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flywheel energy calculator 주제에 대한 자세한 내용은 여기를 참조하세요.
Flywheel Energy Storage Calculator
Enter your values: Units: Metric (grams, mm). English (ounces, inches). Mass: Diameter: RPM: Results: Disk: Kinetic Energy: Joules. Inertia:
Source: www.calculatoredge.com
Date Published: 1/13/2022
View: 7260
Flywheel energy storage calculator – Disaster Risk Reduction
Flywheel energy storage calculator – kinetic energy, inertia, centrifugal force, surface speed ; Units: · English (ounces, inches) ; Mass: ; Diameter ; RPM.
Source: drr.ikcest.org
Date Published: 12/16/2021
View: 3804
kinetic energy, inertia, centrifugal force, surface speed – GISLite
Flywheel energy storage calculator – kinetic energy, inertia, centrifugal force, surface speed. Category: Classic physics.
Source: www.gislite.com
Date Published: 2/9/2022
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Flywheel Energy Storage Calculator | Mechanical Engineering
Calculate Flywheel Energy Storage for free. flywheel, energy, storage, mechanical, engineering, Calculators.
Source: calculatorsedge.com
Date Published: 7/18/2022
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Flywheel Energy Calculator
Enter the flywheel moment of inertia (kg-m^2) and the angular velocity (rad/s) into the calculator to determine the Flywheel Energy.
Source: calculator.academy
Date Published: 9/20/2022
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Flywheels – Kinetic Energy – The Engineering ToolBox
Angular Velocity – Convert Units · 1 rad = 360o / 2 π =~ 57.29578 · 1 rad/s = 9.55 rev/min (rpm) = 0.159 rev/s (rps) …
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주제에 대한 기사 평가 flywheel energy calculator
- Author: H95Tv
- Views: 조회수 966,980회
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- Date Published: 2017. 10. 22.
- Video Url link: https://www.youtube.com/watch?v=PnuWS4enJI0
How much energy can a flywheel hold?
The energy efficiency (ratio of energy out per energy in) of flywheels, also known as round-trip efficiency, can be as high as 90%. Typical capacities range from 3 kWh to 133 kWh. Rapid charging of a system occurs in less than 15 minutes.
How do you calculate flywheel energy?
Kinetic Energy goes as 1/2*I*w2. For flywheels I =1/2MR2. If we measure w in revolutions per second then the stored energy of a flywheel is approximately 6MR2 x w2 (RPS) For M=140 kg and R=50cm this yields a required w of 500 RPS or 30,000 RPM.
How much energy does a flywheel produce?
The spinning speed of modern flywheel energy storage system can reach up to 16,000 rpm with a capacity of up to 25 kWh. Flywheel have low maintenance costs, and their life-span can be long. There is no greenhouse emission or toxic material produced when flywheels are working, so it is very environment-friendly.
What is flywheel formula?
Moment of inertia of a flywheel is calculated using the given formula; I = N m N + n ( 2 g h ω 2 − r 2 )
Can a flywheel power a house?
The flywheel has a diameter of one metre and weighs three tonnes, and can be placed in the garden of a private house. The system capacity should be increased, initially, to 20 kWh, and then 50 kWh, to eventually reach 24 hours of storage.
How long can a flywheel battery spin?
The flywheels absorb grid energy and can steadily discharge 1-megawatt of electricity for 15 minutes.
How do I know what size flywheel I need?
1) COUNT THE NUMBER OF DRILLED AND TAPPED HOLES ON YOUR FLYWHEEL. 2) MEASURE THE DISTANCE FROM THE CENTER OF ONE DRILLED AND TAPPED HOLE TO ANOTHER (MEASURING ACROSS THE CENTER LINE OF THE CRANK SHAFT) [DIMENSION “C”].
How is flywheel rpm calculated?
Then to get the ticks per milisecond you take the last IME reading, minus the first IME reading, then divide by the time. You then times by 7 to get the flywheel ticks p/s and finally times by 60 and divide by a motors full rotation (260 – 360) to get the RPM.
How is flywheel HP calculated?
The equation to calculate horsepower is simple: Horsepower = Torque x RPM / 5,252.
Are flywheels efficient?
Flywheel storage systems
The stored energy is the sum of the kinetic energy of the individual mass elements make up the flywheel. In order to optimize the energy-to-mass ratio, a flywheel needs to spin at its maximum possible speed (Freris, 1990). The energy efficiency of such systems is about 80%.
What is kinetic energy of flywheel?
The kinetic energy stored in flywheels – the moment of inertia. A flywheel can be used to smooth energy fluctuations and make the energy flow intermittent operating machine more uniform. Flywheels are used in most combustion piston engines. Energy is stored mechanically in a flywheel as kinetic energy.
How is energy stored in a spinning flywheel?
Flywheel energy storage systems (FESS) employ kinetic energy stored in a rotating mass with very low frictional losses. Electric energy input accelerates the mass to speed via an integrated motor-generator. The energy is discharged by drawing down the kinetic energy using the same motor-generator.
How is flywheel torque calculated?
- Where Tfw is the Flywheel Torque (N-m)
- m is the flywheel mass (kg)
- r is the radius (m)
- a is the angular acceleration (rad/s^2)
How do you calculate rotating flywheel torque?
In this experiment a flywheel is so mounted that torques can be applied to it by hanging a mass M from the free end of a string, the remainder of which is wrapped around the axle. The torque due to the weight is τ = Tr where T is the tension in the string and r the radius of the axle.
What are the 4 functions of flywheel?
- #1. Engine Balance.
- #2. Engine Start.
- #3. Drivetrain Stress Reduction.
- #4. Engine Speed Soothing.
- #5. Weight Manipulation.
How fast can a flywheel spin?
Flywheels are typically made of steel and rotate on conventional bearings; these are generally limited to a maximum revolution rate of a few thousand RPM. High energy density flywheels can be made of carbon fiber composites and employ magnetic bearings, enabling them to revolve at speeds up to 60,000 RPM (1 kHz).
How do I know what size flywheel I need?
1) COUNT THE NUMBER OF DRILLED AND TAPPED HOLES ON YOUR FLYWHEEL. 2) MEASURE THE DISTANCE FROM THE CENTER OF ONE DRILLED AND TAPPED HOLE TO ANOTHER (MEASURING ACROSS THE CENTER LINE OF THE CRANK SHAFT) [DIMENSION “C”].
