Transcript On-line Flow Rate and Pressure Analysis with Sensor Fusion

Advances in
Molding Technology
David Kazmer
University of Massachusetts Lowell
Introduction
Who Is David Kazmer?
1985
1990
1995
2000
2005
Opening Remarks

Product designs remain inefficient



Minority of applications leverage simulation
Wasting material, cycle time, added value…
Processes are thought of as “proscribed”


Significant opportunities exist
Better observability through sensor fusion


Multiple sensors with real-time analysis
Better controllability through process design

Control of initial & boundary conditions
Vision: Gate-Level Control of
Flow Rates & Cavity Pressures

“Decoupled Molding”




Decouple the mold from the molding machine
Decouple the gates from each other
Decouple filling from the packing at each gate
Requires two major advances:


Real-time process simulation
Improved melt valves
Real Time Process Simulation
1-D Flow In A Tube

Hagen-Poiseuille Flow



Viscous, laminar flow (constant viscosity)
Relates flow rate, pressure, and viscosity
R 4 P
Q
8L
Flow conductance, k, defined as:
Q R 4
k

P 8L
Flow Network Analysis


Consider a two-branched hot runner system
Geometry & flow conductance known

Develop flow conductance matrix
 Q1   k12
Q   k
 2   12
Q3   0
 
Q4   0
Q5   0
  
Q6   0
01
k12
 k12  k 23  k 24
k 23 3
k 24
0
0
5
0
0
k 23
k 24
0
 k 23 2k 35
0
04
 k 24  k 46
k 35
0
k 35
0
6
 k 35
0
k 46
0
0   P1 
0   P2 
0   P3 
 
k 46   P4 
0   P5 
 
 k 46   P6 
Flow Network Analysis
1

Apply boundary conditions:



P1, P5, & P6 observed
Q2, Q3, & Q4 equal 0
Solve on-line in real-time
Q11   k12
Q
Q0   k
 2   12
Q03   0
   
Q04   0
Q
Q55   0
  
Q66   0
Q
3
2
5
000 0
0 0 00   P1obs00
0 0 P1obs
P1 
 Q1  kk1212
 2 2




0 k 24
 k01212 kk23232kk2424 4 1kk2323 1
k 240   P2 00
0 0  PP
2 2

 0  kk2323
0
1 kk2323
2kk35035 1 0 00   P3k35k 35 0 0  PP
33

 

   
0
0
1
0

2
0
1
k
k
0
0


k
k


k
k
0
0
k
k
P
PP
2424
46
46 46  
4 4
  2424

 46 4 
obs 
Q5  00 0
0
1kk3535 0  1 0 00   P5
k35k 35 0 0 P5obs
P5 
  
  obs 
  obs 
0
000 1
0 k 46
k461  P6 00  
k 46k 46P6P6 
Q6  00 0
4
6
Notes

Previous approach is relatively easy


Hot runner geometry known
Constant viscosity assumed



“Newtonian”
Flow conductance matrix pre-computed
and remains constant
Able to invert matrix in microseconds

Definitely feasible for 64+ cavities
Not so accurate: ignores
shear heating and shear thinning
Rheological
Modeling

Newtonian
1000

Ellis Model
  
0

 1 
 1 2 
  



 1
Viscosity (Pa Sec)

100
Cross-WLF
WLF Model
Newtonian
Power Law
 (T , P)
 (, T , P)  0
 
1  ( 0* )1n

0 (T , p)  D1 exp(
A1 (T  T )
)
*
A2  (T  T )
*
Ellis
10
T  Tt
1
10
100
Shear Rate (1/sec)
1000
10000
Three levels of flow analysis

Newtonian: previously described


Modified Ellis model



Fast but least accurate
Analytical solutions for temperature & flow
Very fast solution
Full mold filling simulation



Simultaneous solution of differential eq’s
Iterative solution required
CPU intensive
Ellis Solution:
Temperature Field

