Ultra-precision diamond machining is a promising technique for non-rotationally symmetrical surfaces with sub-micrometer form accuracy. The measurement and compensation processes in the fabrication process must be conducted carefully to achieve high form accuracy. However, significant challenges remain to improve the measurement accuracy and machining efficiency. Because of the remounting process, the off-machine measurements would reduce the efficiency. On the other hand, contact-type measurements can cause physical damage to some soft materials. To overcome these problems, a noncontact on-machine measurement (OMM) system is developed using two optical probes, and a two-step compensation strategy is proposed to generate a modified tool path. To verify the accuracy of the proposed measurement system, OMMs were performed on a spherical mirror using this system and were later compared with off-machine measurements. To evaluate the compensation strategy, an off-axis paraboloid mirror was diamond-machined and compensated using the proposed method. The results show that the OMM system and compensation strategy are effective for improving the form accuracy while simultaneously enhancing the machining efficiency.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Compared to conventional optical components, non-rotationally symmetrical surfaces (NSSs) are more advantageous for imaging and non-imaging systems and can significantly reduce the light path and improve imaging quality [1–3]. NSSs provide designers more flexibility with respect to the practical requirements in the optimal design process [4,5]. Several scientific studies on NSS design have been conducted; these have helped extend the application of NSSs to various fields, such as, aerospace, illumination, and biomedical engineering [3–7]. However, challenges remain regarding surface generation in the manufacturing process.
In the last decade, several methods and tools based on ultraprecision lathe have been utilized to manufacture NSSs, including ultraprecision grinding [8,9], fast tool servo (FTS) [10–12], and slow tool servo (STS) [13–15]. Unlike other fabrication processes [16,17], ultraprecision manufacturing technology using diamond turning machines can be used to directly obtain optical surfaces and manufacture NSSs for infrared optical components [18,19]. Ultraprecision grinding produces very accurate surfaces using a high-speed rotating tool and is well suited for hard and brittle materials. However, when it comes to obtaining optical surfaces, the very low feed rate during the finish grinding makes the process inefficient . In the FTS/STS process, the diamond tool oscillates along the Z-axis as the workpiece rotates on the ultraprecision diamond turning lathe. The FTS system has oscillating limits, with a maximum range of lower than 1 mm in most cases, and an additional axis is necessary to oscillate the tool . On the other hand, in the STS method, the Z-axis of the machine slides to oscillate the tool, and all the axes are fully coordinated in their position. Thus, the oscillation range of the tool can easily exceed 25 mm and an accurate surface with nano-scale roughness and sub-micrometer form accuracy can be obtained using the STS process [13,20].
Although these methods can be used to produce different types of NSSs, the STS method remains a very promising technique for machining surfaces with large aperture and high asphericity. Because of the uncertainties in the mechanical, environmental, and human factors, the machining process is usually not perfect, and the manufacturing errors may reduce the form accuracy [8,21,22]. In ultra-precision machining, although human errors can be controlled and avoided, the residual errors need to be reduced or eliminated using an appropriate compensation strategy .
Obtaining surface profile measurements of a machined workpiece is a critical step in the compensation process . Commercial measuring devices, such as, 3D high-precision profilometer (UA3P) and the form Talysurf profilometer (Taylor Hobson), provide height profiles in the off-machine mode for tool path compensation [22–25]. However, remounting errors can be induced in the compensation data after conducting the off-machine measurements and may affect the subsequent compensation cycles. Thus, the errors are affected by the precision fixtures and the remounting method. Compared to off-machine measurements, on-machine measurements (OMMs) not only provide test data in a short time period but can also reduce the environmental interferences and avoid repeated remounting procedures; this approach is more efficient and has lower risk [9,22].
