**Abstract:** This paper presents a computer-aided testing system designed to evaluate the positional accuracy of ultra-precision lathes. The system employs a laser interferometer to measure the linear positioning accuracy of the servo workbench, utilizing the original control device and a self-developed interface circuit. Through numerical control programming, both static and dynamic position accuracy can be monitored in real time, and the overall measurement accuracy of the system is thoroughly analyzed.
**Keywords:** laser interferometer; positioning accuracy; ultra-precision lathe; computer-aided testing
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**1. System Structure**
The UPCAT (Ultra-Precision Computer-Aided Testing) system, as illustrated in Figure 1, consists of three main components: the servo feed mechanism, the computer control and data acquisition system, and the sensors. The servo feed system includes an AC servo motor, a ball screw, and an air float plate. The DISTAXL-IM-20B laser interferometer, developed by Japan Precision Co., Ltd., is a compact fiber-optic laser length meter that operates as a closed system without direct integration with the CNC system. To enable closed-loop control of the servo system, we modified the interferometer and created a custom interface circuit connected to the main control computer. This interface not only supports data acquisition but also provides programmable interrupt signals for real-time data capture.
The numerical control system was implemented using an 8098 microcontroller, which is installed as a plug-in board into the host computer’s expansion slot. A custom communication protocol ensures seamless interaction between the host and the microcontroller. Additionally, the environmental parameter measurement system was developed in-house, connecting the measuring and control devices via a GPIB bus.
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**2. System Measurement Accuracy Analysis**
Based on the principles of laser interferometry, the main sources of error in this experiment include:
- **δ1: Performance error of the laser interferometer**
Caused by the stability of the laser wavelength, with a precision of 0.1 ppm. For a maximum travel distance of 120 mm, the systematic error is calculated as:
$$
\Delta_1 = 0.12 \times 10^{-6} \times (\pm 0.1) = 0.012\ \mu m
$$
- **δ2: Wavelength correction error**
Due to changes in air refractive index caused by temperature, pressure, and humidity. After corrections, the error is estimated as approximately:
$$
\Delta_2 \approx 0.015\ \mu m
$$
- **δ3: Abbe error**
Arises from the angular misalignment between the motor axis and the laser beam. By fitting error curves and analyzing guide rail straightness, the Abbe error is found to be about:
$$
\Delta_3 \approx 0.083\ \mu m
$$
- **δ4: Misalignment between the measurement axis and the table movement direction**
This error is minimized through compensation techniques and is estimated at around:
$$
\Delta_4 \approx 0.0022\ \mu m
$$
- **δ5: Thermal expansion error**
Due to temperature fluctuations affecting the workbench and other components. With controlled environmental conditions, the thermal error is:
$$
\Delta_5 \approx 0.023\ \mu m
$$
Combining all these errors, the total measurement accuracy of the UPCAT system is better than **0.1 μm**.
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**3. Position Accuracy Assessment**
**3.1 Static Position Accuracy Evaluation**
According to GB10931-89, a statistical method is used to assess the static positioning accuracy. Multiple measurements are taken at different positions, and the average and standard deviation are calculated. The repeat positioning accuracy is defined as $ R_i = 6S_i $, and the one-way positioning accuracy is given by:
$$
A_u = (\text{max}(x_i + 3S_i)) - (\text{min}(x_i - 3S_i))
$$
**3.2 Dynamic Position Accuracy Evaluation**
For dynamic accuracy, the “Circular Curve Test Method†is applied. Using interpolation commands, the machine tool moves along a circular path, and the actual position is compared with the commanded position to calculate the dynamic error. This method provides a comprehensive evaluation of the machine's performance during continuous motion.
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**4. Software Development**
The testing program was written in C and tested on a 386-compatible computer. The program block diagrams are shown in Figures 5 and 6. These diagrams illustrate the flow of the test process, including data acquisition, signal processing, and error analysis.
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**5. Conclusion**
- The use of a computer-aided testing system allows for denser sampling points, improving the accuracy of error curve fitting.
- Environmental factors such as temperature and humidity were carefully considered and compensated for, enhancing measurement reliability.
- The system significantly improves measurement efficiency and data processing accuracy.
- Real-time dynamic position accuracy testing enables a comprehensive evaluation of the machine tool’s performance.
This system offers a reliable and efficient approach to evaluating the precision of ultra-precision lathes, supporting high-quality manufacturing and quality control processes.
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