Calibration of a polygon using three autocollimators

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Calibration of a polygon using three autocollimators

Citation for published version (APA):

Amaradasa, A. A. (1971). Calibration of a polygon using three autocollimators. (TH Eindhoven. Afd.

Werktuigbouwkunde, Laboratorium voor mechanische technologie en werkplaatstechniek : WT rapporten; Vol. WT0274). Technische Hogeschool Eindhoven.

Document status and date: Published: 01/01/1971

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-_.._ - - - . , . - - - 1

titel:

rapport von d. ,.«:tie: Laboratorium voor Lengtemet ing.

-_._-biz. 1 van

8

bIz.

rapport nr. 021'1 codering: M 8

f

trefwoord: H()q.kn-,~hl')g _

I

datum: 19 april 1971 aantal biz. f) geschikt voor publicati. in: I I I P.C. Veenstra CALIBRATION OF A POLYGON USING THREE AUTOCOLLlMATORS.

A.A. Amaradasa

Drs. J. Koning

In this experiment an attempt was made to calibrate a 12-sided precision polygon using three autocollimators simultaneously. Two auto collimators were used for measuring and the third was used as a fiducial indicator. A comparative account of the measurements performed by the two measuring autocollima-tors is given in the report.

A complete analysis of the whole experiment including the accuracies of the measurements could not be conducted for want of time. Prof. dr.

technische hogeachool eindhoven

laborotori"'" voor IMchanl,che technologi. en wmplootstechniek

progno,. aut.ur(s): hoogleraar: s.cti.leider: samenvatting , - - - _..

_ _ . _

-~

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rapport nr. 0.1.

r

't

Part I

1 . CALIBRATION OF A POLYGON USING THREE AUTOCOLLIMATORS

5

-biz. %. van 19 biz.

10 f - 20'- 30- 35- 50-1.1. Introduction

Angular measurements are frequently necessary in connection with engin-eering operators and the required accuracy varies according to the par-ticular application. In engineering metrology this aspect of angular measurement strictly includes the continuous measurement of angles in

the division of a circle.

In general there are several methods of dividing used in precision engineering, but the polygon method provides a very accurate method of circular dividing.

As such the polygon is normally used to calibrate rotary tables which are a widely used device in engineering for setting and measuring angles.

Thus it is essential that the included angle between the measuring faces of the polygon have a value equal to the nominal value within a few seconds of arc.

In this investigation an attempt has been made to calibrate a pre-cision polygon by using three autocollimators simultaneously.

1.2. General description

A 12-sided polygon was used in the experiment and the three

autocolli-TAl. 5 TA 54-1

mators used were HILGER WATTS - 135075' 222935 and 126346.

One of the autocollimators was used as the fiducial indicator and the other two were used in taking measurements. The idea of using three autocollimators simultaneously was to see whether the two measuring autocollimators in combination with the fiducial autocollimator, yiel-ded consistent observations under the same experimental conditions.

Considering the availability of space on the table on which the apparatus were assembled, measurements were restricted to only three symmetrical positions (a), (b) and (c) of the autocollimator and the

principle outlying the method is described in QFpe~di~ R

The three positions are illustrated in Fig. 1 Appendix - A

tKhnI8che

hogoschool eindhoven i

I

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In position (a) the autocollimators are placed facing the adjacent ::-tdt'S

BA, AL, LK. Let the autocollimators be denoted by I, II, III

respecti-vely. II is the fiducial indicator. This autocollimator is correctly

adjusted to get an image of the crosswjre~.. Initially the other two

autocollimators I and III are positioned approximately so that they make with II the nominal angle of the prism.

If the readings on I and III are noted, exact adjustment of these enable the angles 8, p, to be measured.

If the polygon is now rotated in an anticlockwise direction so that each face of the polygon in turn faces the fiducial autocollimator,

it is possible to get a series of 12 values for each of the angles 8

and p. Thus the exterior angles A, B, .•• L of the polygon can be

calculated, (see table 1, page

7 ),

(theory discussed in Appendix

R ).

If the experiment is now repeated for positions (b) the

~lr,,', /, ....:~',f'.,,'; ..,

sums (A+B), (B+C), ••• etc.

.,.4'"

are

ob-tained (see table 2, page d ). 1.3. Method r---ra-p-p-ort...,....-nr-.-O-l..-T-4---·---~---b-IZ-.-3--Va-n-a-b-IZ.l

f - - - . - - _ . - - - -

~

I

5 - 01-1Q r- 20'- 15- 25r-- SOr-- 35r--1.4. Progress of investigation

For the investigation to be of any practical value, the first position (a) only was used in estimating the results as direct measurements of the angles could be obtained for this position. Position (b) was used merely to check the consistency of the results obtained for position

(a). The observations for position (c) have not been given as it is

suspected that a systematic factor had influenced these observations.

