NATIONAL BUREAU OF STANDARDS REPORT

3483

ANALYSIS OF TOOL HEATING PROBLEM

William F, Roeser

To

Materials Division

Structures Research Department

U, S. Naval Civil Engineering Research & Development LaboratoryConstruction Battalion Center

Port Hueneme, California

<NBp>

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
U. S. DEPARTMENT OF COMMERCE

Sinclair Weeks, Secretary NATIONAL BUREAU OF STANDARDS

A. V. Astin, Director

THE NATIONAL BUREAU OF STANDARDS

The scope of activities of the National Bureau of Standards is suggested in the following listing of

the divisions and sections engaged in technical work. In general, each section is engaged in specialized research, development, and engineering in the field indicated hy its title. A brief description

of the activities, and of the resultant reports and publications, appears on the inside of the back

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^Office of Basic Instrumentation ^Office of Weights and Measures.
NATIONAL BUREAU OF STANDARDS REPORT

NBS PROJECT NBS REPORT

1004-10-4708 July 28, 1954 3483

ANALYSIS OF TOOL HEATING PROBLEM

By

William F. Roeser

To

Materials Division

Structures Research Department

U, S. Naval Civil Engineering Research & Development Laboratory

Construction Battalion Center

Port Hueneme, California

<NBS>

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

The publication, i

unless permission 25 , D. C. Such p

cally prepared If

A j jr 11- 1 1 ,1 or in part, is prohibited Approved tor public release by the

. 1

• Standards, Washington Director of the National Institute of ,, , report has been specm- Standards and Technology (NIST) report for its own use, on October 9, 20 1 5.

ANALYSIS OF TOOL HEATING PROBLEM

by

William F. Roeser

1. INTRODUCTION

Our ideas of hotness and coldness are fundamentally derived from our

sensations; and though, in some instances, we may have cause to distrust the

information which we obtain through these channels, it does not follow

that we should, even were it possible, discard entirely these foimdations

for our knowledge of the phenomena connected with the tool heating problem.

For example, if various objects in a room are touched successively, it

will be found that the metal objects feel cooler than the other objects,

even though they are all at essentially the same temperature. The

reason for this is that the sense of touch does not inform us directly

of the temperature of an object, but of the rate at which an area of our

skin gains or loses heat. Thus to control the hotness or coldness of

metallic objects we must seek means of controlling the rate of heat exchange between the object and the sensitive portion of the skin.

Although we are not able to give an exact solution because of uncertainties in effects due to callous skin, perspiration, contact

pressure, etc., we can give some of the more important factors that

govern the rate of heat transfer.
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2. TOOLS WITH SOLID HANDLES OF ONE MATERIAL

Assume that we have two semi-infinite solids A and B at uniform temperatures Tj^ and Tg, respectively. Let C^, P^, and be the heat capacity

per unit mass, the density, and the thermal conductivity, respectively, of

material A; and Cg, Pp, and Kp be the values for the corresponding properties of material B. (Any set of units may be used, provided they are

consistent.

)

It can be shown mathematically that, if these two bodies are suddenly

brought into intimate thermal contact, the temperature (T3 ) of the interface is given by

dent of time.

The above problem is given in Section 42 of “Modern Operational

Mathematics in Engineering” by R, V. Churchill.

In the handling of implements, we are concerned with a material of

finite size and the human hand. It is true that neither of these is a

It should be noted that the temperature of the interface is indepensemi-infinite solid, but for short periods of time they may be considered

- 3 -

as such. Thus, if an implement with a handle of material A at a uniform

temperature is firmly gripped by the hand (material B), the temperatiare

of the surface of the skin will come to a temperature T3.

The rate of heat transfer from the surface of the skin to the temperature and pain receptors below the skin should be very closely proportional to (T3 - Tb).

A few simple experiments were made to determine if the above relationship held, approximately, for the gripping of implements of different

materials with the hand. The implements were heated in an oven to various

temperatures, and the maximum temperatures at which two observers agreed

that they could handle them without undue discomfort were established.

These values are given in the second column of the following table. The

third column gives approximate values of the ratio

T~H Fa

„ T^b Pb Kb

for the different materials and the fourth column gives the calculated

values of the skin temperature.

Material

"a R. Skin T( Op Op

Carbon Steel 119 0,89 116.8

Plastic (Used for tool handles) 158

* 0.30 116.4

n « n tt tt 160 0.29 116.4

Hardwood (sp.gr. =• 0.82) 169 0.24 115.5

Softwood (sp.gr. - 0.5) 183 0.16 112,1

Considered average 116.
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In the above calculations, Tg was taken as 98.6°F, and the values of

C'Bj body were taken to be the same as those of water*

Even though the temperatures of the implement handles ranged from

119° to 183°F, the temperature of the skin came to approximately the same

value in each instance, indicating that the rate of heat transfer was

nearly the same in each case.

According to the above relationship, the human tongue should stick

to steel at any temperature below 23.8°F.

