Elektrische Kontakte

Von

Ragnar Holm Dr. phil.

unter Mitarheit von Else Holm Dr. phil.

heide St. Marys (Pa.)

Mit 194 Ahhildungen

D ri tt e vollig neuhearbeitete Auflage

des Buches von R. Holm, Die technische Physik

der elektrischen Kontakte

In englischer Sprache

Springer-Verlag Berlin Heidelberg GmbH

1958

Electric Contacts Handbook

By

Ragnar Holm Ph.D.

aided by Else Holm Ph. D.

both of St. Marys (Pa.)

With 194 Figures

Third completely rewritten edition

of "Die technische Physik der elektrischen Kontakte"

by R.Holm

Springer-Verlag Berlin Heidelberg GmbH

1958

ISBN 978-3-662-23790-8 ISBN 978-3-662-25893-4 (eBook)DOI 10.1007/978-3-662-25893-4

Alle Rechte, insbesondere das der Übersetzung in fremde Sprachen, vorbehaltenOhne ausdrückliche Genehmigung des Verlages ist es auch nicht gestattet,

dieses Buch oder Teile daraus auf photomechanischem Wege(Photokopie, Mikrokopie) zu vervielfältigen

© by Springer-Verlag Berlin Heidelberg 1958Originally published by Springer-Verlag OHG., Berlin/Göttingen/Heidelberg in 1958

Softcover reprint of the hardcover 3rd edition 1958

Die Wiedergabe von Gebrauchsnamen, Handelsnamen, Warenbezeichnungen usw.in diesem Buche berechtigt auch ohne besondere Kennzeichnung nicht zu der An-nahme, daß solche Namen im Sinne der Warenzeichen-und Markenschutz-Gesetz-gebung als frei zu betrachten wären und daher von jedermann benutzt werden dürften

Preface

Circuit breakers, relays, terminals, microphones, current collectors and commutators, all operate with electric contacts. Industry is making extensive use of contacts with ever-increasing demands on efficiency. The need of up to date reliable theories as well as of formulas and tables for applications is becoming pressing. This book is an attempt to meet this need.

As is the case in many other branches of technology today, problems which arise in the field" of electric contacts involve insight in various other disciplines of physics, including parts which have not yet developed to such an extent that they. are treated in elementary text books. Con­sidering the lack of introductions to some topics of this kind it is felt that orienting chapters, for instance, on the tunnel effect, the theory of the arc, the structure of carbon, and the band theory of electric conduction in solids might be valuable for many readers. In order not to burden the main text with such chapters they have been presented as appendices.

Several chapters have been devoted to the theory offriction and wear. One might question whether this theory is pertinent to the topics of electri­cal contacts. To answer we recall that the theory of friction has received essential contributions from investigations on electrical contacts; more­over, frictional and electrical contact phenomena are largely intercon­nected, for instance, in the theory of commutation and other important subjects of undisputed relevance to this book. For this reason a rather e:rlended treatment of friction and wear is presented.

The concise title of this book can only be gained at the expense of the adequateness. Whereas the title tells too little concerning the friction chapters it announces too much with respect to some other items which certainly belong to the large field of electric contacts, namely thermo­electric phenomena and contacts with semiconductors. The reason for this unilaterality is that thorough handbook articles exist concerning thermoelectricity and contacts with semiconductors to which the author could not present any competition.

It will be appropriate to shed some light on certain particular features of the task of the author. Many branches of electrotechnology, for instance, the theory of transformers, have had for a long time well established physical backgrounds, but any theoretical treatment of the contact phenomena here presented is of a recent date. It is therefore not

VI Preface

surprising that the relevant literature presents different and sometimes even misleading and contradictory interpretations, as well as data of limited validity. On many occasions investigations have been cited as proving certain conclusions, although these may differ more or less from the inferences made by the workers themselves. In this book, in cases when the conclusioIl& given seem to be plain enough, arguments about different meanings have been omitted. It is felt that this method is favorable for the student. The attempt has always been made to clearly bring out the limits of validity of important statements.

In accordance with the practical aim of the book formulas have been presented so as to be easily adapted to the performance of computations. In the tables, especially those of Appendix X which provide material constants, units have been chosen to fit the equations without conver­sion. The choice of units has caused some hesitation. V Brious experts recommended the use of the mks system, which actually has been used in this book for electrodynamic calculations. But, because the centimeter is a more tangible unit than the meter for the small dimensions of the contact constriction and has been employed almost entirely in the liter­ature on contacts, the cm and the A = 10-8 cm, have been used for the dimensions of contact constrictions and film thickness. The conversion from cm to m is easily made.

