Inkjet printhead performance enhancement by feedforward input design based on two-port modeling

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Inkjet printhead performance

enhancement by feedforward input

design based on two-port modeling

PROEFSCHRIFT

ter verkrijging van de graad van doctor

aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus Prof. dr. ir. J.T. Fokkema,

voorzitter van het College voor Promoties,

in het openbaar te verdedigen op

maandag 12 februari 2007 om 12.30 uur

door

Matthijs Benno GROOT WASSINK

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Prof. dr. ir. D.J. Rixen

Samenstelling promotiecommissie:

Rector Magnificus voorzitter

Prof. ir. O.H. Bosgra Technische Universiteit Delft, promotor Prof. dr. ir. D.J. Rixen Technische Universiteit Delft, promotor Prof. dr. ir. J. van Eijk Technische Universiteit Delft

Prof. dr. ir. M. Steinbuch Technische Universiteit Eindhoven Dr. ir. J.F. Dijksman Philips Applied Technologies Eindhoven Prof. dr. D. Lohse Technische Universiteit Twente

Dr. ir. S.H. Koekebakker Oc´e-Technologies B.V.

Prof. ir. R.H. Munnig Schmidt Technische Universiteit Delft, reservelid

This research is supported by Oc´e-Technologies B.V. in Venlo, The Netherlands.

The research reported in this thesis is part of the research program of the Dutch Institute of Systems and Control (DISC). The author has successfully completed the educational program of the graduate school DISC.

ISBN 978-90-9021484-9

Copyright c 2007 by M.B. Groot Wassink

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Voorwoord

Degene die het promoveren associ¨eren met vier jaar lang zwoegen achter een com-puter in een hokje op de universiteit, kan ik direct een illusie armer maken: de afgelopen vier jaar hebben mij in ieder geval het tegendeel bewezen. Zo heb ik de enorme vrijheid in het onderzoek, het verdiepen en verbreden van kennis en vaardigheden, het samenwerken met Oc´e en het deelnemen aan internationale con-ferenties ervaren als een combinatie die uniek is bij een eerste ’baan’. Toegegeven, het zwoegen klopt wel af en toe, maar ja, bij welke baan heb je dat nou niet? Kortom: het is een prachtige tijd geweest. Maar wat het vooral mooi heeft gemaakt is de samenwerking met een (flink) aantal mensen. In dat kader gaat mijn grootste dank uit naar Okko. Hij heeft mij zowel de vrijheid als steun gegeven bij het opzetten en uitvoeren van dit onderzoek: zijn onovertroffen kennis en inzicht is van enorm belang geweest bij de totstandkoming van dit proefschrift. Ook Daniel ben ik veel dank verschuldigd. De inhoudelijke discussies vanuit zijn expertise heb ik enorm gewaardeerd en hebben het behaalde resultaat aanzienlijk verbeterd.

Daarnaast heb ik het geluk gehad om tijdens de promotie vier goede afstudeerders te hebben kunnen begeleiden: Anton, Niels, Ferry en Pieter. Het pressiemiddel ’de exponentiele functie’ heeft zeer zeker effect gehad: jullie resultaten zijn dan ook terug te vinden in dit boekje, waarvoor dank! Ook dank aan Oc´e voor het mogelijk maken van dit onderzoek en de ondersteuning die ik vanuit Venlo heb gekregen: Sjirk, Herman, Rob, Marc en vele anderen dank!

En wat zou promoveren zijn zonder mede-lotgenoten? Met veel plezier denk ik terug aan de vele humorvolle en relativerende gesprekken tijdens de talloze koffie-en lunchpauzes. Dank daarvoor aan alle oud-collega’s van de vroegere vakgroep Systeem- en Regeltechniek en het huidige Delft Center for Systems and Control. Het zijn er teveel om op te noemen... Tot slot: Elske, ouders, familie en vrienden, ook jullie dank voor jullie begrip en luisterende oren de afgelopen jaren!

Matthijs Groot Wassink, Den Haag, December 2006.

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Introduction

The importance of inkjet technology as key-technology for today’s industry has been and still is the driving force behind the major improvements that this technology has undergone over the last decades. This thesis contributes to that development of inkjet technology. As justification of our particular research approach, an in-ventory of the current state of the art of this technology is essential. To that purpose, this chapter presents a characterization of inkjet technology. As a re-sult, the limitations of current designs will emerge, based on which several possible research directions are identified.

1.1 Inkjet technology

In this section, a historical overview is presented of inkjet technology. Simul-taneously, the unique capabilities of piezoelectric inkjet technology compared to other forms of inkjet technology are addressed as well. Next, an inventory of the applications of piezoelectric inkjet technology is given illustrating its versatile functionality.

1.1.1 A historical overview

The rapid development of inkjet technology started off around the late fifties. Since then, literally countless inkjet devices have seen the light of day. In this overview, the attention is mainly restricted to the development towards the two most important inkjet concepts of today, namely piezoelectric and thermal inkjet, see Fig 1.1. At the end of this section, both concepts are discussed vis-`a-vis. For a more extensive overview of the history of inkjet technology, one is referred to [Pon00].

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inkjet technology continuous drop on demand binary deflection multiple deflection ... thermal piezoelectric ... electrostatic squeeze bend push shear (DOD) (CIJ) (TIJ) (PIJ)

Figure 1.1: Classification of inkjet technology

and English physicist Lord Rayleigh. Though Plateau was the very first to publish on this field with his article ’On the recent theories of the constitution of jets of liquid issuing from circular orifices’ in 1856 ([Pla56]), most of the credit belongs to Lord Rayleigh. He published a series of founding papers including ’Instability of jets’ in 1878 ([Ray78]), ’On the instability of cylindrical fluid surfaces’ in 1892 ([Ray92b]), and ’Investigations of capillarity’ in 1899 ([Ray92a]). Still, it took several decades before application of these physical principles took place in work-ing devices. The first pioneerwork-ing work in that direction was performed in the late 1940s by an employee of the Radio Corporation of America (RCA), who invented the first drop-on-demand device. By means of a piezoelectric disc, pressure waves could be generated that caused a spray of ink drops, see Fig. 1.2. However, this invention was never developed into a commercial product.

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1.1 INKJET TECHNOLOGY 3 Minograf of the Siemens-Elema company released in 1952. Instead of being an inkjet printer, it was merely a voltage recorder quite similar to current seismic apparatus.

The early work of Plateau and Lord Rayleigh and the two jet-writing concepts can be regarded as first steps towards inkjet printing. The rapid growth of electronic information systems in the late sixties induced a renewed scientific interest and started research into the two major directions of inkjet technology: continuous inkjet (CIJ) and drop-on-demand (DOD), see Fig. 1.1. During the sixties, progress was established in three important regions:

• DOD thermal inkjet. With sudden steam printing, a researcher from the Sperry Rand Company basically invented thermal inkjet printing, see Fig. 1.3. By boiling aqueous ink at certain time instances, a drop of ink could be gen-erated. The strength of this design clearly was not acknowledged, since the company did not elaborate this idea into a commercial product. The idea was abandoned until the late seventies when Canon and Hewlett Packard (HP) picked it up.

