The History Of The Flywheel Biology Essay
For over 1000s of old ages, flywheels have been used in thrower wheels and spindle wheel coils Gowayed et al. , 2002 The construct of hive awaying energy in a rotating disc day of the months as far back as 2400 BC when revolving wheels were used by Egyptians to handcraft clayware. In fact, flywheel systems were widely used in mundane life ( Genta, 1985 ) : in warring chariots, H2O pumps and even power coevalss. However, these conventional flywheels are non every bit efficient as energy storage devices due to the big sum of mass required for the comparatively meager sum of energy stored non to advert the capableness of presenting power for merely a comparatively short period.
The coming of the industrial revolution brought about the important progresss of the flywheels. In the eighteenth century, Man witnessed the widespread usage of metal in the building of machines and shortly, flywheel had found its manner into steam engines. This development of the flywheel had been attributed to the plants of James Watt. With flywheels made of dramatis personae Fe, a higher mass minute of inactiveness could be achieve and therefore a important weight salvaging every bit good. During the industrial revolution, James Pickard developed a solution for transforming reciprocating to rotary gesture with the combination of a grouch and flywheel. And it was non till the last 30 old ages that we witness high public presentation flywheels being significantly developed with pronounced betterment and show the possible as energy storage systems in a broad scope of applications.
The energy crisis of so 1970s marked the beginning of another important epoch for the development of flywheels as the demand to seek for an alternate energy storage implement. Large sum of money were invested by the authoritiess of many states into the development of flywheel energy storage engineering with subsequent constitution of research plans in the development of flywheel devices as alternate energy storage systems ( Genta, 1985 ) . However, development gait since to decelerate down as fuel monetary values begin to stabilized in the early 1980s.
That peculiar clip period was however a important development epoch for the flywheel ; during which the usage of flywheels are explored and developed for electrical vehicles. In add-on it was besides explored as a device to assist public-service corporations pull off peak power demand. With the incorporation of high specific strength advanced composite stuffs into flywheel designs, weight decreases and strength increase can be achieved ; and this can non be achieved with the usage of metallic metal. However, the usage of flywheels can yet be commercialized even with the important betterments in the design construct of flywheel as it remains a challenge still to plan flywheel systems that are cost competitory to other energy storage devices. In add-on, complexs, though stronger than metal, would necessitate the usage of advanced bearings due to the inability to defy certain forces exposed in high public presentation application ( Kim, T.H. 2003 ) .
The 1990s witnessed developments in stronger, lightweight composite stuffs, magnetic bearings and other electronic devices, and all of which contribute to the exciting development of the flywheel. Excessively high rotational velocity could now be reached, with a subsequent increase in energy stored, doing them a possible campaigner once more for energy storage system of superior public presentation. As a sum-up, the betterment in the flywheel speedy energy recovery, high efficiency, low care and long service life, high sum of stored energy per unit volume and mass, high end product power degrees, every bit good as lower merchandise and operational cost ( Horner, 1996 ) every bit good as environmental friendly constituents are all that have made the flywheel energy storage system a executable option.
1.1.2 Flywheel as an Energy Storage Device
Flywheel energy storage ( FES ) has, in assorted past researches, turn out its high quality over conventional battery engineering based energy storage system in footings of its higher energy denseness, lastingness, rapid charge and discharge capableness, every bit good as its tolerance over a broad scope of temperature with really infinitesimal environmental concerns ; and with the advancement in power electronics, loss decreases techniques and advanced stuffs, the so apparently impossible thought of economical flywheel energy storage ( FES ) devices are no longer chimeral ( Hebner et al, 2002 ) . In fact, all of the prepossessing features mentioned briefly above ( in comparing with those that of conventional battery system ) are what that consequence in the advanced flywheel systemsaa‚¬a„? appeal as one of the fast- gaining attending option for energy storage devices. ( Arvin & A ; Bakis, 2006 )
Figure 1.1 Schematics of the basic constituents of a flywheel energy storage system ( Rojas 2003 )
Figure 1.2 Energy flow in flywheel energy storage system
A flywheel is an inertial energy storage system where the revolving mass maps as the energy storage consideration. While connected to the motor ( perchance electrical motor ) , a flywheel can be accelerated to a specific angular speed. In this procedure, electrical energy was converted into kinetic energy and the revolving inactiveness of the composite rotor Acts of the Apostless to hive away this signifier of mechanical energy. When the demand arises, the mechanical energy can be transformed back to electrical power by the motor. Therefore, the motor in the flywheel system acts non simply as a motor to speed up the energy hive awaying procedure but besides as a generator in retrieving the transformed electrical energy.