The preparation of this book required the fulfillment of various con­ditions. It was necessary that the author be a physicist with long and intimate connections with industry and with facilities to carry out fun­damental experiments. For favorable facilities of this kind the author is greatly indebted to two firms, in the laboratories of which he has made most of his investigations, namely, the Siemens-Konzern of Berlin, Ger­many, a..nd the Stackpole Carbon Company of St. Marys, Pa., USA. During his time in Berlin the interest of and support of Dr. HuMANN

VON SIEMENS and Professor lIANs GEBDIEN, the director of the Siemens Forschungs Laboratorium, was particularly valuable. The support of the Management of the Stackpole Carbon Company while this book was in preparation is gratefully acknowledged.

Another requirement has been the teamwork with my wife, Dr. phil. ELSE HOLM. I wish to acknowledge the help of my assistants in Berlin: F. GULDENPFENNIG, Drs. KmScmsTEIN,' STOBMEB, Fmx. and KORNER, whose names are quoted in the text and in the list ofliterature. I am greatly indebted for valuable discussions to Professors H. BUSCH (see § 11), W. MEIsSNEB (see § 26), S. MROZOWSXI (see § IV), W. SCHOTTKY, DI:s. J. A. BECKEB (see § 7), W. E. CAMPBELL, F. KESSELBING, and A. E. MIDDLETON (see § 35), and to my present colleagues at Stackpole Carbon Company,particularlyDr.E.I.SHoBEBTandMr.W.G.KBELLNEB.Several figures have been reproduced from the literature with due permission for

Preface VII

which I am thankful. The respective author and the reference are cited in the pertinent captions.

The author, in 1941, published a book titled Die techniscke Physik der elelctrisehen Kontalcte (Editor Springer, Berlin) and, in 1946, a revised edition Electric Oontacts (Editor H. Geber, Stockholm). Although the present book is entirely rewritten except for certain passages and is enlarged, it has similarity with the older books in the disposition a.nd has taken over many figures. We, therefore, might be justified. in regarding it as a third edition of Die teehniscke PhY8ik der elelctrischen Kontalcte, this time in English language.

FinaJIy it is a pleasure to express my particular thanks to the editors, the Springer-Verlag of Berlin, for the kind invitation to write this book and for an excellent printers performance.

St. Marys (Pa.), August 1957 Ragnar Holm

Contents Page

List of the most frequently used symbols and abbreviations ...........•.. XVI

Part I

Stationary Contacts

§ 1. Introduction. A simplified summary of the theory of stationary electric contacts....................................................... 1

§ 2. The contact surface ............................................. 8 § 3. The contact resistance. General theory . . . . . . . . . . . . . • . . . . . . . . . . . . . .. 10 § 4. Calculation of constriction resistances with constant resistivity. . . . . . . . 13

Problem A. 14. - Problem B. 15. - Problem C. Elliptic a-spot. 15. - Pro­blem D. Circular a-spot. 16. - Problem E. 18. - Problem F. The influence of the elliptic shape of the contact area on the constriction resistance expressed by a shape factor. 18.

§ 5. Constriction resistances when conditions deviate from those in § 4, but with !? still being a constant. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Problem A. Spreading resistance. 20. - Problem B. Constriction resistance when the a-spot is covered with a film. 21. - Problem C. Metallic contact with many a-spots. 22. - Problem D. The constriction resistance R(n,-a, l) of a coherent contact area with n insulating spots. 24. - Problem E. Distorted constriction. 24.

§ 6. Thermal constriction resistance ................................... 25 § 7. Films on contacts ............................................... 27

A. Different types of films. 27. - B. Aging of contacts. 31. - C. Tunnel resistance of contact films. 32.

§ 8. The contact surface as a function of load and elastic as well as plastic properties of the members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 A. Elastic deformatio\l. 33. - B. Plastic deformation. 34. - C. In­fluence of temperature and contact duration on the contact area. 37.

§ 9. The relation between contact load and resistance, particularly at moderate and high load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 39 A. Introduction with description of Fig. (9.01). 39. - B. Crossed rod contacts. 42. - C. Explanation of the dashed lines in Fig. (9.01). 44. - D. Diversified measurements. 45. - E. Use of diagram (9.01) in practice. 46. - F. Contact preloaded with a high P. 47.

