mechatronic design of an active printhead alignment ... · mechatronic focussing. high accuracy...

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Mechatronics xxx (2006) xxx–xxx

Mechatronic design of an active printhead alignment mechanismfor wide format printing systems

Arnoud Notenboom, Dennis Bruijnen *, Eric Homburg, Rene v.d. Molengraft,Linda v.d. Bedem, Maarten Steinbuch

Technische Universiteit Eindhoven, Department of Mechanical Engineering, Control Systems Technology Group, P.O. Box 513,

5600 MB Eindhoven, The Netherlands

Received 27 September 2006; accepted 16 October 2006

Abstract

In this paper, the mechatronic design of an active printhead alignment mechanism for multi-printhead inkjet printers is presented. Theposition of each printhead can be independently controlled for the purpose of printhead alignment, by which print quality is improvedwithout tightening the manufacturing tolerances. The design of a short stroke movable printhead mechanism with an actuator is dis-cussed, aiming at a positioning accuracy within 10 lm. A dynamic finite element model is developed to determine the eigenfrequencies,mode shapes and transfer functions of the printhead guidance mechanism. The principle is validated in closed loop by various tests with arealized prototype. The experimental results show that static as well as dynamic alignment errors are compensated for within the require-ment whereas the manufacturing tolerances can even be lowered.� 2006 Elsevier Ltd. All rights reserved.

1. Introduction

Recent developments of new types of ink, paper andmore efficient printheads have contributed to a higher pro-ductivity and an improved print quality in inkjet printing[1,2]. The inkjet technique is characterized by high colorquality and relative low pricing. In Wide Format PrintingSystems (WFPS), where formats such as A1 and A0 areprinted, the inkjet technique is universally applied.

Print quality is determined by a lot of factors, includingresolution, dot positioning accuracy, color, the printingsurface and human visual perception [3]. The work in thispaper will focus on the dot positioning accuracy of aWFPS, and more specifically on the alignment of the print-heads. Most of the alignment errors follow from manufac-turing tolerances, leading to small dimensional and form

0957-4158/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.mechatronics.2006.10.001

* Corresponding author.E-mail address: [email protected] (D. Bruijnen).

Please cite this article in press as: Notenboom A et al., Mechatronictronics (2006), doi:10.1016/j.mechatronics.2006.10.001

variations in the printer components. Also, vibrationsand thermo-mechanical effects in the system can deterioratethe positioning accuracy of the printheads.

For improving printhead alignment, tightening of man-ufacturing tolerances is expensive, and also calibrationtechniques [4] can only be used to nullify static misalign-ments. While the printer performance requirementsincrease, at some point it becomes lucrative to measurethe alignment errors and minimize them by active control.For example, constant and systematic dot positioningerrors can be compensated for with sub-resolution accu-racy by regulating the jet-timing of the printheads. How-ever, this method is only possible in carriage movementdirection. Compensation for static and dynamic misalign-ment via active control has not been investigated yet.

This paper presents an approach, where each printheadis provided with a sensor, actuator and a short stroke guid-ing mechanism, to enable independent regulation of theprintheads for alignment in paper transport direction. Thisapproach is inspired by lenses in DVD-players and otheroptical devices [5,6], which are flexibly suspended for

design of an active printhead alignment mechanism ..., Mecha-

mailto:[email protected]

2 A. Notenboom et al. / Mechatronics xxx (2006) xxx–xxx

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mechatronic focussing. High accuracy levels are achievedin this field.

The mechatronic design of the new actuated printheadmechanism will be discussed, aiming at a positioning accu-racy within 10 lm over a stroke of 300 lm. Challenges arethe high operating temperatures up to 130 �C and a low-cost design. Also, a suitable actuator will be designed fordriving the printhead. Simultaneous with the mechanicaldesign, the dynamic performance of the printhead guidingmechanism will be investigated, using eigenmode analysesand transfer functions determined by FEM calculations.An important advantage of this approach is that thedynamic behavior of the design is well understood inadvance. Furthermore, an indication of the controllabilityis given, and necessary steps can be taken early in thedesign process for improving the performance.

A general system description of a WFPS will be givenfirst, including the requirements and boundary conditionsof the new design. Next, the guiding mechanism and print-head suspension are explained, after which the actuatordesign will be described. Then, the dynamic FEM simula-tions of the guiding mechanism, as well as the controllerdesign are discussed. After that, a thermal experimentsare presented and finally the conclusions are drawn.

