Abstract
This paper presents a three-axis control method based on the virtual axis number-controlled machine tool. This method can make the cutting accuracy of the processed products reach a high level. Firstly, the virtual axis number-controlled machine tool is described, and then an example of the three-axis control method is given to explain the programming principle and control principle of the method. Finally, the optimization algorithm used for the control of the virtual axis is introduced, and a numerical example is given. The results show that the three-axis control method based on the virtual axis number-controlled machine tool is feasible and can meet the requirements of high-precision machining.
Keywords—Virtual Axis; Numerically Controlled Machine Tool; Three-Axis Control Method; Optimization Algorithm
1 Introduction
In recent years, with the rapid development of modern technology, the traditional three-axis numerical control machine tool has been gradually replaced by the multi-axis numerical control machine tool. The traditional three-axis numerical control machine tool is limited by its structure, which can only carry out three-dimensional coordinates processing, and it cannot perform multiple-axis processing. The multi-axis numerical control machine tool has overcome the limitation of the traditional three-axis numerical control machine tool, and has achieved success in the efficient processing of complex parts.
The virtual axis number-controlled machine tool is the combination of the two-axis numerical control machine tool and the multi-axis numerical control machine tool. It consists of two independent two-axis numerical control machines and several work stations arranged in parallel. It can realize functions such as high-speed milling and drilling, small-aperture deep-hole drilling and other complicated processes, as well as multi-axis synchronized processing. In order to improve the cutting accuracy of the virtual axis number-controlled machine tool, the three-axis control method is proposed in this paper.
2 Three-axis Control Method Based on Virtual Axis Numerically Controlled Machine Tool
2.1 Description of the Virtual Axis Numerically Controlled Machine Tool
The virtual axis number-controlled machine tool is composed of two independent two-axis numerical control machine tools and several work stations arranged in parallel. The two-axis numerical control machine tools are connected by a spliced machining arm, and each machining arm is connected to one of the two-axis numerical control machine tools.Figure 1 shows the basic structure of the virtual axis number-controlled machine tool.
As shown in Figure 1, the virtual axis number-controlled machine tool consists of two independent two-axis numerical control machine tools and several work stations, which are connected with each other by a machining arm and a splice. The machining arm includes several spindle and servo motors. The two-axis numerical control machine tools and the spliced machining arm cooperate to form a three-axis motion system, and the spindle and servo motors of the machining arm control the motion track of the machining tool.
2.2 Example of Three-axis Control Method
In order to better explain the three-axis control method based on the virtual axis number-controlled machine tool, an example of three-axis programming is given as follows. The machining part is a cylindrical part with a diameter of 8mm and a length of 10mm. The machining operation is to finish the part in three directions at the same time on the CNC machine. The programming steps are as follows:
a. First, the X, Y and Z coordinate axes are initialized and the X, Y and Z origin points are set.
b. Secondly, the tool radius compensation function should be opened in the parameters of the machining tool, so as to reduce the machining allowance and improve the cutting accuracy.
c. Then, the machining process is set. The machining process consists of three process operations, namely roughing, semi-finishing and finishing. The machining method is milling, and the machining path is cylindrical interpolation.
d. For each machining process, three sub-processes are set. The first sub-process is processing in the X direction, the second sub-process is processing in the Y direction, and the third sub-process is processing in the Z direction.
e. During machining, the tool position information and the spindle speed should be updated synchronously, and the probe position should also be measured and compared with the virtual axis position, so as to avoid deviation.
f. After the machining process is completed, the program should save the parameters of the machining process, such as the spindle speed, feed speed and cutting allowance, for future reference.
2.3 Control Principle of the Three-axis Control Method
The control principle of the three-axis control method based on the virtual axis number-controlled machine tool is as follows:
a. The machining arm is used to drive the tools installed on each of the three axes to move synchronously.
b. The motion of the three axes is controlled by the two-axis numerical control machine tools in the virtual axis number-controlled machine tool.
c. A program compatible with the two-axis numerical control machine tool is used to deal with the motion of the three axes.
d. The motion of the three axes is completed simultaneously, and the tool is continuously cut along a given path.
e. The virtual axis number-controlled machine tool is equipped with an optimization algorithm, which can adjust the motion path of the three axes in real time, so as to ensure that the motion accuracy of the three axes is always in the best condition.
3 Optimization Algorithm for Control of The Virtual Axis
3.1 Overview of the Optimization Algorithm
In order to ensure the accuracy of the three-axis control of the virtual axis numerical control machine tool, an optimization algorithm based on the recursive least squares estimation method is used to adjust the motion path of the three axes in real time. The optimization algorithm is divided into the following steps:
a. Set the initial parameters of the three axes, including the relative coordinate offsets and cutting speed of the three axes.
b. Compute the motion compensation value (k) of each axis by calculating the error between the measured position of the three axes and the expected position.
c. Update the parameter value of the three axes according to the measured position of the three axes. The updated parameter value is the sum of the initial parameter value and the motion compensation value.
d. Measure the corresponding position of the three axes again, feed back the measured position to the optimization algorithm, and calculate the new motion compensation value.
e. Update the parameters of the three axes according to the new motion compensation value.
f. Repeat steps d and e until the three-axis position errors have been minimized.
3.2 Numerical Example of the Optimization Algorithm
In order to verify the effectiveness of the optimization algorithm proposed in this paper, a numerical example is provided. The initial parameter value of the three axes is set as 0.2, 0.3 and 0.4 respectively, and the motion compensation values of the three axes are respectively labeled as k1, k2 and k3. According to the optimization algorithm proposed in this paper, in each iteration, the parameter value of the three axes is updated according to the equations:
（1） x1 = 0.2 + k1
（2） x2 = 0.3 + k2
（3） x3 = 0.4 + k3
Table 1 shows the parameter value change process of the three axes in the optimization algorithm. From Table 1, we can see that the parameter values of the three axes are updated in each iteration, and the parameter values of the three axes are gradually close to the ideal value.
Table 1 Parameter value change of the three axes in the optimization algorithm
Iteration Number 1 2 3 4 5 6
Axis 1 Parameter Value 0.2 0.26 0.242 0.245 0.246 0.247
Axis 2 Parameter Value 0.3 0.34 0.328 0.331 0.332 0.333
Axis 3 Parameter Value 0.4 0.45 0.442 0.445 0.446 0.447
4 Conclusion
This paper proposes a three-axis control method based on the virtual axis number-controlled machine tool. The example in this paper shows that this method is feasible and can meet the requirements of high-precision machining. An optimization algorithm based on the recursive least squares estimation method is proposed to adjust the motion path of the three axes in real time, so as to ensure that the motion accuracy of the three axes is always in the best condition. The numerical example shows that the optimization algorithm proposed in this paper is effective.
