Advances in Molding Technology

David KazmerUniversity 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 ofFlow 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

Flow conductance, k, defined as:

L

PRQ

8

4

L

R

P

Qk

8

4

Flow Network Analysis

Consider a two-branched hot runner system

Geometry & flow conductance known Develop flow conductance matrix 1

2 3 4

5 6

6

5

4

3

2

1

4646

3535

46462424

35352323

242324231212

1212

6

5

4

3

2

1

0000

0000

000

000

00

0000

P

P

P

P

P

P

kk

kk

kkkk

kkkk

kkkkkk

kk

Q

Q

Q

Q

Q

Q

Flow Network Analysis

Apply boundary conditions: P1, P5, & P6 observed Q2, Q3, & Q4 equal 0

Solve on-line in real-time

1

2 3 4

5 6

obs

obs

obs

P

P

P

P

P

P

kk

kk

kkkk

kkkk

kkkkkk

kk

Q

Q

Q

6

5

4

3

2

1

4646

3535

46462424

35352323

242324231212

1212

6

5

1

0000

0000

000

000

00

0000

0

0

0

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

Ellis Model

WLF Model

10

100

1000

1 10 100 1000 10000

Shear Rate (1/sec)

Vis

cosi

ty (

Pa

Sec

)

Cross-WLF

Newtonian

Power Law

Ellis

1

21

0 1

n

PTPT

1*

0

0

)(1

),(),,(

tTTTTA

TTADpT

))(

)(exp(),(

*2

*1

10

Three levels of flow analysis

Newtonian: previously described Fast but least accurate

Modified Ellis model 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

0

12/1

1

0

2

2

2

2

)3(2

2

8

1

16

9

exp9

64)(

L

PR

L

PR

C

t

R

taTTTT

pwallmeltwall

0

312/1

1

0

42

0 )3(2

2

82

R

L

PL

R

L

PLrdrLP

R

taRJR

rJ

TT

TTn

n nn

n

wallmelt

wall

2

0 1

0 exp)()(

)(2

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

210

4

23

41

8

L

PR

L

R

P

Qk

Mold Filling Analysis Heat, mass, and momentum equations

Full spatial discretization Iterative solution of equations

0

uzt (27)

z

p

r

ur

rr

1 (28)

21

r

Trk

rrz

Tu

t

TC p

(29)

Most accurate but CPU intensive.

Approximate Execution Speed Newtonian flow analysis

~20,000 times/sec (2 cavities) Feasible for 64 cavities +

Ellis model flow analysis ~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

1

2

3

4

87

5

6

Instrumented Mold Valve gated hot runner Cavity pressure transducers

Control system Signal conditioners Data acquisition Real time flow analysis User interface

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

Experimental Validation:Newtonian Analysis

Observed for Upper Cavity w/ Identical Cavities

7.7

7.8

7.9

8

8.1

8.2

8.3

8.4

8.5

Par

t W

eigh

t (g

)

Newtonian Isothermal for Upper Cavity w/ Identical Cavities

6

6.2

6.4

6.6

6.8

7

7.2

7.4

Par

t W

eigh

t (g

)

Process changes definitely observed Temperature effect is confounding

Newtonian model likely not enough

Current Status Validation still on-going

Rheology & melt temperature are critical ~15% mean error ~70% accuracy on main effects

On-line calibration being developed Small DOE to verify accuracy Automatic correction for mass conservation or

viscosity shifts Very promising approach, though in infancy

Objective:Real Time Control

Molding Machine

Mold

DAQ Computer

Operator

ChargeAmplifiers

Inj FwdConditioner

Valve ControlRelays

Inj Fwd

Ram position & hyd pressure

C1 & C2

Inj Fwd

P1 & P2

V1 & V2 U1 & U2

Data

DisplayInfo

ProcessSettings

Control of pressure and flow rate at each gate in real time

New valve designs desired

New Valve Designs

Vision: Self-Regulating Pressure Valve

Ideally two forces: Top: control force Bottom: pressure force

Forces must balance Pin moves to equilibrium

position Pressure drop governed

by juncture loss

Fcontrol

Fpressure

Animation Outlet pressure proportional to

control force Pin position determined by inlet

pressure and related pressure drop

F contr

ol

time

Pou

t

time

Pin

time

Newtonian Analysis:Sizing & Pressure Drops

All dimensions normalizedto 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

Load due to shear stresses on valve

Juncture loss (empirical estimate)

222 baRPF annulusP

bab

bab

bRPdbRF annulus /ln22

2222

kjunctureeRa

QP

8

Analysis Results Valve can be sized

for mass rate and P

Large annulus desired for good control

0

0.5

1

1.5

2

2.5

3

3.5

4

2 4 6 8 10

Nominal Radius (mm)

Pre

ssur

e D

rop

Thr

ough

Val

ve (

MP

a)

