FLYWHEELS

Flywheels store kinetic energy (energy of motion) by mechanically confining motion of a mass to a circular trajectory. The functional elements of the flywheel are the mass storing the energy, the mechanism supporting the rotating assembly, and the means through which energy is deposited in the flywheel or retrieved from it.

Energy can be stored in rings, disks, or discrete weights, with spokes or hubs connecting the storage elements to shafts, and bearings supporting the assembly and allowing it to rotate. Energy may be transferred into or out of the wheel mechanically, hydraulically, aerodynamically, or electrically.

HISTORY

Ubiquitous in rotating machinery, flywheels have been used as a component of manufacturing equipment since their application in potters' wheels before 2000 b.c.e.

Flywheels attained broad use during the Industrial Revolution. In the embodiment of this era, flywheels used heavy rims built from cast iron to damp pulsations in engines, punches, shears, and presses. Often the pulsations to be damped arose from reciprocating motive forces or reciprocating end processes. The conversion of reciprocation into rotation enabled formatting of the flow of this energy. The most important types of formatting were transportation of energy by shafts, conversion of torque and speed by gears, and damping by flywheels.

Flywheels are found in internal-combustion engines, where they damp out torque pulses caused by the periodic firing of cylinders. In this application, energy is stored very briefly before it is used—for less than one revolution of the wheel itself.

The evolution of flywheel materials and components and a systemic approach to design have led to the development of stand-alone flywheel energy storage systems. In these systems the rotating element of the flywheel transfers energy to the application electrically and is not directly connected to the load through shafting. These systems typically store energy that is released over many revolutions of the wheel, and as a system may be used in place of electrochemical energy storage in many applications. By being separate and distinct from the process it supports, the stand-alone flywheel system may use materials and components optimally. Of the various flywheel types, stand-alone systems will typically have the highest energy and power density as well as the highest rim speed and rotation rate.

TECHNOLOGY

The kinetic energy stored in the flywheel rotor is proportional to the mass of the rotor and the square of its linear velocity. Transformed into a cylindrical system, the stored kinetic energy, KE, is where ω is the rate of rotation in radians per second and J is the moment of inertia about the axis of rotation in kilogram-meter². For the special case of a radially thin ring, the moment of inertia is equal to its mass, m, multiplied by the square of its radius, r. This radius is also known as the radius of gyration.

Stress in the rim is proportional to the square of linear velocity at the tip. When rotor speed is dictated

by material considerations, the linear velocity of the tip is set, and rotation rate becomes a dependent parameter inversely proportional to rotor diameter. For example, a rotor with a tip speed of 1,000 meters per second and a diameter of 0.3 meter would have a rotation rate of about 63,700 rpm. If the diameter were made 0.6 meters instead, for this material the rotation rate would be about 31,850 rpm.

To maximize stored energy, the designer seeks to spin the rotor at the highest speed allowed by the strength of the materials used. There is a trade-off between heavier, lower-strength materials and stronger, lighter materials. For a thin rim, the relationship between rim stress and specific energy or energy stored per unit mass of rim is given by where σ_h is the hoop stress experienced by the ring in newtons per square meter, and ρ is the density of the ring material in kilograms per meter³. Thus high specific energy corresponds directly to high specific strength: σsh/ρ and rotors made from carbon composite may be expected to store more energy per unit weight than metal rotors.

Since energy is proportional to the square of speed, high performance will be attained at high tip speed. Rims produced from carbon fiber have attained top speeds in excess of 1,400 meters per second and must be housed in an evacuated chamber to avoid severe aerodynamic heating.

The flywheel rim is connected to a shaft by spokes or a hub. The rotor experiences high centrifugal force and will tend to grow in size while the shaft will not. The spoke or hub assembly must span the gap between the shaft and the rim, allowing this differential growth while supporting the rim securely. Highspeed composite rims may change dimension by more than 1 percent in normal operation. This large strain or relative growth makes hub design especially challenging for composite flywheels.

Bearings support the shaft and allow the flywheel assembly to rotate freely in applications where the flywheel is a component in a more extensive rotating machine, the rim and hub are supported by the shafting of the machine, and no dedicated bearings are used. In stand-alone systems, flywheel rotors are typically supported with hydrodynamic or rolling element bearings, although magnetic bearings are sometimes used either to support part of the weight of the rotor or to levitate it entirely.

Compact, high-rim-speed, stand-alone flywheel systems may require that the bearings run continuously for years at many tens of thousands of revolutions per minute. Smaller rotors will operate at higher rotation rates.

Historically, flywheels have stored and discharged energy through direct mechanical connection to the load. The flywheel may be affixed to the load or may communicate with the load through gears, belts, or shafts. Stand-alone flywheel systems may convert electrical energy to kinetic energy through a motor, or convert kinetic energy to electricity through a generator. In these systems the flow of energy into and out of the flywheel may be regulated electronically using active inverters controlled by microprocessors or digital signal processors.

FUTURE ADVANCES

The flywheel has become an integral energy storage element in a broad range of applications. New designs and innovations in current designs and diverse opportunities for bettering flywheel performance continue to emerge.

The modern stand-alone flywheel embodies a number of sophisticated technologies, and advances in these technologies will yield further improvement to this class of flywheel. Flywheel progress will track development in power electronics, bearings, and composite materials. Power electronics such as active inverters and digital signal processors will continue to become power dense, reliable, and inexpensive. Rolling element and magnetic bearings will mature to a point where decades-long operating life is considered routine.

The energy stored in a flywheel depends on the strength of the rotor material. Carbon fiber tensile strength remains well below theoretical limits. Expected increases in strength along with reduction in cost as the use of this material expands will translate into more energy dense, less expensive rotors.

Progress, which is likely to be incremental, is certain to improve the performance and energy efficiency of all applications.

Donald A. Bender

See also: Bearings; Conservation of Energy; Heat and Heating; Kinetic Energy; Materials; Potential Energy; Storage; Storage Technology; Tribology.

BIBLIOGRAPHY

Genta, G. (1985). Kinetic Energy Storage. London:

Butterworths.

Post, R. F.; Fowler, T. K.; and Post, S. F. (1993). "A High-Efficiency Electromechanical Battery." Proceedings of the IEEE 81(3).

Post, R. F.; and Post, S. F. (1973). "Flywheels." Scientific American 229(Dec.):17.

U.S. Department of Energy. (1995). Flywheel Energy Storage Workshop. Springfield, VA: U.S. Department of Commerce.