Numerical Simulation of Electrophotography Processes · the modeling and numerical simulation of...
Transcript of Numerical Simulation of Electrophotography Processes · the modeling and numerical simulation of...
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Hiroyuki KawamotoWaseda University, Tokyo
NIP24 Plenary II : September 9, 2008 @Pittsburgh
Numerical Simulation of Electrophotography Processes
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Outline
◆ Overview of the recent progress of simulation technology for the development of electrophotography processes- especially developed in Japan
◆ Promotion of simulation technology and education of young engineers in Japan
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Charging, Exposure and Fusing Systems
EXPOSE
FUSE
CHARGE
tonerpaper
S N
NS
laser
OPC drum
M
- based on the mechanics of continuous media- formulated as a set of multi-component,
nonstationary, and nonlinear partial differential equations- numerically solved by the iterative FEM or FDM.
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Development, Transfer and Cleaning Systems
TRANSFER
CLEANING
tonerpaper
S N
NS
laser
OPC drum
M
- dynamics of toner and/or carrier particles- the discrete element method (DEM) - direct observation with a high-speed microscope camera
DEVELOPMENT
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1. Charging
S N
NS
OPC drum
CHARGE
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Charging Devices
BCR
OPC
micro-discharge
contact charger roller
OPC
coronadischarge
corotorn/scrotron
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Modeling of Contact Charging(one-dimensional analytical)
rc
dtqtVεε0
)()( =■charged voltage
+−=+ )(
)()()()( 0 tV
tztzdtV
dttq th
r
ra
rεεεε∆• charge density
Micro discharge takes placewhen (gap voltage)>(Paschen Vth)
H. Kawamoto (Fuji Xerox) 1993
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Calculated and Measured Charging Characteristics
H. Kawamoto (Fuji Xerox) 1993
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Analysis of Strip Image Defect due to AC Voltage Application
H. Kawamoto (Fuji Xerox) 1993
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Analysis of Image Defect due to DC Voltage Application
M. Kadonaga (Ricoh) 1999
- expanded to 2D field
- circumferential transport of charge
OPC
contact roller
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Vp=-1400 V
Vp=-1800 V
Vp=-1000 V
0 1400μC/m2
0 1000μC/m2
0 1800μC/m2
observed image defect calculated charge density
M. Kadonaga (Ricoh) 1999
Analysis of Image Defect due to DC Voltage Application
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■ Ozone Synthesis
e-+O2→2O+e- O+O2+O2→O3+O2
■ Plasma Reaction Rate
drrnnKSR
r oero∫= π2
(O3/sec)
Plasma Ozone Synthesis
H. Kawamoto (Fuji Xerox) 1994
- based on Townsend theory
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Measured and Calculated Ozone Concentration
(ppm)
10
1
0.1
exp. cal.
600 Hz ○450 ▲300 ■150 ●
0.5 1 2AC voltage (kV)
ozoneconcentra-
tion
H. Kawamoto (Fuji Xerox) 1994
Ozone Generation■ corotron 100■ contact charger roller 2
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Modeling of Corona Charging
( )
( )
( ) ( )
pp p
p
p e
n e
n
nn n
np
div Rt
d
nn n
n n
n
n
n
iv Rt
div e
n
E n
E
E
µ
µ
ε
∂+ = −
∂∂
+ − = −∂
= −
■ conservation of charges
■ Poisson’s equation
0pE E= ( ) thresholdof coronaonset at wire
■ boundary condition
coronadischarge
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Numerical Result
effects of rotation and resistivity of OPC
OPCAB
0pdiv Jtρ∂+ =
∂
0pJ E vσ ρ= +
initial 0 Vcal. -863 Vexp. -900 V
initial -250 Vcal. -886 Vexp. -925 V
Y. Watanabe (Ricoh) 1990
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Flow Analysis of Ionic Wind
( )F ρ φ= −∇■Aerodynamics (3D)
Navier-Stokes
( )gg g
uu u p u F
tρ
ρ µ∂
+ ⋅∇ = −∇ + ∆ +∂
( )( ) ρε φ∇ −∇ =
( )( ) 0t
µ φρ ρ∂+∇ −∇ =
∂
■Discharge Field (2D, unipolar)
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Calculated Velocity Distribution
H. Okamoto (Fuji Xerox) 2002
utilized to improve blur of toner dust
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2. Exposure
EXPOSE
S N
NS
laser
OPC drum
M
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Formation of Latent Image(3D, time-dependent, 3-unknowns)
( )
( )
( ) ( )
p e
nn
pp p
p n
p
n
en
n
div Rt
n div Rt
di
nn n
v
n
n
n
n n
n
E
E
eE
µ
µ
ε
∂+ = Γ −
∂
∂− = Γ −
∂
= −
■
■
Poisson'Equation
conservation of charges
CTL
CGL
Laser Beam
-
+++++
-
-
--
OPC
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Calculated Transient Charge Distribution
sub scan
beam size: 30 µm
main scan
Y. Watanabe (Ricoh) 2000
• Calculated field strength can predict threshold of development.
