The energy-storage capacity of a flywheel is determined from its polar moment ofinertia / and its maximum safe running speed. The necessary inertia depends on thecyclic torque variation and the allowable speed variation or, in the case of energystorageflywheels, the maximum energy requirements. The safe running speeddepends on the geometry and material properties of the flywheel.Flywheels store energy. Indeed, flywheels are used as energy reservoirs, and this usewill be discussed in Sec. 18.4. Their principal use in machine design, however, is tosmooth the variations in shaft speed that are caused by loads or power sources thatvaryirTa cyclic fashion. By using its stored kinetic energy 0.5/co2 to absorb the variationsin torque during a machine cycle, a flywheel smooths the fluctuating speed of amachine and reduces undesirable transient loads. The effect of a flywheel is thereforefundamentally different from that of a regulator: A flywheel limits the speedvariation over one cycle and has minimal effect on the average speed; a regulatoruses negative feedback to maintain a selected average speed with only secondaryeffects on the speed during a cycle.The flywheel has other features which have to be considered in design. Its size,speed, and windage effect can all be used to advantage in providing a secondaryfunction as part of a clutch, gear, belt pulley, cooling fan, pump, gyroscope, or torsionaldamper.
If the torque-angle curve for a machine cycle is available from experimental dataor a dynamic analysis, U is determined from the areas between the curve and theaverage-torque line. If the external torque input or load is not constant, it can becombined with the torque-angle curve for the machine. If the loading torque and thedriving torque are not synchronized or have an unknown phase difference, a worstcasecombination should be used. The areas under the curve can be determinedusing a planimeter or by graphic or numerical integration as shown in Chap. 4. (Seealso Example 4 or consult the user handbook for your programmable calculator orcomputer.) Unless C5 is accurately known and the curve is from a worst case or ishighly repeatable, precision in integrating is not warranted.