Previous studies have focused on on-machine compensation using contact-type probes , such as, a ruby probe. For example, Chen et al. presented a compensation approach for the grinding of tungsten carbide aspheric molds based on an OMM using a sapphire microprobe of size 0.5 μm; the aspheric surface had a high form accuracy of 0.177 μm after three compensation cycles . Dong et al. introduced an on-machine 3D profile measurement approach using a digital length gauge MT60 with a touch-trigger probe; the deviation between the OMM results and the results obtained using a Zygo interferometer with a Φ400 mm optical plane was lower than 0.07 μm . Shibuya et al. presented a novel spiral scanning probe measurement system for micro-aspheric surfaces, including a scanning stage and a contact-type displacement sensor . Although contact-type measurement systems can be applied to off-machine and OMMs, the contact-type method requires compensating for the contact point errors induced by the probe radius . Even for some softer materials, the high-hardness probe slide can cause physical damages and scratches. In recent years, OMM methods using noncontact probes have been studied for micro-aspheric surfaces and NSSs . For example, Li et al. presented a novel measurement strategy and an error-compensation model for the measurement of a large propeller blade in on-machine laser measurement systems; the measurement accuracy was at the micron level . Zhu et al. presented an on-machine multi-axis measuring system for determining the 3D microstructures of a curved compound eye using a scanning tunneling microscope. The OMM method was used to ascertain the characteristics of the micro-aspheric surface; however, the corresponding tool path compensation method was not described [30,31]. Based on the above discussion, for an improved profile error compensation strategy, the following requirements must be satisfied: the surface figure metrology should be accurate enough to reconstruct the profile errors rapidly, and the compensated tool path should possess high location accuracy for eliminating these errors.
Considering the high precision and nondestructive requirements, a noncontact measurement system seems promising to characterize the surface profile in the on-machine mode . Nevertheless, effective OMM and tool path compensation methods for on-machine compensation using noncontact-type probes, especially for the surface compensation in an STS process, are still lacking. In this paper, an OMM system mounted on a diamond turning lathe based on noncontact-type probes is presented. Moreover, a two-step compensation strategy (TCS) based on the OMM method integrated with an STS process is proposed. The TCS objective is to extract and process the OMM data from the probes to modify the initial numerical control code generated by the DIFFSYS software . Subsequently, the uncertainties in the TCS and experimental setup are analyzed. To verify the accuracy and feasibility of the proposed method, we fabricate a spherical mirror with an STS using the OMM method and an off-axis paraboloid mirror using the TCS.
2. On-machine measurements and tool path compensation methods
2.1 On-machine measurement using noncontact-type probes
Most noncontact probe systems for OMM are optical, because they are convenient for engineering applications. A chromatic confocal probe is typically used for high-precision and fast rate measurement. Figure 1 shows the schematic of a chromatic confocal probe. In the confocal chromatic system, an LED sends a white light beam through the lens that refracts the emerging light into spectral waves . These spectral waves are directed toward the surface being measured and subsequently reflected back and analyzed using a spectrometer. Only the specified wavelength that is best focused on the measured surface passes through the mechanical filter i.e., the pinhole. The spectral waves will be refracted onto a CCD camera. Through the location of the peak value of the signal on the CCD camera, the distance between the probe head and the measured surface can be calculated.
To measure the machined surface in the on-machine mode, the chromatic confocal probes are mounted on an ultraprecision diamond turning lathe. Figure 2 shows the schematic of the manufacturing and OMM system. The OMM system is built on the ultraprecision diamond turning lathe with nano-scale motion accuracy and high stability. After the rough cutting, the surface profile of the workpiece can be measured based on the similar STS path generated by the DIFFSYS software. Unlike the rough cutting path, the spiral scanning path has a tighter spacing between the successive turnings for a high sampling rate. Based on the Z-axis slide and C-axis rotation, the 3D spiral path represents the actual locus of the probe tip. Although the spiral scanning method results in an accurate surface profile, a scanning centering error may severely affect the final measurement result [30,34]. Therefore, as shown in Fig. 2, the optical probe A is first aligned with the center of rotation of the spindle. For the centering alignment of the measuring probe, Du et al. presented a fast centering method using a tilted flat mirror . Because of the very small spot size of the optical probe tip, the center part of the on-machine workpiece can be considered an approximation of the tilted flat mirror. At the beginning of the measurement, the centering method is applied to the on-machine workpiece, and the starting position of the optical probe A can be aligned and ascertained.