1.5. Summary

The tables of observations given in Appendices B,C.

~- show how the measurements taken with the two measuring autocollimators

compare with each other.

~~ 1.6. Concluding remarks

A better comparison of the possibilities of the two measuring autocol-limators, as well as the accurate determination of the angles could be

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'f +-t---,---',~~,~',' I

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Ilz.

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van

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5 10 15 20 25 30 35 50

done by taking each one of the autocollimators separately and conducting the experiment for all the possible positions (a), (b), •.. etc.

In this particular case, the space of the table on which the appa-ratus were assembled, imposed restrictions on such a series of measure-ments.

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rapportIV. 0 2..

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DETERMINATION OF STANDARD DEVIATION

I - HILGER & WATTS

0 5 -Autocollimator Autocollimator II -Autocollimator III

-"

"

TA 1.5

-135075 TA 54-1

-222935 - 126346 10 - 15-

20-Standard deviation (of combinations).

I with II III with I I

3.0 4.0 1.8 5.9 3.5 5.6 2.5 6.3 2.5 6.3 1.7 5.5

1

I 25f- 30-1.3 2.7 1.1 S = 3.5 - 1.1 = 2;4 = 0.8 sec.

19

5.4 5.2 6.7 '

-~-:-~-=-~-:-;-:-;-:::~---j

19

3 I

Standard deviation of the single autocollimator.

I alone II alone III alone

35f- !Or-21.8 3.8 21.5 3.6 21.6 3.1 21.7 3.4 21.3 3.4 21.5 3.4 21.5 3.1 21.8 3.5 21.4

I

3.0

-:-:-;~~~=;~~;-:-~~~-:-~~~~:-t-~--:-~~~-:-~~~~:-I

19

3

I

II

19 I

4.6 4.5 4.2 4.1 3.8 4.3 4. 1 4.1 4.1 4.6-3.8

=

0 3 .8

=

0.27' SIlI=

19

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rapport nr. b'<'

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van

a

biz. o _{APPENDIX -}

_A

Theory 5 10 15 20 25 +

°

2, ... etc. A EO EO

-12

(30 -

f~J

B = [30 -

~~]

360 = 12x + x = 300

Now from earlier relations,

From the geometry of Fig.l (b), it is clear that

A

=

x +

°

₁ Similar relations B = x

+°

2, ..• etc. hold. Adding up we have 30 35 50

Similar relations hold for autocollimator III of Fig.l (a). Using the same reasoning as above it can be proved that, for position (b)

A + B == y +

°

1

B + C = y +

°

2, .•. etc.

(

L6]

Similar relations as for position (a), VIZ. (A+B) = [60 -

12

+

°

1, etc.

are obtained.

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rapport nr.02..

1

'r

Or- APPENDIX -

B

biz. t van eY biz.

I

5

-Results obtained for position (a)

Angle Autocollimator I Autocollimator III

10

-

A 30° + 0.4" 30° 1. 7" B 30° + 1 .4" 30° + 1 •6" C 30° - 2.6" 30° - 1 . 5II D 30° + 0.2" 30° + 0.2" 15

-E 30° - 0.5" 30° + 0.3" F 30° - 3.0" 30° - 2.5" G 30° + 1.5" 30° + I .6" 20 " -30° + 0.9" 30° + H I .3" I 30° - 2.5" 30° - 1 . 8" J 30° + 2.6" 30° + 1 .5" 25

-

K 30° + 2.8" 30° + 2.5" L 30° - 1.3" 30° - 1. 4" 30-

35-

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10 15 20 25 30 50

rapport nr.

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_a

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--

APPENDIX - C

"-Direct measurements from position (b) Comparison with position (a)

_I

-Angle Autocollimator I Autocollimator I I Autocollimator I Autocollimator I I

A+B 600 + 0.5" 600 +

A"

600 + 1.8" 600 - 0.1" f -B+C

-

1.5" - 0.6"

-

I .2" + 0.1" C+D - 2.0" - 1.5" - 2.411

_-

_I_.3" D+E + 0.9" + 0.2"

-

0.3" + 0.511 ;-E+F - 3.0" - 4.6" - 3.5" - 2.2" F+G

-

I .9"

- 0.3"

- 1.5" - 0.9" ' -+ 3.5" I .5" + 2.4" + 2.9" G+H + H+I - 1.6"

-

I .6"

-

I .6" - 0.5"

I+J

+ I .8" + 0.8" -0.1" - 0.3" f -J+K + 5.4" + 5.7" + 5.4" + 4.0" K+L + I • I " + 1.6" + 1 •5" + I . I " I -- 2.8" - 1.0" - 0.911 _{- 3.1"} L+A f - .< f I

-W'orkpl.Cltstechniek

_{techniKh. hog.school}

_eindhovttn

Calibration of a polygon using three autocollimators