NBSIR 75-908

CHARACTERIZATION OF SHARP POINTS

AND EDGES BY ELECTRICAL

BREAKDOWN

Julius Cohen

Product Engineering Division

Center for Consumer Product Technology

Institute for Applied Technology

August 1975

Prepared for Center for Consumer Product Technology

Institute for Applied Technology

National Bureau of Standards

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

James A. Baker, III, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Final
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Table of Contents

Page

INTRODUCTION 1

BACKGROUND . 1

EXPERIMENTAL APPARATUS AND PROCEDURE 2

EXPERIMENTAL RESULTS 3

1. Negative polarity on specimen 3 2. Positive polarity on specimen 4

DISCUSSION 4

CONCLUSIONS 6

RECOMMENDATIONS 6

Appendix: Calculation of electric field at the tip of a hyperboloidal point-to-plane gap . 7

Acknowledgment 8

Bibliography 9

INTRODUCTION

Some consumer products, especially those of sheet metal, have hazardous

sharp edges or points. It is particularly serious if toys are so deficient, as they are handled by incautious children.

An instrument has been developed at NBS for characterizing sharp edges

by mechanical means with use of a synthetic material as a cut indicator.

Evaluation of results requires operator judgement; the device is not

applicable to points also, and operation could be tedious if examining long

edges.

An electrical breakdown method, if workable, would appear to be

advantageous: (1) results might be more accurate and precise; (2) it may

be applicable to both edges and points; (3) application would be rapid. It was considered worthwhile, therefore, to do a limited pilot study aimed at

determining feasibility of using the phenomenon of electrical breakdown of

gases to characterize sharp edges and points. This work is described

below.

BACKGROUND

Electrical breakdown in gases is used extensively by industry for many

important applications, among these dust removal by electrical

precipitation, high-speed printing, electrochemical processes, radiation

detection (Geiger counter), ore preparation, de-emulsif ication of crude

oil-brine mixtures, and discharge of static electricity from surfaces of

wool and paper. It may be possible to use the phenomenon also to

characterize edges on consumer products as safe or hazardous with regard to

potential for causing punctures, cuts, or lacerations.

Electrical breakdown of air or other gases will occur if a sufficiently

high voltage is applied through an external circuit to two physically

separated conductors. If one of the conductors is a sharp point or edge

and the other a plane at a suitable distance, the electric field will be

very large at the former and small at the latter, and breakdown will be

associated with the highly electrically-stressed point.

The discharge may or may not be visible, audible, or olfactible. It

may be manifest as a burst, a streamer, or a sustained glow. In any event

the mechanisms of breakdown are exceedingly complicated and arise when the

electric field-initiated gas plasma reaches a critical state. The plasma,

generally containing electrons and ions of both polarities, may be affected

by photon emission as well as the electric field, and it varies spatially

as well as temporally.

In general, breakdown at threshold will depend on gas composition

(e,g,, moisture content in air), point or edge radius and shape, applied

potential, and gap. Water vapor facilitates breakdown, as do dust specks.
Figure 1 Illustrates the dependence of field at the tip of a point on

its sharpness (details of the calculation are Riven in the Appendix). The

radius at the tip is related to focal length, plotted as abscissa; tlie

larger the focal length, the larger the radius and the less sharp the

point. The field is seen to be large for very sharp points, or small focal

lengths, and to depend sensitively on sharpness over only a very narrow

range of focal lengths; for the relatively less sharp points, field is

fairly insensitive to degree of sharpness. This suggests that small

voltages and small gaps can be used when working with very sharp points,

but that use of large voltages and large gaps would be advantageous when

trying to characterize points which are not extremely sharp.

Figures 2 and 3 are experimental curves, replotted from the data of

other investigators, for the discharge threshold potential of point-toplane gaps vs. radii, with gap lengths as indicated; the former is for

positive spherical points, and the latter is for conical points of negative

polarity. The qualitative features of the curves shown in both figures are similar: The dependence of threshold potential on radius is greatest for

small radii and large gaps, in agreement with the inferences drawn from

figure 1 and discussed previously.