2. System description

2.1. The WFPS setup

A schematic view of a WFPS is given in Fig. 1. A car-riage containing a set of printheads moves in x-directionover a guidance, a ±1.5 m aluminum extrusion profile.With constant carriage speed vc, the printheads jet ink onthe print medium underneath. By stepwise feeding of theprint medium in y-direction, a print is built up in strokes.

The printheads have a rigid ceramic body with globaldimensions l · w · h = 80 · 20 · 120 mm. A uniform massm of 0.15 kg and a coefficient of thermal expansion(CTE) a of 5 lm/m K are assumed. Before printing, theink in the printhead is heated to 130 �C.

The manufacturing tolerances on the carriage and theprintheads mainly result in static misalignments, in the

Fig. 1. Schematic representation of a WFPS including the printheadalignment system.


order of few tens of lm. Dynamic disturbances are causedby the guidance. Despite the polished bearing surfaces, aslight waviness (profile error) will generally exist. An ampli-tude of maximum 100 lm and resulting frequencies up to10 Hz are assumed for vc,max = 1–2 m/s. Also guidancevibrations will occur when printing where the eigenfrequen-cies depend on the position of the carriage. The dominantvibration frequency is in the order of 101 Hz. Although theprintheads may be mutually aligned in case of guidancevibrations, the misalignment with respect to the print med-ium will be visible on the print.

2.2. Mechatronic concept

A mechatronic solution is proposed, by which eachprinthead is actuated and controlled in y-direction. Thedynamic principle of the concept is explained by the modelshown in Fig. 2. The printhead mass m is connected to thecarriage by means of a damper d and spring k, dependingon the guiding mechanism. The carriage at position yc,showing small amplitudes Ad for frequencies fd, introducesdisturbances on the printhead position yp. Position yp willbe measured with respect to an absolute reference indepen-dent of all disturbing sources, and will be controlled bymeans of an actuator force Fact.

The equation of motion can be formulated as

m€yp þ dð _yp � _ycÞ þ kðyp � ycÞ ¼ F act: ð1Þ

where the variables yp, yc and Fact are a function of time. Itis preferred to keep k and d low, because then disturbancesfrom yc have minimal influence on the printhead positionyp. Furthermore, a minimal actuator force Fact will beneeded, resulting in a light and compact actuator withlow power consumption.

In order to compensate for the static misalignments andthe low frequent profile error within 10 lm, a minimumbandwidth of about 50–100 Hz is specified for the controlsystem of the actuated printhead. Vibrations up to thisbandwidth will be reduced by the control system. Dynam-ical position errors in x-direction must be prevented in thedesign since they cannot be compensated by the jet-timing.Only a few lm of error amplitude is allowed. At last, thesystem must be able to resist the high temperatures causedby the printheads.

Fig. 2. Dynamic model of the actuated printhead concept.


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2.3. Absolute reference

For accurate alignment of all printheads in y-directionand for accurate positioning with respect to the print med-ium, an absolute position measurement is required. A thinstring will be tightened along the guidance (Fig. 1) and willserve as an absolute reference. A useful sensing methodwith an accuracy of 1 lm is presented in [7]. The sensoris based on a charged coupled device, which captures shad-ows of the string created by two light emitting diodes. Theshadow positions are used to reconstruct the printheadposition with respect to the printer frame, whereas stringresonances are filtered out in software using robustnotches.

3. Guiding mechanism

The printhead needs to follow an accurate linear move-ment, for which several principles are explained in [8–10].Five of the six Degrees of Freedom (DOF) of the printheadneed to be fixed. Only the y-translation must be free for asmall linear movement. A parallel leaf spring mechanism asshown in Fig. 3 is particular suitable for this purpose. Theprinciple is based on elastic elements, with the advantagesof no hysteresis, no wear and no play. In order to preventthe printhead from being over-determined, one leaf springis given an elastic hinge, releasing its rotational constraintaround the y-axis.