In addition, the spindle in the STS uses an optical encoder to close the position loop in the position mode , and the spindle speed can be varied in this mode. The surface profile data acquisition of the spiral scanning process can be done easily; however, it is difficult to obtain the location of the optical probe A in real time. If the C-axis encoded data of the machine and the profile data of the probe A can be obtained simultaneously with a high-speed acquisition, the measured surface can be reconstructed in the on-machine mode. In most cases, the encoded data of the machine are not open source for the commercial machine. For the OMM system, the measurement is based on polar coordinate (ρ, θ) with a spiral path. To obtain an accurate positioning of the spindle rotation, another measuring probe B, shown in Fig. 2, is mounted on the spindle platform to provide feedback on the position. The probe B is used to obtain the rotation angle θ of the spindle and the accurate uniform motion of the spindle along the X-axis can help us to calculate the polar coordinate (ρ, θ). The cylindrical surface of the vacuum chuck is divided into several segments using accurate markers with special angles, as shown in Fig. 2. The probe B can easily detect these markers along the contour of the cylinder when the spindle is working in the STS mode. Figure 3 shows the control diagram for the in situ noncontact measurement system. During the spiral scanning process, the data measured from the optical probes A and B are simultaneously acquired using a computer control system with a high-speed acquisition card. The surface profile errors can be obtained by probe A, and the spindle position can be determined by probe B in real time. By combining the surface profile errors and the position information, the machined surface can be rapidly reconstructed in the on-machine mode.
The performance of the measurement system depends on the quality of the mechanical guiding system, the stability of the metrology frame, and the behavior of the measuring probes. The in situ measurement system is built on a Z motion stage with a horizontal straightness value lower than 0.3 μm (full 300 mm travel). The spindle is placed on an X motion stage with a horizontal straightness value lower than 0.3 μm (full 350 mm travel). Moreover, the workpiece is fixed on the spindle with a C-axis positioning accuracy lower than 1″. To measure the machined surface, the specific scanning trajectory is generated to drive the measuring probe A. To obtain the actual C-axis position of the spindle, the markers are placed on the vacuum chuck with an angle accuracy lower than 0.5°. Because the angle accuracy is proportional to the number of markers, we can adjust the number of markers for an optimal performance or even adopt a grating line displacement transducer for ultra-precision position detection.
2.2. Two-step compensation strategy
The OMM strategy is first executed to introduce the profile errors into the subsequent compensation. The two-step compensation strategy is implemented to reduce the profile errors along the spiral trajectory in the first compensation step and the radial errors in the second compensation step. Compared to contact-type probes, optical probes tend to be more susceptible to environmental and material factors . Because the measurement process for the STS method can last for a relatively long period, environmental factors, such as, temperature and humidity, affect the stability of the measured result in practice. After the first compensation step, the measurement errors must be introduced into the machined surface. In this case, the focus in the second compensation step is on the measurement uncertainty due to the environmental factors.
Figure 4 shows the flowchart of the fabrication process of the TCS on the ultraprecision diamond turning lathe. As shown in Fig. 5(a), the initial optical surface is manufactured using the STS process, and the surface profile errors are measured using the spiral scanning method. Based on the measured data, we can easily reconstruct the machined surface using a low-pass filter and spline interpolation. Thus, the corresponding cutting path after error compensation can be calculated using the reconstructed surface to generate a modified numerical control code. Subsequently, the on-machine workpiece is remanufactured based on the modified numerical control code. The profile error compensation along the spiral trajectory is considered the first compensation step. As shown in Fig. 5(b), the radial profile is measured along the radial direction for the second compensation step. Considering the relatively short measurement time period in the radial scanning path, the environmental errors can be ignored. Thus, the surface profile measured using the radial scanning method is applied to modify the previous numerical control code. For every circumferential profile of the machined surface, the radial profile error is subtracted from the inside to the outside. After the profile error compensation, the OMM results help verify the accuracy of the workpiece and whether further compensation is required can be decided accordingly.
