Composite Flywheel: A Mechanical Alternative

BY RAVI KUMAR REVANTH KUMAR III B.TECH II B.TECH ravi_mech@yahoo.co.in revanth_mec@yahoo.co.in

Department of Mechanical Engineering Sree Visvesvaraya Institute of Technology and Science Chowdarpally, Mahabubnagar – 509 204.

Abstract

The conventional flywheel characterized by low speed and high density demanded a

call for carrying out research to find viable alternative. Composite flywheel can be a

promising modification for these flywheels. In this context, flywheels made from

composite materials like epoxy, glass fiber reinforced plastic, carbon fiber reinforced

plastics is proved to be successful.

Composite flywheels have gained much interest recently as an alternative to fuel

cells or Acid batteries. The construction employs basic metallurgy to ceramic,

polymer/co-polymer, and carbon fiber techniques. The advanced flywheel made of high

strength composite filaments is able to operate at a safe speed range of 42,000 rpm to

65,200 rpm releasing large amounts of power i.e... 750 kW for about 20 seconds or even

about 100 kW for up to one hour. It requires Magnetic bearings as speeds increase, to

reduce friction found in conventional mechanical bearings.

This paper presents a theoretical approach to optimal design of flywheels to optimize

the Specific Energy Density (SED) of flywheels. The work presented also considers the

application of composite flywheels as a source of energy accumulation and less density to

strength. An overture has been made to calculate the various stresses in the design of

composite flywheel and those obtained are compared with the conventional flywheel. It

can be inferred that by using composite materials, a conventional flywheel with a weight

reduction of 22.35 % to 33.18% may be fabricated.

A Microsoft Visual basic program is developed to design the composite flywheel in

shortest period of time with more accuracy. The viability of Flywheel energy storage in

aerospace applications is also examined.

A future attempt may be made to analyze the stresses in the composite flywheel by

varying the thickness of laminates, with the aid of Analysis System Software (ANSYS).

Keywords: Composite flywheel, SED, composite filament, FES, Magnetic bearing

Introduction

What is a flywheel? Archeologists describe the flywheel as an early example of industrial

automation; it was used in the potter’s wheel to enable the production of pottery at a rate

faster than hand molding. Later, several forms of engine technology required flywheel for

damping the effect of shaft speed fluctuations. They are universally appreciated as a

kinetic store of energy.

Fly wheel energy storage grows in proportion to flywheel mass and square of its

rotational velocity. Selection of rotating speed and mass is limited by stress.

KE =

Where,

m = mass

r = mean radius

ω = angular velocity of rim in radians per sec

A flywheel is traditionally composed of metals like cast iron, steel which are

characterized by low speed and high density but a composite flywheel is considered to

have more kinetic storage per weight

Up until recently most satellites used batteries to store energy for those

times when the solar cells couldn't produce enough electricity for the satellite. But

Batteries in space have the same problem as batteries on earth. They wear out after about

1000 heavy charge/discharge cycles, and while they are wearing out their capacity is

continually reduced. To the rescue comes the high speed composite flywheel that runs at

100,000 RPM and are made mostly of plastic and carbon fiber. They use magnetic

bearings which have no contacting parts unlike ordinary bearings which wear out too fast.

What are composite materials?

Composite materials are a new class of materials that combine two or more

separate components into a form suitable for structural applications. While each

component retains its identity, the new composite material displays macroscopic

properties superior to its parent constituents, particularly in terms of mechanical

properties and economic value. Resin Composites, Metal Composites, Carbon-Carbon

Composites, Hybrid Metal Carbon-Carbon Composites and Hybrid Resin Carbon-Carbon

Composites are a few prominent examples of composite materials.

Why make composite flywheels?

The faster we can spin a flywheel and the more massive we can make it, the

flywheel, and the more kinetic energy we can store in it. However, at extreme speeds,

even metal flywheels can literally tear themselves apart from the shear forces which are

generated. Further, the energy storage characteristics of the flywheel are influenced more

strongly by its maximal rotational velocity than by its mass.

Manufacturing of composite flywheel:

The flywheel rim and arbors are constructed using a combination of Toray M30S

intermediate modulus graphite, Toray T700 standard modulus graphite, and

Owens-Corning S2 fiberglass (Table) the resin is a Fiberite 977-2 thermosetting epoxy

resin system toughened with thermoplastic additives.

Mechanical Properties:

Conventional materials Vs Composite materials:

Two important mechanical properties of any system are its tensile strength and

stiffness

Density  [kg/m3] 

Strength  [MN/m2] 

Specific strength  [MNm/kg] 

Steel  (AISI 4340)

7800   1800  0.22

Cast Iron 7200 1600 .19

Alloy  (AlMnMg)

2700   600  0.22

Titanium  (TiAl6Zr5)

  4500 1200  0.27

GFRP  (60 Vol% E-Glass)

2000 1600  0.80

CFRP  (60 Vol% HT Carbon)

1500   2400 1.60

Source: www.theflywheel.com

 

Importance of epoxy

Epoxy is a prominent resin used in manufacture of composite flywheel.