• Latent image created by an isolated dot spreads even if the thickness of OPC is 10 µm.
• Latent image created by one-by-one dot is suppressed by adjacent dots.
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3. Development
toner DEVELOPpaper
S N
NS
OPC drum
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Two Approaches for Toner/Carrier Dynamics
• Continuous ModelNavier-Stokes
- (Hitachi Printing, Ricoh, Fuji Xerox, ---), 2000
( , , , , , )
i i i i i i mechanical electrostatic magnetic
x y z
m x c x k x F F F
x x y z θ θ θ
+ + = + + +
=
&& &
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2
i=1
• Discrete ModelDiscrete Element Method (DEM)
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Mechanical Interaction
particle i
particle j
dashpot spring
joint
slider
spring
dashpot
particle iparticle j
Mechanical Interaction between Beads (Voigt model )
fn
δspring
δ
fn
linear
non-linear(Hertz contact)
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Mixing of Toner and Carrier Particles in Auger
H. Mio (Kyoto Fine Particle Technology) 2007
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Magnetic Interaction
• magnetic force
( ) jjmjjjmj BpMBpf ×=∇⋅= ,
∑≠=
−
⋅+−
+
+−
=
N
iji ij
iij
ij
ijij
jj
j
a
a
135
3
3
0
382
1
'82
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rpr
r
rp
Bp
µµ
µµ
µπ due to
mag.roller
due to other particles
x
z
yrj
j-th particlepj
i-th particlepi
ri rijB’
• magnetic dipole moment
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Design of Magnetic Roller
T. Seko (Fuji Xerox) 2004
utilized to improve pole pattern of magnetic rollerthat can efficiently mix toner/carrier particles.
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Magnetic Brushes
Simulation
Experiment
Photoreceptor
Development Sleeve
Photoreceptor
Development Sleeve
H. Kawamoto (Waseda) 2007
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Two-Component Development
H. Mio (Kyoto Fine Particle Technology) 2007
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Direct Observation of Development by High Speed Camera
H. Kawamoto (Waseda) 2007
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4. Transfer
toner
TRANSFER
paper
S N
NS
OPC drum
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Electrostatic Field in Transfer Process
discharge
potential distribution
Discharge
Nip area
10mmDischarge
Nip area
10mm
Paper
Transfer roller
OPC
OPC
Paper
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OPC
Toner
T=0ms T=4.5ms T=9.0ms
OPC
Toner
T=0ms T=4.5ms T=9.0ms
OPC
Toner
T=0ms
OPC
Toner
T=0ms T=4.5msT=4.5ms T=9.0msT=9.0ms
on OPC on paper
Toner Dynamics in Roller Transfer System
M. Kadonaga (Ricoh) 2004
Toner particles scatter due to electrical discharge.
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Hollow Defect and Toner Scattering
0.2 mm
Line image
Hollow defects
(a) Hollow defects (b) Toner scattering
0.1 mm
hollow defect toner scattering
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Hysteresis of Toner Compression
fn
δ
δ
fn
non-linear(Hertz contact)
N. Nakayama (Fuji Xerox) 1997
elastic plastic
hysteresis
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Hollow Defect and Toner Scattering
191 µm
23 µm
(g) Transferred from (d)(λ=46.2 %)
(a) Developed toner layer(εh=0.0, p=0.0 kPa)
(c) Compressed 2(εh=0.134, p=31.7 kPa)
(d) Compressed 3(εh=0.259, p=168.8 kPa)
(f) Transferred from (c)(λ=89.2 %)
(b) Compressed 1(εh=0.045, p=0.7 kPa)
(e) Transferred from (b)(λ=84.6 %)
N. Nakayama (Fuji Xerox) 1997
low compression
medium compression
high compression
on OPC (before transfer)
toner scattering
hollow defect
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5. Fusing
toner
FUSE
paper
S N
NS
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Visco-Elasticity of Toner
High Fusing Temp.Low Fusing Temp.
