flywheel experiment errors

Experiment: Determination of Moment of Inertia of a Fly Wheel

Experiment: Determination of moment of Inertia of a Fly Wheel

Theory: The flywheel consists of a weighty round disc/massive wheel fixed with a strong axle projecting on either side. The axle is mounted on ball bearings on two fixed supports. There is a little peg on the axle. One end of a cord is loosely looped around the peg and its other end carries the weight-hanger.

Suppose, the angular velocity of a wheel is ω and its radius r. Then lineal velocity of the wheel is, v = ωr. If the moment of inertia of a body is I and the wheel is rotating around an axle.

Then its rotational kinetic energy, E = ½ Iω 2 .

Apparatus: An iron axle, a heavy wheel, some ropes, a mass, stopwatch, meter scale, slide calipers.

Description of the apparatus:

The flywheel was set as shown with the axle of the flywheel straight or parallel. A polystyrene tile was placed on the floor to avoid the collision of the mass on the floor.

(1) First of all, let us measure the radius of the axle by a slide caliper.

(2) Then for the determination of a number of rotation a mark by chalk is put on the axle and a rope is wound on the axle. At the other end of the rope a mass m is fastened and if it is dropped from position R, the wheel after rotating a few times, the weight with the rope will fall to position S. The wheel makes m 1 number of rotation to touch the point S and time for this drop is noted from the stopwatch.

Now the rope is again wound on the axle and the mass is fastened on the other end of the rope. From position R the mass is allowed to fall to the ground and as soon as it touches the ground, the stopwatch is started. When the axle comes to rest the stop wealth is stopped. Total time and the number of rotation of the wheel before it comes to rest are noted i.e., a total number of rotation (n 2 ) as noted.

Table 1: radius (r) of the axle B

Table 2: Determination of time and number of rotation

Calculation : If the axis takes time t for n 2 number of rotation, the average angular velocity,

ω 2 = (2πn 2 )/t

The axle acquires zero velocity with uniform retardation from angular velocity ω, so its average angular velocity,

ω 2 = (ω + 0) / 2 = ω/2

or, (2πn 2 )/t = ω/2

or, ω = 4πn 2 rad S -1

Then, I = (2mgh – mω 2 r 2 ) / ω 2 (1+ n 1 / n 2 ) = ….. g.cm 2 = ….. Kg.m 2

By inserting the value of n 2 , ω can be found out. By increasing the values of m, ω, r, h, n 1 , n 2 and g in an equation; the moment of inertia of the heavy wheel can be found out.

Precautions:

In the axle, a rope is to be wounded in such a way that while unwinding from the wheel it can easily drop on the ground.

• There should be the least friction in the flywheel.
• A number of rotation n and time t is to be unwired correctly.
• The length of the string should be less than the height of axle from the floor.
• Height ‘h’ is to be measured from the mark on the axle.
• ‘h’ is to be measured correctly.
• There should be no kink in string and string should be thin and should be wound evenly.
• The stopwatch should be started just after detaching the loaded string.

Applications: The main function of a flywheel is to maintain a nearly constant angular velocity of the crankshaft.

• A small motor can accelerate the flywheel between the pulses.
• The phenomenon of precession has to be considered when using flywheels in moving vehicles.
• Flywheels are used in punching machines and riveting machines.

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MOMENT OF INERTIA OF FLYWHEEL

This experiment is an introduction to some basic components of rotational dynamics to develop an understanding of Moment of Inertia

Torque and Mass Moment of Inertia

If a body is free to rotate about a fixed axis, then a torque is required to initiate or change the rotational motion of the body.

The torque τ ⃗ of a force about an axis is given by the cross-product of the force F ⃗ and the distance from the axis of rotation

The net torque is proportional to the angular acceleration α ⃗ of the body and shall exist during the entire time the torque acts. The equation is given as

Where I is the constant of the body known as the Mass Moment of Inertia about the specified axis of rotation. Mass moment of inertia (also known as rotational inertia) is a measure of a body’s resistance to a change in its rotation direction or angular momentum. The moment of inertia depends not only on the mass but also the distribution of the mass around the axis. Just as the mass is a measure of resistance of linear acceleration, mass moment of inertia is a measure of resistance to angular acceleration.