Most gas breakdown studies have been made with a positively charged

point rather than one charged negatively, as the latter has been found to

introduce additional complications: (1) the breakdown being a cathodecontrolled phenomenon Is extremely sensitive to the surface properties of

the point such as condition, kind of metal, and surrounding gas; (2)

threshold potentials are difficult to determine accurately and precisely

the initial currents normally will be very low and falsified thresholds

will result from statistical lags; on the other hand, if thermal or photoelectric means is used to emit electrons from the point, too many

electrons can mask the threshold,

EXPERIMENTAL APPARATUS AND PROCEDURH:

A circuit diagram of the high-voltage breakdown tester is shown in

figure 4, A fixed voltage of 2500 V is applied across a specimen point or edge and parallel plane—initially the gap length is sufficiently large so that breakdown does not occur. By means of the reversing switch, a positive or negative polarity can be imposed on the specimen as desired.

Initially the specimen is made to have positive polarity and the gap

length gradually decreased until incipient breakdown is detected by

observing the current meter; currents the order of nanoamperes are detectable. Also a neon bulb glows when breakdown occurs. The threshold

gap length is then measured by means of a micrometer arrangement. The

voltage is then removed, the gap length increased, and the procedure is

repeated, but with opposite polarity on the specimen.

In ordinary circuits without voltage regulation, when breakdown occurs

the current rises and forces the voltage across the gap to drop. This

2
makes determination of the threshold gap length difficult and adversely

affects the precision of the measurement. In the present circuit, a diode

has been incorporated, to maintain constant voltage across the gap (prior

to breakdovm and) during the breakdown process significantly above the

threshold of breakdown. This seems to improve the precision of the

threshold gap length measurement.

A wide variety of samples were Investigated: common household items

such as razor blades (dull and sharp), needles, nails and knives; sheared

edges of different metals; and special ground conical points and ground

rounded edges of known tip radii and included angles.

EXPERIMENTAL RESULTS

1. Negative polarity on specimen

Figure 5, a bar graph, shows the threshold gap length required to

obtain incipient breakdown when -2500 volts are applied between various

objects (including commercial items) and the plane, known intuitively or

from experience to be either safe or hazardous. The larger the gap length,

the smaller the applied macroscopic field, and the more ready the

breakdown; sharper objects are assumed to break down easier-l.e. at larger

gap lengths-than duller objects, A needle point, the sharpest object

tested, is seen to break down at the largest gap length, as expected, and

the next sharpest object, a scalpel tip, breaks down at the next largest

gap length. On the other hand, dull and smooth edges, incapable of

cutting, break down at the smallest gap lengths. Note that the

measurements are sensitive enough to distinguish new from used razor

blades, new from used saw blades, and rough from smooth edges on sheared

metal strips. The kind of metal used for sheared samples, however, had

little Influence on the results.

A vertical line on the graph arbitrarily drawn at a gap length of 0.52 mm divides the safe from the hazardous objects: If the threshold gap

length of an object is <0.52mm, the object is found to be safe, if >0.52

ram, hazardous.

Figure 6 shows curves of the threshold gap length for special rounded

edges of known Included angles and edge radii, as Indicated. Each solid curve Is for a set of edges having equal angles, but different radii; the

dashed curve is for edges fabricated as sharp as practicable, and denoted

by (zero) 0 radius.

In general, the smaller the included angle and the smaller the radius,

the sharper the edge. Note from the solid curves that for Included angles

15°, 30° and 60°, the threshold gap length decreases as the edge radius

Increases (edges become less sharp), as expected; for the 90° Included

angle, however, the threshold gap length decreases as the edge radius

Increases, then becomes essentially constant with increasing radius c^

figures 2 and 3,

3
The dashed curve shows that threshold gap length decreases as included

angle increases (edges become less sharp), for samples with edges of zero radius. The breakdown of samples with larger radii is not well behaved,

probably due in part to imprecision in measurement.

Figure 7 shows threshold gap length for special conical points of known

included angles and point radii, as indicated. Note that as a group the

sharpest points (i.e., those with small included angle and tip radius)

break down at the largest gap lengths (>0.5 mm) and the dullest points

break down at the smallest gap lengths (<0.3 mm), which is the desired

behavior, but that the individual data points within the group of sharp or

dull points do not appear well behaved. The threshold gap lengths of the

intermediate points (<0.5 mm and >0.3 mm) show little dependence on sharpness, or anamolous behavior (60° and 75" included angle).

