This article focuses on use of computational fluid dynamics (CFD) software in the design of ink-jet printers with accuracy equivalent to laser printers. CFD codes track sharp interfaces through arbitrary deformations and to apply the correct normal and tangential stress boundary conditions. CFD software solves the governing equations for fluid flow, heat transfer, and chemistry at several thousand discrete points on a computational grid in the flow domain. Engineers using CFD can obtain solutions for problems with complex geometries and boundary conditions. The CFD analysis yields values for fluid velocity and fluid temperature throughout the solution domain. CFD software cut the production time of the first ink-jet printer in the Lexmark International Inc, Lexington, KY, 7000 lines by helping engineers to determine the tolerances needed to align dots fired from the printhead on the printed page. Engineers at Lexmark have also developed custom lumped-parameter models that provide a faster but less comprehensive model of ink-jet operation, and use these frequently for parametric studies. The combination of the two modeling approaches is helping to improve the performance and reduce the cost of Lexmark printers.
IN TODAY'S MARKET for electronic products, being first to market with a next-generation product is a key competitive advantage. From mechanical engineers' point of view, that typically means being the first to overcome a critical technological hurdle or develop a key capability. For Lexmark International Inc, in Lexington, Ky., the goal of being first to market with a 1,200- by 1,200-dotper- inch (dpi) ink-jet printer required the company's engineers to devise a means of firing drops of ink only about 60 microns in diameter through a printhead every 0.0001 second and place those drops accurately on the page. That, in turn, meant modeling the moving free surface of the ink drops-something that can't be simulated with conventional software. Moreover, the process is difficult to study in the laboratory because the printhead fires in a mostly enclosed chamber and thus can't be filmed.
One key to successfully bringing the printer to market was the use of computational-flu id-dynamics (CFD) codes to track sharp interfaces through arbitrary deformations and to apply the correct normal and tangential stress boundary conditions. "The CFD results quickly showed what level manufacturing tolerances had to be held to in order to align the dots on the page to within 12.5 microns," said Jack Morris, senior development engineer at Lexmark, "That made it possible to save about one person-year in development time."
Lexmark is a global developer, manufacturer, and supplier of printing products, including laser, ink-jet, and dot-matrix printers. The printer line in this case, the Lexmark 7000, is unique among desktop printers on the market in that it uses black and color printheads with a total of 400 print elements crafted by excimer laser, which substantially increase resolution without sacrificing speed. Excimerlaser- crafted ink-jet technology provides more-precise dot placement than the previous generation of thermal ink-jet technology, according to the company. The dpi rating of 1,200 by 1,200 is 38 percent higher than that of its nearest competitor, which is rated at 1,440 by 720 dpi.
Establishing a competitive advantage in tills field is complicated by the fact that a thermal ink-jet printhead is a tiny but quite complex device. A short electrical pulse is applied to a heater that contacts the ink in a channeL The ink superheats and forms a vapor bubble. As the vapor bubble grows, it transllllts momentum to the surrounding fluid and ejects ink out of the nozzle in the form of welldefined drops. In essence, the bubble acts as a pump that drives the drop out of the head and onto the paper. Mter the drop is ejected, the vapor bubble collapses and ink refills the channel.
Besides breaking the 1,200-dpi barrier, the Lexmark 7000 also offers a new type of printhead design. Traditionally, the nozzle is electroformed, while the flow structure containing the ink channel is separately produced from polymeric materials with the channels etched using photolithography. In the 7000, the nozzle and flow structure are combined into a single plastic component. The channels are cut by an excimer laser, reducing the cost of the assembly and providing better alignment between the holes in the nozzle and the flow structure. The integrated nozzle-plate/ flow structure is mounted on a wafer that contains the elements that heat the ink.
The increased dpi rating of the new printer means that it req uires more-accu rate dot placemen t than previous printers. With the new design, that accuracy is largely controlled by the alignment ·between the combined nozzle- plate / flow structure and the wafer conta ining the heater elements. With the new printer producing a dot, or "pel," just 60 microns in diameter, placement needs to be controlled within 12.5 ITucrons to meet Lexmark's quality requirements. Before releasing the product to n'lanufacturing, Lexmark engineers had ·to know how sensitive placement was to the alignment and geometry of these critical components. T he simple answer-making the alignment as accurate as possible-would have driven the price of the printer to a level above the competition.