A typical flywheel energy storage system consists of five primary constituents ( Lazarewicz et al. , 2006 ) , viz. the rotor, the bearings, the motor/generator unit, the vacuity enclosure and the power electronics.
A rotor consists of a hub and rim. As the rim is the chief revolving mass of the rotor, it is rather easy to grok the fact that the rim Acts of the Apostless to hive away most of the energy whereas the hub maps to link to the rim to a shaft.
The revolving flywheel shaft on the other manus is supported by bearings which could either be of the mechanical or magnetic assortment. These bearings allow for low opposition to rotor rotary motion. However, magnetic bearings are preferred over mechanical 1s due to the energy loss associated with energy loss.
The motor, as the 3rd major constituent introduced, acts to speed up the rotor when electrical energy us supplied to it ; whereas the generator acts to pull out electrical energy from the revolving rotor by slowing the rotor. This is in conformity with the rule of preservation of energy. As a consequence of the rotor slowing, torsion is necessarily produced and is typically transferred between the rotor rim and the motor unit via the hub and the shaft. In add-on, as the happening of input and end product events are non coincident, the combination of the motor and generator into a individual functional unit is typically done to the advantages of weight and cost decrease ( Hebner et al. 2002 ) .
In add-on, a low force per unit area, vacuity environment is maintained via the usage of a force per unit area vas enclosure, which serves besides to back up the structural gathering of the flywheel and bearing system. This vacuity compartment besides serves to house all of the revolving constituents of the flywheel to cut down aerodynamic retarding force. Other than that, such a compartment is besides important in protecting the system from ruinous failure as a effect of high energy dust.
The power electronics on the other manus act as the interface between the motor/ generator unit and that of the electrical power system by change overing the input power into a suited electrical signal for the operations of the motor/ generator unit.
Flywheel energy storage devices have the possible to hive away a higher sum of energy per unit mass than typical chemical batteries. Where design weight is of major concern, and where maximal energy storage is a cardinal necessity, flywheel energy storage systems seem to offer the most appealing capablenesss. This is peculiarly so in infinite applications where the important design weight necessitates the demand for a high energy storage capacity in the smallest available size and mass ( and therefore weight ) . Other than its high specific energy denseness, flywheel besides possesses superior specific power and when used with magnetic bearings and advanced motor/ generator system, more than 90 % of the storage energy can be retrieved, an efficiency far more superior than that if conventional chemical batteries are used where the rescued energy constitutes less than 80 % of the energy input. In add-on, the increase of the sum of energy stored in flywheels can be achieved via the addition of velocity of the revolving rotor while chemical batteries would perchance necessitate some reassembling of the connexions from analogue to consecutive.
Flywheels are really effectual devices in avoiding imbalanced or outsize design of power systems due to the manner they store energy and this is particularly important in the rescue of peak power on demand. For instant entree to the coveted efficiency of energy storage every bit good as energy required, flywheels repeat the charging and discharging rhythm. This procedure of bear downing and dispatching occurs at a rapid velocity as both procedures occur in the really same motor/generator. In add-on, the flywheel life will non be affected with the big sum of bear downing and reloading rhythms whereas chemical batteries undergoing a similar procedure will necessitate a replacing after every few old ages. In add-on, flywheel, as a mechanical type of battery, is besides tolerant of the appendage of temperatures and as flywheels do non incorporate acidic and other risky stuff, flywheels are easy handled during fabrication procedure, and disposed of at the terminal of the flywheelsaa‚¬a„? life rhythms.
Flywheel energy storage systems had since found its manner into assorted applications such as transit and infinite orbiters, to call a few. In transit, flywheel systemsaa‚¬a„? deep recharge and rapid bear downing capableness, the ability to supply high pulsations of power every bit good as the tolerance to a broad operating temperature scope every bit good as the thirster runing life on top of weight decrease make flywheel systems an obvious pick in replacing chemical batteries in nomadic applications such as electric vehicles. ( Hebner et al 2002 ) .
A dependable, steady province power quality is of critical importance for critical fabrication, infirmaries, and cyberspace waiters. In this context, the flywheel energy storage systems have besides found its manner into electrical burden levelling application such as in guaranting an uninterruptible power supply by supplying a smooth and effectual passage between a chief power beginning when necessary ( Hebner et al 2002 ) This is one of the current capableness of the flywheel and it seems assuring that as the engineering improves in the close hereafter, flywheel could perchance be applied to top out power managing, where extra energy produced us stored and later released at the peak clip in energy ingestion.