2. Positive polarity on specimen

Tests made with positive polarity on the specimen generally showed the

threshold gap length to be virtually independent of sharpness; the

threshold gap length was "0.5 mm, corresponding to a macroscopic breakdown

field of "50 kV/cm. Exceptions were the sharpest objects such as the

needle point, scalpel tip, and the sharpest conical points.

DISCUSSION

The relative sharpness and hazard potentJ.al of some of the special

rounded edges had been evaluated previously by applying a known force

between the test edge and human skin, in vitro, and observing the percent

depth of cut, if any. If there were no cut, but only a groove made in the

epidermis, we assume here that the test edge is safe. That data shows

considerable scatter due to the effect of various skin samples (texture,

condition, age, etc.) and to imprecision in the test method; nevertheless

our appraisal of the data enables a qualitative evaluation of sharpness and

hazard potential to be made.

The results of the present work on rounded edges were compared to the

skin cut data for test edges restricted to 17.8 newtons (N) (4 poundsforce) and 35.6 newtons (8 pounds force). At higher forces, many rounded

test edges, safe under normal conditions may cut. The test edges used for

human skin cut data are tabulated below according to designation, included

angle, and radius.

1 J. R. Sorrells and R. E, Berger, "Some Cutting Experiments on Human Skin

and Synthetic Materials", NBS Report NBSIR 73-262 (Oct. 1973).

4
Table 1. Test edges used for human skin cut data

Designation Included angle Radius

(o) (mils)

A 60 0

B 90 0

K 105 0

F 90 0

G 15 2 H 30 2

I 60 2 J 15 4

K 90 2

Table 2, below, compares the ranking of sharpness obtained from human skin

cut data and breakdown data. The comparison is considerd fair,

particularly for the shapest specimens; however, as precision of the

breakdown data has not been determined, the ranking should be considered

approximate and tentative.

Table 2, Comparison of human skin cut data and breakdown data

Human skin cut data samples ranked in decreasing sharpness

17,8 N A B G E I F H J K

35,6 N A B E G F H I J K

Breakdown data A B (G,F) H K K I J

Of more significance is the comparison of characterization of edges as hazardous or safe, and here the correspondence in the two methods is

considered excellent: for the 17,8 N force, electrical breakdown correctly

classified 8 of the 9 samples; for the 35,6 N force, all 9 samples were correctly classified. In figure 6 a horizontal line at approximately 0,465 mm is used to separate the data into hazardous and safe regions, (If it is

desirable to correlate breakdown data with skin cut data obtained at higher

forces, another line can be arbitrarily drawn.)

Attempts ^o compare the breakdown data for the special conical points

with results of other testing were inconclusive because of insufficient

data

,

That breakdown in the present work was sensitive to sample geometry if

the polarity on the sample were made negative, but not if made positive, is

explained thusly: With specimen polarity positive, for the relatively

2 B, J, McGuire, J, R, Sorrells, and J, D, Moore, "Resistance of Human Skin

to Puncture and Laceration", NBS Report NBSIR 73-123 (Feb, 10, 1973),

5
small voltage and gap lengths used, breakdown depends predominantly on the

composition of the air. If the applied voltage and gap length were made

sufficiently large, the results might depend on sample geometry as well.

On the other hand, when specimen polarity is negative, it acts as a cathode

supplying charge carriers which facilitate the breakdown process.

Electrical breakdown then occurs at smaller macroscopic electric fields

(greater gap lengths) and depends on specimen geometry as well as the air

composition,

CONCLUSIONS

Electrical breakdown in air can be used effectively to characterize

sharp metallic edges, and it appears to have limited usefulness for

characterizing sharp metallic points.

When relatively low applied voltages and small gap lengths are used, as

in the present work, the polarity on the specimen must be made negative.

The results of the present work on special metallic rounded edges are

in good agreement with previous human skin-cut data obtained for the same rounded edges,

RECOMMENDATIONS

1, Continuance of work on this project is considered worthwhile,

2, Although electrical breakdown has been proven effective for

characterizing sharp metallic edges, the results for points, while

considered fair, are not as convincing, and further work is desirable:

higher applied voltages and gap lengths, and a more sensitive current

indicator may improve the results. Additional tests on skin using a larger

assortment of points may also be desirable for purposes of comparison with

breakdown data,

3, Exposed edges and points on consumer products may not be bare

metal, but lacquered or painted. These coatings are electrically non- conductive and also may alter the morphology of the edge or point. In any

event, breakdown phenomena are expected to be strongly affected by the

coatings and should be investigated. It may be desirable to investigate

the effect on breakdown of an additional thin coating of an electrical

conduc tor,

A, Many toys are fabricated in such a way that exposed edges are bare

metal. Here, an instrument (based on breakdown) designed and developed for

field use should be useful as a rapid accept/ rej ect inspection method.