Balance shear heating, heat conduction,
and heat convection
 1
P  R 4

 P 

P  2L  rdr  L
 L


0
 L  80
 L 
R
2
21 / 2 1 R 3
2(  3)0

T  Twall
2 J 0 ( n r )

exp   n2 ta
Tmelt  Twall n0 (  n R) J 1 (  n R)

T  Twall  (Tmelt

 PR  2 1

 9 2




  at 

64
t  L  8 0

16


 Twall ) 2 exp

9
R2

 C p   PR  1 2 1 / 2 1 


 




  L  2(  3) 0 
Ellis Solution:
Flow Field


Temperature estimated at each portion of
the hot runner
Viscosity computed in each flow segment


Conductance matrix formed at each time step
Flow conductance matrix established with
analytical relation (rod)
 1

Q
R   4  RP  
k

1 

P 8 0 L   3    2 L 1 2  


4
Mold Filling Analysis

Heat, mass, and momentum equations
 
 u   0
t z
1   u  p
 r  
r r  r  z
T  1   T 
 T
2
C p 
u

 rk
  
z  r r  r 
 t


Full spatial discretization
Iterative solution of equations
Most accurate but CPU intensive.
Approximate Execution Speed

Newtonian flow analysis



Ellis model flow analysis



~20,000 times/sec (2 cavities)
Feasible for 64 cavities +
~5,000 times/sec (2 cavities)
Feasible for up to 64 cavities
Mold filling simulation


~1,000 times/sec (2 cavities)
Feasible for up to 8 cavities, possibly more
System Development

Instrumented Mold



Valve gated hot runner
Cavity pressure transducers
1
Control system




Signal conditioners
Data acquisition
Real time flow analysis
User interface
2
3
4
5
6
7
8
Simulation Outputs

Continuous feedback of



Cavity pressures
Flow rates
Prior to mold opening




Part weight / short / flash conditions
Part shrinkage
Melt viscosity estimates
Other quality attributes
Demonstration







Ba
rr e
Ba l T
rr e m
Ru el T p L
nn e m o w
Ru er p H
i
nn Te
m gh
Co er T p
ol e m Lo w
Co ant p
ol Te H ig
an m
h
Tr t Te p L
o
an m
w
Tr sfer p H
a n P ig
sf os h
e
In r P Lo w
j V os
In elo H ig
c
Pa j Ve ity h
ck loc Lo
Pa Pr ity w
ck ess Hig
Pr ure h
e
Pa ssu L ow
ck re
Pa Tim H ig
ck
e h
Ti
L
m ow
e
Hi
gh
8.2
8.1
8
Part Weight (g)
8.3
7.9


Process changes definitely observed
Temperature effect is confounding

Ba
rr e
Ba l T
rr e m
Ru el T p L
nn e m o w
Ru er p H
i
nn Te
m gh
Co er T p
ol e m Lo w
Co ant p
ol Te H ig
an m
h
Tr t Te p L
a n m ow
Tr sfer p H
a n P ig
sf os h
e
In r P Lo w
j V os
In elo H ig
c
Pa j Ve ity h
ck loc Lo
Pa Pr ity w
ck ess Hig
Pr ure h
e
Pa ssu L ow
ck re
Pa Tim H ig
ck
e h
Ti
L
m ow
e
Hi
gh
Part Weight (g)
Experimental Validation:
Newtonian Analysis
Observed for Upper Cavity w/ Identical Cavities
8.5
Newtonian Isothermal for Upper Cavity w/ Identical Cavities
7.4
8.4
7.2
7
6.8
6.6
6.4
7.8
6.2
7.7
6




Newtonian model likely not enough



Current Status

Validation still on-going




On-line calibration being developed



Rheology & melt temperature are critical
~15% mean error
~70% accuracy on main effects
Small DOE to verify accuracy
Automatic correction for mass conservation or
viscosity shifts
Very promising approach, though in infancy
Objective:
Real Time Control

Control of pressure and flow rate at
each gate in real time
Inj Fwd
Molding
Machine
Mold
Ram position & hyd pressure
C1 & C2
V1 & V2