3.1. Leaf spring characteristics

During printing, sideward acceleration levels ax up to50 m/s2 can be expected, mainly due to reversal of the car-riage. An inertial force Fi = m Æ ax will act on the center ofmass of the printhead. The resulting moments MA, MB andforces FA, FB on the leaf spring ends will cause an x-deflec-tion of the printhead and its nozzle axis, directly resultingin dynamic dot-positioning errors. Expressions for the noz-zle deflections dA, dB at both sides of the printhead are

Fig. 3. Leaf spring mechanism and printhead mounting.


given by (2a) and (2b), which are based on standard formu-las from linear beam theory [11]:

dA ¼F A‘

3

3EIy�MA‘

2

2EIyþ uyðp � ‘=2Þ ð2aÞ

dB ¼ 2 � F Bð‘=2Þ3

3EIyþ uy � p ð2bÞ

uy ¼F A‘

2

2EIy�MA‘

EIyð3Þ

Herein, E is Young’s modulus, Iy the area moment of iner-tia of the leaf spring and p represents the mid leaf springposition with respect to the nozzle axis. The printhead rota-tion uy is determined by the full leaf spring. AssumingMA = Fi(hcm � p + ‘/2) �MB, MB = FB Æ ‘/2 and FA =FB = Fi/2, then both (2a) and (2b) can be simplified to

dðpÞ ¼m � ax

124‘3 þ ðp2 � hcmpÞ‘

� �EIy

: ð4Þ

Thus, in the configuration as in Fig. 3, all the nozzles willdeflect equally, regardless of p. In Fig. 4, the nozzle deflec-tion d(p) is plotted. A set of steel leaf springs with dimen-sions ‘ · w · t = 25 · 20 · 0.25 mm is considered, resultingfrom a compromise between a low translation stiffness, ahigh in-plane leaf spring stiffness and the limited spacearound the printhead. The nozzle deflection appears equalto zero for p � 0 and p � 0.06 m.

Also important is the nozzle position sensitivity for tem-perature gradients and thermo-mechanical effects in theprinthead, which decreases when the leafs springs aremounted close to the nozzle axis (p! 0). However, thepaper under the printhead as in Fig. 3 bounds the positionof the leaf springs by p P ‘/2. In this case, a nozzle deflec-tion of several micrometers will remain. A further reduc-tion can be achieved by:

• Further increase of the in-plane stiffness.• Optimizing the leaf spring geometry.

Fig. 4. Nozzle displacement of printhead loaded with 50 m/s2.


Fig. 5. Deformation of different leaf spring geometries under load. Thickness t and length ‘ are kept constant.


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Although most common, the first option will conse-quently lead to a higher power dissipation of the actuator.Only t and ‘ of the leaf springs can be varied, influencingthe translation stiffness by (t/‘)3.

In the second approach, the nozzle displacements arereduced by forcing the printhead to rotate around its noz-zle axis. This can be explained by a 2D FEM-model madewith Marc/Mentat [12], as shown in Fig. 5. Three differentleaf spring geometries are examined for the load case whereMA = 0.40 Nm and FA = 3.75 N are applied at the bottomof the leaf spring, which holds for p = ‘/2.

With the ordinary leaf spring (a), the printhead rotatesaround the leaf spring’s center, resulting in an x-displace-ment at the nozzle axis. The trapezoid (b) shows less deflec-tion, because the deformation will mainly concentrate inthe narrower part of the leaf spring, lowering the centerof rotation. With the V-form leaf spring (c), the center ofrotation is moved directly under the leaf spring where thearms of the V-form cross, and coincides with the nozzleaxis. When the leaf springs deform under the inertial loadsfrom the printhead, the nozzles will stand still. Because thenozzles are less sensitive for y-rotations than x-transla-tions, the V-form will result in a better dot-positioning.Later in this paper will be shown that the V-form also sup-presses the modal displacements of the nozzles at the low-est eigenfrequency excited by reversal of the carriage.However, for optimal functioning of this principle, theover-determined DOF around the y-axis of the second leafspring should be released at the nozzle axis.

3.2. Sled design

From a dynamical point of view, fixing the leaf springdirectly to the printhead as in Fig. 3 is attractive becauseof the minimal mass and high guiding stiffness. However,easy and proper fixing of the leaf springs is difficult whenthe printhead must be detachable for replacement. A totalof 12 DOFs should be fixed; six per leaf spring end. Alsomicroslip should be taken care of when using clamped


joints, because of the many heating cycles and the differ-ence in coefficient of thermal expansion (CTE) betweenthe printhead body and leaf springs. Considering thesefacts, a light and stiff sled for mounting on the printheadis applied as an alternative. An open design for easy print-head detachment is realized by fixing both the actuator andsensor to the sled. The applied stainless steel material (AISI420) prevents corrosion on essential contact surfaces. A rel-ative low CTE of 10 lm/m K will keep the difference inexpansion with the ceramic printhead small. Furthermore,a symmetrical design will minimize positioning errors dueto thermo-mechanical effects. A detailed overview of theprinthead fixation and the sled design is given in Fig. 6.

