Принципы нанометрологии (1027506), страница 61
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Abbe errors result fromparasitic rotations in combination with an offset between the probed positionon the object and the position where the measurement is taken. Abbe errorscan be minimized by moving the sample instead of the probe and having thevirtual intersection of the laser beams coincide with the probe centre (as on theNMM in section 9.4.1.2). The maximum Abbe offset that remains has to beestimated, in order to quantify the maximum residual Abbe error.
The rotational errors can be measured with an autocollimator or a laser interferometerwith angular optics (see section 5.2.9). The NMM (see section 9.4.1.2) usesdouble and triple interferometers to measure the angular deviations duringoperation and actively correct for them – this greatly reduces the Abbe errors.The mirror flatness can be measured on a Fizeau interferometer (seesection 4.4.2). The angle between the orthogonal mirrors can be measured byremoving the mirror block from the instrument and using optical techniques(for example, by comparison with a calibrated optical square). It is alsopossible to calibrate the orthogonal mirror block directly, by extending it withtwo additional mirrors and calibrating it as if it were a four-sided polygon[53].
Alternatively, the squareness can be determined using a suitable calibration artefact on the miniature CMM (see below).9.6.2 Calibration of linescale-based miniature CMMsFor a linescale-based miniature CMM, such as the Zeiss F25 (see section9.4.1.1), the traceability is indirect via the linescales. The linescales areperiodically compared to a laser interferometer in a calibration. The calibrated aspects are the linearity, straightness and rotational errors. Thesquareness between the axes is determined separately, by a CMMmeasurement on a dedicated artefact.283284C H A P T ER 9 : Coordinate metrologyFor the linearity determination, a cube-corner retro-reflector is mountedin place of, or next to, the probe.
The offset between the centre of the retroreflector and the probe centre is kept as small as possible, in order to minimize the Abbe error in the linearity determination. Care must also be takento minimize the cosine errors during the linearity calibration. Alignment byeye is good enough for large-scale CMMs, but for miniature CMMs with theirincreased accuracy goal, special measures have to be taken. For the calibration of the F25 a position-sensitive detector (PSD) has been used for alignment [54]. The return laser beam is directed onto the PSD and the run-outover the 100 mm stroke reduced to a few micrometres. This translates intoless than 1 nm of cosine error over the full travel.Straightness and rotations can be measured with straightness and rotational optics respectively.
Because of the special construction of the F25,some errors are dependent on more than one coordinate. The platformholding the z axis moves in two dimensions on a granite table. This meansthat instead of two separate straightness errors, there is a combinedstraightness, which is a function of both x and y. The same holds for therotations around the x and y axes. This complicates the calibration, bymaking it necessary to measure the straightness and rotations of the platform along several lines, divided over the measuring volume.The results of the laser interferometer calibration can be used to establishwhat is commonly referred to as a computer-aided accuracy (CAA) correctionfield. Figure 9.12 shows the results of a laser interferometer measurementof straightness (xTx) on the F25 with the CAA correction enabled [54].FIGURE 9.12 Straightness (xTx) measurement of the F25 with the CAA correctionenabled.ReferencesIn this case, there was a half-year period between the two measurements.The remaining error is a result of the finite accuracy of the original set ofmeasurements used to calculate the CAA field, the finite accuracy of thesecond set of measurements and the long-term drift of the instrument.
Themaximum linearity error is 60 nm.The squareness calibration of the F25 cannot be carried out with a laserinterferometer, so an artefact is used. During this measurement a partialCAA correction is active, based on the laser interferometer measurementsonly. The artefact measurement consists of measuring a fixed length in twoorientations. For the xy squareness, one of these measurements will be alongthe xy diagonal, the other in an orientation rotated 180 around the y axis.The squareness can then be calculated from the apparent length differencebetween the two orientations. The artefact can be a gauge block, but it isbetter to use an artefact where the distance is between two spheres, since theprobe radius does not affect the measurement. Because the principle of thesquareness calibration is based upon two measurements of the same length,it is particularly important that this length does not drift between themeasurements.