The experiment consists of estimating the mass moment of inertia of the flywheel system. A flywheel is a heavy thick circular discs designed for storing rotational energy. It is generally made of cast iron or steel along is mounted on an axle free to rotate on ball bearings. In other words, it’s a kind of system that needs a large force to start or stop spinning. The capacity of storing / shedding of kinetic energy depend on the rotational inertia of the flywheel.

In real life, flywheels come in all shapes and sizes. For obtaining the maximum moment of inertia per volume, most flywheels have a heavy outer circular rim with spokes. They may be mounted on the crankshaft of machines such as turbines, steam engines, diesel engines etc. This makes the engine run smoothly by storing kinetic energy when the machines are on higher loads and maintains that constant angular velocity during idle conditions.

Mass Moment of Inertia of Flywheel

The Mass Moment of Inertia of cylindrical objects about an axis passing through the centre can be given by the equation

I = (mr^2)/2.

The flywheel in this experiment is a solid disc of mass M1 and radius R attached to a shaft of mass M2 and radius r. So the moment of inertia of the flywheel system is given as

I = Σ (mr^2)/2= (M_1 R^2)/2+(M_2 r^2)/2

For complex geometries, the mass moment of Inertia of the flywheel can be estimated by measuring the approximate mass of different simplified geometrical components and adding the Mass Moment of Inertia about the central axis (from the known equations of MI of rings, cylinders, rods, etc).

Experimental Setup and Theory

In the experiment, a hanging mass m attached to the end of a spring, the remainder of which is wrapped around the axle is allowed to fall initiating the necessary torque τ ⃗ to the flywheel system initially at rest. Suppose that the string is wrapped around the axle n times and that a mass m is suspended from its free end and the system is released at time t = 0. As the mass accelerates downward, the flywheel attains an angular acceleration α ⃗. Because of the friction in the bearings, there will be an additional torque in the direction opposite to the motion of the flywheel. This frictional torque (α_f ) ⃗ depends upon a number of factors such as speed of rotation, coefficient of friction, etc but shall be assumed to be a constant value for simplicity.

If T is the tension in the string, then the net torque exerted by the wheel is

The net force on the mass m is

If the frictional torque is constant, then the angular acceleration of the system, (α_f ) ⃗, is also constant The flywheel will achieve a maximum angular velocity at the instant when the string detaches from the axle. The axle will continue to rotate until all the work is used to overcome the friction in bearings. Finally, the axle will stop rotating against the frictional forces.

Theoretical Calculations

As the slotted weight falls a particular height, it loses its potential energy. The loss in potential energy during unwinding is converted into its translation kinetic energy and rotational kinetic energy of flywheel. Some of the energy is lost in overcoming frictional forces in the bearings. Applying the law of conservation of energy at the instant the mass hits the ground.

(P.E)m = (R.K.E.)F + (L.K.E.)m + Frictional losses

The loss of potential energy (P.E)m of the slotted weights as it hits the ground is given as

(P.E)m = m g h = mg (2 π r n)

Note that we have neglected the thickness of the cord since radius of elastic cord cannot be determined experimentally. Another source of error is the slipping of the cord from the axle during unwinding.

The rotational kinetic energy of the flywheel (R.K.E)f can be given by

(R.K.E.)m = ½ Iω^2

The gain in linear Kinetic Energy (L.K.E)m of the slotted weights just before the mass touches the ground is given as (L.K.E.)m = ½ mv^2

If ω is the angular speed of the disc just as the mass hits the ground, then the final velocity of slotted weights is given by

The frictional losses are mainly due to friction in the axle and bearing assembly of the apparatus. We assume that the bearing frictional losses per unit rotation to be a constant value Wf. The total bearing friction depends on the number of wounds of cord around the axle

Bearing friction at the end of n1 rotations = n Wf

It is worth mentioning that air friction acting on the surface of the rotating disc as well as the moving weights may also result in losses which are ignored here.

Applying the individual equations in the law of conservation of energy, we obtain

Now, even after the mass detaches from the axle, the flywheel will continue to rotate. The angular velocity of the flywheel would decline gradually and finally come to a rest when all is rotational kinetic energy of flywheel (R.K.E)f is spent to overcome the frictional forces. If N is the number of rotation made by the flywheel after the string has left the axle then

Substituting the values of v and Wf in the equation,

Solving the equation for I, we obtain the following equation for mass moment of inertia of a flywheel which is,

The maximum angular velocity ω in the above equation can be found out by calculating the average velocity ωa as the flywheel comes to a final stop.

