`(cid:69)(cid:381)(cid:3)(cid:437)(cid:374)(cid:258)(cid:437)(cid:410)(cid:346)(cid:381)(cid:396)(cid:349)(cid:460)(cid:286)(cid:282)(cid:3)(cid:282)(cid:349)(cid:400)(cid:272)(cid:367)(cid:381)(cid:400)(cid:437)(cid:396)(cid:286)(cid:3)(cid:381)(cid:396)(cid:3)(cid:396)(cid:286)(cid:393)(cid:396)(cid:381)(cid:282)(cid:437)(cid:272)(cid:410)(cid:349)(cid:381)(cid:374)(cid:854)(cid:3)(cid:367)(cid:349)(cid:272)(cid:286)(cid:374)(cid:400)(cid:286)(cid:282)(cid:3)(cid:410)(cid:381)(cid:3)(cid:393)(cid:437)(cid:396)(cid:272)(cid:346)(cid:258)(cid:400)(cid:286)(cid:396)(cid:3)(cid:381)(cid:374)(cid:367)(cid:455)(cid:856)
`
`0301
`
`EX1008 (Part 2 of 3)
`Yita v. MacNeil
`IPR2020-01138
`
`
`
`5.1
`
`Introduction
`
`5.2 Overall Cooling Heat Balance
`
`285
`
`Once the part has been heated and formed to shape by contact with the cool mold
`surface, it must be cooled and rigidified. Then the part and its web must be separated
`by trimming. When thermofon'ning a reactive polymer such as thermosetting
`polyurethane or a crystallizing one such as nucleated CPET‘, the formed shape is
`rigidified by holding it against a heated mold to continue the crosslinking reaction or
`crystallization.
`In most cases. rigidifying implies cooling while in contact with a
`colder mold. For automatic thin«gage formers, the molds are usually actively cooled
`with water flowing through channels. Free surfaces of medium- and heavy-gage sheet
`are frequently cooled with forced air, water mist or water spray. For amorphous
`polymers, cooling of the formed part against a near-isothermal mold rarely controls
`the overall thermoforming cycle. For crystalline and crystallizing polymers such as
`PET, PF and HDPE, the cooling cycle can be long and can govern overall cycle time.
`When the sheet has cooled sufficiently to retain its shape and, to a large extent.
`its dimension, it
`is stripped from the mold and transferred to a trimming station.
`where the web is separated from the product. Requisite holes. slots and cut-outs are
`drilled. milled or burned into the part at this time. Thin-gage roll-fed sheet can be
`either trimmed on the mold surface immediately after forming or on an in-line
`mechanical trimming press. Heavier-gage formed sheet is usually removed from the
`mold and manually or mechanically trimmed on a remote station. Trimming is really
`a solid phase mechanical process of crack propagation by brittle or ductile fracture.
`Care is taken when trimming brittle polymers such as PS or PMMA to minimize
`microcracks. With brittle polymers,
`the very fine sander, saw or microcrack dust
`generated by mechanical fracture can be a serious problem. Other polymers such as
`PP and PET are quite tough and require special cutting dies. Dull steel-rule dies
`cause fibers or hairs at the cutting edge of thin-gage fiber-forming polymers such as
`PET and PP. Slowly crystallizing polymers pose registry problems when in-line
`trimming presses are used. The Speed of trim cutting and the nature of the cutting
`surface control
`the rate of crack propagation through the plastic. There are no
`exhaustive studies of the unique trimming and cutting characteristics of thermo-
`formed polymers and so much information must be inferred from other sources
`including extensive studies on the machining of plastics.
`
`5.2 Overall Cooling Heat Balance
`
`it is assumed to be at an
`As a first approximation, as the sheet touches the mold.
`average. equilibrated temperature, Tm“, as described in Section 3.l3. When the
`
`The unique processing conditions for crystallizing polyethylene tcrophthalate (CPET) are de-
`scribed in detail in Chapter 9. Advanced Thermoforrning Processes.
`
`(cid:926)(cid:3)(cid:1005)(cid:1013)(cid:1013)(cid:1010)(cid:3)(cid:18)(cid:258)(cid:396)(cid:367)(cid:3)(cid:44)(cid:258)(cid:374)(cid:400)(cid:286)(cid:396)(cid:3)(cid:115)(cid:286)(cid:396)(cid:367)(cid:258)(cid:336)(cid:856)(cid:3)(cid:4)(cid:367)(cid:367)(cid:3)(cid:396)(cid:349)(cid:336)(cid:346)(cid:410)(cid:400)(cid:3)(cid:396)(cid:286)(cid:400)(cid:286)(cid:396)(cid:448)(cid:286)(cid:282)(cid:856)(cid:3)
`© 1996 Carl Hanser Verlag. All rights reserved.
`(cid:69)(cid:381)(cid:3)(cid:437)(cid:374)(cid:258)(cid:437)(cid:410)(cid:346)(cid:381)(cid:396)(cid:349)(cid:460)(cid:286)(cid:282)(cid:3)(cid:282)(cid:349)(cid:400)(cid:272)(cid:367)(cid:381)(cid:400)(cid:437)(cid:396)(cid:286)(cid:3)(cid:381)(cid:396)(cid:3)(cid:396)(cid:286)(cid:393)(cid:396)(cid:381)(cid:282)(cid:437)(cid:272)(cid:410)(cid:349)(cid:381)(cid:374)(cid:854)(cid:3)(cid:367)(cid:349)(cid:272)(cid:286)(cid:374)(cid:400)(cid:286)(cid:282)(cid:3)(cid:410)(cid:381)(cid:3)(cid:393)(cid:437)(cid:396)(cid:272)(cid:346)(cid:258)(cid:400)(cid:286)(cid:396)(cid:3)(cid:381)(cid:374)(cid:367)(cid:455)(cid:856)
`No unauthorized disclosure or reproduction; licensed to purchaser only.
