Improved Design of Film Cassettes 解题思路

ImprovedDesignofFilmCassettesSolutionprocessoutline

Howcanthecassettesberedesignedtomakethemlighter?

Materialchoice:useamaterialwithlowerdensity.

Somedimensionalchanges:canyoumaketheplatesthinner?

Whatcannotchangeinaredesign?

Widthandlengthdimensionsmuststaywithfilmsize.Needtokeepthesamestiffnesstobending.

Transparencytox-raysmustbethesameorbetter.

Materialcannotleaveartifactsontheimage(wovencarbonfibercompositeswon’twork)Thus,materialmustbehomogeneous(withintheimageresolution)withinitsplaneWhatdoesstiffnessofacassettemean?Howdoyouquantify?

Resistancetodeflection.

AdvancedStrengthofMaterialsbookgivesadefinitionforflexuralrigidity.Dependsonelasticmodulusofmaterialandthicknessofplate.Modulusunaffectedbymaterialprocessing.Whatareothereffects,otherthanweightofchangingmaterial?

Transparencytox-rayschanges

Absorptioncoefficientincreaseswithatomicnumber–needlowZmaterialsEnvironmentalcompatibilitySafetyWhatareothereffectsofchangingthickness?

Transparencytox-raysdecreaseswiththickness(exponentially).Tomakelightplatesforx-raycassettesweneedamaterialwith

1)Highx-raytransmission2)Highelasticmodulus3)Lowdensity

Thefollowinglinkswillgetyoustartedwithsomeinformationonx-rayradiography:

http://en.wikipedia.org/wiki/Radiographyhttp://en.wikipedia.org/wiki/Medical_radiographyhttp://en.wikipedia.org/wiki/Industrial_radiographyForagivenmaterial,howthickmustitbetomeetthestiffnessrequirement?

Stiffnessofaplatecanbequantifiedbytheflexuralrigidity.Withsomesearchingyoushouldbeabletofindareferencethatgivestheflexuralrigidityas

Eh3,D?2121????whereEisYoung’smodulus,?isPoisson’sratioandhistheplatethickness.Thus,thethicknessneededforagivenmaterialis

?12Do1?v2?h???

E??

??1/3,

whereDoistheflexuralrigidityoftheoriginaldesign.Themassoftheplateswithanew

materialwillthenbe

m?wlh?.

Thefractionalchangeinmasswithanewmaterialisgivenby

?12Do1?v2????Em???

mo?oho??1/3,

where?oandhoarethedensityandthicknessintheoriginaldesign.Noticethatthewidthand

lengthcanceloutandareirrelevantsincetheydonotchangewiththenewdesign.Thebestmaterialforaplatedesignedtoaspecifiedstiffnesswhiletryingminimizethemassisamaterialwiththesmallestvalueof

?1?v2????

E??

??1/3.

IfyouassumethatPoisson’sratiodoesnotvarymuchbetweenmaterials(anassumptionnot

needed)youcanminimizethemassoftheplatebymaximizingthematerialindex

E1/3?.

This,however,doesnotincludethenecessitytomaintainthex-raytransmissibilityoftheplateequaltoorbetterthantheoriginaldesign.

Howdowecalculatethex-raytransmissionofaplate?

Thex-raytransmissionisgivenby

I

?exp???h?.IoHereIoistheincidentx-rayintensityandIisthetransmittedintensitywhile?isthex-raylinearattenuationcoefficient.Valuesof?arenotusuallytabulatedastheydependonthecompositionofthematerialanditsdensity.Whatismorereadilyfoundisthequantity(???),themassattenuationcoefficient,forvariouselements.Thetransmissionisthencalculatedas

?????I

?exp????????h?.Io????

Thevalue1/?isthethicknessofmaterialthatattenuatesthex-raybeambyafactorof1/ewhichismoreeasilyphysicallyunderstood.Youcanfindafullerdescriptionofattenuationat

http://en.wikipedia.org/wiki/Mass_attenuation_coefficientTheNationalInstituteofStandardsandTechnologymaintainsthreedatabasesgivingmassattenuationcoefficients:

http://physics.nist.gov/PhysRefData/XrayMassCoef/cover.htmlhttp://physics.nist.gov/PhysRefData/Xcom/Text/XCOM.htmlhttp://physics.nist.gov/PhysRefData/FFast/Text/cover.htmlAnothersourceformassattenuationcoefficientsisMucalontheWeb

http://csrri.iit.edu/mucal.htmlX-raytubesdonotproduceasingleenergy(orwavelength)ofx-raysbutinsteadproduceaspectrumofx-rays.Theenergyofx-raysisusuallystatedinkeVorkilo-electron-Volts.Thisisaunitofenergyderivedfromthefactthatanelectrontravelingthroughavoltagedropwillgainenergy.Inanx-raytubeelectronsatahighvoltagewithrespecttoametaltargetacceleratetowardsthattargetstrikingit.Thedecelerationoftheelectronbythetargetproduces

electromagneticradiationintheformofx-rays.Thehighestenergyx-raypossibleisproducedfromalloftheenergyoftheelectronbeingconvertedtoanx-ray.Ifthex-raytubeissetat75kV,thehighestenergyx-raysproducedwillbe75keV.Mostofthex-raysproducedhavealowerenergyandaspectrumisproducedwithapeakinenergyatabout2/3ofthetubevoltage.Themassattenuationcoefficientsareforelements.Formaterialscomposedofmorethanoneelement,thelinearattenuationcoefficientiscomputedas

???