The construct of flywheel is besides non fresh in the intercrossed electric vehicles ( HEVs ) industry, where little burning engine is operated while the vehicle is traveling at a changeless velocity. The acceleration procedure is executed with the excess power provided by the extra battery power provider. This extra power, on the other manus is generated and stored in the battery when the vehicle brakes such that no extra power is wasted in the signifier of heat dissipation generated by the clash during brakes. At the present minute, flywheel seems assuring in being usage for intercrossed coachs as chemical battery is expensive.
In infinite applications, light weight, compact with high energy denseness storage capableness devices are extremely sought after. With addition public presentation demands on infinite systems, infinite plans had had to do systematically immense attempt in cut downing rim mass to increase warhead capacity every bit good as cut down launch/ fiction costs. Although chemical batteries had long been a sure beginning of energy but flywheel offers much better weight and life benefits every bit good as the possible to hive away a larger sum of energy at a lower weight, non to advert the capableness to be used as attitude control actuators in replacing reaction flywheel assemblies and command minute gyros.
In 2000, Truong et al introduced the Flywheel Energy Storage Demonstration Project, initiated at the NASA Glenn Reasearch Center as a possible replacing for the Battery Energy Storage System on the International Space Station ; whereas Fausz et Al. had, in the really same twelvemonth reported that the Flywheel Attitude Control, Energy Transmission and Storage ( FACETS ) system could unite all or parts of the energy storage, attitude control, and power direction and distribution ( PMAD ) subsystems into a individual system, this significantly diminishing flywheel mass ( and volume ) . Therefore, in infinite applications, important weight decreases for orbiters could, and have hitherto, been achieved with the usage of the multi-function high velocity flywheel system which non merely maps as energy storage but besides in supplying a gyroscopic consequence for attitude control. ( Bitterly, 1998, Hebner et al. , 2002 )
But even until late, the historical development of flywheels and their utilizations has mostly been dependent on progresss in both stuffs and machine engineering, coupled with chance and necessity ( Horner, et Al, .1996 ) However with technological promotions in such a rapid gait, it is non difficult to imagine the position of flywheels in the close and distant hereafter.
1.1.3 The Use of Composite and Fiber- Reinforced Materials in Flywheel Design
The kinetic energy stored in a flywheel rotor increases linearly with mass but quadratically with rotational velocity. . With the increasing demand for high energy storage, flywheels in present applications are frequently designed for high angular speeds ; and these correspond to big centrifugal tonss and accordingly a higher circumferential and radial emphasiss, i.e. the dominant emphasis distribution are hoop emphasiss ( concentric ) . In this context, the usage composite stuffs with fibres of high unidirectional strength would be desirable. ( Shah, 2008 )
For a fixed axis rotary motion, the energy stored in a thin revolving pealing rotor is
[ 1.3.1 ]
I = the rotor minute of inactiveness
A°A?aˆ?A? = is the rotor angular speed.
It seems executable that to increase the stored energy, the mass of the flywheel must be increased and therefore its minute of inactiveness. However, it must be noted that the energy is merely linearly proportional to the mass of the flywheel whereas the energy is relative to the square of the rotational velocity. These dealingss indicate that the rotational velocity for a given radius will hold a higher influence to the energy denseness than that of the mass of the flywheel ; and to accomplish a high rotary motion velocity, a high strength per weight stuff must be used. Further derivations of the equations below will explicate this status.
Figure 1.3.1 Free organic structure diagram of a thin- ring revolving mass component for come closing the critical velocity of a flywheel rotor ( Shah, 2008 )
Resultant force along the hoop and circumferential waies
[ 1.3.2 ]
[ 1.3.3 ]
= force summing ups in the radial way
= force summing ups in the circumferential way
diabetes mellitus = mass of the mass component located at radius R
rdA°A?A“?’ = arc length of the mass component located at radius R
Ar = radial acceleration of the mass component located at radius R
From equation [ 1.3.3 ] ,
[ 1.3.4 ]
With [ 1.3.5 ]
A?A?= mass component denseness
V=mass component speed
B=mass component breadth
Utility equation [ 1.3.5 ] into [ 1.3.4 ] and knowing that V=rA°A?aˆ?A? and for A°A?A“?’ & lt ; & lt ; 1sindA°A?A“?’/2=dA°A?A“?’/2, the undermentioned equation is obtained
[ 1.3.6 ]
The tensile emphasis in the circumferential way
[ 1.3.7 ]
The emphasis in a thin- ring rotor is:
[ 1.3.8 ]
It is observed that the maximal velocity accomplishable by a flywheel rotor is limited by the strength of the stuff from which it is made. The critical velocity of the thin ring rotor can be approximated as
[ 1.3.9 ]
Where is the material ultimate strength.