§ 10. Contact resistance on freshly cleaned contacts at very small contact loads 48 § 11. The inductance of a current constriction. Skin effect . . . . . . . . . . . . . . . . . 52

A. Inductance. 52. - B. The skin effect. 54.

§ 12. Electrodynamic repulsion in a symmetric contact of a non-magnetic material. . . .......... . . ....... . .. . . . . .. . .. .. . . . ... . . . .. . . . . .. .. 55

Contents IX

§ 13. The cap]'citance of a contact. Electrostatic attraction in a contact . . . . . 56 Example A. Crossed rod contacts. 57. - Example B. Quasiflat contacts. 58. - Example C. JOHNSoN·RAHBEK effect. 58.

§ 14. Measurement of the load bearing contact area.. . . ...... . ......•...• 59

§ 15. The relationship between electric potential and temperature in a current constriction which is symmetric with respect to the contact surface; that is, the rp-f} relation ........................................ 65

§ 16. The rp-f} relation in cases of dissymmetry . • . . . . . . . . . . . . . . . . . . . . . . .. 70 Case A. Dissymmetry in regions of the constriction which are distant from the contact. 70. - Case B. Contact between highly different materials. 71. - Case C. Contact between moderately different metals. 72. -Case D. Heat enters across Ao' 72. - Case E. THOMSON effect is present. 73. - Case F. The rp-I) relation in the environment of a bimetallic contact. 75.

§ 17. KOHLER effect ................... '" . .. .......... . . ............. 75

§ 18. The influence of the JOULE heat on constriction resistance. . . . . . . . . . .. 78 Example A. WIEDEMANN-FRANZ-LoRENZ law is valid. 80. - Example B. Semi-conducting material. 82. - Example C. Heat flowing across Ao. 82.-Example D. Independant of whetherWIEDEMANN-FRANZ-LoRENZ law is valid. 84.

§ 19. Distribution of the temperature in a symmetric constriction with circular contact surface at given current. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 85 Example A. €I and k are constant. 85. - Example B. Corresponding to Example A in § 18. 86. - Example C. Corresponding to Example B in § 18.86.

§ 20. Temperature distribution in the constriction of a contact with circular contact surface and members with very different conductivities ....... 87 Example A. 88. - Example B. 89.

§ 21. Resistance - voltage characteristics of clean symmetric contacts. Soften-ing and melting voltages ......................................... 90

§ 22. Development of the temperature in a current constriction ............ 95 A. Introduction. 95. - B. Remarks concerning the diagrams. 98. -Co'Moving contact. 101. - D. Temperature development in a cylinder. 103. - E. Cooling of a previously heated contact region. 104. -F. Examples. 104.

§ 23. The growth of tarnish rums on metals ............................. 105 A. Fundamentals of the theory. 105. - B. Passivating ffims. 110. -C. Tarnishing of various base contact materials. 110. - D. Tarnishing of noble metals. 115.

§ 24. Water ffims, local cells and rusting ................................ 116 A. Thickness of water rums. 116. - B. Rusting by means of electro­chemical attack. Local cells. 117.

§ 25. Thermoelectric effects ....................................••..... 118

§ 26. Observations on the tunnel effect ................................. 121 A. Introduction. Method. 121. - B. Observations giving a. 125. -C. Measured a compared with the theoretical value. 127. - D. Super conductivity of contacts. 128.

x Contents

§ 27. Fritting oftarnish films . . . .. .. .. .. . . . .. .. .. . . . . .. . . .. .. .. .. . . . ... 130 A. Introduction. 130. - B. A-fritting. General appearance of the process. 131. - C. Cessation voltage of fritting. 132 - D. The frit bridges. 137. - E. B-fritting. 139. - F. The coherer. 141. - G. Defritting. 141. -H. Initial stage of fritting. 141. - I. Recent investigations of fritting. 142.

§ 28. RU-characteristics of contacts with thin alien films ..............•..• 146

§ 29. Adherence in dry contacts which are not heated to any influential extant by the current ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 150

§ 30. Adherence in contacts that are heated by the current passing through them. Resistance welding ........................................ 154

§ 31. About stationary contacts in practice ............................... t58 A. General survey of the role that contact films play in practical contacts. 159. - B. Measurements in F. L. on contacts made without impact or sli­ding. 162. - C. Clamped contacts. Screw. 16.5.

