|
The relationship between
angles and linear dimensions is defined by
trigonometry. Sine, cosine and tangent functions
allow to calculate these relationships. Because an
angle diverges as distance from the origin
increases, so too, increases the tangential
component. Therefore, it is not appropriate to
specify a
rotary tables accuracy in linear values,
unless a maximum envelope (diameter) is also
specified.
It is not difficult to
determine the linear relationships to their
respective angles, within a specific envelope. Let's
equate 1 arc second (see definition in Glossary) to
some common linear measurements. For our discussion,
we'll use 0.000004848 as the tangent of 1 arc
second. Since the trig functions provide
dimensionless ratios, 0.000004848 (usually rounded
to (0.000005) applies to any unit of linear measure,
just be consistent.
To use the charts below,
locate your required linear tolerance, and the
maximum radius to be worked, the resulting
intersection shows the corresponding nominal index
accuracy, in arc seconds (unless specified, i.e.,
[°] = deg.; ['] = min.), required for the
application. If your tolerance zone or working
radius falls between two values, use the tighter
requirement.
|
Tolerance |
Working Radius (Inches) |
|
|
1 |
2 |
3 |
4 |
5 |
6 |
10 |
12 |
18 |
20 |
24 |
30 |
36 |
40 |
48 |
|
0.010" |
½° |
¼° |
10' |
8' |
6' |
5' |
3' |
2' |
2' |
1' |
1' |
1' |
30 |
30 |
30 |
|
0.005" |
¼° |
10' |
5' |
4' |
3' |
2' |
2' |
1' |
1' |
30 |
30 |
30 |
20 |
20 |
15 |
|
0.003" |
10' |
5' |
4' |
3' |
2' |
2' |
1' |
1' |
30 |
30 |
30 |
20 |
20 |
15 |
10 |
|
0.002" |
5' |
3' |
2' |
2' |
1' |
1' |
30 |
30 |
30 |
20 |
15 |
10 |
10 |
10 |
10 |
|
0.001" |
3' |
2' |
2' |
1' |
30 |
30 |
20 |
20 |
15 |
10 |
10 |
10 |
5 |
5 |
5 |
|
0.0005" |
1' |
1' |
30 |
30 |
20 |
15 |
10 |
10 |
5 |
5 |
5 |
5 |
2 |
2 |
2 |
|
0.0003" |
1' |
30 |
20 |
15 |
10 |
10 |
5 |
5 |
5 |
3 |
3 |
3 |
2 |
1 |
1 |
|
0.0001" |
20 |
10 |
5 |
5 |
3 |
3 |
2 |
2 |
1 |
1 |
1 |
0.5 |
0.5 |
0.2 |
0.2 |
|
0.00005" |
10 |
5 |
2 |
2 |
2 |
1 |
1 |
1 |
0.5 |
0.5 |
0.5 |
0.2 |
0.2 |
0.2 |
0.1 |
|
0.00001" |
2 |
1 |
1 |
0.5 |
0.2 |
0.2 |
0.2 |
0.1 |
0.1 |
0.1 |
* |
* |
* |
* |
* |
Table 1 [inch values]
|
Tolerance |
Working Radius (Millimeters) |
|
|
25 |
50 |
75 |
100 |
125 |
150 |
200 |
250 |
375 |
500 |
750 |
1000 |
1500 |
|
0.25 mm |
½° |
¼° |
10' |
8' |
6' |
5' |
4' |
3' |
2' |
1' |
1' |
30 |
30 |
|
0.1 mm |
10' |
5' |
4' |
3' |
2' |
2' |
1' |
1' |
30 |
30 |
15 |
15 |
10 |
|
0.05 mm |
5' |
3' |
2' |
1' |
1' |
1' |
30 |
30 |
20 |
15 |
10 |
10 |
5 |
|
0.025 mm |
2' |
1' |
1' |
30 |
30 |
30 |
15 |
15 |
10 |
5 |
5 |
5 |
3 |
|
0.01 mm |
1' |
30 |
20 |
15 |
10 |
10 |
10 |
5 |
5 |
3 |
3 |
1 |
1 |
|
0.005mm |
30 |
15 |
10 |
10 |
5 |
5 |
5 |
3 |
3 |
2 |
1 |
1 |
0.5 |
|
0.0025 mm |
15 |
10 |
5 |
5 |
3 |
3 |
2 |
2 |
1 |
1 |
0.5 |
0.5 |
0.2 |
|
1 µm |
5 |
3 |
2 |
1 |
1 |
1 |
0.5 |
0.5 |
0.5 |
0.2 |
0.1 |
0.1 |
0.1 |
|
0.5 µm |
2 |
1 |
1 |
0.5 |
0.5 |
0.5 |
0.2 |
0.2 |
0.2 |
0.1 |
* |
* |
* |
Table 2 [metric values] |