This paper illustrates the survey of a flywheel, where the flywheel which is made of unstained steel was required to run at 6000 revolutions per minute. The theoretical account of the flywheel was created and stress analysis was performed utilizing the 2D theoretical account, during the experiment consciously the engagement of the theoretical account was modified in order to accomplish most accurate and close consequences. Final consequence of the experiment of maximal rotational emphasis recorded as about 331 MPa, which ca n’t make any sort of distortion or disfunction in the flywheel even at maximal velocity of 6000 revolutions per minute, so the theoretical account should be considered as acceptable. Modal analysis of the 3D theoretical account was performed every bit good to presume the natural frequence occurs during get down up. Consequence shows that first five manners of frequences are below 150 Hz while runing maximal velocity. The stress analysis of the theoretical account was chiefly concerned about the maximal emphasis developed in that runing velocity of 6000 revolutions per minute and the effects of that maximal emphasis on the stuff. On the other manus 3D modal analysis was performed to acquire an thought about the frequence and distortion of the flywheel. Both the consequence shows that the flywheel theoretical account is equipped to manage 6000 revolutions per minute velocity in footings of both emphasis and quiver extent, So the theoretical account is acceptable.

## Aims

Flywheel is a big wheel connected to the crankshaft provides the impulse to maintain the crankshaft turning without the application of power, through the energy generated during the power shot. This energy is besides used to drive the crankshaft, linking rods and Pistons during the three idle shots of the 4-stroke rhythm. This makes for a smooth engine velocity. The flywheel forms one surface of the clasp and is the base for the ring cogwheel ( Auto Guide, 2011 ) . The flywheel is a disc that is approximately 12 to 15 inches in diameter. On a standard transmittal auto, the flywheel is a heavy Fe disc that doubles as portion of the clasp system. On automatic equipt vehicles, the flywheel is a stamped steel home base that mounts the heavy torsion convertor. The flywheel uses inactiveness to smooth out the normal engine pulsations. Therefore flywheel can be defined as ‘A heavy-rimmed rotating wheel used to minimise fluctuations in angular speed and revolutions per minute, as in a machine topic to fluctuation in thrust and burden ‘ . This study describes stress analysis of this type of flywheel utilizing its 2D theoretical account and average analysis utilizing 3D theoretical account, which were tested at maximal velocity of 6000 revolutions per minute. The maximal emphasis developed and the distortion due to quiver was closely scrutinized and all obtained consequence informations were recorded and compared with deliberate consequences to understand the failure status of the flywheel.

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This experiment had two chief aims. The first aim was to detect the degree of emphasis developed in the flywheel when it rotates in that maximal velocity of 6000 revolutions per minute, and besides to notice that the emphasis developed in the flywheel is acceptable or non with proper probe. Second aims was to look into the failure status of the flywheel which may happen due to the quiver caused by the natural frequence probably to bring forth at that maximal operating velocity, supplanting and distortion of the form of the flywheel besides was to be taken in consideration. Finally optimisation or some recommendations to do for better public presentation of the theoretical account if necessary.

This study presents the process of the experiment with all minute inside informations required for repeat of the experiments. Mathematical computation for the flywheel emphasis so presented. After this the consequences obtained in the experiment is described and discussed with possible reading of existent life scenarios. Finally few remarks are made about the optimisation of the theoretical account.

## Procedure

The theoretical account of flywheel was foremost created in CAD and saved as ‘The Initial Graphics Exchange Specification ( IGES ) format which is the standard format used to interchange geometric theoretical accounts between assorted CAD and CAE systems. The initial theoretical account created in CAD system was required to mend before get downing the emphasis and modal analysis and the repairing was done manually by importing the IGES file into ANSYS under SMOOTH ( no defeaturing ) option as this option in ANSYS does non mend the IGES files automatically therefore it was performed manually utilizing standard geometric tools. The file was imported by Utility Menu & gt ; File & gt ; Import & gt ; IGES. Then the theoretical account was repaired by canceling unneeded lines and making few excess lines as demand of the experimental theoretical account. The half subdivision of the flywheel 2D theoretical account created after mending is shown in the Figure 1.1 below.

