Caliper disk brakes are commonly used disk brakes. Bicycle brakes are
the best-known examples. The wheel rim constitutes the disk. Friction
lining on the caliper contacts only a small portion of the disk surface,
leaving the remainder exposed to dissipate heat. Figure (1) shows a
hydraulically actuated caliper disk brake that uses a ventilated disk. Air
circulation through the interior passages provides substantial additional
cooling. Disk brakes can conveniently be examined on the front wheel of
larger motorcycles. The cooling or heat dissipating characteristics of
brakes are discussed her in.
Fig.(1) Caliper disk brake, hydraulically operated
Energy Absorption and Cooling
The basic function of a brake is to absorb energy, that is, to convert
kinetic and potential energy into friction heat, and to dissipate the
resulting heat without developing destructively high temperatures.
Where brakes are used more or less continuously for extended periods of
time, provision must be made for rapid transfer of heat to the surrounding
atmosphere. For intermittent operation, the thermal capacity of the parts
may permit much of the heat to be stored and then dissipated over a
longer period of time. Brake parts must be designed to avoid
objectionable thermal stresses and thermal distortion .The basic heat
transfer equation is:
H = time rate of heat dissipation (W or hp)
C = overall heat transfer coefficient (W per m
per °C, or hp per in
A = exposed heat-dissipating surface area (m
ts = average temperature of heat-dissipating surfaces (°C or °F)
ta = air temperature in the vicinity of the heat-dissipating surfaces (°C or
The ability of brakes to absorb large amounts of energy without reaching
destructive temperatures can be increased by
(1) Increasing exposed surface areas, as by fins and ribs.
(2) Increasing air flow past these surfaces by minimizing air flow
restrictions and maximizing the air pumping action of the rotating parts,
(3) increasing the mass and specific heat of parts in immediate contact
with the friction surfaces, thereby providing increased heat storage
capacity during short periods of peak braking load.
The sources of energy to be absorbed are primarily three.
1. Kinetic energy of translation:
2. Kinetic energy of rotation:
3. Potential (gravitational) energy, as in an elevator being lowered or an
automobile descending a hill:
(Weight times vertical distance) (4)
The rate at which heat is generated on a unit area of friction interface is
equal to the product of the normal (clamping) pressure, coefficient of
friction, and rubbing velocity. Manufacturers of brakes and of brake
lining materials have conducted tests and accumulated experience
enabling them to arrive at empirical values of pV (normal pressure times
rubbing velocity) and of power per unit area of friction surface (as
horsepower per square inch or kilowatt per square millimeter) that are
appropriate for specific types of brake design, brake lining material, and
service conditions. Table (1) lists typical values of pV in industrial use.
Table(1) Typical Values of Pressure Times Rubbing Velocity Used
in Industrial Shoe Brakes
Short-Shoe Drum Brakes
Drum brakes are of two types:
(1) Those with external shoes that contract to bear against the outer
(cylindrical) drum surface
(2) Those with internal shoes that expand to contact the inner drum
Figure(2) shows a schematic representation of a simple external
drum brake with a “short shoe” that is, a shoe that contacts only a
small segment of the drum periphery. Force F at the end of the
lever applies the brake. Although the normal force (N) and the
friction force (fN) acting between the drum and shoe are
distributed continuously over the contacting surfaces.
Fig.(2) Short shoe drum brake
The short-shoe analysis assumes these forces to be concentrated at
the center of contact. The complete brake assembly is shown in
Figure (2-a). Free-body diagrams of the basic components are
given in Figures (2-b and c). Drum rotation is clockwise.
Taking moments about pivot A for the shoe and lever assembly, we
From summation of moments about O for the drum,
Solving equation (5) for N and substituting in equation (6) gives
(self energizing) (8)
Torque T is the inertial and load torque required for equilibrium, and it is
numerically equal to the friction torque developed by the brake.
Equation (8) is labeled “self-energizing” because the moment of the
friction force ( fNa) assists the applied force (F) in applying the brake.
For counter-clockwise drum rotation, the direction of the friction force
would be reversed. This would cause it to oppose the application of the
brake, making the brake self-de energizing. The derivation of the
equation for the de energizing brake is the same as for the self-energizing
brake, except that the signs of the friction force terms are reversed:
(self- de energizing) (9)
Returning now to self-energized braking (clockwise drum rotation), note
that the brake is self-locking if the denominator of Eq. (8) is zero or
negative. Thus, for self-locking,
For example, if f = 0.3, self-locking (for clockwise drum rotation) is
obtained if b 0.3a. This is illustrated in Figure (2-d). A self-locking
brake requires only that the shoe be brought in contact with the drum
(with F = 0) for the drum to be “locked” against rotation in one direction.
Because the brake in Figure (2)has only one shoe (block), the entire force
exerted on the drum by the shoe must be reacted by the shaft bearings.
Partly for this reason, two opposing shoes are almost always used.
The two-shoe external drum brake shown in Figure(3) has shoes 80 mm
wide that contact 90° of drum surface. For a coefficient of friction of 0.20
and an allowable contact pressure of 400 kN per square meter of
projected area, estimate:
(a) The maximum lever force F that can be used, (b) the resulting braking
(c) The radial load imposed on the shaft bearings.
Assume short-shoe drum brake.
Fig.(3) Two shoe drum brake
The free body diagram for all the components of the two shoe drum brake
can be shown in figures (3-b) to (3-f).
1- The force analysis begins with floating lever 5 because it receives
the applied force F.
Taking moments about O25 establishes
2- For the link 4 ,
but in opposite direction.
3- Link (3)
On the left shoe (link 3), the applied force is H43 (which is equal and
opposite to H34). The short-shoe analysis assumes that the normal and
friction forces applied by drum 6 act at the center of the shoe as shown.
The normal force is H63 and the friction force is H63 multiplied by the
given friction coefficient of 0.2.
Summation of moments about O13 gives:
Normal and friction forces H62 and V62 acting on shoe 2 are determined in
the same manner. The moment equation has an additional term because
both horizontal and vertical forces are applied by link 2:
Horizontal and vertical forces applied to drum 6 are equal and opposite to
corresponding forces applied to the shoes. If as assumed the drum angular
acceleration is zero, the load torque T (which tends to continue the
clockwise direction of rotation) is equal to (2.11F + 1.41F) times the
drum radius, or 0.880F N.m.
Forces applied at fixed pivot O16 are H16 = 3.46F and V16 = 0.70F.
The allowable value of F is governed by the allowable pressure on the
self-energized shoe. The projected area of the shoe is the 80