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comsol-paper.pdf
Press and Blow Plunger Cooling
Pierre Lankeu Ngankeu, EMHART Glass, 89 Phoenix Ave, Enfield, CT 06082
[email protected]
Ernesto Gutierrez Miravete, Rensselaer at Hartford, 275 Windsor st, Hartford, CT 06120
[email protected]
Abstract: In the container forming process, the
Press and blow process is used to form the
parison. It consists of driving a metallic plunger
upward into the gob. While P&B has had the
advantage of reducing container weight by as
much as 33% [1], the plunger-gob can induce
micro-checks that weaken container strength.
Therefore plunger temperature is very critical
and typically these parts are changed on a daily
basis solely based on observation and operator
experience. As the glass industry moves towards
fully automated forming machines it is necessary
to understand what happens to a plunger over
time, as it goes through many press cycles. We
intend to model the heat transfer due to the glass
contact on the plunger during several P&B
cycles using COMSOL Multiphysics. We expect
to produce a thermal profile history of the
plunger showing how different plunger cooling
schemes affect plunger temperature over time.
made out of steel
k = 54
W
m⋅K
[2]
with coatings
such as tungsten carbide. Every precaution is
taken to prevent the glass from sticking to the
plunger to avoid creating defects. Therefore,
plunger cooling is critical for process control. In
this study we look at a Narrow neck press and
blow (NNPB) plunger currently used at the
Emhart Glass Research Center (EGRC) in
Windsor, CT (Fig.2). In our analysis we will not
solve for the flow of glass along the plunger
surface. We will look at the interaction between
the inside cooling and the outside heating of the
plunger by the hot gob. We will initially use
simple axissymmetric plunger geometry to
define our problem, and then use it as a template
to model the EGRC plunger.
Glass fills up to here
Fig1. Neck Ring Line
Press & Blow Process
Keywords: container forming, heat transfer,
press and blow, glass
1. Introduction
The P&B plunger is in contact with the glass
from the moment the gob loading ends to the
instant the molds open for parison invert. During
the glass contact time, the glass covers the
plunger up to the neck ring line (Fig.1). Thus the
whole plunger length is not subjected to any heat
transfer from the glass. The plungers are usually
Fig2. EGRC Plunger
1
2.2 Governing Equations
We are solving the heat equation at the
2. System Description
2.1 Model Geometry
The 2D axissymmetric plunger geometry (Fig.3)
has the shape of a hollow rectangle with a length
of 100mm, an inner radius of 15mm and an outer
radius of 25mm. This plunger thickness is 10mm
and uniform across its length. The six edges
constitute the boundaries of our 2D
axissymmetric plunger. On the other hand, the
EGRC plunger (Fig.4) has the form of a long
hollow torus tapered to a half hollow sphere. Its
thickness varies between 2mm at the tip of the
plunger to 1.6mm at the neck ring line.
Moreover, it is 138mm long from the neck ring
line to the tip. The surfaces inside and outside
the plunger constitute this model boundaries.
While the 2D axissymmetric geometry was
generated using COMSOL Multiphysics drawing
toolbox, our 3D model geometry was imported
as an IGES file from an existing ProE drawing.
boundaries [2]: k ⋅ ∇
θ =
∂θ
∂t
Where θ = θ (t , x, y , z ) is the temperature as a
function of time and space, and k is the thermal
conductivity. In this analysis we assume a
constant thermal conductivity. For the 2D
axissymmetric plunger the equation becomes
 ∂ 2θ 1 ∂θ ∂ 2θ  ∂θ
k ⋅  2 + ⋅
+ 2  =
and for the
r
∂
r
∂
t
∂
r
∂
z


2
2
 ∂ θ ∂ θ ∂ 2θ  ∂θ
3D plunger k ⋅ 
.
+ 2 + 2  =
2
∂y
∂z  ∂t
 ∂x
2.3 Global Assumptions
In order to simulate the heat flow of glass down
the plunger length we will need to define
functions that shift the heat flow down the
vertical axis. We will assume that it takes 1s for
the glass to cover the plunger up to the neck ring
line, and 1s for the interval of time between
presses where the plunger is not in direct contact
with the glass. Hence, we are defining a 2s
second cycle where the plunger is subjected to
conductive and radiative heat transfer from the
glass while being cooled from the inside. Then, it
is subjected to inside cooling, thermal radiation
and some natural convection. We assume a
constant glass temperature Tglass = 1273K, an
emissivity epsi = 0.7 both defined as global
expressions. Define Stefan-Boltzmann’s constant
sigma = 5.6696E-08. In order to distribute the
heat flow down the plunger, we introduce the
functions zs (t ) (Fig.5) in 2D and ys(t ) (Fig6) in
3D, so that:
1
3
2
6
4
2
5
Fig3. 2D Axissymmetric Plunger Geometry