What happens to the flywheel as energy is used from it?
When energy is required, the motor functions as a generator, because the flywheel transfers rotational energy to it. This is converted back into electrical energy, thus completing the cycle. As the flywheel spins faster, it experiences greater force and thus stores more energy.
Does a flywheel always spin?
So, you might think the flywheel spins all the time. That’s not true. The flywheel does not spin when in neutral. This is because the input shaft that connects to the clutch plate; then to the pressure plate which connects to the flywheel is designed to spin freely when the vehicle is in neutral.
Kinetic Energy, Inertia, Centrifugal Force, Surface Speed
Flywheel Energy Storage Calculator Enter value and click on calculate. Result will be displayed.
Enter your values: Units: Metric (grams, mm) English (ounces, inches) Mass: Diameter: RPM: Results: Disk: Kinetic Energy: Joules Inertia: Kg mA2 Ring: Kinetic Energy: Joules Inertia: Kg mA2 Centrifugal Force: Newtons kgs Surface Speed: M/Sec
Flywheel energy storage
Flywheel energy storage (FES) works by accelerating a rotor (flywheel) to a very high speed and maintaining the energy in the system as rotational energy. When energy is extracted from the system, the flywheel’s rotational speed is reduced as a consequence of the principle of conservation of energy; adding energy to the system correspondingly results in an increase in the speed of the flywheel.
Most FES systems use electricity to accelerate and decelerate the flywheel, but devices that directly use mechanical energy are being developed.[1]
Advanced FES systems have rotors made of high strength carbon-fiber composites, suspended by magnetic bearings, and spinning at speeds from 20,000 to over 50,000 rpm in a vacuum enclosure.[2] Such flywheels can come up to speed in a matter of minutes – reaching their energy capacity much more quickly than some other forms of storage.[2]
Main components [ edit ]
The main components of a typical flywheel
A typical system consists of a flywheel supported by rolling-element bearing connected to a motor–generator. The flywheel and sometimes motor–generator may be enclosed in a vacuum chamber to reduce friction and energy loss.
First-generation flywheel energy-storage systems use a large steel flywheel rotating on mechanical bearings. Newer systems use carbon-fiber composite rotors that have a higher tensile strength than steel and can store much more energy for the same mass.[3]
To reduce friction, magnetic bearings are sometimes used instead of mechanical bearings.
Possible future use of superconducting bearings [ edit ]
The expense of refrigeration led to the early dismissal of low-temperature superconductors for use in magnetic bearings. However, high-temperature superconductor (HTSC) bearings may be economical and could possibly extend the time energy could be stored economically.[4] Hybrid bearing systems are most likely to see use first. High-temperature superconductor bearings have historically had problems providing the lifting forces necessary for the larger designs but can easily provide a stabilizing force. Therefore, in hybrid bearings, permanent magnets support the load and high-temperature superconductors are used to stabilize it. The reason superconductors can work well stabilizing the load is because they are perfect diamagnets. If the rotor tries to drift off-center, a restoring force due to flux pinning restores it. This is known as the magnetic stiffness of the bearing. Rotational axis vibration can occur due to low stiffness and damping, which are inherent problems of superconducting magnets, preventing the use of completely superconducting magnetic bearings for flywheel applications.
Since flux pinning is an important factor for providing the stabilizing and lifting force, the HTSC can be made much more easily for FES than for other uses. HTSC powders can be formed into arbitrary shapes so long as flux pinning is strong. An ongoing challenge that has to be overcome before superconductors can provide the full lifting force for an FES system is finding a way to suppress the decrease of levitation force and the gradual fall of rotor during operation caused by the flux creep of the superconducting material.
Physical characteristics [ edit ]
General [ edit ]
Compared with other ways to store electricity, FES systems have long lifetimes (lasting decades with little or no maintenance;[2] full-cycle lifetimes quoted for flywheels range from in excess of 105, up to 107, cycles of use),[5] high specific energy (100–130 W·h/kg, or 360–500 kJ/kg),[5][6] and large maximum power output. The energy efficiency (ratio of energy out per energy in) of flywheels, also known as round-trip efficiency, can be as high as 90%. Typical capacities range from 3 kWh to 133 kWh.[2] Rapid charging of a system occurs in less than 15 minutes.[7] The high specific energies often cited with flywheels can be a little misleading as commercial systems built have much lower specific energy, for example 11 W·h/kg, or 40 kJ/kg.[8]
Form of energy storage [ edit ]
Moment of inertia: J m = ∫ m r 2 d m {\displaystyle J_{m}=\int _{m}r^{2}\,\mathrm {d} m} Angular velocity: ω m = 2 π ⋅ n m {\displaystyle \omega _{m}=2\pi \cdot n_{m}} Stored rotational energy: W kin = 1 2 J m ω 2 {\displaystyle W_{\text{kin}}={\frac {1}{2}}J_{m}\omega ^{2}}
Here m {\displaystyle m} is the integral of the flywheel’s mass, and n m {\displaystyle n_{m}} is the rotational speed (number of revolutions per second).
Specific energy [ edit ]
The maximal specific energy of a flywheel rotor is mainly dependent on two factors: the first being the rotor’s geometry, and the second being the properties of the material being used. For single-material, isotropic rotors this relationship can be expressed as[9]
E m = K ( σ ρ ) , {\displaystyle {\frac {E}{m}}=K\left({\frac {\sigma }{\rho }}\right),}
where
E {\displaystyle E} m {\displaystyle m} K {\displaystyle K} σ {\displaystyle \sigma } ρ {\displaystyle \rho } 3].
Geometry (shape factor) [ edit ]
The highest possible value for the shape factor[10] of a flywheel rotor, is K = 1 {\displaystyle K=1} , which can be achieved only by the theoretical constant-stress disc geometry.[11] A constant-thickness disc geometry has a shape factor of K = 0.606 {\displaystyle K=0.606} , while for a rod of constant thickness the value is K = 0.333 {\displaystyle K=0.333} . A thin cylinder has a shape factor of K = 0.5 {\displaystyle K=0.5} . For most flywheels with a shaft, the shape factor is below or about K = 0.333 {\textstyle K=0.333} . A shaft-less design[12] has a shape factor similar to a constant-thickness disc ( K = 0.6 {\textstyle K=0.6} ), which enables a doubled energy density.