Figure 1.3: Sudden steam printing (US Patent 3,179,042)

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in 1971 a printer of this type. The Inktronic Teletype machine in the late 1960s was marketed by the Teletype company.

• Continuous inkjet. The major achievement in CIJ was the synchroniza-tion of the jet breakup. By adding periodic (acoustic) actuasynchroniza-tion, the ran-dom drop formation process becomes synchronized to that period as was predicted by Lord Rayleigh. Consequently, the resulting droplets can be charged and deflected to the desired position. Main players in the field were Sweet of the Stanford University who came up with the Inkjet Oscillograph. This device was elaborated for use by the Stanford Research Institute (SRI) for inkjet bar coder work for Recognition Equipment Incorporated (REI). The A.B. Dick Company elaborated Sweet’s invention to be used for charac-ter printing. With their Videojet 9600 in 1968, it was the first CIJ printing product ever.

Despite these developments in inkjet technology, the products that came to the market can be characterized as unreliable and having a poor print quality. In the seventies, the DOD electrostatic pull principle was abandoned due to poor printing quality and reliability. The development of DOD thermal principle was put on hold. Of the principles in development, only CIJ remained and was de-veloped further. In addition, the seventies are marked with the emergence of the DOD piezo-electrical inkjet, abbreviated as PIJ, principle. More specifically, these developments comprised the following:

• CIJ with binary drop deflection. This approach is depicted in Fig. 1.4. The charged droplets are deflected to the paper or to the gutter where it is recycled. This track of research and development continued the work that was started in the sixties. Main players are the A.B. Dick Company, REI, the Mead Company, and IBM. The A.B. Dick company and REI continued their work in bar code printing. The Mead company introduced DIJIT in 1973 used for advertising purposes. The huge research efforts of IBM resulted in one product only, the IBM 6640.

HV drop generator charge electrode high voltage deflection plate gutter paper

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1.1 INKJET TECHNOLOGY 5 • CIJ with multiple drop deflection. This approach is illustrated in Fig. 1.5. Two companies that were involved in this branch of CIJ were the Sharp and Applicon company. The former released their Jetpoint in 1973, the latter their color image printer in 1977.

HV drop generator charge electrode high voltage deflection plate gutter paper

Figure 1.5: CIJ with multiple drop deflection

• DOD piezo-electrical inkjet. Generally, the basis of piezo-electrical inkjet (PIJ) printers is attributed to three patents. The first one is that of Zoltan of the Clevite company (US Patent 3,683,212), proposing a squeeze mode of operation. The second one of Stemme of the Chalmer University (US Patent 3,747,120) utilizes the bend mode of piezoelectric operation. Finally, Kyser and Sears of the Silonics company (US Patent 3,946,398) used a diaphragm mode of operation. Common denominator of these three patents is the use of a piezoelectrical unit to convert a pulse of electrical energy into a mechanical pressure to overcome the surface tension forces holding the ink at a nozzle. Drops are only created when an actuation pulse is provided, hence drop-on-demand. Obviously, the main discriminator between these patents is the used dominating deformation mode of the piezoelectric mate-rial together with the geometry of the ink channels. The patents of Howkins (US Patent 4,459,601) describing the push mode version and Fischbeck (US Patent 4,584,590) proposing the shear mode, completed the now commonly adapted categorization of printhead configurations. In general, four types of PIJ printheads can be distinguished, namely the squeeze, push, bend, and shear mode, see Fig. 1.6.

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shear

squeeze bend

push

Figure 1.6: Classification of piezoelectrically driven inkjet printheads

All the inkjet printers that had been introduced so far had failed to be com-mercially successful. It proved to be extremely difficult to combine print quality, throughput, cost, and reliability all into one single inkjet printing device with ei-ther CIJ or PIJ. Though CIJ is capable of attaining high throughput, it required high costs to achieve the required high print quality in addition to reliability. With PIJ, it turned out to be problematic to achieve both excellent print qual-ity and reasonable throughput simultaneously. The realization of high densqual-ity of piezoelectric actuators was difficult. Consequently, it was impossible to miniatur-ize the design to an acceptable format.

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devel-1.1 INKJET TECHNOLOGY 7 opment was translated in a great number of patents, practically giving Canon the means to control the TIJ market. Of the companies that Canon licensed its patents to, HP was the only company that could keep up the pace with Canon. The milestones in TIJ printing are so extensive that a list is omitted.

After the introduction and immense success of TIJ, PIJ research efforts were largely diminished. Only a few companies continued their research into PIJ. In the nineties, only a few companies that conducted research in PIJ were left, among which Spectra, Xaar, Seiko-Epson, Trident, and Lexmark. CIJ-based printers and research practically disappeared, except for some sporadic publications (e.g. [Die98], [Sch99], [Hei00]). An important impulse to PIJ research was provided by ongoing developments in the manufacturing of multilayer piezoelectric actuators. One of the major barriers now had been lifted: that of miniaturization. Epson’s advances in piezoelectric transducer fabrication have allowed it to remain com-petitive.

Despite the eminent success of TIJ printing, there are some fundamental advan-tages of PIJ over TIJ:

• Ink properties. TIJ only works with aqueous inks whereas PIJ can work with a broad latitude of ink properties, including hotmelt ink. This is favorable in two ways. First, certain applications require a special type of material to be deposited such that PIJ is the only technology capable of doing so. Second, the types of ink that can be used with PIJ results in general in a higher print quality.

• Durability. PIJ printers have a higher durability than their TIJ equivalents. Typically, a PIJ nozzle is capable of jetting around 10 billion drops per lifetime whereas a TIJ nozzle is only capable of around 200 million droplets. The reason for that is the harm that is posed to the heater element of a TIJ printer. Each time a droplet is jetted, it is heated and cooled quite quickly successively. This affects the life-time considerably.

• Attainable jetting frequency. PIJ printers can achieve higher jetting frequen-cies than TIJ printers.

• Drop-size modulation. Since control of the bubble collapse is not possible with TIJ, drop-size modulation is fundamentally not possible with TIJ. With PIJ, the necking of the drop-formation process can be controlled and therefore gives an opportunity for drop-size modulation. This can be used to further increase the resolution and thus print-quality.

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Also, current applications of inkjet technology simply require the sketched unique capabilities of PIJ that the TIJ technology is unable to provide.

1.1.2 A generic manufacturing technology

A fundamental strength of the PIJ technology is its ability to deposit a wide variety of materials on various substrates in certain patterns. Next to this char-acteristic, several additional advantages can be mentioned that apply to inkjet technology in general. To start with, its on-demand character makes it a very flexible manufacturing technology. Furthermore, when used for manufacturing, the use of PIJ printing usually reduces the number of manufacturing steps neces-sary. Additionally, due to its additive character, there is a reduction of the use of possibly expensive materials or equivalently a reduction in waste as well. Finally, it is a non-contact and non-contaminating process which can be very favorable in a manufacturing process. Altogether, these characteristics make inkjet technology a very versatile manufacturing technology.