From the permutation of equation [ 1.3.9 ] into [ 1.3.1 ] , the specific energy stored in the rim is obtained
[ 1.3.10 ]
K= Flywheel form factor ( Typically 1 for unvarying emphasis phonograph record and 0.5 for thin ring )
The dependence of the maximal specific energy stored in the flywheel on the specific strength of the stuff is therefore observed. With the demand for high specific energy in flywheel rotor design, the usage of suited stuff is therefore of paramount importance.
Due to their high stiffness to strength, composite stuffs have successfully been established in flywheel rotor design. Fiber reinforced complexs are peculiarly attractive for usage as flywheel stuffs due to their high strength and low denseness ( Takahashi et al. , 2002 ) The usage of composite stuffs in flywheel designs offer legion advantages over metallic metals, including weight and increased strength. This is due to the high tensile strength of the fibre reinforcement stage.
In 1986, a composite flywheel rotor was developed by Potter and Medicott for used in vehicle applications. In 1995, the survey by Curtiss, et Al. shown that the composite Carbon fibre epoxy phonograph record rotor is capable of a 38 % higher rim velocity or 91 % greater rotor energy denseness than a rotor built of an isotropic high strength to burden ratio Titanium or steel metals.
The C fibre reinforced plastic ( CFRP ) flywheel proposed by Kojima, et Al. ( 1997 ) shown that high-modulus graphite/epoxy fibril wound composite flywheel is able to revolve at a higher velocity. The polar woven flywheel by Huang ( 1999 ) was shown to possess weight nest eggs characteristics every bit good as the betterment in life and dependability of the sum ballistic capsule system, and in 2002, the Multi-Direction Composite ( MDC ) flywheel systems was reported by Gowayed and Flowers. The MDC flywheel system studied employed a new attack to beef up flywheels with extra support in the radial way along with the typical hoop way support.
In fact, analytical and numerical attacks had over the old ages been presented to find the emphasis, and displacement distribution of the rotor. With the increasing demand for high energy storage, flywheels in present applications are frequently designed for high angular speeds ; and these correspond to big centrifugal tonss and accordingly a higher circumferential and radial emphasiss. And the finding of these emphasiss every bit good as the ply orientation became particularly important.
Equally early as 1977, Danfelt et Al. published an analytical method for a intercrossed multi-rim flywheel with ply-by-ply fluctuation of stuff belongingss and based on the premise of axisymmetry. The method by Danfelt was subsequently extended by Tzeng ( 1997,2003 ) which accounts for viscoelasticity effects. In add-on, the original method by Danfelt had besides been supplemented by a series of researches by Ha with extra consideration of the intervention between next rims and changing fibre angles ( Ha et al. , 1998 ) , the rim radii of legion material lay- ups for a changeless angular speed ( Ha et al. 1999b ) , residuary emphasiss due to the hardening procedure ( Ha et al. , 2001 ) and the subsequent research on a split- type hub ( Ha et al. , 2006 ) . The consequence of rim thicknesses and angular speed was studied by Arvin and Bakis ( 2006 ) while Fabien ( 2007 ) studied the optimum uninterrupted fluctuation of fibre angle in a single-material rotor.
Other than that, finite component attacks have besides been used for emphasiss and supplanting calculations which, though computationally more demanding, have gained importance for the analysis and design optimisation of flywheel rotors because of the greater mold deepness offer by such methods.
It is besides possible to piece the flywheels as a loanblend with rims of different stuffs in a sequence of increasing ratio of stiffness per denseness value E/A?A? for increasing radius, R ( Arvin & A ; Bakis, 2006 ) utilizing a method called aa‚¬A“ballastingaa‚¬A? . From their surveies, with circumferential fibre support, the radial emphasis distribution is strictly tensile with a maximal placed about in the midline between the inner and outer radii. But with two-material rotor, the radial emphasiss turn compressive in the part near the stuff interface due to the lower stiffness of the interior stuff which would ensue in greater enlargement. A compressive emphasis minimal therefore exists at the stuff interface, with two tensile emphasis upper limit found near to the innermost and outermost radius. Despite the addition in circumferential emphasis degree for the outer composite carbon/epoxy rim, such a status still arises due to the lower radial emphasiss as a consequent of rotor strength increase. After all, composite stuffs are by and large weaker in the transverse way than in the longitudinal way.
As fiber support is typically aligned in the circumferential way, radial tensile emphasis is frequently more important in comparing with the other manner of emphasiss due to the weaker strength in this way. Therefore, the dominating emphasiss are typically those of the circumferential and radial emphasiss. In this context, much attempt had been invested to heighten the efficiency of the composite flywheel rotors by using stress decrease methods. In position of this method, Danfelt et Al. ( 1997 ) suggested a sandwich-like rim layup with a compliant stuff between the composite rims of one stuff to diminish interlaminar emphasis transmittal.