§ 32. Dimensioning a contact with respect to its heating .................• 169

§ 33. Contact effects in carbon microphones ............................. 172

§ 34. Contact noise in a stationary contact .............................. 183

§ 35. Contact with semiconductors. Rectification. Transistors. Static electri-fication ........................................................ 188 A. Introduction. 188. - B. Contact between a metal and a semiconductor and its rectifying property. 188. - C. The p-n-junction. 190. -D. Types of semiconducting rectifiers. 191. - E. Remarks about transistors. 194. - F. Remark concerning the contact between silicon carbide crystals. 195. - G. Static electrification. 195.

§ 36. Carbon-pile rheostats. Electric resistance of pressed powders •• . . . • . . .• 196

Part II

Sliding Contacts

§ 37. Survey concerning friction and wear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 199 A. Introduction. 199. - B. The friction work resulting from plastic deformation. 200. - C. The adherence term of the friction. 201. -D. The increase of the contact area during sliding. 203. - E. Coulombs law of friction. 204. - F. About the characteristic value of I' '"=' ion freshly cleaned metal contacts in air. 205. - G. Friction in bimetallic con­tacts. 206. - H. Friction between non-conducting members. 207. -I. Devices for the investigation of friction. 207. - J. Rolling friction. 207. - K. The influence of adhesion wear on friction. 209. - L. The work of the adhesion friction. 209.

§ 38. Early observations on the high friction in clean metallic contacts in vacuum, and the influence of admitted gases ....................... 210

§ 39. Boundary lubrication .... , ............ , .......................... 212 A. Features of boundary lubrication. 212. - B. DiscuBBion of two competing theories of boundary lubrieMion. 216. - C. Lubricating practice. 221. - D. Beilby layer. 221. - E. Properties required of bearing materials. 222. - F. Ball bearings. 224.

Contents XI

§ 40. Theory of friction and wear on carbon contacts. Lubrication by means of solid lubricants as graphite and molybdenum disulphide ............. 224 A. Introduction. 224. - B. Friction of carbon brushes as dependent on the orientation of graphite basal planes. 226. - C. High altitude effect on brush wear. 227. - D.Adjuvants. 229. - E. Graphite and molybde. num sulfide powder as lubricant. 229.

§ 4t. Measurements on specific friction force ............................. 231 § 42. Stick-slip motion. The temperature in ccrrentless sliding contacts ..... 234

A. Stick-slip or jerky motion. 234. - B. The temperature in current-1eBS sliding contacts. 235.

§ 43. Statistical study of the electric conduction and the friction of sliding contacts. Radio-noise in sliding contacts ........................... 237

§ 44. Friction wear in metallic contacts without current . . . . . . . . . . . . . . . . . .. 242 A. Introduction. 242. - B. Size and frequency of wear fragments appearing during periods of adhesive wear. 243. - C. Details of the formation of wear detritus. 244. - D. Why liquids, even the deposit from air humidity, are able to influence wear without greatly affecting the friction coefficient. 245. - E. The work necessary to break off a wear fragment. 245. - F. Formula for claBSification of types of friction wear. 246. - G. Friction wear in currentless sliding contacts represented by 2 . 106 Z, which is calculated employing the hardness, H, of the softer member. 248. - H. Wear in sliding contacts of measuring apparatus. 253.

§ 45. Electrical performance of carbon brushes on rings and commutators when arcing is excluded ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 254 A. Introduction. 254. - B. Early investigations on the dark collector film. 255. - C. Chemical analysis of the collector film. 259. - D. Structure of the film. 259. - E. Oscillographic investigations of frittings of the collector film. 259. - F. More about the film generation particularly in the "static" state. 262. - G. Two brushes in the same track. 264.

§ 46. The temperature in a contact between a carbon brush and a copper ring or commutator .................................................. 265 A. Introduotion. 265. - B. Supertemperature of the contact surface above the temperature of the bulk of the ring. 266. - C. The temper­ature in the hottest section of the brush. 267.

§ 47. Wear and friction in the brush-ring contact ........................ 269 A. Introduction. 269. - B. Influence of the current on the wear in absence of arcs. 269. - C. Numerical data of brush qualities. 272. -D. Abrasion of the slip ring. 273. - E. Wear in the brush-commutator contact in case of arcing. 274. - F. Friction between an electrographite brush and copper ring. 275.

§ 48. Commutation problems .......................................... 216 A. Introduction. 276. - B. Computation of cardinal conditions for good commutation. 279. - C. Arcing. 281. - D. Numerical example referring to a d.c generator with 2 poles for about 50 amp. 283. -E. Brush contacting several segments simultaneously. 284. - F. So. called short-circuit currents in the brush. 285. - G. The importance of the elasticity of the brush for the commutation. 287. - H. The appropriate value of the emf V to be induced in an armature winding by the field of the interpoles. 288.

