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NATL INST OF STANDARDS & TECH R.l.C. United States Department of Commerce

sr,,.j.any4Thlrl°aPe1,S National InstitutG of standards and Technology

QC100 .05753 N0.1271 1989 V198 C.I NIST- ^ >

NIST

PUBLICATIONS"1

NIST Technical Note 1271

Thermal Effects of Handling

Ball Bars

Jianying Shi, Ted Doiron, and Bruce Borchardt

QC

100

U5753

#1271

1989

C.2
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Clcioo

NIST Technical Note 1271

Thermal Effects of Handling

Ball Bars

Jianying Shi

TIanJIn University

Peopies Republic of China

Ted Doiron

Bruce Borciiardt

Precision Engineering Division Nattonal Institute of Standards and Technology

Galthersburg, MD 20899

October 1989

e

<f

U.S. Department of Commerce

Robert A. Mosbacher, Secretary

National Institute of Standards and Technology

Raymond G. Kammer, Acting Director
National Institute of Standards U.S. Government Printing Office For sale by the Superintendent

and Technology Washington: 1989 of Documents

Technical Note 1271 U.S. Government Printing Office

Natl. Inst. Stand. Technol. Washington, DC 20402

Tech. Note 1271

1 5 pages (Oct. 1 989)

CODEN: NTNOEF
Thermal Effects of Handling Ball Bars

Jianying Shi

Tianjin University

Peoples Republic of China

and

Ted Doiron, Bruce Borchardt

Precision Engineering Division

Center for Manufacturing Engineering

National Institute of Standards and Technology

Gaithersburg, MD 20899

Ball bars are a primary method of testing coordinate measuring

machines. The accuracy of the method depends critically on the

stability of the length of the bar. This study shows the primary

thermal relaxation time for ball bars to be near 15 minutes and

explores the size and duration of thermal effects for two bars of

different materials.

Keywords: ball bar, coordinate measuring machine, CMM, dimensional

metrology, thermal effects

1. Introduction

The current techniques to substantiate the accuracy of three-dimensional

coordinate measuring machines are documented in ANSI standard B89.1.12M. One

option calls for the use of a ball bar system, like that shown in figure 1, to

generate a very precise spherical motion for the measuring machine. The bar

consists of a center rod, two end pieces with precision balls, and two magnetic

sockets which have spherical bearings matched to the balls.

The rod has threaded holes in each end and usually a plastic handle in the

middle to insulate the bar thermally from the operator's hand. The ball bar set

has three or more center bars of different lengths. The end pieces, which have

the precision balls attached, are screwed into the center bar. The magnetic"

sockets are mated to the balls to provide angular motion with less than 125

nanometers of runout. One socket is mounted on the CMM table, and the other in

the probe holder. The magnets are strong enough that the machine can be moved

by hand in any path on the spherical section allowed by the length of the bar.

On computer driven machines the bar is used without one or both of the sockets.

The ball is repeatedly positioned in the measurement volume and the CMM probe

is used to measure positions of the free ball/balls.
Using this system the operator can generate spherical motions which are uniform

in radius to better than 1 micrometer (yum) . By recording the apparent positions

given by the CMM the geometry errors will appear as deviations from a sphere.

The accuracy of this test depends only on the repeatability of the motion of

the bar in the socket, measured as the runout, and the constancy of the bar

length. Since the runout depends primarily on the original manufactured

geometry, it is not likely to change during the measurement. The length of the

bar, however, is dependent on its temperature.

When the ball bar is assembled, some heat from the operator will transfer into

the ball bar, setting up a gradient both within the bar and with respect to the

measuring machine environment. As the bar cools it will change length in

proportion to the temperature change. This work is an exploration of the size

and duration of these effects for two geometrically similar ball bars, one made

of steel and one made of invar-*-

.

2. Heat Transport for Ball Bars

The geometric response to temperature changes in the ball bar is given by the

thermal expansion equation^:

AL = at AT at = 11.5 X 10"^ /°C for steel

= 1.2 X 10'^ /°C for invar

where a^ is the thermal expansion coefficient.

