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Cosine Error in Indicator Readings
Here we examine cosine error with an dial indicator. An
indicator is commonly used by machine builders, operators, maintenance,
tooling, and inspection personal to measure in 0.0001" and 0.001mm or smaller
resolutions. Whenever we use any precision measuring instrument we expect
that the reading we get from the instrument is the actual dimension.
This will not be the case if we do not account for cosine error as
demonstrated below.
This example uses a finger dial indicator to show that a correction factor is
needed to account for cosine error. The indicator used in this example reads the
correct dimension when the finger is parallel to a flat work-piece or tangent to
a curved surface. Cosine error occurs when the finger is not parallel to the
workpiece.
|
Correction Factor Table |
|
Angle Degrees |
Multiply by |
|
10 |
0.98 |
|
20 |
0.94 |
|
30 |
0.86 |
|
40 |
0.76 |
|
50 |
0.64 |
|
60 |
0.50 |
Suppose angle a as shown in
the picture to right is 60 degrees and the indicator reads .004". According to the
Correction Factor Table, for a 60 degree angle one must multiply the reading by
0.50 to account for cosine error. .004 x 0.50 = .002". The true dimension is .002" not .004" as the indicator read.
Keep in mind though, this is not true of all indicators.
Some manufacturers build their indicators to read correctly with the finger at a 10, 15, or 20 degree angle to the workpiece. They do that because one cannot slide
a flat workpiece under the indicator without hitting the body of the indicator with
the finger parallel to the workpiece. Regardless, cosine error must be accounted
for with these indicators too. The point here is one must know the indicator being used to achieve accurate results. Read the indicator's documentation
or consult the manufacturer for this information.
There is an exception to this. The demonstated example has been for the most common
indicator
which have a ball
tip. There are also fingers that have a flame shaped tip
 . Cosine error is automatically accounted for with these within a designated number of degrees as long as the finger remains within
those degrees of parallel to
the workpiece. This is because as the angle of the finger
increases, the contact point gets farther away from the pivot point
therefore lengthening the distance between the contact point and the pivot point
of the finger.
Cosine error also applies to button type indicators in a different way. The difference is
the button shaft must be perpendicular to the workpiece or there will be cosine error.
Interferometer Lasers
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