ThermoformingThermoforming2.810 Professor Tim GutowskiThermoformingHeaterPlastics sheetClamping*Vacuum*** Source: R. Ogorkiewicz, “Engineering Properties of Thermoplastics.”; ** http://www.arrem.com/designguide/dgprocesscap.htmThin cornerHeat Transfer in ThermoformingHeatingconvectionq&radiationq&radiationq&conductionq&Coolingconvectionradiationqq&&&conductionq&Radiation Heat Transfer between two parallel platesσ = 5.67 x 10-8W/m2K4)(1111424121TTq −σ−ε+ε=&ex. ε1ε2= 1 (black bodies)T1= 533oK (heater)T2= 293oK (plastic at room temperature)q = 4.2kW/m2at T2= 180oC = 453oK (forming temperature)q = 2.3kW/m2See Lienhard Text Ch 10 on Radiation Heat TransferHeating Time est. (Kydex sheet)ρ= 1.35 g/cm3tTwcqp∆∆ρ=&ρ= 1.35 g/cm3w = 1/16 in or 1.59 mmCp= 1.21 J/goK∆T = 180 – 20 = 160oK∆∆∆∆t = 130 secTemperature regimes for polymersLog E(t)TemperatureTgTmSemi-crystalline PolymerTemperatureTgTmLog E(t)TemperatureTgTg+60°CAmorphous PolymerViscoelastic Effects During processingUnloaded sampleCoiled polymer chainLoaded sampleExtended polymer chainLoaded samplePolymer chains tend to exist in coiled configurations. Loading the sample can extend the chain and alter the mechanical behavior. Generally, abrupt, high rates of loading will extend the chain and lead to elastic effects. On the other hand, gradual slow rates of loading allow the chain to more or less retain its coiled configuration, with a resulting primarily viscous responseRubber Elasticity∆W = F ∆L = ∆G = ∆H –T∆SF∆W = F ∆L = ∆G = ∆H –T∆Sideal rubber ∆H = 0; T, P constantF =-T (∆S/∆L)note that the change in entropy is negativeSimple Viscoelastic Systemε&dsdsεεεσσσ&&&=+==2 :itycompatibil Kinematic :mEquilibriu ForceddssdsEεµσεσεεε&&&&===+; :behavior veConstituti2 :itycompatibil Kinematicεµσσµ&&2 gives This =+EModulus ElasticViscosity Newtonian"" :isconstant Time tic viscoelasThe==Eµλ)1(2 0at 0 I.C. with 2 : oSolution tλεµσσεµσσλtet−−====+&&&behavior ous visc2 i.e. / of valuesLargeεµσλλ&≈>>tt i.e. / of valuesSmallλλtt<<behavior elastic 2 behavior thens,let 2 ))/1(1(2 i.e. / of valuesSmallεσεελεµλεµσλλEttttt≈=⋅=−−≈<<&&&“FAST” t <<λElastic“SLOW” t >>λViscous“INBETWEN” t ~ λViscoelasticTemp. Dependence of Time constant, λTEeERTE00∆≅=µµλArrheniusRubber elasticityApproximationRTEe∆≅0λλApproximatione≅0λλ(For better accuracy, use Time-Temp shift, WLF eqn.)Example: PMMA Temp λ40°C 114 yrs100°C Tg135°C 3.5 millisecViscous behavior of “silly putty”deformation patterns d(Ah) = A dh + h dA = 0dA/A = - dh/hDeformation PatternsThermoformingVariations on the processDrape FormingVacuum FormingVacuum Snap-Back FormingBillow Vacuum FormingThermoforming PatternsVacuum holesVariations on the processPlug-assist Vacuum Forming Plug-assist Pressure FormingPressure Reverse Draw with Plug-assistedProduction EquipmentShow VideoDouble diaphragm formingFormingtoolCuringtoolFormer MIT grad student Sam TruslowMIT Building 35Prototype machine at BoeingDiaphragm forming of CompositesDemo part for
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