Abstract : This paper introduces a computer-aided test system for the position accuracy of ultra-precision lathes. The laser interferometer is used to detect the linear positioning accuracy of the ultra-precision lathe servo workbench. The system uses the original control device and the self-developed interface circuit with the laser interferometer. The static and dynamic position accuracy of the workbench is detected in real-time through numerical control programming, and the measurement accuracy of the system is analyzed.
Keywords: laser interferometer positioning accuracy ultra-precision lathe computer aided testing
Abstract:This paper introduces a computer-aided test system of the positional accuracy in super-precision lathe.By using laser interferometer, it can make an on-line detection of the linear positional accuracy of the servo platform in super-precision lathe.It The adopting the original control device and the self-made interface circuit of the laser interferometer.Through digital control programming, it can make real-time detection about the static and dynamic positional accuracy of the platform.It also analyses the handling accuracy of this system.
Keywords:laser interferometer positional accuracy super-precision lathe computer-aided test
1 system structure
The UPCAT system schematic diagram shown in Figure 1, it consists of three parts: servo feed mechanism, computer control and data acquisition systems, sensors. Servo feed system is mainly composed of AC servo motor, ball screw and air float plate. The DISTAXL-IM-20B laser interferometer is a fiber-optic combined small laser interference lengthmeter developed by Japan Precision Co., Ltd. It is a closed system and does not provide its own interface with the CNC system. In order to use it to form a servo The position of the feed system is closed-loop, and we have appropriately modified it and designed a set of interface circuits with the main control computer. This interface circuit can provide programmable data through the timer/counter in addition to the data acquisition function of the laser. Interrupt trigger signal for real-time data acquisition. In the design of the numerical control system, in order to reduce the burden on the main control computer and improve the precision of the interpolation operation of the numerical control system, the numerical control device is completed by a 8098 single-chip microcomputer system. It is plugged into the expansion slot of the host computer in the form of a plug-in board. There is a set of custom interface protocols between the host and the host. The environmental parameter measurement system of UPCAT is developed by us. The measurement device and control device are connected by GPIB bus.
Figure 1 UPCAT system structure diagram
2 system measurement accuracy analysis
According to the measuring principle of the laser interferometer, the installation structure of the machine tool and the placement of the measuring head and the mirror on the workbench, the measurement errors of this experiment mainly include: the performance error of the laser interferometer itself, the wavelength correction error of the laser interferometer, and the system The thermal expansion error, Abbe error, and the error caused by different axes of the laser beam and the movement direction of the table.
2.1 The performance error of laser interferometer δ1
The error is mainly caused by the stability of the laser wavelength, and the precision of the laser interferometer used is 0.1 ppm. The magnitude of this error is directly proportional to the measured distance. When the maximum movable distance of the table is 120mm, the systematic error of the laser interferometer is:
Δ1=0.12×10-6×(±0.1)=0.012μm (1)
2.2 Laser Interferometer Wavelength Correction Error δ2
The laser interferometer uses the wavelength of the laser in vacuum as a length reference. In the actual measurement, the laser beam passes through the air, and the wavelength changes with the change of the air refractive index n, and the relationship between the refractive index of the air and the ambient temperature T, the pressure P, and the humidity H is as follows: 
(2)
Assuming that the laser wavelength in the atmosphere is λ and λ0 in the vacuum, then λ = λ0/n. Among various environmental parameters, the temperature has the greatest influence on the measurement accuracy. In the superfinishing shop, the distribution of the temperature field changes along the height direction. Therefore, we place the platinum resistance temperature sensor close to the laser beam and on the same level to measure as accurately as possible. The influence of temperature changes on the precision of the laser interferometer. After using the formula above to correct the wavelength of the laser interferometer, the effect of each environmental parameter on the wavelength is as follows: change in air temperature 1°CPa, ± 0.3ppm, change in atmospheric pressure 25mmHg (1mmHg = 133.322Pa): ± 0.8ppm, relative Humidity 70% change: ± 0.1ppm, according to the measured results, the environmental parameters T, P, and H in the ultra-precision workshop were controlled at ± 0.05 °C, ± 0.4mmHg, ± 0.5%, respectively,
Δ2=(±0.05×0.3)+(±0.4)×0.8/25)
+(±0.5)×0.1/25≈0.015μm (3)
2.3 Abbe error δ3
Abbe error is caused by the angle between the axis of the motor and the laser axis. The ultra-precision lathe used in the experiment had a T-shaped layout and the air spindle was mounted on a Z-axis slide. Therefore, we did not allow the laser's measurement axis to be coaxial with the motor, but instead it was mounted on the side of the table, as shown in Figure 2. Shown, θe caused Abbe error δ3, θ consists of two parts, the first part of the angular position of the laser sensor relative to the slide θi; another part of the θ2 caused by the straightness error of the guide, Figure 3 shows the unidirectional tendencies in the presence of θ1 Near-position error ei, we can easily fit the error curve by
Ei=ei'(a2+k2xi) i=1 to 120 (4)
Ei'=d×10-6sin(2πxi/P)+(a1+k1xi) i=1～120 (5)
In the formula, yi=a2+k2xi represents the laser measurement axis, yi=k1xi represents the pitch error of the ball screw, a1 is the Abbe error, and P is the pitch of the ball screw.