`
`0302
`
`0302
`
`
`
`2136
`
`Cooling and Trimming the Part
`
`[Refs on p. 379]
`
`average sheet temperature reaches the set temperature, Tm, as given in Table 2.5,
`the sheet
`is assumed to be sulficiently rigid to be removed from the mold
`surface. Typically,
`the amorphous polymer set
`temperature is about 20°C or
`40°F below its glass transition temperature, T3. The crystalline polymer set temper-
`ature is about 20°C or 40°F below its melting temperature, Tm”. During the
`cooling time,
`the mold temperature is assumed to be essentially constant at
`Tm“. The amount of heat to be removed by the coolant flowing through the mold
`Is given as:
`
`onlyrncr = v‘ - pcp(TI:quil _ Tut}
`
`=v* - pcp'AT=V* - pAH
`
`(5.1}
`
`where V“ is the volume of plastic, p is its density and er, is its heat capacity]. Heat
`is removed from the free sheet surface by convection to the environmental air. Heat
`is removed from the sheet surface against the mold surface by conduction through
`the mold to the cuclant. The coolant fluid removes the heat by convection, The heat
`load at any point on the mold surfaCe depends on the sheet thickness, 11”., at that
`point. Sheet thickness, as noted in Chapter 4, is not uniform across the mold surface.
`The heat load at any point is given as:
`
`qlocal = p - cp ' [local I AT
`
`{5‘2}
`
`This is the heat to be removed from a given region during the cooling portion of the
`total cycle, Beam. The local heat flux then is:
`
`glottal
`v _
`= _
`Qiocai ——BIW P 0,:
`
`,
`
`AT
`._
`610ml
`
`tlucal
`
`_
`(5 3)
`
`The units on qi’m. are lthm2 or Btuffi2 - h ' 0F. The total heat load during this time
`is given as:
`
`QM... = Iqruul 51‘
`
`The total heat load per unit time on a steady-state process is given as:
`
`Qsleady Ital: = thul ' N
`
`(5-4}
`
`{5-5)
`
`where N is the number of parts produced per unit time. The units on Qmm mu, are
`kW or Btu/h.
`At steady-state conditions, this energy is removed by the coolant system and by
`convection to the environmental air. Mold, coolant and air temperatures increase
`until the steady state is reached.
`
`'
`
`The last equality relates the amount of heal removed to the differential enthalpy, AH. of the
`polymer. This expression should be used if the polymer is crystalline and molten during the
`forming step and is solidifying during the cooling step.
`
`(cid:926)(cid:3)(cid:1005)(cid:1013)(cid:1013)(cid:1010)(cid:3)(cid:18)(cid:258)(cid:396)(cid:367)(cid:3)(cid:44)(cid:258)(cid:374)(cid:400)(cid:286)(cid:396)(cid:3)(cid:115)(cid:286)(cid:396)(cid:367)(cid:258)(cid:336)(cid:856)(cid:3)(cid:4)(cid:367)(cid:367)(cid:3)(cid:396)(cid:349)(cid:336)(cid:346)(cid:410)(cid:400)(cid:3)(cid:396)(cid:286)(cid:400)(cid:286)(cid:396)(cid:448)(cid:286)(cid:282)(cid:856)(cid:3)
`© 1996 Carl Hanser Verlag. All rights reserved.
`(cid:69)(cid:381)(cid:3)(cid:437)(cid:374)(cid:258)(cid:437)(cid:410)(cid:346)(cid:381)(cid:396)(cid:349)(cid:460)(cid:286)(cid:282)(cid:3)(cid:282)(cid:349)(cid:400)(cid:272)(cid:367)(cid:381)(cid:400)(cid:437)(cid:396)(cid:286)(cid:3)(cid:381)(cid:396)(cid:3)(cid:396)(cid:286)(cid:393)(cid:396)(cid:381)(cid:282)(cid:437)(cid:272)(cid:410)(cid:349)(cid:381)(cid:374)(cid:854)(cid:3)(cid:367)(cid:349)(cid:272)(cid:286)(cid:374)(cid:400)(cid:286)(cid:282)(cid:3)(cid:410)(cid:381)(cid:3)(cid:393)(cid:437)(cid:396)(cid:272)(cid:346)(cid:258)(cid:400)(cid:286)(cid:396)(cid:3)(cid:381)(cid:374)(cid:367)(cid:455)(cid:856)
`No unauthorized disclosure or reproduction; licensed to purchaser only.
`
`0303
`
`0303
`
`
`
`5.3 Cooling the Formed Shape
`
`287
`
`5.3 Cooling the Formed Shape
`
`Consider a typical cooling step. The sheet of variable thickness but known tempera-
`ture is pressed against a slightly irregular surface of a mold. The properties of the
`mold material are known and uniform throughout its volume. Chapter 6. Coolant of
`known properties flows through uniformly spaced channels in the mold. The free
`surface of the part is also cooled. At any instant, the temperature profile through the
`various layers of material is as shown in schematic in Fig. 5.]. The rate at which the
`energy is removed from the plastic to ambient air and coolant depends on the sum
`of resistances to heat transfer through each of these layers. Heat removal by the
`coolant is the primary way of cooling the formed part- Transfer to the environmental
`air is a secondary method but it can be quite important when trying to optimize cycle
`time. There are two aspects to heat removal from the formed polymer sheet to the
`coolant. The first deals with the oVerall heat transfer at steady state conditions. The
`second focuses on certain aspects of cyclical transient heat transfer.