If N revolutions take a time t, then the average angular is given by

The above two equations give us a direct relationship between maximum angular velocity, number of rotations after detachment and the time required to complete that revolution

The experimental moment of inertia calculated by the equation may be slightly different from the theoretical moment of inertia because of the following criteria The thickness of the cord is assumed to be negligible. The bearing friction per rotation was assumed to be a constant value throughout the rotation. The air frictional losses are ignored. Any slip between the cords and the axle during unwinding is ignored

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Moment of inertia of a flywheel

An interesting investigation to see what factors can affect the moment of inertia of a flywheel.  This is good to discuss errors in measurements (such as counting rotations) and would be good to develop improvements.

This resource has been provided by Keith Gibbs.

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Flywheel Moment of Inertia Lab Report

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Introduction

The determination of the moment of inertia of a flywheel is a crucial aspect of engineering, particularly in the design of engines and machinery. The moment of inertia is a measure of an object's resistance to changes in its rotational motion. In the context of a flywheel, it plays a significant role in maintaining the stability and efficiency of various mechanical systems, such as piston-driven engines.

The primary objective of this experiment is to find the moment of inertia of a flywheel and then compare it with the theoretical value.

This comparison allows us to assess the accuracy of our measurements and calculations, ultimately leading to the identification of any percentage error in our readings. Understanding the moment of inertia of a flywheel is essential because it influences the selection of an appropriate flywheel to ensure the smooth and efficient functioning of pistons and other mechanical components.

The following apparatus and materials were used for this experiment:

• Flywheel apparatus

A flywheel is a mechanical device designed to efficiently store rotational energy and resist any changes in rotational energy due to its large moment of inertia.

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In the context of an engine, a flywheel plays a crucial role in the smooth movement of a piston. During the engine cycle, there is only one power stroke (Expansion stroke), and in all other strokes, power must be supplied for piston movement, which comes from the flywheel. The flywheel stores energy from the power stroke in the form of rotational kinetic energy and releases this energy to drive the piston during other strokes.

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Thus, a flywheel provides continuous power output in situations where the energy source is not continuous.

There are two main types of flywheels:

• Rimmed Flywheel: This type of flywheel derives its moment of inertia mainly from the rimmed part rather than the shaft or hub.
• Shaftless Flywheel: This flywheel eliminates shafts or hubs and has a higher energy-storing capacity due to higher energy density. However, it requires mechanisms like magnetic bearings for operation.

Moment of Inertia:

Moment of inertia is a property of a body that resists changes in its rotational movement when subjected to an external force like torque. It is specified using an axis whose position is not fixed and is a measure of the body's resistance to angular acceleration. Moment of inertia is an additive property, and it can be calculated for bodies with specific shapes using integral calculus.

Experimental Setup

The flywheel apparatus used in this experiment was properly lubricated to minimize frictional errors. The height of the string was set to be equal to the length of the string. The string was tightly wound around the axle of the flywheel. A mass 'm' was attached to the free end of the string. When this mass falls, it unwinds the string and sets the flywheel into rotational motion. The flywheel continues to rotate due to its rotational inertia but eventually comes to rest due to frictional forces.

• Determine the distance 'd' over which the mass 'm' falls by measuring the length of the string, including the height of the hanger. Record the mass of the hanger.
• Place a suitable mass on the hanger, wind the string around the axle of the flywheel, and position the hanger on the small circular platform beneath the flywheel. Release the platform and simultaneously start the timer. Stop the timer as soon as the string detaches from the axle.
• Repeat step 2 by changing the mass on the hanger 4 or 5 times.
• Measure the diameter of the axle and record the radius and mass of the flywheel.
• Calculate the linear acceleration using the formula: a = 2d/t^2
• Similarly, calculate the angular acceleration of the shaft and flywheel using the linear acceleration and their respective radii.
• Calculate the resulting torque using the formula: torque = rT
• Now, calculate the experimental value of the moment of inertia using the formula: I = (τ 2 - τ 1 ) / (α 2 - α 1 )