A few Mechanical properties of epoxy;

State: Cycloaliphatic

Application: casting resins and compounds

Tensile Strength (MPa)   3416

Tensile Strength (MPa)   56 - 83

Compressive Strength (MPa)

at yield or break

104 - 138

Flexural Strength (MPa)

at yield or break

  69 - 90

Elongation at break (%)   2 – 10

Deflection Temperature (ºC) 94 - 233

Specific Gravity  1.16 - 1.21

Melting Temperature (ºC) Melting Temperature (ºC)

Merits of composite flywheel

Compact

Energy storage system more efficient

Less weight

Long life

High efficiency

Low maintenance

No aerodynamic noise

De merits

Safety concerns

High material costs

Expensive magnetic bearing

Applications:

Composite Flywheels are not only used for Electric Vehicles and Hybrid Electric but it

also finds space applications.

DESIGN OF COMPOSITE FLY WHEEL

In the design of composite flywheel, the following is usually considered

1. power developed or energy stored

2. speed of the drive or flywheel

3. material used

The following requirements must be met for the design of fly wheel

(a)The flywheel should have sufficient strength so that it will not fail under any working

conditions with in the desired limit

(b)The cost of the flywheel should not be so much that it will not fail under operating

condition.

(c)With the mountings of flywheel, the vibration set up in the engine parts and the base

should be minimum. This is the most desirable, feature of the flywheel mounting.

(d)The alignment of the flywheel and other parts such as shafts, keys should be

considered because they effect on the performance of the flywheel and also total engine

(e)The lubrication of the engine fly wheel should be satisfied wherever required

Energy stored in flywheel:

When flywheel absorbs energy as in the case of internal combustion engines, velocity

increases and the stored energy is given out, the velocity or speed diminishes.

Total kinetic energy E = i /2

i = mass moment of inertia of flywheel about the axis of rotation in KgMts .

ω = mean angular speed of the flywheel in Rad / sec.

i = MK For rim type.

i = MK / 2 for disc type.

K = Radius of gyration of flywheel in mts.

M = Mass of fly wheel in kgs.

Fluctuation of energy

If the velocity of flywheel changes, energy it will absorb or gives up is proportional to the

difference between the initial and final speeds, and is equal to the difference between the

initial and final speeds, and is equal to the difference between energies which could give

out, if brought to a full stop position that which is still stored in it at the reduced velocity.

E = = MAX - MIN

= i ω /2 - i ω /2

= i / 2 (ω - ω )

= i / 2(ω - ω ) x (ω + ω )

= i x ω (ω - ω ) ω= (ω + ω )/2

= i x ω (ω - ω )/ ω

E = = i x ω x Cs

R = Mean radius of rim.

Cs = Co-efficient of fluctuating speed.

K = Radiation of gyration.

K = R (Assumption)

E = = Fluctuation of energy.

ω = Mean angular velocity of flywheel.

M = Mass of flywheel rim.

DETERMINATION OF MASS OF FLYWHEEL

Only the weight of fly wheel rim is considered

E = = i x ω x Cs

CALCULATION OF MASS FOR RIM TYPE OF FLY WHEEL

i = M x K (for rim type of fly wheel)

= M x K x ω x Cs

M = / (K x ω x Cs)

M = / (K x ω x 0.03) (for I.C Engines Cs = 0.03)

M = Mass of the rim

CALCULATION OF MASS FOR DISK TYPE OF FLY WHEEL

i = M x K / 2

= M x K x ω x Cs / 2

M = x 2 / (K x ω x Cs)

M = / (K x ω x 0.03) (for I.C Engines Cs = 0.03)

M = Mass of the disc

DESIGN OF RIM

Let, work done per cycle or energy supplied per cycle = P x 60 / n.

P = power transmitted in Watts.

n = Number of working strokes per minute. = N in case of two stroke engine

= N / 2 in case of four stroke engine

We Know Density = Mass / Volume.

Mass of the rim M = Density x Volume of the rim.

M = x x D x W x t.

M = x x D x 2 x t W=2 x t

t = M / x x D x 2

W=2 x t

W = Width of rim in Mts.

D = mean diameter of flywheel in Mts.

t = thickness of rim in Mts.

Knowing the ratio between which is usually taken as 2

W / t = 2.

We may find the width and thickness of rim. When the flywheel is to be used as pulley,

the width of the rim should be taken 2 to 4 greater than the width of belt

DESIGN OF DISK

Mass of the disk M = Density x Volume of the rim.

Mass of the disk M = x x D x t /4.

t = M x 4 / x x D (square)

D = Outer diameter of disk in Mts.

t = thickness of disk in Mts.

= Density of disk in Kg / Mts

DESIGN OF ARMS

Arms are subjected to bending stresses. So they are considered to be elliptical

cross section. Arms are considered as cantilever beams because maximum bending

moment in the Arm occurs at the Hub end.