Figure 1.1: 2D Model of the flywheel

After making and executing the emphasis analysis of the 2D theoretical account, the theoretical account was modified to 3D theoretical account. At first the engagement and the tonss of the 2D theoretical account was removed and so the 3D theoretical account created by Modelling & gt ; Operate & gt ; Extrude & gt ; Areas & gt ; About Axis, The country of the 2D theoretical account was selected and so it was extruded about Y axis by 360A° . Figure 1.2 below shows the created 3D theoretical account.

Figure 1.2: 3D Model of the flywheel

## 2D Stress Analysis

First Element Type was chosen as PLANE42 in Preprocessor & gt ; Element Type & gt ; Add for the emphasis analysis, and the Element Behaviour K3 was specified as Axisymmetric, so that ANSYS could cognize that it needs to be an axisymmetric solution. Then in Material Model elastic belongingss i.e. Young ‘s Modulus and Poisson ‘s ratio of the experimental metal chromium steel steel was mentioned as 205 GPa and 0.3 severally. In following measure the whole cross-section country needed to travel into x-axis and that was done by Modelling & gt ; Move/Modify & gt ; Areas so by seting the value in axis beginning consequently. After adverting the elastic belongingss the theoretical account was meshed utilizing smart size 4 which created a harsh mesh all over the theoretical account with 388 elements. Grid independent survey was performed for the emphasis analysis so the engagement was started from coarse and so bit by bit was being made finer for more accurate consequence. A grid independent consequence minimizes the influence of the elements or the theoretical account. In pattern a chromium steel steel flywheel has tonss of little metal atoms within itself, which bonds really strongly between each other, seting elements on the computing machine package generated theoretical account by engaging is to acquire the existent feel of practical metal theoretical account or more specifically the atoms inside it. Although it is non possible to make same figure of elements as existent atoms by package generated theoretical account, therefore the grid independent survey is being performed so that it can be said that the consequence is element or particle independent means the figure of atoms or elements does non act upon the consequences any longer. The flywheel was required to revolve in a velocity of 6000 revolutions per minute, therefore it was given as a burden for the solution in Solution & gt ; Define Loads & gt ; Apply & gt ; Structural & gt ; Inertia & gt ; Angular Velocity & gt ; Global and the value was mentioned for Y axis in rad/s. In order to defy the supplanting of the whole theoretical account along the axes restraint were given at the top and bottom line both in x axis and in y axis by Solution & gt ; Define Loads & gt ; Apply & gt ; Structural & gt ; Displacements & gt ; On Lines. At last the emphasis analysis consequence was plotted in Nodal Solution under contour secret plan.

## 3D Modal Analysis

New analysis was started for the 3D theoretical account in order to run the modal analysis by taking Solution & gt ; Analysis Type & gt ; New Analysis & gt ; Modal. Element type was chosen as SOLID95. Then the elastic belongingss were specified in same procedure as 2D emphasis analysis. The volume of the theoretical account was so meshed utilizing smart size 10 with tetrahedral, mapped free engagement. Loads were given in same topographic points as the old analysis, merely the supplanting restraints are given around the countries instead than the top and bottom lines. Before run the solution No. of Modes & A ; No. of Manners to spread out was defined as 7, and Expand Mode form was checked as yes. Then End Frequency was set as 300. Harmonizing to the demand of the experiment foremost five set of frequence was to be noted, 7 manners were chosen to do certain that no manners data get lost same manner the terminal frequence is non known before solution so it is a good pattern to set the terminal frequence rather more than what is expected originally. Finally the distortion consequences were checked in Deformed Shape under Plot Results. The quivers of the theoretical account can be checked utilizing the Animation option by Utility Menu & gt ; Plot Controls & gt ; Animate & gt ; Deformed Shape.

## Consequences

Highest runing velocity is 6000 revolutions per minute, to work out the job in Ansys it was required to change over to Radian. Thus,

6000 revolutions per minute = = 628.3 rad/sec

The above value was set as burden while work outing the job. Material of the flywheel is unstained steel, elastic belongingss of the stuff are really of import in footings of emphasis and quiver analysis. Concluding consequences or failure status depends to some extent on these belongingss. The Table 1.1 below shows the elastic belongingss of chromium steel steel. From the given informations it is possible to gain the failure status of unstained steel as a stuff.