Material properties [ edit ]
For energy storage, materials with high strength and low density are desirable. For this reason, composite materials are frequently used in advanced flywheels. The strength-to-density ratio of a material can be expressed in Wh/kg (or Nm/kg); values greater than 400 Wh/kg can be achieved by certain composite materials.
Rotor materials [ edit ]
Several modern flywheel rotors are made from composite materials. Examples include the carbon-fiber composite flywheel from Beacon Power Corporation[13] and the PowerThru flywheel from Phillips Service Industries.[14] Alternatively, Calnetix utilizes aerospace-grade high-performance steel in their flywheel construction.[15]
For these rotors, the relationship between material properties, geometry and energy density can be expressed by using a weighed-average approach.[16]
Tensile strength and failure modes [ edit ]
One of the primary limits to flywheel design is the tensile strength of the rotor. Generally speaking, the stronger the disc, the faster it may be spun, and the more energy the system can store. (Making the flywheel heavier without a corresponding increase in strength will slow the maximum speed the flywheel can spin without rupturing, hence will not increase the total amount of energy the flywheel can store.)
When the tensile strength of a composite flywheel’s outer binding cover is exceeded, the binding cover will fracture, and the wheel will shatter as the outer wheel compression is lost around the entire circumference, releasing all of its stored energy at once; this is commonly referred to as “flywheel explosion” since wheel fragments can reach kinetic energy comparable to that of a bullet. Composite materials that are wound and glued in layers tend to disintegrate quickly, first into small-diameter filaments that entangle and slow each other, and then into red-hot powder; a cast metal flywheel throws off large chunks of high-speed shrapnel.
For a cast metal flywheel, the failure limit is the binding strength of the grain boundaries of the polycrystalline molded metal. Aluminum in particular suffers from fatigue and can develop microfractures from repeated low-energy stretching. Angular forces may cause portions of a metal flywheel to bend outward and begin dragging on the outer containment vessel, or to separate completely and bounce randomly around the interior. The rest of the flywheel is now severely unbalanced, which may lead to rapid bearing failure from vibration, and sudden shock fracturing of large segments of the flywheel.
Traditional flywheel systems require strong containment vessels as a safety precaution, which increases the total mass of the device. The energy release from failure can be dampened with a gelatinous or encapsulated liquid inner housing lining, which will boil and absorb the energy of destruction. Still, many customers of large-scale flywheel energy-storage systems prefer to have them embedded in the ground to halt any material that might escape the containment vessel.
Energy storage efficiency [ edit ]
Flywheel energy storage systems using mechanical bearings can lose 20% to 50% of their energy in two hours.[17] Much of the friction responsible for this energy loss results from the flywheel changing orientation due to the rotation of the earth (an effect similar to that shown by a Foucault pendulum). This change in orientation is resisted by the gyroscopic forces exerted by the flywheel’s angular momentum, thus exerting a force against the mechanical bearings. This force increases friction. This can be avoided by aligning the flywheel’s axis of rotation parallel to that of the earth’s axis of rotation.[citation needed]
Conversely, flywheels with magnetic bearings and high vacuum can maintain 97% mechanical efficiency, and 85% round trip efficiency.[18]
Effects of angular momentum in vehicles [ edit ]
When used in vehicles, flywheels also act as gyroscopes, since their angular momentum is typically of a similar order of magnitude as the forces acting on the moving vehicle. This property may be detrimental to the vehicle’s handling characteristics while turning or driving on rough ground; driving onto the side of a sloped embankment may cause wheels to partially lift off the ground as the flywheel opposes sideways tilting forces. On the other hand, this property could be utilized to keep the car balanced so as to keep it from rolling over during sharp turns.[19]
When a flywheel is used entirely for its effects on the attitude of a vehicle, rather than for energy storage, it is called a reaction wheel or a control moment gyroscope.
The resistance of angular tilting can be almost completely removed by mounting the flywheel within an appropriately applied set of gimbals, allowing the flywheel to retain its original orientation without affecting the vehicle (see Properties of a gyroscope). This doesn’t avoid the complication of gimbal lock, and so a compromise between the number of gimbals and the angular freedom is needed.
The center axle of the flywheel acts as a single gimbal, and if aligned vertically, allows for the 360 degrees of yaw in a horizontal plane. However, for instance driving up-hill requires a second pitch gimbal, and driving on the side of a sloped embankment requires a third roll gimbal.
Full-motion gimbals [ edit ]
Although the flywheel itself may be of a flat ring shape, a free-movement gimbal mounting inside a vehicle requires a spherical volume for the flywheel to freely rotate within. Left to its own, a spinning flywheel in a vehicle would slowly precess following the Earth’s rotation, and precess further yet in vehicles that travel long distances over the Earth’s curved spherical surface.
A full-motion gimbal has additional problems of how to communicate power into and out of the flywheel, since the flywheel could potentially flip completely over once a day, precessing as the Earth rotates. Full free rotation would require slip rings around each gimbal axis for power conductors, further adding to the design complexity.
Limited-motion gimbals [ edit ]
To reduce space usage, the gimbal system may be of a limited-movement design, using shock absorbers to cushion sudden rapid motions within a certain number of degrees of out-of-plane angular rotation, and then gradually forcing the flywheel to adopt the vehicle’s current orientation. This reduces the gimbal movement space around a ring-shaped flywheel from a full sphere, to a short thickened cylinder, encompassing for example ± 30 degrees of pitch and ± 30 degrees of roll in all directions around the flywheel.
Counterbalancing of angular momentum [ edit ]
An alternative solution to the problem is to have two joined flywheels spinning synchronously in opposite directions. They would have a total angular momentum of zero and no gyroscopic effect. A problem with this solution is that when the difference between the momentum of each flywheel is anything other than zero the housing of the two flywheels would exhibit torque. Both wheels must be maintained at the same speed to keep the angular velocity at zero. Strictly speaking, the two flywheels would exert a huge torqueing moment at the central point, trying to bend the axle. However, if the axle were sufficiently strong, no gyroscopic forces would have a net effect on the sealed container, so no torque would be noticed.
To further balance the forces and spread out strain, a single large flywheel can be balanced by two half-size flywheels on each side, or the flywheels can be reduced in size to be a series of alternating layers spinning in opposite directions. However this increases housing and bearing complexity.
