1 Introduction
The emergence of virtual axis CNC machine tools is considered to be the most revolutionary machine tool design breakthrough of this century. If the structural advantages of this new machine tool are fully utilized, it is possible to open up a new way to greatly improve the performance of the machine tool.
Through analysis, it is found that for a virtual axis machine tool based on the principle of Stewart platform, the reasonable motion range of the rotating coordinate is much smaller than that of the conventional five-axis CNC machine tool (usually only 20 to 30 degrees, and the five-axis machine tool can reach 90 degrees or more. ), and as the angle of rotation increases, the effective working space of the machine tool is greatly reduced. Although the composite structure can expand the corner range, the structure is complicated and it is difficult to ensure high rigidity. Therefore, the ordinary virtual axis machine tool is not suitable for processing large-scale, multi-coordinate moving parts. However, from another point of view, the complex parts that require multi-coordinate machining in actual production are, after all, a few, and the dominant ones are the processing of ordinary conventional parts. Therefore, it is more practical to study how to use the structural characteristics of the virtual axis machine tool to exert its advantages in the high-speed and high-efficiency machining of conventional parts.
The basic idea of ​​the virtual axis machine simulation three-axis control method is to simulate the control method of the existing three-axis CNC machine tool, and control the six-degree-of-freedom movement of the virtual axis machine tool. From the external characteristics, the virtual axis machine tool and the conventional three Coordinate CNC machine tool equivalent. In this way, not only the existing mature three-coordinate automatic programming system can be directly used for the virtual axis machine with six degrees of freedom, but also the translation of the spindle unit by the imitation three-axis control, greatly expanding the work of the virtual axis machine tool. Space makes it play a bigger role. In addition, by simulating three-axis control, the complexity of the control system can be effectively reduced, thereby significantly reducing the cost of the machine tool, and facilitating the popularization and application of the new type of machine tool.
2 Advantages of conventional machining of virtual axis machine tools A typical structure of a virtual axis machine tool can be attributed to a so-called "six-bar platform structure". The specific meaning is that one end of six variable length drive rods (referred to as drive rods) is fixed on a static platform (such as a foundation or a machine tool frame), and the other end of the drive rod is coupled with the movable platform, that is, coupled to the spindle unit. Thus, adjusting the length of the six drive rods allows the spindle and tool to make the desired feed motion relative to the workpiece. By precisely controlling the feed motion by the control system, the workpieces that meet the requirements can be machined.
In view of the unparalleled advantages of conventional CNC machine tools, these advantages are necessary for high-speed, high-precision machining, so they are used as efficient machining equipment for conventional parts to maximize their advantages.
3 The basic principle of imitation three-axis control
Since there is no guide rail guided in a fixed direction in the virtual axis machine tool, the tool movement axes X, Y, Z, etc. required for NC machining do not really exist. Therefore, even if only three-dimensional tool motion is required (the attitude is constant only the position change), It is also necessary to perform six degrees of freedom control on the moving platform.
The imitation three-axis control method is a control method for simulating a conventional three-coordinate CNC machine tool according to the structural characteristics of the virtual axis machine tool. The starting point is that when machining a conventional part with a virtual axis machine, the tool mounted in the spindle only needs to perform three-dimensional translational motion, and its attitude is a fixed value. Thus, although the spindle unit fixed to the moving platform has six degrees of freedom of motion, only three translational degrees of freedom are involved in real-time calculations. For this purpose, the tool position is represented by the coordinates Xm, Ym, Zm of the tool center or end center in the machine coordinate system, and the displacement is calculated in real time by the three-coordinate interpolation algorithm. At the same time, a tool coordinate system whose origin is located at the center of the tool center or end face is established. The coordinate axes Xt, Yt and Zt are parallel to the Xm, Ym and Zm axes of the machine coordinate system. The attitude of the moving platform is represented by the rotation angle of the tool coordinate frame around the Xm, Ym, and Zm axes, and is set to a fixed value. In this way, real-time calculation and real-time control of the movement of the three coordinates of Xm, Ym and Zm are carried out on the moving platform, and the real-time control of the rotation of the moving platform around the Xm, Ym and Zm axes can be realized. The degree of freedom control, in turn, achieves the three-coordinate linkage control of the tool motion. Because this method does not require real-time calculation of the attitude of the moving platform, it can not only effectively reduce the calculation of the virtual and real mapping and linkage control, but also incorporate the control of the six-degree-of-freedom virtual axis machine tool into the conventional three-coordinate number S-controlled machine tool control. The scope of this new machine tool is controlled by means of a mature three-coordinate control method.
According to the structure of the virtual axis machine tool, since the directly controllable controlled amount in the machine tool is the length Li (i = 1, 2, ..., 6) of the six driving rods supporting the spindle components, that is, the actual movement axis of the machine tool ( Referring to the real axis), it is necessary to control the motion of the moving platform with full degree of freedom, so as to achieve precise control of the tool's motion trajectory. It is necessary to convert the moving platform motion command (virtual axis command) into the real axis space to execute and pass Realized inverse mapping of real axis space to imaginary axis space.
