SYMBOLS

Radius of average elastic contact spot Radius of average plastic contact spot Aspect ratio of free fiber length, i.e. Lfree/d Area of macroscopic brush/substrate interface Total area of contact spots; P H or Eq. (20.45) in the plastic or elastic case Total area of plastic contact spots (equal to P H) Factor to correct flash temperature for overall brush heating Specific heat Fiber diameter Mechanical density of brush or substrate material Brush diameter in sliding direction Ellipticity of contact spot (ratio of long to short axis) Averaged Young's modulus of brush and substrate materials Packing fraction, percentage of metal in brush volume at interface Force applied to a fiber end, deflecting it by normal to its axis Factor (< 1) by which flash temperature is reduced compared to 6.T0, i.e. of an asperity on an insulating substrate at zero velocity Hardness of brush material in units of 5 x 108N/m2, the average hardness of copper Meyer hardness of brush or substrate, whichever is the smaller Current conducted through brush Current density through brush Dimensionless constant in the Holm-Archard wear law K* when expressed in terms of dimensionless wear Factor by which of must be divided to correct for peripheral tunneling Probable value of K2 at the safe pressure, Psafe The thermal conductivity of the brush material in units of Acu Electrical brush loss per ampere conducted LE for the "standard case", i.e.,s-h-m-O-f-3-v-1 Fiber length from contact spot to brush current connection Free fiber length between the interface and the nearest fixed point Same as i Li,equiv but in regard to heat transfer resistance Length of solid fiber brush material of same electrical resistance (subscripts j = 0, C, or F for body, constriction and film resistance, respectively) Mechanical brush loss per ampere conducted LM for the "standard case", i.e.s-h-m-¢)—t-O-v-1 Minimum loss per ampere conducted, obtained by adjusting pressure to fimin so that LE = LM Sliding distance Loss per ampere conducted equal to Holm's "softening voltage" (equal to 0.12V for copper) Total brush loss per ampere conducted

The total loss per ampere conducted at Amin, i.e. when the pressure is adjusted to obtain LM = LE The coefficient of friction in units of 0.35, its conservative value Number of spot diameters through which, on average, a contact spot slides before it forms a wear particle Number of contact spots at brush/substrate interface Number density of contact spots at brush/substrate interface Macroscopic pressure at interface between sliding solids Brush pressure: P/AB Brush pressure at which the total heat evolution is (nearly) minimized Average local pressure at contact spots Average local pressure at elastic contact spots Average local pressure at plastic contact spots Brush pressure at which expected dimensionless wear is in the 10 -10 range Value of pa (namely N 3 x 10-4fH) at the transition between elastic and plastic contact spots Normal force between brush and substrate Value of P at Ptrans, i.e. the transition between elastic and plastic contact spots Local heat evolution at contact spots per unit area and time Average heat evolution at brush-substrate interface per unit area and time Characteristic dimension of contact spot (i.e. normally its radius) Radius of the asperity forming an elastic, "Hertzian" contact spot (in fiber brushes, normally r, d/2) Electrical resistance of a brush, in a well-constructed metal fiber brush equal to RF Brush resistance at condition of minimum loss, i.e. at pB

= /3min Ptrans Constriction resistance of a brush Film resistance of a brush Electrical resistance of the brush body o-F/K2 in units of 10-12 S2 m2, the most common value of o.F. Gap width through which effective tunneling can take place (— 0.5 nm) Function by which the flash temperature is modified on account of contact spot ellipticity Thickness of surface film Sliding velocity of brush on substrate Highest sliding velocity at which LE = LM can be achieved for V < Vsat Characteristic velocity Relative velocity (Peclet number) Relative velocity of contact spots on substrate (almost always = vr) Relative velocity of contacts spots on brush (almost always = 0) Wear volume "Melting voltage" as defined by Holm, see Table 20.2 "Softening voltage" as defined by Holm, see Table 20.2 Heat developed per unit area and time at the brush/substrate interface

Lr,min

na Heat conducted per unit area and time through fiber brush from interface to cooled fiber-end

WE Rate of electrical heat evolution, i.e. the part of W due to Joule heat WM Rate of mechanical heat evolution, i.e. the part of W due to friction Zo Function describing the velocity dependence of contact spots for e = 1

and Ar = 0 *(Asterisk) Pertaining to the "standard brush" with

s-h-m-4)—t-S-v-1 Number of contact spots per fiber end Ratio PB if/trans The value of /3 yielding equal friction and Joule heating, approximating the condition of minimum flash temperature as well as minimum heat loss

i3safe The /3-value (namely believed to confer wear rates AC/Ls < 10 —10

Average bending angle of the free fiber lengths on account of applied force Angle of inclination of brush body relative to the sliding interface

8 The fiber diameter in units of 50 gm, its most typical value 813 Incidental local change of /3 at fiber-ends on account of surface

undulations A Elastic deflection of fiber end at interface, normal to Lfree

At Reduction of brush length through wear At/LS Dimensionless wear rate AT "Flash temperature": Rise of contact spot temperature above ambient A Tave Temperature rise at fiber brush as a whole A Tcond Temperature drop due to heat conduction from interface to cooled end

of fiber brush A Tcor = BAT Flash temperature corrected for superimposed overall brush heating ATE Contribution to flash temperature through Joule heat ATE A TE for the "standard case" of s = h=m=4)=1= f A TM Contribution to flash temperature through friction heat ATM ATM for the "standard case" ATmin Near-minimum flash temperature, obtained at WM = WE or

equivalently LM = LE, at which also W is nearly minimized A nin ATmin forthe"standardcase" ofs-h-m-4,—£—S-v-1 A Tp = nqr/4A

Flash temperature at zero velocity on a thermally insulating substrate

m A Tave Temperature rise at monolithic brush as a whole m A Tspot Flash temperature at contact spot of monolithic brush APa Averaged electrical resistivity of brush and substrate materials K = A./Dc Thermal diffusivity KB = JAB/DBCB Thermal diffusivity of brush material

Thermal conductivity AB Thermal conductivity of brush material

Thermal conductivity of surface film material