Flywheel stores the energy when supply is greater than the requirement and release energy when requirement

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Comparative Study of Different Geometry Flywheelby Analytical and Ansys Samshette S.M.1, Swami M.C.2 1

(Student of M.E.Mechanical Department, M.S.Bidve Engineering College Latur,Maharashtra,India.) 2 (Mechanical Department, M.S.Bidve Engineering College Latur,Maharashtra,India.)

Abstract : Flywheel stores the energy when supply is greater than the requirement and release energy when requirement is greater than supply. In Present work initially we design different geometry of flywheel like solid, rim, section cut and six spoke flywheel keeping constant mass.Then we calculate various functional value of flywheel like kinetic energy, specific energy stress etc. for respective flywheel. From this comparative study we conclude six spoke flywheel store more kinetic energy then other flywheel. Lastly with the help of ANSYS we calculate Von-Mises Stress & total deformation of flywheel. From ANSYS we conclude all results are valid & permissible range. Keywords : Flywheel Design, Stress,Kinetic Energy, Ansys.

I. Introduction Flywheel is a rotating mechanical element which is store energy of rotational form[1] Flywheels used to achieve smooth operation of machine [2]. Flywheel stores the energy when supply is greater than the requirement and releases energy when requirement is greater than supply[3]. The stored kinetic energy relies on the mass moment of inertia and rotational speed [3]. The performance of a flywheel can be attributed to three factors, i.e., material strength, geometry (cross- section) and rotational speed [4]. Flywheels have become the subject of extensive research as power storage devices for uses in vehicles [4].Flywheel energy storage systems are considered to be an attractive alternative to electrochemical batteries due to higher stored energy density, higher life term, and deterministic state of charge and ecologically clean nature [4]. Flywheel is basically a rechargeable battery [4]. Present investigation deals with kinetic energy Storing capability of different geometry of flywheel, functional value and stress produced in respective flywheel with the help of analytical and ANSYS.

II. Design Of Different Geometry Flywheel 2.1. Design Of Solid Disk Flywheel Various parameters of solid disk flywheel are given as follows. Material used for solid disk flywheel Gray Cast Iron Outer diameter of disk (Do disk) = 500 mm Inner diameter of disk (Di disk) = 130 mm Outer diameter of hub (Do hub) = 130 mm Inner diameter of hub (Di hub) = 50mm Width of hub (Whub) =80mm Width of disk (Wdisk) =38mm Density (ρ) = 7510 kg/m3 [5] Poisons ratio (υ) = 0.23[5] Moment of Inertia (M.I.) of solid disk flywheel = 1.7594 kg-m2[7]N = 750RPM [6] Mass of solid disk flywheel = 60Kg [7] Table: 1 Calculation of various Functional values of solid disk flywheel Functional values Angular velocity (ω) Surface speed (vs) Energy stored in flywheel (Ek) Specific energy( Ek,m) Energy Density ( E k,v)

Formula 2×π×N/ 60 [6] π×D×N / 60 [6] ½ × Itotal× ω2[6] Ek/ Mtotal[6] (Ek/ Mtotal)× ρ[6]

Calculation 2×π×750 / 60 π×0.500×750/ 60 ½ × 1.7594 ×78.532 5.402/ 60 0.090×7510

Value 78.53 rad/sec 19.63 m/s 5.402 KJ 0.090 kJ/kg 679.029 KJ/m3

Table:2 Calculation for Stress in solid disk flywheel Stress Tangential Stress( t) Radial Stress( r) Resultant Stress

Formula & Calculation 2

3+ 8

(Rihub2+Rodisk2-

7510×(78.53)2 2

3+ 8

3+0.23

2 3+0.23

8

3+

R2mean)[6]

(0.0252+0.2502-

(Rihub2+Rodisk2-

7510×(78.53) √t2+r2

8

Value(Mpa) 1+3

Rihub 2×Rodisk 2 R2 2

1+3×0.23 3+0.23

0.13752)

− R2)[6]

0.788

2

(0.025 +0.250 -0.000625x0.625/0.1375 2-.13752)

= √0.9952+0.7882[6]

