Fernando Rodriguez presents 'From printing models to practical solutions: Understanding printing speed constraints and improving image quality in real scanning printers.'

1. Digital Printing Technologies
From printing models to practical solutions:
Understanding printing speed constraints and improving
image quality in real scanning printers
The IJC – October 2017
© 2017 Meteor

2.  Ideal printer:
▪ Printing mechanism: transfer of matter with arbitrary shape at any
addressable location
▪ Geometrical factors: unconstraint shapes, random placement
▪ Matter: assembly, function
© 2017 Meteor
Ideal vs. Real Printers

3.  2D ideal dot printer:
▪ Printing mechanism
• 2D dot array placement, array elements individually addressable
▪ Placement mechanism
• 2D discretized addressable plane
▪ Material properties
• Pure spectral emitter
© 2017 Meteor
Ideal vs. Real Printers

4.  Real printer:
▪ Printing mechanism
• Inkjet nozzle drop ejection + drop wetting & spreading on substrate
▪ Placement mechanism
• Electro-mechanical with substrate or nozzle transport (encoder,
motor driver and controller)
▪ Material constraints
• CMYK broad spectral absorption
© 2017 Meteor
Ideal vs. Real Inkjet Printers

5.  Nozzle acoustics
▪ Physical dimensions
▪ Fluid speed of sound
▪ Resonant modes
 Fluid properties affecting drop formation
▪ Time scales:
• Density, surface tension & viscosity
▪ Cavitation
Inkjet drop formation model
© 2017 Meteor Inkjet Ltd.
“On the instability of jets” & “On the Capillary Phenomena of Jets” by Lord Rayleigh (1878)
“Dynamics of Piezo-electric Printheads”, Chapter 2, “Inkjet Technology for Digital Fabrication”, J. Frits Dijkman & Anke Pierik (2013)

6.  Rayleigh jet break-up
▪ Cylindrical flow breaking into
drops
▪ Radial perturbation instability
analysis
• Potential flow theory plus
Lagrange dynamics
• No dissipation, surface
tension potential
 Two main results
 Adding mass conservation
 Drop max nozzle velocity vs.
acoustic frequency
Drop formation & nozzle acoustics I
© 2017 Meteor Inkjet Ltd.
𝜆 ≈ 9 ∙ 𝑅 𝑛
𝜏 ≈
𝜌
𝛾
∙ 𝑅 𝑛
ൗ3
2
𝑅 𝑑 ≈ 1.9 ∙ 𝑅 𝑛
𝑣 𝑛
𝑚𝑎𝑥
≈ 9 ∙ 𝑅 𝑛 ∙ 𝑓𝑎
𝑓𝑎 ≈
𝑣 𝑛
𝑚𝑎𝑥
9 ∙ 𝑅 𝑛
≈
2𝑔ℎ
9 ∙ 𝑅 𝑛
𝑓𝑎 =
𝑣 𝑛
𝑚𝑎𝑥
𝜆

7.  Fluid parameters:
▪ Density: 1kg/L
▪ Drop speed: 7m/s
▪ Surface tension: 0.032 N/m
Example of a typical inkjet fluid
© 2017 Meteor Inkjet Ltd.
0
5
10
15
20
25
30
35
40
45
0
50
100
150
200
250
0 10 20 30 40 50
Dropformationtime[us]&Firingperiod[us]
DropVolume[pl]&Maxfiringfreq[kHz]
Nozzlediameter [um]
drop V [pl]
max freq [kHz]
max period [us]
drop formation t [us]

8. Drop formation & nozzle acoustics II
© 2017 Meteor Inkjet Ltd.
pulse width 460us
pulse width 660us
pulse width 850us
“A low-cost, precise piezoelectric droplet-on-demand generator”
Daniel M. Harris1 · Tanya Liu2 · John W. M. Bush1
Exp Fluids (2015) 56:83
DOI 10.1007/s00348-015-1950-6
𝜆 ≈ 9 ∙ 𝑅 𝑛
2 ∙ 𝑅 𝑛
𝑅 𝑑 ≈ 1.9 ∙ 𝑅 𝑛
𝑓𝑎 ≈
𝑣 𝑛
𝑚𝑎𝑥
9 ∙ 𝑅 𝑛
Rayleigh Helmholtz
WFM