Applications [ edit ]
Transportation [ edit ]
Automotive [ edit ]
In the 1950s, flywheel-powered buses, known as gyrobuses, were used in Yverdon (Switzerland) and Ghent (Belgium) and there is ongoing research to make flywheel systems that are smaller, lighter, cheaper and have a greater capacity. It is hoped that flywheel systems can replace conventional chemical batteries for mobile applications, such as for electric vehicles. Proposed flywheel systems would eliminate many of the disadvantages of existing battery power systems, such as low capacity, long charge times, heavy weight and short usable lifetimes. Flywheels may have been used in the experimental Chrysler Patriot, though that has been disputed.[20]
Flywheels have also been proposed for use in continuously variable transmissions. Punch Powertrain is currently working on such a device.[21]
During the 1990s, Rosen Motors developed a gas turbine powered series hybrid automotive powertrain using a 55,000 rpm flywheel to provide bursts of acceleration which the small gas turbine engine could not provide. The flywheel also stored energy through regenerative braking. The flywheel was composed of a titanium hub with a carbon fiber cylinder and was gimbal-mounted to minimize adverse gyroscopic effects on vehicle handling. The prototype vehicle was successfully road tested in 1997 but was never mass-produced.[22]
In 2013, Volvo announced a flywheel system fitted to the rear axle of its S60 sedan. Braking action spins the flywheel at up to 60,000 rpm and stops the front-mounted engine. Flywheel energy is applied via a special transmission to partially or completely power the vehicle. The 20-centimetre (7.9 in), 6-kilogram (13 lb) carbon fiber flywheel spins in a vacuum to eliminate friction. When partnered with a four-cylinder engine, it offers up to a 25 percent reduction in fuel consumption versus a comparably performing turbo six-cylinder, providing an 80 horsepower (60 kW) boost and allowing it to reach 100 kilometres per hour (62 mph) in 5.5 seconds. The company did not announce specific plans to include the technology in its product line.[23]
In July 2014 GKN acquired Williams Hybrid Power (WHP) division and intends to supply 500 carbon fiber Gyrodrive electric flywheel systems to urban bus operators over the next two years[24] As the former developer name implies, these were originally designed for Formula one motor racing applications. In September 2014, Oxford Bus Company announced that it is introducing 14 Gyrodrive hybrid buses by Alexander Dennis on its Brookes Bus operation.[25][26]
Rail vehicles [ edit ]
Flywheel systems have been used experimentally in small electric locomotives for shunting or switching, e.g. the Sentinel-Oerlikon Gyro Locomotive. Larger electric locomotives, e.g. British Rail Class 70, have sometimes been fitted with flywheel boosters to carry them over gaps in the third rail. Advanced flywheels, such as the 133 kWh pack of the University of Texas at Austin, can take a train from a standing start up to cruising speed.[2]
The Parry People Mover is a railcar which is powered by a flywheel. It was trialled on Sundays for 12 months on the Stourbridge Town Branch Line in the West Midlands, England during 2006 and 2007 and was intended to be introduced as a full service by the train operator London Midland in December 2008 once two units had been ordered. In January 2010, both units are in operation.[27]
Rail electrification [ edit ]
FES can be used at the lineside of electrified railways to help regulate the line voltage thus improving the acceleration of unmodified electric trains and the amount of energy recovered back to the line during regenerative braking, thus lowering energy bills.[28] Trials have taken place in London, New York, Lyon and Tokyo,[29] and New York MTA’s Long Island Rail Road is now investing $5.2m in a pilot project on LIRR’s West Hempstead Branch line.[30] These trials and systems store kinetic energy in rotors consisting of a carbon-glass composite cylinder packed with neodymium-iron-boron powder that forms a permanent magnet. These spin at up to 37800rev/min, and each 100 kW unit can store 11 megajoules (3.1 kWh) of re-usable energy, approximately enough to accelerate a weight of 200 metric tons from zero to 38 km/h.[29]
Uninterruptible power supplies [ edit ]
Flywheel power storage systems in production as of 2001 have storage capacities comparable to batteries and faster discharge rates. They are mainly used to provide load leveling for large battery systems, such as an uninterruptible power supply for data centers as they save a considerable amount of space compared to battery systems.[31]
Flywheel maintenance in general runs about one-half the cost of traditional battery UPS systems. The only maintenance is a basic annual preventive maintenance routine and replacing the bearings every five to ten years, which takes about four hours.[7] Newer flywheel systems completely levitate the spinning mass using maintenance-free magnetic bearings, thus eliminating mechanical bearing maintenance and failures.[7]
Costs of a fully installed flywheel UPS (including power conditioning) are (in 2009) about $330 per kilowatt (for 15 seconds full-load capacity).[32]
Test laboratories [ edit ]
A long-standing niche market for flywheel power systems are facilities where circuit breakers and similar devices are tested: even a small household circuit breaker may be rated to interrupt a current of 10000 or more amperes, and larger units may have interrupting ratings of 100000 or 1000000 amperes. The enormous transient loads produced by deliberately forcing such devices to demonstrate their ability to interrupt simulated short circuits would have unacceptable effects on the local grid if these tests were done directly from building power. Typically such a laboratory will have several large motor–generator sets, which can be spun up to speed over several minutes; then the motor is disconnected before a circuit breaker is tested.
Physics laboratories [ edit ]
Tokamak fusion experiments need very high currents for brief intervals (mainly to power large electromagnets for a few seconds).
Also the non-tokamak: Nimrod synchrotron at the Rutherford Appleton Laboratory had two 30 ton flywheels.
Aircraft launching systems [ edit ]
The Gerald R. Ford-class aircraft carrier will use flywheels to accumulate energy from the ship’s power supply, for rapid release into the electromagnetic aircraft launch system. The shipboard power system cannot on its own supply the high power transients necessary to launch aircraft. Each of four rotors will store 121 MJ (34 kWh) at 6400 rpm. They can store 122 MJ (34 kWh) in 45 secs and release it in 2–3 seconds.[35] The flywheel energy densities are 28 kJ/kg (8 W·h/kg); including the stators and cases this comes down to 18.1 kJ/kg (5 W·h/kg), excluding the torque frame.[35]
NASA G2 flywheel for spacecraft energy storage [ edit ]
This was a design funded by NASA’s Glenn Research Center and intended for component testing in a laboratory environment. It used a carbon fiber rim with a titanium hub designed to spin at 60,000 rpm, mounted on magnetic bearings. Weight was limited to 250 pounds. Storage was 525 W-hr (1.89 MJ) and could be charged or discharged at 1 kW meaning a Specific Energy of 5.31 W-hr/kg and Power Density of 10.11 W/kg.[36] The working model shown in the photograph at the top of the page ran at 41,000 rpm on September 2, 2004.[37]
Amusement rides [ edit ]
The Montezooma’s Revenge roller coaster at Knott’s Berry Farm was the first flywheel-launched roller coaster in the world and is the last ride of its kind still operating in the United States. The ride uses a 7.6 tonnes flywheel to accelerate the train to 55 miles per hour (89 km/h) in 4.5 seconds.