Θ1≈arcsink2×2π/360 (6)
Figure 2 position error curve
Figure 3 Abbe error diagram
In this way, the measurement error caused by θ1 can be separated out. Abbe error is mainly caused by the straightness error of the guide rail without considering the influence of θ1. When the straightness error of the guide rail is 0.05μm/120mm,
Δ3≈θ×e=(±0.05/120)×200≈0.083μm (7)
2.4 Error δ4 caused by inconsistency between measuring axis and table moving direction
As shown in Fig. 4, δ4 = AC'. δ4 is mainly caused by θ1 and can be expressed as δ4'. From equations (4) and (5), we can derive the following equation:
Δ4'=ei-ei'=ei-ei/(a2+k2xi) (8)
(9)
Using equation (8), δ4' can be compensated, and the remainder of δ4 is mainly composed of the assembly error between the air float slide and the guide rail and the manufacturing error of the ball screw itself. According to the assembly requirements of the machine tool, θ ≤ 40 "≈ 193.92μ rad, then δ4 ≈ 0.0022μm.
Figure 4 Measurement axis misalignment error
2.5 System deformation due to thermal expansion δ5
The experimental results show that a steel rod with a diameter of 10mm and a length of 25mm has an axial elongation of approximately 1μm for every 0.1°C increase in temperature. Therefore, the thermal disturbance has a large influence on the accuracy of the system. This error can be achieved by the following measures: To control: 1 using granite as a workbench, which is characterized by almost no residual stress, good thermal stability, the thermal expansion coefficient is only one-third of steel, about 3.8-6 / °C; 2 strictly control the ambient temperature, When the temperature of the ultra-precision workshop is controlled at ±0.05°C
Δ5=3.8×10-6(±0.05)×120×10-3≈0.023μm (10)
2.6 Measurement Error Integration The measurement accuracy of the device is the result of the above comprehensive effects of the errors. According to the synthesis theory of the measurement error, 
(11)
It can be seen from the above equation that the measurement accuracy of the UPCAT system is better than 0.1 μm.
3 Position accuracy assessment
3.1 Evaluation of Static Position Accuracy According to GB10931-89, “Evaluation Method of Position Accuracy of Digitally Controlled Machine Toolsâ€, we use a position accuracy assessment method based on the principle of mathematical statistics. This assessment method requires that m target positions Pi be selected on the full stroke. Positioning n times in both positive and negative directions, n ≥ 5, and xij is the positional deviation in the ith measurement. A large number of statistical results show that xij obeys the law of normal distribution, so that a limited number of sub-sample statistics can be used. 
The (average) and S (standard deviation) approximations replace the maternal statistics μ (mathematical expectation) and σ (standard error) for n approaching infinity, taking ±3S as the dispersive width, and calculating the positional accuracy of each Evaluation index. 
(12)
If the repeat positioning accuracy of a certain target position is Ri=6Si, the one-way positioning accuracy of the target position is:
Au=(xi+3Si)max-(xi-3Si)min (13)
3.2 Evaluation Method of Dynamic Position Accuracy The evaluation method of position accuracy of CNC machine tools specified in GB10931-89 is only applicable to the static accuracy of the machine tool, or point-to-point motion accuracy (PTP) measurement, and does not apply to dynamic position accuracy, or It is a measure of the accuracy of continuous motion (CP). In recent years, a standard dynamic position accuracy detection method called “Circular Curve Test Method†has been used internationally to evaluate the dynamic position accuracy of CNC machine tools.
The circular position interpolation command (xcmd, ycmd) can be expressed as
XK=R×cosθ yk=R×sinθ (14)
In the formula, R-arc radius,
θ - Swing angle during interpolation of kth step.
The interpolation command at step k+1 is (xcmd,ycmd)
Xk+1=xk×cos(△θ)-yk×sin(△θ)
Yk+1=yk×cos(△θ)-xk×sin(△θ) (15)
In the formula, Δθ is the increment of the swing angle of the k+1 step and can be calculated as follows
(16)
In the formula, ΔS is the moving length of the k+1th, ΔT is the sampling time, and V is the feed speed.
In this way, we can use equations (14) to (16) to calculate the position command for circular interpolation, and send the servo motor to drag the table along the guide rail. At the same time, the UPCAT system can use the interrupt mode to read the X, Y direction position signals in real time, and use our software to analyze the dynamic position error of the machine.
4 Software Development
The experimental program was compiled in C language and debugged on a 386 compatible machine. The block diagram of the program is shown in Figure 5 and Figure 6.
Figure 5 test program block diagram
Figure 6 Dynamic Test Block Diagram
5 Conclusion
1 As a result of the use of computers for auxiliary testing, the possibility of densification of the sampling points is made possible, which can greatly improve the accuracy of the various error curves finally fitted, providing a reliable guarantee for the error compensation when positioning the table.
2 In the measurement process, the influence of various environmental factors on the measurement accuracy was taken into account, and corresponding compensation was performed to improve the measurement accuracy.
3 The use of computers for auxiliary measurements has greatly improved the measurement efficiency. At the same time, the processing of measurement data has also become efficient and accurate.
4 Using a computer-aided test system, the dynamic position accuracy of the machine tool can be tested in real time, which facilitates a comprehensive evaluation of the machine tool's performance indicators.
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