In the past, the only way to determine this sensitivity would be to build and test a large number of printheads to different dimensions, probably varying the size of each piece by about 2 microns. This would have been an expensive manual process that would have occupied the time of about a dozen people for a full month. In the highly competitive ink-j et printer business, a week's difference in the introduction date can make a signifi cant difference in a product's profitability.
Lexmark already had a competitive advantage because its engineers had considerable experience in simulating the operation of an ink-j et printhead using fluid- dynamics codes. CFD software solves the gove rning equations for fluid flow, heat transfer, and chemistry at several thousand discrete points on a computational grid in the flow domain. Engineers using CFD can obtain solutions fo r probl ems with complex geometries and boundary conditions. The CFD analysis yields values for fluid velocity and fluid temperature throughout the solution domain.
Simulati on of the ink-j et printing process is one of the most challenging CFD tasks. of course, the ink-jet bubble is very small-on the order of20 nanograms- and the ej ection process lasts only about 20 microseconds. But the biggest challenge of all is keeping track of the free surface of the bubble. Modeling problems where surface tension plays an important part require accurate resolution and tracking of fluid surfaces. They also need an evaluation of surface curvatures as well as the ability to sense where and how a fluid adheres to solids.
The differences among various CFD codes, however, complicated the use of CFD in this case. For this application, the code must be capable of modeling surface tension. Some packages model free liquid interfaces as a de nsity disc ontinuity; unfortunately, these methods smooth interfaces over a few grid cells and do not account for the sharp change in tangential flow velocity that generally exists at such interfaces.
According to Lexmark engineers, one software package that can model ink-jet printing accurately is FLOW-3D from Flow Science Inc. in Los Alamos, N.M. This package provides algorithms that track sharp liquid intelfaces through arbitrary deformations as well as apply the correct-. normal and tangenti al stress b oundary conditions. This program also saves mod eling time beca use its method offers the simplicity of a rectangular grid with the confo rming properties ofa body-fit ted grid.
Lexmark engineers created a half-symmetry model of the fi ring chamber and nozzle throat that extended about 100 microns into the ink-supply channel. The finest area of the mesh is at the center of the heater where the bubble is created. At this point, each cell is only about a 2- micro n cube. The most important boundary condition was the pressure-time profile used to drive the bubble. Engineers used an internally developed program to generate this profile.
Once they had built and solved their model, the engineers faced the difficult challenge of validating its accuracy. Bubble formation is nearly impossible to view. The best method yet is to take a microscopic high-speed picture perpendicular to the direction of travel of the drop. The camera speed is only 60 frames per second, but Lexmark engineers use a high-speed flash to expose up to 10 shots on a single frame at 1-microsecond intervals. In this application, the engineers used proprietary methods to measure th e r ise time of the new design-the time that it takes to refill the structure after firing the dro ps-and de termined th e size and velo city of the drop. All three measurements match ed the model's predi ctions within the accuracy of the experimental measurements.
After that, Lexmark engineers simply ran a series of FLOW- 3D models in whi ch they modified the position of the nozzle/flow structure piece in relation to the wafer in small steps. They then determined the effect on dot placement in the program's graphic output. By graphing nozzle/ flow-structure alignment versus dot placement, they were able to determine exactly what le-yel of manufacturing tolerances needed to be maintained to provide the required print quality. This process took one person one week, helping to get the product out the door faster and significantly reducirtg engirteering costs.
The LeXlnark 7000 has been j udged a commercial success. Sales have so exceeded the company's plans that emergency orders had to be placed for more parts to keep the product on the shelves. LeXlllark commissioned a printquality test of the newest color ink-j et printers to assess the ability of each one to reproduce scanned photographs. "The Lexmark 7000 was the clear-cut wirtner," according to Genoa Technology Inc. in Moorpark, Calif., which conducted the test. In the test, consumers also rated the black text generated by the LeXlllark 7000 as equal to that from a 600-dpi laser printer. A second generation of print-. ers that uses this technology, the LeXlnark 7200 and 7200V, has since been introduced to bring photo realistic printing to the consumer market.
Engineers at Lexmark have also developed custom lumped-parameter models that provide a faster but less comprehensive model of ink-jet operation, and use these frequently for parametric studies. The combination of the two modeling approaches is helping to improve the performance and reduce the cost ofLeXlnark printers, which are two keys for maintaining a market leader's momentum.