Specifying Linear Scale Accuracy
(1) Unbalanced accuracy specification - maximum minus minimum error This method simply specifies the maximum error minus the minimum error from the accuracy graph, as shown below. It is of the form: E = ( α + β L) µm. L is the effective range (mm), and α and β are factors specified for each model. For example, if a particular type of scale has an accuracy specification of (3 + ——3—L 1000 ) µm and an effective range of 1000 mm, E is 6 µm. Scale error at any point in range relative to start of range
Positional Indication accuracy The 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 figure 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.
Laser length measuring machine counter
Computer
Digital counter
Maximum difference in scale error: E(µm)
Error
0
Effective range
X Measuring point
Cube corner Fixture
Interferometer Optical axis of laser beam
(2) Balanced accuracy specification - plus and minus about the mean error This 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 (retrofit) scale unit specifications.
Laser source
Scale unit Movable table
Overview of Accuracy Inspection System
0 Error
Maximum error about mean error: ±—E (µm) 2
Mean error
The accuracy of the scale at each point is defined in terms of an error value that is calculated using the following formula:
Effective range
X Measuring point
A linear scale detects displacement based on graduations of constant pitch. Two-phase sinusoidal 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 20 µm, interpolated values can generate a resolution of 1 µm. The accuracy of this processing is not error-free and is called interpolation accuracy. The linear scale's overall positional accuracy specification depends both on the pitch error of the graduations and interpolation accuracy.
Error = Value indicated by Laser length measuring machine − Corresponding value indicated by the linear scale
A 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 the right.
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