NBSIR 73-136

Measurements of Cylindrical Standards

Ralph C. Veale

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

March 14, 1973

Final Report

U, S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NBSIR 73-136

MEASUREMENTS OF CYLINDRICAL STANDARDS

Ralph C. Veale

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

March 14, 1973

Final Report

U. S. DEPARTMENT OF COMMERCE. Frederick B. Dent. Secretary

NATIONAL BUREAU OF STANDARDS. Richard W. Roberts. Director

Measurements of Cylindrical Standards

Introduction

Cylindrical standards may be sent to the Bureau for calibration listed as cylinders, rolls, plugs, plug gages, wires,

thread wires, plain setting plugs or possibly other names. Regardless of what they are called, they can generally be put in

one of two categories: (1) thread measuring wires and (2) other

cyl inders

.

It is necessary to establish which they are because the

reported value of most thread wires is not the true diameter

but a deformed diameter to approximate the deformation that will

occur when the wire is used to measure a thread. A separate

manual has been prepared on how to measure thread wires , NBS

Report No. 10 987. In almost all cases they will be compared

to two sets of NBS master wires.

The second category can be further divided into two groups:

the first being those cylinders for which we have master cylinders

and the second, those for which we do not. At the present time,

we have only one set of calibrated master cylinders consisting of

16 cylinders from 1/16 inch to 1 inch in increments of 1/16 inch.

We also have another set which has never been calibrated consisting

of decimal inch sizes. They go from 0.05 inch to 0.3 inch in increments of 0.05 inch and from 0.3 inch to 1 inch in 0.1 inch
i nc rcniiMits . This sot will hv c.ilLbratod in the near future.

In both cases the measurement technique is essentially the

same, i.e. we compare the unknown (or unknowns) to two masters,

one master serving as the restraint and the other as a check.

In all cases a gage block combination will serve as the restraint

and the check will be either a gage block combination or an NBS

master cylinder. The latter is felt to be more desirable in

that it is certainly faster and it allows us to maintain a

history of our cylindrical standards. A set of cylindrical

check standards enables us to detect systematic errors that could

be missed using two gage block combinations. The disadvantage

of the system is that until we build up a history of the cylinders,

we know the length of the gage block more accurately than we know

the diameter of the cylinder.

This is not to say that the preceding method is the only

way cylinders can be measured. There are inter ferometric techniques using the thread wire interferometer or ball interferometer

and a polychromatic viewer. Work has been done showing that the

Zeiss Optimeter and a fringe counter can be used. Cylinders

can be and often are calibrated with a gage block comparator.

Commercial instruments can be bought specifically for cylinder

measurement which employ a variety of both optical and mechanical techniques. In principle, all of them work but the

instruments must be properly constructed, considerable care must be

2
taken in making the measurements and all the proper corrections

must be made. A common error is to use a comparator with ball

contacts to measure a cylinder by comparing it to a gage block

and not apply a deformation correction. The difference between

ball to plane and ball to cylinder deformation is not always trivial,

especially where the probe diameter is nearly the same size or

larger than the cylinder. As an example, 2.2 microinches must

be added to the value of a 1/8 inch steel cylinder which has

been measured in this manner under a one pound force assuming

the comparator is of the single probe type having a diamond

contact with a radius of curvature of 0.0625 inch.^''"'^

It is our belief that the method described below is the

best method currently available at the Bureau. It is obviously

impossible to maintain a set of masters for every conveivable

size that might come in, so our measuring process will be

described assuming the cylinder is an odd size.

Measurement Procedure

The cylinder is first examined by taking Talyrond* traces.

One may find the out -of -roundness so bad that an accurate measurement makes little sense. In this case, one stops and consults

^Certain coramerical equipment, instruments, or materials are identified in this paper in order to adequately specify the

experimental procedure. In no case does such identification

imply recommendation or endorsement by the National Bureau of

Standards , nor does it imply that the material or equipment

identified is necessarily the best available for the purpose.

3
with Lhe cusLomer on the besL course to take. No strict rules

can be given other than it must be remembered that the uncertainty

of the measurement cannot be smaller than the model ambiguity

(see appendix V). The model ambiguity can usually be reduced,

however, by defining the diameter to be measured.