3. Error analysis
The proposed OMM system is built on a diamond-turning machine, which is used for measuring various types of NSS, performing two independent motions in the X and Z directions under the control of two independent linear encoders. The measuring probe A was installed on an ultraprecision vertical translation stage. If the probe A is not installed in parallel with the diamond tool, it would generate machining and measuring errors. Generally, the performance of the OMM system depends on the adjustment of the measuring probes, the quality of the mechanical guiding systems, and the environmental factors. The systematic errors can be characterized and compensated; however, the random errors represent the uncorrectable errors. Thus, the systematic errors of the measurement system are analyzed, and the results are as follows.
3.1 Center alignment errors
Ultra-precision machining requires a high-precision center alignment for the diamond tool and the measuring probe. The former is a key factor to produce a better shape profile, which can be aligned by cutting a standard spherical reflector. The measured profile of the workpiece is mainly affected by the latter. After the diamond tool is centered on the ultraprecision diamond turning lathe, an efficient centering method is employed for the center alignment of the optical probe using a tilted flat mirror. The main step involves mounting the tilted flat mirror on the vacuum chuck so that the mirror rotates with the spindle. Because of the centering error of the optical probe, the distance measured by the probe is approximately sine-shaped. When the centering error of the measuring point is aligned with the rotation center of the spindle, the amplitude of the distance is reduced, and the sine shape may disappear. The resolution of the optical probe is 0.1 μm, and the tilt angle of the flat mirror is 5°. The center alignment error of the probe can be expressed as follows.Eq. (1), the corresponding centering error is 0.57 μm.
As shown in Fig. 6, O is the rotation axis of the spindle, and O’ is the position of the diamond tool or the probe tip. During the manufacturing process, P1 is the ideal cutting point, and P0 is the actual cutting point when the centering error is considered. Assuming that the horizontal tool centering error is δx1 and the height error is δy1, the actual cutting point P0(x0, y0) is substituted by the ideal point P1(x1, y1). The position of point P0(x0, y0) can be expressed as follows.
During the measurement process, P0 is the ideal measuring point, and P2 is the actual measuring point when the centering error is considered. Assuming that the horizonal probe centering error is δx2 and the height error is δy2, the actual profile point P2 (x2, y2) is considered the ideal point P0(x0, y0). Thus, the position of point P2 can be expressed as follows.
The design surface can be described as f = z(x, y), and the actual machined surface can be described as g = s(x, y). The form error due to the tool centering error is expressed as δz(x0, y0), and the measurement error due to the probe centering error is expressed as δm(x0, y0).
3.2 Machine motion errors
When the proposed manufacturing and measuring processes are applied to the ultraprecision diamond turning lathe, any motion errors of the spindle and the slide induce shape errors in the finished machined surface. Compared to the rotation error of the spindle with a C-axis positioning accuracy of ± 1″, the slide error of the Z-axis with the spindle can have a greater influence on the surface form accuracy, including the out-of-straightness component and the out-of-parallelism component, as shown in Fig. 7(a). To accurately measure the slide error, a cylinder workpiece machined using the ultraprecision diamond turning lathe is chosen as the benchmark. After the cylinder workpiece was produced using the Z-axis slide, the measuring probe is mounted in the opposite position of the diamond tool. The out-of-straightness component is obtained using the measuring probe, and the out-of-parallelism component is evaluated using least-squares fitting. Figure 7(b) shows the practical influence of the machine motion error for the OMM. This motion error can be evaluated by qualifying the straightness of the motion and the acceptance angle of the probe, as follows.
3.3 Tool-surface intersection
Because the surface is produced by the motion of the diamond tool attached to the workpiece, the nose radius of the tool induces changes in the cutter contact points and causes an over-cut area on the workpiece. When the tool path is generated by the DIFFSYS, the cutting depth can be modified for tool radius compensation by calculating the over-cut depth of the cutter contact points based on the design profile. However, the test path cannot be compensated because of the lower number of test points on the optical probe. Figure 8(a) shows that the cutting point and the testing point may not be identical at the edge of the machined surface profile. Thus, the actual compensation cutting depth is obtained using modified spiral scanning. Figure 8(b) shows the spiral path of the manufacturing process and the modified spiral path of the measuring process.