The Incredible Hulk roller coaster at Universal’s Islands of Adventure features a rapidly accelerating uphill launch as opposed to the typical gravity drop. This is achieved through powerful traction motors that throw the car up the track. To achieve the brief very high current required to accelerate a full coaster train to full speed uphill, the park utilizes several motor-generator sets with large flywheels. Without these stored energy units, the park would have to invest in a new substation or risk browning-out the local energy grid every time the ride launches.
Pulse power [ edit ]
Flywheel Energy Storage Systems (FESS) are found in a variety of applications ranging from grid-connected energy management to uninterruptible power supplies. With the progress of technology, there is fast renovation involved in FESS application. Examples include high power weapons, aircraft powertrains and shipboard power systems, where the system requires a very high-power for a short period in order of a few seconds and even milliseconds. Compensated pulsed alternator (compulsator) is one of the most popular choices of pulsed power supplies for fusion reactors, high-power pulsed lasers, and hypervelocity electromagnetic launchers because of its high energy density and power density, which is generally designed for the FESS.[38] Compulsators (low-inductance alternators) act like capacitors, they can be spun up to provide pulsed power for railguns and lasers. Instead of having a separate flywheel and generator, only the large rotor of the alternator stores energy. See also Homopolar generator.[39]
Motor sports [ edit ]
A Flybrid Systems Kinetic Energy Recovery System built for use in Formula One
Using a continuously variable transmission (CVT), energy is recovered from the drive train during braking and stored in a flywheel. This stored energy is then used during acceleration by altering the ratio of the CVT.[40] In motor sports applications this energy is used to improve acceleration rather than reduce carbon dioxide emissions – although the same technology can be applied to road cars to improve fuel efficiency.[41]
Automobile Club de l’Ouest, the organizer behind the annual 24 Hours of Le Mans event and the Le Mans Series, is currently “studying specific rules for LMP1 which will be equipped with a kinetic energy recovery system.”[42]
Williams Hybrid Power, a subsidiary of Williams F1 Racing team,[43] have supplied Porsche and Audi with flywheel based hybrid system for Porsche’s 911 GT3 R Hybrid[44] and Audi’s R18 e-Tron Quattro.[45] Audi’s victory in 2012 24 Hours of Le Mans is the first for a hybrid (diesel-electric) vehicle.[46]
Grid energy storage [ edit ]
Flywheels are sometimes used as short term spinning reserve for momentary grid frequency regulation and balancing sudden changes between supply and consumption. No carbon emissions, faster response times and ability to buy power at off-peak hours are among the advantages of using flywheels instead of traditional sources of energy like natural gas turbines.[47] Operation is very similar to batteries in the same application, their differences are primarily economic.
Beacon Power opened a 5 MWh (20 MW over 15 mins)[18] flywheel energy storage plant in Stephentown, New York in 2011[48] using 200 flywheels[49] and a similar 20 MW system at Hazle Township, Pennsylvania in 2014.[50]
A 0.5MWh (2 MW for 15 min)[51] flywheel storage facility in Minto, Ontario, Canada opened in 2014.[52] The flywheel system (developed by NRStor) uses 10 spinning steel flywheels on magnetic bearings.[52]
Amber Kinetics, Inc. has an agreement with Pacific Gas and Electric (PG&E) for a 20 MW / 80 MWh flywheel energy storage facility located in Fresno, CA with a four-hour discharge duration.[53]
Wind turbines [ edit ]
Flywheels may be used to store energy generated by wind turbines during off-peak periods or during high wind speeds.
In 2010, Beacon Power began testing of their Smart Energy 25 (Gen 4) flywheel energy storage system at a wind farm in Tehachapi, California. The system was part of a wind power/flywheel demonstration project being carried out for the California Energy Commission.[54]
Toys [ edit ]
Friction motors used to power many toy cars, trucks, trains, action toys and such, are simple flywheel motors.
Toggle action presses [ edit ]
In industry, toggle action presses are still popular. The usual arrangement involves a very strong crankshaft and a heavy duty connecting rod which drives the press. Large and heavy flywheels are driven by electric motors but the flywheels turn the crankshaft only when clutches are activated.
Comparison to electric batteries [ edit ]
Flywheels are not as adversely affected by temperature changes, can operate at a much wider temperature range, and are not subject to many of the common failures of chemical rechargeable batteries.[55] They are also less potentially damaging to the environment, being largely made of inert or benign materials. Another advantage of flywheels is that by a simple measurement of the rotation speed it is possible to know the exact amount of energy stored.
Unlike most batteries which operate only for a finite period (for example roughly 36 months in the case of lithium ion polymer batteries), a flywheel potentially has an indefinite working lifespan. Flywheels built as part of James Watt steam engines have been continuously working for more than two hundred years.[56] Working examples of ancient flywheels used mainly in milling and pottery can be found in many locations in Africa, Asia, and Europe.[57][58]
Most modern flywheels are typically sealed devices that need minimal maintenance throughout their service lives. Magnetic bearing flywheels in vacuum enclosures, such as the NASA model depicted above, do not need any bearing maintenance and are therefore superior to batteries both in terms of total lifetime and energy storage capacity.[citation needed] Flywheel systems with mechanical bearings will have limited lifespans due to wear.
High performance flywheels can explode, killing bystanders with high speed shrapnel. While batteries can catch fire and release toxins, there is generally time for bystanders to flee and escape injury.