1.2 Literature Review
1.2.1 Interlaminar emphasiss of Composite Laminates
Interlaminar emphasiss arise when there are discontinuities in the burden way, such as free borders and notches. ( Wilkins, 1983 ) . In peculiar, theoretical accounts with a important sum of curvature. This is because the presence of high interlaminar emphasiss due to the consequence of shell curvature could ensue in delamination and perchance failure of the laminate at a lower burden than that predicted by in-plane failure standards had they non been decently accounted for. ( Edward, K.T. , Wilson, R.S. and McLean, S.K. ,1989 ; Lagace, P.A. , 1983 ) The accurate finding of interlaminar emphasiss are therefore important in the design of laminated composite theoretical accounts as the interfacial surfaces of a laminate represent planes of minimal strength ( Pagano, N.J. & A ; Pipes, R. B. , 1973 ) .
Classical laminated home base theory ( CLPT ) was formed in concurrence with the kinetical premises of Kirchhoff classical home base theory by presuming a layerwise plane province of emphasis. However, 2-D CLPT theory entirely is non sufficient to explicate stress concentration phenomena in assorted lightweight buildings in air power vehicle, such as the free-edge consequence where all-out 3-D and remarkable emphasis Fieldss occur in the interfaces between two dissimilar beds along the free borders of thermally and/ or automatically laden laminates ( Mittelstedt & A ; Becker, 2003 ) which decay quickly with increasing distance from the laminate border. Such stress localisation jobs is caused by the discontinuous alteration of the elastic stuff belongingss of the laminate plies at the interfaces and might ensue in premature failure of the laminate. This is therefore an country of concern by interior decorators and much researched has been done since the early 1970s, with the surveies initiated by of Pipes and Pagano on the free border effects in laminated constructions.
Early on analytic surveies were conducted by Hayashi ( 1967 ) on border emphasis effects dwelling of anisotropic plies and adhesive beds reassigning interlaminar shear emphasiss. In early 1970s, Pagano and Pipes besides introduced estimate equations for interlaminar normal emphasiss in the interfaces and was expanded by Conti/ De Paulis in 1985 for the stress- estimate in angle-ply laminates and the computation of interlaminar emphasis distribution through the laminate thickness. Whitney simple emphasis estimates in 1973 did non carry through the continuity conditions in the interfaces, although Whitney premise of merchandises of exponential and trigonometric maps did fulfilled the equilibrium conditions and the given traction-free boundary conditions.
Researchs in the country of free border effects were besides done utilizing assorted attacks by Tang and Levy ( 1975 ) with layerwise series enlargement, Hsu and Herakovich ( 1977 ) with border supplanting Fieldss in the signifier of trigonometric and exponential footings, Wang & A ; Dickson ( 1978 ) with the enlargement of the supplanting Fieldss into series of Legendre multinomials. However, much disagreement has been reported.
In 1981, series enlargements for the emphasiss in the interior laminate parts and in the locality of the free laminate borders by Bar-Yoseph/Pian.CLPT was recovered in the interior laminates with this zero-order attack and unknown parametric quantities obtained by minimising the laminate complementary potency. The subsequent work by Bar-Joseph used the rule of minimal complementary potency, taking to an characteristic root of a square matrix job. The attack used by Bar-Yoseph allowed the continuity of interlaminar emphasiss in the interfaces every bit good as the fulfillment of the conditions of grip free surfaces of the laminate.
The force balance method by Kassapoglou/Lagace in 1986 and 1987 was developed. Stresss were assumed to dwell of layerwise merchandises of in-plane exponential footings and multinomials through the thickness with accommodations done on the thickness footings to fulfill the continuity of all interlaminar emphasiss in the laminate interfaces and such that they blend into CLPT in the interior laminate parts. Despite its simpleness, the force balance method exhibited good public presentation even for midst laminates and was therefore farther explored and refined by other writers.
The effects of transverse shear and continuity demands for both supplantings and interlaminar emphasiss on the composite interface was accounted for by Lu and Liu in developing an Interlaminar Shear Stress Continuity Theory ( ISSCT ) capable of being used for finite component preparation ( Lu, X. , Liu, D. , 1990 ) . Through that peculiar theory, interlaminar shear emphasis could be obtained straight from the constituent equations. But as the distortion in the thickness way was neglected during the preparation of the theory, the interlaminar normal emphasis could non be calculated straight from the constituent equations. Other than that, a little disagreement between the consequences of theirs and that of Pagano snap solution in the interlaminar shear stresses little aspect ratios composite laminates was observed ( Pagano, N.J. 1969 ) .
