Injection molding

Injection Molding
2.810 Fall 2002
Professor Tim Gutowski


Short history of plastics
1862
1866
1891
1907
1913
1926
1933
1938
1939
1957
1967

first synthetic plastic
Celluloid
Rayon
Bakelite
Cellophane
PVC
Polyethylene
Teflon
Nylon stockings
velcro
“The Graduate”

Outline
Basic operation
Cycle time and heat transfer
Flow and solidification
Part design
Tooling
New developments
Environment


Readings
Tadmore and Gogos


Molding and Casting pp584 -610

Boothroyd Dewhurst


Design for Injection Molding pp 319 - 359

Kalpakjian see Ch 18
Injection molding case study;Washing machine
augers; see on web page


30 ton, 1.5 oz (45 cm3) Engel

Injection Molding Machine
for wheel fabrication

Process & machine schematics
*

*

Schematic of thermoplastic Injection molding machine
* Source: />

Process Operation
Temperature: barrel zones, tool, die zone
Pressures: injection max, hold
Times: injection, hold, tool opening
Shot size: screw travel
Processing window
Temp.

Thermal
degradation
Flash
Shortshot

Melt

Pressure


Typical pressure/temperature cycle
*

*

Time(sec)

Cooling time generally dominates cycle time

tcool

* Source: />
2
(
half thickness )
=

α
α = 10 −3 cm3 sec for polymers

Time(sec)


Calculate clamp force, & shot size
F=P X A = 420 tons
3.8 lbs = 2245 cm3
=75 oz

Actual ; 2 cavity 800 ton


Clamp force and machine cost

Heat transfer

Note; αTool > αpolymer

1-dimensional heat conduction equation :
qx

qx + ∆qx

Fourier’s law

Boundary Conditions:

∂q
∂
( ρ ⋅ c p ⋅ T )∆x∆y = − x ∆x∆y
∂t
∂x
∂T
qx = −k
∂x
∂T
∂ 2T
∂T
∂ 2T
ρ ⋅ cp
= k 2 or
=α 2

∂t
∂x
∂t
∂x
1st kind
2nd kind
3rd kind

T ( x = x' ) = constant
∂T
( x = x' ) = constant
∂x
∂T
−k
( x = x' ) = h (T − T∞ )
∂x
−k

The boundary condition of 1st kind applies to injection molding since the
tool is often maintained at a constant temperature


Heat transfer
Tii
t
TW

-L

x

+L

Let Lch = H/2 (half thickness) = L ; tch = L2/α ;
∆Tch = Ti – TW (initial temp. – wall temp.)

T − TW
x
α ⋅t
; ξ = + 1; FO = 2
Non-dimensionalize: θ =
Ti − TW
L
L

Dimensionless equation:
Initial condition
Boundary condition

Separation of variables ;
matching B.C.; matching I.C.

∂θ
∂ 2θ
= 2
∂FO ∂ξ
FO = 0

θ =1

ξ =0
ξ =2

θ =0
θ =0

θ (ξ , FO ) = ∑ f ( FO ) g (ξ )


Temperature in a slab
Centerline, θ = 0.1, Fo = αt/L2 = 1

Bi-1 =k/hL


Reynolds Number
Reynolds Number:

V2
ρ
inertia
ρVL
L
Re =
=
V
µ
µ 2 viscous
L

For typical injection molding

ρ = 1 g cm3 = 103 N m 4 s 2 ; LZ = 10 −3 m thickness
V≈

−1

Part length 10
=
;
Fill time
1s

For Die casting

µ = 103 N ⋅ s m 2

3 ⋅103 ×10 −1 ×10 −3
Re ≈
= 300
−3
10

* Source: />
Re = 10 −4


Viscous Shearing of Fluids
F

v

F/A

v
τ =µ
h

µ

h
1

F v
∝
A h

v/h

Newtonian Viscosity

Generalization:

τ = µγ

τ
= η (γ )
γ

γ : shear rate

Injection molding

“Shear Thinning”
~ 1 sec-1 for PE

γ

Typical shear rate for
Polymer processes (sec)-1
Extrusion
Calendering
Injection molding
Comp. Molding

102~103
10~102
103~104
1~10


Viscous Heating
P
F ⋅v F v
v
=
= ⋅ = µ 
Vol Vol
A h
h

Rate of Heating
= Rate of Viscous Work
Rate of Temperature rise

Rate of Conduction out

ρ ⋅ cp

dT
v
= µ 
dt
h

2

or

dT
µ
=
dt ρ ⋅ c p

2

v
 
h

2

dT
k d 2T
k ∆T
=
~
dt ρ ⋅ c p dx 2 ρ ⋅ c p h 2
Viscous heating µv 2
=
Conduction
k∆T

Brinkman number

For injection molding, order of magnitude ~ 0.1 to 10


Non-Isothermal Flow
Flow rate: 1/t ~V/Lx

v

Heat transfer rate: 1/t ~a/(Lz/2)2

Flow rate
V ⋅ L2z
1 VLz Lz
~
=
⋅

Heat xfer rate 4α ⋅ Lx 4 α Lx

Small value
=> Short shot

For injection molding

Flow rate
1 10cm / s × 0.1cm 0.1cm
~
⋅
= 2.5
−3
2
Heat xfer rate 4 10 cm / s
10cm
For Die casting of aluminum

Flow rate
1 10cm / s × 0.1cm 0.1cm
−2
~
⋅
≅
10
Heat xfer rate 4 0.3cm 2 / s
10cm
* Very small, therefore it requires thick runners

Injection mold

die cast mold


Fountain Flow
*

**

* Source: ; ** Z. Tadmore and C. Gogos, “Principles of Polymer Processing”


Shrinkage distributions
sample

Transverse direction

V=3.5cm/s

V=8cm/s

* Source: G. Menges and W. Wubken, “Influence of processing conditions on Molecular Orientation in Injection Molds”


Gate Location and Warping
Sprue

2.0

60°

2.0

Before shrinkage

1.96

Shrinkage
Direction of flow – 0.020 in/in
Perpendicular to flow – 0.012

60.32°

1.976

After shrinkage

Air entrapment
Gate

Center gate: radial flow – severe distortion

Diagonal gate: radial flow – twisting

Edge gate: warp free, air entrapment

End gates: linear flow – minimum warping

Effects of mold temperature and
pressure on shrinkage
LDPE

LDPE

0.030

PP

0.025

Acetal

0.025

0.020

Nylon 6/6

0.020

Shrinkage

Shrinkage

0.030

0.015

0.010

0.015

Acetal
PP with
flow
PP across
flow

0.010
0.005

0.005

Nylon
6/6

PMMA

PMMA
0.000

0.000
100

120

140

160

180

200

Mold Temperature (F)

220

240

6000

10000
8000

14000
12000

18000
16000

Pressure on injection plunger (psi)


Where would you gate this part?


Weld line, Sink mark

Gate

Weld line

Mold Filling

Solidified part

Sink mark
* Source: />
Basic rules in designing ribs
to minimize sink marks


Injection Molding
*

*

* Source: />