?mat??mat?wi?????,

i??iwherewiaretheweightfractionsoftheelementscomprisingthematerialand?matisthedensityofthematerial.Thefollowinglinkwillgiveyousomefurtherinformationonx-rayradiographyandleadyoutosomeinformationgivingguidanceonx-rayenergiesusedinmedicalradiography.

http://www.xray2000.co.uk/Someexamplecalculations

Table1givessomeselectedattenuationcoefficientsthatcanbeusedasaguidefor

calculatingthemforothermaterials.Youwillwanttoconsidersomerelevantmaterialsinyourreportsnotgivenhere.Whywerethecalculationsdonefor50and100keVx-rays?Thisissomethingyoushouldanswerinyourreports.Notethattablescanbeaneffectivewaytocommunicatenumericalinformation.Youwoulddowelltoincludetheminyourreports.Table1.X-raymassandlinearattenuationcoefficientsforselectedmaterials.

??(g/cm3)--2.2502.7204.5400.9050.85630.1437

SubstanceHCAlTiPP(C3H6)**wt%CinPPwt%HinPP

For50keVx-rays?????2(cm/g)(cm-1)0.351--0.1880.42300.3510.95471.1915.40710.2110.19131/?(cm)--2.361.050.185.24For100keVx-rays?????2(cm/g)(cm-1)0.291--0.1510.33980.1690.45970.2711.23030.1710.15481??(cm)--2.942.180.816.46Table2providesacomparisonofsomecandidatematerialstoa1mmthickaluminumplatewhentheyaredesignedtohavethesameflexuralrigidityandmaybeusedasanexampleforyourowncalculations.Notethatthethicknessisdifferentthanthatspecifiedinyourproblem.Noticethata“PercentWeightChange”columnhasbeenincluded.Whilemass(orweight)istheprimaryperformance,thepercentweightchangeismostconvenientforthereadertoconsiderincomparingthenumberstotheoriginaldesign.Astheauthorofreports,trytoconsiderhowbesttocommunicateyourideasandresultstothereader.

Table2.Comparisonoftheperformanceofseveralmaterialsforthex-raycassetteplates.MaterialAluminumTitanium

PolypropyleneAl-PP-AlDensity(g/cm3)2.714.510.905-ElasticModulus(GPa)691031.35-Poisson'sThicknessRatio(mm)0.331.000.340.840.353.69-0.128+1+0.128Mass(g)406.50569.54501.21239.81PercentWeightChange0.0+40.1+23.3-41.0Discussionofsolution

Noticethattitaniumproducesaheavierplateeventhoughitisthinnerbecauseitsdensityissignificantlyhigher.Itwouldfailonx-raytransmissiongroundsaswell.Polypropylene

producesaheavierplateeventhoughithasasignificantlylowerdensity.Thisisduetoitsmuchlowermodulusnecessitatingamuchthickerplatetoachievethenecessaryflexuralrigidity.Youwillfindthatberylliumisanidealcandidatebutisveryexpensiveandconsideredtoxic.Coatingitmayprovideasolutionbutinawearapplication(slidingcassettesintoslotsforexposureanddeveloping)itmaynotbesuitablebecausethisiswhereitstoxicityissuesreallymanifestthemselves.Particulateberylliumcausesberylliosisinafractionofthepopulationanditisdeadly.ThisfactcanbedeterminedfromtheMaterialDataSafetySheetforberyllium.YouwillfindanumberofsourcesforMSDSontheweb.

AnothermaterialwithaverygoodvalueofE1/3/??iscarbonfibercomposite.Thiswillnotworkinthisapplication,however.Youshouldbeabletodescribewhy.Whatmaterialpropertyisrelevanthere?(hint:homogeneity)

Anarticle/advertisementisincludedamongtheresourcesforthismodule.This

documentillustratesthesolutiontothisproblemusedbyonecompany.Bymakingasandwichstructureofdifferentmaterialsyoucanengineerasignificantlyimprovedplate.Allthematerialsinthesandwichmustberelativelytransparenttox-raysbutbyplacingastiffermaterialontheoutside,youplaceitwhereitcandothemostgood.Theinnermaterial’spurposeistoplacethestiffermaterialawayfromtheneutralaxisandyouwantamaterialwithminimalx-ray

attenuation.Youshouldbeabletoexplainthemechanicsifyouproceedwithsuchasolution.