Assuming the quality of the cylinders is reasonably good,

three traces should be made on each cylinder -- at the center

and about 1/16 inch from the ends. Here again, there may be

exceptions such as the NBS Pressure Section will often specify

exactly how many and where they want traces made. The next step

is to measure the variation in diameter along the cylinder.

This is done using the same machine that will be used to make

the diameter measurement -- a modified Pratt and Whitney measuring machine. The ways of the modified Pratt and Whitney have

been carefully scraped so that the headstock can be moved without appreciably altering the parallelism of the jaws. One inch

of travel can be obtained with the screw without moving the

headstock. \ ^- ^'

The regular tailstock has been replaced by one having

flexure springs which give very nearly linear motion over a

short range. The measuring force is set by a dead weight placed

on the pan under the machine rather than the more common but

less accurate coil spring. When setting the machine force, the

4
transducer is adjusted with no weight on the pan until the dial

reads zero.

Movement of the left anvil moves the transducer pickup. The

signal is amplified and displayed on the meter of the amplifier.

On the low scale each division is two microinches with an 80 micro

inch range and each division on the high scale is 1/2 microinch

with a 20 microinch range. Using the appropriate scale of the

meter, the jaws are brought to the correct separation either by

turning the screw or moving the heads tock.

Measurements are then made at several places along the

cylinder to determine the variation in diameter from the midpoint. In some cases, we will report all of these values and

in others it is sufficient just to give a maximum value. If

we know how the cylinder being measured will be used, we can

usually make this decision with no difficulty. As an example,

suppose the cylinder being calibrated will be used only to calibrate other cylinders. Then it is apparent that one can define

a gage point to be used, which will usually be at the center.

If there is an out -of -roundness problem, the plane of measurement can also be defined. In this case, the diameter at the

end is of no importance as long as they are used only for transfer standards. On the other hand, if the cylinder is to be used

as a go or no go plug gage then the end value would be very

5
significant. The rule that we follow is to give the customer

as much information about the cylinder as is economically feasible. We try to avoid doing work that is not needed but we don't

withhold information that has been gathered. If we are uncertain

as to what the customer wants or how they are to be used, a phone

call is made to the person who will be using our report.

Having decided that we want to measure the cylinder to the

best reasonably obtainable accuracy, we first get a value accurate

to about 50 microinches by measuring it in a standard measuring

machine. A combination from a grade 2 set of gage blocks is then

wrung to the nearest 0.0001 inch of that size and we again measure the cylinder by comparing it to the combination using the modified Pratt and Whitney. Some of the blocks may deviate appreciably

from nominal so we use the corrections listed in the calibration

report. This measurement which is not taken with any great

amount of care will give a value for the cylinder which is accurate to about 15 or 20 microinches.

From our grade 1 sets, we then wring two more combinations

such that they are within 25 microinches or less of what we expect the cylinder to be. Of course if we are measuring class XXX

gages, we can safely assume that the actual size will be very

close to the nominal size and we can skip the first two steps.

We also maintain a fractional gage block set so fewer blocks are

required to be wrung together in measuring fractional size cylinders.

6
IL i.H very difficult to wriiij/, blocks whose thickness is less than

0.1 irxch and the wringing of such sizes should be avoided if possible.

One way to avoid combinations made with thin blocks is to include

another block as part of the test item. Suppose we had a 0.038 wire

to measure, we could then choose a 0.140 as our nominal and compare

a 0.102 block and the wire to the 0.140 block. There are of course

other combinations that would work equally well. The diameter of

the wire in this case would be the measured value minus the actxaal

value of the 0.102 block. The term "block combinations" is used

here to mean one or more blocks.

Measuring a one inch cylinder does not require wringing several

blocks together; one simply selects two 1 inch blocks. If more

than one block is used in our combination and if we are still trying to get the best reasonably obtainable value, the combination

should then be measured rather than using the sum of the individual

blocks. This work is currently being done at the Bureau by the

Mass, Length and Volume Section. In a combination involving several

blocks, it is necessary to check the parallelism as they are wrung

together to insure that the complete stack will be parallel. Two

blocks that are not parallel can often be made so by changing their

relative positions. For small combinations up to about 0.5 inch,

we can do this on the Acme viewer which is a Fizeau type interferometer. For the larger sizes, we ask the gage block group to both

wring and measure the combination.