The printhead must be fixed to the sled in all 6 DOFs,preferably close to the nozzle axis since accuracy is onlyrequired there. This is achieved by two balls, pressed inthe underside of the printhead, and resting in conical centerholes made in the bottom plate of the sled, where each ballfixes 3 DOFs. One DOF (in y-direction) should be released,for free expansion of the printhead during heating. There-fore, a small parallellogram around the center hole is made(see Fig. 7). Finally, the rotation around the y-axis, whichDOF is less important, is fixed by clamping the printheadto a thin rod at the center of mass. In this way, a printheadsuspension is created with minimal hysteresis. For accurateprinthead positioning, the sensor is mounted near the ther-mal center Tc of the printhead with respect to the sled.

During reversal, the balls in the printhead will apply asideways inertial load Fball of 3.75 N onto the sled (seeFig. 6). A preload force is needed to fix the balls in the con-ical center holes (standard apex angle 60�). Therefore, mag-nets will be glued next to each ball, attracting the printheadto the bottom plate. Like normal iron, AISI 420 stainlesssteel has also good ferromagnetic properties. A comparisonof commonly used magnet materials is shown in Table 1.High printhead temperatures up to 130 �C should beregarded, otherwise a permanent loss of magnetizationcould occur. A safe choice is Samarium–Cobalt (SmCo),which also minimizes volume and weight due to its relative


Fig. 7. Parallellogram for thermal expansion of the printhead; made bywire EDM.

Fig. 6. (a) Printhead fixation in all DOFs. (b) Acting forces on the sled design.


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high strength. The applied magnets provide an attractingforce of 8 N total.

The bottom plate allows for torsion around the y-axis inorder to eliminate the over-determination caused by thetwo leaf springs. In theory, the bottom plate has moreinternal DOFs, but the dominant dynamics are not affectedsince the eigenfrequencies are sufficiently high, as will beshown later.

The carriage of a WFPS will in general contain severalprintheads. For a high productivity of the WFPS, the print-heads should be arranged closely spaced. For this purpose,the sleds are staggered alternately with 1 mm in y-directionas in Fig. 8. In this way, the V-form leaf springs do not take

Table 1Overview of some commonly used permanent magnets [13,14]

Magneticmaterial

Remanence, Br

(T)Coercivity, H c

(kA/m)Thermal stability

Br=�C H c=

�C

Ferrite 60.4 250 �0.2% +0.4%SmCo 1.0–1.1 700 �0.03% �0.2%Alnico 1.0–1.2 100 �0.02% �0.03%NdFeB 1.2–1.3 850 �0.11% �0.6%


in much space. In order to keep the printheads in-line, theprinthead joints of the of the staggered sleds are shiftedback.

3.3. Fabrication

Most of the sled components can be made by commonmanufacturing processes, which are inexpensive in massproduction. However, the parallellogram in the bottomplate is quite complex for which wire EDM (Electrical Dis-charge Machining) must be used. This is an expensive pro-cess, but costs can be saved by stacking the 3 mm thinbottom plates in production. All components of the sled,including the leaf springs, are welded together to preventmicroslip in the system. High precision has been obtainedby using laser welding, where the heat supply during weld-ing is minimal.

3.4. Stiffness, linearity and hysteresis

In Table 2 the guiding stiffness of the leaf spring mech-anism is shown, emphasizing the low stiffness in sled move-ment direction ky compared to the other directions. Themeasured value is a bit lower, which is likely due to finitestiffness of the joints. Also a small hysteresis is noticed(Fig. 9), which is about ±1.5 lm (±0.3% full range). Thelinearity of the guiding mechanism has been found±1.6% full-scale. No discontinuities are measured when

Curie temperature(�C)

Maximum operatingtemperature (�C)

Relativecost

450 300 1750 250 20850 450 6310 80–150 10


Fig. 8. Staggering of the sleds for minimal spacing.

Table 2Guiding stiffness of the leaf spring mechanism (at center of massprinthead)

Parameter Modeled (kN/m) Measured kN/m

Stiffness kx 425 –Stiffness ky 7 6.0Stiffness kz 1100 –

Fig. 9. Hysteresis of the sled around neutral position (full range �250 to250 lm; 5 cycles).


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the sled is moved through the neutral position, whichmeans that the internal stresses in unloaded state areminimal.

