Improvement of Drive Energy Efficiency

in a Shear Mode Piezo Inkjet Head

Yoshio Takeuchi, Hiroshi Takeuchi, Katsuaki Komatsu, Shinichi Nishi

Summary

Recent improvements of inkjet printer technology

enabling the high print quality and high-speed

printing have been remarkable, however, for higher-

speed printing, the development of multi-channel

inkjet head whose energy efficiency is higher, is

necessary. We have analyzed an ink flow in a

shear mode piezo inkjet head and an ink droplet

forming process through computational simulation.

By using the results of the simulation, we designed

optimum shapes of an actuator, an ink channel and

a nozzle, and made a prototype of inkjet head

employing a funnel type nozzle. Then we

experimentally confirmed an improvement of the

drive efficiency.

Abstract

The recent acceleration in high print quality and

high-speed inkjet printers commands the

development of an energy efficient multi-channel

print head to accommodate these ever-advancing

printers. In response, we have computationally

simulated a shear mode inkjet head in order to

analyze its fluid flow dynamics and jet forming

process. As a result, we have been able to

optimize the shape of the actuator, channel, and

nozzle of the inkjet head. In particular, a funnel

type nozzle has proven to provide good energy

efficiency in a prototype print head based on the

results of our simulation and analysis.

1 Introduction

For increasing the printing speed of the inkjet

printer, the improvement of the ink-ejecting rate of

the print head is a matter of course, and the number

of channels needs to be increased.

For increasing the number of channels, the problem

in the structure including the manufacturing is

important, and it is also important to improve the

drive efficiency to minimize energy necessary for

droplet ejection, for controlling deterioration of print

quality and droplet ejection stability caused by

temperature rise of the print head during printing.

In order to overcome this problem, we analyzed the

drive efficiency characteristics of a shear mode

piezo inkjet head through computer simulation.

The shear mode piezo inkjet head is a head driven

by shearing stress generated by applying an

electrical field in the direction perpendicular to the

polarization direction of the piezoelectric material.

The characteristic of an actuator composed of such

piezoelectric material was analyzed by using a finite

element method simulation software that can make

a structure and an electrical field to be coupled, and

for the ink flow within the print head and for the

process of droplet ejection from the nozzle, a finite

difference method simulation software which can

analyze free surface flow, was used.

The electric energy applied to the actuator, the

elastic energy applied to the ink in channels, and

the kinetic energy of the droplet were estimated

through the simulation, and the relationship

between the factors (such as shapes of actuator

and channel, nozzle shape, piezoelectric material,

adhesive layer, ink characteristics, drive voltage

waveform) and drive efficiency, was analyzed.

Herein, the relationship between the shape of inkjet

head and drive efficiency will be mainly discussed.

2 Structure of the inkjet head and driving energy

Fig. 1 Structure of shear mode piezo inkjet head

Fig. 1 is a structural view of a shear mode piezo

inkjet head. When grooves are mechanically

formed in a PZT (lead zirconate titanate) substrate,

channels and actuators which are walls of channels

are formed. A cover plate is bonded on the upper

surface of the walls, and a nozzle plate is bonded

on the front surface of the substrate, and the ink is

fed into the channels.

Fig. 2 PZT actuator (cross section)

A sectional view of the actuator that is cut at a right

angle to the flow direction of channel is shown in

Fig. 2. When an electrical field is applied in the

direction orthogonal to the polarization direction of

the PZT, actuators are deformed, and the ink in the

channel is pressurized. When the pressure wave

generated in the channel is reflected between

nozzles and the common ink chamber, and

resonated, the pressure applied to the nozzle

change in time, and an ink droplet is ejected.

Fig. 3 Droplet ejection process

A result of the simulated droplet ejection process is

shown in Fig. 3. For low voltage drive, the drive

waveform shown on the upper part in Fig. 3 is used.

When the voltage is changed, pressure generates

within the channel, after that, it oscillates at a

resonance frequency and gradually attenuates.

(middle in Fig. 3). At the time of the rise of voltage

applied in the direction in which the volume of

channel is increased, negative pressure is

generated. When the negative pressure reaches

the peak of the positive pressure after a half period,

the voltage is applied in the direction in which the

channel volume is decreased, that is, in the reverse

polarity to the first rise of the voltage. Then the

positive pressure for droplet ejection is reinforced.

The result of the simulation of the time change of

the pressure in the channel and the process of

forming droplet from the nozzle, is shown in the

lower part of Fig. 3(1).

Fig. 4 Resonance frequency vs. droplet ejection

For the higher speed and higher print quality, it is

necessary to enhance the pressure resonance

frequency in the channel. The reason for this is

that the droplet volume is inversely proportional to

the resonance frequency, as shown by the following

expression.

Vd = pr2 × v/(2 × f)

 Vd: Volume of droplet r: Radius of the nozzle

 v: Velocity of droplet f: Resonance frequency

The computation result of the relationship between

the resonance frequency of the pressure applied to

the nozzle and values of the necessary pressure for

constant velocity of a ejected droplet is shown in

Fig. 4. When the frequency is increased, the

necessary ejection pressure increases rapidly, that

is, the drive voltage is increased.