3.4 Measurement drift and noise
Because of the environmental uncertainties and thermal effects, measurement drift and noise errors are introduced in the surface profile. When the measurement of the workpiece lasts a few minutes in the on-machine mode, these effects are significant. Figure 9(a) shows the measurement drift and noise data for a five-min period. The blue line represents the raw data of the optical probe when it is fixed on the platform, and the red line represents the measured data after filtering to characterize the trend of the measurement drift. The trend of the red curve is increasing with the measuring time and fluctuates at certain times. Figure 9(b) shows the environmental temperature and relative humidity during the OMM; the latter may have a greater effect on the measurement results. When the optical probe is mounted on a stable platform, the measured data fluctuate based on the changes in the relative humidity. To address this issue in the noncontact-type probes, the TCS, explained in section 2.2, is used to reduce the measurement errors.
4. Experiments and results
4.1 Spherical mirror measured by the OMM method
The experiments were carried out on a Nanotech 450UPL (Moore Co. Ltd, US), which has a T-shaped configuration with a spindle and two slides (X-slide and Z-slide). The horizontal straightness of the Z motion stage is 0.063 μm (full 300 mm travel) and that of the X motion stage is 0.129 μm (full 350 mm travel). Table 1 lists the detailed measurement results of the ultraprecision lathe. The schematic of the OMM setup, shown in Fig. 2, consists of two optical probes and a vertical translation stage. The vertical translation stage is a stepper actuator-driven platform with a resolution of 0.096 μm. The programming resolution of the Windows operating system is 0.01 nm. The feedback resolution of X-axis and Z-axis is 0.034 nm. The C-axis position accuracy is 0.6 arc s. The position accuracy of the X-axis and Z-axis can be less than 10 nm in the experiments. And the high position accuracy of C-axis, X-axis and Z-axis would provide a better performance of the OMM system.
The Precitec optical probes for noncontact distance and thickness measurements have a wide measuring range from a few microns to several millimeters. Considering the measuring range and accuracy, the optical probe with a measuring range of 300 μm was chosen for the experiments. Table 2 lists the detailed parameters. The measuring accuracy of the probe  can be expressed as follows.
A spherical mirror with a radius of curvature of 500 mm, a diameter of 60 mm, and a decentered value of 7 mm is manufactured using the STS process. Probe A is adjusted to the same height as the spindle axis using the tilted flat mirror. The cylindrical surface of the vacuum chuck is divided into eight segments, and the angles are marked with polyimide tape. Thus, probe B can detect the angle of the C-axis rotation when the workpiece is measured in the STS mode. During the spiral scanning process, the raw data from probe A and position sensor B are simultaneously acquired by the control system. Thus, the data of the profile errors and rotation angular markers are acquired during the same time period. Combined with the co-ordinate information of probe B, the points measured by probe A can be accurately localized on the machined surface.
Figure 10(a) shows the corresponding times for the measured angular markers and the profile errors. The OMM duration time of the spherical mirror is about 60 second. Using the high-precision interferometer, the off-machine results of the spherical mirror can be benchmarked. Figures 10(b) and 10(c) show the OMM result and off-machine result measured using the Zygo interferometer. The surface form errors of the PV value of the OMM and off-machine measurement are 0.341 μm and 0.376 μm respectively. Figure 10(d) shows the radial profile errors of the OMM and off-machine measurement results. The OMM results are highly correlated with the off-machine results. Therefore, the proposed system exhibits a high accuracy for the OMM and can also be applied to other non-rotationally symmetrical optical surfaces.
4.2 Off-axis paraboloid mirror manufactured by the TCS
An off-axis paraboloid mirror is designed and manufactured to verify the effectiveness of the TCS. Table 3 lists the parameters of the mirror and the cutting conditions. After centering the diamond tool by cutting the sphere of the oxygen-free high-conductivity copper, the workpiece of the closest sphere was mounted on the vacuum chuck and aligned symmetrically along the rotation axis using the linear variable differential transformer. At this point, the height of the tool and the probe A can be in line with the rotation axis of the spindle. Figure 11 shows the experimental setup used for the fabrication and OMM.
