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A New Comparator for the high-accurate dimensional and form calibration
M. Neugebauer, F. Lüdicke
Physikalisch-Technische Bundesanstalt, 38116 Braunschweig, Germany
Abstract
A comparator was developed for the measurement of both diameter and form of cylinders, spheres and cubes in only a single specimen setting using a contact probe technique. The measurement volume is 160 mm x 100 mm x 120 mm, and the uncertainty (k=2) aimed at is 0,01 µm per 100 mm length for calibrations outside diameters, form and parallelism. The measured values obtained from outside diameter comparision measurements between four of PTB's standard length comparators and the new comparator agree within ± 20 nm.
Basic operation principles
Fig. 1 shows the principle for the measurement of outside diameter by means of two probing systems according to the Abbe principle.
Fig. 1: Measurement of a cylinder diameter carried out with two probing systems. P specimen, R form reference, L laser interferometer, S plane mirror, T probing system, X carriage, Y horizontal frame, Z vertical carriage, C rotating table, T_S measuring frame of probe, L_L interferometer frame
At first the 5 mm ruby contacting balls of the two probing systems touch opposite sides of the specimen ensuring definite contact (a). By shifting the carriages step by step to about 10 mm displacement, measured with the laser interferometers, the sensitivity coefficients of the probing systems and also the respective x-positions of the contacting balls can be determined. After this the two contacting balls, which have been adjusted in relation to each other before, touch mutually beside the specimen and the new x-positions are determined (b). The diameter is determined from the four x-positions. The residual deviation resulting from elastic compression is negligibly small owing to the very small contacting force of 1 mN per mm displacement. When outside diameters are measured by means of two probing systems, the diameter of the contacting ball is of no significance.
For the measurement of inside diameters, one probing system is shifted from one side of the specimen to the other. The uncertainty component contributed by the contacting ball diameter which has been determined before enters into the measurement result. For the measurement of inside diameters, one probing system is shifted from one side of the specimen to the other. The uncertainty component contributed by the contacting ball diameter which has been determined before enters into the measurement result.
Fig. 2 shows the principle of measurement of the form of a cylinder using a form reference ring. Cylinder and form reference ring are simultaneously probed and thus the form deviations are compared.
Fig. 2: Measurement of the form of a cylinder using a form reference ring. P specimen, R form reference, L laser interferometer, S plane mirror, T probing system, X carriage, C rotating table, Y horizontal frame, Z vertical carriage, T_S measuring frame of probe, L_L interferometer frame
The disturbing influences due to guiding errors and vibrations are included in both results and can be eliminated provided that the connection between the two probing systems and between specimen and form reference are stable and the properties of the two probing systems are equalized.
The form reference for large rings is a plug and for cubes a flat surface. The form references have been manufactured from Zerodur, offering optical surface quality. Their form deviations can be used as correction values to be determined by error separation methods.
Comparator for diameter and form
The comparator for diameter and form has been installed in PTB's clean room center to minimize disturbing influences of dust particles on the contact probe technique (Fig. 3). The comparator is controlled by a UNIX host computer which is connected with terminals outside the clean room and in offices by a local network.
Fig. 3: Comparator for Diameter and Form
An horizontal frame supported by air-bearings moves on a granite plate. In this frame moves a vertical carriage also guided by air-bearings and held by counterbalance weights. A rotating table takes up the facility where cylinders and spheres are measured; another facility has been provided for the measurement of cubes. In the centre of these facilities, a device has been installed to centre, level and rotate the specimens automatically. The form references arranged beside it are manually adjusted.