The physical arrangement of batteries can be designed to match a wide variety of configurations, whereas a flywheel at a minimum must occupy a certain area and volume, because the energy it stores is proportional to its angular mass and to the square of its rotational speed. As a flywheel gets smaller, its mass also decreases, so the speed must increase, and so the stress on the materials increases. Where dimensions are a constraint, (e.g. under the chassis of a train), a flywheel may not be a viable solution.[citation needed]
See also [ edit ]
References [ edit ]
FLYWHEELS and ENERGY STORAGE
To optimize the energy-to-mass ratio the flywheel needs to spin at the maximum possible speed. This is because kinetic energy only increases linerarly with Mass but goes as the square of the rotation speed.
Rapidly rotating objects are subject to centrifugal forces that can rip them apart. Centrifugal force for a rotating object goes as:
M*w*w*R
Thus, while dense material can store more energy it is also subject to higher centrifugal force and thus fails at lower rotation speeds than low density material.
Tensile Strength is More important than density of material.
Long rundown times are also required –> frictionless bearings and a vacuum to minimize air resistance can result in rundown times of 6 months –> steady supply of energy
Flywheels are about 80% efficient (like hydro)
Flywheels do take up much less land than pumped hydro systems
Some Network Resources Related to Flywheels
Consider a solid disc flywheel of radius 50 cm and mass 140 kg. How fast would it have to spin to have a store the equivalent amount of energy that is stored in just 10 kg of gasoline when burned in an internal combustion engine:
10 kg of gasoline = 140 KWH
Engine has 15% efficiency –> 21 KWH of useable energy
Flywheel has a conversion efficiency of 80%
Flywheel must therefore store 21/.8 = 26.25 KWH
Kinetic Energy goes as 1/2*I*w 2 . For flywheels I =1/2MR 2 .
. For flywheels I =1/2MR . If we measure w in revolutions per second then the stored energy of a flywheel is approximately 6MR 2 x w 2 (RPS)
x w (RPS) For M=140 kg and R=50cm this yields a required w of 500 RPS or 30,000 RPM
The required energy storage is 26 KWH/140 Kg = .18 KWH/kg which excees the energy storage density of steel – hence such a flywheel requires construction out of carbon fiber.
Compressed Air:
Has high energy storage capacity compared to the alternatives. About 10 times higher per cubic meter than water.
One example (in Germany) to date:
Storage reservoir is underground cavity in a natural salt deposit
The storage volume is 300,000 cubic meters
Sheer weight of the salt deposit is able to pressure confine the air reservoir
Air is compressed to 70 atm (1000 lbs per square inch)
Compression is done by electrically driven air compressors
System delivers 300 Megawatts for 2 hours by using the compressed air to drive a turbine
Difficult to measure the efficiency of this system. Two major contribution to the inefficiency: Energy required to cool the air as it is being put into storage –> this is a critical requirement (see below) Energy required (usually from fuel) to expand the cool air taken from storage as it entires the turbine.
Desireable design feature would be recycle the waste heat from the compression stage and use it to reheat the air during expansion stage
For gases, Pressure is directly related to Temperature (Ideal Gas Law)
If the temperature of the air at 1 atm is 20 C, how much will the temperature raise if we increase the pressure to 100 atm.
For air, increase in T goes approximately as increase in P to the 1/4 power when T is measured in Kelvins
100**1/4 is about 3.5, so the temperature of the air increases by a factor (20 +273) = 293 * 3.5. This is about 1100 K or 830 C –> which would melt the salt reservoir!
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Moment Of Inertia Of Flywheel
Moment Of Inertia Of Flywheel
Moment of inertia of a flywheel is calculated using the given formula;
\(\begin{array}{l}I = \frac{Nm}{N+n}(\frac{2gh}{\omega ^{2}}-r^{2})\end{array} \)
Where I = moment of inertia of the flywheel.Here, the symbols denote;
m = rings’ mass.
N = flywheel rotation.
n = number of windings of the string.
h = height of the weight assembly.
g = acceleration due to gravity.
r = radius of the axle.
Or, we can also use the following expression;
mgh = ½ mv2 + ½ Iω2 + n 1 E
Flywheels are nothing but circular disc-shaped objects which are mainly used to store energy in machines.
Determining The Moment Of Inertia Of Flywheel
To determine the moment of inertia of a flywheel we will have to consider a few important factors. First, we have to set up a flywheel along with apparatus like a weight hanger, slotted weights, metre scale and we can even keep a stopwatch.
Then we make some assumptions. We will take the mass as (m) for the weight hanger as well as the hanging ring. The height will be (h). Now we consider an instance where the mass will descend to a new height. There will be some loss in potential energy and for which we write the equation as;
P loss = mgh
Meanwhile, there is a gain in kinetic energy when the flywheel and axle are rotating. We express it as;
K flywheel = (½) Iω2
I = moment of inertia
ω = angular velocity
Similarly, the kinetic energy for descending weight assembly is expressed as;
K weight = (½) Iv2
Here, v = veocity
We also have to take into account the work that is done in overcoming the friction. This can be found out by;
W friction = nW f
In this case,
n = number of windings of the string
W f = work done in overcoming frictional torque
If we state the law of conservation of energy then we obtain;
P loss = K flywheel + K weight + W friction
We will substitute the values and the equation will now become;
mgh = (½)Iω2 + (½) mv2 + nW f
Moving on to the next phase, we look at the flywheel assembly’s kinetic energy that is used in rotating (N) number of times against the frictional torque. We get;
NW f = (½ ) Iω2 and W f = (1 / 2N) Iω2
Further, we establish a relation between the velocity (v) of the weight assembly and the radius (r) of the axle. The equation is given as;
v = ωr
We have to substitute the values for W f and v.
