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*Brakes - University of Brakes Caliper disk brakes are commonly used disk brakes. Bicycle brakes are*

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Brakes

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

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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:

(1)

H = time rate of heat dissipation (W or hp)

C = overall heat transfer coefficient (W per m 2 per °C, or hp per in

2 per

°F)

A = exposed heat-dissipating surface area (m 2 or in

2 )

ts = average temperature of heat-dissipating surfaces (°C or °F)

ta = air temperature in the vicinity of the heat-dissipating surfaces (°C or

°F)

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)

2. Kinetic energy of rotation:

(3)

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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

surface.

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

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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.

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Taking moments about pivot A for the shoe and lever assembly, we

have :

(5)

From summation of moments about O for the drum,

(6)

Solving equation (5) for N and substituting in equation (6) gives

(7)

(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,

(10)

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.

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Ex:

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

torque.

(c) The radial load imposed on the shaft bearings.

Assume short-shoe drum brake.

(a)

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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.

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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:

0.08)=0

Or

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:

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Or

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