4. Actuator design

4.1. Actuator specification

A linear voice coil actuator will be used for actuating theprinthead. This type of actuator is fast, works contact-freeand has no cogging forces, which makes the actuatorattractive for high precision positioning applications. Alow-cost voice coil actuator, meant for high temperatureenvironments, is designed with the help of FEM. Therequired actuator force Fact is determined by simplifying(1) to

m€yp þ kyyp ¼ kyyc � F act; ð5Þ


where the damping d of the leaf spring guiding mechanismis neglected. In the desired situation when yp ’ yp ’ 0, theactuator only needs to cancel the disturbance from the car-riage kyyc, by which the right hand side approximates 0.myp could become nonzero due to printer frame oscilla-tions, however, because of the high mass of the printerframe, the acceleration amplitude is low and the disturbingforce on the printhead is negligible compared with the leafspring force. The maximum force delivered by the actuatorwill then be

F act � ky � jyc;maxj ð6Þ

which will result in 1 N when yc,max is taken 150 lm. Neo-dymium Iron Boron (NdFeB) based magnets are often ap-plied in powerful and compact actuator designs. However,the heat generation in the printhead and coil may lead totoo high ambient temperatures for the magnet (Table 1).For the same considerations as mentioned in the sled de-sign, SmCo magnets will also be used in the actuator. Fur-thermore, an advantage of SmCo magnets is the betterthermal stability, providing a nearly steady force constantover a wide temperature range.

4.2. Simulation

Using a magnetostatic FEM-model made with ANSYS[15], a rectangular actuator is designed, as shown inFig. 10. The final dimensions are the result of some itera-tive calculations, in order to achieve the highest ratio gen-erated force per actuator volume. An optimum is foundwhen the thickness of the magnet and the air-gap are equal.The coil is made 1 mm wider than the magnets, to obtaina steady force constant over the total stroke of 300 lm.

Fig. 11 shows the FEM-model of the magnetic circuit.Because of the symmetry, modeling only half of the actua-tor is sufficient. For the magnet, a remanence Br = 1 T anda coercivity Hc = 700 kA/m are taken, assuming a linearrelationship. The yoke is modeled using a typical B-Hcurve of iron, including magnetic saturation at flux densi-ties above 2 T. For the air a relative permeability lr = 1is taken. In the air-gap, a mean magnetic flux densityBgap = 0.33 T is found, where a maximum flux density of0.44 T appears at the surface of the magnet. Assuming astatic situation, the force generated by the actuator canbe expressed by

F act ¼ Bgap � I � Lw ¼ Bgap � V c � J ð7Þ

where I is the supplied current, Lw and Vc are the wirelength and coil volume within the magnetic field respec-tively, and J the current density in the coil. A safe valuefor J is about 5 A/m2, for preventing excessive heat gener-ation in the coil during continuous operation. Reluctanceforces, counteracting the magnetic field, can be neglectedsince they become only significant at current density levelsof 10 A/m2 and higher. Finally, the required coil volumeVc and yoke height hy will be 600 mm3 and 13.5 mmrespectively.


Fig. 12. Dynamic behavior of the actuator; H ¼ F out

I in

.

Fig. 10. Exploded view of the designed actuator (a) and the dimensions in mm (b).

Fig. 11. Magnetic flux lines and flux density in one side of the magneticcircuit.


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4.3. Testing the prototype actuator

For having more possibilities with testing, the actuatorbuilt for the experimental setup is made a bit more power-ful than required. The yoke height hy has been chosen22 mm. A thermoset coil base is glued to the coil formounting the coil to the sled.

Several static as well as dynamic measurements are per-formed to examine the suitability of the actuator. The gen-eral specifications of the actuator are given in Table 3, andthe dynamic response is shown in Fig. 12. For the dynamicmeasurement, the yoke has been attached to a frictionlesslinear guide. The coil, connected to the fixed world, is sup-plied with a random noise current, while the yoke position

Table 3General actuator specifications (measured at 20 �C)

Number of coil windings, N ±250Cross section, A ±24 mm2

Wire diameter (copper) 0.25 mmCoil resistance, Rc 7.45 XSelf-induction L in yoke 3.06 mHMean B in air-gap 0.34 TCoil mass (incl. cap) 11.6 gMaximum force constant 3.85 N/ADeviation force constant (300 lm stroke) 61%Max. continuous force, F (J = 5 A/mm2) 1.85 N


x is being measured. The generated output force is deter-mined using F out ¼ m � €x, where m is the moving mass ofthe linear guide including the yoke. The sampling fre-quency was taken 4096 Hz.

