Machine Design II Prof. K.Gopinath & Prof. M.M.Mayuram. Flywheel. A flywheel is an inertial energy-storage device. It absorbs mechanical

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1 Flywheel A lywheel is an inerial energy-sorage device. I absorbs mechanical energy and serves as a reservoir, soring energy during he period when he supply o energy is more han he requiremen and releases i during he period when he requiremen o energy is more han he supply. Flywheels-Funcion need and Operaion The main uncion o a ly wheel is o smoohen ou variaions in he speed o a sha caused by orque lucuaions. I he source o he driving orque or load orque is lucuaing in naure, hen a lywheel is usually called or. Many machines have load paerns ha cause he orque ime uncion o vary over he cycle. Inernal combusion engines wih one or wo cylinders are a ypical example. Pison compressors, punch presses, rock crushers ec. are he oher sysems ha have ly wheel. Flywheel absorbs mechanical energy by increasing is angular velociy and delivers he sored energy by decreasing is velociy T 1 YLE Tm T1 A B D θ max min A B D θ Figure 3.3.1

2 Design Approach There are wo sages o he design o a lywheel. Firs, he amoun o energy required or he desired degree o smoohening mus be ound and he (mass) momen o ineria needed o absorb ha energy deermined. Then lywheel geomery mus be deined ha caers he required momen o ineria in a reasonably sized package and is sae agains ailure a he designed speeds o operaion. Design Parameers Flywheel ineria (size) needed direcly depends upon he accepable changes in he speed. Speed lucuaion The change in he sha speed during a cycle is called he speed lucuaion and is equal o max - min Fl max min We can normalize his o a dimensionless raio by dividing i by he average or nominal sha speed ( ave ). max min Where avg is nominal angular velociy o-eicien o speed lucuaion The above raio is ermed as coeicien o speed lucuaion and i is deined as max min

3 Where is nominal angular velociy, and ave he average or mean sha speed desired. This coeicien is a design parameer o be chosen by he designer. The smaller his chosen value, he larger he lywheel have o be and more he cos and weigh o be added o he sysem. However he smaller his value more smooher he operaion o he device I is ypically se o a value beween 0.01 o 0.05 or precision machinery and as high as 0.0 or applicaions like crusher hammering machinery. Design Equaion The kineic energy E k in a roaing sysem 1 I( ) Hence he change in kineic energy o a sysem can be given as, 1 E I K m max min EK E E 1 ( + ) max avg min ( )( ) 1 E K I s avg avg E E I 1 E I k s avg Thus he mass momen o ineria I m needed in he enire roaing sysem in order o obain seleced coeicien o speed lucuaion is deermined using he relaion

4 ( )( ) 1 E K I s avg avg E I k s avg The above equaion can be used o obain appropriae lywheel ineria I m corresponding o he known energy change E k or a speciic value coeicien o speed lucuaion, Torque Variaion and Energy The required change in kineic energy E k is obained rom he known orque ime relaion or curve by inegraing i or one cycle. θ@ max ( T l T avg) d θ E K θ@ min ompuing he kineic energy E k needed is illusraed in he ollowing example Torque Time Relaion wihou Flywheel A ypical orque ime relaion or example o a mechanical punching press wihou a ly wheel in shown in he igure. In he absence o ly wheel surplus or posiive enregy is avalible iniially and inermedialy and enery absorbion or negaive energy during punching and sripping operaions. A large magiidue o speed lucuaion can be noed. To smoohen ou he speed lucuaion ly wheel is o be added and he ly wheel energy needed is compued as illusraed below

5 Torque A Area B Area D A rms 7 00 Average 0 min max Sha angle ime θ Area Area Figure 3.3. Accumulaion o Energy pulses under a Torque- Time curve From Area E Accumulaed sum E Min & max A o B min@b B o max@ o D D o A Toal Energy E E@min (-6 03)-(+0 073) Nmm Figure 3.3.3

6 Torque Time Relaion wih Flywheel Torque 0.05 Average 0 Time Sha angleθ 360 Figure Geomery o Flywheel The geomery o a lywheel may be as simple as a cylindrical disc o solid maerial, or may be o spoked consrucion like convenional wheels wih a hub and rim conneced by spokes or arms Small ly wheels are solid discs o hollow circular cross secion. As he energy requiremens and size o he lywheel increases he geomery changes o disc o cenral hub and peripheral rim conneced by webs and o hollow wheels wih muliple arms.