The importance of PIJ printing for the industry is best illustrated by the large range of applications. Due to this wide variety of applications it is practically impossible to present a complete overview. Also, each categorization of the ap-plications remains artificial to some extent. Nevertheless, the following division is adopted:

• Graphics. Most likely, inkjet technology is first associated with this field of applications. This is hardly surprisingly given the huge amount of (desktop) printers present in offices and the like. Accordingly, the amount of printer types is also large. A subdivision can be made based on for example the type of ink used (e.g. aqueous, hotmelt, UV-curable), substrate (e.g. paper, textile, food, canvas), and format (e.g. narrow or wide format printing). Some of these fields are dominated by TIJ printing, others by the PIJ print-ing. In general, PIJ printers are utilized in case the ink cannot be deposited by TIJ printers or the required quality is high.

• Displays. In the display market, PIJ technology is used to manufacture Flat Panel Displays (FPD), Liquid Crystal Displays (LCD), color filters (a part of LCDs), Polymer Light Emitting Diodes (PLED), and flexible displays. The accompanying performance criteria are one of the major driving forces behind much research and development efforts concerning PIJ. Examples can be found in e.g. [Has02; Ben03].

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1.2 SYSTEM DESCRIPTION 9 as Radio Frequency Identification (RFID) tags, wearable electronics, solar cells, fuel cells, and batteries. Challenges for the PIJ technology within this field include the spreading of the ink and the required guarantees of conti-nuity of the jetted lines. Examples of the manufacturing of electronics with PIJ technology can be found in e.g. [Hei05; Szc05; Kno05].

• Life science. This market is rapidly expanding with new requirements for precise dispensing of DNA and protein substances. The high costs of these fluids make PIJ technology with its precision placement and tight flow con-trol an excellent dispensing tool. Applications include the use for DNA re-search, various medical purposes such as dosing of drugs, and food science. A quite futuristic application is the use of inkjet printing for the fabrication of living tissue. Examples can be found in [Che96; Jam98; Coo01; Rad05]. • Chemical. Within this market, the PIJ technology is mainly used as tool

for research purposes. Again, the unique capacity of the technology for dispensing small doses of liquids specifically makes it useful for this market. Applications include material and substrate development as well as coating purposes. Examples can be found in [Oht05; Nak05]

• Optical. Jetting of UV-curable optical polymers is a key technology for the cost-effective production of micro-lenses. These tiny lenses are used in devices from fiber optic collimators to medical systems. The ability of PIJ technology to precisely jet spheres in variable but consistent drop sizes provide opportunities for the cost reduction of existing optical components and innovative new designs, see e.g. [Cox96; Che02; Bie04].

• Three-dimensional mechanical printing. This category claims the PIJ tech-nology as tool for rapid prototyping, small volume production, and the pro-duction of small sensors. Examples can be found in [Wal02; Voi03; Yeo04]. As discussed, performance requirements imposed by various applications are quite strict. In light of future applications, it is expected that these requirements will become even tighter. In combination with current limitations, this motivates ongoing research, as will be discussed in Section 1.2.3.

1.2 System description

1.2.1 An archetypal PIJ printhead

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1. Basic working principle. Though the operation of a PIJ printhead involves many fields of science, a major role is assigned to that of acoustics. 2. The ink channel design. Despite the sketched diversity in printhead designs,

four basic components keep returning. These include the channel itself, the nozzle, the ink supply, and the piezo-unit.

3. The operation of printheads. Typically, actuation pulses are manually shaped input pulses based on physical insight of the design.

The work presented in this thesis focusses on the common principles of PIJ print-heads, among which the ones listed above, yet will be elaborated on one particular PIJ printhead design. Since the fundamental characteristics of this design does not differ from most other PIJ printhead designs, the results presented through-out this thesis will be still generally applicable. So to speak, the employed PIJ printhead design is truly an archetypical one.

In this section, a description of the working principle of the used PIJ printhead design is given. At the same time, it provides a perfect example of the three sketched characteristics above. Here, the focus lies on the basics rather than the details of the design. Those will be discussed in Chapter 3 and 4. Note that various experimental curves shown in the remainder of this chapter have been measured with one of the experimental printheads, see Chapter 3.

x=0 [reservoir] x=L [nozzle] t Vpuls ink channel piezo unit 1 2 3 4 5

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1.2 SYSTEM DESCRIPTION 11 ink channel ink channel substrate piezo unit piezo unit

Figure 1.8: A schematic view of an a cross-section of a PIJ printhead

used as actuator and sensor. Physically, it senses the force that results from the pressure distribution in the channel acting on the piezo’s surface that borders the channel. This force creates a charge on the piezo-unit. Since only changes in charge are measured, in fact the time derivative of the instantaneous present force is sensed. Furthermore, since the resulting voltage drop of this current over a resistance is measured, we have that a voltage is the resulting sensor signal. For the trapezoidal pulse used for actuation, a typical sensor signal is depicted in Fig. 1.9, p. 13. Typically, around 75 nozzles per inch are integrated in an array that forms a printhead.

To fire a droplet, a trapezoidal pulse is provided to the piezo actuator, see Fig. 1.7. Then, ideally, the following occurs, see e.g. [Bog84; Ant02]. To start with, a neg-ative pressure wave is generated in the channel by enlarging the volume in the channel (step 1). This pressure wave splits up and propagates in both directions (step 2). These pressure waves are reflected at the reservoir that acts as an open end and at the nozzle that acts as a closed end (step 3). Note that the negative pressure wave reflecting at the nozzle causes the meniscus to retract. Next, by decreasing the channel’s volume to its original value a positive pressure wave is superimposed on the reflected waves exactly when they are located in the middle of the channel (step 4). Consequently, the wave traveling towards the reservoir is canceled whereas the wave traveling towards the nozzle is amplified such that it is large enough to result in a droplet (step 5).

Another common denominator is the operation of an PIJ printhead. For most designs, an input wave form is manually shaped based on physical insight in the working of a printhead. Clearly, for the design presented here, the actuation pulse is tuned to the first eigenfrequency of the ink channel. Additionally, some-what more complex waveforms are designed for purposes like smaller droplets and damping of the residual vibrations. Details will be discussed in Chapter 4.

1.2.2 Limitations of current designs

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• Drop-speed. The resulting droplets are required to have a certain speed, typically around several m/s.

• Drop-volume. Depending on the application under consideration, the perfor-mance requirement concerning volume typically varies from 5 to 15 picoliter. Smaller drop-volumes are for example required with the manufacturing of PolyLEDs. The smallest drop-volumes are around 2 to 3 picoliter. For some applications, it is required that the drop-size can be varied during opera-tion. For example, for large areas that need to be covered large drops are desired, whereas for high resolution printing small drops are desirable. This is referred to as drop-size modulation.

• Drop-speed and -volume consistency. The variations in drop-volume and drop-speed between successive drops and between the nozzles must stay within a certain percentage band, typically ranging from 2 to 15 percent. This is to avoid irregularities in the printed object. In this thesis, only drop-to-drop consistency is considered.

• Drop-shape. The drop-shape is influenced negatively by the formation of tails or satellite drops. These are highly undesirable for the quality of the print. For example, for the production of PolyLEDs, tails or satellites induce cross-contamination.

• Jet straightness. The droplets have to be deposed in a straight line to the substrate, typically within 5 to 14 mrad accuracy. Note that as the drop-volume decreases, this requirement becomes even more important.