Let

a = Major axis of the arm.

b = minor axis of the arm.

M = Bending moment in the arm.

n = Number of arms.

Tmax = Maximum torque transmitted by the shaft.

Rmean = Mean radius of the rim.

Rhub = Diameter of the hub.

Z = section modulus for the cross-section of the rim.

= Permissible Bending stresses of the rim.

Assuming = /2.

We know that the load at the mean radius of the rim F = Tmax / Tmean

Load on each arm = Tmax / Rmean x n.

Maximum bending moment lies on the arm of the hub.

M = Tmax (Rmean – Rhub) / Rmean x n

We know that M / I = / y

M / Z =

Z = x b x a / 32

Z = x 4 x b /32 a= 2 x b

b = (32 x M / x II x 4)

a = 2 x b

We may find the value of a and b

STRESSES IN FLY WHEEL RIM

1) Tensile stress due to centrifugal force

The tensile stress in the rim due to the centrifugal force assuming that the rim

is constrained by th arms is determined in a similar way as thin cylinder subjected to

internal pressure.

Let = Tensile or Hoop stress.

We know = x v in N / Mts

2) Tensile bending stress caused by Restrain of arms

The tensile bending stress in the rim due to the restraint of the arms based on the

assumption that each portion of the rim between a pair of arms behave like a beam fixed

at both ends and uniformly loaded such that lengths between find ends.

L = x D / n

Where n = Number of arms, this may vary from 4 to 12. Then uniformly

distributed load ‘F’ per meter length will be equal to the centrifugal force between a pair

of arms.

F = W x t x x R x ω in N / Mts.

Maximum bending moment M = F x L / 12

Section modulus Z = b x t / 6

Bending stress = M / Z

= 19.74 x x v x R / n x t.

3) Total stresses in Rim = +

If the arms of fly wheel do not stretch at all and were placed very close together,

then centrifugal force will not set up stress in the rim. In other words will be zero. On

other hand if the arms are stretched enough to allow free expansion of the rim due to the

arms, will be zero.

It has been by G.lanza the arms of a flywheel stretch about ¾ of the

amount necessary for free expansion. Therefore the total stress in the rim

= 3/4 + 1/4

= x v (.75 + (4.935 x R / n x t)).

R = Mean radius of flywheel in Mts.

= density in Kg/ Mts

= Angular speed of flywheel in rad / sec.

V = Linear velocity of fly wheel in cu / sec.

= Tensile or hoop stress in N / Mts

= Bending stress in N / Mts

4) Residual stresses

This includes shrinkage stress impact stress, and stresses caused by operating

torques and imperfection in the material. They are taken into account by the use of

suitable factor of safety.

STRESSES IN FLY WHEEL ARMS

1) Tensile stress due to centrifugal force

Due to the centrifugal force acting on the rim, the arms will be subjected

to direct tensile stress whose magnitude is same as the tensile stress in the arms

= ¾ = x v x ¾

2) Bending stress due to the torque being transmitted

Due to the torque transmitted from the rim to shaft or from the shaft to

rim, the arms will be subjected to bending, because they are required to carry the full

torque load. In order to find out the maximum bending momentum on the arms.

It may be assumed as cantilever beam fixed at the hub and carrying a

concentrated load at the free end of the rim.

Let T = Torque transmitted.

R = Mean radius

r = radius of hub

z = section modulus of the arm

Load on each arm = T / R x n

And Maximum bending momentum which lies on the arm at the hub

M = T x (R – r)/ R x n

Bending stress in arm = M / Z = T x (R-r)/ R x n x z.

Total tensile stress in arms at hub end = +

Conclusion

The future seems to lie in the Composite flywheel specified by low density to

strength and Specific Energy Density (SED). It can be concluded that by using composite

materials, a conventional flywheel with a weight reduction of 22.35 % to 33.18% may be

fabricated. The weight reduction in flywheel may boost Aerospace explorations.

The Cost of fabricating isn’t encouraging, nevertheless, composite flywheels wheels

are a viable option for many applications, and will continue to attract new users as their

technology improves.

References:

1. D.J.Kim, D.G.Lee and S.K.Choi, Proceeding of Optimization of flywheel design,

Journal of Current Science, Volume 2, April 2001, Pg No’s 24-29.

2. W. F. Punch III, R.C. Averill, E.D. Goodman, S. C. Lin, and Y. Ding, February

2002,“Design Using Genetic Algorithms - Laminated Composite Structures”, IEEE

Expert, Vol. 10 (1), Pg No’s 42-49.

3. Machine design, R S Khurmi, 2003 edition, Pg No’s:701-741

4. Design of machine elements, V. B Bhandari, 23rd reprint 2005, Pg No’s: 628-647

5. Design Data Book, K.Mahadevan, K.Balaveera Reddy, Pg No’s: 352-356

Websites:

www.theflywheel.com

www.tribologysystems.com

Guided by

M.Naveen Babu,

Asst.professor,

Dept. of Mech Engg..