Inj Fwd
Inj Fwd
Conditioner
Charge
Amplifiers
Valve Control
Relays
DAQ
P1 & P2
U1 & U2
New valve designs desired
Data
Computer
Display
Info
Process
Settings
Operator
New Valve Designs
Vision:
Self-Regulating Pressure Valve

Ideally two forces:



Fcontrol
Top: control force
Bottom: pressure force
Forces must balance


Pin moves to equilibrium
position
Pressure drop governed
by juncture loss
Fpressure
Animation
Fcontrol
time
time
Pout

Outlet pressure proportional to control
force
Pin position determined by inlet pressure
and related pressure drop
Pin

time
Newtonian Analysis:
Sizing & Pressure Drops






All dimensions normalized
to inlet radius, R
aR: outer diameter
bR: inner diameter
cR: extension diameter
dR: annulus length
eR: valve pin position
Analysis of Pressure &
Shear Stress Loads

Load due to pressure drop across valve

FP  Pannulus R 2 a 2  b 2


Load due to shear stresses on valve


b
a2  b2 
F  dbR   Pannulus R b 

2
2b lna / b 
2

2
Juncture loss (empirical estimate)
Pjuncture
8Q

aeRk
Analysis Results
Valve can be sized
for mass rate and P


400
25 kg/hr
3.5
Pressure Drop Through Valve (MPa)
Pressure Drop Through Valve (MPa)
4
Large annulus desired
for good control
50 kg/hr
3
100 kg/hr
200 kg/hr
2.5
2
1.5
1
0.5
0
Pressure Force
300
Shear Stress Force
200
Resultant Force
100
Strength
Limit
0
Control
Limit
-100
-200
2
4
6
Nominal Radius (mm)
8
10
0
0.2
0.4
0.6
0.8
Ratio of Inner to Outer Diameter, b/a
1
Advanced Analysis

Axisymmetric 2D numerical simulation
developed including acceleration effects
The continuity equation
1 
ru    w  0  u  u  w  0
r r
z
r r z
(1)
Momentum equation
r-component
  2u  2u 1 u u 
u
u
u
1 p
u
w

  2  2 

t
r
z
 r
z
r r r 2 
 r
(2)
z-component:
  2 w  2 w 1 w 
w
w
w
1 p
u
w

  2  2 
t
r
z
 z
z
r r 
 r
(3)
Energy equation
  T  1 T   T 
T
T 
 T
2
  kz
u
w 0
 kr
  kr
    C p 
r  r  r r z  z 
r
z 
 t
(4)
General Results

Confirms feasibility of low force valve


Primary results





Balance of control & pressure forces
Pressure drops
Shear rates
Bulk temperatures
Q=f(P)
Guidance for design
-0.005
0
Inlet
0.005
0.01
0.015
0.02
Outlet
0.025
0.03
0.035
0.04
0.045
20
15
10
5
0
-5
x 10
-3
Outlet Melt Pressure as a
Function of Control Force
7
Ideal
6
Non-Newtonian
Outlet Pressure (MPa)
Newtonian
5
4
3
2
Confirms closed loop melt
pressure control without
pressure feedback.
1
0
0
500
1000
Control Force (N)
1500
2000
Dynamic Response & Position
as a Function of Control Force
6
2000 N
Valve Pin Position (mm)
5
Pin hovers near a closed position.
4
3
Dynamics driven by resultant force.
2
1600 N
1
1200 N
800 N
400 N
0
0
0.02
0.04
0.06
Time (sec)
0.08
0.1
Outlet Bulk Temperature as a
Function of Control Force
10
9
Indicates limits
on shear heating
(sizing guidance)
Bulk Temperature Rise (C)
8
7
6
5
4
3
2
1
0
0
500
1000
Control Force (N)
1500
2000
Design and Implementation

Valvepressure
designedisand built
Melt
 Inlet diameter
proportional
to of 8 mm
pneumatic
pressure
 In-line configuration