`
`Mold
`
`Surface Irregularities
`
`Plastic Shoal
`
`Coolant Filrn fiesislance
`Content
`
`
`
`Air Gan
`
`Free Surtace Film Resistance
`
`
`
`To
`
`
`
`Ambient Environment
`
`
`
`Series Thermal Flesistances
`
`Figure 5.1 Schematic of various thermal resistances for sheet cooling against thermoforming mold
`
`(cid:926)(cid:3)(cid:1005)(cid:1013)(cid:1013)(cid:1010)(cid:3)(cid:18)(cid:258)(cid:396)(cid:367)(cid:3)(cid:44)(cid:258)(cid:374)(cid:400)(cid:286)(cid:396)(cid:3)(cid:115)(cid:286)(cid:396)(cid:367)(cid:258)(cid:336)(cid:856)(cid:3)(cid:4)(cid:367)(cid:367)(cid:3)(cid:396)(cid:349)(cid:336)(cid:346)(cid:410)(cid:400)(cid:3)(cid:396)(cid:286)(cid:400)(cid:286)(cid:396)(cid:448)(cid:286)(cid:282)(cid:856)(cid:3)
`© 1996 Carl Hanser Verlag. All rights reserved.
`(cid:69)(cid:381)(cid:3)(cid:437)(cid:374)(cid:258)(cid:437)(cid:410)(cid:346)(cid:381)(cid:396)(cid:349)(cid:460)(cid:286)(cid:282)(cid:3)(cid:282)(cid:349)(cid:400)(cid:272)(cid:367)(cid:381)(cid:400)(cid:437)(cid:396)(cid:286)(cid:3)(cid:381)(cid:396)(cid:3)(cid:396)(cid:286)(cid:393)(cid:396)(cid:381)(cid:282)(cid:437)(cid:272)(cid:410)(cid:349)(cid:381)(cid:374)(cid:854)(cid:3)(cid:367)(cid:349)(cid:272)(cid:286)(cid:374)(cid:400)(cid:286)(cid:282)(cid:3)(cid:410)(cid:381)(cid:3)(cid:393)(cid:437)(cid:396)(cid:272)(cid:346)(cid:258)(cid:400)(cid:286)(cid:396)(cid:3)(cid:381)(cid:374)(cid:367)(cid:455)(cid:856)
`No unauthorized disclosure or reproduction; licensed to purchaser only.
`
`0304
`
`0304
`
`
`
`238
`
`Cooling and Trimming the Part
`
`[Refs on p. 379]
`
`Batlle
`
`Mold Insert
`
`Flow Channel
`
`
` VI
`'IIIIIIIIAFOICFEOL'L‘.‘
`
`Figure 5.2 Typical serpentine coolant flow channel through thermoforming mold
`
`5.4 Steady State Heat Balance
`
`Consider the limiting case where all the energy is transferred directly to the mold and
`thence to the coolant. Typically, coolant lines are drilled or cast on a discrete. regular
`basis parallel to the mold surface (Fig. 5.2). Heat removal by coolant depends on
`convection heat transfer, or fluid motion'. The total amount of energy removed by
`the coolant embedded in the mold is given as:
`
`Q = UA AT
`
`(5.6}
`
`where U is the overall heat transfer coefiicient. A is the coolant surface area and AT
`is the increase in coolant temperature between inlet and outlet portions of the flow
`channel. The overall heat transfer coefficient includes all How resistances between the
`
`sheet and the coolant. It is usually written as:
`
`(5.7}
`
`ER,
`
`l 6
`
`where Ri represents the it_h resistance to heat transfer. As seen in Fig. 5.1, for flowing
`fluids, there is a convective film resistance at the conduit surface, linDhc, where nD
`is the circumference of the conduit. If the coolant fluid is not kept clean. the coolant
`channel can become coated with residue, thus increasing thermal resistance. This
`
`'
`
`This section deals only wiLh the convection heat transfer coefficient of coolant flowing through
`lines in the mold- Section 6.4 considers coolant pressure drop-flow rate relationships for the
`specification of coolant line size.
`
`(cid:926)(cid:3)(cid:1005)(cid:1013)(cid:1013)(cid:1010)(cid:3)(cid:18)(cid:258)(cid:396)(cid:367)(cid:3)(cid:44)(cid:258)(cid:374)(cid:400)(cid:286)(cid:396)(cid:3)(cid:115)(cid:286)(cid:396)(cid:367)(cid:258)(cid:336)(cid:856)(cid:3)(cid:4)(cid:367)(cid:367)(cid:3)(cid:396)(cid:349)(cid:336)(cid:346)(cid:410)(cid:400)(cid:3)(cid:396)(cid:286)(cid:400)(cid:286)(cid:396)(cid:448)(cid:286)(cid:282)(cid:856)(cid:3)
`© 1996 Carl Hanser Verlag. All rights reserved.