Stainless Steel

Young ‘s Modulus

( Modulus of Elasticity )

– Tocopherol –

Ultimate Tensile Strength

– Su –

( 106 N/m2, MPa )

Output Strength

– Sy –

( 106 N/m2, MPa )

( 106 A pounds per square inch )

( 109 N/m2, GPa )

Stainless Steel, AISI 302

860

502

Steel, Structural ASTM-A36

200

400

250

Steel, High Strength Alloy ASTM A-514

760

690

*courtesy to engineeringtoolbox.com

Table 1.1: Stainless steel Steel belongingss

Calculating the emphasis on a flywheel is non easy and it is required to work out different types of equations. The form of the flywheel is a complex geometrical form which besides is a load for acquiring accurate consequences. There is a consecutive forward expression for ciphering emphasis in a rotational phonograph record,

Stress = Rim denseness A- Radius2 A- Spin speed2

But accurate practical consequence in a peculiar point of the flywheel construction can be calculated utilizing the undermentioned expression,

The centrifugal burden ( F ) moving on the thin rim with the thickness I”r can be calculated by,

F = 2Iˆ A-I?r2I”rhA-I‰2

I? : denseness of the stuff

R: radius of the ring

H: thickness of the rotor

I‰ : angular speed

The stress distribution of thin, axis-symmetric discs is merely dependent on the radius ( R ) and non on the thickness of the rotor ( H ) . Therefore it is possible to compose the status of equilibrium for the emphasis distribution as shown in equation below,

: strain, perp: normal to the fiber

: shear, || : analogue to the fiber

And the status of strain equilibrium is:

perp

Together with the stuff belongingss the undermentioned differential equation for the strains in radial and digressive way can be found and implemented in the finite component theoretical account,

=0

Digressive emphasis, ( )

*courtesy toBurg.P.V, Swiss Federal Institute of Technology

## Discussion of Consequences

The flywheel is made of unstained steel ; yield emphasis of chromium steel steel i.e. the sum of emphasis after which a lasting distortion occurs in the stuff and ultimate tensile strength for chromium steel steel which refers the interrupting point of the stuff. This belongingss or informations helps to understand the potency of the stuff in instance of managing immense emphasiss. Harmonizing to the informations given in Table 1.1, it is clear that the flywheel can take about 502 MPa emphasis without any distortion, when the emphasis is more than 502 MPa but less than 860 MPa so the flywheel will deform for good but still would non interrupt. The belongings varies with different types of chromium steel steels in market, Table 1.1 below shows their several belongingss.

## 2D Stress Analysis

For the emphasis analysis 2D theoretical account created and the job was solved utilizing the component every bit Axisymmetric as antecedently mentioned. The ground of taking axisymmetric is the second theoretical account is half cross-section of the existent theoretical account and it is symmetrical about the centreline of the axle. After making the theoretical account it was meshed with 388 elements by Smart size 4, consequence showed the maximal rotational emphasis developed was 272 MPa in the thin shell of the flywheel. Figure 1.3 ( a ) shows the initial engagement below.

Figure 1.3 ( a ) : Initial engaging with smart size 4

Contour secret plan of Nodal solution Stress in X-direction: In Nodal solution, Ansys obtains a uninterrupted distribution where it determines the norm at each node of the values of all elements connected to the node and besides within each component ; it linearly interpolates the mean nodal value obtained in the old measure ( Ansys, 2007 ) . Thus it helps to presume the sum of maximal emphasis developed more accurately. As the flywheel is in gesture about Y-axis, therefore its rotational force is moving on X-axis, therefore emphasis in X-direction is being taken into history. Figure 1.3 ( B ) shows the contour secret plan nodal solution consequence below.