In the rough machining stage, the designed surface is produced by the STS cutting based on the initial numerical control code. Figure 12(a) shows the OMM result of the rough machining. We extract the height profile errors from the spiral scanning for the first circumferential compensation (Fig. 12(a)). Figure 12(b) shows the OMM result after the first compensation step, which has a rotational symmetry. Figure 12(c) shows the height measurement along the circumference with a radius of 50 mm. The blue curve, in Fig. 12(c), represents the profile error before the first compensation step, and the red curve represents the error after the first compensation step. The corresponding profile error decreases from a PV value of 2.894 μm to a value lower than 1 μm. However, the profile error along the radial direction varies continuously and rapidly, as indicated in the blue curve shown in Fig. 12(d). This radial profile error is due to the measuring drift of the probe, as described in Section 3.4.
After the first compensation step, the measuring drift is corrected by the next circle based on the radial profile measurement. Because of the relatively short time in the on-machine mode, the radial profile can reflect the machined surface. We integrate these data into the previously modified numerical control code for the second compensation step. The blue curve, in Fig. 12(d), represents the radial profile error before the second compensation step, and the red curve represents the error after the second compensation step. After the second compensation step, the form accuracy is significantly improved along the radial direction. After the profile error compensation, an optical surface with a sub-micrometer form accuracy can be easily obtained using the TCS. During the machining of the off-axis paraboloid mirror, the OMM duration time of the first compensation step is about 200 second, and the OMM duration time of the second compensation step reduce to 15 second. As shown in Fig. 13(a), the OMM result of the PV value of the profile error is 0.345 μm, and the RMS value is 0.115 μm. Figure 13(b) shows the surface shape measured using the Zygo interferometer; the PV value is 0.302 μm, and the RMS value is 0.066 μm. Figure 13(c) shows the surface shape subtraction between the on-machine and off-machine measurements. Because the image resolutions of the two measurement methods are different, a bilinear interpolation method was used to stretch the images. Finally, the PV value of the calculation result is found to be close to 0.2 μm, and the RMS value is lower than 0.1 μm. Compared with the measurement result of the Zygo interferometer, the OMM measurement result can accurately reflect the real surface shape. The machined surface after the two-step compensation shows a remarkable improvement of the surface form accuracy. Thus, the proposed OMM and compensation methods have high precision and reliability, which can be further applied to improve form accuracy of the non-rotationally symmetric surface.
An in situ noncontact measurement system together with a two-step compensation strategy is presented for improving the surface form accuracy and achieving high efficiency in the ultra-precision diamond machining. In addition, the main influencing factors, including center alignment errors, machine motion errors, and tool nose radius compensation, were investigated. A spherical mirror was measured in the on-machine mode. Compared to the off-machine measurement, the proposed system can be used to obtain a measured surface profile with a measuring accuracy of approximately 0.1 μm for the machining compensation. Thereafter, an off-axis paraboloid mirror was diamond-machined and compensated by applying the TCS. The surface profile error was reduced to a value of 0.3 μm in terms of the peak-to-valley value as a result of the machining compensation. The results verify the accuracy of the TCS. The OMM system can be potentially applied to the nondestructive testing of rotationally and non-rotationally symmetric surfaces. The OMM and TCS methods help avoid the remounting process and significantly increase productivity. The OMM system has great potential for fabricating various other types of NNSs and can possibly be applied to other turning lathes, such as, an ultra-precision grinding machine. Because a significant amount of liquid is used for tool cooling, the relative humidity during the OMM may influence the measurement results for ultra-precision grinding machines. The TCS can be helpful to improve the optical surface accuracy.
National Key R&D Program of China (No. 2016YFA0401304); National Natural Science Foundation of China (Nos. 61621001, 11427804, and U1731242); and National Scientific Instrument and Equipment Development Major Project of Ministry of Science and Technology of China (No. 2012YQ04016403).
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