`(cid:69)(cid:381)(cid:3)(cid:437)(cid:374)(cid:258)(cid:437)(cid:410)(cid:346)(cid:381)(cid:396)(cid:349)(cid:460)(cid:286)(cid:282)(cid:3)(cid:282)(cid:349)(cid:400)(cid:272)(cid:367)(cid:381)(cid:400)(cid:437)(cid:396)(cid:286)(cid:3)(cid:381)(cid:396)(cid:3)(cid:396)(cid:286)(cid:393)(cid:396)(cid:381)(cid:282)(cid:437)(cid:272)(cid:410)(cid:349)(cid:381)(cid:374)(cid:854)(cid:3)(cid:367)(cid:349)(cid:272)(cid:286)(cid:374)(cid:400)(cid:286)(cid:282)(cid:3)(cid:410)(cid:381)(cid:3)(cid:393)(cid:437)(cid:396)(cid:272)(cid:346)(cid:258)(cid:400)(cid:286)(cid:396)(cid:3)(cid:381)(cid:374)(cid:367)(cid:455)(cid:856)
`No unauthorized disclosure or reproduction; licensed to purchaser only.
`
`0305
`
`0305
`
`
`
`5.4 Steady State Heat Balance
`
`289
`
`
`Table 5.1 Fouling Factors for Coolant Lines'
`
` Condition
`
`Fouling factor
`(mum - h -"F)—‘
`
` Velocity <3 l'tfs Velocity >3 l'tfs
`
`
`Treated make-up
`cooling tower water
`
`
`
`Treated make-up
`cooling tower water
`City water
`City water
`River water
`River water
`Treated bOiler
`feedwater
`Trusted boiler
`feedwater
`Industrial heat
`transfer oil
`Ethylene glycol
`Glycerine-watcr
` Brine
`Temperature c [25"F
`
`Brine
`Temperature > 125°F
`0.002
`Steam
`
`' Information extracted from [I] by permission of copyright holder
`
`0
`
`[I].
`resistance is called a fouling factor, )3". Fouling factors are given in Table 5.l
`The resistance through the mold depends on the relative shapes of the mold surface
`and the coolant channels, and is usually described as l fSkm, where S is a shape factor
`and it...
`is the thermal conductivity of the mold material. Since polymer sheet does
`not press tightly against the mold surface, there is a conductive resistance owing to
`trapped air. Uh, Although there may be other thermal resistances, these are the
`primary ones. So the overall heat transfer coeflicient. U.
`is written as:
`
`
`+—+—+fi'
`
`(5.8}
`
`lnterfacial Resistance
`
`In most heat transfer processes, intimate or perfect contact between the hot and cold
`solids is assumed. Imperfect contact causes resistance to heat flow. Mold surface
`waviness and microscopic roughness or asperities reduce physical contact (Fig. 5.3).
`Increasing pressure against
`the sheet
`increases physical contact and reduces the
`resistance to heat transfer. In general. energy is transmitted across the interstices by
`a combination of:
`
`(cid:926)(cid:3)(cid:1005)(cid:1013)(cid:1013)(cid:1010)(cid:3)(cid:18)(cid:258)(cid:396)(cid:367)(cid:3)(cid:44)(cid:258)(cid:374)(cid:400)(cid:286)(cid:396)(cid:3)(cid:115)(cid:286)(cid:396)(cid:367)(cid:258)(cid:336)(cid:856)(cid:3)(cid:4)(cid:367)(cid:367)(cid:3)(cid:396)(cid:349)(cid:336)(cid:346)(cid:410)(cid:400)(cid:3)(cid:396)(cid:286)(cid:400)(cid:286)(cid:396)(cid:448)(cid:286)(cid:282)(cid:856)(cid:3)
`© 1996 Carl Hanser Verlag. All rights reserved.
`(cid:69)(cid:381)(cid:3)(cid:437)(cid:374)(cid:258)(cid:437)(cid:410)(cid:346)(cid:381)(cid:396)(cid:349)(cid:460)(cid:286)(cid:282)(cid:3)(cid:282)(cid:349)(cid:400)(cid:272)(cid:367)(cid:381)(cid:400)(cid:437)(cid:396)(cid:286)(cid:3)(cid:381)(cid:396)(cid:3)(cid:396)(cid:286)(cid:393)(cid:396)(cid:381)(cid:282)(cid:437)(cid:272)(cid:410)(cid:349)(cid:381)(cid:374)(cid:854)(cid:3)(cid:367)(cid:349)(cid:272)(cid:286)(cid:374)(cid:400)(cid:286)(cid:282)(cid:3)(cid:410)(cid:381)(cid:3)(cid:393)(cid:437)(cid:396)(cid:272)(cid:346)(cid:258)(cid:400)(cid:286)(cid:396)(cid:3)(cid:381)(cid:374)(cid:367)(cid:455)(cid:856)
`No unauthorized disclosure or reproduction; licensed to purchaser only.
`
`0306
`
`0306
`
`
`
`290
`
`Cooling and Trimming the Part
`
`[Refs on p. 379]
`
`Cold. Rigid or Heavy-Gage sham Trapped Air
`‘Afl
`\ VW \\
`
`Hot. Flexible or Thin—Gage Sheet
`
`E"‘*--—-v *'
`
`Cold Mold
`
`Mold Asmrilies
`
`Hot Mold
`
`Figure 5.3 Interfacial resistance between sheet and thennoi'on'ning mold surface. Left shows sutr
`stantial thermal resistance owing to large air gap. Right shows reduced thermal resistance
`
`- Conduction at the asperities.
`Conduction through the interstitial fluid, and
`II Radiation.
`
`The resistance is thus a function of:
`
`II The contacting material properties such as
`Relative hardness.
`
`Thermal conductivity,
`Surface roughness and
`Flatness,
`I The conductivity and pressure of the interstitial fluid, and
`o The pressure applied against the free surface of the sheet.