The operation process of the system is as follows: Firstly, the tool motion trajectory is generated in real time according to the input information given by the part NC program, that is, the desired motion amount of the tool along the Xm, Ym, Zm coordinates in the virtual axis space is solved; then, through the virtual real map calculation, The desired motion amount of the virtual axis is converted into the motion command value of the six-drive rod; finally, the length of each drive rod is decoupled and controlled, so that the actual length is consistent with the desired length, and the virtual structure is implicitly realized by the machine structure. The inverse mapping can obtain the tool motion trajectory that meets the requirements of the instruction and ensure that the tool attitude is a given constant value.
4 virtual axis space tool motion trajectory generation
The tool trajectory generation task is to convert the tool path given by the part NC program (the geometric curve in the imaginary axis space independent of time and machine characteristics) into discretes related to time and machine characteristics (such as acceleration and deceleration characteristics). Tool trajectory. The solution process is as follows:
Establishment of mathematical model
In order to ensure the accuracy of trajectory generation, a parameterized direct interpolation algorithm is adopted in the imitation three-axis control. The main point is to create a parametric mathematical model that is easy to calculate for the imputed curve:
x=f1(u)
y=f2(u)
z=f3(u) (1)
Where u is a parameter, u∈[0,1]
It is required to use the function calculation for real-time trajectory calculation, and it only needs to be added, subtracted, multiplied, and divided by a few times.
For example, for circular interpolation, the specific form of equation (1) is: (2)
In the formula, M is a constant matrix. When the interpolation point is in the first to fourth quadrants, the values ​​are:
r——Arc radius
In this way, the trajectory calculation can be performed in an absolute manner, that is, the calculation of the coordinates of each trajectory point is performed based on the origin of the model coordinates, thereby eliminating the accumulated error and effectively ensuring the speed and accuracy of the interpolation calculation.
Acceleration and deceleration control
In order to make the generated tool motion track meet the requirements of the machine acceleration and deceleration characteristics, the optimal acceleration and deceleration curve can be determined according to the dynamic characteristics of the machine tool and stored in the control system. During the system operation, first scan several blocks before and after, analyze the change trend of feed rate, determine the desired feed speed F; then read the feed speed override K on the operation panel, and use it to correct F, get the target Feed rate Fnew, Fnew=K
.
F; further, compare Fnew with the current feed speed Fold, and calculate the instantaneous feed rate Fk (mm/min) of the current sampling period according to the acceleration/deceleration characteristic curve of the machine tool.
Speed ​​and error control
Since the interpolation calculation is not a static geometric calculation, it must make the distance between the current interpolation point and the previous interpolation point meet the requirements of feed rate and acceleration and deceleration, and also ensure the interpolation line between the two points. The error between the segment and the interpolated curve is within a given tolerance. For this reason, it is necessary to control the interpolation straight line length Dtk with the instantaneous feed rate as the control target and the allowable error as the constraint condition.
The method is as follows:
First, according to the instantaneous feed rate Fk given by the acceleration and deceleration calculation, the desired chord length in the current sampling period (the length of the interpolation straight line segment without constraint) is calculated by the following formula: (3)
In the formula Dt1 - hope chord length, mm
T——sampling period, ms
Then, calculate the constraint chord length based on the error relationship of the sampling interpolation: (4)
Where e is the allowable error between the interpolated trajectory and the desired trajectory
r——The radius of curvature of the desired trajectory at the interpolation point Finally, the value of Dtk is determined according to the relative sizes of Dt1 and Dt2. That is, if the chord length Dt1 is desired to be smaller than the constraint chord length Dt2, the current interpolation straight line segment length Dtk=Dt1, otherwise Dtk=Dt2.
Interpolation trajectory calculation
The task of the interpolation trajectory calculation is: in each sampling period, the coordinate value of the current point on the interpolation trajectory is calculated in real time according to the interpolation straight line segment length Dtk obtained above. The calculation process is as follows:
First, find the Du of the current interpolation period based on the following relationship between the parameter increments Du and Dt: (5)
Du/ds in the formula - the rate of change of the parametric variable to the arc length of the curve
Due to the high interpolation frequency, the arc length is very close to the chord length in one sampling period, so du/ds≈Du/Dt can be made in the actual calculation. In this way, u is taken as an increment Du, and the corresponding Dt is obtained to obtain the desired du/ds.
Although this approximation has a small effect on the feed rate, it does not have any effect on the accuracy of the interpolation trajectory. In the sampling interpolation, the trajectory accuracy is the main contradiction. The coordinate calculation of the interpolation point must be absolutely accurate, and the accuracy of the interpolation point along the trajectory movement speed is in a secondary position, and a slight error can be allowed. The result obtained in this way not only ensures the accuracy of the trajectory but also increases the calculation speed.