The theoretical value of the moment of inertia is given by: I = Mr 2

Observations and Calculations

Given data:

• Wheel radius = 6.7 inches
• Spindle radius = 0.5 inches
• Acceleration due to gravity (g) = 386.22 inches/s 2
• Wheel weight = 68.5 lb
• Distance of hanger = 45.7 inches

Calculations:

Mean value of the moment of inertia of the flywheel = 15351 lb·inches 2 = 0.6 kg·m 2

Theoretical value of the moment of inertia of the flywheel = 0.8 kg·m 2

Total percentage error in this experiment = 25%

The observed percentage error in this experiment raises important considerations. Several factors could contribute to the deviation between the experimental and theoretical values of the moment of inertia. One potential source of error is the measurement of time, which could be influenced by human reaction time and stopwatch accuracy. Additionally, the height and length measurements may have introduced inaccuracies.

Another factor to consider is frictional forces experienced by the flywheel during its rotation. Friction can lead to energy losses, which may not have been accounted for in our calculations. Additionally, variations in the flywheel's behavior due to factors like air resistance and imperfections in the apparatus could contribute to the observed error.

This experiment aimed to determine the moment of inertia of a flywheel and compare it to the theoretical value. While the mean experimental value of moment of inertia was found to be 0.6 kg·m 2 , the theoretical value was 0.8 kg·m 2 , resulting in a total percentage error of 25%. This discrepancy suggests that there were inaccuracies in our measurements and assumptions.

Potential sources of error include measurement precision, frictional losses, and variations in the behavior of the flywheel. To improve the accuracy of future experiments, more precise measurement tools and techniques should be employed. Additionally, efforts to minimize friction and control external factors that affect the flywheel's motion should be considered.

Despite the observed error, this experiment provides valuable insights into the practical challenges of measuring moment of inertia and highlights the importance of considering various factors in engineering applications.

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• Moment Of Inertia

Moment Of Inertia Of Flywheel

Moment of inertia of a flywheel is calculated using the given formula;

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;

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) Iω 2

I = moment of inertia

ω = angular velocity

Similarly, the kinetic energy for descending weight assembly is expressed as;

K weight = (½) Iv 2

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)Iω 2 + (½) mv 2 + 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 ) Iω 2 and W f = (1 / 2N) Iω 2

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;

We have to substitute the values for W f and v.

mgh = (½) Iω 2 + (½ )mr 2 ω 2 + (n / N) x ½ Iω 2

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:

• Moment Of Inertia Of Circle
• Moment Of Inertia Of A Quarter Circle
• Moment Of Inertia Of Semicircle
• Moment Of Inertia Of A Sphere
• Moment Of Inertia Of A Disc

Parallel Axis Theorem

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Flywheel experiment

1. INTRODUCTION

A flywheel is a mechanical device with a significant moment of inertia used as a storage device for rotational energy 1 . The rotational energy stored enables the flywheel to accelerate at very high velocities, and also to maintain that sort of velocity for a given period of time. The force that enables the flywheel to attain such velocities also produces energy to slow down the flywheel’s motion.

The objectives of the experiment are;

• To determine the friction torque due to the bearings, T f  
• To determine, experimentally, the moment of inertia, I, for the flywheel.
• To estimate the moment of inertia, using simple equations.
• To compare the experimental value of I with the estimate and suggest reasons for any discrepancies.

To calculate friction torque, it is assumed that the energy lost due to bearing friction is equal to the potential energy lost by the mass during unwinding and rewinding:

               Mg(H 1 -H 2 ) = T f  θ                                                                   . . . . . (1)

Where, m        = applied mass (kg)

               H 1         = original height of mass above some arbitrary datum (m)

               H 2         = final height of mass above the same datum (m)

               T f            = friction torque (Nm)

               θ                    = total angle turned through during unwinding and rewinding (rads)

To calculate the angular acceleration, (α),

              S = u t + a t 2 /2                                                                  . . . . . . . .(2)

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and       α =a/r                                                                                . . . . . . . . (3)

where, s             = distance travelled by mass during decent (m)

             u             = initial velocity of mass (=0)

             t              = time to travel distance s (s)

             a             = linear acceleration of mass (m/s 2 )

             r              = effective radius of the flywheel axle (m)