`
`The interface coefficient. ha, is a measure of thermal resistance across the gap. It is
`similar in concept to the confection heat transfer in that resistance to heat flow
`decreases with increasing value of ha. For perfect contact. h. 400.
`In thermoforrning. the interstitial fluid is air, perhaps at a substantially reduced
`pressure. If the interface is a uniform air gap of 5:0.025 cm or 0.010 in and air
`thermal conductivity is kg, = 0.029 WXm - “C or 0.016?T Btu/ft - h ' “F. the value for
`hll
`is about 114 WWI-“C or 20 Btu/ftz-h‘W. Contact heat transfer coeflicient
`values between flowing polymer melts and mold surfaces of about ha: 568
`Wim2*°C or 100 Btuff'tz-h-“F have been reported in injection molding [2—4].
`Similar values are expected here. For two surfaces in contact, hll = limp”. where p is
`the applied pressure and hm depends on the relative waviness and roughness of the
`two surfaces1 Table 5.2 [5]. As seen. n has a value of about 2/3 for both rigid-rigid
`and rigid-flexible material contact in vacuum. Values for him are typically 50 times
`greater in air than in hard Vacuum.
`There are no available data for interfacial resistance during thennof'omting of
`softened plastic sheet against various types of mold surfaces. For hot sheet pressed
`against a relatively smooth. heated mold surface at a relatively high differential
`pressure,
`it
`is expected that an appropriate value for h, would be about 568
`W/rn2 - ”C or 100 Btufft2 . h - “F. For rapidly cooling and rigidizing plastic sheet
`pressing against a highly textured, cold mold surface with a modest differential
`pressure, an appropriate value range for h“ of 114 to 284 W/rnz-“C or 20 to
`
`(cid:926)(cid:3)(cid:1005)(cid:1013)(cid:1013)(cid:1010)(cid:3)(cid:18)(cid:258)(cid:396)(cid:367)(cid:3)(cid:44)(cid:258)(cid:374)(cid:400)(cid:286)(cid:396)(cid:3)(cid:115)(cid:286)(cid:396)(cid:367)(cid:258)(cid:336)(cid:856)(cid:3)(cid:4)(cid:367)(cid:367)(cid:3)(cid:396)(cid:349)(cid:336)(cid:346)(cid:410)(cid:400)(cid:3)(cid:396)(cid:286)(cid:400)(cid:286)(cid:396)(cid:448)(cid:286)(cid:282)(cid:856)(cid:3)
`© 1996 Carl Hanser Verlag. All rights reserved.
`(cid:69)(cid:381)(cid:3)(cid:437)(cid:374)(cid:258)(cid:437)(cid:410)(cid:346)(cid:381)(cid:396)(cid:349)(cid:460)(cid:286)(cid:282)(cid:3)(cid:282)(cid:349)(cid:400)(cid:272)(cid:367)(cid:381)(cid:400)(cid:437)(cid:396)(cid:286)(cid:3)(cid:381)(cid:396)(cid:3)(cid:396)(cid:286)(cid:393)(cid:396)(cid:381)(cid:282)(cid:437)(cid:272)(cid:410)(cid:349)(cid:381)(cid:374)(cid:854)(cid:3)(cid:367)(cid:349)(cid:272)(cid:286)(cid:374)(cid:400)(cid:286)(cid:282)(cid:3)(cid:410)(cid:381)(cid:3)(cid:393)(cid:437)(cid:396)(cid:272)(cid:346)(cid:258)(cid:400)(cid:286)(cid:396)(cid:3)(cid:381)(cid:374)(cid:367)(cid:455)(cid:856)
`No unauthorized disclosure or reproduction; licensed to purchaser only.
`
`0307
`
`0307
`
`
`
`Table 5.2 Contact Resistance and Conductance [5] he =h1p'
`
`(Units on hc = Wl'm2 ‘ “C or Btug’ft" ' h - °F)
`(Units on p are MP3. or lbrfinzl
`
`5.4 Steady State Heat Balance
`
`291
`
`Material
`contact
`
`Elastic deformation
`theory
`Hard—to-hard
`Hard-to-hard
`Hard-to—soft
`
`Contact coefficient. h:
`
`{Blufftl - h - ”F}
`
`223
`
`n
`
`2'8
`
`213
`1:6
`
`50 Btu/ft2 ' h - “F should be considered for first cooling time estimates. Section 5.6 on
`computer simulation of the cooling process explores the relative efl'ect of interfacial
`resistance on time-dependent sheet cooling.
`
`Shape Factor
`
`For thin metal molds, heat is conducted very rapidly from the plastic to the coolant.
`For relatively thick molds of:
`
`Plaster,
`Wood‘
`Epoxy.
`Glass fiber-reinforced unsaturated polyester resin {FRP},
`Pressed fiberboard, or
`Any other nonmetallic material,
`
`heat transfer is slowed by low mold material thermal conductivity. If the coolant
`system is considered to be coplanar with the mold surface (Fig. 5.4}, the resistance to
`heat transfer per unit length (L = 1), across a mold D units thick is given as:
`D
`5 _.
`'I'l'l
`k
`
`5.9
`
`l
`
`(
`
`R...