DOI: 10.9790/1684-12530106

0.995

1.296

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Comparative Study of Different Geometry Flywheelby Analytical and Ansys 2.2.Design Of Rim Flywheel Various parameters of optimal solid disk flywheel are given as follows. Material used for solid disk flywheel Gray Cast Iron Outer diameter of rim (Do rim) = 500 mm Inner diameter of rim (Di rim) = 440 mm Outer diameter of hub (Do hub) = 120 mm Inner diameter of hub (Di hub) = 50mm Width of plate (Wplate) =22mm Thickness of rim (Trim) =30mm Density (ρ) = 7510 kg/m3[5]Poisons ratio (υ) = 0.23[5] Moment of Inertia(M.I.) = 2.283 kg-m2[7]N = 750RPM[6] Mass of rim flywheel = 60Kg[7] Table:3Calculation of various Functional values of rim flywheel Functional values Angular velocity (ω) Surface speed (vs) Energy stored in flywheel (Ek) Specific energy( Ek,m) Energy Density ( E k,v)

Formula 2×π×N/ 60[6] π×D×N / 60[6] ½ × Itotal× ω2[6] Ek/ Mtotal[6] (Ek/ Mtotal)× ρ[6]

Calculation 2×π×750 / 60 π×0.500×750/ 60 ½ × 2.283 ×78.532 7.039/ 60 0.1173×7510

Value 78.53 rad/sec 19.63 m/s 7.039 KJ 0.1173 kJ/kg 880.92 KJ/m3

Table: 4 Calculation for Stress in rim flywheel Stress Tangential Stress( t)

Formula & Calculation 2

3+ 8

7510×(78.53)2 2 3+

Radial Stress( r) Resultant Stress

(Rihub2+Rodisk2-

8

3+0.23 8

Value(Mpa) 1+3 3+

R2mean)[6]

(0.22o2+0.2502-

Rihub 2×Rodisk 2 (Rihub2+Rodisk22 3+0.23

7510×(78.53)

8

R2

2

1+3×0.23 3+0.23

− R )[6]

2 0.0484×0.0625

(0.220 +0.250 -

1.533

0.2352)

2

0.235x0.235

0.0168

0.2352)

t2+r2 = √1.5332+0.1682[6]

1.533

2.3.Design Of Section Cut Flywheel Various parameters of optimal solid disk flywheel are given as follows. Material used for solid disk flywheel Gray Cast Iron Outer diameter of rim (Do rim) = 500 mm Inner diameter of rim (Di rim) = 440 mm Outer diameter of hub (Do hub) = 120 mm Inner diameter of hub (Di hub) = 50mm Width of hub (Whub) =85mm Width of rim (Wrim) =85mm Width of plate (Wplate) =24mm Thickness of rim (T rim) =30mm Density (ρ) = 7510 kg/m3[5]Poisons ratio (υ) = 0.23[5] N = 750RPM[6] Mass of optimized solid disk flywheel = 60Kg [7] Moment of Inertia(M.I.) of optimized solid disk flywheel = 2.337 kg-m2[7] Table:5Calculation of various Functional values of section cut flywheel Functional values Angular velocity (ω) Surface speed (vs) Energy stored in flywheel (Ek) Specific energy( Ek,m) Energy Density ( Ek,v)

Formula 2×π×N/ 60 [6] π×D×N / 60 [6] ½ × Itotal× ω2[6] Ek/ Mtotal[6] (Ek/ Mtotal)× ρ[6]

Calculation 2×π×750 / 60 π×0.500×750/ 60 ½ × 2.337 ×78.532 7.206/ 60 0.1201×7510

Value 78.53 rad/sec 19.63 m/s 7.206 KJ 0.1201 kJ/kg 901.951 KJ/m3

Table:6Calculation for Stress in section cut flywheel Stress Tangential Stress( t)

Formula & Calculation Vs2 7510×(19.63)2

Value(Mpa)

Bending Stress( b)

