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In the graphics industry, concepts are being developed where the images are transferred using wide, flexible belts. To achieve pattern match, the positioning precision of the belts is very important. Because of roller misalignment and other imperfections, the belts may tend to drift, or track.
The ABAQUS/Explicit simulation to predict tracking consists of several steps. First, find the belt shape, as it is stretched around the rollers. Second, apply tensioning device forces and roller misalignments. Finally, initiate belt rotation, transient and steady state. Several modeling and simulation techniques have been applied to overcome instabilities in the system.
The simulation has been validated within a few tens of microns per second by comparison with measurements performed on a test bench, where known roller misalignment and tracking corrective tension forces have been introduced.
The analysis technique is currently applied by the client routinely to lead the design process. However, because design results are proprietary, only test bench models and results may be presented.
1. Introductory remarks
The current presentation is part of consulting work performed at Manta Corporation. The reader is requested to understand that due to confidentiality considerations, the extent and level of detail of disclosed material must remain limited.
2. Belt image transfer technology
Due to limited space and confidentiality considerations, we are not able to discuss the image transfer technology currently under development in detail. The basic difference with traditional technology is that the image is transferred by a belt, rather than by a drum. The belts are very thin and are stretched over a number of smooth rollers, mounted on a frame laid out as required by the various stations of the imaging operation. In particular, when more than one color is involved, or for double-sided options, high positioning accuracy is required to assure stable picture quality. Belt tracking (sometimes also called 'belt walk') is the undesired phenomenon of lateral belt motion, i.e. in the direction of the roller axes, transverse to the image transport direction. Belt tracking is primarily caused by so-called roller tilt, i.e., not perfectly parallel roller axes.
Obviously, when unchecked, this phenomenon will compromise image quality. To correct belt tracking, a control system is used. As part of this system, one of the rollers is made movable and attached to a tensioning device. In order to design the control system and estimate the corrective forces applied to the system through the tension springs, it is necessary to predict the magnitude and direction of belt tracking.
For studying the tracking in detail, a three-roller test bench was built. This unit was instrumented and the observed measurements were compared with the analysis predictions as presented in this paper.
3. Belt system instabilities
While a test bench is useful for verifying tracking effects experimentally for a specific configuration, it is necessary to have a predictive tool for evaluating future concepts and leading the design during product development.
Ironically, the great image stability requirements are to be met using a system that has inherent sources of low stability of its own. These instabilities can be observed with the naked eye, when viewing the belt surface against the light, as a pattern of transversal waves. The waves can be observed constantly moving when the belt is in operation and they will occur even in the most precisely built and well-aligned system. Fortunately, the waves themselves have little influence on image positioning and quality. However, the instabilities that are their root cause can pose a challenge from an analytical standpoint, as discussed below.
Consider the simple, two-roller belt system of Fig. 1 (a). This small test bench system, with a 200 mm wide belt stretched over two rollers 120 mm apart, was used for early modeling studies and is useful for explaining the nature of the instabilities. Because the belt is very thin compared to other system dimensions, its bending stiffness is nearly zero. Thus, the overall stiffness (normal to the shell direction) is almost entirely dependent on the membrane tension stress that occurs when stretching the belt with the rollers in one direction. In the transversal direction, no tension can be applied and consequently, no tension stiffness contribution can be generated.
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