Quick Guide to Precision Measuring Instruments

43/76

PG41Quick Guide to MeasurementComputerLaser length measuring machine counterLaser sourceInterferometerOptical axis of laser beamCube cornerFixtureComputerDigital counterLaser length measuring machine counterLaser sourceInterferometerOptical axis of laser beamCube cornerFixtureScale unitMovable tableThe accuracy of the scale at each point is dened in terms of an error value that is calculated using the following formula: Error = Value indicated by the linear scale − corresponding value of laser inspection systemA graph in which the error at each point in the effective positioning range is plotted is called an accuracy diagram.There are two methods used to specify the accuracy of a scale, unbalanced or balanced, described below.Positional Indication accuracyThe accuracy of a linear scale is determined by comparing the positional value indicated by the linear scale with the corresponding value from a laser length measuring machine at regular intervals using the accuracy inspection system as shown in the gure below. As the temperature of the inspection environment is 20˚C, the accuracy of the scale applies only in an environment at this temperature. Other inspection temperatures may be used to comply with internal standards.(1) Unbalanced accuracy specication - maximum minus minimum error This method simply species the maximum error minus the minimum error from the accuracy graph, as shown below. It is of the form: E = (α+ βL)µm. L is the effective measuring range (mm), and α and β are factors specied for each model. For example, if a particular type of scale has an accuracy specication of (3 + 3L̶̶̶1000 )μm and an effective measuring range of 1000mm, E is 6µm.(2) Balanced accuracy specication - plus and minus about the mean errorThis method specifies the maximum error relative to the mean error from the accuracy graph. It is of the form: e = E ±̶ 2 (μm). This is mainly used in separate-type (retrot) scale unit specications. A linear scale detects displacement based on graduations of constant pitch. Two-phase sine wave signals with the same pitch as the graduations are obtained by detecting the graduations. Interpolating these signals in the electrical circuit makes it possible to read a value smaller than the graduations by generating pulse signals that correspond to the desired resolution. For example, if the graduation pitch is 20µm, interpolated values can generate a resolution of 1μm. The accuracy of this processing is not error-free and is called interpolation accuracy. The linear scale's overall positional accuracy specication depends both on the pitch error of the graduations and interpolation accuracy.Overview of Accuracy Inspection SystemSpecifying Linear Scale AccuracyScale error at any point in range relative to start of range0ErrorEffective positioning rangeX Measuring pointMaximum difference in scale error: E(µm)0ErrorEffective positioning rangeX Measuring pointMaximum error about mean error E : ±— (µm) 2Mean error