In order to get a squareness value which applies to the wholemeasurement volume, the two spheres should be as far apart as possible andplaced symmetrically within the measurement volume.9.7 References[1] Bosch J A 1995 Co-ordinate measuring machines and systems (CRC Press)[2] Flack D R, Hannaford J 2005 Fundamental good practice in dimensionalmetrology NPL Good practice guide No.
80 (National Physical Laboratory)[3] ISO 10360 part 1: 2000 Geometrical product specifications (GPS) Acceptance and reverification tests for coordinate measuring machines(CMM) - Part 1: Vocabulary (International Organization for Standardization)[4] Flack D R 2001 CMM probing NPL Good practice guide No. 43 (NationalPhysical Laboratory)[5] ISO 10360 part 6: 2001 Geometrical product specifications (GPS) Acceptance and reverification tests for coordinate measuring machines(CMM) - Part 6: Estimation of errors in computing Gaussian associatedfeatures (International Organization for Standardization)[6] Barakat N A, Elbestawi M A, Spence A D 2000 Kinematic and geometricerror compensation of coordinate measuring machines Int. J.
Machine ToolsManufac. 40 833–850[7] Satori S, Zhang G X 2007 Geometric error measurement and compensationof machines Ann. CIRP 44 599–609285286C H A P T ER 9 : Coordinate metrology[8] Schwenke H, Knapp W, Haitjema H, Weckenmann A, Schmitt R,Delbressine F 2008 Geometric error measurement and compensation formachines - an update Ann. CIRP 57 660–675[9] Lee E S, Burdekin M 2001 A hole plate artifact design for volumetric errorcalibration of a CMM Int.
J. Adv. Manuf. Technol. 17 508–515[10] Schwenke H, Franke M, Hannaford J, Kunzmann H 2005 Error mapping ofCMMs and machine tools by a single tracking interferometer Ann. CIRP 54475–478[11] ISO 10360 part 2: 2009 Geometrical product specifications (GPS) - Acceptance and reverification tests for coordinate measuring machines (CMM) Part 2: CMMs used for measuring size (International Organization forStandardization)[12] ISO 10360 part 3: 2000 Geometrical Product Specifications (GPS) - Acceptance and reverification tests for coordinate measuring machines (CMM) Part 3: CMMs with the axis of a rotary table as the fourth axis (InternationalOrganization for Standardization)[13] ISO 10360 part 4: 2000 Geometrical Product Specifications (GPS) - Acceptance and reverification tests for coordinate measuring machines (CMM) Part 4: CMMs used in scanning measuring mode (International Organizationfor Standardization)[14] ISO 10360 part 5: 2000 Geometrical Product Specifications (GPS) Acceptance and reverification tests for coordinate measuring machines(CMM) - Part 5: CMMs using multiple-stylus probing systems (InternationalOrganization for Standardization)[15] ISO/TS 15530 part 3: 2004 Geometrical product specifications (GPS) Coordinate measuring machines (CMM): Technique for determining theuncertainty of measurement - Part 3: Use of calibrated workpieces or standards (International Organization for Standardization)[16] ISO/TS 15530 part 4: 2008 Geometrical product specifications (GPS) Coordinate measuring machines (CMM): Technique for determining theuncertainty of measurement - Part 4: Evaluating CMM uncertaintyusing task specific simulation (International Organization forStandardization)[17] Balsamo A, Di Ciommo M, Mugno R, Rebaglia B I, Ricci E, Grella R 1999Evaluation of CMM uncertainty through Monte Carlo simulations Ann.CIRP 48 425–428[18] Takamasu K, Takahashi S, Abbe M, Furutani R 2008 Uncertainty estimationfor coordinate metrology with effects of calibration and form deviation instrategy of measurement Meas.
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