`
`where krrl is the mold material thermal conductivity. Thermal conductivity values for
`many mold materials are given in Table 2.7. For round discrete conduits (Fig. 5.5)
`[6], a shape factor, S, is used:
`
`where S is given by:
`
`l
`Rm=m
`
`S=——2"————
`In 335mb ZED
`D
`P
`
`(5.10)
`
`(5.1l)
`
`(cid:926)(cid:3)(cid:1005)(cid:1013)(cid:1013)(cid:1010)(cid:3)(cid:18)(cid:258)(cid:396)(cid:367)(cid:3)(cid:44)(cid:258)(cid:374)(cid:400)(cid:286)(cid:396)(cid:3)(cid:115)(cid:286)(cid:396)(cid:367)(cid:258)(cid:336)(cid:856)(cid:3)(cid:4)(cid:367)(cid:367)(cid:3)(cid:396)(cid:349)(cid:336)(cid:346)(cid:410)(cid:400)(cid:3)(cid:396)(cid:286)(cid:400)(cid:286)(cid:396)(cid:448)(cid:286)(cid:282)(cid:856)(cid:3)
`© 1996 Carl Hanser Verlag. All rights reserved.
`(cid:69)(cid:381)(cid:3)(cid:437)(cid:374)(cid:258)(cid:437)(cid:410)(cid:346)(cid:381)(cid:396)(cid:349)(cid:460)(cid:286)(cid:282)(cid:3)(cid:282)(cid:349)(cid:400)(cid:272)(cid:367)(cid:381)(cid:400)(cid:437)(cid:396)(cid:286)(cid:3)(cid:381)(cid:396)(cid:3)(cid:396)(cid:286)(cid:393)(cid:396)(cid:381)(cid:282)(cid:437)(cid:272)(cid:410)(cid:349)(cid:381)(cid:374)(cid:854)(cid:3)(cid:367)(cid:349)(cid:272)(cid:286)(cid:374)(cid:400)(cid:286)(cid:282)(cid:3)(cid:410)(cid:381)(cid:3)(cid:393)(cid:437)(cid:396)(cid:272)(cid:346)(cid:258)(cid:400)(cid:286)(cid:396)(cid:3)(cid:381)(cid:374)(cid:367)(cid:455)(cid:856)
`No unauthorized disclosure or reproduction; licensed to purchaser only.
`
`0308
`
`0308
`
`
`
`292
`
`Cooling and Trimming the Part
`
`[Refs on p. 379]
`
`
`
`Figure 5.4 Schematic of coplanar coolant flow channel and mold surface. cancept frequently called
`flooded cooling
`
`/
`
`HotSheet
`
`Coolant Channel
`
`P
`|-——'|
`
`D
`
`Mold
`
`see
`
`Figure 5.5 Geometric factors for mold shape factor analysis
`
`the thermal
`that
`is apparent
`It
`Figure 5.6 gives this equation in graphic form.
`resistance of the mold decreases with increasing value of S. which is achieved with
`many large~diameter coolant lines placed relativer close to the mold Surface. The
`typical value range for S is 2 s 533. Example 5.1 illustrates the relative effects of
`these parameters on mold thermal resistance.
`
`Example 5.] Shape Factors and Mold Thermal Resistance
`
`Determine the relative thermal resistance: for the following two molds:
`
`Mold i: Thin—walled aluminum maid with k," : i3i muff: It °F, having d = i/2-in
`water lines on P = 2 in centers, with the center-line being D = l in from the mold
`surface.
`
`(cid:926)(cid:3)(cid:1005)(cid:1013)(cid:1013)(cid:1010)(cid:3)(cid:18)(cid:258)(cid:396)(cid:367)(cid:3)(cid:44)(cid:258)(cid:374)(cid:400)(cid:286)(cid:396)(cid:3)(cid:115)(cid:286)(cid:396)(cid:367)(cid:258)(cid:336)(cid:856)(cid:3)(cid:4)(cid:367)(cid:367)(cid:3)(cid:396)(cid:349)(cid:336)(cid:346)(cid:410)(cid:400)(cid:3)(cid:396)(cid:286)(cid:400)(cid:286)(cid:396)(cid:448)(cid:286)(cid:282)(cid:856)(cid:3)
`© 1996 Carl Hanser Verlag. All rights reserved.
`(cid:69)(cid:381)(cid:3)(cid:437)(cid:374)(cid:258)(cid:437)(cid:410)(cid:346)(cid:381)(cid:396)(cid:349)(cid:460)(cid:286)(cid:282)(cid:3)(cid:282)(cid:349)(cid:400)(cid:272)(cid:367)(cid:381)(cid:400)(cid:437)(cid:396)(cid:286)(cid:3)(cid:381)(cid:396)(cid:3)(cid:396)(cid:286)(cid:393)(cid:396)(cid:381)(cid:282)(cid:437)(cid:272)(cid:410)(cid:349)(cid:381)(cid:374)(cid:854)(cid:3)(cid:367)(cid:349)(cid:272)(cid:286)(cid:374)(cid:400)(cid:286)(cid:282)(cid:3)(cid:410)(cid:381)(cid:3)(cid:393)(cid:437)(cid:396)(cid:272)(cid:346)(cid:258)(cid:400)(cid:286)(cid:396)(cid:3)(cid:381)(cid:374)(cid:367)(cid:455)(cid:856)
`No unauthorized disclosure or reproduction; licensed to purchaser only.
`
`0309
`
`0309
`
`
`
`5.4 Steady State Heat Balance
`
`293
`
`Maid 2: Thick-waited pioster maid with km = LO Stuff! 31 °F, having :1: l/2—in
`water fine: on P = 4 in centers. with the center-line being D = 2 in from the maid
`surface.
`
`Mold I
`
`Mold 2
`
`Pfd = 4. Did = 2. From Fig. 5.6. S = 2.
`l
`I
`
`Hid—:8. Dfd=4. From Fig. 5.6. S: 1.6.