These requirements are only explicitly concerned with the drop itself. The fol-lowing important two requirements are more related to the jetting process:

• Productivity. The productivity of a PIJ printhead is mainly determined by the jetting frequency, defined as the number of drops that a channel jets within a certain time, and the amount of nozzles per inch (npi-ratio), see [Bru05] for details. Though these two parameters are highly dependent on the specific design of printhead, typically it is around 10-20 kHz at 50-100 npi to guarantee acceptable productivity.

• Stability. Stability of the jetting process is one of the most important perfor-mance requirements for PIJ printheads. In this context, stability is defined as the absence of nozzle failure per a certain amount of jetted drops, e.g. one failure per one million jetted drops.

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1.2 SYSTEM DESCRIPTION 13 the printhead. In this thesis, we restrict ourselves to the requirements posed for the drop itself plus the two requirements concerning the jetting process itself. Meeting these performance requirements is severely hampered by the following operational issues that are associated with the design and operation of printheads as discussed in Section 1.2.1. Major issues that are generally encountered are the following:

• Residual vibrations. After a drop has been jetted, the fluid-mechanics within an ink channel are not at rest immediately: apparently traveling pressure waves are still present. These are referred to as residual vibrations. In Fig. 1.9, the system’s response to a standard actuation pulse is depicted. Also, the time instant of drop-ejection is indicated (around 17 µs in Fig. 1.9). Usually, the fixed actuation pulse is designed under the assumption that a channel is at rest. To guarantee consistent drop properties, one has to wait for these residual vibrations to be sufficiently damped out to fulfill this assumption. Since this takes about 100 to 150 µs, it limits the maxi-mally attainable jetting frequency with all the consequences concerning the productivity and drop-consistency of a printhead. If the presence of resid-ual vibrations is ignored and the jetting frequency is increased nonetheless, drop-properties start varying. As example, the so called Drop-on-Demand (DOD) speed curve is depicted in Fig. 1.9, showing the dependency of the drop-speed on the jetting or DOD frequency. As can be seen, considerable speed fluctuations result.

0 10 20 30 40 50 60 70 80 90 100 −2 −1 0 1 2 3 4x 10 −6

Integrated sensor signal [Vs]

Time [µs] 2 4 6 8 10 12 14 16 18 20 2 2.5 3 3.5 4 4.5 Droplet speed [m/s] DOD frequency [kHz]

Figure 1.9: Residual vibrations (left, measured response (black) and the corre-sponding actuation pulse (gray, scaled)) and its effect on the DOD-speed curve (right)

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1. Electrical cross-talk. This form of cross-talk usually does not play a significant role. It occurs at the level of electrical circuits that are present in any printhead to operate the channels, for example in the form of leakage currents.

2. Acoustic cross-talk. The phenomenon that pressure waves within one channel influence other channels is called acoustic cross-talk. It can occur via the ink reservoir. Though it is a more important effect than electrical cross-talk, the overall influence can generally be considered small.

3. Structural cross-talk. Structural cross-talk can occur in many ways. For example, as can be seen in Fig. 1.8, all piezo-fingers are connected to a substrate. As a result, deformation of one piezo-unit induces a deformation of the neighboring units. Another path is via the defor-mation of a channel itself. As a result, the volume of the neighboring channels changes also which induces pressure waves in those channels. The deformation of the printhead structure can originate from two sources. The first one is the result of a channel being actuated and is referred to as direct voltage cross-talk. The second one is the result of the occurring pressure wave that causes deformation of the channel and is called indirect or pressure cross-talk.

0 10 20 30 40 50 60 70 80 90 100 −1 −0.5 0 0.5 1 1.5 2 2.5 3x 10 −6 Time [µs]

Integrated sensor signal [Vs]

−10 −8 −6 −4 −2 0 2 4 6 8 10 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 Channel number [−] Droplet speed [m/s]

Figure 1.10: Cross-talk (left, measured response of an actuated channel (gray) and a neighboring channel (black)) and the consequences on the drop-speed (right)

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1.2 SYSTEM DESCRIPTION 15 to 4.2 m/s. As can be seen, the effect of cross-talk on the drop-speed in particular is substantial. Though this figure only shows the drop-speed, cross-talk influences other drop-properties as well.

To minimize the effects of cross-talk, a number of measures have been taken. First, operation of ink channels is designed such that two neighboring chan-nels are not actuated simultaneously. However, this limits the possibilities considerably. Also, ink channels are actuated with a small delay to allow the worst effects to be damped out. Another measure to minimize the effect of cross-talk involves the printhead design itself. As can be seen in Fig. 1.11, the amount of piezo-units is twice that of the design depicted in Fig. 1.8. The redundant piezo-units B bordering the piezo-unit A form a so called bridge structure that provide additional stiffness to the design. If piezo-unit A is actuated to jet a droplet, the piezo-units B (short circuited) reduce the effects of structural cross-talk. However, this reduces the variations in drop speed only slightly. Furthermore, it is a costly solution, since the number of required piezo-unit for an array doubles. Also, it limits the attainable npi-ratio. ink channel substrate piezo unit B piezo unit B piezo unit A

Figure 1.11: A schematic view of an a cross-section of a PIJ printhead with a bridge structure

• Changing/varying dynamics. There are various phenomena that account for changing or varying dynamics. First, some materials suffer from aging and their properties change over time. For example, piezo-material has a notorious reputation when it comes to aging. Second, due to the extreme sensitivity of an ink channel’s behavior for small changes in material proper-ties, ink channel dynamics vary even within a range of a couple of channels. Changing or varying dynamics in combination with fixed actuation pulses affect the performance negatively. Conventional measures to minimize these effects, such as enforcing strict material properties during production, are usually very expensive and boost the cost of production considerably. • Robustness against disturbances. There are a number of disturbances

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of a PIJ printhead itself influences the performance negatively. Using one fixed actuation pulse simply cannot handle these issues effectively.

These operational issues form boundaries for the attainable performance and hence are a major drive behind the research and development conducted into inkjet technology. An inventory of solution strategies for these limitations is pre-sented in the following section.

1.2.3 Towards a controlled environment

Applications of inkjet technology as presented in Section 1.1.2 impose tight perfor-mance criteria on the printheads. In the near future, these perforperfor-mance require-ments become tighter. For some of these applications, even today’s performance already is insufficient. Given these facts, several operational issues have been identified in Section 1.2.2 that exactly limit the attainable performance. These observations provide a clear motivation for ongoing research in the field of inkjet technology.

The objective of this section is to identify suitable research directions that can improve the performance of PIJ printheads in face of the operational issues. To obtain such an inventory of possible solution strategies, it is necessary to first distance oneself from the specific PIJ printhead and focus on the various disci-plines involved in printhead engineering. In this section, after having obtained an overview of these disciplines and their individual contributions, the focus again shifts to the printhead design itself and it is discussed how the various disciplines can offer solution strategies to the issues at hand.

Research and development of the PIJ technology require a wide variety of dis-ciplines to be involved, see Fig. 1.12. After all, due to the complexity of inkjet systems, it is impossible to attribute all the necessary specialist knowledge to one engineering domain. While restricting to the design and development of a PIJ printhead only, already the following disciplines are typically represented in printhead engineering:

• Applied physics. The role of applied physics consists mainly of gaining fundamental understanding of the relevant phenomena that form the basis of a PIJ printhead. This is of great importance during practically every phase of printhead development. Typical examples include studies into the drop-formation process, the inclusion of air-bubbles, and the assessment of print quality.

