Ch13 math

©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e

Extruder Screw

Figure 13.5 Details of an extruder screw inside the barrel.

Flight Angle A

The Flight Angle A can be determined from the following relationship.

tanA = pitch / πD (eq. 13.4)

A = tan-1(p / (πD))


Volume Flow Rate

Drag flow results from friction between the viscous liquid and the two opposing surfaces moving relative to each other.

Qd = 0.5vdw (eq. 13.5)

v = velocity of the moving plate, in/sec (m/s)

v = πDN cos A (eq. 13.6)

D = screw flight diameter, in. (mm)

N = screw rotational speed, rev/sec


Volume Flow Rate


Qd = 0.5vdw

d = distance separating the two plates, in. (m)

d = dc (eq. 13.7)

dc = screw channel depth, in. (mm)


Volume Flow Rate


Qd = 0.5vdw

w = the width of the plates perpendicular to velocity direction, in. (m)

w = wc = (πDtanA – wf)cosA (eq 13.8)

Reduces to wc = πDsinA (eq 13.9)

wc = screw channel width, in. (mm)

A = flight angle

wf = flight land width, in. (mm)©2007 John Wiley & Sons, Inc. M P Groover, Fundamentals of Modern Manufacturing 3/e

Volume Flow Rate


Qd = 0.5vdw

Qd = 0.5 π2D2NdcsinAcosA (eq 13.10)


Volume Flow Rate

Back pressure flow in the barrel will reduce the material being moved by drag flow.

Qb = pπDdc3sin2A /12ηL (eq. 13.12)

p = head pressure in the barrel, lb/in2 (Mpa) L = length of the barrel, in. (m) η = viscosity of polymer melt, lb-sec/in2 (N-s/m2)


Volume Flow Rate

Melt flow is the difference between drag flow and back pressure flow.

Qx = Qd – Qb

Qx = 0.5π2D2NdcsinAcosA - pπDdc3sin2A /12ηL


Extruder and Die Characteristics

If back pressure is zero, then the flow would equal drag flow denoted as Qmax.

Qmax = 0.5π2D2NdcsinAcosA (eq. 13.14)

If back pressure was so great that there was no flow, then Qd = Qb The maximum head pressure would be pmax

pmax = 6πDNLηcotA / dc2 (eq. 13.15)



The actual operating parameters will lie somewhere between Qmax and pmax.

Qx = Ksp (eq. 13.16)

Qx = flow rate, in.3/sec (m3/s)

p = head pressure, lb/in2 (MPa) Ks = shape factor for the die, in.5/lb-sec (m5/Ns)

for a circular die, Ks is:

Ks = πDd4 / 128ηLd (eq. 13.17)



The actual operating parameters will lie somewhere between Qmax and pmax.

Ks = πDd4 / 128ηLd (eq. 13.17)

Dd = die opening diameter, in. (m)

η = melt viscosity, lb-sec/in2 (N-s/m2)

Ld = die opening length, in. (m)



Shrinkage

Reduction in linear size during cooling from molding to room temperature

Polymers have high thermal expansion coefficients, so significant shrinkage occurs during solidification and cooling in mold

Typical shrinkage values: Plastic Shrinkage, mm/mm (in/in)

Nylon‑6,6 0.020

Polyethylene 0.025

Polystyrene 0.004

PVC 0.005


Compensation for Shrinkage

Dimensions of mold cavity must be larger than specified part dimensions:

Dc = Dp + DpS + DpS2 (eq. 13.19)

where Dc = dimension of cavity, in. (mm)

Dp = molded part dimension, in. (mm)

and S = shrinkage value

Third term on right hand side corrects for shrinkage in the shrinkage

Ch13 math

Technology

Transcript of Ch13 math