Although, stiffly bonded laminated composite stuffs theoretical accounts are ever assumed in conventional analysis ; but it must be noted that hapless bonding and low shear modulus could ensue in a non-rigid composite interface. As a continuance of the ISSCT, Lu and Liu ( 1992 ) later developed the Interlayer Shear Slip Theory ( ISST ) based on a multilayer attack in look intoing the consequence of interfacial bonding on the behaviour of composite laminates. The Hermite three-dimensional form maps was used as the insertion map for composite bed assembly in the thickness way, and the closed-form solution is obtained for the instances of cylindrical bending of cross-ply laminates with non-rigid interfaces. However, consequences shown that at some particular locations, viz. remarkable points, the transverse shear emphasis or in-plane normal emphasis remains insensitive to the status of interfacial bonding.
A closed- signifier solution was subsequently derived by Lee and Liu ( 1992 ) for the complete analysis of interlaminar emphasiss for both thin and thick composite laminates subjected to sinusoidal distributed burden. The theory was proven to fulfill the continuity of both interlaminar shear emphasis and interlaminar normal emphasis at the composite interface and besides the interlaminar emphasiss could be determined straight from the constituent equations
An accurate theory for interlaminar emphasis analysis should see the transverse shear consequence and continuity demands for both supplantings and interlaminar emphasiss on the composite interface. It is besides advantageous if the preparation is variationally consistent so that it can besides be used for finite element preparation. ( Kant, T. , Swaminathan, 2000 )
Using the first order shear distortion theory, the interlaminar stresses in laminated composite cylindrical chevrons under dynamic burden are studied. Dynamic equations of equilibrium are solved by a combination of Navier attack and a Laplace transform technique. Dynamic magnification factor is calculated for the emphasiss and warps for assorted types of burden and for different values of the geometric parametric quantities. ( Bhaskar, K. & A ; Varadan, T.K. , 1993 ) .
Higher order layerwise theorectical model has been used by Plagianakos and Saravanos ( 2008 ) in foretelling the inactive response of thick composite and sandwich composite home bases. The displacement field in each discrete bed through the thickness of the laminate include quadratic and three-dimensional multinomial distributions of the in- plane supplantings, every bit good as the additive estimates assumed by additive layerwise theories in add-on to the Ritz- type exact solution used to give the structural response of the thick construction. The preparation has been found to be particularly robust in comparing to linear layerwise theory due to the figure of distinct beds used to pattern the thick laminate through thickness and in the anticipation of interlmainar shear emphasiss at the interface. In add-on, the theory used besides offers a better scope of pertinence due to the better truth offered.
Over the old ages, many documents look intoing the effects of interlaminar emphasiss had been published. The finite difference method with classical snap theory was used by Pipes and Pagani for finding the behavior of finite width laminate in unvarying axial strain and where interlaminar emphasis at the free border is found to be of a significantly immense sum. Other surveies shortly ensued such as the disturbance solution techniques by Hsu and Herakovich, the finite difference method utilizing big elements with complex emphasis field by Rybicki ; and Wang and Crossman finite difference method, every bit good as the approximative analytical solution by Pagano and Wang and Choi. However, all of these surveies involve the interlaminar stresses at the free borders of finite composite laminates.
It is nevertheless, good acknowledged that interlaminar emphasiss arise such as to fulfill equilibrium at locations with in-plane emphasis gradients ( Saeger, Lagace & A ; Dong,2002 ) , and material discontinuity within a construction is another beginning of originating in plane emphasis gradients, and hence, interlaminar emphasis appear near the stuff discontinuities. ( Tahani, 2005 )
Rose/ Herakovich, in 1993, farther explore the force balance method of Kassapoglou/Lagace with the debut of extra footings for the consideration of the discontinuous alteration of the elastic stuff belongingss in the interfaces and which accounted for the local mismatches in Poisson ratio and coefficient of common influence between next beds. There are reported betterments in the attendant emphasis field. However, such betterments are besides accompanied with a more demanding computational attempt for the minimisation of the complementary potency. In a similar survey done by Kim/Atluri in 1995, thermic and mechanical tonss were analyzed by false emphasis forms which besides accounted for both the local mismatches in Poisson ratio ( similar to that of Rose/ Herakvich ) and coefficient of common influence by using several mismatch footings in the emphasis representations. An attack that agreed to equilibrium demands and the given boundary conditions, the unknown emphasis maps were determined by application of the rule of minimal complementary energy of the laminate.