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1.2 SYSTEM DESCRIPTION 17 (a) Mechanical engineering. A mechanical engineer applies physical prin-ciples to (re)design a certain device, in this case a PIJ printhead. Their expertise mainly aims at the application of the concepts of for example (fluid) dynamics, strength of materials, and applied thermodynamics. (b) Electrical engineering. Electrical engineering is a discipline that deals with the application of electricity. Their contribution covers a wide range from the selection of suitable actuators and sensors, designing and testing electrical networks that support the functioning of a PIJ printhead, to the digital signal processing to manipulate the relevant signals.

(c) Software engineering. This computer science discipline is concerned with developing large software applications. Their involvement with printhead engineering usually comes at a later stage, when the print-head is mounted in the complete printing system. Therefore, their role is somewhat limited during the design of a PIJ printhead itself. (d) Systems and control. Engineers specialized in systems and control deal

with both the design and operation of a printhead, though main em-phasis is given to the control part. For example, based on knowledge of the system optimal input pulses can be designed.

Mechatronic engineers form the core of the printhead engineering team. After all, a printhead truly is a mechatronic device. An important remark concerns the role of systems and control that is so often associated with mechatronics. Though the systems and control discipline is acknowledged as being an important aspect, the application thereof lags considerably behind, especially in the field of printhead engineering.

• Materials engineering. Materials engineering is a multidisciplinary field fo-cusing on functional solids, whether the function served is structural, elec-tronic, thermal, or some combination of these. Their work within the print-head engineering focuses on the choice for materials, keeping an eye on issues such as manufacturability, cost, and function. This discipline plays an important role in printhead engineering, since the consequences of these choices have high impact for example on the cost per nozzle.

• Chemical engineering. The involvement of chemical engineering in the de-sign of a PIJ printhead confines itself mainly to the ink. The influence of ink properties on the functioning of a PIJ printhead however is large. Though the development of ink can be performed quite independently from that of the printhead, it is important that some critical parameters of ink, e.g. viscosity, are established in mutual consult.

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particular perspective. A categorization of the various research directions can be given as follows:

• Mechanical (re)design. This solution approach to the operational issues comprises a mechanical redesign of the printhead, either by starting from scratch, applying only minor changes, or anything in between. Some possible (combinations of) directions include:

(a) Geometry. The geometry of an ink channel or an entire printhead influences the performance considerably. A few examples thereof are the following. A reduction of the channel-length induces the creation of smaller droplets. The way the ink is supplied to an ink channel largely determines the boundary condition of a channel and thus the operation of a printhead. An investigation in the geometry in all its details therefore is a suitable research direction in face of the operational issues encountered.

(b) Actuation. Actuation is one of the key-issues in printhead design. For example, the specific implementation of the piezo-electrical actuation not only determines the amount of cross-talk, but also the controlla-bility and observacontrolla-bility of the jetting process. Even the choice for a piezo-electrical actuator could be subject of discussion.

(c) Material. The choice of materials also has its influence on the operation of a printhead. An example is the wetting of the nozzleplate that might be solved by using a different type of coating. Also, the cost of manufacturing is largely dependent on the choices regarding material as well.

• Ink properties. Apart from the printhead itself, the ink plays an extremely important role in the jetting process. Rather than focussing on the print-head design itself, the ink is an important research direction as well. As illustration, recall that the drop-formation is largely dependent on the ink properties.

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1.2 SYSTEM DESCRIPTION 19 does not automatically result in adopting a truly mechatronic approach, i.e. with the proper attention to systems and control, to solve the performance limiting is-sues. In Fig. 1.12, the sketched characterization of current printhead engineering is schematically depicted in the figure on the left. Here, the systems and control approach plays only a modest role. In our view, however, a more prominent part for systems and control in general, and the application of control to PIJ print-heads in particular, is indispensable to lift current performance limitations of PIJ printheads. In Fig. 1.12, the importance of systems and control within printhead engineering is depicted in the figure on the right. To get a better understanding for systems and control as solution strategy for the operational issues, the major benefits of this approach are inventoried.

applied physics mechatronics materials engineering chemical engineering applied physics mechatronics materials engineering chemical engineering systems & control systems & control

Figure 1.12: Characterization of printhead engineering: current situation (left) and with the proposed direction (right)

Basically, systems and control can play a crucial role in two ways. To start with, its systematic approach to the functioning of complex systems in the aggregate offers structuring of the research and focus on the major performance determin-ing mechanisms. Second, it provides an additional degree of freedom to enhance the performance of PIJ printheads by means of control. These added values of systems and control within printhead engineering are advantageous for the im-provement of existing printhead designs as well as for the development of new ones. For example, the use of control is a very cost-beneficial option to enhance the performance of existing PIJ printheads without having to perform a redesign. Also, during the design of new printhead, both the systematic approach and the additional degree of freedom in the form of control provide tools to tune the de-sign such that optimal performance can be achieved.

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im-portance. Next to feedback control, feedforward control can be considered. For systems that act predictable based on their physical design, feedforward control is a suitable option. A PIJ printhead fulfills this requirement perfectly. Here, feed-forward is considered as tool for the design of actuation signals for PIJ printheads. To the best of our knowledge, the use of feedforward for this purpose has been virtually unexplored. The related field of input shaping has been investigated at least at one occasion, see [Jon97].

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Chapter 2

Problem formulation

In this chapter, the discussion in the introduction of this thesis is formalized in a research objective. This objective is then divided in three main research questions. Finally, the structure of this thesis is outlined.

2.1 The research objective

In the previous chapter, the main performance limiting operational issues that are commonly encountered in PIJ technology have been discussed. Given the fact that performance criteria for PIJ printhead applications become increasingly tight, these boundaries must be lifted to be able to meet future requirements. Based on an inventory of solution strategies that can resolve these operational issues, a systems and control approach has been chosen to be explored in this thesis. To the best of our knowledge, this research direction has been formerly unprecedented within the printhead engineering community, at least in the open literature. Therefore, only few work is available that can serve as starting point for the research conducted here. In this light, the research objective to fully ex-plore the possibilities of systems and control for PIJ printheads is formulated as: Develop a unifying modeling and control framework for a PIJ printhead to inves-tigate the possibilities and limitations of current designs in face of the commonly encountered operational issues.

Let us clarify the various elements present in this objective. To start with, ’a unifying modeling and control framework ’ relates first and foremost to the two basic ingredients of a systems and control approach, namely modeling and con-trol. To possess unifying properties in light of the research presented here, a model should describe the functioning of a printhead on a system level, incorporating all performance relevant dynamics. The input as well as a firm theoretical

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ground for these dynamics is often provided by the various disciplines involved in printhead engineering. The resulting model therefore is able to relate the overall performance of a PIJ printhead on a system level to the various detail studies performed by the various research groups within printhead engineering. Hence, the classification ’unifying’ is adopted. In addition, a solid control framework enables the systematic exploration of the to be introduced feedforward control option together with the obtained insight to come up with practical solutions to the operational issues at hand. Together, such a unifying modeling and control framework provide a solid basis to systematically ’investigate the possibilities and limitations of current designs in face of the commonly encountered operational issues’. The word ’possibilities’ reflects the utilization of the resulting framework to lift current boundaries posed by the ’commonly encountered operational issues’ to enhance the attainable performance of PIJ printheads. At the same time, new boundaries are expected to emerge. These more fundamental ’limitations’ of cur-rent printhead designs can however offer valuable insight to be used in the design process of future PIJ printheads. The generality of the research conducted in this thesis and the various results is emphasized by the use of the phrases ’current de-signs’ and ’commonly encountered ’. The results obtained throughout this thesis apply to more PIJ printheads than the ones considered here.

