act on the deriva
42、tive of the actual position, not on the derivative of the position error, i.e. Kd (1-z-1)/T is multiplied by the negative position feedback, y(k) instead of e(k) at Eq. (2). For the z-axis, using the derivative of position instead of that of position error allowed more aggressive PID gains. Based on
43、 the plant model at Eq. (1), the control loop employed an H robust controller at 2 kHz sampling frequency. A mixed sensitivity problem was solved to design an H controller in continuous-time and the resulting continuous time controller was converted to a discrete-time model. The mixed sensitivity sp
44、ecification for H control design in continuous-time waswhere S(s) is the sensitivity function, T(s) is the complementary sensitivity function, K(s) is the desired H controller, 1/|wp(s)|, 1/|wt(s)| and 1/|wu(s)| put upper bounds on the magnitude of S(s) (for performance), T(s) (for noise attenuation
45、) and K(s) S(s) (to penalize large inputs), respectively. The H optimal controller was obtained by solving the problem2Fig. 7 shows other design parameters used in the z-axis control design and the final sensitivity function from the computed H controller. The final sensitivity function S(s) clearly
46、 shows that the H controller has double integral action in low frequency range as intended with the shape of 1/|wp(s)|. The designed H controller was converted to a discrete-time controller K(z) for a 2 kHz sample and hold rate and implemented on a DSP board for tests. The final H controller K(z) wa
47、s a 5th order controller.The classical feedback sensitivity function S(s) is the transfer function from the reference signal r(t) to the control error signal e(t), i.e. e(t) = S(s)r(t). To compare tracking performance between the designed H controller and PID controller, a fixed-amplitude sine wave
48、of varying frequencies was injected as a command signal and the corresponding error signal was measured and the ratio of their magnitude versus frequency was plotted in Fig. 8. Thus it is an empirical sensitivity function plot and we can estimate the level of tracking performance from this plot. The
49、 H controller shows 0.4% tracking error for 1 Hz sine command, but 10% from PID controller in this particular design. It is due to the intended double integral action from H control design. Similarly other H controllers were designed for the x- and y-axes but the tracking performance from H control was similar to that from PID control in the x- and y-axes which have voice coil motors and LM guides.A circular referenc