Figure 1.3 ( a ) : Contour secret plan of smart size 4

The thin shell corners in the home base shows the ruddy musca volitanss i.e. maximal rotational emphasis developed at that part. At the outmost part of the flywheel holding maximal thickness therefore it has more mass than the thin shell near cardinal axial ; due to the rotary motion of the home base centrifugal force generated and the thick portion of the wheel creates a pull in that thin part attached with strong cardinal mass. Therefore due to gyroscopic consequence of the flywheel in thin disc signifier immense sum of emphasis is developing in that part.

One of the aims of this experiment was to detect this maximal sum of emphasis, so that dependability of the flywheel can be defined. In order to carry through that a grid independent survey has been made by increasing the figure of element every clip. If the developed emphasis is non so high so the theoretical account can be considered as a good theoretical account. The grid independent survey was performed by altering the mesh from Smart size 4 to Smart size 3 which increased figure of element s to 714 but the maximal rotational emphasis came same as old consequence i.e. 272 MPa. Elementss and consequences are shown in Figure 1.4 below.

Figure 1.4: Engagement and contour secret plan of smart size 3

Smart size 2 had 924 elements and that type of engagement was applied for the whole country of the theoretical account. Changing to Smart size 2 was to look into that the solution has achieved grid independence or non as both the old 2 solution consequences were indistinguishable, but increasing the figure of elements changed the solution consequence and it indicates a minimum alteration i.e. 279 MPa. Due to this alteration in consequence another repeat of experiment was performed with Smart size 1 which produced 1576 figure of elements including nodes and properties. It was being observed that the consequence were unbroken altering as the x constituent of rotational emphasis indicates 298 MPa. Figure 1.5 represents both the engagement where Figure 1.6 ( a ) and 1.6 ( B ) shows the consequences severally.

924 elements

1576 elements

Figure 1.5: Element secret plans of smart size 2 & A ; 1

Figure 1.6 ( a ) : Plot consequence of smart size 2

The figure above clearly indicates the part where maximal rotational emphasis is developing. Chiefly both the corners are point of involvement and emphasis is distributing through the thin home base.

Figure 1.6 ( B ) : Smart size 1 secret plan consequence

Further repeat was performed every bit good, this clip merely polishing four lines of that next part where upper limit emphasis has developed ; this is to go on the grid independent survey and besides to increase the elements of those lines to acquire more accurate consequence. Number of elements was increased to 2649 giving a all right mesh peculiarly in that thin part. This all right engagement of Line refinement 2 increased attendant rotational emphasiss every bit good, it recorded as 332 MPa. The consequence varies by 34 MPa so another polish was tried to accomplish grid independence i.e. stable consequence so that much more element or atoms in existent chromium steel steel flywheel can non impact the consequence every bit good. Line refinement 3 increased elements to 27007, a immense sum of addition about 25000 more elements are at that place in this new engagement which produced maximal rotational emphasis 331 MPa. Harmonizing to the addition of element figure maximal emphasis besides should increase or varies, but both the consequences are near even later consequence recorded less. So it can be said that the solution has achieved grid independence. Line refinement 2 and 3 engaging shown in Figure 1.7 below, where Figure 1.8 ( a ) and 1.8 ( B ) are the secret plan consequences severally.

2649 elements

27007 elements

Figure 1.7: Line refinement 2 & A ; 3 engagement

Figure 1.8 ( a ) : Contour secret plan of line polish 2

Figure 1.8 ( B ) : Contour secret plan of polish 3

Final consequence represents that maximal rotational emphasis developed in the thin shell subdivision of flywheel rim at maximal velocity of 6000 revolutions per minute is about 331 MPa, which is good below 502 MPa i.e. output strength of chromium steel steel. It indicates that the theoretical account of flywheel can manage 6000 revolutions per minute expeditiously without any lasting distortion or any accident. From the facets of maximal rotational emphasis degree the theoretical account is good equipt and should considered to be acceptable.

## 3D Modal Analysis

Modal analysis of the 3D theoretical account show shown above was performed in order to detect the manners of quiver occur during operation at highest velocity. Flywheel is likely to go through through natural frequence, this frequence leads to its failure. The experiment was performed to presume the sum of quiver and the distortion occurs.