Once heat is added to the bar, at the ends from the operator's hands during

assembly for example, the heat has two paths. First, the heat will flow in the

bar, reducing the gradient but maintaining the same average temperature.

Second, the heat will be transferred to the environment via radiation,

conduction and convection. Since this second transfer to the environment

depends directly on the area of contact between the environment and the bar, if

the heat from the end of the bar disperses quickly throughout the bar, the added

exposed warm surface will increase the heat transport and bring the bar to the

environmental temperature more quickly.

The heat transport inside the bar is governed by the gradient and the thermal

diffusivity. The general one dimensional heat transport equation can be written

as

:

a^T = 1 ar a. = 0.13 x lO'"* mVs for steel

ax^ a. at = 0.30 X lO""* m^/s for invar.

This shows that for a given spatial thermal gradient, the higher the thermal

diffusivity the faster the gradient will equilibrate. Thus the response of the

invar will be faster than the steel by a factor of 2. Since assembling the bar causes heat transfer mainly at the ends this factor may be significant depending

on the relative magnitudes of the conduction to the radiation/convection into

the environment.

In summary, the relative values of the thermal expansion coefficients of the

metals imply that the dimensional effects of handling the invar bar will be
smaller by a factor of about 10. The differences in the thermal diffusivity

imply that the thermal gradients along the bar, caused by handling the ends

during assembly, should dissipate more quickly in the invar bar.

The actual heat transfer between the air and the bar is a combination of

radiation and convection. Simple calculations show that both transfer channels

are of the same magnitude. The use of a fan near the measuring machine is not

recommended, however, since altering the thermal environment of the machine may

produce changes in the CMM geometry. For small temperature differences the heat

flow is proportional to the temperature difference between the bar and the air.

If a small fan is used to produce forced convection the cooling rate would be

expected to be considerably enhanced. This implies that the bar-air temperature

difference will exhibit an exponential decay with a characteristic time t :

(Tbar-Tair) = AT e'"-''

All of the data was analyzed to obtain this decay time t .

3 . Experiments

The two ball bars were tested for changes in length and temperature under two

different initial conditions. Each bar had six calibrated thermistors attached

in the positions shown in figure 1. The thermistors were placed on the bar,

covered by a layer of insulation, and held in place by tape.

3.1 Experiment 1

The first tests were to measure the basic thermal time constant, r, for the bar

to decay to ambient temperature. Each of the bars in turn were placed in a refrigerator and cooled to near 10°C. The experiment proceeded as follows.

A bar was removed from the refrigerator and placed on a stand. The stand was on the table of a coordinate measuring machine (CMM) . The temperature of each

of the thermistors was recorded every minute. At the same time the CMM was used

to measure the overall length of the bar.

Typical measurements of both bar temperatures are shown in figure 2; they are very similar. All of the thermistors show basically the same response, except

those near the center. The bar has a plastic handle in the center to carry and

manipulate the bar during setup. The thermistors near the handle show that the

combination of heat conduction through the handle and radiation from the

operator's hand caused the center of the bar to heat up preferentially, although

when the heat sources were removed the decay constant to the ambient conditions

was the same as the other parts of the bar.

A semi-log plot of the same data is shown in figure 3. All of the thermistors

show nearly the same relaxation time. The lines which vary the most are those

closest to the handle, i.e., those which had thermal interaction with the

technician setting up the test. These data are not useful for the relaxation

time calculation because of the stray heat.

The thermal response of the two bars in this test was expected to be very

similar. The important dimension for this test is the diameter of the bar
because the air surrounds the bar on all sides. Both bars have the same diameter, less than 2 cm. The thermal diffusivity difference in the bars, which

is their only significant difference, is not important because the thermal

gradient across the bar diameter is too small to cause detectible differences

in the response of the bars.