mgh = (½) Iω2 + (½ )mr2ω2 + (n / N) x ½ Iω2
If we solve the equation for finding the moment of inertia, we obtain;
\(\begin{array}{l}I = \frac{Nm}{N+n}(\frac{2gh}{\omega ^{2}}-r^{2})\end{array} \)
⇒ Check Other Object’s Moment of Inertia:
Parallel Axis Theorem
FLYWHEEL ENERGY STORAGE CALCULATOR
FLYWHEEL ENERGY STORAGE CALCULATOR 136
Flywheel energy storage (FES) works by accelerating a rotor (flywheel) to a very high speed and maintaining the energy in the system as rotational energy. When energy is extracted from the system, the flywheel’s rotational speed is reduced as a consequence of the principle of conservation of energy, adding energy to the system correspondingly results in an increase in the speed of the flywheel. Most FES systems use electricity to accelerate and decelerate the flywheel, but devices that directly use mechanical energy are being developed. Advanced FES systems have rotors made of high strength carbon-fiber composites, suspended by magnetic bearings, and spinning at speeds from 20, 000 to over 50, 000 rpm in a vacuum enclosure. Such flywheels can come up to speed in a matter of minutes reaching their energy capacity much more quickly than some other forms of storage. Main components A typical system consists of a flywheel supported by rolling-element bearing connected to a motorgenerator. The flywheel and sometimes motorgenerator may be enclosed in a vacuum chamber to reduce friction and reduce energy loss. First-generation flywheel energy-storage systems use a large steel flywheel rotating on mechanical bearings. Newer systems use carbon-fiber composite rotors that have a higher tensile strength than steel and can store much more energy for the same mass. To reduce friction, magnetic bearings are sometimes used instead of mechanical bearings. = Possible future use of superconducting bearings =The expense of refrigeration led to the early dismissal of low-temperature superconductors for use in magnetic bearings. However, high-temperature superconductor (HTSC) bearings may be economical and could possibly extend the time energy could be stored economically.
Find the Flywheel Energy Storage of any number for free. Enter the values below to calculate Flywheel Energy Storage. #flywheel #energy #storage #mechanical #engineering
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Flywheel Energy Calculator
Enter the flywheel moment of inertia (kg-m^2) and the angular velocity (rad/s) into the calculator to determine the Flywheel Energy.
Flywheel Energy Formula
The following equation is used to calculate the Flywheel Energy.
Ef = .5*I*w^2
Variables:
Where Ef is the Flywheel Energy (Joules)
I is the flywheel moment of inertia (kg-m^2)
w is the angular velocity (rad/s)
How to Calculate Flywheel Energy?
The following two example problems outline the steps and information needed in order to calculate the Flywheel Energy.
Example Problem #1:
First, determine the flywheel momentum of inertia (kg-m^2). In this example, the flywheel moment of inertia (kg-m^2) is measured to be 9. Next, determine the angular velocity (rad/s). For this problem, the angular velocity (rad/s) is calculated to be 5. Finally, calculate the Flywheel Energy using the formula above:
Ef = .5*I*w^2
Inserting the values from above and solving the equation with the imputed values gives:
Ef = .5*9*5^2 = 112.5 (Joules)
Example Problem #2:
Using the same process as example problem 1, we first define the needed variables outlined by the formula. In this case, the values are provide as:
flywheel moment of inertia (kg-m^2) = 9
angular velocity (rad/s) = 3
Entering these values into the formula or calculator above gives us:
Ef = .5*9*3^2 = 40.5 (Joules)
Flywheels – Kinetic Energy
A flywheel can be used to smooth energy fluctuations and make the energy flow intermittent operating machine more uniform. Flywheels are used in most combustion piston engines.
Energy is stored mechanically in a flywheel as kinetic energy.
Kinetic Energy
Kinetic energy in a flywheel can be expressed as
E f = 1/2 I ω2 (1) where E f = flywheel kinetic energy (Nm, Joule, ft lb) I = moment of inertia (kg m2, lb ft2) ω = angular velocity (rad/s)
Angular Velocity – Convert Units
1 rad = 360 o / 2 π =~ 57.29578 o
1 rad/s = 9.55 rev/min (rpm) = 0.159 rev/s (rps)
Moment of Inertia
Moment of inertia quantifies the rotational inertia of a rigid body and can be expressed as
I = k m r2 (2) where k = inertial constant – depends on the shape of the flywheel m = mass of flywheel (kg, lb m ) r = radius (m, ft)
Inertial constants of some common types of flywheels
wheel loaded at rim like a bicycle tire – k =1
flat solid disk of uniform thickness – k = 0.606
flat disk with center hole – k = ~0.3
solid sphere – k = 2/5
thin rim – k = 0.5
radial rod – k = 1/3
circular brush – k = 1/3
thin-walled hollow sphere – k = 2/3
thin rectangular rod – k = 1/2
Moment of Inertia – Convert Units
1 kg m2 = 10000 kg cm2 = 54675 ounce in2 = 3417.2 lb in2 = 23.73 lb ft2
Flywheel Rotor Materials
Material Density
(kg/m3)
Design Stress
(MPa) Specific Energy
(kWh/kg) Aluminum alloy 2700 Birch plywood 700 30 Composite carbon fiber – 40% epoxy 1550 750 0.052 E-glass fiber – 40% epoxy 1900 250 0.014 Kevlar fiber – 40% epoxy 1400 1000 0.076 Maraging steel 8000 900 0.024 Titanium Alloy 4500 650 0.031 “Super paper” 1100 S-glass fiber/epoxy 1900 350 0.020
1 MPa = 10 6 Pa = 10 6 N/m 2 = 145 psi
Pa = 10 N/m = 145 psi Maraging steels are carbon free iron-nickel alloys with additions of cobalt, molybdenum, titanium and aluminum. The term maraging is derived from the strengthening mechanism, which is transforming the alloy to martensite with subsequent age hardening.
Example – Energy in a Rotating Bicycle Wheel
A typical 26-inch bicycle wheel rim has a diameter of 559 mm (22.0″) and an outside tire diameter of about 26.2″ (665 mm). For our calculation we approximate the radius – r – of the wheel to
r = ((665 mm) + (559 mm) / 2) / 2
= 306 mm
= 0.306 m
The weight of the wheel with the tire is 2.3 kg and the inertial constant is k = 1.
The Moment of Inertia for the wheel can be calculated
I = (1) (2.3 kg) (0.306 m)2
= 0.22 kg m2
The speed of the bicycle is 25 km/h (6.94 m/s). The wheel circular velocity (rps, revolutions/s) – n rps – can be calculated as
n rps = (6.94 m/s) / (2 π (0.665 m) / 2)
= 3.32 revolutions/s
The angular velocity of the wheel can be calculated as
ω = (3.32 revolutions/s) (2 π rad/revolution)
= 20.9 rad/s
The kinetic energy of the rotating bicycle wheel can then be calculated to
E f = 0.5 (0.22 kg m2) (20.9 rad/s)2
= 47.9 J
Energy output from the flywheel Calculator
How to Calculate Energy output from the flywheel?