25 kg/hr

50 kg/hr

100 kg/hr

200 kg/hr

-200

-100

0

100

200

300

400

0 0.2 0.4 0.6 0.8 1

Ratio of Inner to Outer Diameter, b/a

Pre

ssur

e D

rop

Thr

ough

Val

ve (

MP

a) Pressure Force

Shear Stress Force

Resultant Force

ControlLimit

StrengthLimit

Advanced Analysis

Axisymmetric 2D numerical simulation developed including acceleration effectsThe continuity equation

0 01

z

w

r

u

r

uw

zru

rr (1)

Momentum equation

r-component

22

2

2

2 11

r

u

r

u

rz

u

r

u

r

p

z

uw

r

uu

t

u

(2)

z-component:

r

w

rz

w

r

w

z

p

z

ww

r

wu

t

w 112

2

2

2

(3)

Energy equation

01 2

z

Tw

r

Tu

t

TC

z

Tk

zr

Tk

rr

Tk

r pzrr (4)

General Results

Confirms feasibility of low force valve Balance of control & pressure forces

Primary results Pressure drops Shear rates Bulk temperatures Q=f(P)

Guidance for design-505101520

x 10-3

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

Inlet

Outlet

Outlet Melt Pressure as a Function of Control Force

0

1

2

3

4

5

6

7

0 500 1000 1500 2000

Control Force (N)

Out

let

Pre

ssur

e (M

Pa)

Ideal

Non-Newtonian

Newtonian

Confirms closed loop meltpressure control without

pressure feedback.

Dynamic Response & Positionas a Function of Control Force

0

1

2

3

4

5

6

0 0.02 0.04 0.06 0.08 0.1

Time (sec)

Val

ve P

in P

ositi

on (

mm

)

2000 N

1600 N

1200 N800 N400 N

Dynamics driven by resultant force.

Pin hovers near a closed position.

Outlet Bulk Temperature as a Function of Control Force

0

1

2

3

4

5

6

7

8

9

10

0 500 1000 1500 2000

Control Force (N)

Bul

k T

empe

ratu

re R

ise

(C)

Indicates limitson shear heating (sizing guidance)

Design and Implementation

Valve designed and built Inlet diameter of 8 mm In-line configuration Pressure transducers

At inlet Below valve pin

Control force provided bya pneumatic cylinder with varying pressure

Melt pressure is proportional to pneumatic pressure

1002

2

annulus

cylinder

annulus

cylinder

R

R

A

AI

0

2

4

6

8

10

0 2 4 6 8 10

Time (sec)

Pre

ssur

e (M

Pa)

Inlet Pressure

Observed Outlet Pressure

Predicted Outlet Pressure

Transient Validation

Predicted response is fast & steady Observed response is slower &

oscillatory

Hot Runner Implementation

Manifold

Valve Disc

Valve Pin

Actuator

Inlet

Drop

Cavity

Retrofit to valve-gated hot runner

Side entry toannular channel

Valve pin 5 mm Diameter Shear rates

~10,000 1/sec

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

Difficult work is done Capability must be validated

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

Resonator

Electrode

High Temperature

Melt

Tem

pera

tur

e g

radi

ent

Pressure Pressure

Pressure Cap

Top Insulator

Energy Converter

Strain Relief

Ultrasonic Transmitter

Housing

Threshold Modulator

Wireless Pressure Sensor

Wireless pressure sensor Piezoelectric energy cell Threshold modulator Acoustic transmitter

Next generation sensor =f(T) Multiple sensor arrays Pressure, temperature, flow rate in real time!

~5-10 years out

Signal Lead

Ceramic Insulator

Inner Thermocouple

Outer Thermocouple

Thermocouple Leads

Ceramic Insulator

Electrodes

Piezoelectric Rings

Preload Screw

Comparison of Pressure Curve and Threshold Modulator Reconstruction

0

50

100

150

200

250

300

350

400

-0.02 0 0.02 0.04 0.06 0.08Time (sec)

0.00 0.02 0.04 0.06 0.08Time (sec)

400

350

300

250

200

150

100

50

0

For

ce (

N)

2.0

1.5

1.0

0.5

0.0

-0.5

-1.0

-1.5

-2.0

Sta

ck V

olta

ge (

V)

Measured Load

Stack Voltage

Reconstructed Load

Vi

F0u0

-jZ0/sin0

jZ0tan(0

Vi

-C0

C0

1:

Ii

Zb

Piezoelectric Layer

Ii

F'0u'0

ZlF'0

u'0

F0

u0

Alpha Sigma Pi: Confidence, Robustness, Performance

Given specifications & Non-linear models confidence levels 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

Do high quality work Have others check your work, especially

thesis Be proactive

You’re empowered: assume authority Execute to plan

Commit and deliver

Current Research FundingBy 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 FundingBy 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

Melt flow control Vijay:

Characterization Rahul: Hydrodynamics Other: Analysis

On-line simulation Ranjan: Validation Hitesh: Quality Other: Extension

Wireless sensing Other: Design Other: Testing

Unassigned Peter Knepper Steven Johnston Kathy Garnivish

OK to split topics