N4T L INSr Of STAND 1 TECH R 1

NBSIR 74-601 AlllOM GEM31S

NIST

PUBLICATIONS

A Survey of the Temporal Stability of

Angle Blocks

Ralph C. Veale

Charles P. Reeve

Institute for Basic Standards

National Bureau of Standards

Washington. D. C. 20234

November 1974

Final

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U.S. DEPARTMENT OF COWMERCE

NATIONAL BUREAU OF STANDARDS

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100

.U55

#74-501

1974

NBSIR 74-601

A SURVEY OF THE TEMPORAL STABILITY OF

ANGLE BLOCKS

Ralph C. Veale

Charles P. Reeve

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

November 1974

Final

U.S. DEPARTMENT OF COMMERCE, Rogers C.B. Morton. Secretary

NATIONAL BUREAU OF STANDARDS. Richard W. Roberts. Director

Contents

Page

Introduction 1

1. Analysis of Measuring System 2

2. Stability Study 4

2.1 Master Values 4

2.2 Measurement Process 4

2.3 Analysis of Test Blocks 4

Conclusion 5

References 6

Appendices

Table I 7

Table II 8

Table III 9

Graphs 1 through 12 10-20

A Survey of the Temporal Stability of Angle Blocks

by

Ralph C. Veale and Charles P. Reeve

Introduction

Angle blocks are wedge-shaped specimens made from either steel or chrome carbide with extremely flat faces. The squareness of the angle

faces to the top and bottom of the gage are also held to close tolerances.

They tend to serve as working standards in angle measurement in much the same way as gage blocks serve the area of length. They come in sets of

various sizes that can be wrung together to form almost any angle to the

nearest second. The first set developed by Dr. Tomlinson of NPL [1]-'- in

1937, consisted of twelve gages of the following sizes:

1, 3, 5, 9, 27, 41 degrees

1, 3, 9, 27 minutes

3, 9, 27 seconds.

Any angle to 81 degrees can be produced from this combination and a square

in steps of 3 seconds. The most common set found in the United States con- sists of 16 blocks of the following sizes:

1, 3, 5, 15, 30, 45 degrees

1, 3, 5, 20, 30 minutes

1, 3, 5, 20, 30 seconds.

Most of the major metrology labs in the U.S. have master sets that are used to calibrate working sets.

Because the standard for angle measurement is the circle which is

exactly 360 degrees, NBS possesses no unique capability (as in mass

"'"Numbers in brackets indicate references given at the end of this

paper.

1
measurement) for angle measurement. Any lab properly staffed and equipped can potentially measure angle blocks as well as the Bureau of Standards .

The Bureau does, however, calibrate a large number of sets and is

repeatedly asked how often it Is necessary to calibrate the sets which

are used as physical standards. A previous report on the stability of

optical flats (NBSIR 73-232) indicated the flats had not significantly

changed over the period studied. Enough data is now available for a similar study of angle blocks.

In order to determine the stability of the blocks, it is necessary

to have a measurement system under statistical control so that an uncertainty in the measurement system cannot be interpreted as a temporal change

in the article being measured. This report will therefore be divided into

two parts, (1) an analysis of the measuring system and (2) a study of the

stability of the angle blocks.

1. Analysis of the Measuring System

For several years prior to 1962, measurements were made by comparing

the test blocks to an NBS master set by interf erometry . In 1962, the

masters were recalibrated and a new system put into effect. It consisted

of comparing the test blocks with the NBS master set using two autocollimators with a differential readout which means the master and the test do

not have to be identically positioned. Also at this time, an additional

set was introduced into the measuring process which served as a check

standard. This procedure has been in use for about twelve years so we have now accumulated a ten year history for several sets. Measurements on angle blocks are made twice a year, usually in February and August.

Seven years ago we introduced a second check set made from chrome

carbide into 'the measuring system. The carbide set is scheduled to soon be elevated to our master set. The method of taking data was changed in

1971 to enable us to get more statistical control over the measurement

process. An intercomparison design was employed whereby test blocks and

check standards were measured against the master block with redundancy.