6
Appendix: Calculation of electric field at the tip of a hyperboloidal

point-to-plane gap.

E^, the field at the tip of the hyperboloidal point is

E

= 2y

o alog(4t/a)

where V is the applied voltage, a is the focal distance at the tip

and % is the gap length.

7
Acknowledgment

The author acknowledges the contributions to this work of M. L,

Greenough who suggested the problem and carried out most of the

experimental work. Thanks are due Dr. 0, Petersons for useful discussion,

8
Bibliography

Loeb, Leonard B., Electrical Coronas (University of California Press,

Berkeley and Los Angeles, 1965), This large book is a compilation of

informative but widely scattered literature on the exceedingly complex

subject of electrical breakdown in gases, with emphasis on the basic

physical processes. A difficult book to comprehend, descriptions are much

too detailed for all but the most ardent devotees of the breakdown art.

Nevertheless, the book is a useful reference source and does impart an appreciation for the many experimental parameters which govern the

breakdown process.

Miyoshi, Y. , ibid, pp. 383-392.

A report of an intensive study of the point (usually negative)-to - plane cornona over a very extended range of point diameters, gap lengths, point

materials and pressures in clean dry air,

Tamura, T., Proc. Phys. Soc. (Japan) 16^, 2503 (1961); jj, 1434 (1962); Jap.

J. Appl. Phys. 2_, 492 (1963).

Accounts of theoretical and experimental work in air and other gases of

breakdown at positive needle points, in which photoelectric ionization of

the gas is a determining factor. Effects of gas pressure and point radii

on the absorption of photons by the gas are included.

Loeb, L. B., Parker, J. H. , Dodd, E, E. , and English, W. N., Rev. Sci,

Instr., 21, 42 (1950).

Contains the results of a calculation of the axial field for a point,

representated by the hemispherically capped cylinder, against an infinite

plane.

Loeb, Leonard B., Basic Processes of Gaseous Electronics (University of

California Press, Berkeley and Los Angeles, 1955).

Gives a detailed treatment of the fundamentals of electrical carriers in

gases. Field ionization, radiation, photoelectric ionization, diffusion,

impact ionization, gas pressure, recombination and space charges all

participate,

Herrastein, W., Ach. Elektrotech, 45 209, 279 (1960).

9
Reports on studies of the discharge threshold potential of positive

spherical points of various radii as a function of gap length. Both planes

and concentric spheres were used as cathodes,

Bowdler, G, W,, Measurements in High-Voltage Test Circuits (Pergamon Press,

New York and Oxford, 1973).

An easily readable treatise concerned mainly with experimental techniques

in high-voltage measurements, it contains useful sections on application to

corona and associated breakdown phenomena.

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10
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Curves of threshold gap length for rounded edges of kno\>m included angles

and edge radii. Kach solid curve is for a set of edges having equal angles,

but different radii; the dashed curve is for edges fabricated as, sharp as pract icable.
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NBS-1 14A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBSIR 75-908

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Characterization of Sharp Edges and Points

by Electrical Breakdown

5. Publication Date August 1975

6. Performing Organization Code

7. AUTHOR(S)

Julius Cohen

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE ^ WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 4460122

11. Contract/Grant No.

12. Sponsoring Organization Name and ( omplctc AJdres.s (Street, City, State, ZIP)

Same as above

- "' '

13. Type of Report & Period Covered

Final

14. oponsoring 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.)

Experiments were made to determine the feasibility of using the phenomenon of

electrical breakdown in air to characterize sharp metallic edges and points.

A fixed voltage was applied between a sample edge or point and a parallel

plane, and threshold gap length for breakdown observed. Results were quite

favorable for edges, but not for points, and the polarity on the sample was required to be negative.

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

)

Consumer products; electrical breakdown; gases; hazard; high voltage; sharp edges;

sharp points; threshold

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