The rule of minimal complementary theory was used by Bhat and Lagace ( 1994 ) to measure the interlaminar stresses at stuff discontinuities. In their analytical theoretical account, the laminate is formed by the meeting of two countries of different lay-ups. The two dissimilar parts were bonded along a consecutive interface analogue to the thickness co-ordinate. The emphasiss are represented in eigenfunctions fulfilling the equilibrium conditions and solved after obtaining the differential equations of the job via the rule of minimal complementary energy. The consequences of which were disintegrating exponential maps. These instances can happen as mentioned by Bhat and Lagace at parts of implants within adaptative constructions for illustration when detectors were implanted within laminated complexs via the film editing of the laminate plies to do leeway for the arrangement of that detector. In add-on, harm caused by impact is besides a good known illustration of stuff discontinuity due to the fact that the stuff belongingss of the impact are typically reduced in comparing with the other parts. All of these material discontinuities were shown by Bhat and Lagace as parts where interlaminar stresses develop.
Till day of the month, much has been done on interlaminar emphasiss. However, there are few probes of interlaminar emphasiss in revolving beams and discs done. A layerwise laminated beam theory is developed by Tahani ( 2006 ) utilizing a layerwise laminated home base theory to develop a layerwise laminated beam theory and it is used to analytically analyse and foretell the 3-dimensional emphasis field in the locality of stuff discontinuities in revolving composite beams with general laminations. Displacement equations of gesture are obtained by utilizing Hamilton rule. The consequences obtained from this theory are compared with those obtained by a finite component method. The consequences obtained from this theory are compared with those obtained by utilizing a finite component method. The correlativity among the consequences indicates the theoretical attack is executable as a conceptual design tool. The consequences indicate that there are terrible out-of-plane emphasiss in parts near the sudden passage of stuff belongingss ( material discontinuities ) . These emphasiss can originate heterogenous harm in the signifiers of delamination and transverse snap and may do the harm to propagate to a significant part of the beam, ensuing in a important loss of strength and stiffness. Hence, these emphasiss must be considered in design of such constructions.
1.3 Problem Statement
The intent of the proposed survey is to look into the interlaminar emphasis behavior of the flywheel rotor via the Finite Element Method.
The proposed survey is identified of being of importance as the presence of high interlaminar emphasiss due to the consequence of shell curvature could ensue in delamination and perchance failure of the laminate at a lower burden than that predicted by in-plane failure standards had they non been decently accounted for. ( Edward, K.T. , Wilson, R.S. and McLean, S.K. ,1989 ; Lagace, P.A. , 1983 ) The accurate finding of interlaminar emphasiss are therefore important in the design of laminated composite theoretical accounts as the interfacial surfaces of a laminate represent planes of minimal strength ( Pagano, N.J. & A ; Pipes, R. B. , 1973 ) . However, few probes of interlaminar emphasiss have been done in revolving rotors.
In add-on the optimisation of fiber orientation in minimising the interlaminar stresses is another end in the proposed survey. Finally, the proposed survey would take to future research in footings of delamination and failure standards.
The survey of the interlaminar emphasiss of the rotor would be performed in two phases. The first involves the usage of the finite component method and the 2nd, an analytical theoretical account to back up the consequences obtained from the finite component method.
1.4.1 Finite Element Analysis
Finite component method ( FEM ) , frequently referred to as finite component analysis ( FEA ) is a numerical computational technique aimed at obtaining approximative solution of boundary value jobs for a broad category of technology jobs in peculiar those related to complex snap and structural analysis job. FEM has been widely used for the computation of physical supplanting, temperature, heat flux, unstable speed. Finite component ( FE ) method is besides identified as an effectual implement in analysing intricate system of laminated composite construction and had been found to be of peculiarly utile in the survey of structural response, break and failure every bit good as the progressive harm behavior of composite constructions.
Two dimensional ( 2D ) elements have been extensively utilized in the yesteryear. Other than being computationally less demanding, two dimensional elements are besides found to be produce consequences of important truth far from the boundaries. However, while patterning near stuff and geometrical anomalousness, or near traction- free borders, three dimensional ( 3D ) FE theoretical accounts are of paramount importance to give consequences of superior truth albeit being computationally more demanding than that of 2D theoretical accounts.
Gowayed et Al. ( 2002 ) performed structural flywheel rotor design analyses accounting for two and 3-dimensional characteristics of a multidirectional composite rotor, every bit good as nonaxisymmetric tonss. A big figure of design parametric quantities related to flywheel operation were involved such as flywheel geometry, stuff features, material layup, and spacial emphasis distribution and values. Several optimisation analyses were carried out. It was found that although FEM-based solutions were computationally more clip intensive than closed signifier non-linear scheduling, solutions from FEM provided greater truth and sum of item.
