There is an increasing demand in the computer industry to produce better, faster, and cheaper printers. To satisfy this demand, a number of design-related fluid dynamics problems become important. While these problems have traditionally been solved through trial-and-error experimentation, the recent collaboration between the UK CFD group and LexMark International Inc. has demonstrated the usefulness of CFD analysis in the design process.
Three case studies are presented here: 1) the installation of a centrifugal drying fan, 2) the dependence of ink roller coating on ink supply, and 3) acoustic noise reduction analysis of a laser printhead. All these studies were performed on real grid geometries obtained from actual equipment designs. The CFD calculations were made using a commerical code, Fluent (version 5.0) on computer facilities at the University of Kentucky.
| 1. Installation of Centrifugal Fan
A critical factor determining the page/minute (ppm) rate of an inkjet printer is drying time. The drying process within the printer as the paper emerges is primarily effected by blowing air across the paper. In a version of an inkjet printer, the designers were unsatisfied with the drying performance of the centrifugal drying fan. Presented wih the fan data and design configuration, the UK CFD group first developed a geometry and grid that mimicked the current flow conditions. After running simulations to represent the current configuration, several alternate configurations were calculated, the object being to enhance the airflow rate without increasing the power required by the fan. The results of this study are shown below. On the left is the original design, in which the fan is approximately centered within the region defined by the flow guide bar and the outer casing. The figure illustrates the magnitude and direction of the airflow, with red indicating a strong flow, blue a weak flow. As can be seen, the paper (located at the bottom boundary) receives surprising little drying flow in this arrangement. Basic fluid dynamics suggested a simple solution to this problem: by shifting the fan so that it is more off-center so that the fan forces air into a more narrow region and then out through an expanding region, an advantageous pressure gradient is established to further drive the flow. This concept was borne out in CFD testing -- the new configuration (bottom, right) pushes a much greater volume of air, creates a much stronger flow at the paper surface, and thereby effects faster drying. All this from a simple relocation of the the exact same fan with the exact same casing, a simple correction from a manufacturing perspective. Top right: Views of the fan |
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2. Ink transferrence through rollers
The process of transfering ink from a resevoir to paper in a particular printer design is accomplished through a series of rollers, as shown in the schematic. The ink is picked up from the ink reservoir by one roller (A), excess ink is scraped off by a blade (B), the ink is transferred to a second roller (C) and then applied to the paper (D). The critical design question is to optimize the process to get the required ink to the paper while maximizing the number of pages that can be printed for a given ink supply. The UK CFD group performed a series of simulations examining the transferrence process depending on the amount of ink allowed into the roller system, ranging from "full" to "starve" The simulation results represented both the fluid properties and the deformation of the roller coating itself due to the fluid pressure generated in the process.
| 3. Laser Printhead Noise Reduction
The most involved collaboration between UK CFD and Lexmark was the investigation of the acoustics of the Optra S series printhead assembly. As shown, the printhead is a complicated structure including a polygon scanner, numerous lenses and mirrors, and an irregular outer casing. The polygon scanner rotates typically in the range of 24,000-35,000 rpm. At this high rate of rotation, acoustic noise can be generated from mechanical imbalances, electromagnetic torque pulses, bearing operation, and aerodynamics. Aerodynamic noise has two main sources: a high-pitched pure tone due to vortex shedding at the tips of the polygon, and a more broad-band noise due to complex interactions of the airflow and the surrounding walls of the printhead. The former noise is readily reduced by enclosing the polygon with a cylindrical cap, as is done in this printhead. The latter noise is far more difficult to predict, and since significant changes to the printhead housing are expensive and time-consuming, it is advantageous to evaluate the casing acoustics early in the design process. Previously, the acoustics of the housing were determined from trail-and-error experimental studies. A discovery from this process was that a small bar placed near the scanner opening significantly reduced the aerodynamics noise in the printhead. The objective of the UK CFD study was to demonstrate why this would be the case. Top right: View of the printhead apparatus |
 
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To do this, the first step required was to recreate the flow geometry of the printhead in a series of overlapping grids and appropriate boundary conditions. Lexmark provided details on the 8 parts of the printhead in the form of IGES files from I-DEAS (a CAD/CAM program from SDRC). These files formed the basis for grid construction, but it was found that the grid-generation tool for Fluent, Gambit (version 1.0), had some difficulty with these highly detailed constructs. Thus, minor adjustments to the geometry were made to remove complicated but unimportant details. The final CFD geomtery represented the exact shape of the housing, the rotating polygon scanner, the rectangular base of the scanner including the motor power connector, the small lens, the large lens, the mirror, the laser diode assembly an the anit-ghost shield. The modeled cover included the cylindrical cap and the recess for the power connector. The tiny noise-reduction bar was included as well in some simulations.
The volume grid was generated through a zonal method with volume grids in adjacent zone communicating through their interfaces. In the computations described here, the smallest grid scale was 0.8 mm and the largest 4.0 mm. The final mesh contained about 500,000 tetrahedral/pyramidal/hexahedral volume elements, with 50% of the elements inside the scanner chamber itself. |
| For the computation, a cylindrical region about the polygon scanner was solving in a rotating frame (allowing the the scanner to be treated as a fixed wall boundary), with the remaing regions solved in a stationary reference frame. At 30,000 rpm, the maximum effective Mach number in the flow is about 0.2, allowing the flow to be treated as incompressible. The only entrance/exit plane for the air was a constant pressure boundary at the bottom of the chamber containing the large lens. Standard wall functions were used at solid boundaries. The computational results were obtained using second-order upwind schemes and the standard two-equations k-e turbulence model. Convergence of the flow was assumed when the residual of the continuity equation dropped by more than 3 orders of magnitude; this effectively corresponded to a residual drop of 4-5 orders of magnitude in the momentum equations.
To determine the effect of the noise-reduction bar, simulations were performed both with and without the bar on similar grids. The large-scale flow results indicate that the dominant flow in this system was across the inlet/outlet plane of the scanner chamber, in other words the gap in which the bar is located. Futher investigation revealed that the bar altered the flow at this opening in two significant manners. First, by reducing the maximum flow velocity from 15 m/s to 12 m/s. Second, there were significant changes in the flow near the left-end of the opening between the putative bar location and the small gap between the cylindrical scanner side wall and the anti-ghost side wall. In both case, there is a strong inflow between the anti-ghost and scanner side walls. In the original case, this causes the outflow near the scanner side wall to bend abruptly upon leaving the scanner chamber, wrapping sharply back to join the inflow to the small gap. This sharp acceleration in the vicinity of a solid surface is a likely candidate for acoustic noise. By adding the bar, the abruptness of the bending is mitigated both by the bar and by a small re-circulation zone that is generated between the cylindrical cap wall and the bar. This results in a much smoother outflow and, we believe, a much quieter printhead. Top right: Pathlines of the flow in/out of the scanner chamber without noise-reduction bar |
 
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Relevant Publications
Xiong, G., P.G. Huang, C.A. Saunders, and P.J. Heink, 2000. "CFD Simulation of Laser Printhead -- A Case Study on Noise Reduction". Proceedings of the Third International Symposium on Scale Modeling, September 10-13. ISSM3-0123