7
while tile combinations are being measured, the measuring

machine is checked. The amplifier is not solid state and can

change with time, therefore, it is calibrated often, usually

before starting any new job. This is done by using special

brass fixtures which are kept with the machine. They are pressed

over the anvils of the measuring machine and rotated slightly

until they feel firm. One fixture has three balls attached to

the end and the other fixture has one. This contact system is

better for calibrating the amplifier than wringing in that it is

more accurate and much faster. Two gage blocks are chosen such

that their difference is slightly less than full scale reading.

The low scale is usually used as its resolution is adequate and

the range on the high scale is often too small. Past experience

has shown that the scale is linear. The difference between the

blocks is then measured and the magnification factor, K, is the

actual difference between the blocks divided by the measured

difference.

Next, after removing thfe ball fixtures, the anvils are

stoned to remove any burrs. A special stone (a gage block stone

whose faces are parallel) is used. Both the stone and anvil

are cleaned and the stone is brought on scale as if we were

going to measure it. The stone is then moved in a circular

path parallel to the jaws until it seems to wring. Occasionally

a burr will appear on the jaws that cannot be removed with the

8
stone but requires a diamond lap. This is done only by someone

familiar with lapping techniques.

A set of optical parallels is then used to verify that the

faces are flat and parallel. Any value for either flatness or

parallelism error greater than 2 microinches is considered excessive. As a final check, a gage block should easily wring

to either of the jaws. The magnification factor, the date and

any changes made to the machine are recorded in a log book.

How accurately we measure the temperature while making the

measurements depends on the size and composition of the test

cylinder. The linear coefficient of thermal expansion is about

11.5 parts per million per degree Celsius for steel and varies

from near zero for some of the ceramic materials such as Cervit

to around 30 parts per million for some metal alloys. If we are

measuring a 0.1 inch or less steel cylinder, we can safely ignore

temperature when working in our temperature controlled rooms. If

we are measuring a two inch carbide piston using steel gage blocks,

we not only must measure the temperature of each individual piece

accurately, but we also need to know the coefficient of expansion

for each of the materials.^

Most cases will lie between these two extremes and a mercury

thermometer and "soak plate" are adequate. The gage blocks, cylinders

1. Appendix IV lists the coefficient of most of our blocks.

9
and thermometer are left on the "soak plate" to equalize. They

should be covered with a clean towel to minimize the effect of

uneven radiant heating. The transducer is a source of heat, so

the soak plate should be placed away from the tailstock. Equations are available to determine the time to achieve temperature

equalibrium, but the time is a function of so many variables

that it is impratical to compute it in each case. When measuring pieces of dissimilar metals, allow 10 to 20 minutes for

the smaller sizes and about two or three hours for a one inch

cylinder. Less time is required if all the items are of the same

metal and more if the test item has a low thermal conductivity

such as glass.

Data Analysis

There are many ways that the data can be taken, but our

statistical group feels that the best system when we have from

one to three test items is a permutation shown in the following

diagram where #1 is the master block, #2 is the check standard

and #3 is the test cylinder and R is the reading of the measuring

machine.

Rl R2 R3

#1 #2 #3

R4 R5 R6

#2 #3 #1

R7 R8 R9

#3 #1 #2

10
If there nrv two test cylliKlers, the reading would be a 4x4 matrix and a 5 x 5 matrix for three test items. Each

set must be completed without Interruption using approximately

the same length of time for each reading.

Tongs should be used to handle the blocks and cylinders

while making the measurements. A bit of practice is necessary

to develop the technique of picking up a gage block combination

with tongs and inserting it between the jaws in a manner such

that the block wrings to each jaw. It is best to first put

just the edge of the block between the jaws then move it to the

center with the same motion used to wring a gage block to a

platen. When the measuring force is one pound or under, increasing the force with another pair of tongs by pushing the

left anvil against the block while centering it seems to give

a tighter wring. It is customary to use a one pound force for

all the measurements except where there is some logical reason

not to such as a small copper wire where the force might permanently deform the wire. The cam release which moves the left

anvil to the open position must be opened and closed at least

once before making the first measurement. Also after moving

the right anvil with the screw, it should be pushed hard to

the right to remove the oil film between the thread flanks. If

this is not done, the measurements will show a large drift with

t ime

.

11
The stnndard deviation of an individual reading will be

between 1 1/2 to 2 microinches depending on the size of the piston

and the skill of the operator; therefore, the number of sets of

readings one must take will vary. It may be necessary to take as

many as ten sets (3x3 matrix) to keep the random component of

the transfer under 1 micro inch which is what we usually aim for.