Equation (l) can be rearranged to read

'fA = Ts

(Tg - Tg) fcg Pg Kg

r 'A Pa Ka

Substituting for T3, 116®, the maximum temperature of the surface of the

skin that can be tolerated and for Tg, Cg, Pg, and Kg, the values for the

body, we have

T^ = 116 f

0.66

pA Pa %

where is in ®F and and are in Cal, Cm, Gram, ®C and Sec

units.

This equation gives the maximum temperature, Tj^, at which an implement can be handled in terms of Cji^, P^, and

Even though the above relationship is based upon the assumption that

the two bodies considered are semi-infinite solids (which they are not),

and even though no account was taken of the amount of moisture or
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callousness of the hands, it gives a basis for the selection of materials

which we believe to be in general agreement with experience.

3. TOOLS WITH COATED HANDLES

With different thicknesses of clear coatings of Plastisol R-2101 (a

vinyl chloride) on steel rods, we found that the maximum temperature at

which the coated rods could be handled varied with the thickness as shown

in Figure 1. Apparently a l/l6-inch coating was just as effective as one

of infinite thickness.

We can now set up the following relationship for steady-state heat

transfer

q/a

K (T - Ts) _ Ka ("^A - Tg)

D

Da

where q/a is the heat transfer per unit area from a steel rod, through a

coating, and to the skin, K and are the thermal conductivities of the

plastisol used and of any similar material that might be used, respectively,

and D and are the corresponding minimum thicknesses of coating that will

permit the implement to be handled at the maximum tolerable temperatures of

T and Ta, respectively. Substituting the known values for K, T, Tg, and

D in equation (4), we have

0.11 Da (in cm)

K, = (Ta - Ts)

From equation (3) Ta-T. =

- 0.66

/Ca Pa 4

©

©

STEEL

RODS

COATED

WITH

PLASTIfiiOL

R-2IOI

o

Ulyodwoosia inoHiiM qhionvh

HOIHM iV (d.) 3aniVd3dlAI3i l/MflWIXVW

COATING

THICKNESS,

INCH

- 6 -

Eliminating (T^ - Tg) and collecting terms, we have

(in cm) - 6.0

f ©

(in inches) ” 2.36

(Ca, P^, & Ka in Cal., Cm, G, °C, Sec)

It is seen from equations (6) and (8) that any reduction in the values

of Ca and Pa of the coating material will increase both the maximum temperature at which the implement can be handled and the minimum thickness

necessary to permit the in^^lement to be handled at the maximum temperature.

As an example, if Ka is maintained constant and the product, Ca P;^, reduced

by a factor of 4, both (Ta - Tg) and Da are increased by a factor of 2.

Any reduction in the value of K^ will increase the maximum temperature at

which the implement can be handled and will decrease the minimum thickness

of the coating necessary to permit the implement to be handled at the

maximum temperature. As an example, if and Pa are maintained constant

and Ka reduced by a factor of 4, (Ta - Tg) is increased by a factor of 2

and Da is decreased by a factor of 2. All this means is that the rate

of heat transfer through the coating ( q/a in equation (^) has been

maintained constant.

The maximum temperature, 160°F, at which we could handle the plastics

used in our experiments is so near the temperatures that tool handles might
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attain when exposed to the sun that consideration should be given to any

means of reducing their temperature. In some experiments which we made

in the period June 22, to July 1, 1954> l/2-inch steel rods coated with

1/L6 inch of plastic and painted black attained a temperature of 60°F

above the ambient, 90°F, when exposed to the sun. Under the same conditions, similar specimens painted white attained a temperature of 42 . 5*^

above the ambient, while those without any paint attained a temperature

of 57.5°F above the ambient.

The maximum temperature rise attained by any of the specimens was

that of the one with a plastic coating painted black. If we express

this temperature rise as 100 per cent, the following table gives the

corresponding increase in temperature of other specimens exposed under

similar conditions. All the temperatures measiured were that of l/2-inch

steel rods to which the coatings were applied.

Relative Temperature Rise

Coating

lA6 in. plastic, painted black

No plastic, painted black

1/16 in. clear plastic, no paint

None, cleaned

l/l6 in. plastic, painted white

No plastic, painted white

Above Ambient,

Exx>ressed in Per Cent

100

97.5

96

95

71

69
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From these data, it woiold appear advisable to consider adding a

white filler to the plastic. This would not only aid in keeping the

handle cooler, but also should reduce the cost of the plastic coating

as well as making it more stable. We believe that the use of metallic

powders as a filler should be avoided, since these would probably increase the conductivity of the coating material and would not aid in

keeping the handle cool.

In the selection of a plastic with the desired thermal characteristics, such properties as the resistance to abrasion, greases, cleaning solvents, etc., should not be overlooked.

If any use is made of the above analysis, it is hoped that the

limitations of the mathematical analysis due to assunqjtions involved

and of the results based upon only a few simple experiments, are

borne in mind. If they are not, someone might get his fingers burnt,

literally.
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THE NATIONAL BUREAU OF STANDARDS

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