§ 49. Current collectors for trolley cars ................................. 288

XII Contents

partm

Electric Phenomena in Switching Contacts

§ 50. Definitions and high power breakers .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 290 A. Introduction. 290. - B. Breaking of a-c 290. - C. Vacuum switches. 292. - D. Direct current switches. 292. - E. Quenching circuits. 293. -F. Material transfer at switching. 293.

§ 51. Ignition of arcs in switches ....................................... 293 A. Introduction. 293. - B. Electric breakdown in the gap between clean metallic electrodes at atmospheric pressure. 293. - C. Ignition of an arc in a closing contact. 295. - D. Drawn arcs. Floating. 297. -E. Reignition of the arc. 299.

§ 52. Discharge transients ............................................. 302 § 53. VI-characteristics of the stationary arc in air, and their use for cal-

culating the duration of short arcs ................................ 304 A. Introduction. 304. - B. Observations on breaking contacts. 304. - C. The use of VI-characteristics for determination of arc durations. 310. - D. Simplified VI-characteristics in normal atmosphere. 311. -E. Determination of I", and V", by aid of one oscillogram and Diagr. XI. 314. - F. Use of the resistance line together with arc-characteristics for the problem of how a constant current is shared between an arc and an ohmic resistance both in parallel. 314. - G. Survey of the method of applying the resistance line together with arc characteristics. Condition of stability. 315. - H. Semiconducting resistors parallel to the arc. 315. -I. Vacuum arc. 316.

§ 54. Electric Oscillations generated by d-c arcs ......................... 316 § 55. Bouncing ...................................................... ' 318 § 56. Mechanical erosion and tarnishing phenomena that are typical for sliding

and switching contacts .......................................... 321 A. Introduction. 321. - B. Mechanical material transfer. 322. - C. Cata­lytic effects in switching contacts. 323. - D. Frictional oxidation. 323. - E. Oxidation in the arc. 324.

§ 57. Methods to suppress or minimize arcing during switching ............. 326 A. Introduction. 326. - B. Quenching by means of a resistor. 326. -C. Capacitive quenching. 327. - D. Arc quenching in the contact rectifier. 328. - E. Weakening of the arc between barriers, magnetic blowout. 329. - F. Motion of an arc in a magnetic field. 330.

§ 58. Arc duration in contact making with voltage below 200 to 300 volts ... 331 A. Introduction. 331. - B. Calculations with respect to the wiring Diagram (58.02) with initially charged capacity. 331. - C. Inductance 1 = 0, and consequently p = 0 in the circuit (58.02). 334. - D. Float-ing. 335. - E. Empirical formula for t., the life of the arc, in the circuit (58.02).336. -F. BatteryinsteadofC, equivalent to C = 00.337.

§ 59. Arc duration on breaking contact. Single circuit .................... 338 A. Ohmic circuit according to wiring diagram of Fig. (59.01). Operation in air. 338. - B. Ohmic circuit. Operation in a vacuum. 338. -C. Inductive circuit according to wiring diagram in Fig. (59.04). Capa-city of the leads neglected. Operation in air. 338. - D. The quantity of electricity, q, that flows through a drawn arc with the life time t •• 341. - E. InfI.uence of the capacity of the leads. 342.

Contents XIII

§ 60. Arc duration and other phenomena in an arc quenching circuit according to wiring Diagram (60.01) ........................................ 342 A. General equations for the quenching circuit when quenching an arc on breaking contact: T in position a. 343. - B. Case of Va"'" constant. 343. - C. Va"'" V m and arc current / a considerably greater than I,... 344. - D. Va differing slightly from Von' and the short circuit current, I", lying in the range between 1m and a few amp. 345. - E. Note con­cerning the position of T. 347. - F. Empirical formula for the calcula­tion of the arc life at constant opening velocity of the circuit of Fig. (60.01) under such conditions that the arc generates oscillations. 347. - G. Con­dition for no breakdown of the gap between the separating electrodes. 349.­H. Calculation of the voltage V, between the electrodes as function of the time, t, in case of no arc. 350.

§ 61. Quenching of arcs by resistance parallel to the operating contact or parallel to the inductive coil .............. '. . . . . . . . . . . . . . . . . . . . . . .. 352 A. Quenching with r in positon a. 352. - B. Arc quenching with r in position b. 354.

