Performance Analysis of an Industrial Inkjet Printing Head Using the ...

52 / APRIL 2008 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 9, No.2RRsescρ kse=(12)2( 2 × A )ρ ksc=(13)2( 2 × A )where A is the cross-sectional area of the sudden expansion andcontraction, K se is the loss coefficient of the sudden expansion, andK sc is the loss coefficient of the sudden contraction, which areempirically determined.3. 1D Lumped Analysis3.1 Numerical AnalysisThe one-dimensional lumped model solutions were obtainednumerically using a fourth-order Runge-Kutta integration algorithmto solve the differential equations. A flow chart of the program isshown in Fig. 7.3.2 Verification of the 1D ModelThe performance of the model was evaluated when the voltagewaveform depicted in Fig. 8 was applied. The waveform consistedof five parts: 1.5 μs of falling (t 1 ), 6.5 μs of holding (t 2 ), 1.5 μs ofrising (t 3 ), 14.5 μs of holding (t 4 ), and 1.5 μs of falling (t 5 ). Theoperating driving voltage ranged from -15 to +40 V. The viscosityand surface tension of the ink were 4.8 cPs and 0.025 N/m,respectively. The simulated and measured results are compared inTable 1 Both the predicted droplet velocity and drop volumematched well with the experimental results.(a) from restrictor to chamber (b) from chamber to nozzleFig. 5 Flow in the (a) restrictor and (b) nozzleFig. 6 A simplified shape of the meniscus in a circular orifice2.4 InertanceWhen ink flows through a thin passage, the inertia of the ink isrepresented by the inertance. The inertance is given byLM = β ⋅ ρ(14)AFig. 7 Flow chart of the 1D analysis programwhere β is an empirical coefficient and A is the cross-section area.2.5 MeniscusThe pressure generated by deflecting an elastic vibrator isbalanced with the action of the fluid surface tension in the orifice. Toestimate the pressure of a meniscus with a circular cross-section, weassume that the profile of the meniscus maintains a parabolic shape,as shown in Fig. 6:2⎛ ⎞= ⎜ 1 rz Zmax −⎟(15)2⎝ R ⎠The pressure change driven by the equilibrium condition betweenthe surface tension and the generating pressure is4σΔP=D216 ⋅ Zmax2 2n 16 ⋅ Zmax+ D n(16)Fig. 8 Waveform of the driving voltage signal applied to the inkjetheadTable 1 Comparison between simulated and measured resultsDroplet volume[pl]1D analysis(predicted)Experiment(measured)Error(%)24.2 27.5 12where Z max is the maximum displacement of the meniscus, R is thenozzle radius, and σ is the surface tension.Jetting velocity[m/s]3.6 3.8 6

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 9, No.2 APRIL 2008 / 534. Results: Jetting PerformanceFig. 9 Flow rate at the nozzle for various restrictor depthsUsing the one-dimensional lumped analysis, we characterized theflow rate at the nozzle for various restrictor depths, as shown in Fig. 9.Since a decrease in the restrictor depth caused the flow resistance atthe restrictor to increase, the fluid moving into the nozzle alsoincreased. Therefore, as depicted in Fig. 10, the droplet volumeincreased with the restrictor depth. The Helmholtz resonancefrequency of the inkjet printing head decreased with the reduction ofthe restrictor depth, as shown in Fig. 11. This phenomenon influencedthe characteristics of the inkjet head jetting frequency. Figure 12shows the droplet volume for various jetting frequencies up to 20 kHz.At a restrictor depth of 130 μm, the droplet volume did not changewith variations in the ejection frequency. However, at a restrictordepth of 42 μm, the droplet volume dramatically changed withvariations in the jetting frequency due to insufficient ink supply.5. ConclusionsFig. 10 Droplet volume and velocity for various restrictor depthsSimplified one-dimensional lumped modeling approach wasdeveloped and applied to the design of an industrial inkjet head. Theconfiguration of the inkjet printing head was simplified to theequivalent electric circuit using lumped elements, which wereacquired theoretically from the governing equations. The resultsdemonstrated that the one-dimensional lumped analysis accuratelyevaluated the performance of the designed inkjet printing head. Theyalso helped us to understand the effect of the driving voltagewaveform on the increase in the droplet velocity and the reduction ofthe droplet size, which is important for directly writing on printedcircuit boards. Our modeling approach can be used as a tool toimprove the design of piezoelectric inkjet printing heads, resulting inbetter jetting performance.REFERENCES1. Legierse, P. E. J., “Inkjet Printing in the Electronics Industry,”Digital Production Printing and Industrial Applications: Eye onthe Future, Vol. 1, pp. 197-200, 2001.2. Stephen, F., “Inkjet Technology and Product DevelopmentStrategies,” Torrey Pines Research, pp. 198-201, 2000.3. Kyser, E. L., Collins, L. F. and Herbert, N., “Design of anImpulse Inkjet,” Journal of Applied Photographic Engineering,Vol. 7, No. 3, pp. 73-79, 1981.Fig. 11 Helmholtz resonance frequency for various restrictor depths4. Kyser, E. L. and Sears, S. B., “Method and Apparatus forRecording with Writing Fluids and Drop Projection Meanstherefore,” U.S. Patent, No. 3946398, Siliconics Inc., 1976.5. Sim, W., Park, S-J., Park, C., Kim, C. S., Yoo, Y., Yang, C., KimS., Kim, Y., Yang, J., Joung, J. and Oh, Y., “Analysis of theDroplet Ejection for Piezoelectric-driven Industrial InkjetHead,” NSTI-Nanotech, Vol. 2, pp. 528-533, 2006.Fig. 12 Droplet volume for various jetting frequencies