A computer program is used to analyze the data. The program requires a temperature value for each set of readings. Also,

it requires the measuring force, magnification factor, master and

check standard values and the type of material and coefficient

of expansion for both the blocks and the piston.

If a computer is not available, the values of the diameters

can still be determined using a slide rule or desk calculator.

The readings are first multiplied by K to get what the reading

would have been if there were no error in the amplifier. The

product of the size, coefficient of thermal expansion and deviation from nominal 20° Celsius is subtracted from each value to

get what the reading would have been if all the pieces were at

exactly 20°. Next, the amount of deformation is added to each

reading on a cylinder to get the undeformed diameter. The deformation equation that we are now using is the empirically

derived Bochmann equation although many feel its values are

subject to question, especially for very small diameter cylinders.

This problem is being investigated and we will probably soon be

12
converting to a theoretical equation. Because line contact is

involved, the deformation in most cases is small and an error of

where M is the total deformation, C is a constant depending on

the material, P is the force in pounds, L is the length of contact and D is the diameter in inches. The value for C that we

~6 -6 use is .22. x 10 for a steel cylinder and .170 x 10 for a

carbide cylinder.

Because of the stiffness of the flexure springs, the actual

measuring force is the same as the pan weight only when the reading

is zero. The total low scale is 0.75 ounce. What this means is

that if the machine is set for one pound and the reading on a

cylinder is + 20 microinches, the actual force is one pound plus

20/80 X .75 ounces or about 16.2 ounces. The computer program

takes this into account; however, because it is such a small

correction, it can be safely ignored when doing the calculations

by hand.

The last step in calculating the piston diameter is to average

all the values. The difference between the test and the master is

subtracted from the best value of the master to get the cylinder

diameter. The same is done for the test standard. If the test

standard is not within 3 microinches of its best value, the

20 to 30 percent is negligible. The Bochmann equation is:

13
measurement set should be considered out of control and not used.

Computing a standard deviation for an individual reading

involves a considerable amount of work so it is easier to do

several sets and compute a standard deviation of each set which

can be done from the familiar equation.

If the standard deviation is greater than two microinches, it

means that not enough care is being taken in making the measurements. At least six sets of readings (five degrees of freedom) must be taken for the standard deviation to be meaningful.

In doing a 5 x 5 matrix, we might take a lesser number of sets

and perhaps just make an estimate of the standard deviation from

the range.

The accuracy statement in the test report should list the

total uncertainty as the sum of the three standard deviation

random component of error of the measuring process and the additional systematic errors involved. The random component is

computed from the data but estimating the systematic errors

involves a combination of science, art and guesswork. The block

combinations used in our laboratory carry an estimated uncertainty of 1 microinch. When added to the random component of

error, this yields an uncertainty of about two microinches.

14
There is some uncertainty in every correction that we have

used. The values for the amplifier magnification factor, temperature, coefficient of expansion, machine force and Hertzian

correction are certainly not exact and contribute some error.

The contributing factor of all these is a function of the size of

the piece to be measured. A complete error analysis study could

be made but this has not been done, therefore, we add an estimated half microinch to the uncertainty to account for these

factors.

Another error is introduced by the lack of parallelism of

the machine jaws; this error is independent of cylinder size.

About one microinch is a reasonable guess for this, thus making

the total uncertainty around 3 1/2 microinches.

Although there is no fixed format on exactly how a calibration report should be written, it should follow somewhat the

example given in Appendix III. Appendixes I and II are examples

showing one data set taken for a piston and the calculations used

to arrive at its best value based on the one set of measurements.

References

[1] Hertz, H. , Miscellaneous Papers (translated by Jones, D. E.

,

and Schott, G. A.). Macmillan and Co., Ltd., London, 1896

pp. 146-183. Contains English translations of the papers

from Journal Reine und angewandte Mathematik (Crelle). Vol.

92, 1881, pp. 156-171, and Verhand Vereins Beforder

Gewerbef leisses , Nov. 1882.

15
/
APPENDIX III

Report of Calibration L

For: One Carbide Piston

Submitted by: The Super Accurate Gage Co.

