Mechanical Energy Storage
There are two basic types of energy storage that result from the application of forces upon materials systems. One of these involves changes in potential energy, and the other involves changes in the motion of mass, and thus kinetic energy. This chapter f
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Mechanical Energy Storage
6.1
Introduction
There are two basic types of energy storage that result from the application of forces upon materials systems. One of these involves changes in potential energy, and the other involves changes in the motion of mass, and thus kinetic energy. This chapter focuses upon the major types of potential energy and kinetic energy storage. It will be seen that it is possible to translate between these two types of energy, as well as to convert these energies to heat or work.
6.2
Potential Energy Storage
Potential energy always involves the imposition of forces upon materials systems, and the energy stored is the integral of the force times the distance over which it operates. Thus ð Energy ¼ ðforceÞ ðdistanceÞ ð6:1Þ Consider the application of a tensile stress upon a solid rod, causing it to elongate. This is illustrated simply in Fig. 6.1. The stress σ is the force per unit cross-sectional area, and the resultant fractional change in length Δx/x0 is the strain ε. In metals the strain is proportional to the force, and this can be represented as a stress/strain diagram, as shown in Fig. 6.2. The proportionality constant is the Young’s modulus Y, and this linear relation is called “Hooke’s Law.”
© Springer International Publishing Switzerland 2016 R.A. Huggins, Energy Storage, DOI 10.1007/978-3-319-21239-5_6
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6 Mechanical Energy Storage
Fig. 6.1 Simple example of the elongation of a solid rod as the result of an applied tensile force upon its ends
Fig. 6.2 Schematic stress/strain diagram for an elastic metal
If this mechanical deformation is elastic, the work W that is done on the spring is the area under the stress/strain curve. This is obviously proportional to the magnitude of the applied stress. That is W¼
1 1 σε ¼ Yε2 2 2
ð6:2Þ
If this mechanical process is reversible without any losses, the work is equal to the amount of stored energy in this simple system.
6.3 Energy Storage in Pressurized Gas
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Fig. 6.3 Schematic stress/strain curve for rubber
In metals and ceramics Young’s modulus is a constant up to a critical value of the stress, called the yield point. This is because the interatomic forces in such materials are linear at small displacements. At higher values of stress, however, there can be plastic (nonreversible) deformation, and then, ultimately, fracture. In polymers and rubbers Young’s modulus can vary with the value of the strain, due to the action of different physical processes in their microstructures. An example of a stress/strain curve for a common rubber is shown schematically in Fig. 6.3. The deformation of a metallic spring in a mechanical clock, and the use of stretched rubber bands to power model airplanes are simple examples of this type of stored mechanical potential energy.
6.3
Energy Storage in Pressurized Gas
Everyone who has had to pump up a bicycle tire knows that that process requires work, and that the required force becomes greater as the pressure increases. If there is a leak, or the valve is opened, the gas stored i
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