Further, when the number of channels or the drive

frequency is increased to improve printing speed

and print quality, the generated heat (including the

heat generated in the drive circuit) also increase

rapidly.

Wa = (1/2)× C × V2 × A × fd × N

 Wa: Total generated heat,

 C: Electrostatic capacity of the actuator,

 V: Drive voltage

 fd: Drive frequency

 A: Waveform coefficient

 N: Number of channels

Some part of this generated heat, namely the heat

generated by the dielectric loss of the piezoelectric

material forming the actuator, and by the resistance

of electrode transfer to the ink in the channel, and

causes the ink temperature rise. Because of the

short distance between the actuator and the ink, ink

temperature rises in a very short time, and changes

in ink characteristics cause fluctuations of the

droplet velocity and droplet volume, resulting in a

decline in print quality. Further, when the

temperature rise is remarkable, there is a risk that

stable ejection can not be achieved.

3 Shape of inkjet head and drive efficiency

3.1 Actuator and ink channel

A calculated example of the actuator displacement

by voltage application is shown on the left side in

Fig. 5. The compliance (displacement /force) of

the actuator is calculated as a counter pressure

displacement by the internal pressure rise on the

right side in Fig. 5. The ratio of the compliance of

an actuator to the compliance of the ink in the

channel is called the compliance ratio (kcr). The

compliance ratio shows the ratio of the volume

change of the actuator by pressure difference

between the channels to the volume change of

pressurized ink in channel.

Fig. 5 Actuator deformation analysis

Pressure P generated in the channel by voltage

application can be calculated using the following

expression. Herein, . is a constant determined by

the channel drive pattern. The generated pressure

is decreased because the actuator is forced back

by the rise of internal pressure in the channel.

P = 2 × (.x/W) × B × V/(1 + . × kcr)

 .x: an averaged displacement of the actuator

 by unit voltage application

 V: Drive voltage

 W: Channel width

 B: Bulk modulus of the ink

The speed of the pressure wave propagating in the

channel is also changed depending on the value of

the compliance ratio. The reason is that the

change of volume of the ink by the channel internal

pressure is practically increased by the deformation

of the actuator, that is, bulk modulus of the ink is

apparently decreased. Therefore, the change of

shape also influences on the resonance frequency,

then the attention must be paid.

Propagation speed of pressure wave

C0 = (B/.)1/2/(1 + . × kcr)1/2

 .: Density of ink

Resonance frequency of pressure wave

f = C0(1 + a)/4L

 a: Shape factor

 L: Channel length

Since the generated pressure is proportional to the

displacement of the actuator, it is essential to

design so that the displacement per unit of applied

voltage is increased. The relationship between the

displacement and the elastic energy applied to the

ink is determined by the following expression.

E = (1/2) × B × (x/W)2 × L × H × W

 E: Elastic energy of to the ink

 x: Average displacement of the actuator

 L: Channel length

 W: Channel width

 H: Channel depth

Further, the relationship between pressure P

generated in channel and the energy is expressed

by the following expression:

E = (1/2) × P2 × L × H × W/B

Fig. 6 Voltage sensitivity vs. channel width

Fig. 6 shows an example to calculate how the ratio

of voltage sensitivity and compliance ratio are

changed when the channel width is changed under

the constant channel pitch (channel width +

actuator thickness). When the channel is shallow,

even when the channel width increases, the

compliance ratio (dashed line) is only slightly

increased, then the voltage sensitivity (solid line)

does not drop. When the channel depth is

increased, the compliance ratio increases rapidly,

then the voltage sensitivity drops sharply as the

channel width increases. Fig. 7 shows the

relationship between channel width and elastic

energy in which the channel depth is a parameter.

When channel depth is decreased, even when

voltage sensitivity is high, the elastic energy is

lowered because the section area of the channel is

decreased.

Fig. 7 Ink elastic energy vs. channel width

It is important to design the shapes of the actuator

and channel so that efficiency of conversion from

input electrical energy to ink elastic energy

increases. However, it must be realized that the

electrostatic capacity of the actuator changes

depending on its shape. The electrostatic capacity

is proportional to the channel length and to its

depth, and is inversely proportional to the thickness

of the actuator. Further, the optimum cross

sectional shape changes depending on the

characteristic of the piezoelectric material

(piezoelectric constant, relative dielectric constant,

elastic constant), the characteristic of the ink (bulk

modulus) or an adhesive layer (1). The resonance

frequency of the channel is also influenced by the

cross sectional shape, however, it is almost

inversely proportional to channel length. Fig. 8

shows how the resonance frequency is changed for

the channel length.