A constant relationship exists between Iin and Fout for awide range of frequencies. The force constant is found3.85 N/A (11.7 dB). In the specified bandwidth range ofthe printhead controller (50–100 Hz), the maximum phaseloss is less than 3� after compensating for the samplingdelay.1 Therefore, the influence of the actuator on thedynamic performance of the printhead controller will beminimal. The small phase loss is expected to be causedby the effect of Eddy currents in the actuator yoke.

5. Eigenmode analysis

An eigenmode analysis is used to gain insight in thedynamics of the designed system, or rather to see if thedynamic specifications can be achieved. For example, thecontroller stability performance tradeoff largely dependson the existing eigenfrequencies in the system. The designedguiding mechanism has a complex mass and stiffness distri-

1 The DAC’s zero-order hold used in the experimental setup causes alagging effect on Iin.



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bution, and therefore, a FEM model is made with Marc/Mentat [12], with which a modal analysis is performed.

5.1. FEM Model description

The model is composed of 3D solids (sled) and shell ele-ments (leaf springs), which are connected with transitionelements. To simulate the free moving carriage, the leafspring ends are fixed in all DOFs except for the x-direction,and a total mass of 3 kg is added here. The printhead, aswell as the sensor and actuator coil, are modeled as nodes

Table 4Calculated eigenfrequencies of the guiding system

Mode # Frequencies (Hz) Mode shape description

1 28.3 Sled movement in leaf spring guiding2 234.4 Printhead rotation around nozzle axis3 292.4 1st bending mode of sled4 486.9 2nd bending mode of sled5 700.3 3rd bending mode of sled6 1051.0 S-curving of bottom plate (xy-plane)7 1664.7 Sled movement in x-direction8 1794.2 Torsion mode of side plate

Fig. 13. 2nd–5th eigenmode o


with an equivalent mass and inertia. They are connected tothe sled by means of rigid body elements.

5.2. Eigenfrequencies and mode shapes

In Table 4 the resulting eigenfrequencies of the systembelow 2 kHz are shown. The rigid body mode in x-direc-tion is omitted. The 1st eigenmode can be described bythe sled translating in the leaf spring guiding, like a simplemass-spring system. A large gap exists between the 1st and2nd eigenfrequency which is, as designed, due to the rela-tive low translational stiffness (for low actuator power)combined with a high stiffness for all other DOFs.

Of more interest are the following eigenmodes shown inFig. 13. The printhead’s center of mass is marked with a‘ � ’ sign. The 2nd eigenmode shows modal displacementsin x-direction, in contradiction to the other depicted eigen-modes, which mainly occur in the yz-plane. As a conse-quence, the carriage drive which provides the movementin x-direction over the guidance, will excite the 2nd eigen-mode, for example by reversal. However, the precautionstaken by the introduced V-form leaf spring force a print-

f sled including printhead.



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head rotation around the nozzle axis in the eigenmode,thereby minimizing the nozzle displacements.

The other three eigenmodes follow from bending of thethin sled design. Despite the relative high printhead mass,the eigenfrequencies are kept high, mainly by fixing theprinthead joints (ball supports) close to the leaf springs,where the sled stiffness is high.

Fig. 14. FRF of the sled design including printhead; H ¼yp

F act

.

Fig. 15. Modeled transient response of nozzles when reversing thecarriage.

5.3. Transfer functions

With the modal displacements U = {Uin,Uout} andeigenfrequencies {x1 . . . xn} from FEM, a state spacemodel can be constructed in modal form [16]:

_xðtÞ ¼ AxðtÞ þ BuðtÞ; yðtÞ ¼ CxðtÞ þ DuðtÞ ð8Þ

in which

A ¼On�n In�n

�K �Da

� �; ð9Þ

B ¼On�m

U in

� �; ð10Þ

C ¼ Uout0 Ok�n� �

; ð11ÞD ¼ Ok�m

� �; ð12Þ

where the mass matrix is scaled to unity. Uin (n · m) con-tains m columns of input nodes, Uout (n · k) k columnsof output nodes, where index n represent the number of ex-tracted eigenmodes. Matrices K and Da are the stiffness anddamping matrix, which are both diagonal, with respectivelyfx2

1 . . . x2ng and 2fixi on their diagonal axes. Finally, fi rep-

resent the modal damping factor for each eigenmode i. InMatlab [17], frequency response functions (FRF) are de-rived from the state space model and simulations in thetime domain are performed.