The observed standard deviation of a single measurement was compared with

the historical value as a check on the process stability. This new method

gave the same precision for each block and required fewer measurements

than before. The data taken prior to 1971 has since been examined to

determine the standard deviation of the measurement process at that time.

In a few cases the measurements were made using a least squares solution

and the random component of the measurement uncertainty was available.

The 30 and 45 degree blocks are difficult to measure well using the

differential system described, but are easily measured using the "closure

2
technique" which does not require a master. The closure teclinique simply

compares an x degree block to each of the 360/x intervals of x degrees on

an indexing table. The measurements are restrained by the fact that the sum of the intervals on the indexing table is exactly 360 degrees. The

one second blocks were also measured by a "reversal" technique not re- quiring a master. The blocks are simply rotated 180 degrees and the difference between the 0 and 180 degree readings is twice the angle of the

block.

The 1 second, 20 second, 20 minute, 5 degree and 45 degree blocks

have been chosen as representative of the entire set. The one standard

deviation random error component of the measuring process for each series

of measurements for these five block sizes is given in Table 1. Errors in

flatness of the faces and out-of-squareness of the faces to the base and

top coupled with individual errors in the autocollimator will usually cause

a block to give a different value when supported on its top rather than its

base. The difference is usually around 0.1 second but occasionally may be

as high as 0.5 second. Our measurement protocol called for measuring the

blocks both ways and averaging. In a few of the measurements taken sev- eral years ago, it was not possible to tell if this practice had been

followed. In other cases, it definitely had not been followed. This

partially accounts for the wide range of standard deviations in Table I. Also because these numbers are the standard deviation of the mean and not

an individual measurement, they vary depending on the amount of work put

into each series. Some of the numbers are the result of only two com- parisons with the master and others as many as eight . The numbers were

also operator dependent - careful operators tended to get a lower standard

deviation than careless ones. Additional factors such as whether the autocollimator with 0.1 second or 0.01 second readout was used caused fluctuations in the standard deviation.

Since 1971 the standard deviation has been constant for each block

size because the within-group (or short term) variability of our measurement process has been very stable. Each year thereafter the observed

standard deviation of a single measurement has not differed significantly

from the 1971 value.

A least squares first order polynomial (a straight line) was fitted

to the data from each block from all the sets chosen. Table II gives the

standard deviation of the reported values relative to the best fitting

straight line for each of the sixteen blocks in twelve sets. Unlike Table I which is a measure of the within group variance. Table II shows the

between group variance adjusted so a linear change in the block would not

be reflected in the standard deviation. It is not surprising that the between group standard deviation is larger than the within group due to the

variations in the measurement process over the past years.

3
2. Stability Study

If the measured value of a block has changed over a period of time

it may be due to (1) the master set has changed (2) the measurement process was out of control or (3) the test block has actually changed.

2.1 Master Values

The original calibration of our master set was a lengthy process

involving measuring the individual blocks by interf erometry (and other

techniques) and then measuring the sums and differences of various wrung

combinations. Several of the blocks have been checked by numerous techniques since this original calibration and have shown no detectable change.

We have also almost completed an "absolute" calibration on our chrome car- bide set of masters. (A paper explaining in detail the method used will

be published at a later date.) We have a seven year history of comparison

measurements between this set and the master set. The measurements are

in good agreement and we are therefore convinced there has been no change

in the master set within our ability to measure.

2.2. Measurement Process

The measurement process was analyzed in section 1. Tables 1 and II

verify that it has been stable over the twelve year period.

2.3 An Analysis of the Test Blocks

Over one hundred sets have been calibrated during the past twelve

years producing a voluminous amount of data to examine. We decided to

limit our investigation to our own two check sets and only the test sets

which have been calibrated at least five times during the period covered.

A cursory examination was made of every set which had been in at least

twice which indicated the sets we chose were representative and there

were no exceptional cases not covered. Table III lists the slope in arc seconds per year of the least squares line fit to the data. In all cases

the slopes were found not to be significantly different from zero. To

better illustrate the results of the tables, graphs of the calibrated

values have been drawn for the fi^'^e selected block sizes in the two NBS

check sets. The NBS-25 set is made of stainless steel and the NBS-7 set

is made of chrome carbide.