To determine, experimentally, the moment of inertia (I exp );

     T – T f = (I + m r 2 ) α                    where T = m g r             . . . . . . . . . (4)

To calculate a theoretic value for I. The equation is;

     I = MR 2 /2                                                                              . . . . . . . . (5)

Where M            = mass of flywheel (kg)

              R            = radius of flywheel (m)

3 . EXPERIMENTAL PROCEDURES

3.1     DESCRIPTION OF THE TEST EQUIPMENT

• Flywheel (disc and axle)
• Pencil (to mark distance)
• Mass (known) and mass holder

                                 Flywheel

                         (disc + Axle)

         A        

             C          H 1

         String

        H 2

A known mass          B

Figure 3.1a

3.2   PROCEDURE

• The string is wrapped around the flywheel in a clockwise direction, which in turn lifts the known mass that is attached to the bottom of the string to a point close to the flywheel (point A on fig 3.1).
• The string, with the mass attached to it, is then allowed to wind down the flywheel until the mass reaches its lowest point (point B on fig 3.1), which is timed with a stop watch.
• The distance between points A and B is measured as H 1 .
• After reaching its lowest point, the mass then bounces back and starts to travel in the opposite direction, but then stops at a particular point (point C on fig 3.1).
• The distance between points B and C is measured as H 2 .
• The experiment is then repeated again, so as to improve reliability and accuracy of the supposed result.

3.3   RESULT                                                                                                        Table 3.3

H 1  = Original height of mass after it unwinds from the flywheel

H 2  = Final height of mass after bouncing back in opposite direction

 θ = Total angular displacement (rads)

r   = Effective radius of the axle = 13.75x10 -3 m.

Radius of shaft and rope (r) = 0.01375m

Mass of flywheel = 6.859kg

Radius of flywheel = 0.1m

Radius of axle = 0.0125m

4.  ANALYSIS OF RESULTS

To calculate the moment of inertia of the flywheel;

             T – T f = (I + m r 2 ) α                    where T = m g r  

Make ‘I’ the subject of the formula;

            I exp = (T – T f  )/α – (m r)

then, the value of T(applied torque) is;

   = 0.1 x 9.81 x (13.75x10 -3 )

   = 13.49x10 -3  Nm

To calculate T f (frictional torque);

T f  = mg (H 1  – H 2 )/θ

    = (0.1 x 9.81 x 0.77)/ 56

    = 1.35x10 -2  Nm

To calculate the angular acceleration (α);

α = 2H 1 / (r x t 2 )

    = (2 x 0.98)/ (13.75x10 -3  x 22.88 2 )

    = 0.27ms -2

I exp  = (13.49x10 -3  – 1.35x10 -2 )/0.27 - (0.1 x [13.75x10 -3 ] 2 )

       = 3.7x10 -5  – 1.89x10 -5

       = 1.81x10 -5  kgm 2

To calculate the theoretic value for the moment of inertia;

I theory  = MR 2 / 2

            = 6.859 x (0.1) 2  / 2

            = 3.43 x 10 -2  kgm 2

% error  = [(Expected Value – Actual value)/ Expected Value] x 100

               = [3.4x10 -2 / 3.43x10 -2 ] x 100 = 99.13%

5. DISCUSSIONS/CONCLUSION

Following the analysis of my results, the values of I experiment  and I theory  differ by fairly a significant amount i.e. (a percentage error of 99.13%). The errors that led to the difference in the two values can be categorize into two sub-groups called “Measurement errors” and “Procedural errors”.

Measurement Errors.

• Errors may perhaps have crept up while measuring the distances of H 1  and H 2 . These distances could have possibly been marked incorrect if the points were not marked at eye level, which could have lead to errors in the final value. However, these errors could have been minimised by taking more repeated readings, or even recording the experiment with the use of a video camera in order to help in checking for these kind of errors.
• Furthermore, another error that could have affected the final value was the timing of the stopwatch while measuring H 1  and H 2 . This human error can be significantly reduced via total concentration of everyone involved in the experiment.

Procedural Errors.

The motion of the mass that was attached to the spring could have been affected by factors, such as the air resistance and friction, which would lead to easy energy loss during the experiment. This could have also led to some errors in the final value.                                                                                

This error could have been minimised by doing the experiment in a closed system, which would have not just minimised errors, but also increase the accuracy and reliability of the result.