2.2 A decomposition in research questions

In this section, the research objective is decomposed in three main research ques-tions. Together, the solutions to these questions provide an overall solution to the research objective of this thesis.

Question 1: How should a PIJ printhead be modeled given its intended use for the proposed systems and control approach?

Basically, this research question is closely related to the suitability of the PIJ model for the purposes in mind. Within the advocated systems and control ap-proach, the role of the model is versatile. For one, the model should provide insight in the working of a PIJ printhead, both for the implementation of control and the use for (re-)design purposes. Also, it should facilitate the implementation itself of (feedforward) control. Several additional requirements could be formu-lated. Now, the better the model fulfills these and other requirements, the more beneficiating the systems and control approach can become.

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2.3 A DECOMPOSITION IN RESEARCH QUESTIONS 23

Question 2: Can we design actuation wave forms which will be implemented as feedforward control such that the performance of current PIJ printheads is improved?

As discussed previously, the introduction of control provides an additional de-gree of freedom to a PIJ printhead. Without having to perform a redesign of an existing printhead, its performance can be optimized by a simple tuning of a controller. For new designs, the performance can be increased by taking the pres-ence of the control into account. Now, for both existing and new PIJ printhead designs, the question arises how the incorporation of control can help to overcome the operational issues and thereby enhancing the performance of PIJ printheads. A related, but certainly equally important question concerns to what extent the attainable performance can be increased.

In this thesis, feedforward is investigated. Given the fact that an PIJ printhead acts predictably based on its physical design and is inherently stable, feedforward control is the most suitable choice. More specifically, given the highly repetitive character of the jetting process, Iterative Learning Control (ILC) is a logical choice as control strategy. Though ILC has proven its value for high-precision motion systems, it has not been used in the field of inkjet technology yet. A systematic exploration of the possibilities of ILC given the operational issues is therefore a fitting approach to this research question. Additionally, the generic character of the proposed framework renders it generally applicable to a broad range of PIJ printheads.

For the implementation of control, an important issue concerns the choice for the controlled and manipulated variable. Two options are considered in this thesis, namely piezo-based and laser-vibrometer based ILC. Though this choice is highly dependent on the particular PIJ design at hand, there is no loss of generality. Question 3: Can we improve current PIJ printheads such that some basic limi-tations with respect to the attainable performance are lifted?

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2.3 The structure of this thesis

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Chapter 3

Experimental exploration

In this chapter, the experimental setup used to investigate PIJ printheads is dis-cussed in detail. Special attention is given to the sensor functionalities present. Then, the various PIJ printheads that are used during the research are introduced. The relevant printhead dynamics of these PIJ printheads are identified and the re-sults are presented. Here, these experimental rere-sults are not shown for validation or control purposes. For that, one is referred to Chapter 5 and 7. Instead, the data are used to be able to from this point relate the main topics covered in this thesis directly to actual verifiable data. In our view, such an approach contributes to the verifiability of our research according to [Buc95].

3.1 Description of the experimental setup

A schematic overview of the experimental setup is depicted in Fig. 3.1. The ex-perimental setup itself is depicted in Fig. 3.2. With this setup, PIJ printheads can be investigated in various ways. The only actuator is the piezo-unit of the inkjet printhead. Three sensors are available in this setup. First, the piezo-unit not only can be used as actuator but also as sensor. Second, the meniscus (ink-air inter-face in the nozzle) movements can be captured by the laser-vibrometer. Third, properties of the resulting droplet can be monitored by a CCD camera. These sensor functionalities will be discussed in detail in the subsequent subsections. The PIJ printheads under investigation use a hotmelt type of ink that require heating of the printhead. The required reference temperature is reached by a PID controller (Eurotherm 2408), which measures the printhead’s temperature with thermocouples and controls the input voltages by means of heating elements. Next, to monitor the ink level inside the reservoir, a level sensor is incorporated in the printhead. Furthermore, a printhead is mounted in vertical direction with the nozzles faced down, similar to its position in an inkjet printer. To avoid that

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waveform generator amplifier switch board scope CCD camera + microscope laser-vibrometer + detector pc air pressure unit temperature control unit ink level indicator mirror (45 deg.) strobe light actuation signal piezo sensor signal image meniscus velocity printhead

Figure 3.1: A schematic overview of the experimental setup

the ink simply flows out of the nozzles under the influence of gravity, an air pres-sure unit (TS 9150G) makes pres-sure that the prespres-sure in the ink reservoir remains below the ambient pressure.

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3.1 DESCRIPTION OF THE EXPERIMENTAL SETUP 27

Figure 3.2: The experimental setup

3.1.1 Piezo sensor signal

The first and most important sensor functionality discussed is that of the piezo-unit. For a detailed discussion on the piezo-unit, one is referred to Chapter 4. Here, the fundamentals are treated, required for the explanation of the simulta-neous use of the piezo-unit as actuator and sensor.

As generally known, a piezo can be used as actuator or sensor, see e.g. [Waa91]. For that, one uses the piezo’s indirect (actuator) and direct (sensor) piezo-electric effect. The former comprises the following. If an electrical potential V is applied to the piezo-unit, a deformation of the piezo-unit u results. The latter refers to the following phenomenon. If a force F is applied to a piezo’s surface, an electric charge q results. Together, this behavior can be described as:

u q = d 1/k C d V F (3.1) with C the piezo’s capacity, d the piezoelectric charge constant, and k the stiffness of the piezo. Schematically, (3.1) can be represented as two-port, as depicted in Fig. 3.3. The piezo-unit is bilaterally coupled with an impedance Zcrepresenting

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Chapter 4. For an introduction of the two-port modeling approach, one is referred to the next chapter.

V q u F

+

₊

+

C d d 1 k Zc

Figure 3.3: The piezo-block: the ink-channel as impedance

Now, rather than using the piezo-unit as either actuator or sensor, during the research presented in this thesis it is used as actuator and sensor simultaneously. This is accomplished as follows. The measured signal q is made up of two con-tributions. The first is that of the applied actuation voltage V via the piezo’s capacity C and is referred to as the direct-path. The second contribution orig-inates from the force F exerted by the ink in the channel via the piezoelectric charge constant k and is referred to as the indirect-path. Since only this second contribution is the required sensor signal, it has to be extracted from the mea-sured signal q. However, the contribution of the direct-path is considerably larger than that of the indirect-path, being typically 10-20 mA and 50-100 µA, respec-tively. Consequently, it is difficult to measure the sensor signal (indirect-path) simultaneously while using the piezo as actuator. Basically, there are two options to do so still:

1. Using software-compensation. Given knowledge of the applied electrical field V and the availability of an accurate model of the piezo’s capacity C, the contribution of the direct-path can be computed. By subtracting this contribution from the measured signal q, the required sensor signal can be established, see e.g. [Dos92; And94]. Note that for the discrimination between the direct and indirect-path in our case, a rather accurate model has to be available. The model inaccuracies should be at least significantly smaller than the sensor signal that one is trying to obtain.