§ 62. Distinct types of arcs in relay contacts ............................ 354 A. Introduction. 354. - B. The power balance in the short arc deter­mines the prevalence of the evaporation from the anode. 355. - C_ The plasma arc. 356. - D. Remarks. 357.

§ 63. Material transfer in switching contacts ........................... " 358 A. Definition of the major types of material transfer. 358. -B. Material transfer at contact opening. 359. - C. Material transfer at contact make. 363.

§ 64. Measurement of the material transfer in switching contacts, particularly with normal electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 363 A. Introduction with definition of electrode types and symbols. 363. -B. Determination of the amount of material transfer that is produced by plasma arcs between normal electrodes. 364. - C. Method to determine w. and w. in general. 365. - D. Measurements of bridge transfer in opening contacts. 366. - E. Determination of the coefficient r" which according to Eq. (63.10) characterizes the material transfer in short arcs between normal electrodes. 368. - F. The final length. 8"., of the short arc. 370. - G. Abnormal, short arcs with zero or a small material transfer from the anode. 371. - H. The amount of material transfer during floating. 372. - I. The disintegration of the cathode in glow discharges. 373 - J. Material transfer at contact closure without bouncing. 374.

§ 65. Bridge material transfer in the shape of pips and spires .............. 375

§ 66. Theory of the electric material transfer in switching contacts. History of this theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 376 A. History. 376. - B. Explanation of the material transfer caused by the arc. 378. - C. Present theory of the bridge transfer. 379 - D. THOMSON effect. 379. - E. PELTIER effect. 383. - F. KOHLER effect. 384. -G. Comparison between calculated and observed magnitudes of the bridge transfer. 388.

§ 67. Numerical example on the calculation of material transfer for a silver contact with capacitive arc quench ............................... 387

§ 68. Mercury switches. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 388

XIV Contents

§ 69. Application of statistics to surety of contact make .................. 300 A. Introduction. 390. - B. Testing surety of contact make with single macro contacts. 391. - C. Effect of twin contacts. 393.

§ 70. The choice of contact material and contact shape for practical appli-cations ........................................................ 394 A. Permanent contacts. 394. - B. Micro contacts. 394. - C. High repetitive operation relay contacts. 395. - D. Light duty relays for medium frequencies. 396. - E. Medium duty circuit breakers and contactors. 396. - F. Heavy duty circuit breakers with up to thousands of amperes and volts. 396. - G. Sliding contacts for resistors and apparatus. 397. - H. Remark about non-welding in carbon and wolfram­carbide contacts. 397.

Part IV

History

§ 71. History of early investigations on contacts ......................... 398 A. Contact resistance. 398. - B. Microphone and coherer. 401. - C. Current constriction. 405.

Appendices

§ I. Hardness, strain hardening, atomic diffusion phenomena as recovery and creep ....................•..............•...•.•..•......... 407 A. Survey of the theory of plastic deformation of solid bodies and of diffusion phenomena. 407. - B. Hardness as defined by the ball inden­tation test. 410. - C. Brittle materials. 413. - D. The work consumed by a plastic deformation. 414.

§ II. Electronic conduction in solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .• 414 A. Energy band scheme. 414. - B. Distribution of the electrons on the energy levels of a band, with speoial reference to the conduction band of a metal. 416. - C. Potential barrier. Thermionio emission of electrons, 419. - D. Addenda about 'Y}, 11- and p-conduotion. 420. - E. Semicon­duction. 421. - F. Potential barriers and equilibrium conditions in contacts. 424. - G. The thermal conductivity, k, and the law of WIEDE­

MANN, FRANZ and LORENZ. 428.

§ III. Tunnel effeot. Thermionic emission and field emission . . . . . . . . . . . . . . .. 429 A. Theoretioal basis for the caloulations. Classes I and II of calculation procedure. 429. - B. Field emission and thermionio emission enhanced by the SCHOTTKY effect. 433. - C. Tunnel resistivity. 435. - D. Comparison between tunnel ourrent and thermionic current acoording to formula (Ill,13).437. - E. Tunnel effeot when both electrodes are of the same semi-conducting material. 438. -F. Remark concerning the field strength. 439. - G. Tunnel current across a gap that surrounds a metallic contact consisting of a circular spot with the radius a. 439.