• Lynn White, Jr., “Theophilus Redivivus”, Technology and Culture , Vol. 5, No. 2. (Spring, 1964), Review, pp. 224-233 (233) 1  
•  Lynn White, Jr., “Medieval Engineering and the Sociology of Knowledge”, The Pacific Historical Review , Vol. 44, No. 1. (Feb., 1975), pp. 1-21 (6)

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Error estimation of moment of inertia of a flywheel

• Thread starter angelina
• Start date Dec 10, 2004
• Tags Error Estimation Flywheel Inertia Moment Moment of inertia
• Dec 10, 2004
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A PF Multiverse

angelina said: it states "since gt^2/2h >> 1,

angelina said: i think % error of n2 should be multiplied by a 2

FAQ: Error estimation of moment of inertia of a flywheel

What is the purpose of estimating the moment of inertia of a flywheel.

The moment of inertia of a flywheel is an important parameter to determine the rotational motion and stability of the flywheel. It is used to calculate the amount of energy that can be stored in the flywheel and how it will respond to external forces.

How is the moment of inertia of a flywheel calculated?

The moment of inertia of a flywheel can be calculated by multiplying the mass of the flywheel by the square of its radius and adding the product of the mass and the square of the distance from the axis of rotation to the center of mass. This calculation can be simplified for a cylindrical flywheel by using the formula I = 1/2 * m * r^2, where I is the moment of inertia, m is the mass, and r is the radius.

What factors can affect the accuracy of the moment of inertia estimation for a flywheel?

The accuracy of the moment of inertia estimation for a flywheel can be affected by several factors such as the precision of the measurements of the flywheel's mass and dimensions, the alignment of the flywheel's axis of rotation, and the presence of any external forces or torques. Additionally, any imperfections in the shape or material of the flywheel can also impact the accuracy of the estimation.

How can the uncertainty in the moment of inertia estimation be minimized?

To minimize the uncertainty in the moment of inertia estimation, it is important to use precise and accurate measurements and to repeat the calculation multiple times to ensure consistency. It is also important to consider the effects of external forces and torques, and to minimize any imperfections in the flywheel's shape or material. Utilizing more advanced measurement techniques, such as computer simulations, can also help to improve the accuracy of the estimation.

Why is it important to estimate the moment of inertia of a flywheel accurately?

Estimating the moment of inertia of a flywheel accurately is crucial for various engineering and scientific applications. It helps in designing efficient and stable flywheels for energy storage systems, as well as in understanding and predicting the behavior of rotating systems. Inaccurate estimations can lead to unexpected results and potentially dangerous situations, making it important to strive for the most accurate estimation possible.

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EXPERIMENT U4 MOMENT OF INERTIA OF FLYWHEELS

In this experiment, the moment of inertia of flywheel is being studied by variating the point of mass of flywheel. The experiment is conducted by recording the time taken for the respective point of mass to being rotated by a fixed load until the point where the load is escaping from the flywheel and the number of rotations done after be independent from the load. The moment of inertia then is calculated by substituting the data obtained from the experiment and the experimental value is calculate and compared to the experimental one.

Free related PDFs Related papers

This paper presents the details of construction and implementation of an automated data acquisition (DAQ) system for an undergraduate laboratory experimental setup that is intended to measure the moment of inertia of a flywheel (without disassembling the setup), using the falling mass method. The developed DAQ system is a microcontroller-based system which has facilities to calculate a value for the moment of inertia of the flywheel directly, using the acquired data.It employs optical sensors to detect the position of a known mass attached to one end of a string wound around the flywheel axel, count the number of turns made by the flywheel before releasing the mass and after releasing the mass and measure the time taken for the mass to fall through a known distance.Measurements were taken under nine different conditions by changing the mass and its fall-through height with both manually operated and automated experimental setup. The average of the measured values of the moment of inertia of the flywheel under the two operation modes are found to be manua 2 l 0.348 0.005 kg m

Abstract: In present investigation, to counter the requirement of smoothing out the large oscillations in velocity during a cycle of a I.C. Engine, a flywheel is designed, and analyzed. By using Finite Element Analysis are used to calculate the stresses inside the flywheel, we can compare the Design and analysis result with existing flywheel

