and that rotates upon bearings in the arms does not start to wobble as the axle wears through the arms.) The scientific and engineering discipline that deals with the lubrication, friction, and wear of moving parts is tribology, an interdisciplinary field that encompasses materials science, mechanical engineering, chemistry, and mechanics. Failure As mentioned, wear is a concern for moving parts in a machine. Other concerns that lead to failure include corrosion, erosion, thermal stress and heat generation, vibration, fatigue loading, and cavitation. Fatigue is related to large inertial forces, and is affected by the type of motion that a moving part has. A moving part that has a uniform rotation motion is subject to less fatigue than a moving part that oscillates back and forth. Vibration leads to failure when the forcing frequency of the machine's operation hits a resonant frequency of one or more moving parts, such as rotating shafts. Designers avoid these problems by calculating the natural frequencies of the parts at design time, and altering the parts to limit or eliminate such resonance. Yet further factors that can lead to failure of moving parts include failures in the cooling and lubrication systems of a machine. One final, particular, factor related to failure of moving parts is kinetic energy. The sudden release of the kinetic energy of the moving parts of a machine causes overstress failures if a moving part is impeded in its motion by a foreign object. For example, consider a stone caught on the blades of a fan or propeller, or even the proverbial "spanner/monkey wrench in the works". (See foreign object damage for further discussion of this.) Kinetic energy of the moving parts of a machine The kinetic energy of a machine is the sum of the kinetic energies of its individual moving parts. A machine with moving parts can, mathematically, be treated as a connected system of bodies, whose kinetic energies are simply summed. The individual kinetic energies are determined from the kinetic energies of the moving parts' translations and rotations about their axes. The kinetic energy of rotation of the moving parts can be determined by noting that every such system of moving parts can be reduced to a collection of connected bodies rotating about an instantaneous axis, which form either a ring or a portion of an ideal ring, of radius rotating at revolutions per second. This ideal ring is known