The characteristic time r found for the bars is 15 minutes. Since most

metrology equipment is not kept in refrigerators , a more realistic example is as follows. Suppose the bar is taken from the gage lab at 20 °C, and brought out

to a metrology area in the shop which is 23°C. The initial gradient between the

bar and the atmosphere is 3°C. After 16 minutes the gradient will be reduced

by a factor of 1/e , to 1.1°C. The temperature of the bar at different times is

given in table 1

.

TABLE 1

Time Temperature

20

15 21.82

30 22.54

45 22.82

60 22.93

75 22.97

These temperatures would be roughly the same for the invar and steel bars. The

length of the bars would be very different, however. The length of each bar was measured at the same time the temperature data were taken. The lengths of the

invar and steel bars are sho\vrn in figure 4. The change in length of the steel was found to be about 10 times greater than the change in the invar bar, as expected from their thermal expansion coefficients.

Using the thermal expansion coefficients of each bar, the lengths of the bars

at the given times in our example are shown in table 2

.

TABLE 2

Length (mm)

Time Temperature Invar Steel

20 900 900

15 21.82 900.002 900.019

30 22.54 900.003 900.026

45 22.82 900.003 900.029

60 22.93 900.003 900.030

75 22.97 900.003 900.031

equilibrium 23.00 900.003 900.031

In using a ball bar, according to the ANSI B89.1.12M standard, the absolute

length is not important. What is important is that the length be constant

during the measurement. According to this example, a steel ball bar must be

allowed to stand in its new environment about 1 hour before it will be in

equilibrium at the 1 micrometer level. For the invar bar the time is roughly

15 minutes. For larger temperature differences the times would be somewhat
larger, although since the response is exponential, any reasonable difference

would not be much larger than those in the example.

3 . 2 Experiment 2

The second experiment was to measure the thermal and dimensional response to the

assembly of the bar by a technician. The bar was mounted as in experiment 1 and

the data taking computer was started. The ball on one end was then removed and

then replaced as it would be in actual use. The thermal response was found to

vary considerably depending on the type of gloves used and the time involved in

the assembly. A typical data run for the invar bar is shown in figure 5.

The six lines are the temperature responses of the six thermistors. At time=10

minutes one of the ball holders was unscrewed from the bar and replaced. The

thermistors lines are in the order they were placed on the bar, with the

manipulated ball the top plot. Both the thermistors nearest the joint show 1°C

rises in temperature. The next thermistor from the end shows less effect, and

the thermistors on the other end of the bar show negligible effects. Essentially there are two heat transfers going on, the transfer into the air via

radiation and convection, and conduction down the bar. Since there are more heat paths in this experiment than in experiment 1, the thermal relaxation time

is smaller.

Figure 6 shows semi -log plots of the response of thermistors on the steel and

invar bars. The size of the temperature change and the details of the

relaxation depend on the time the bar is handled and how the bar is held. In

general, the relaxation times for both bars were between 10 and 14 minutes,

slightly less than the 16 minutes found in experiment 1. This is, of course,

due to the conduction of some of the heat down the bar to the undisturbed

volume. When both ends are manipulated, the major part of the center of the bar

is still undisturbed and forms a heat sink only slightly less efficient than

when only one end is manipulated.

When the bar is assembled, inserting the balls on both ends, the largest

temperature change is only about 1-2 degrees over less than 1/2 of the bar

volume. Using the larger number, the average temperature of the bar rises 1°C

and then returns to ambient conditions exponentially with a characteristic time

of 12 minutes. Under these conditions the steel bar would expand 10 micrometers

and would return to within 1 micrometer of its original size in about 30

minutes. The invar bar, with a change in temperature of 1°C expands only 1 micrometer, so no waiting period is necessary.

4 . Summary

The temperature response of both invar and steel are very similar. The

relaxation to ambient conditions from both small and large perturbations are nearly identical. The characteristic relaxation time for both bars under a homogeneous change in temperature was found to be about 16 minutes . I-Jhen the

bar is assembled, it was found that the ends can rise in temperature a few

degrees, but due to the unchanged temperature of the middle of the bar the

relaxation time is reduced to about 12 minutes.
The length of the invar ball bar, due to its lower thermal expansion coefficient

is much less sensitive to changes in temperature. In most cases the invar bar

can be assembled and used immediately. The steel bar will need 30 minutes to

equilibrate in air, and somewhat less if put in contact with a thermal sink at

ambient conditions. Since the bar and its ends are round, the contact area with

the sink will be small and the 30 minutes will not be reduced dramatically.

