Airbus A320 Brakes Dimensioning

Power

Friction wear coefficient

prof. P.C. Astori - 2 - A.A. 2013/2014

Airbus A320 Brake Dimensioning G. Montrofano, R. Rota

3. Problem characterization and method of solution

3.1 Kinetic energies comparison

In order to correctly dimension the braking block, it is important to consider the kinetic energy

involved in case of normal landing or in case of rejected take-off. In particular, the report will

consider the most critic between the two situations, which means choosing the one that needs the

greater amount of energy. In this way, the other one will result over-dimensioned.

In each case, the necessary kinetic energy is given by the usual equation:

where in case of landing and in case of rejected take-off and stands for

the respective velocity. However, the braking block is supposed to convert in heat by friction at

most the 80% of the entire kinetic energy, because the remaining is wasted due to the

aerodynamic resistance (considered that spoilers are not running). Finally the kinetic energy is

equally consumed by the braking wheels and each of them dissipates an amount of energy equal

to:

3.2 Mass, dimensions and numbers of disks

Each brake consumes the kinetic energy due to friction and converts it into heat. So, for each

braking wheel, the energetic balance is given by:

During such heat exchange, the volume of the braking blocks can be considered constant, as they

must not deform. This is why every block is composed of several disks: thanks to this solution the

temperature distribution is well-balanced and the block suffers a lower thermal stress. Obviously,

since steel, carbon and beryllium have different specific heat capacities, the quantity of material

depends on the material itself. By the end such differences will be considered implied.

Known the mass, the volume it fills can be found through the very definition of density:

The total thickness of the braking block matches the ratio between the volume and a single disk

area:

where and stand for the maximum and minimum radius of the brakes slots.

In the end, dividing the total thickness for the depth of every single disk, the result, at the most

rounded up, is the minimum number of disks required.

prof. P.C. Astori - 3 - A.A. 2013/2014

Airbus A320 Brake Dimensioning G. Montrofano, R. Rota

3.3 Load distribution on MLG and NLG

It is possible to define the load distribution on MLG and NLG and the horizontal acceleration

balancing forces and moments acting on the aircraft (see fig. 2):

The reaction force is considered insignificant and . Furthermore, because of

weight distribution, .

3.4 Braking torque

Similarly to what has been done in the previous point, the braking torque is determined by the

moments equilibrium on the wheels. The sum of the braking torque of each wheel is equal to the

total one.

where .

3.5 Maximum pressure among disks

An alternative formula that can be used to calculate the braking torque is:

Since is already known, the same equation is useful to find the maximum pressure among

the disks. In particular:

 is the total friction surface. The number between brackets

specifies how many sides of the disks are in contact with each other;

 is the distance between the wheel axis and the centroid of the friction surface;

 is the friction coefficient between disks.

3.6 Dissipated specific energy and power

The energy dissipated per unit area for each wheel is:

The power dissipated per unit area for each wheel is:

3.7 Brake linings' wear for each landing

After a landing, the volume of powdered brake lining depends on the friction wear coefficient:

Dividing the result for the friction area, it is possible to establish the thickness reduction of the

disks after each landing:

prof. P.C. Astori - 4 - A.A. 2013/2014

Airbus A320 Brake Dimensioning G. Montrofano, R. Rota

4. Problem data

4.1 Aircraft Data

Maximum take-off weight

Maximum landing weight

Maximum landing speed

Rejected take-off speed

Number of braking wheels

Height of center of gravity (from ground)

NLG-MLG pitch

Static weight distribution

Friction coefficient (with ground)

4.2 Brakes Data

Maximum disk temperature

Disk thickness

Rolling wheel diameter

Minimum brakes slot diameter

Maximum brakes slot diameter

Friction wear coefficient

Friction coefficient between disks

4.3 Steel Data

Density

Specific heat

4.4 Carbon Data

Density

Specific heat

4.5 Beryllium Data

Density

Specific heat

prof. P.C. Astori - 5 - A.A. 2013/2014

Airbus A320 Brake Dimensioning G. Montrofano, R. Rota

5. Calculus development

5.1 Unit of measure conversions

5.2 Kinetic energies comparison

5.3 Mass, dimension and numbers of disks

prof. P.C. Astori - 6 - A.A. 2013/2014

Airbus A320 Brake Dimensioning G. Montrofano, R. Rota

5.4 Load distribution on MLG and NLG

5.5 Braking torque

5.6 Maximum pressure among disks

5.7 Dissipated specific energy and power

5.8 Brake linings' wear for each landing

prof. P.C. Astori - 7 - A.A. 2013/2014