9.  There is a fundamental relationship between radius (drop
volume), fluid speed, and acoustic frequency of the nozzle
▪ The piezo electric driving waveform pulse duration and the acoustic
properties of the fluid in the nozzle need to be chosen and designed in
accordance with the preferred drop volume
• Only small adjustment in drop volume are possible through
waveform manipulation (worth doing in many applications)
▪ Greyscales in inkjet are broadly limited to multiples of the preferred
drop volume
• Greyscale printing is slower than binary printing
Drop formation & nozzle acoustics III
© 2017 Meteor Inkjet Ltd.
𝑣 𝑛
𝑚𝑎𝑥
𝜔 𝑎 ∙ 𝑅 𝑛
≈ 1

10. ▪ The multi-drop approach required for greyscale inkjet printing
produces a limited number of dot diameters on the media
• Special screening algorithms are required for digital inkjet printing
Drop formation & nozzle acoustics IV
© 2017 Meteor Inkjet Ltd.
0
1
2
3
4
5
6
7
8
0
2
4
6
8
10
12
80% 85% 90% 95% 100% 105% 110% 115%
Dropvolume[pl]
Dropvelocity[m/s]
Pulse amplitude [V]
Pulse amplitude vs. drop velocity & drop volume
Drop velocity [m/s]
Drop mass [ng]
Linear (Drop velocity [m/s])
Linear (Drop mass [ng])
0
1
2
3
4
5
6
7
8
0
1
2
3
4
5
6
7
8
2 3 4 5 6 7 8
Dropvolume[pl]
Dropvelocity[m/s]
Pulse duration [us]
Pulse amplitude vs. drop velocity & drop volume
Drop velocity [m/s]
Drop mass [ng]
Poly. (Drop velocity [m/s])
Poly. (Drop mass [ng])

11.  Waveform amplitude and slope
control
▪ Voltage scalable (printhead
calibration)
 Complex waveforms
▪ Optimal drop formation
▪ Widest range of ink formulations
▪ Increased printing speed
© 2017 Meteor
Drop formation & nozzle acoustics V

12.  Electro-mechanical
▪ Encoder errors
▪ Insufficient resolution
▪ Mechanical backslash
▪ Vibrations
▪ Alignment
 Drop substrate interaction
▪ Paper/ink substrate expansion
 Drop air interaction – aerodynamics effects
▪ Air viscosity flow induced drag
▪ Drop induced eddies
Inkjet drop placement errors
© 2017 Meteor Inkjet Ltd.

13.  Stokes drag viscous force in the z axis
 Gravity and buoyancy
 The equation of motion in z axis is
 The solution is of the form
Aerodynamics effects – a simple model
© 2017 Meteor Inkjet Ltd.
𝐹𝑑𝑟𝑎𝑔 = 6 ∙ 𝜋 ∙ 𝜂 ∙ 𝑅 𝑑𝑟𝑜𝑝 ∙ 𝑣
𝐹𝑔 = 𝜌 𝑑𝑟𝑜𝑝 − 𝜌 𝑎𝑖𝑟 ∙ 𝑔 ∙
4
3
∙ 𝜋 ∙ 𝑅 𝑑𝑟𝑜𝑝
3
𝜌 𝑑𝑟𝑜𝑝 − 𝜌 𝑎𝑖𝑟 ∙ 𝑔 ∙
4
3
∙ 𝜋 ∙ 𝑅 𝑑𝑟𝑜𝑝
3
- 6 ∙ 𝜋 ∙ 𝜂 ∙ 𝑅 𝑑𝑟𝑜𝑝 ∙ 𝑣 = m ∙
𝑑𝑣
𝑑𝑡
𝑣 𝑡 = 𝑣0 ∙ 𝑒−𝐵𝑡 + 𝑣 𝑡𝑒𝑟𝑚 ∙ 1 − 𝑒−𝐵𝑡

14.  Stokes drag viscous force in the y axis
 The flow speed parallel to the media is laminar (Couette flow)
 Solving the equation of motion numerically
Aerodynamics effects – a simple model
© 2017 Meteor Inkjet Ltd.
𝐹𝑑𝑟𝑎𝑔 = 6 ∙ 𝜋 ∙ 𝜂 ∙ 𝑅 𝑑𝑟𝑜𝑝 ∙ 𝑣 𝑓𝑙𝑜𝑤 − 𝑣 𝑦 = 𝑚 ∙
𝑑𝑣 𝑦
𝑑𝑡
N. Link et al. / Chemical Engineering and Processing 48 (2009) 84–91
𝑣 𝑦
𝑖+1 = 𝑣 𝑦
𝑖 + ∆𝑡 ∙ 𝐵 ∙ 𝑘 ∙ 𝑧 𝑖 − 𝑣 𝑦
𝑖