In the FRF analysis, the input is the actuator nodeand the output is the sensor pick-up position, which bothare directed in y-direction. A modal damping of 1%(f = 0.01) is assumed for all modes. In Fig. 14, the modeledFRF of the guiding mechanism is shown. The mass-springbehavior is clearly visible. The stiffness is dominatingbefore the 1st eigenfrequency (slope-0), and the mass after(slope-2). The 2nd eigenmode (234.4 Hz) is absent, whichimplies that none of the considered modal displacementsare in y-direction. Theoretically, the actuator and sensorcannot excite the system or measure displacements otherthan in y-direction. Around the 3rd mode, the phase dropsthrough �180� without returning, which will limit thebandwidth of the controller. However, due to the slope-2between 40 and 200 Hz, the bandwidth specification of50–100 Hz should not be a problem in the controllerdesign.

Also, an FRF measurement has been performed on theprototype, in the same way as described for the actuatordesign. The results show a strong similarity with theFEM model. The amplitudes and slopes match, and the


eigenmodes only differ about 10% in frequency. However,the 4th mode is strongly present in the measured FRF,whereas the 3rd and 5th modes are more damped. The lat-ter is probably due to coulomb friction in the ball contacts,which is not considered in the model.

The state space system is also used to simulate the timeresponse of the printhead position for a reversing carriage.The input acceleration (ax = 5 m/s2) is taken a force stepfunction applied on the leaf spring ends. The outputs ofthe model, the nozzle positions and the printhead’s centerof mass with respect to the carriage are shown in Fig. 15.The V-form leaf spring is found to be effective in suppress-ing the nozzle displacements. The maximum deflection is<1 lm, which is a factor 20 less than the deflection of thecenter of mass. The 2nd eigenmode is hardly visible; onlya small high frequent ripple in the nozzle responses existsdue to the 7th eigenmode.

6. Controller design

An experimental setup (Fig. 16) has been built for test-ing the mechatronic design. Two leaf spring guided sleds


Fig. 16. The experimental setup, including frame (1), fiber optic sensor (2)and printhead dummies (3).

Fig. 17. The control system of the actuated printhead suspension.

Fig. 18. Nyquist diagram of the control systems with a standard lead filterand the designed controller.


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with aluminum printhead dummies are mounted in a steelframe, which represent the carriage. The string sensor, asdiscussed in Section 2, was under construction during theexperiments. Therefore, a fiber optic sensor (Philtec D64-EQ) has been used as a replacement for measuring the sledposition.

A control prototyping platform, RTAI-Linux with Mat-lab/ Simulink /RTW combined with TUeDACS hardware[18] is used for actuating the printhead. The control schemeis given in Fig. 17, where Cfb(s) represents the feedbackcontroller and H(s) the transfer function as given byFig. 14. Also an optional feedforward control is indicatedwith Cff(s). Two kinds of disturbances are distinguished:the guidance profile error dg(xc) and varying disturbancesdv(t) e.g. by rail vibrations or thermo-mechanical effects.

Fig. 19. Sensitivity for disturbances d from the carriage.

6.1. Loop shaping and feedforward

A stabilizing controller Cfb(s) is designed and optimizedusing a loop shaping procedure for feedback control. As astarting point a lead filter has been taken, providing a sys-tem bandwidth of 75 Hz, which is tuned in the frequencydomain, satisfying a robustness margin of jSj6 6 dB.

A notch and a 2nd order low pass filter are applied inorder to suppress the high frequent noise and the system’s


4th eigenmode at 450 Hz in the open loop. Also, an inte-grator is added to improve the low frequent behavior andcompensating static position errors. The nyquist diagramin Fig. 18 shows the stability property and robustness ofthe feedback control. Gain and phase margins of 9.6 dBand 30.2� are obtained respectively.

According to Fig. 17, the sensitivity for disturbances d(s)can be described by

ypðsÞdðsÞ ¼

ky � HðsÞ1þ CfbðsÞHðsÞ

¼ ky � H psðsÞ ð13Þ

where Hps(s) is the process sensitivity. The results in Fig. 19show a maximum sensitivity around 50–60 Hz. The lowfrequent sensitivity is reduced by the I-action, whereasthe mass-spring system acts as a filter for frequencies fd

above the first system eigenfrequency.Feedforward is added to improve the performance of

the controlled system. The guiding profile error, which isin fact the major disturbing source for the printhead posi-tioning in y-direction, shows a systematic dependency ofthe carriage position xc. These errors can be measured ina calibration cycle, as also is done with the jet-timing. Bymeans of a lookup table, the stored profile error dg(xc)can be compensated for using feedforward (see Fig. 17).The feedforward function Cff is determined by

dgðxcÞky þ dgðxcÞCff ¼ 0 ) Cff ¼ �ky ð14Þ

where ky can be found in Table 2. Only stiffness feedfor-ward is required for compensating dg(xc). Other types of


Table 5Estimated thermal drift Dp of the printhead in x-, y- and z-direction

Direction Causedby

Distance d CTE a Dp

(lm)

x Carriage Printhead!printhead:

140 mmmax.

