Heat to be Dissipated during Braking
The energy absorbed by the brake and transformed into heat must be dissipated to the surrounding air in order to avoid excessive temperature rise of the brake lining. The upon the mass of the brake drum, the braking time and the heat dissipation capacity of the brake. The highest permissible temperatures recommended for different brake lining materials are given as follows :
1. For leather, fibre and wood facing = 65 – 70°C
2. For asbestos and metal surfaces that are slightly lubricated = 90 – 105°C
3. For automobile brakes with asbestos block lining = 180 – 225°C
Since the energy absorbed (or heat generated) and the rate of wear of the brake lining at a particular speed are dependent on the normal pressure between the braking surfaces, therefore it is an important factor in the design of brakes. The permissible normal pressure between the braking surfaces depends upon the material of the brake lining, the coefficient of friction and the maximum rate at which the energy is to be absorbed. The energy absorbed or the heat generated is given by
E = Hg = μ.RN.v
= μ.p.A.v (in J/s or watts) ...(i)
where μ = Coefficient of friction,
RN = Normal force acting at the contact surfaces, in newtons,
p = Normal pressure between the braking surfaces in N/m2,
A = Projected area of the contact surfaces in m2, and
v = Peripheral velocity of the brake drum in m/s.
The heat generated may also be obtained by considering the amount of kinetic or potential energies which is being absorbed. In other words,
Hg = EK + EP
where EK = Total kinetic energy absorbed, and
EP = Total potential energy absorbed.
The heat dissipated (Hd) may be estimated by
Hd = C (t1 – t2) Ar ...(ii)
where C = Heat dissipation factor or coefficient of heat transfer in W /m2 / °C
t1 – t2 = Temperature difference between the exposed radiating surface and the surrounding air in °C, and
Ar = Area of radiating surface in m2.
The value of C may be of the order of 29.5 W / m2 /°C for a temperature difference of 40°C and increase up to 44 W/m2/°C for a temperature difference of 200°C.
The expressions for the heat dissipated are quite approximate and should serve only as an indication of the capacity of the brake to dissipate heat. The exact performance of the brake should be determined by test.
It has been found that 10 to 25 per cent of the heat generated is immediately dissipated to the surrounding air while the remaining heat is absorbed by the brake drum causing its temperature to rise. The rise in temperature of the brake drum is given by
t = Hg / (m.c) ...(iii)
where t = Temperature rise of the brake drum in °C
Hg = Heat generated by the brake in joules,
m = Mass of the brake drum in kg, and
c = Specific heat for the material of the brake drum in J/kg °C.
In brakes, it is very difficult to precisely calculate the temperature rise. In preliminary design analysis, the product p.v is considered in place of temperature rise. The experience has also shown that if the product p.v is high, the rate of wear of brake lining will be high and the brake life will be low. Thus the value of p.v should be lower than the upper limit value for the brake lining to have reasonable wear life. The following table shows the recommended values of p.v as suggested by various designers for different types of service.