Page 471 - Wind Energy Handbook

MECHANICAL BRAKE 445

brake disc. The rate of energy dissipation is equal to the product of the braking
torque and the disc rotational speed, so in the latter stages of braking the rate of
energy dissipation cannot sustain the high surface temperatures and they begin to
fall again.
The coefficient of friction for pads of resin-based materials is sensibly constant at
a level of about 0.4 at temperatures up to 2508C, but begins to drop thereafter,
reaching 0.25 at 4008C. Although in theory the brake can be designed to reach the
latter temperature, in practice the varying torque complicates the calculations and
leaves little margin of error against a runaway loss of brake torque. Accordingly
3008C is often taken as the upper temperature limit for resin-based pads.
Sintered metal pads have a constant coefficient of friction of about 0.4 up to a
temperature of at least 4008C, but manufacturers indicate that the material can
perform satisfactorily at temperatures up to 6008C on a routine basis, or up to 8508
intermittently. Wilson (1990) reports a reduced friction coefficient of 0.33 at 7508C.
Such temperatures cannot be realized in practice because the temperature of the
disc itself is limited to 6008C in the case of spheroidal graphite cast iron or to a
much smaller value in the case of steel (op. cit.).
Clearly the use of the more expensive sintered brake pads allows the brake disc
to absorb much more energy. However, the sintered metal is a much more effective
conductor of heat than resin-based material, so it is often necessary to incorporate
heat insulation into the calliper design to prevent overheating of the oil in the
hydraulic cylinder. A method of calculating brake-disc temperature rise is given in
the next section.

7.6.3 Calculation of brake disc temperature rise

The build up in temperature across the width of a brake disc over the duration of
the stop can be calculated quite easily if a number of assumptions are made. First,
the heat generated is assumed to be fed into the disc at a uniform intensity over the
areas swept out by the brake pads as the disc rotates. This is a reasonable
approximation for a high-speed shaft-mounted brake and for a low-speed shaft-
mounted brake with several callipers until rotation has almost ceased, but the
energy input by this stage is much lower. Within the disc heat flow is assumed to
be perpendicular to the disc faces only, i.e., radial flows are ignored.
Consider a brake-disc slice at a distance x from the nearest braking surface, of
thickness ˜x and cross-sectional area A. The rate of heat flow away from the nearest
_
braking surface entering the slice is Q ¼ kA(dŁ=dx) (where Ł is the temperature
Q
and k the thermal conductivity) and the rate of heat flow leaving it on the far side is
_
_
Q
Q Q þ (dQ=dx). The temperature rise of an element of thickness ˜x over a time
interval ˜t is given by
2
_
Q
dQ d Ł
˜ŁA˜xrC p ¼ ˜Q ¼ ˜x˜t ¼ kA ˜x˜t
dx dx 2
where r is the density and C p is the specific heat, so that