# Heat Transfer Simulation Technology Utilized for Thermal Control Design of the Belt Roll Fuser

Based on the technology of xerography, Fuji Xerox has achieved color reproducibility, productivity, and product liability approaching offset printing on its on-demand printers. In developing the fusing units of the Color 1000/800 Press (i.e., on-demand production printers equipped with a multifunctional system), Fuji Xerox studied and adopted a design approach that uses simulation technology.

The belt roll fuser (BRF) of production printers (Color 1000/800 Press) adopted a heating method that prevents a drop in fuser temperature when transporting paper by utilizing multiple heat sources, in order to maintain fusing belt temperature at a certain level. The three heat rolls are equipped with multiple lamps with independent heat distribution to allow for even and quick heating, as well as to maintain the predefined temperature (Fig. 1). In this way, the BRF features a structure largely different from that of conventional fusing units in that multiple heat sources heat the fuser belt, which makes it difficult to design its heating control mechanisms. To address this problem, Fuji Xerox has devised a new and simple model that combines independently modeled components, and established a simulation technology that satisfies both temperature prediction accuracy and calculation speed.

Given its thin-walled belts and rolls that characterize the BRF, we presumed that the temperatures of rolls are uniform in the direction of thickness. Based on this hypothesis, we adopted a one-dimensional axis direction model for rolls. For belts, we employed a two-dimensional, in-plane direction model that transports heat in the rotating direction. In this way, we reduced the time needed for analysis. We also developed an interaction model that represents the most important heat transfer phenomenon that occurs between heat rolls and the rotating fusing belt (Fig. 2). In order to construct this interaction model, we numerically analyzed the heat transfer that occurs when components with different temperatures contact each other, and found that the total amount of heat transferred from higher-temperature components to lower-temperature ones was almost proportional to the temperature gap of those components just before contact. Then, a proportional constant was predetermined as a heat exchange coefficient by simple heat transfer simulations in considering the following determinant factors: material type, material thickness, and contact time (Fig. 3). In this manner, we utilized the relation between the temperature gap before contact and the total amount of transferred heat, and constructed an interaction model that simulates heat transfer phenomena in the thickness direction between components. In sum, heat transfer phenomena in the fuser were represented in a model incorporating the three models mentioned above: the one-dimensional model for rolls, the two-dimensional model for a belt, and the interaction model.

The precision of the model's temperature predictions has been further improved by estimating such coefficients as heat dissipation from the surface of the belt and rolls into the air, heat transfer from the edges of rolls to the bearings, and the rise time of lamps relative to actually measured data. We have also developed a heat analysis tool that can simulate with changing parameters in accordance with actual fusing system operations, thereby enabling a simulation design that optimizes such conditions as the heat generation of lamps, as well as a control algorithm using thermal sensors. Errors observed with this analysis tool's temperature prediction accuracy were no larger than a few degrees in absolute value, which was precise enough to utilize the tool for complicated BRF design.