At the upper left hand part of each graph is the observed long term

slope (m) of the calibrated values. These values are also given in table III. The worst case of slope was for the 5° block of set number 10.

Its graph (p. 20) indicates an upward trend, but each of the 3 standard

deviation uncertainty bands overlaps which indicates that no significant

change has occurred.

4
Conclusion

Examination of the histories of these sets of angle blocks reveals

that there is a significant between-time component of error in the measured values. This error seems to be fairly consistent in all twelve of

the sets, and it is not significantly correlated with the block size.

None of the blocks exhibited a significant change in value over the ten

year period, so it can be concluded that these angle blocks are stable over long periods of time. It should be noted that the 1", 30°, and 45°

blocks, which were calibrated "absolutely" most of the time, show roughly

the same long term variation as the other sizes.

The large between-time component of error can probably be explained

by the inability to duplicate the exact measurement conditions each time

a block was calibrated. The out-of-flatness and out-of-squareness of the

individual blocks combine with certain alignment errors in the autocollimators and the angle block support to produce an effect which is unique

to each calibration. When more is learned about the nature of these

errors, it may be possible to compensate for them and reduce the observed

between-time component of variation significantly.

5
References

[1] Kioyle, C. H. , Production of Combination Angle Gages, The Engineer,

Sept 1, 1950, p237-8 Machy (London)

[2] Farago, Francis T., Handbook of Dimensional Measurement, Industrial

Press Inc., New York, 1968.

[3J Parsons, S.A.J. , Metrology and Gauging, MacDonald and Evans Ltd.,

London, 1970.

6
TABLE I

SHORT TERM STANDARD DEVIATION OF THE MEASUREMENT PROCESS

One Standard Deviation of the Mean

seconds

Date 1" Block 20" Block 20' Block 5° Block 45° Block

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2-70 .022 .025 .022 .020 .059

7-70 .042 .034 .035 .039 .104

2-71 .028 .028 .028 .028 .073

8-71 .028 .028 .028 .028 .073

2-72 .028 .028 .028 .028 .073

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NBS-1 14A (REV. 7-73)

U -S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. l'l!Hl.l( A riON OK Kl- I'OK I' NO. NBSIR 74-601

2. Ciov't Aft c'ss ion No.

3. Kill picnl Ai ( r sMoll No .

4. rn i.i: and sum titli-;

A Survey of the Temporal Stability of Angle Blocks

5. I'uliiuaiion n.iic November 1974

6. 1^1- r lor ni 1 n g Organ i / ai ion ( oili

7. AU I HOR(S) ^^^^ C. Veale and Charles P. Reeve

8. I'erloniiing Organ. Ki port No, NBSIR 74-601

9. PERFORMINC. ORGANIZATION NAME AND ADORKSS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Pro|i Tt/ i'.isk/Work lltiit N,>. 2321121

1 1. < onlrai t /Cirant No.

12. Sponsorinp Organization Name and C omplete Addres.s (Street, City, State, ZIP)

Same as No. 9

13. 1 ypr of Ki port &: I'enoil

( ovrredFinal

14. Sponsoring Agcm y ( odr

15. SUFPl.EMENTARY NOTES

16. .ABSTRACT (A 200-word or less factual summary ol most significant information. If document includes a significant

bibliography or literature survey, mention it here. )

The National Bureau of Standards is often asked how frequently a set

of angle blocks should be calibrated. In order to provide a basis

for answering that question, a survey was made of the long-term stability of several sets of angle blocks over a ten-year period. Data

is given concerning the short-term and long-term variability of the

measurement process as well as the observed long-term slope of the

computed values. The conclusion is that a significant long-term variation in the measurement system does exist, but the long-term slope of

the blocks which were surveyed is not significantly different from zero.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons

)

Angle block; between time variation; calibration; measuring system; stability;

standard deviation; statistical analysis.

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