§ IV. Structure, electric and thermal conductivity of carbons. . . . • . . . • . . . . .. 440 A. Introduotion. Graphite latice. 440. - B. Carbon grades. 442. -C. Graphitization. 443. - D. Electric conductivity of carbons. 444. -E. Heat conductivity of carbons. 447.

§ V. Hydrodynamic or thick film lubrication •...........•............• 448

Contents xv § VI. Remarks about threadlike metallic formations . . . . . . . . . . . . . . . . . . .. 453 § VII. Some fundamental formulas concerning the electric discharge ....... 455

A. Introduction. Kinetic fundamentals. 455. - B. Drift velocity. 456. -C. Thermal ionization. Saha's equation. 457. - D. Plasma. 457. -E. Current in vacuum restricted by the space charge of the current carriers. 458.

§ VIII. General theory of the arc that appears in relays ........ . . . . . . . . .. 459 A. Introduction. 459. - B. Reminder of elements of the theory of elec-tric discharges in gases. 460. - C. Thickness of the cathode layer and metal vapor pressure within it. 462. - D. Definition of the examples. 463. - E. Current density J+ of the positive ions and J. of the primary electrons, at the cathode. 465. - F. h as a function of T and p. 465. -G. Comparison with measurements. 467. - H. Power balance at the cathode. 467. - I. Summary of the results concerning cathode pheno­mena. in arcs between non-refractory electrodes. 469. - J. The power ba.la.nce at the anode. 470. - K. Cathode of refractory materials as carbon and wolfram. 471. - L. Why is the voltage ofa short arc of the order of 10 V? 471. -M. Moyement of the arc spot. 472. -N.Current­voltage characteristics of arcs. Arc life. 473.

§ IX. Calculation of the size of the load bearing area and of the pressure

§X. §XI.

on it in experiments by BOYD and ROBERTSON [1] ................. 475 476 481

Author and literature index .......................................... 4.83

Subject index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 514

List of the most frequently used symbols and abbreviations

a and c are indices, referring to anode and cathode, § 62, 63, 64, VIll. a.-spot discrete, continuous and conducting contact area. A contact can have many

a-spots, § 2 to 6, 14, 31, 43. a radius of an a-spot, cm. b radius of a perfectly conducting sphere replacing the contact surface in model

(1.02), § 1, 4, 11, 22. c thermal capacity, J cm-a, § 22. cps = cycles per second, in german Hz. e charge of the electron, 1.60· 10-19 coul, § II, III, VII. ev electron volt. emf electromotoric force. I relative humidity: f = 0.4 means 40%, § 47, X. 9 is employed as a symbol for gram, as well for force as for mass. h pitch of a screw, cm, § 31; thickness of lubricating layer, § V. h PLANCK constant, 6.63 . 10-27 erg sec = 4.14· 10-15 ev sec, § III. hll quantum of energy, erg. k BOLTZMANN constant, 1.38.10-18 erg deg- 1 = 8.69.10-5 ev deg- 1, § VIII. ~ k T average energy of one degree of freedom. k = ko(1 + PO) thermal conductivity, W cm- 1 deg- 1, § 6,15, 19,20, X 1 small inductance, Hy, § 60. m mass of the electron, 0.91 • 10-17 g, § III. p pressure, g cm-s, in some tables ton cm- 2, § t, 2, 8, 14, I, V, VIII. q quantity of electricity passing through a single discharge, coul, § 58, 59, 60,

63,64. r radius, cm. r resistance in quench-circuit, n, § 57, 60, 61. r latent heat of vaporization, J cm-a, § VIII, X. rms root mean square. 8 distance of travel of sliding contact member, § 40, 44, 45. 8 gap, also arc length, cm, § 53, 59, 62. 8 bridge length, cm, § 66. l time, sec, sometimes hr. t. duration of arc, sec, § 58-61. 11 velocity. 10 evaporated volume of the solid metal in cms coul- l , § 63.