When the bar is brought into a different thermal environment, both bars will

take some time to equilibrate. For a 3°C change the invar bar will be within

1 micrometer of its equilibrium length in about 15 minutes . The corresponding

time for the steel bar is 60 minutes

In summary, the invar bar will be ready to use some 15 to 45 minutes faster than

the steel bar, depending on the thermal changes imposed on the bar by travel

and assembly. The significance of these differences in waiting times for the

different bars depends on the setup and test procedures of the user.

5. References

1. The authors thank Sheffield Measurements Inc. for the loan of an invar

ball-bar for these tests.

2. "The Heat Transfer Problem Solver," Staff of Research and Education

Association, Research and Education Association, 1984.
THERMISTORS

HANDLE

Figure 1. Ball bar with the relative positions of the six thermistors used to

monitor the bar temperature.
S ~b

^ ^

]

24 48 72 96 120

Time Cminu"tes)

25rZ r~i r"

24 48 72 96 120

Time (minu"tes)

Figure 2. Response of steel and invar bar temperatures when initial temperature

was 5°C.
"t

^ ^ 1

u

L.3

-P

1-

(D

Q_

E

(D

10

1 z

1

24 48 72 96 120

Time Cnninu"tes)

r"-

24 48 72 96 120

Time (minu"tes)

Figure 3. Semi- log plot of the data in figure 2, showing exponential decay of

temperature difference between the bar and the air.
899.5

"t^ ^ 1

899.3

9 00. 9 r—

24 48 72 96 120

Time (nninu1:es)

900. 7L

24 48 72 96 120

Time Cminu"tes)

Figure 4. The length of each of the bars during the temperature changes shown

in figure 2

.

10
I r^ v/

15 30 45

Time (minutes)

Figure 5. Temperature response of the invar bar to removing and replacing one

of the balls. The top line shows the thermal response of the thermometer on the

assembled end of the bar. The thermometers in the graph are in the same order

as those on the bar, with the top line closest and the bottom furthest away from

the handling point.

11
/-\

u

03

L.3

rd

Q)

Q_

E

(D

U

(DL.

rd

L

Q)

Q.

E

(D

h15 30 45

Time (minu"tes)

IE m \^ ^r^

60

15

Time

30 45 60

Cmi nu1:es )

Figure 5. Semi-log plot of the thermal response of both the steel and invar

bars to the heat input during hand assembly.

12
NBS-n4A (REV. 2-ec) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1, PUBLICATION OR

REPORT NO.

NIST/TN-1271

2. Performing Organ. Report No. 3. Publication Date

October 1989

4. TITLE AND SUBTITLE

Thermal Effects of Handling Ball Bars

5. AUTHOR(S)

Jianying Shi, Ted Dolron, Bruce Borchardt

6. PERFORMING ORGANIZATION (If joint or other than N6S, see /nstruct/ons; NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

(formerly NATIONAL BUREAU OF STANDARDS)

U.S. DEPARTMENT OF COMMERCE

GAITHERSBURQ, MD 20889

7. Contract/Grant No.

80 Type of Report & Period Covered

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

Same as item # 6

10. SUPPLEMENTARY NOTES

Q]J Document describes a computer program; SF-185, PIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual surr\mary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

Ball bars are a primary method of testing coordinate measuring machines. The accuracy

of the method depends critically on the stability of the length of the bar. This

study shows the primary thermal relaxation time for ball bars to be near 15 minutes

and explores the size and duration of thermal effects for two bars of different

materials.

12. KEY WORDS (Six to twelve entries; alohabetical order; capitalize only proper names; and separate key words by semicolons)

ball bar; coordinate measuring machine; CMM; dimensional metrology; thermal effects

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PRINTED PAGES

15

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