International Journal of Engineering Research and Technology (IJERT), 2014

https://www.ijert.org/analysis-of-flywheel-used-in-petrol-engine-car https://www.ijert.org/research/analysis-of-flywheel-used-in-petrol-engine-car-IJERTV3IS051286.pdf A flywheel used in machines serves as a reservoir 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 more than supply. For example, in I.C. engines, the energy is developed only in the power stroke which is much more than engine load, and no energy is being developed during the suction, compression and exhaust strokes in case of four stroke engines. The excess energy is developed during power stroke is absorbed by the flywheel and releases its to the crank shaft during the other strokes in which no energy is developed, thus rotating the crankshaft at a uniform speed. The flywheel is located on one end of the crankshaft and serves two purposes. First, through its inertia, it reduces vibration by smoothing out the power stroke as each cylinder fires. Second, it is the mounting surface used to bolt the engine up to its load. The aim of the project is to design a flywheel for a multi cylinder petrol engine flywheel using the empirical formulas. A 2D drawing is drafted using the calculations. A parametric model of the flywheel is designed using 3D modeling software Pro/Engineer. The forces acting on the flywheel are also calculated. The strength of the flywheel is validated by applying the forces on the flywheel in analysis software ANSYS. Structural analysis, modal analysis and fatigue analysis are done on the flywheel. Structural analysis is used to determine whether flywheel withstands under working conditions. Fatigue analysis is done for finding the life of the component. Modal analysis is done to determine the number of mode shapes for flywheel Analysis is done for two materials Cast Iron and Aluminum Alloy A360 to compare the results. Pro/ENGINEER is the standard in 3D product design, featuring industry-leading productivity tools that promote best practices in design. ANSYS is general-purpose finite element analysis (FEA) software package. Finite Element Analysis is a numerical method of deconstructing a complex system into very small pieces (of user-designated size) called elements. INTRODUCTION:

I. Introduction Flywheel is a heavy rotating body which serves as an energy reservoir. The flywheel stores the energy in the form of kinetic energy during the period when the supply of energy from the prime mover is more than the requirement of energy by the machine, and releases it during the period when the requirement of energy by the machine is more than the supply of energy by the prime mover. In this work stress induced in a flywheel was studied and considered different parameters such as speed, material, outer diameter of flywheel, diameter of spoke and number of spoke.

— Flywheels serve as kinetic energy storage and retrieval devices with the ability to deliver high output power at high rotational speeds as being one of the emerging energy storage technologies available today in various stages of development, especially in advanced technological areas. There are many causes of flywheel failure among them one of is the non-linear behavior of the flywheel. Hence in this work evaluation of non-linear stresses in the flywheel for different material is done. The design of flywheel is used by solid work software. The software used for analysis and apply forces for validation of flywheel is ANSYS. The FEA of flywheel is considering centrifugal forces on its comparative non-linear analysis is done for von-mises stress, shear stress and deformation of the flywheel made of Cast iron and aluminium alloy. The paper also gives a topology optimization approach in reducing the mass of flywheel.

https://www.ijert.org/a-review-paper-on-structural-and-parametric-analysis-of-composite-flywheel https://www.ijert.org/research/a-review-paper-on-structural-and-parametric-analysis-of-composite-flywheel-IJERTV3IS120185.pdf Flywheel energy storage (FES) can have energy fed in the rotational mass of a flywheel, store it as kinetic energy, and release out upon demand. For example, in I.C. engines, the energy is developed only in the power stroke which is much more than engine load, and no energy is being developed during the suction, compression and exhaust strokes in case of four stroke engines. The excess energy is developed during power stroke is absorbed by the flywheel and releases its to the crank shaft during the other strokes in which no energy is developed, thus rotating the crankshaft at a uniform speed. The current paper is focused on the analytical design of flywheel & FEM analysis flywheel used in Press. Different types of forces acting on flywheel & design parameters has taken into consideration for optimizing design of flywheel By using ANSYS stresses obtained & compared with analytical calculations, also weight is compared.

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Error-corrected quantum computers require access to so-called magic states to outperform classical devices. Now, a study has shown that coherent errors can drive error-correcting codes into high-magic states that could be a resource for universal quantum computing.

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