P. 0. Box 777

Fort Gary, Montana

The diameter of the piston was measured midway between ends in

the plane passing through the scribed index marking. Variations

from the midpoint diameter at either end in the same plane were

also measured. The values at 20° Celsius are as follows:

Midpoint Diameter Deviation from Midpoint Diameter

inches microinches

1/16" from 1/16" from

marked end unmarked end

0.9999634 +1.4 -0.8

The measurement was made by comparing it to two gage block com- binations of known length using one as the restraint and the other

as the check. The three standard deviation for random error was

0.9 microinch. Additional sources of error are believed not to

exceed 3 microinches giving a total uncertainty of 3.9 microinches.

Talyrond traces are enclosed showing the profile of the piston

at the measured positions.

Measurements made by

For the Director,

Chief

Section

Division, Institute

P. 0. No.

Test No.

Date
APPENDIX IV

Coefficient of Linear

Manufacturer Thermal Expansion

or (Parts per Million

Trade Name Material Per Degree Celsius)*

Quartz 0.4

Brown & Sharp, C.E.J. Steel 11.2

Ellstrom Chromium plated on Steel 11.5

DoAll Steel 11.7

DoAll Stainless 10.3

Fonda ' Chrome Carbide 8.1

Fonda Steel 11.5

Fonda Tungsten Carbide 6.5

Fonda Tantalum carbi.de and tungsten carbide 4.6

Hommel Steel 11. 7

Jansson Steel 11.5

C.E.Johansson Steel 11.5

Matrix O 4- n n 1 bteei lU. /

Pratt & Whitney Chrome Carbide 8.1

Pratt 6e Whitney Steel 11.5

Pratt & Whitney Tungsten carbide 4.8

Van Keuren Steel 11.5

Webber Chrome Carbide (new) 8.4

Webber Steel 11.7

Webber Tungsten Carbide 6.5

Webber Chrome Carbide (old) 7.2

Zeiss Steel 11.5

" Used in the NBS Optical Physics Division.
APPENDIX V

Investigated Object: The material thing which is the subject of the

measurement process.

Concept

Unit:

Unit Error

Model

Signal

Model Ambiguity

The parameters, length, mass, volume, etc., which

appear in the equations of theoretical physics.

The arbitrary scale on which the magnitude of the

parameter is expressed.

The difference between the scale on which the

magnitude of the parameter is expressed and the

scale on which it (arbitrarily) should be expressed.

The theory which relates a material property of the

investigated object to the concept the object is

presumed to embody and predicts the signal produced

by the object.

That physical property or influence by which the

measuring algorithm detects and measures the

embodiment of the concept of interest in the

investigated object.

The difference between the embodiment of the concept

in the investigated object to that embodiment pre -

sumed in the Model ; i.e. the difference between the

signal observed and the signal predicted.
1
Measurement Algorithm: The prescription by which the magnitude of

desired property is extracted from the object. It

includes the instrument, all relevant procedures,

environmental factors and calculations, etc., involved.

Algorithm Error: The difference between the assumed response of the

measurement algorithm to the signal from the object

and its response during the measurement.

Measurement Station: An independent location, apparatus or environment

where a measurement algorithm is implemented.

Prototype: An investigated object that is its own Model.

FORM NBS-114A (1-71) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBSIR 73-136

2. Gov't Accession No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Measurements of Cylindrical Standards

5. Publication Date

6. Perfonning Organization Code

7. AUTHOR(S)

O 3 1 Till P \/0£>lc»

8. Performing Organization

NBSIR 73-136

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/ Work Unit No.

11. Contract/Grant No.

12. Sponsoring Organization Name and Address

Same

13. Type of Report & Period

Covered

t lual

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

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

bibliography or literature survey, mention it here.)

Cylinders are widely used in industry and standards labs as a form of length

transfer. The measurement algorithm used by the dimensional technology section

to determine the diameters of master cylinders is given in detail. It has been

found that a mechanical transfer from inter ferometrically measured gage blocks

is the most satisfactory method.

17. KEY WORDS (Alphabetical order, separated by semicolons)

Calibration; cylinders; rolls; plug gages; wire standards.

18. AVAILABILITY STATEMENT 19. SECURITY CLASS

(THIS REPORT)

21. NO. OF PAGES

1 1 UNLIVUTED.

UNCL ASSIFIED

[U FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

22. Price

USCOMM-OC 6S244.P7I