12 lm/m K(Steel)

25.2

y Sensormount

CCD! Tc

printhead:25 mm 20 lm/m K

(Mean)7.5

z Leafsprings

Bottomplate!carriage:

25 mm 12 lm/m K(Steel)

4.5

Fig. 20. Printhead position errors due to profile deviations (upper andmiddle figure) and rail vibrations (lower figure).

Fig. 21. The testing setup with open isolating box


ARTICLE IN PRESS

feedforward, for example velocity and acceleration com-pensation, are not required since the printhead is kept fixedwith respect to the absolute reference. In theory, a perfectcompensation is possible. However, imperfections in guid-ing linearity, hysteresis and force constant of the actuatorcan still give small deviations.

6.2. Disturbance rejection

The system response in the time domain has beentested for a number of sinusoidal disturbances d(t). Thelow frequent guiding profile error has been simulatedwith frequencies fd of 1 and 10 Hz and amplitude Ad =150 lm. The results of the measurements are shown inFig. 20.

The feedback control alone appears not sufficient forreducing all the low frequent positioning errors withinthe requirement of 10 lm. When using stiffness feedfor-ward, the systematic part of the disturbance can be reducedto 6 1 lm. Only small non-systematic disturbances willbe left, which can be compensated for by the feedbackcontrol.

7. Thermal analysis

Temperature measurements have been carried out onthe experimental setup to examine the effects of a heatedprinthead in the new design. The test setup is shown inFig. 21.


First, a measurement under steady state conditionshas been performed where the printheads are heated to60 �C. In the second measurement, a constant airflow of1 ± 0.1 m/s is guided along the setup in x-direction to sim-ulate working conditions when the carriage is moving overthe guiding rail. Because convection is dominant over radi-ation, the temperature values can be scaled linearly to thecase that the printheads are 130 �C. This scaling is impor-tant for the CCD location which may not exceed 70 �Cto operate properly.

In the second measurement, the wind flow of 1 m/scauses a forced heat convection. This is most interestingat the sensor position and the carriage frame, where thethermal shrinkage will cause positioning errors of the print-head. The scaled temperature drop DT for all componentsexcept the dummy is about 15 �C. An indication of thethermal drift is given by

Dp ¼ DT � a � d ð15Þ

where d is the distance between the considered components,and a the CTE. For the x-, y- and z-direction the thermaldrifts are estimated in Table 5.

The thermal drifts in y- and z-direction are within therequirements and besides, all the printheads in the carriagewill have about the same drift by which the alignment erroris even less. Drift in x-direction can be compensated withjet-timing. Based on the experiments on the design, it isexpected that the printhead alignment errors also can be


Fig. 22. Temperature measurements: (I) is measured under still air conditions, whereas in (II) a 1 m/s wind flow is guided along the setup.


ARTICLE IN PRESS

kept within the requirements under high temperature print-ing conditions (Fig. 22).

8. Conclusions

In this paper, a mechatronic solution for compensatingalignment errors in paper transport direction of inkjetprintheads is presented, with the main purpose to improvethe print quality of a WFPS. The mechanism, consisting ofa leaf spring guided sled with a voice coil actuator andstring sensor, is designed by means of FEM simulations.In this approach, the system’s dynamical behavior has beenexamined and optimized, and the obtained FRF has servedas a starting point for the design of a stabilizing controlsystem.

The design allows an easy printhead replacement, com-bined with an exact constraint sled connection, by whichthe minimal hysteresis provides a high reproducibility.Most components can be made by common manufacturingprocesses, which saves costs.

Experimental tests have proven that the controlled sys-tem including stiffness feedforward, is able to compensateposition errors due to low frequent guiding profile devia-tions to less than 1 lm. Static misalignments are reducedto 0 by the I-action of the feedback control. For WFPSthis means that the manufacturing tolerances in paperdirection can even be lowered. The position error due tohigher frequent rail vibrations is reduced with minimal10 dB. Also, in carriage direction, the proposed V-formleaf springs keep the nozzle axis in place. Disturbancesand inertial forces on the printhead have minimal impacton the nozzle deflection. From the improvements of indi-vidual printhead positioning, a better print quality of theWFPS can be expected with the new printhead alignmentsystem.


References

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