Analysis of Drop-On-Demand Ink Jet Print Head for Rapid Prototyping
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Analysis of Drop-On-Demand Ink Jet Print Head for Rapid Prototyping Dong-Youn Shin1, Paul Grassia2 and Brian Derby1 1 Manchester Materials Science Centre, UMIST, Grosvenor St., Manchester, M1 7HS, UK 2 Department of Chemical Engineering, UMIST, PO Box 88, Manchester, M60 1QD, UK ABSTRACT The rapid prototyping industry is growing dramatically because of its high potential to reduce product design and prototyping cycles. One of the recent technologies in this field is 3D printing using conventional ink jet technology. In order to maximize the capability of this process, it is required to understand the operating mechanism and drop formation process. The current work focuses on the mechanism of a piezoelectric cylindrical actuator and the hydrodynamic characteristics inside a print head in order to achieve more realistic boundary conditions for the numerical simulation of the drop formation process. Linearised Navier-Stokes equations for Newtonian fluid flow are solved analytically for the pump section with a constant radius and for the nozzle section with a tapering angle. Results from the developed solutions are input to Flow 3D and it is observed that analytical pressure histories show better agreement with numerical results than axial velocity histories. The presented analytic model can be used for fully further drop formation simulation as an upstream pressure boundary within an acceptable tolerance. INTRODUCTION The analysis of conventional drop-on-demand ink jet print heads for the solid freeform fabrication has been a key issue to predict the drop size and its velocity but it has conventionally been done by numerical methods which require considerable time and effort, even though its geometry is relatively simple. Dijksman, however, produced an analytic model of the oscillatory fluid behaviour of a print head, this showed good agreement with his experimental results [1]. His approach, however, may not be sufficient to explain the fluid behaviour at a tapered nozzle unless the taper angle is small and the taper length is short compared to chamber dimensions. In addition, his model requires a modification for a thick walled tube. The present model modifies his slightly compressible fluid model to allow for the analysis of a thick walled chamber section actuated by a cylindrical piezoelectric tube by introducing a 2D quasi-static solution, which generalizes the radially polarised one employed by Bugdayci et al. [2]. With these modifications, the intrinsic speeds of sound of different fluids are determined because the pressure wave generation depends on the acoustic characteristics of the fluid contained in the chamber. After determining the speed of sound of a fluid and its pressure wave generated by the radial motion of the piezoelectric actuator, pressure and axial velocity histories near the nozzle tip will be solved analytically and compared with numerical results computed by Flow 3D [Flow Science, Inc., Los Alamos, NM].
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Nomenclature C1, C2 i
J0( ), J1( ) P(z) P*(r) r1 Vz(r,z)
η(r,t) ν θ ρf σ ω
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