0 ms
25 ms
35 ms
45 ms
55 ms
dwell timetemp[℃]heat
roller
S. Hasebe (Fuji Xerox) 2007
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6. Cleaning
toner
S N
NS
OPC drumCLEAN • generation of acoustic noise
• low cleaning performance of spherical toner
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Acoustic Noise from Cleaner Blade
cleaner blade■ Low Speed
– stick-slipH. Kawamoto (Fuji Xerox) 1995
■ Rated Speed
– coupled non-linear vibration
M. Kasama (Fuji Xerox) 2006
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Cleaning Performance of Spherical Toner Particles
µ =0.96, θ =30deg, kw=10N/m,a/b=1.0
µ =0.96, θ =30deg, kw=10N/m,a/b=1.23
a
b
a
b
a
b
blade surface
photoreceptor
toner
spring
θ
a
b
a
b
a
b
blade surface
photoreceptor
toner
spring
θ
N. Nakayama (Fuji Xerox) 2004
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7. Paper Handling
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Improvement of Paper Pathfor Image Scanner
output imagereaderreader
O. Takehira (Ricoh) 2000
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Application for Paper Feeder
paper
tray
H. Seki (Ricoh Printing Systems) 2006
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Promotion of Simulation Technology and Education of
Young Engineers in Japan
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Academic Committees
Three Japanese academic committees to promote the modeling and numerical simulation of electrophotography processes• The Imaging Society of Japan (ISJ)
- education of young engineers- publish of textbook
• The Japan Society of Mechanical Engineers (JSME)- technology exchange on a give-and-take basis
• The Japan Society for Precision Engineering (JSPE)- paper handling
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Simulation Seminar
The seminar is conducted every year for 15 students.
Students are young engineers in industries.
They do exercise with their own note PC.
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Example of Exercise (Thermal Analysis of Belt Nip Fuser)
fuser belt
Students must complete the calculation at the end of one-day lecture !!
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Electrophotography
Process & Simulation
Published by The Imaging Society of Japan
Edited by Hirakura (Ricoh) & Kawamoto
Textbook
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Concluding Remarks
Simulation technology has been developed and widely utilized for the development of electrophotography machines,
The electrophotography processes are no longer a black box.
although it had been believed that the simulation is ineffective for the electrophotography.
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AcknowledgementI would like to express my sincere gratitude to my colleagues:
Dr. M. Kadonaga (Ricoh)Dr. Y. Watanabe (Ricoh)Mr. O. Takehira (Ricoh)Dr. N. Kuribayashi (Ricoh Printing)Dr. N. Nakayama (Fuji Xerox)Dr. M. Kasama (Fuji Xerox)Dr. T. Ito (Fuji Xerox)Mr. H. Okamoto (Fuji Xerox)Mr. M. Nakano (Canon)Dr. H. Mio (Kyoto Fine Particle Technology)
for their beneficial suggestions and discussions.
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Thank you for your attention.
For more informationHiroyuki Kawamoto, Prof.Waseda UniversityShinjuku, TokyoPhone/FAX: +81-3-5286-3914E-mail: [email protected]://www.kawamoto.mech.waseda.ac.jp/kawa/
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end
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Electrophotograpy Processes
tonerDEVELOP
EXPOSE
TRANSFERFUSE
paper
S N
NS
laser
OPC drum
M
CLEAN
CHARGE
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History of ElectrophotographyTechnology
tech-nology automaticautomatic improvementimprovement digital/colordigital/color
multi-functionmulti-function
‘50 ‘60 2000‘90‘80‘70
Schaffert, 1965Schaffert, 1965 Williams, 1984Williams, 1984Schein, 1988Schein, 1988
approach analytical
numerical
continuous mechanics(FDM, FEM)
particle dynamics (DEM)
• Xerox 914
Trial and Error Analytical Modeling
Numerical Simulation