Composite Flywheel: A Mechanical Alternative BY RAVI KUMAR III B.TECH
[email protected]
REVANTH KUMAR II B.TECH
[email protected]
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 =
1 2 2 mr ω 2
Where, m
= mass
r
=
ω
=
mean radius 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
Source: www.theflywheel.com
2400
1.60
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) Tensile Strength (MPa) Compressive Strength
3416 56 - 83 (MPa) 104 - 138
at yield or break Flexural Strength
(MPa)
at yield or break Elongation at break (%) Deflection Temperature (ºC) Specific Gravity 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
69 - 90 2 – 10 94 - 233 1.16 - 1.21 Melting Temperature (ºC)
•
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 ω 2 /2 i = mass moment of inertia of flywheel about the axis of rotation in KgMts 2 . ω = mean angular speed of the flywheel in Rad / sec.
i = MK 2
For rim type.
i = MK 2 / 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 1 = ∆ E = MAX
ke
- MIN ke
= i ω 1 2 /2 - i ω 2 2 /2 = i / 2 (ω 1
2
- ω2 2 )
= i / 2(ω 1 - ω 2 ) x (ω 1 + ω 2 ) = i x ω (ω 1 - ω 2 ) =ixω
2
ω= (ω 1 + ω 2 )/2
(ω 1 - ω 2 )/ ω
E 1 = ∆ E = i x ω 2 x Cs R = Mean radius of rim. Cs = Co-efficient of fluctuating speed. K = Radiation of gyration. K = R (Assumption) E 1 = ∆ 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 1 = ∆ E = i x ω 2 x Cs
CALCULATION OF MASS FOR RIM TYPE OF FLY WHEEL i = MR x K2
(for rim type of fly wheel)
∆ E = M R x K 2 x ω 2 x Cs M R = ∆ E / (K 2 x ω 2 x Cs) M R = ∆ E / (K 2 x ω 2 x 0.03)
(for I.C Engines Cs = 0.03)
M R = Mass of the rim CALCULATION OF MASS FOR DISK TYPE OF FLY WHEEL i = MD x K2 / 2 ∆ E = M D x K 2 x ω 2 x Cs / 2 M D = ∆ E x 2 / (K 2 x ω 2 x Cs) M D = ∆ E / (K 2 x ω 2 x 0.03)
(for I.C Engines Cs = 0.03)
M D = 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 R = Density x Volume of the rim. M R = ρ x Π x D x W x t. M R = ρ xΠ x D x 2 x t2
W=2 x t
t = MR / ρ xΠ 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 D = Density x Volume of the rim. Mass of the disk M D = ρ x Π x D 2 x t /4. t = M D x 4 / ρ x Π x D (square) D = Outer diameter of disk in Mts. t = thickness of disk in Mts.
ρ = Density of disk in Kg / Mts 3
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.
σ BEND = Permissible Bending stresses of the rim. Assuming σ BEND = σ TENSILE /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 = σ BEND / y M / Z = σ BEND Z = Π x b x a 2 / 32 Z = Π x 4 x b 2 /32
a= 2 x b
b = (32 x M / σ BEND x II x 4)
1/ 3
a=2xb 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 σ t = Tensile or Hoop stress. We know σ t = ρ x v
2
in N / Mts 2
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= Π xD/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 ρ x R x ω 2 in N / Mts. Maximum bending moment M = F x L 2 / 12 Section modulus Z = b x t 2 / 6 Bending stress σ BEND = M / Z = 19.74 x ρ x v
2
x R / n 2 x t.
3) Total stresses in Rim = σ t + σ BEND 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 σ t will be zero. On other hand if the arms are stretched enough to allow free expansion of the rim due to the arms, σ BEND 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
σ TOTAL = 3/4 σ t + 1/4 σ BEND =ρ x v
2
(.75 + (4.935 x R / n 2 x t)).
R = Mean radius of flywheel in Mts.
ρ = density in Kg/ Mts 3 ω = Angular speed of flywheel in rad / sec. V = Linear velocity of fly wheel in cu / sec.
σ t = Tensile or hoop stress in N / Mts 2 σ BEND = Bending stress in N / Mts 2
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
σ t = ¾ σ HOOP = ρ x v
2
x¾
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 σ BEND = M / Z = T x (R-r)/ R x n x z. Total tensile stress in arms at hub end σ TOTAL = σ t + σ BEND
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.
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Websites: www.theflywheel.com www.tribologysystems.com
Guided by M.Naveen Babu, M .Tech ( CAD / CAM ) Asst.professor, Dept. of Mech Engg..