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3.1 DESCRIPTION OF THE EXPERIMENTAL SETUP 29 direct-path. Again, by subtracting both measured signals, the indirect-path or sensor signal can be obtained.

V q u F 'piezo' 'ink' direct-path 'piezo' indirect-path 'ink' + + + + + + C d d 1 k Zc

Figure 3.4: Division into a piezo- and ink-block diagram

A drawback of software compensation relates to the required accuracy of the piezo model. Since modeling of the piezo’s capacity C is extremely difficult given its nonlinear behavior, this method is hard to implement. On the other hand, hardware compensation requires that both piezo-units are exactly the same. Small differences, e.g. due to drift or production tolerances, are always present. This influences the accuracy of the resulting sensor signal negatively. Of both methods, hardware compensation is the only feasible method to simultaneously use the piezo as actuator and sensor in case of a PIJ printhead. To minimize the effects of piezo capacity differences, the following measures are taken:

'piezo'

'piezo' 'ink'

_-

₌

'ink'

full channel empty channel

+ +

Figure 3.5: The basic principle to obtain the actuation and sensor signal simul-taneously as used in the piezo-sensing device

• Temperature differences. Differences in piezo capacity occur due to temper-ature differences of both piezo-units. By isolating the PIJ printhead these differences are satisfactorily minimized.

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• Influence of structural effects on the sensor measurement. Even though the ink channel is empty, a small contribution due to the deformation of the structure may be present in the indirect-path. This effect can be neglected though.

For details, one is referred to [Gro03]. The measured frequency response of the electronic conditioning of the piezo-sensing device, i.e. the subtraction as shown in Fig. 3.5, is depicted in Fig. 3.6. Note that modeling of the piezo-unit itself, i.e. the piezo-block as depicted in Fig. 3.3, is postponed until Section 4.2.5. Appar-ently, as can be seen in Fig. 3.6, the magnitude as well as the phase are distorted for the low and high frequency range. However, for the frequency range of inter-est, roughly from 20 kHz up to 250 kHz, the resulting sensor signals are minimally affected by the piezo-sensing device.

101 102 103 104 105 106 −35 −30 −25 −20 −15 −10 −5 0 5 Magnitude [dB] Frequency [Hz] 101 102 103 104 105 106 −150 −100 −50 0 50 100 Phase [deg]

Figure 3.6: Measured FR of the piezo-sensing device

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3.1 DESCRIPTION OF THE EXPERIMENTAL SETUP 31 resulting sensor signal. A typical sensor signal as result of a standard trapezoidal actuation pulse is depicted in Fig. 3.14, p. 43.

The following remarks are in order. First, the piezo sensor is located in the channel whereas the droplet formation takes place in the nozzle. Second, due to the integrating character of the sensor the resulting signal is an average of the pressure that is present in a channel. Finally, since all the piezo’s are connected to the same substrate, the actuation as well as sensing is influenced by structural cross-talk. Despite all these facts, the current sensor signal can be regarded as representative for the jetting process.

3.1.2 CCD camera

A second sensor functionality is provided by the Charge-Couple Device (CCD) camera equipped with a microscope, that can observe the generated droplets. A stroboscope provides a short light flash at a defined instant after the droplet is ejected and an image is obtained on which the droplet seems to be fixed in the air. A necessary requirement for this approach to succeed is that the repeatability of the drop formation is high. Then, since both the time duration and the distance that the droplet has traveled are known, an estimate of the droplet speed can easily be obtained. Moreover, it is possible to estimate the volume of the droplet, because the droplet diameter can be determined. Other information which can be obtained concern the droplet’s angle, the formation of satellites and the stability of the jetting process. A great advantage of the CCD camera is that direct informa-tion about a droplet is obtained. Unfortunately, this informainforma-tion is only available at discrete time instants. In case the drop formation is not repeatable, a more expensive high-speed camera could be used to obtain the required drop properties. Note that the resulting droplet properties are the result of image processing. By altering some of the parameters of this process, e.g. the threshold used for the black-white conversion, the outcome may change. This affects the quality of the measurements negatively.

3.1.3 Laser-Doppler interferometry

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interferometer or laser-vibrometer it is possible to measure the velocity of the meniscus inside a nozzle. Here, the meniscus surface is the moving object which reflects the beam. Unfortunately, this type of measurement can only be applied to a small range of the dynamics. It is namely not possible to jet during this measurement, without taking special measures.

In the experimental setup, the laser-vibrometer is used to measure the meniscus velocity. It consists of a Polytec OFV-5000 vibrometer controller containing a Polytec VD-02 velocity decoder. Furthermore, a Polytec OFV-512 fiber inter-ferometer and a Polytec OFV-130-3 micro-spot sensor head complete the setup. The resulting laser beam of approximately 3 µm in diameter is aligned via a mirror in the center of a nozzle that has a diameter of 32 µm. It is assumed that a Poiseuille velocity profile occurs in the nozzle during operation, such that the laser-vibrometer setup measures the maximum velocity. Due to the use of a laser-vibrometer via a mirror that is situated directly in front of the nozzle exit, the experiments are restricted to the non-jetting situation. Practically, this means that only experiments at a lower voltage can be performed. However, if it is assumed that the ink channel behaves linearly, the resulting learned actuation pulses at a lower voltage can be scaled up to a jetting voltage and implemented. This important linearity assumption will be discussed in detail in the subsequent chapters. The following remarks are in order. First, the impossibility to use meniscus-based ILC in a jetting situation does not conflict with its intended use as design tool for wave forms. Second, a sensor that is integrated in the printhead as replacement of the laser-vibrometer is currently being developed, see [Gro06a]. Then, limitations with respect to the used voltage are removed.

The following remarks are in order with respect to the use of the laser-vibrometer: • Laser alignment. Due to the reflective property of the nozzleplate, align-ment of the laser beam is quite difficult. Initial alignalign-ment is performed based on a camera image of the laser-spot on the nozzleplate. Since the wetting is clearly visible, the jetting channel can easily be established. The final alignment takes place by observing the resulting sensor signal on the scope. The expected amplitude of the response is known from calibration experiments conducted earlier.

• Sensor output. A remaining issue concerns the physical interpretation of the resulting sensor signal. If the laser is not aligned in the center of the nozzle, it is not known what velocity is measured. This might still be the maximum component of the meniscus.

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3.2 DESCRIPTION OF THE EXPERIMENTAL PRINTHEADS 33 • Heating of the ink. The heating of the ink by the laser can be neglected due

to the low power intensity of the laser beam.