Below the vertical carriage an air-bearing system made of alumina ceramics with two carriages is arranged in the x-direction (cf. Fig. 1) . The two carriages, each with an oil-damped probing system and a plane mirror, are driven independently of each other by Inchworm piezo motors [1]. These movements are measured by one plane mirror interferometer each [2]. The sensitivities and the static characteristics of the probing systems are calibrated by means of the laser interferometers and the dynamic properties are optimized and adapted with a special measurement device comparable to the surface simulator described by Bosse et al in [3]. The temperatures of solids and air are measured with Pt 100 resistance thermometers regularly calibrated against two Pt 25 standard thermometers. As highly precise slip rings are used, temperature measurements on the rotating table are possible. The refractive index of air used to correct length measurements by interferometry is determined by the parameter method according to Edlén and by means of an absolute measuring refractometer which is similar to that described by Hou and Thalmann [4] but with changes in the overall length and in tube flushing.
Comparison of outer diameter measurement
Since 1995 a comparison of diameter measurements has been carried out between three of PTB's standard length comparators at a 80 mm gauge block of Zerodur. Since the beginning of 1997, the new comparator has participated in this comparison.
Figure 4 illustrates the results of this comparison with the given uncertainty (k=2), resp. the uncertainty of the new comparator aimed at. The values of the diameter given for the new comparator are the average of 6, resp. 2 series of measurements comprising more than 300 measurements over 3 weeks. The standard deviation of these 8 series is 7 nm.
Fig 4: Comparison of diameter measurements of a 80 mm Zerodur gauge block, differences of measured values and given, resp. aimed uncertainty (k=2),
sigma = interference gauge block comparator,
u, nu =length comparators [1, 8],
lambda = comparator for diameter and form
The diameter calibrated by means of the four comparators lies within the range of the uncertainty of the comparators and agree within ± 20 nm. The apparent shortening of the gauge block of about 20 nm approximately agrees with the shortening specified by Bayer-Helms, Darnedde and Exner in [5] for one Zerodur probe of this age without special thermal posttreatment.
Conclusion
The results of the diameter measurement comparison indicates the capability of the new comparator of calibrating the outside diameter with an uncertainty of less than 20 nm. It will be the next task in the field of outside diameter measurements to estimate the uncertainty according to the ISO Guide [6] and to try to reduce the uncertainty further down to 10 nm. For inside diameter measurements, a method was developed and tested with the aim of calibrating the diameter of contacting balls with an uncertainty U < 15 nm without deinstallation of the probing system. For form measurements with form references a method was tested to optimize and adapt the dynamic properties of the probing systems. The main advantages of the described comparator for calibrating diameter and form are:
- Realization of complex measuring tasks requiring a great number of measuring points (e.g. cylindricity and volume determination) and decrease of the uncertainty for combination of the diameter and form values measured, because the diameter and form measurements were carried out in one specimen setting.
- Reduction of the stochastic uncertainty contribution due to automatic measurements under favourable environmental conditions (very good temperature stability and clean-room conditions).
- Reduction of the uncertainty of outside diameter calibrations because the diameter of the contacting balls does not need to be known.
- Reduction of the influence of guiding errors and vibrations on form measurements because form references will be used for calibration.
References
[1] Henderson, D.: A new Inchworm Motor for industrial nanopositioning applications. In: American Society for Precision Engineering, Proceedings 12(1995), p.p.215 - 218
[2] Sommargren, G.E.: A new laser measurement system for precision metrology. In: Precision Engeneering 9 (1987), p.p. 179 - 184
[3] Bosse, H.; Krüger, R.; Löhr, W.; Lüdicke, F.: Oberflächensimulator für die dynamische Kalibrierung von Längenmeßtastern. In: tm Technisches Messen 61(1994), p.p. 82 - 88
[4] Hou, W. und Thalmann, R.: Accurate measurement of the refractive index of air. In: Measurement 13(1994), p.p. 307 - 314
[5] Bayer-Helms, F., Darnedde, H., Exner, G.: Längenstabilität bei Raumtemperatur von Proben der Glaskeramik "Zerodur". In: Metrologia 21 (1985), p.p. 49-57
[6] Guide to the Expression of Uncertainty in Measurement International Organisation for Standardisation ISO (1995)