Flywheels

32: Sakshi Jadhav, 33: Rishab Jadhav, 45: Ameya Joshi, 46: Ranbeer Kadam, 47: Sonal Kadam 

Guide: Prof. Rajkumar Bhagat

 

Flywheels

A flywheel serves as a reservoir when used in machines, which stores energy during the period when the supply of energy is more than the requirement and releases it during the period when the requirement of energy is less than the supply. For example, the energy developed in the internal combustion engines during expansion or power stroke is much more than the engine load, and no energy is developed during suction, compression, and exhaust strokes in the case of four-stroke engines and during compression in two-stroke engines.

It stores the energy when the supply is more than the requirement and releases when the requirement is more than the supply.

In machines where the operation is not continuous like punching machines, shearing machines, riveting machines, crushers, etc., the flywheel stores energy from the power source during the greater portion of the operating cycle and gives it up during a small period of cycles. So, the energy from the power source to the machines is supplied at a constant rate throughout the operation.

Types of Flywheels

Following are the types of flywheels used in vehicles:

1. Solid disc flywheel
2. Rimmed flywheel
3. High-velocity flywheel
4. Low-velocity flywheel

 1. Solid Disc Flywheel

•  Solid Disc Flywheel is used in a single flywheel thresher and it is made up of cast iron. The solid disc flywheel consists of a flywheel hub and disc.
•  While considering the design calculations for solid disk flywheel, various parameters are used as inputs like dimensions of the solid disk flywheel. Also, resulting functional values are calculated.

2. Rimmed Flywheel

• The rim-type flywheel has a lower rotary speed compared to a solid disc-type wheel of equal weight and diameter. A flywheel can be formed of high-strength steel for minimal weight and high energy-storage capacity and produced as a tapered disk, which is thick in the center.
•  The mass of the flywheel is concentrated at the rim only for the rim type of flywheel, i.e., not throughout the radius but only at the radius which is just opposite to disc type, which results in imparting a higher moment of inertia than disc type.

3. High-Velocity Flywheel

•  The high-velocity flywheel has a velocity range between 30000 rpm to 80000 rpm. The maximum velocity that can be reached by this type of flywheel is 100,000 rpm.
• They require less maintenance also it has magnetic levitation bearings.
•  In comparison with a Low-Velocity flywheel, this flywheel is lightweight in the aspect of size or capacity and also expensive.
• This flywheel can be made up of carbon fiber composite.

4. Low-Velocity Flywheel

• The low-velocity flywheel can have a velocity of up to 10000 rpm.
• They are heavy in weight and bulky as compared to High-velocity flywheels. As they don’t contain magnetic levitation, they need a timely maintenance
• Installation of a low-velocity flywheel requires special concrete construction to carry its weight.
• This type of flywheel is available at a low cost compared to the high-velocity flywheel.

Flywheel Construction:

Coefficient of Fluctuation of Speed of Flywheel:

The difference between maximum and minimum speeds during a cycle is called maximum fluctuation of speed.

The ratio of maximum fluctuation of speed to the mean speed is called coefficient fluctuation of speed.

Let N₁ and N₂ be maximum and minimum speeds in r.p.m. during the cycle.

N = Mean speed in r.p.m. 

Coefficient of Fluctuation of speed,

The coefficient of fluctuation of speed is a limiting factor in the design of the flywheel. It varies depending upon the nature of service to which the flywheel is employed.

The reciprocal of the coefficient of fluctuation of speed is called the coefficient of steadiness and is denoted by m.

Energy stored in Flywheel.

Energy stored in a flywheel is kinetic energy and it is given as,

E = ½*I* ω² = ½*m*k²* ω²

As the speed of the flywheel changes from ω₁ to ω₂, the maximum fluctuation of energy is

∆E = ½ *I* [ω²₁ – ω²₂]

     = I* ω²*Cs

     = 2*E*Cs N-m or Joules

It can be written as

 

Application of Flywheel in Punching Press

The function of the flywheel in an engine is to reduce the fluctuations of speed when the load on the crankshaft is constant and the input torque varies during the cycle. When the torque is constant and the load varies during the cycle same function can be performed by the flywheel. Such an application is found in punching press or in the riveting machine. The crank is driven by the motor which supplies constant torque and the punch is at the position of the slider in a slider-crank mechanism.

The load acts only during the rotation of the crank from θ = θ₁ to θ = θ₂ when the actual punching takes place and load is zero for the rest of the cycle. The speeds of the crankshaft will increase too much during the rotation of crank from θ = θ₂ to θ = 2π or θ = 0 and again from θ = 0 to θ = θ₁ unless a flywheel is used because there is no load while input energy continues to be supplied. On the other hand, due to much more load than the energy supplied the drop in speed in the crankshaft is very large during the rotation of crank from θ = θ₁ to θ = θ₂.

Thus, to keep the fluctuations of speed within permissible limits the flywheel has to absorb excess energy available at one stage and has to make up for the deficient energy at the other stage. This is done by choosing the suitable moment of inertia of the flywheel.

Let the energy required for punching the hole be E1. This energy is determined by the size of the hole punched, the thickness of the material, and the physical properties of the material. Let d₁ = Diameter of the hole punched

t₁ = Thickness of the plate

τ_u = Ultimate shear stress for the plate material

The maximum shear force required for punching,

F_s = Area sheared*Ultimate shear stress

    = π* d₁* t₁* τ_u

It is assumed that as the hole is punched, the shear force decreases uniformly from the maximum value to zero.

Work done or energy required for punching a hole, E₁ – ½ * F_s * t₁

Assuming one punching operation per revolution, the energy supplied to the shaft per revolution should also be equal to E₁. The energy supplied by the motor to the crankshaft during actual punching operation,

Balance energy required for punching      = E₁ - E₂

        

This energy is to be supplied by the flywheel by the decrease in its kinetic energy when its speed falls from maximum to minimum. Thus, maximum fluctuation of energy,

The values of θ₁ and θ₂ may be determined only if crank radius (r), length of connecting rod (l), and the relative position of the job with respect to the crankshaft axis is known. In the absence of relevant data, we assume that

Where t = Thickness of the material to be punched

s = Stroke of the punch = 2*Crank radius = 2r

By using the suitable relation for the maximum fluctuation of energy, we can find the mass and the size of the flywheel.

References:

• https://mechanicaljungle.com/types-of-flywheel/
• https://en.wikipedia.org/wiki/Flywheel#:~:text=A%20flywheel%20is%20a%20mechanical,square%20of%20its%20rotational%20speed.&text=Common%20uses%20of%20a%20flywheel,output%20of%20an%20energy%20source.
• https://www.britannica.com/technology/flywheel
• https://www.hubspot.com/flywheel
• Theory of Machines by S. S. Ratan