z = J;- t dimensionleBB substitute for time, § 22. ca

A. apparent contact area. A 6 load bearing area. A • conducting contact area. A • end-surface, § 3 etc.

List of the most frequently used symbols and a.bbreviations

A Angstrom unit = 10-8 cm. B radius of end-surface in model (1-02), § 11, 12. C electrostatic capacity, § 4, 13, 60. D volume of metal deposited from vapor in an arc, § 64. D probability that electrons cross a potential barrier, § III. E electromotive force, emf, volts. E elastic modulus, g cm- B, § 8, X. F electric field intensity, volt cm- I, § 12, III. E energy of electrons. § H. F 8' fritting field intensity, § 27. F. L. research laboratory of the Siemens-Concern, division Holm. a ma.terial transfer caused by an arc, cms, § 64. H magnetic field intensity. H hardness, upper limit for p, g cm- 2, in some tables ton cm-2, § I, X. I electric current intensity, amp. I" short-circuit current. I a arc current. I. minimum current necessary for floating, § 58. 1m minimum current necessary for a permanent are, § 53, VIII, X. I b final current through a contact bridge, § 64. l' ignition current of quenched arc, mathematical variable, § 60. J Current deasity, § VIII. L inductance, Hy, § 59, 60, 61. L coefficient for the law of WIEDEMANN-FRANZ-LoRENZ, § 15, II. M mantle surface, § 4, 5. M torque, cm g, § 31-Nw newton = 0.102 kg. P contact load, g, § 1, 2 etc. Q quantity of electricity, coul, § 4,64. R constriction resistance in one contact member, n, § 1, 3 etc. H total constriction resistance, n, § 1, 3 etc. ROb and R~ measured quantities for determining R, n, § 3 etc. R, film resistance, n, § 3, 7.

XVII

Ru partial resistance between the Ao surface and another equipotential surface AI-" n, § 19.

RU -characteristic giving the contact resistance plotted against the voltage, § 21,28. T absolute temperature, OK. U constriction voltage due to one contact member, § 3,4 etc. U total contact voltage, § 1,3,4 etc. U, liquefying or melting voltage, § 15,21, X. U 11' Fritting voltage, § 27. U. softening voltage, § 21, X. V voltage in general. Va arc voltage, § 51 etc. V m minimum arc voltage, § 53. VI· charakteristic of the arc, § 53. W thermal resistance, W-I deg, § 5. W frictional wear, 10-6 cm3, § 44 and 47. Wo and WI-coefficients in Eqs (47.02) and (47.05) giving brush wear. W. and Wa volume of metal that, during the life time of an arc, evaporates from

the cathode or anode respectively, 10-6 cm3, § 64. Z number used for the classification of frictional wear, § 44. IX temperature coefficient of e, § 15, X.

XVIII List of the most frequently used symbols and abbreviations

fJ

y b OJ

Q

Ii,

e 1]

D e

#0

v g II (1

temperature coefficient of k, § 15, X.

= ; ratio between the axes, '" and fJ, of an elliptic a-spot, § 4.

transfer of material, in 10-6 cm3 per coulomb, caused by the arc, § 64. material deposit, in 10-8 cm3 per coulomb, during arcing, § 64. material evaporated, in 10-8 cm3 per coulomb, during arcing, § 64. = ohm. permittivity (or dielectric constant) of vacuum = 8.85 • 10- 12 faradlm in the mks system. relative permittivity. ratio between load bearing contact areas during sliding and stationary, § 37. coefficient of internal friction, § V. temperature, centidegrees, § 15, 18 etc. superlemperature of the warmest isothermal surface in a constriction (the contact surface in a symmetrical contact), centidegrees, § 15, 18 etc. electric conductivity, mho cm- l, § II. mean free path, § VIII.

magnetic permeability of vacuum = 1.257. 10-6 Hy . m

relative magnetic permeability, § 11. friction coefficient, § 37 etc. parameter of equipotential surfaces of a symmetrical contact with an elliptic contact surface, § 4 etc. frequency, sec-l, § 12. ratio plH, § 8, I. Peltier coefficient, § 16, 66. = (10(1 + ",D) electric resistivity, where eo is associated with the temperature of the end-surfaces, Q cm, § 4, 18 etc. THOMSON coefficient, § 16, 66. tunnel resistivity, Q cm", § III. constant of the THOMSON effect, § 66. prevalent value of arc time in an approaching contact, sec, § 58. electric potential, V, § 15 etc. work function, § II, III. friction force per cm', in formulae g cm-'; in some tables ton cm- I , § 37. symbol for closing contact. symbol for separating contact. this sign is used as a symbol for chapter and appendix; thus § 15 means chapter 15, and § III means appendix III.

N. B.

Propositions, equations, and figures are numbered consecutively within each chapter in the following way: in Fig. (15.04) 15 refers to § 15 and 04 is the number in that chapter.

Numbers in square brackets refer to the list of literature at the end of the book. When more that one author is mentioned, the number refers to the first of these Thus SHOBERT, E. I. [2] is followed by SHOBERT and J. E. DIEHL [3].