Then, calculate the value of the current sampling period parameter: uk=uk-1+Du (6)
Finally, by substituting uk into equation (1), the coordinate values ​​xk, yk, zk of the current point on the interpolation trajectory can be calculated. The above process is repeated until the end of the interpolation is reached, and the entire discretized interpolation trajectory is obtained.
5 virtual and real mapping calculation
How to accurately control the length of the six-drive rod in the real-axis space according to the three-dimensional tool motion command value in the virtual axis space is another key problem for realizing the virtual axis machine simulation three-axis control. In order to solve this problem, the virtual axis motion command generated by the interpolation must be converted into a real axis control command, and the solution process is as follows:
Firstly, according to the requirements of the imitation three-axis machining, the spindle axis of the machine tool should be parallel to the normal of the table plane, and the initial attitude of the spindle is determined to be At=0, Bt=0. And determine the optimal preset position Ct0 of the platform Ct coordinates according to the shape of the part and the processing requirements.
Then, in the return reference point operation before the start of machining, the moving platform is moved to the state of At=0, Bt=0, Ct=Ct0, so that the tool axis is perpendicular to the work surface, and the tool attitude At=0, Bt=0. At this time, according to the structure of the moving platform, the initial positions pxi, pyi, pzi (i = 1, 2, ..., 6) of the upper six support points (the moving end points of the six driving rods) in the tool coordinate system can be obtained.
If the tool path command value generated by the three-axis interpolation calculation is Xk, Yk, Zk at time k, the coordinate value of the 6-end end point in the tool coordinate system should be unchanged to ensure the tool attitude is constant. The coordinate value of the moving end of the drive rod in the machine coordinate system: Xdi=Xk+Pxi
Ydi=Yk+Pyi (i=1,2,...,6)
Zdi=Zk+Pzi (7)
According to the moving end coordinates of the six driving rods obtained above and the static end coordinates of the machine structure, the desired value of the length of each driving rod at time k can be obtained by the following formula, that is, the real axis corresponding to Xk, Yk, Zk Coordinate values: (8)
Where Xji, Yji, Zji - the coordinate values ​​of the six-driver static end point in the machine coordinate system
6 Real-axis space six-axis linkage control
The virtual axis space tool path generation is a kind of coarse interpolation. When the feed rate is high, the coarse interpolation line segment will be longer. Therefore, in order to ensure the smoothness of the linkage of the six drive rods, the following fine interpolation can be performed in the real axis space.
First, the interpolated straight line segment of the imaginary axis space (three-dimensional space) is transformed into a straight line segment of the real-axis space (six-dimensional space) by the virtual-real map, and its length is: (9)
In the formula, Li0——the real axis coordinate value at the beginning of the coarse interpolation period, then find the moving distance of the real axis space trajectory in each fine interpolation period: Dl=L/(T1/T2) (10)
Where T1, T2 - coarse, fine interpolation sampling period, ms
Therefore, the amount of movement of each of the driving rods from the beginning of the straight line segment to the end of the nth fine interpolation period is: DLin = n × Dl × (Li - Li0) / L (i = 1, 2, ..., 6) (11 )
Further, the actual value of each drive rod length at time n can be obtained by the following formula, that is, the real axis motion command value is: Lin=Li0+DLin (i=1, 2,...,6) (12)
Finally, through the decoupling follow-up control system [3] to ensure that the actual length of the drive rod is consistent with the desired length, real-axis linkage control that meets the requirements of the tool path can be achieved.
7 System realization According to the proposed method, a virtual axis machine tool simulation three-axis control system is developed. The basic composition is shown in Figure 3. Based on the Pentium II microcomputer system, the system is equipped with a self-developed interface card on its expansion bus to exchange information between the control system and the drive system. The CNC system software is implemented by C language + 32-bit assembly language mixed programming.
When the system is working, the operator can input the required information through the I/O device such as a floppy disk drive, and can modify the input information through the advanced editing function provided by the system. The operation of the machine tool is controlled by the operator through the computer keyboard and the numerical control operation panel. The information about the system operation is displayed in the form of graphics and data through the color CRT.
The system uses the high-precision digital AC servo system for the real axis L1～L6 of the machine tool to drive control, and each axis adopts closed-loop control mode. The detection device uses a high-precision grating to ensure the displacement accuracy of the real axis.
The switch quantity control part of the system is used to control the logical sequence movement of the machine tool, such as controlling the tool change, pallet exchange, spindle start and stop, cooling system, stroke protection and other aspects of operation. The switch quantity control part will cooperate with the servo control to complete the control of the machine tool working process.
8 Conclusion
The virtual axis machine tool has the advantages of simple mechanical structure, high rigidity, and high speed machining, but also has the disadvantages of small effective rotation angle of rotating coordinates and narrow working area when multi-coordinate machining. Therefore, it should be used in the high-speed, high-efficiency processing of conventional parts. By simulating three-axis control, the complexity of the control system is effectively reduced, thereby significantly reducing the total cost of the machine tool, and facilitating the promotion of the virtual axis machine tool in a large range.
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