`
`‘
`__L_
`“mi 1.5- 1.0
`
`= 0.625
`
`R
`
`The plaster mold has more than 160 times the thermal resistance to heat
`transfer than the aluminum mold.
`
`Factor.S
`
`Shape
`
`o
`
`2
`
`4
`
`a
`
`a
`
`TD
`
`12
`
`14
`
`Coolant Channel Spacing to Diameter Ratio. Pid
`
`Figure 5.6 Effect of coolant line location on mold shape factor
`
`Convection Heat Transfer Coefficient
`
`roll-fed thin-gage thermoformers and on many
`The metal molds on automatic.
`heavy-gage forming operations are actively cooled. with water being the primary
`
`(cid:926)(cid:3)(cid:1005)(cid:1013)(cid:1013)(cid:1010)(cid:3)(cid:18)(cid:258)(cid:396)(cid:367)(cid:3)(cid:44)(cid:258)(cid:374)(cid:400)(cid:286)(cid:396)(cid:3)(cid:115)(cid:286)(cid:396)(cid:367)(cid:258)(cid:336)(cid:856)(cid:3)(cid:4)(cid:367)(cid:367)(cid:3)(cid:396)(cid:349)(cid:336)(cid:346)(cid:410)(cid:400)(cid:3)(cid:396)(cid:286)(cid:400)(cid:286)(cid:396)(cid:448)(cid:286)(cid:282)(cid:856)(cid:3)
`© 1996 Carl Hanser Verlag. All rights reserved.
`(cid:69)(cid:381)(cid:3)(cid:437)(cid:374)(cid:258)(cid:437)(cid:410)(cid:346)(cid:381)(cid:396)(cid:349)(cid:460)(cid:286)(cid:282)(cid:3)(cid:282)(cid:349)(cid:400)(cid:272)(cid:367)(cid:381)(cid:400)(cid:437)(cid:396)(cid:286)(cid:3)(cid:381)(cid:396)(cid:3)(cid:396)(cid:286)(cid:393)(cid:396)(cid:381)(cid:282)(cid:437)(cid:272)(cid:410)(cid:349)(cid:381)(cid:374)(cid:854)(cid:3)(cid:367)(cid:349)(cid:272)(cid:286)(cid:374)(cid:400)(cid:286)(cid:282)(cid:3)(cid:410)(cid:381)(cid:3)(cid:393)(cid:437)(cid:396)(cid:272)(cid:346)(cid:258)(cid:400)(cid:286)(cid:396)(cid:3)(cid:381)(cid:374)(cid:367)(cid:455)(cid:856)
`No unauthorized disclosure or reproduction; licensed to purchaser only.
`
`0310
`
`0310
`
`
`
`294
`
`Cooling and Trimming the Part
`
`[Refs on 13. 3'39]
`
`coolant. There is a thermal resistance between the cool bulk flowing fluid and the
`warmer tube wall (Fig. SJ). The primary dimensionless group used in fluid mechan-
`ics is the Reynolds number, Re;
`
`Re
`
`_Dvp
`u
`
`(5.12}
`
`where D is the tube diameter. v is the fluid velocity. p is the density of the fluid and
`a is its Newtonian viscosity [7]. The Reynolds number is the ratio of inertial to
`viscous forces for the fluid. Slowly moving fluids are laminar when Re (2000.
`Convection heat transfer to slowly moving fluids is poor. Rapidly flowing fluids are
`fully turbulent when Re) l0.[}00 and heat
`transfer is very rapid. Example 5.2
`illustrates the interaction between flow rate and Reynolds number.
`
`Example 5.2 Water as Coolant——Flow Rates
`
`Consider 2t°C or 70°F water flowing through 0.5-1}: or 1.27-cm diameter cootont
`channels. Determine the Reynolds number and the flow characteristic if the velocity
`is a) 0.52ftfs or 0J6m/s and b) 2.6ftz‘s or 0. 7.9mm What are the oot’ametricflow
`rates at these velocities?
`
`The water density is 62.4 lbffti. The viscosity is 0.658 x 10‘3 lbmg’ft ' s. The
`Reynolds number is:
`
`0.5
`Dvp
`R. —T-—v—l-2—ft
`
`_
`n - s _
`1
`lbm
`ft
`V rs- 62.4? 0_.653X l0‘3E—3951 V
`
`For v = 0.52 ftfs: Re 2 2050 and the water is laminar.
`For v = 2.6 ftis: Re = 10.300 and the water is turbulent.
`
`The volumetric flow rate is given as:
`J
`2
`V=Efl-v=0.00136'v E=0.t512-vg—’3.”
`4
`s
`mm
`
`For v= 0.52 ftfs. the flow rate is 0.32 GPM.
`For v = 2.6 ftfs. the flow rate is L6 (3PM.
`
`As discussed in Section 3.6. energy interchange between solid surfaces and
`flowing fluids is by convection. The proportionality between heat flux and thermal
`driving force is the convection heat transfer coefficient. The convection heat transfer
`coefficient is obtained from standard heat transfer theory and experiments. There are
`many methods for calculating values of h,_.. In general, however, the Chilton-Colburn
`analogy between resistance to fluid flow and resistance to thermal energy flow yields
`adequate results [8]. The analogy states:
`
`5: - Pee = as
`
`(5.13)
`
`where St is the Stanton number, P1- is the Prandtl number and f is the coefficient of
`friction or friction factor. The Stanton and Prandtl numbers are:
`
`(cid:926)(cid:3)(cid:1005)(cid:1013)(cid:1013)(cid:1010)(cid:3)(cid:18)(cid:258)(cid:396)(cid:367)(cid:3)(cid:44)(cid:258)(cid:374)(cid:400)(cid:286)(cid:396)(cid:3)(cid:115)(cid:286)(cid:396)(cid:367)(cid:258)(cid:336)(cid:856)(cid:3)(cid:4)(cid:367)(cid:367)(cid:3)(cid:396)(cid:349)(cid:336)(cid:346)(cid:410)(cid:400)(cid:3)(cid:396)(cid:286)(cid:400)(cid:286)(cid:396)(cid:448)(cid:286)(cid:282)(cid:856)(cid:3)
`© 1996 Carl Hanser Verlag. All rights reserved.