Fig. 8 Channel length vs. resonance frequency

3.2 Nozzle

When a nozzle diameter is decreased, the droplet

volume decreases, however, the viscous resistance

in the nozzle is greatly increased, and the energy

loss grows greater. The Fig. 9 shows the

relationship between the nozzle diameter and the

droplet velocity, in which the ink viscosity is a

parameter. In the case where ink viscosity is high, if

the nozzle diameter is decreased, a lowering of ink

velocity is remarkable. The reason is that velocity

down effect of the viscosity is greater than the

velocity up effect of the accelerated flow rate by the

ratio of cross sectional area of the channel to that of

the nozzle.

Fig. 9 Nozzle diameter vs. droplet velocity

Particularly, in the case of high viscosity ink, when

resistance of the nozzle is decreased, the increase

of ink droplet velocity is large. Fig. 10 shows a

change of droplet velocity, in the case of changing

the taper angle of nozzle.

Fig. 10 Taper angle vs. droplet velocity

When a nozzle diameter is small, the influence of

taper angle is great. In order to reduce nozzle

resistance, it is also effective that the length of

nozzle is reduced, whereby however, the stiffness

of the nozzle plate is also reduced, and the

pressure in the channel is lowered by the increase

of compliance, and the fluctuation of the jet

trajectory increases.

Further, the taper angle can not also be increased,

because it affects a jet trajectory accuracy. In

addition, viscous resistance of the nozzle largely

influences on the ink replenishment time after

droplet ejection as well as on attenuation of the

pressure wave, and therefore, attention must be

paid to the design of nozzles (1).

Fig. 11 SEM photograph of nozzle cross section

In order to reduce energy loss and to stabilize the

jet trajectory, a funnel type nozzle shown on the left

side in Fig. 11 shows good characteristics. Fig. 12

is an example in which the droplet velocity was

calculated when the nozzle diameter was changed

on a taper type nozzle and a funnel type nozzle.

Compared to the conventional taper type nozzle

having a small taper angle, a greater increase of

droplet velocity can be expected.

Fig. 12 Nozzle shape vs. droplet velocity

4 Characteristics of the prototype print head

In accordance with the result of the simulation, the

shapes of the actuator and the channel were

designed to achieve high drive efficiency, and a

print head whose nozzle shape was changed from

the conventional taper type to the funnel type was

made on a trial basis. Specifications of the

prototype print head are shown in Table 1. As

drive method of the print head, a so-called 3-cycle

firing by which the ink is ejected every three

channels at a time and the drive of all channels is

completed by 3 cycles was used, because of the

actuators that are shared for the adjoining

channels. Further, an oil-based ink with a

relatively high viscosity was used. The driving

energy necessary for ejection of one droplet in this

print head was 0.45 µJ.

Table 1 Specifications of prototype head

Nozzle

Funnel

Type

Ink

droplet volume

15 pl

Viscosity

10 mPa·sec

drive frequency

13 kHz

surface tension

28 mN/m

number of channels

512 ch.

density

0.89 g/cm3

channel array density

180 dpi

5 Consideration

Driving energy for the shear mode piezo inkjet head

is imparted to the actuator as electrical energy, and

the greater part of the energy is consumed in the

drive circuit, and a part of the rest is converted to

elastic energy in the ink in the channels by a

displacement of the actuator. This elastic energy

propagates in the channel as a pressure wave to

form a standing wave. Then, it pressurizes the ink

in the nozzle to eject a droplet.

The required energy to eject the ink droplet includes

the energy to form the droplet surface and the

kinetic energy of the droplet, and in addition, a

considerable energy is consumed for the flow of the

ink in the nozzle. Further, even after droplet

ejection, more energy is consumed until the

residual oscillation of the ink is terminated.

When the driving energy of the prototype inkjet

head is roughly calculated, the elastic energy of the

ink in each channel is 6 nJ, which is nearly two-digit

smaller than the electrical input energy of 0.45 µJ,

and the droplet surface forming energy is 0.08 nJ,

and the droplet kinetic energy is about 0.22 nJ.

The shapes of the actuator, channel, and nozzle

were optimized based on the computational

simulation analyses, the results were that a

prototype print head proved that its drive efficiency

was twice or more than the conventional one.

6 Conclusion

On the basis of driving efficiency analyses of the

shear mode piezo inkjet head through

computational simulation, the channel shape or

nozzle shape have been optimized, and an inkjet

head of better drive efficiency was made on a trial

basis. If the electrostatic capacity of wiring section

is reduced, the efficiency can further be raised

several times.

Since the fabrication of the shear mode piezo inkjet

head of a multi-channel type is comparatively easy

and a high efficiency drive is possible (3), the shear

mode piezo inkjet head is promising as a head for a

higher speed and a higher print quality printers in

near future.

• References

1) Yoshio Takeuchi, Konica Tech. Rep., Vol 15, 31

(2002).

2) Iwaishi, Miyaki, Kawamura, Kato, Mikami, Japan

Hardcopy 2000 Papers (2000).

3) Alfred Zollner, Peter Moestl, SPIE 2949, 434

(1997).