7 b b D d D 0 D do Figure b D 0 D d a Arm Type Flywheel Figure The laer arrangemen is a more eicien o maerial especially or large lywheels, as i concenraes he bulk o is mass in he rim which is a he larges radius. Mass a larges radius conribues much more since he mass momen o ineria is proporional o mr

8 For a solid disc geomery wih inside radius r i and ou side radius r o, he mass momen o ineria I is m I mk (r m o r + i ) The mass o a hollow circular disc o consan hickness is ombing he wo equaions we can wrie ( ) W γ m π r g g o r i 4 4 ( ) π γ I m r o r g i Where γ is maerial s weigh densiy The equaion is beer solved by geomeric proporions i.e by assuming inside o ou side radius raio and radius o hickness raio. Sresses in Flywheel Flywheel being a roaing disc, cenriugal sresses acs upon is disribued mass and aemps o pull i apar. Is eec is similar o hose caused by an inernally pressurized cylinder γ 3+ v 1+ 3v σ ri + ro r g 8 3+ v γ 3+ v ri r o σ r ri + ro r g 8 r γ maerial weigh densiy, angular velociy in rad/sec. ν Poisson s raio, is he radius o a poin o ineres, r i and r o are inside and ouside radii o he solid disc lywheel. Analogous o a hick cylinder under inernal pressure he angenial and radial sress in a solid disc lywheel as a uncion o is radius r is given by:

9 Radius σ Tang. sress σ r Radial sress Radius The poin o mos ineres is he inside radius where he sress is a maximum. Wha causes ailure in a lywheel is ypically he angenial sress a ha poin rom where racure originaed and upon racure ragmens can explode resuling exremely dangerous consequences, Since he orces causing he sresses are a uncion o he roaional speed also, insead o checking or sresses, he maximum speed a which he sresses reach he criical value can be deermined and sae operaing speed can be calculaed or speciied based on a saey acor. Generally some means o preclude is operaion beyond his speed is desirable, or example like a governor. onsequenly F.O.S (N) N os yield

10 WORKED OUT EXAMPLE 1 A. kw, 960 rpm moor powers he cam driven ram o a press hrough a gearing o 6:1 raio. The raed capaciy o he press is 0 kn and has a sroke o 00 mm. Assuming ha he cam driven ram is capable o delivering he raed load a a consan velociy during he las 15% o a consan velociy sroke. Design a suiable lywheel ha can mainain a coeicien o Speed lucuaion o 0.0. Assume ha he maximum diameer o he lywheel is no o exceed 0.6m. Work done by he press U 0*10 3 *0.* Nm Energy absorbed work done 600 Nm Mean orque on he sha:.* Nm 960 * π* 60 Energy supplied work don per cycle π* 1.88* 6 85 Nm Thus he mechanical eiciency o he sysem is 600 η % 85 There ore he lucuaion in energy is E k Energy absorbed - Energy supplied

11 ( π ) * *6* * Nm E I k ( avg) 0.0 * 960 π kg m ( o i ) π r I. r r. g r Assuming i 0.8 r o π * 4 4 ( ) or 45 mm r 3+γ 1+ 3γ r r r σ g 8 i + o 3+γ σ * σ 0.543* π* N / m 0.556MPa or i σ 150 MPa 150 * ( )( )( )( rad / sec yield N OS 3π )