1. Introduction
The application of linear motors in machine tool feed servo systems has gained increasing attention in the global machine tool industry in recent years. In machine tool feed systems, the biggest difference between using a linear motor for direct drive and the original rotary motor transmission lies in...
In particular, it eliminates all intermediate mechanical transmission links between the electric motor and the worktable (slide), shortening the length of the machine tool feed transmission chain to zero. This transmission method is called "zero transmission." Because of this "zero transmission" method, it brings performance indicators and certain advantages that the original rotary electric motor drive method could not achieve.
Improving the positioning accuracy of the linear motor feed system is one of the keys to its application in CNC machine tools. Therefore, testing and compensating for the positioning error of the linear motor feed is of paramount importance. The dual-frequency laser interferometer is a measuring device specified in international machine tool standards for testing and accepting the positioning accuracy of CNC machine tools [3]. This paper introduces the method of testing the positioning error of CNC linear motor feed using a dual-frequency laser interferometer. The linear model, piecewise linear model and polynomial model of the positioning error are established by using the least squares method, and the positioning error of CNC linear motor feed is compensated. The study shows that the software compensation method can greatly improve the positioning accuracy of the linear motor feed.
2. Linear Motor Feed Positioning Accuracy Test Method
The factors that cause positioning accuracy errors in linear motor feed are complex. The main factors are: (1) manufacturing and installation errors of the grating ruler. The moving part and the fixed part of the grating ruler are installed on the mover and stator base plates of the feed unit, respectively, which inevitably produces certain linear errors; (2) the edge effect of the linear motor causes the force characteristics at both ends of the feed unit to change, affecting the braking of the feed platform, thus producing positioning accuracy errors; (3) random errors caused by the environment. Since no vibration isolation foundation is used, random vibrations of the surrounding environment will be transmitted to the feed unit and the laser interferometer, thus producing errors.
The linear motor feed positioning accuracy was tested using an ML10 laser interferometer from Renishaw, UK. The ML10 laser interferometer provides a high-precision standard for machine tool calibration, offering high accuracy, a large measurement range (linear measurement length 40m, selectable 80m), fast measurement speed (60m/min), high resolution (0.001μm), and good portability. Furthermore, the Renishaw laser interferometer features automatic linear error compensation, facilitating the restoration of machine tool accuracy.
The testing method is as follows:
1. Install all components of the dual-frequency laser interferometer measurement system (see Figure 1).
2. Install an optical measuring device along the feed axis of the linear motor to be measured.
3. Adjust the laser head so that the measuring axis is in a straight line (or parallel) to the axis of the linear motor, that is, align the optical path.
4. Input the measurement parameters after the laser has preheated.
5. Perform the measurement using a linear motor according to the prescribed measurement procedure.
6. Data processing and result output.
In the experiment, the linear motor used a grating ruler as its position sensor , with a resolution of 1 μm and a maximum sampling speed of 1 m/s. To ensure accurate and stable readings, the laser interferometer was set to an accuracy of 0.1 μm (up to 1 nm). The test environment is shown in Figure 3. The environmental conditions at the test site were as follows: atmospheric pressure: 102.53 kPa; room temperature: 21.03 °C; relative humidity: 70.25%; linear motor temperature: 22.07 °C.
To comprehensively and objectively reflect the positioning accuracy of the linear motor feed, corresponding positioning accuracy tests and analyses were conducted under different speeds, accelerations (decelerations), and position conditions. Within a 200mm stroke range, under different speed and acceleration conditions, the positioning accuracy of the feed unit was tested, with a feed step size of 10mm. The test results are shown in Figure 2.
3. Establishment of Linear Motor Positioning Error Model and Software Compensation
Figure 2 shows that: (1) the positioning accuracy increases with the increase of displacement, and the growth rate of accumulated error is different in different position segments; (2) the positioning accuracy has good consistency under different conditions, indicating that the changes in velocity and acceleration have little impact on the positioning accuracy.
In view of the distribution of positioning accuracy (Figure 2), in order to study the effect of various fitting methods, the least squares method was used to reduce the positioning accuracy error by linear, piecewise linear and cubic spline fitting methods on the average positioning accuracy of Figure 1. Compared with linear and piecewise linear fitting, cubic spline fitting retains the advantages of piecewise low-order interpolation and improves the smoothness of the interpolation function, and is increasingly widely used in many fields [5]. The following function was obtained by fitting.
Equation (1) is the linear fitting model, Equation (2) is the piecewise linear fitting model, and Equation (3) is the cubic spline fitting model. The average positioning accuracy at each point is compared with the fitting results in Figure 3. It can be seen that the fitting effect of the piecewise linear model and the cubic spline model is significantly better than that of the linear model. However, the fitting effect of the piecewise linear model at the junction points is worse than that of the spline model; therefore, the cubic spline model is chosen as the actual error compensation model. The maximum deviations of the average positioning accuracy from the polynomial model curve in the positive and negative directions are 1.17 μm and -1.50 μm, respectively, indicating that the spline model can better reflect the actual positioning accuracy.
To improve the positioning accuracy of the linear motor, the distribution curve of the cumulative lead error of the linear motor is predetermined (here we use the distribution curve obtained by Formula 3). Then, based on the distribution curve, the positions where the error increases or decreases are used as feature points, and the points are divided at unequal intervals to obtain the cumulative position error value of each point relative to the absolute zero point. This error data file is stored in the system by a PC for querying and compensation during processing.
When the system is working, the computer obtains the displacement value of the linear motor based on the feedback signal from the grating ruler, and uses this value as a query pointer. The corresponding cumulative error value is then retrieved from the pointer, and the displacement is compensated and corrected based on the error value.
To verify the positioning accuracy of the feed unit after compensation, the positioning accuracy of the linear motor feed unit after compensation under the same conditions is shown in Table 1 and Figure 4. After compensation, the maximum positioning accuracy errors of the linear motor feed unit in the forward and reverse directions after spline model compensation are 1.2μm and -1.5μm, respectively. The positioning accuracy error is significantly reduced throughout the entire range, indicating that spline model compensation for the feed unit is effective.
5. Conclusion
Using laser interferometry and laser wavelength as a reference to detect the positioning accuracy of linear motors is an accurate and practical method. Tests revealed that changes in the feed speed and acceleration of the linear motor have little impact on positioning accuracy. The average positioning accuracy of each point was fitted using linear, piecewise linear, and cubic spline methods with the least squares method, and compensation was applied to compensate for the positioning accuracy of the linear motor feed. The compensation results showed that spline fitting was significantly better than linear and piecewise linear fitting. Error compensation can significantly improve the positioning accuracy of the linear motor feed, enabling it to reach its optimal precision state. This ensures the successful application of linear motors on CNC machine tools.
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