In the proposed survey, the finite component bundle, ANSYS 12.1 will be used due to its high quality in patterning revolving objects. In add-on, the motive to utilize ANSYS was besides due to the fact of the handiness of literature in patterning revolving flywheels.
1.4.2 Analytic analysis of the theoretical account
Typical surveies involved utilizing finite component method to verify the truth of an analytical theoretical account. However, in the proposed survey, an analytical theoretical account would be employed to verify and back up the consequences obtained from the finite component analysis. The analytical theoretical account used was obtained from a survey by Tahani, M. ( 2006 ) . The derivations of the equations as obtained from Tahani, M. ( 2006 ) is as attached in Appendix I. A possible tool to execute the analytical analysis is via the usage of the Fortran plan.
A 3D FEM theoretical account was developed utilizing solid elements for the flywheel rotor. Although computationally more clip consuming, it was used as the purpose of the survey involves look intoing interlaminar emphasiss near stuff discontinuities and of which the 3D theoretical account would supply solutions with greater truth as compared to that of a 2D theoretical account.
The interior ring is made of heavy stuff such that it is capable of defying a greater enlargement compared to the stiffer outer ring. The addition in rotor velocity would so ensue in a greater compressive emphasiss at the interface of the rings. In add-on, multi-ring rim can besides cut down the radial emphasis significantly, and therefore increasing failure velocity.
The material optimized multi-ring rotor designed by Varatharajoo, R. , Salit, M.S. , and Goh, K.H. ( 2010 ) was chosen in the proposed survey to look into the interlaminar emphasiss of the rotor. A theoretical account was built via ANSYS of the same dimensions and stuffs, that is a rotor theoretical account with thickness of 0.0183m, interior radius of 0.1106m and outer radius of 0.1174m.
Due to the cylindrical form of the flywheel, cylindrical co-ordinate is used while patterning the rotor. The cylindrical R ( radial ) coordinates correspond to Cartesian X, cylindrical OA? ( hoop ) corresponds to Cartesian Y and cylindrical Z ( axial ) to Cartesian Z in the ANSYS show. The ANSYS Work Plane can be easy switched with the usage of the CSYS bid in ANSYS where 0 represent Cartesian, 1 represent cylindrical, 2 represent spherical and so on.
Modeling with interface elements with ANSYS has to be done with SOLID elements. However Solid elements give less accurate consequences in comparing to SHELL elements in patterning objects with high curvature. In add-on, SOLID elements besides required a finer mesh to obtain moderately good consequences. Therefore, the proposed theoretical account was modelled with the SOLID- SHELL component, SOLSH 190 which non merely possesses both the capablenesss of SOLID and SHELL elements but besides offers the possibility to use superimposed solid elements with distinguishable bed orientation and stuff type to imitate fiber- strengthened composite stuffs. With such maps, stuff belongingss need non be homogenized in each of the rotor layered rims.
The engagement for the initial theoretical account was done via free, smart sized engaging with element size of 0.0009. This gave a all right mesh of about 131560 SOLSH 190 elements. For the initial theoretical account, 5 beds were modelled. The first bed is of AS4 Carbon fiber composite with two sub- beds in an axissymmetric orientation of 45 and -45 grades. The 2nd bed is of T300 composite with two sub- beds in a similar orientation, the 3rd bed is of M40J composite with two sub-layers likewise orientated as bed 1 and 2. Between the first and 2nd ; and the 2nd and 3rd beds, are the interlaminar bed utilizing Epoxy matrix.
Figure 1.5.1 Ply Orientation for the initial theoretical account.
Below are the stuff belongingss for the complexs [ Daniel and Ishai, 2006 ; Ha and Kim, 1999a ; Rupnowski et. al. , 2005, cited in Shah, M. M. , 2008 and About.com ]
Material ( ANSYS )
AS4 Carbon fibre
A?A? , g/cm3
Table 1.5.1 Material Properties
Figure 1.5.2 Von Misses Stresses Contour Plot for the initial 5 bed theoretical accounts
Mesh sensitiveness analysis will be performed to find the suited figure of elements before taking the Solid Shell elements at the interlaminar bed and replace them with interface elements to ease more in- deepness and accurate probe of the interlaminar emphasiss. Other than that, fiber optimisation would be done. And all of which would perchance be performed by using merely a little subdivision of the rotor ( 45AA° ) alternatively of the full rotor assembly to cut down computational clip.
In add-on to the applied inactiveness tonss, press-fitting tonss will be incorporated to obtain a more accurate consequence for the interlaminar emphasis behavior. And should clip licenses, probe could be done on delamination and check behavior at the interphase between the laminating beds.