3.2 Description of the experimental printheads

A schematic representation and nomenclature of the PIJ printheads used in the research presented in this thesis are depicted in Fig. 3.7. Specific details concern-ing the geometry and physical properties of these printheads are listed in Table 3.1 and 3.2, respectively. All printheads used in this thesis are similar, except for one point. This concerns the presence of the so-called bridge structure, see Fig. 3.8. As discussed in Chapter 1, this bridge structure is used for the minimization of structural cross-talk effects. Some printheads have the bridge structure (233e02 and 293e02) while others have not (DG074). During the discussions throughout this thesis, it is clearly indicated which printhead has been used.

channel

connection

nozzle

reservoir

piezo-finger substrate

Figure 3.7: Nomenclature of an ink channel

channel A channel B substrate piezo unit piezo unit substrate piezo unit B piezo unit B piezo unit A channel A channel B

Figure 3.8: Cross-section of a PIJ printhead without(left) and with (right) bridge structure

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Channel (actuated) length 7.61 mm

height 106 µm

width 266 µm

Channel (not actuated) length 0.40 mm

height 106 µm width 266 µm Connection length 1.06 mm height 230 µm width 230 µm Nozzle length 100 µm diam. (start) 100 µm diam. (end) 32 µm Table 3.1: Data of the printhead geometry

Density ρ 1090 kg/m3

Dynamic viscosity µ 0.011 Pa s

Surface tension ν 0.028 N/m

Speed of sound c 1250 m/s

Effective speed of sound ceff 900 m/s

Table 3.2: Overview of the physical properties of ink

the effect of the changing cross-section can be neglected.

In Table 3.2, a distinction is made between the speed of sound and the effective speed of sound. The former applies for the non-actuated parts of the ink channel. The latter is used for the actuated channel. Due to the fluid-structure interaction, the effective speed of sound is lower. By using these different values for various parts of an ink channel, this effect is accounted for.

Throughout this thesis, it is assumed that all channels are identical. The validity of this assumption as well as the consequences if not, are discussed in Chapter 6 and 7. In Fig. 3.9, an overview of the nomenclature of the various transfer func-tions is provided that is adopted in this thesis. The direct transfer funcfunc-tions are denoted by Ha and Hb, the indirect or cross transfer functions by Hab and

Hba. The identification is performed using two of the three sensor functionalities.

First, the piezo is used as actuator and sensor. This is referred to as piezo-based identification. Second, the laser-vibrometer instead of the piezo-unit is used as sensor. This is referred to as laser-vibrometer based identification.

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3.2 DESCRIPTION OF THE EXPERIMENTAL PRINTHEADS 35 Ha Hb Hab Hba uA uB yA yB channel A channel B ink channel ink channel

Figure 3.9: Nomenclature of two neighboring channels

fr = ceff

λ (3.2)

with ceff the effective speed of sound and λ the wave length of the appropriate

standing wave in an ink channel. In principle, the ink channel’s basic resonance frequency is the 1/4 λ mode, given the fact that one open (reservoir) and one closed (nozzle) end is present. Note that λ equals in our case Lch+ Lco+ Ln.

However, for frequencies up to approximately 100 kHz, the nozzle acts as an open rather than a completely closed end. Therefore, for low frequencies the ink channel acts more as a 1/2 λ resonator, see [Ant02]. This phenomenon can be explained as follows. Suppose that the nozzle dynamics can be described by an equivalent mass-spring-damper system, where the mass represents the ink in the nozzle. For low frequencies, the mass-spring-damper system oscillates whereas for high frequencies it does not. Thus, the mass-spring-damper system, i.e. our nozzle, acts as a low-pass filter. This phenomenon is discussed in more detail in Section 4.2.2.

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theoretical mode frtheoretical measured mode frmeasured ∆ fr

1/2 λ (0.50) 50 kHz 0.48 (≈ 1/2 λ) 48 kHz 2 kHz 2 · 1/2 λ (1.00) 100 kHz 0.91 (≈ 2 · 1/2 λ) 90 kHz 10 kHz 5 · 1/4 λ (1.25) 125 kHz 1.19 (≈ 5 · 1/4 λ) 118 kHz 7 kHz 7 · 1/4 λ (1.75) 175 kHz 1.83 (≈ 7 · 1/4 λ) 182 kHz 7 kHz Table 3.3: Overview of the theoretical and measured (293e02, see Fig. 3.13, p. 41) resonance frequencies in the piezo-based approach

theoretical mode frtheoretical measured mode frmeasured ∆ fr

1/2 λ (0.50) 50 kHz 0.43 (≈ 1/2 λ) 43 kHz 7 kHz 2 · 1/2 λ (1.00) 100 kHz 0.76 (≈ 3 · 1/4 λ) 76 kHz 24 kHz 5 · 1/4 λ (1.25) 125 kHz 1.30 (≈ 5 · 1/4 λ) 129 kHz 4 kHz 7 · 1/4 λ (1.75) 175 kHz 1.71 (≈ 7 · 1/4 λ) 170 kHz 5 kHz Table 3.4: Overview of the theoretical and measured (233e01, see Fig. 3.17, p. 46) resonance frequencies in the laser-vibrometer approach

0 2 4 6 8 10 12 −2 −1 0 1 2 3 4 Position [mm]

Scaled pressure [Pa]

0 2 4 6 8 10 12 −2 −1 0 1 2 3 Position [mm]

0 2 4 6 8 10 12 −3 −2 −1 0 1 2 Position [mm]

0 2 4 6 8 10 12 −4 −3 −2 −1 0 1 2 Position [mm]

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3.3 DESCRIPTION OF THE EXPERIMENTAL PRINTHEADS 37 Finally, one last phenomenon is to be addressed. If the piezo-unit is actuated with a sinusoid at 107 kHz (or a multiple thereof), the ink in the channel below the piezo-unit’s surface oscillates with the same frequency whereas the ink in the remainder of the ink channel, connection and nozzle is almost completely at rest, see Fig. 3.10. Fig. 3.10 is obtained using a finite volume model of the ink channel dynamics, see [Wij04]. Note that this effect is also clearly visible in Fig. 3.17, p. 46. One possible explanation for this phenomenon is the occurrence of destructive interference below the piezo-unit’s surface, and comprises the following. Suppose that the piezo-unit can be modeled as a finite set of point sources each emitting traveling waves in both directions of an ink channel, see Fig. 3.11. If it is assumed that the piezo-unit deforms uniformly over its length (see Section 4.2.5), these point sources oscillate uniformly for every frequency. If the piezo-unit is actuated with a frequency whose wavelength corresponds to the length of the piezo-unit (λ = l), destructive interference occurs. Now, the generated pressure waves for two point sources spaced at exactly d = 1/2 λ are illustrated in Fig. 3.11. As can be seen, the waves of this set of sources are amplified below the piezo-units surface, yet are canceled at any other location. Since the piezo-unit can in principle be represented by an infinite set of point sources spaced at 1/2 λ apart, this effect only is increased if more point sources are taken into account, see Fig. 3.11. As a result, the ink below the piezo-unit is oscillating whereas the fluid-mechanics in the remainder of the ink channel, connection, and nozzle are almost at rest. The frequency at which this phenomenon occurs can be computed as:

piezo unit

substrate

d

Figure 3.11: Illustration of destructive interference phenomenon

fr = ceff

λ =

900

7.61 10−3_s = 118 kHz (3.3)

Inkjet printhead performance enhancement by feedforward input design based on two-port modeling