Energy output from the flywheel calculator uses Energy Output From Flywheel = Moment of Inertia*(Mean angular speed^2)*Coefficient of fluctuation of speed to calculate the Energy Output From Flywheel, The Energy output from the flywheel formula is defined as the product of the moment of inertia of the flywheel, the square of the mean angular velocity, and the coefficient of fluctuation of speed. Energy Output From Flywheel is denoted by U o symbol.
How to calculate Energy output from the flywheel using this online calculator? To use this online calculator for Energy output from the flywheel, enter Moment of Inertia (I), Mean angular speed (ω) & Coefficient of fluctuation of speed (C s ) and hit the calculate button. Here is how the Energy output from the flywheel calculation can be explained with given input values -> 2880 = 1.125*(16^2)*10.
Flywheel Energy Calculator
Flywheel Energy Calculator are physic/math calculator to find Flywheel Energy Storage in rotating flywheel.
Features:
– Instant calculation
– Result are copy able to other app
– Formula are include as reference
– Support up to 16 decimal place
– Support various unit for each input
Formula:
I = Mr²
E = 1/2 Iω²
Where:
E – Energy
I – Inertia
M – Mass of rotor
r – Radius of rotor
ω – Angular velocity
There are many renewable energies such as harnessing solar, wind, hydro, and thermal energies. The only problem is there are no efficient methods of storage. To be able to convert and use renewable energy as electricity there needs to be a process for storing it.
Flywheel energy storage systems use electric energy input which is stored in the form of kinetic energy. Kinetic energy can be described as “energy of motion” in this case the motion of a spinning mass, called a rotor. The rotor spins in a nearly friction-less enclosure. When short-term backup power is required because utility power fluctuates or is lost, the inertia allows the rotor to continue spinning and the resulting kinetic energy is converted to electricity.
Flywheel energy storage (FES) works by accelerating a rotor (flywheel) to a very high speed and maintaining the energy in the system as rotational energy. When energy is extracted from the system, the flywheel’s rotational speed is reduced as a consequence of the principle of conservation of energy, adding energy to the system correspondingly results in an increase in the speed of the flywheel.
Compared with other ways to store electricity, FES systems have long lifetimes (lasting decades with little or no maintenance, full-cycle lifetimes quoted for flywheels range from in excess of 105, up to 107, cycles of use), high specific energy (100–130 W·h/kg, or 360–500 kJ/kg), and large maximum power output. The energy efficiency (ratio of energy out per energy in) of flywheels, also known as round-trip efficiency, can be as high as 90%.
Thanks for your support and do visit nitrio.com for more apps for your iOS devices.
Dale’s Homemade Robots
This is a simple Javascript energy calculator for small ring flywheels made of steel, brass or aluminum. Check the box for material type (steel, brass or aluminum) then enter the OD,ID,thickness and RPM. Mass and kinetic energy will be calculated. Effects of the hub are ignored.
Flywheel Inertial Energy Formula and Calculator
Related Resources: calculators
Flywheel Inertial Energy Formula and Calculator
Machine Design Engineering and Design
Inertial Energy and Angular Acceleration of a Flywheel Formula and Calculator
Flywheels store and release the energy of rotation, called inertial energy. The primary purpose of a flywheel is to regulate the speed of a machine. It does this through the amount of inertia contained in the flywheel, specifically the mass moment of inertia. Flywheels are typically mounted onto one of the axes of the machine, integral with one of the rotating shafts. Therefore, it is the mass moment of inertia about this axis that is the most important design parameter. As stated in the introduction to this chapter, too much inertia in the flywheel design and the system will be sluggish and unresponsive, too little inertia and the system will lose momentum over time.
Figure 1
Solid disk flywheel integral to a rotating shaft
Preview Inertial Energy and Angular Acceleration of a Flywheel Calculator
Inertial Energy of a Flywheel Formulas:
Shown in Fig. 1 is a solid disk flywheel integral to a rotating shaft supported by appropriate bearings at each end. The applied torque (T ) produces an angular acceleration, denoted (α), which in turn produces an angular velocity, denoted by (ω).
The torque (T ) can vary over time; therefore, the angular acceleration (α) and angular velocity (ω) must also vary over time.
The relationship between the torque (T ) and the angular acceleration (α) for a flywheel and shaft assembly rotating about a fixed axis is given by Eq. 1) as
Mean spring force
Eq 1
T = I total α = ( I flywheel + I shaft ) α
Eq. 1.5
α = T / ( I flywheel + I shaft ) = T / I total
where (I total ) is the total mass moment of inertia, which is the sum of the mass moment of inertia of the flywheel (I flywheel ) and the mass moment of inertia of the shaft (I shaft ), both calculated about the axis of rotation.
For a solid disk flywheel with an outside radius (r o ) and inside radius (r i ) mounted on a shaft with an outside radius equal to the inside radius of the flywheel, the mass moments of inertia (I flywheel ) and (I shaft ) are given by the following two formulas as:
Eq. 2
I flywheel = ρ π t ( r o 2 – r i 2 ) 2
Eq. 3
I shaft = ρ π L r i 4
where (t) is the thickness of the flywheel and (L) is the length of the shaft, and where the density (ρ) of the flywheel and shaft are assumed to be the same.
The inertial energy (Einertial) of the flywheel and shaft assembly is given by the relationship:
Eq. 4
E inertial = 0.5 I total ω2
If the flywheel and shaft assembly is accelerated from one angular velocity (ω1) to another angular velocity (ω2), either speeding up or slowing down, the change in inertial energy levels is the work done on or by the system, denoted (Work 1→2), and is given by the relationship
Eq. 5
Work 1→2 = 0.5 I total ( ω2 1 – ω2 2 )
If the system is speeding up, the work done (Work 1→2 ) is positive. Conversely, if the system is slowing down, the work done (Work 1→2 ) is negative.
Converting rpm to rad/s
Eq. 6
rad / sec = rpm * (2 π /rev ) * 1 min / 60 s
Declarations:
L = length (ft, m),
ρ = density (slug/ft3, kg/m3),
r o = outside radius of flywheel (ft, m),
r i = inside radius of flywheel excluding shaft (ft, m),
t = thickness of flywheel (ft, m),
α = angular acceleration (rad/s2)
ω 1, 2 = angular velocity (rad/s)
Related:
Source:
Mark’s Calculations for Machine Design
Thomas H. Brown, Jr.
Faculty Associate
Institute for Transportation Research and Education
NC State University
Raleigh, North Carolina
키워드에 대한 정보 flywheel energy calculator
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