numerical simulation of electrophotography processes

1

Hiroyuki KawamotoWaseda University, Tokyo

NIP24　Plenary II : September 9, 2008 @Pittsburgh

Numerical Simulation of Electrophotography Processes

2

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

3

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.

4

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

5

1. Charging

S N

NS

OPC drum

CHARGE

6

Charging Devices

BCR

OPC

micro-discharge

contact charger roller

OPC

coronadischarge

corotorn/scrotron

7

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

8

Calculated and Measured Charging Characteristics

H. Kawamoto (Fuji Xerox) 1993

9

Analysis of Strip Image Defect due to AC Voltage Application

H. Kawamoto (Fuji Xerox) 1993

10

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

22

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

+ + = + + +

=

&& &

43

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

14

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

35

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

37

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

40

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

42

Improvement of Paper Pathfor Image Scanner

output imagereaderreader

O. Takehira (Ricoh) 2000

43

Application for Paper Feeder

paper

tray

H. Seki (Ricoh Printing Systems) 2006

44

Promotion of Simulation Technology and Education of

Young Engineers in Japan

45

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

46

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: kawa@waseda.jphttp://www.kawamoto.mech.waseda.ac.jp/kawa/

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end

53

Electrophotograpy Processes

tonerDEVELOP

EXPOSE

TRANSFERFUSE

paper

S N

NS

laser

OPC drum

M

CLEAN

CHARGE

54

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