15. Aerodynamics effects – simple model results
© 2017 Meteor Inkjet Ltd.
0.0
1.0
2.0
3.0
4.0
5.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0 200 400 600 800 1000
distance[mm]
dropspeed[m/s]
time [us]
Drop dynamics
v drop [m/s]
v drag [m/s]
distance [mm]
0
20
40
60
80
100
120
140
160
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
2.00 2.50 3.00 3.50 4.00 4.50 5.00
flowdragdistance[um]
equivalentdpierror
drop travelled distance [mm]
Drop flow drag landingoffset
dpi error
distance media [mm]
drop initial velocity V 7 m/s
jet/nozzle diameter d 10 um
density rho 1000 Kg/m^3
jet to droplet diameter ratio 1.9 Rayleigh-Plateau instability
drop diameter 19 um
effective length 14 um
drop volume 3591 um^3
ratio um^3 to pL 0.001
drop volume 3.59 pL
max firing frequency 117.3 kHz
viscosity air 0.018 mPa x s
viscosity water 1.8 mPa x s
viscotity ink 10 mPa x s
terminal speed (Stokes) 1.09 cm/s
speed decay time constant 897.51 seconds
v media 1 m/s
distance to media 5 mm
0
1
2
3
4
5
0.00 50.00 100.00 150.00 200.00
droptravelleddistance[mm]
lateral deviation [um]
Drop flow drag landingoffset

16. Aerodynamics effects – inkjet results
© 2017 Meteor Inkjet Ltd.
Hsiao, W.-K., Hoath, S.D., Martin, G.D. and Hutchings, I.M., paper for NIP28 2012,
'Aerodynamic effects in ink-jet printing on a moving web'
0
2
4
6
8
10
12
14
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
2.00 2.50 3.00 3.50 4.00
flowdragdistance[um]
equivalentdpierror
drop travelled distance [mm]
Drop flow drag landingoffset
dpi error
distance media [um]
v media 3 m/s
distance to media 4 mm
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
2600
2800
2.00 2.50 3.00 3.50 4.00
flowdragdistance[um]
equivalentdpierror
drop travelled distance [mm]
Drop flow drag landingoffset
dpi error
distance media [um]
v media 1 m/s
distance to media 4 mm
drop diameter 80 um

17. Aerodynamics effects – drop induced eddies
© 2017 Meteor Inkjet Ltd.
Rodriguez-Rivero, Castrejón-Pita, and Hutchings: Aerodynamic effects in industrial inkjet printing
Initial disruption High flow initial transient Laminar Couette flow

18. Aerodynamics effects – drop induced eddies
© 2017 Meteor Inkjet Ltd.
Rodriguez-Rivero, Castrejón-Pita, and Hutchings: Aerodynamic effects in industrial inkjet printing
Asymmetric row drop ejection caused by a combination of media
movement viscous flow and drop induced eddies

19.  The physics of the drop ejection and formation mechanisms
impose a number of restrictions between different parameters in
an inkjet system. This forces the designer of a printer to strike a
balance between:
▪ Number of grey levels vs printing speed
▪ Drop volume vs printing speed
 The range of rheological fluids that a printhead can potentially
eject can only be fulfilled with the use of customized excitation
waveforms
Conclusions
© 2017 Meteor Inkjet Ltd.

20.  The aerodynamics effects caused by the airflow between the
printhead and the media causes a drop placement error
▪ This error is a function of the relative speed between printhead and
media
▪ This error is a function of the flow regime between printhead and
media
▪ The above two errors can be minimized by:
• adjusting the timing of the piezo firing
• designing the printing carriage to have a Couette flow profile
 Drop induced eddies cause random placement errors which
cannot be compensated. To reduce this errors is necessary to
▪ Minimize the distance between printhead and media
Conclusions
© 2017 Meteor Inkjet Ltd.

21. enquiries@meteorinkjet.com
© 2017 Meteor
talk with Meteor technical sales support in
Hong Kong, Germany, Shanghai, UK (Cambridge HQ), USA, Japan