2
A
R
cylinder transducers
cylinder
IPressure

 2
 100
Aannulus
 At
inlet Rannulus
 Below valve pin
Control force provided by
a pneumatic cylinder
with varying pressure
Transient Validation

Predicted response is fast & steady
Observed response is slower & oscillatory
10
Inlet Pressure
8
Pressure (MPa)

Observed Outlet Pressure
Predicted Outlet Pressure
6
4
2
0
0
2
4
6
Time (sec)
8
10
Hot Runner Implementation



Retrofit to valvegated hot runner
Side entry to
annular channel
Valve pin


5 mm Diameter
Shear rates
~10,000 1/sec
Inlet
Actuator
Valve Disc
Valve Pin
Manifold
Drop
Cavity
Hot Runner Implementation
Resulting Capability

Cavity pressure control without pressure
transducers!


If cavity pressure transducers are used,
then process simulation can provide flow
rates and other quality estimates
Can measure load on extended valve
pin to completely eliminate pressure
transducers
Conclusion
Closing Statements

Vision is solid


Capability must be validated



Difficult work is done
This is “where rubber hits the road”
What is the best we can do?
Validation & specification nearly done

Commercial feasibility studies in 2005
Two More Quick Projects
Wireless Pressure Sensor
The Alpha-Sigma Project
Wireless Pressure Sensor

Wireless pressure sensor
Piezoelectric energy cell
Threshold modulator
Acoustic transmitter



Ceramic
Insulator
Piezoelectric
Rings
Outer
Thermocouple
Comparison of Pressure Curve and Threshold Modulator Reconstruction
Measured Load
400
Stack Voltage 2.0
300

250
250
200

150
Force (N)
Force
300
350
150
200
100
100
50
50
0
0
Reconstructed 1.5
Load
w=f(T)
Thermocouple
Leads
Signal
Lead
1.0
0.5
Piezoelectric Layer
Stack Voltage (V)
 350
Electrodes
Ceramic
Insulator
Next generation sensor
400
Preload
Screw
Inner
Thermocouple
jZ0tan(0
Multiple sensor arrays
Pressure, temperature, flow rate in real time!
0.00
0.0
-0.5
-1.0
u0
-jZ0/sin0
F0
u'0
Zb
F'0
1:
-1.5

~5-10 years out
0.02
0.04
Time (sec)
0.06
-2.0
0.08
F'0
u'0
Ii
F0
u0
Vi
-C0
Ii
C0
Vi
Zl
Alpha Sigma Pi:
Confidence, Robustness, Performance

Given specifications &




Non-linear models
 confidence levels
s robustness requirements
Provides:




Process windows
Pareto optimal charts
SPC & SQC graphs
Taguchi/Axiomatic methods
Graduate Students
You are important!
I want you to succeed!!
Guidelines

How to address me?



Speaking to me: Dave
Speaking to other faculty: Prof. Kazmer
Speaking to other students:


Kazmer
#^&@@#^%
Guidelines

How to work with me:

Respect and protect my time



Be proactive



Do high quality work
Have others check your work, especially thesis
You’re empowered: assume authority
Execute to plan
Commit and deliver
Current Research Funding
By Sponsor ($ remaining of total)

Mold-Masters ($40k of 80k+ in-kind)
NSF Melt Valves ($120k of $210k)
NSF Sensing ($230k of $900k)

Available money: ~400k of $1200k





~12 student-years + expenses
Enough for all your MS + 2 DEngs
No salary for Kazmer
Current Research Funding
By Topic ($ remaining of total)



Advanced melt flow control ($80k of
$150k)
On-line simulation ($120k of 150k)
Wireless pressure & temperature
sensors ($110k of 420k)
Research Topics by Student
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Melt flow control
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Unassigned
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Peter Knepper
Steven Johnston
Kathy Garnivish
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OK to split topics
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On-line simulation
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Vijay: Characterization
Rahul: Hydrodynamics
Other: Analysis
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Ranjan: Validation
Hitesh: Quality
Other: Extension
Wireless sensing
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Other: Design
Other: Testing