A new analysis was started utilizing Modal Solution option, and so the theoretical account was meshed by Smart size 10 which creates 8970 elements in the theoretical account as shown in the Figure 1.9 below.

Figure 1.9: Elementss of the 3D Model

Based on this engaging Modal Analysis was performed utilizing the same tonss and restraint as 2D analysis. Objective of the experiment was to obtain first five manners of frequences, so No. of Modes was set to 7, to do certain that the consequence secret plans five frequences anyhow. Possible average quivers may happen during the start-up procedure and is shown Figure 1.10 below.

Figure 1.10: First Five manners of quivers

Modal Analysis: A average analysis is performed to find the quiver features ( i.e. , the natural frequences and mode forms ) of the flywheel. In ANSYS, a average analysis is besides the starting point for other, more elaborate, dynamic analyses, such as a harmonic response or a transeunt analysis. In this average quiver analysis of flywheel bearing system, the flywheel was considered as a stiff disc placement at the center of a stiff shaft supported by bearings. The public presentation of the precession in lower frequence and the nutation in high frequence split a batch with the turning rotating frequence due to gyroscopic consequence of the flywheel in thin disc signifier. The splitting manners make the system be parameter dependant. The analysis indicated that there were five flexible manners with frequence under 150 Hz. To get at the velocity of 6000 revolutions per minute, the flywheel has to go through through several quivers and the flexible hub warp

Vibration occurs in first five stairss harmonizing to the tabular array above is shown in Figure 1.11 below.

Figure 1.11: Five manners of quivers

1st, 3rd and 5th sub stairss shows the rigidness of the hub of managing quivers developed at high velocity. This rigidness of a flywheel is really of import to avoid failure conditions in high velocity state of affairs. On the other manus 2nd and 4th sub stairss indicates the flexibleness of the hub, it deflected to a certain extent to neutralize the quiver. Table 1.2 below listed the attendant distortions in each measure and Figure 1.12 shows the comparing of distorted forms.

## Sub Step

## Frequency @

## Distortions

1st

19.956

0.145324

2nd

64.454

0.160338

3rd

64.702

0.160479

4th

129.778

0.186916

5th

130.282

0.186776

Table 1.2: Frequencies in each sub measure

Figure 1.12: Comparison of distorted forms

## Decision

This study has discussed a proposed theoretical account of a flywheel and has analysed the 2D structural emphasis analysis which indicated that the material failure would non go on when the flywheel was speeded up to 6000 revolutions per minute or 628.3 rad/s. Detailed average analysis of the theoretical account has proved that both the stiff manners and the flexible manners were presented in the system. The flexible manner manifested as the hub warp form because of the application of the thin shell with low stiffness.. The aims of this experiment were to look into the potency of the proposed theoretical account of managing utmost velocity without neglecting by emphasis analysis and to construe the consequence with proper justification. Another aim was to do a Modal analysis in order to presume the manners of natural frequence at that highest seed. Both aims were met. By maintaining path of the maximal emphasis developed at that runing velocity of 6000 revolutions per minute or 628.3 rad/s, a concluding end point emphasis is recorded which is good below of the distortion force of the stuff, therefore the flywheel can run that velocity without any major distortion or breakage. Besides the first five manners of natural frequences is recorded to presume the quiver can happen during that runing velocity and the consequences are at a lower place good below 150 Hz, as the 5th manners of frequence is recorded as 130. . The consequence seems practical and acceptable.

This experiment has introduced us to the of import subjects of finite component emphasis analysis of a stuff and the 3D modal analysis which is really of import for quiver analysis of a theoretical account. In the experiment, specifying all the stuff belongingss helps to understand the demands of informations for emphasis & A ; modal analysis. Besides modeling and engagement, tracking the developed emphasis informations improves the apprehension of stress distribution on the theoretical account. For illustration, maximal emphasiss were bring forthing near the corner of the narrow thin shell whereas minimal emphasis were bring forthing near the axis and at the utmost terminal of the rim.

Finally it can be concluded that this experiment builds up a rather good apprehension of finite component emphasis analysis every bit good average analysis, and accomplishing close to accurate consequence utilizing mesh independent survey with affectional practical execution.