Π2Vs2 Do rim/i2Trim Π2x19.632x0.500x7510/42x0.030 ¾ t+¼b ¾ x 2.893+¼ x 29.75

29.75

Total Stress

DOI: 10.9790/1684-12530106

2.893

9.60

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Comparative Study of Different Geometry Flywheelby Analytical and Ansys 2.4.Design Of Six Spoke Flywheel Various parameters of optimal solid disk flywheel are given as follows. Material used for solid disk flywheel Gray Cast Iron Outer diameter of rim (Do rim) = 500 mm Inner diameter of rim (Di rim) = 410 mm Outer diameter of hub (Do hub) = 130 mm Inner diameter of hub (Di hub) = 50mm Width of hub (Whub) =90mm Width of rim (Wrim) =90 mm Density (ρ) = 7510 kg/m3[5]Poisons ratio (υ) = 0.23 [5] Thickness of rim (Trim) =45mm N = 750RPM [6] Mass of optimized solid disk flywheel = 60Kg [7] Moment of Inertia(M.I.) of optimized solid disk flywheel = 2.603 kg-m2[7] Table:7Calculation of various Functional values of six spoke flywheel Functional values Angular velocity (ω) Surface speed (vs) Energy stored in flywheel (Ek) Specific energy( Ek,m) Energy Density ( E k,v)

Formula 2×π×N/ 60 [6] π×D×N / 60 [6] ½ × Itotal× ω2[6] Ek/ Mtotal[6] (Ek/ Mtotal)× ρ[6]

Calculation 2×π×750 / 60 π×0.500×750/ 60 ½ × 2.6038 ×78.53 2 8.026/ 60 0.1337×7510

Value 78.53 rad/sec 19.63 m/s 8.026 KJ 0.1337 kJ/kg 1004.087 KJ/m3

Table:8Calculation for Stress in six spoke flywheel Stress Tangential Stress( t) Bending Stress( r) Total Stress

Formula & Calculation Vs2 7510×(19.63)2 Π2Vs2 Do rim/i2Trim Π2x19.632x0.500x7510/62x0.030 ¾ t+¼b ¾ x 2.893+¼ x 8.815

Value(Mpa) 2.893 8.815 4.373

III. Modelling Of Flywheel

Fig.1 Solid Disk Flywheel

Fig.3 Section Cut Flywheel

DOI: 10.9790/1684-12530106

Fig.2 Rim Flywheel

Fig.4 Six Spoke Flywheel

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Comparative Study of Different Geometry Flywheelby Analytical and Ansys IV. Analysis Of Flywheel Using Ansys 4.1. Analysis Of Soild Flywheel

Fig.5. EquiVon Mises In Solid Flywheel

Fig.6.Deflection in Solid Flywheel

4.1. Analysis Of Rim Flywheel

Fig.7. EquiVon Mises In rim Flywheel

Fig.8. Deflection in rim Flywheel

4.3. Analysis of Section Cut Flywheel

Fig.9. EquiVon Mises In Section cut Flywheel

DOI: 10.9790/1684-12530106

Fig.10. Deflection in Section cut Flywheel

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Comparative Study of Different Geometry Flywheelby Analytical and Ansys 4.4. Analysis Of Six Spoke Flywheel

Fig11. EquiVon Mises In Six spoke Flywheel

Fig.12. Deflection in Six spoke Flywheel

V. Result And Discussion The results obtained for the flywheel on the basis of their functional values and equivalent max. Vonmises stresses and total deformation available into the flywheel. From comparison it is found that energy stored into the flywheel is increasing from solid toSix spoke type flywheel. Equivalent max. Von- mises stresses and total deformation available into the flywheel goes on increasing from solid to spoke type flywheel but it is under permissible limit. Table:9 Various functional value introduced in different flywheel Functional values

Solid Flywheel

Moment of inertia(I) Kg-m2 Kinetic energy(E) stored KJ Spe. Energy KJ/kg Spe. Density KJ/m3

1.7594 5.402 0.090 679.029

Rim Flywheel 2.283 7.039 0.1173 880.92

Section Cut Flywheel 2.337 7.206 0.1201 901.95

Six spoke Flywheel 2.603 8.026 0.133 1004.087

Table:10 Stress introduced in different flywheel Stress(Mpa)

Rim Flywheel 1.533 0.0168 1.533

Solid Flywheel 0.9...