  π 
0.1 ⋅ ABS  sin  t  , t = 2n
zs (t ) = 
  2 

0
,
t = 2n + 1


  π 
0.181367 ⋅ ABS  sin  t  , t = 2n
ys(t ) = 
  2 

0
,
t
=
2n + 1

Fig4. 3D EGRC Plunger Geometry
2
Fig5. zs(t)
Fig7. htop(t)
Fig8. Ttop(t)
Fig6. ys(t)
3. Boundary Conditions
3.1 2D axissymmetric
The boundary conditions are set as seen below
for the 2D axissymmetric case (Fig.4):
Boundary 1 is set as an axis of symmetry r = 0
Boundary 5 is set as thermal insulation ∇θ = 0
Boundaries 2 and 4 are set as heat flux and we
assumed a constant heat transfer coefficient
n • (k ⋅ ∇θ ) = h ⋅ (θ ∞ − θ )
W
h = 250 2
, θ ∞ = 350 K
m ⋅K
Fig9. hplunger(z)
Boundary 3 the top boundary is set as heat flux
n • (k ⋅ ∇ θ ) = h ⋅ (θ ∞ − θ ) + epsi ⋅ sigma ⋅ (Tglass 4 − θ 4 )
h = htop (t ) (Fig.7), θ ∞ = Ttop (t ) (Fig.8).
Boundary 6 is set as a heat flux boundary with
n • (k ⋅ ∇θ ) = h ⋅ (θ ∞ − θ ) + epsi ⋅ sigma ⋅ (Tglass 4 − θ 4 )
h = hplunger ( z − 0.05 + zs (t )) (Fig.9)
θ ∞ = Tplunger ( z − 0.05 + zs (t )) (Fig.10)
Fig10. Tplunger(z)
3
gradient. A plunger initial temperature of 773K
was assumed (typical for standard beer bottles).
At first we tested our set up by solving the 2D
axissymmetric problem for 2 cycles or 4s with
variable time steps between 0.001s and 0.1s and
got it to converge in 3.406s (1648 elements)
using the time dependent solver. We plotted the
contours of temperature on the domain at 1s, 2s,
3s and 4s (Fig.15, 16, 17, 18) as well as the
temperature for the far top corner of our plunger
geometry (Fig.19).
3.2 3D EGRC Plunger
For the 3D EGRC plunger there are 3 groups:
Group1 comprises all outside faces below the
neck ring fill line and is set as thermal insulation
∇θ = 0
Group 2 comprises all inside faces and is set as
heat flux with n • (k ⋅ ∇θ ) = h ⋅ (θ ∞ − θ )
h = 250
W ,
θ ∞ = 350 K
m2 ⋅ K
Group 3 is composed of all outside faces in
contact with the glass and is set as heat flux with
(
n • (k ⋅ ∇θ ) = h ⋅ (θ ∞ − θ ) + epsi ⋅ sigma ⋅ Tglass 4 − θ 4
)
h = hplunger ( y − 0.11605 + ys (t )) (Fig.11)
θ ∞ = Tplunger ( y − 0.11605 + ys(t )) (Fig.12)
Fig13. 2D Axissymmetric mesh
Fig11. hplunger(y)
Fig14. 3D Plunger Mesh
Fig12. Tplunger(y)
4. Mesh and Solution
Both models were meshed using free mesh
parameters in COMSOL Multiphysics (Fig.13).
The 3D mesh (Fig.14) needed to be finer because
of the smaller wall thickness of the plunger to
get a better resolution of the temperature [4]
Fig15. T After 1s
4
From the various plots we established that our
model was working as we can see the plunger
heating up for one second and the cooling for the
next second over and over. We solved the 3D
model in the same fashion using similar choice
of time step and solver. The solution converged
after10min and 47s. Moreover, we also plotted
the temperature at the tip of the plunger as a
function of time for 10 cycles (Fig.20).
Fig16. T After 2s
Fig20. 3D Tip corner temperature vs. Time
After 4s
Fig17. T After 3s
5. Discussion of Results
When we look at the plot of temperature
contours each cycle, it can be observed that the
plunger is getting heating up from cycle to cycle.
Especially at the tip which is usually the hottest
part of the plunger since it is in contact with the
gob for the longest amount of time. As the
plunger goes through this periodic heating and
cooling, it will be somewhat hotter than its initial
temperature. After numerous cycles it heats up to
the point where the gob starts sticking. Clearly
we are making assumptions such as constant heat
transfer coefficients which are not the case in the
glass plant. However, the results are pointing in
the right direction. The 3D results are dependent
on the mesh since a coarse mesh can not properly
resolve the temperature gradient inside the
plunger thickness. There are also dependent on
the cycle time, and type of container. A standard
light beer bottle usually has lower heat content
and faster cycle time than would a typical wine
bottle. Glass type can be a factor since green and
amber glasses do not radiate heat as well as flint
glass [3]. The main observation is that it would
take a lot more cooling from the inside to keep
the plunger within a suitable temperature range
Fig18. T After 4s
Fig19. 2D Tip corner temperature vs. Time
After 4s
5
during pressing. At this point it seems to be a
losing proposition since the inside cooling
cannot keep the plunger temperature down over
time.
6. Conclusion
This model is only the starting point for our
analysis; we could tailor it in the future to
include different type of inside cooling, real
process timing and heat flux data from the field.
I would also be interesting to see how a larger
container production might be affected in
comparison to light weight beer container.
Ultimately, we want to evaluate the effects of
thermal fatigue induced on all mold equipment
to have more control over our process in order to
increase production speed by anticipating mold
equipment swaps and just not only reacting after
detecting defects in the containers. This could
potentially also decrease the scrap rate.
7. References
1. M. Sarwar; A.W. Armitage, Tooling
requirements for glass container production for
the narrow neck press and blow process, Journal
of Materials Processing Technology, Volume
139 Issue1-3, 160-163 (2003)
2. S. Kacaç; Y. Yener, Heat Conduction, Taylor
& Francis, NY (1993)
3. K. Storck; D. Loyd; B. Augustsson, Heat
transfer modeling of the parison forming in glass
manufacturing, European Journal of Glass
Science and Technology Part A, Volume 39
Number 6, 210-216 (1998)
4. M. Hyre; Y. Rubin, Numerical Modeling of
Gob and Container Forming, Fluent user
Conference, (20xx)
6
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