Physical Principle and Technologies Sample Clauses

Physical Principle and Technologies. The kinetic energy stored by a flywheel is given by the following relationship; Ec = Jω2 Where; J is the moment of inertia of the rotating mass ω is rotational speed of the body The inertial moment is function of the mass and the shape of the rotation part. The storable energy is limited by the maximum mechanical stress on the rotating body produced by the centrifugal force. This stress σ is proportional to the density ρ of the material and the square peripheral speed: The storable kinetic energy is given by the following relationship; Ek m A σ ρ Where, A is a dimensionless shape factor depending of the design of the rotating body. Table 34 shows some common designs of flywheels and their shape factor used to store energy. Flywheel type Schematic Shape factor A Constant stress disc 1 Modified constant stress disc 0,931 Conic 0,806 Undrilled plate disc 0,606 Thin coronal 0,5 Full wheel 0,4 Drilled plate disc 0,305 The energy storable in a flywheel is also a function of the material used (the density and the maxim stress). Table 35 gives the maximum theoretical specific energy of different materials with a shape factor of 1: Steel (AISI 4330) 1 800 7 800 32 Aluminium 400 2 700 21 Titanium 850 4 500 26 Glass composite 1 800 2 100 120 Carbon composite 2 400 1 500 220 The maximum specific energy shown in the table above, are purely theoretical because they consider only the flywheel, not all the system as a whole. Apart from the flywheel the electrical machine, vacuum pump, auxiliary control, surrounding wall, bearings, etc., needed to be considered in calculating the specific energy stored in a flywheel, as losses can occur in each component. Bearings are very important to the flywheel because the rotation speeds are very fast (up to 53,000 rpm for common systems) depending on the application. Rotation speed is limited by the stress sustainable by the flywheel material, but also by the type of bearings used. Aerodynamics effect is also important that is why a partial or nearly total vacuum is used in the flywheel chamber to reduce aerodynamic drag, slowing the flywheel and reducing the stored energy. Some materials, like composites, can sustain very high rotation speeds increasing the potential stored energy. To reduce the losses and to limit mechanical wear, special bearings are used. Ball bearings are the most common type of mechanical bearing and are used on slow rotation flywheels. They are simply to use, compact and not expansive, but friction losses are ...