`(cid:69)(cid:381)(cid:3)(cid:437)(cid:374)(cid:258)(cid:437)(cid:410)(cid:346)(cid:381)(cid:396)(cid:349)(cid:460)(cid:286)(cid:282)(cid:3)(cid:282)(cid:349)(cid:400)(cid:272)(cid:367)(cid:381)(cid:400)(cid:437)(cid:396)(cid:286)(cid:3)(cid:381)(cid:396)(cid:3)(cid:396)(cid:286)(cid:393)(cid:396)(cid:381)(cid:282)(cid:437)(cid:272)(cid:410)(cid:349)(cid:381)(cid:374)(cid:854)(cid:3)(cid:367)(cid:349)(cid:272)(cid:286)(cid:374)(cid:400)(cid:286)(cid:282)(cid:3)(cid:410)(cid:381)(cid:3)(cid:393)(cid:437)(cid:396)(cid:272)(cid:346)(cid:258)(cid:400)(cid:286)(cid:396)(cid:3)(cid:381)(cid:374)(cid:367)(cid:455)(cid:856)
`No unauthorized disclosure or reproduction; licensed to purchaser only.
`
`0311
`
`0311
`
`
`
`5.4 Steady State Heat Balance
`
`295
`
`Table 5.3 Prandtl Number Values For Several Coolants
`[9.10]
`
`
`Coolant
`
`Temperature
`(“Fl
`
`(“Cl
`
`Prandtl no.
`
`Air
`Air
`
`Steam
`Steam
`
`Water
`Water
`Water
`Water
`Water
`
`SAE 30 Oil
`SAE 30 Oil
`SAE 30 Oil
`SAE 30 Oil
`SAE 30 Oil
`SAE 30 Oil
`
`Glycerine
`Glycerine
`Glycerine
`Glycerine
`Glycerin:
`Air
`Air
`Air
`
`Light Oil
`Light Oil
`Light Oil
`Light Oil
`
`
`
`0.?2
`0.72
`
`0.96
`0.94
`
`13.?
`6.82
`452
`2.74
`1.88
`
`“70
`340
`[22
`62
`35
`22
`
`31.000
`12.500
`5.400
`2.500
`1.600
`0. 72
`0.7l
`0.685
`
`340
`62
`35
`22
`
`St =
`
`
`h
`
`13ch
`
`p, = E
`at
`
`[5.14)
`
`{5.15)
`
`the
`transfer coefficient. p is the fluid density at
`where h is the convective heat
`appropriate temperature. cl, is the fluid heat capacity, v is the average fluid velocity.
`v = trip. is the kinematic viscosity. and o: = kfpcp, is the fluid thermal diffusivity. In
`essence, Pr is the ratio of inertial to thermal properties and St is the ratio of fluid to
`thermal resistances. Table 5.3 gives appropriate Prandtl number values for several
`coolants [9,10]. As examples, Pr: 7 for room temperature water and Pr 3 300 for
`
`(cid:926)(cid:3)(cid:1005)(cid:1013)(cid:1013)(cid:1010)(cid:3)(cid:18)(cid:258)(cid:396)(cid:367)(cid:3)(cid:44)(cid:258)(cid:374)(cid:400)(cid:286)(cid:396)(cid:3)(cid:115)(cid:286)(cid:396)(cid:367)(cid:258)(cid:336)(cid:856)(cid:3)(cid:4)(cid:367)(cid:367)(cid:3)(cid:396)(cid:349)(cid:336)(cid:346)(cid:410)(cid:400)(cid:3)(cid:396)(cid:286)(cid:400)(cid:286)(cid:396)(cid:448)(cid:286)(cid:282)(cid:856)(cid:3)
`© 1996 Carl Hanser Verlag. All rights reserved.
`(cid:69)(cid:381)(cid:3)(cid:437)(cid:374)(cid:258)(cid:437)(cid:410)(cid:346)(cid:381)(cid:396)(cid:349)(cid:460)(cid:286)(cid:282)(cid:3)(cid:282)(cid:349)(cid:400)(cid:272)(cid:367)(cid:381)(cid:400)(cid:437)(cid:396)(cid:286)(cid:3)(cid:381)(cid:396)(cid:3)(cid:396)(cid:286)(cid:393)(cid:396)(cid:381)(cid:282)(cid:437)(cid:272)(cid:410)(cid:349)(cid:381)(cid:374)(cid:854)(cid:3)(cid:367)(cid:349)(cid:272)(cid:286)(cid:374)(cid:400)(cid:286)(cid:282)(cid:3)(cid:410)(cid:381)(cid:3)(cid:393)(cid:437)(cid:396)(cid:272)(cid:346)(cid:258)(cid:400)(cid:286)(cid:396)(cid:3)(cid:381)(cid:374)(cid:367)(cid:455)(cid:856)
`No unauthorized disclosure or reproduction; licensed to purchaser only.
`
`0312
`
`0312
`
`
`
`296
`
`Cooling and Trimming the