# Paper Temperature Simulation Technology

Highly productive production printers employing the heat-pressure fusing method are susceptible to image quality issues stemming from paper temperature, such as roll marks^{Note1} and paper blocking.^{Note2} In order to prevent these issues, it is thus necessary to lower the paper temperature by using a paper cooling system equipped with a heat sink^{Note3} (hereinafter referred to as "the cooling system"). However, it proved to be difficult to estimate and control the temperature of output paper, because it is influenced by a number of factors (e.g., parameters of the fusing apparatus and cooling system, paper transportation distance, and paper thickness). To address this problem, as shown in Fig. 1, Fuji Xerox constructed a paper temperature simulation model for each of two areas (Area 1 and Area 2). Area 1 begins before the fusing apparatus and ends immediately before the cooling system. Area 2 begins immediately before the cooling system and ends immediately after the cooling system. By constructing and combining these two models, we succeeded in developing simulation technology that is able to estimate the temperature of a wide range of thicknesses of paper.

In the paper temperature simulation for Area 1, the heat conduction equation is used, enabling us to estimate not only the surface temperature of paper but also the temperature distribution in the direction of paper thickness. In the paper temperature simulation for Area 2, models were constructed for the heat sink of the cooling system as well as the transportation of paper, and temperature distribution is calculated by solving the heat conduction equation using the two-dimensional finite difference method.^{Note4}

With these analytical technologies, it is now possible to estimate the surface temperature of paper as well as the temperature distribution in the direction of paper thickness with high precision. Higher fusing temperatures are required for thick paper; thus, the surface temperature of the paper immediately after exiting the fusing apparatus is also high. However, by the time thick paper has reached the point immediately before the cooling system, its surface temperature has dropped to a level even lower than that of thin paper due to the temperature distribution in the direction of paper thickness (Fig. 2). In contrast, because temperature distribution does not influence thin paper as much as thick paper, the surface temperature of thin paper hardly decreases before it reaches the cooling system. Hence, it is necessary to use the cooling system to lower the temperature of thin paper to the appropriate level. After using the simulation technology for Area 2 to examine the relation between paper thickness and paper surface temperature at the point immediately after the cooling system, we discovered that the increase in the paper surface temperature stops at a certain thickness. Even if the thickness of the paper is increased beyond this point, the surface temperature does not continue to rise along with the increase in the thickness of paper (Fig. 3). These simulation results are fairly consistent with the actual measured values.

With these simulation technologies, the temperatures of a wide range of thicknesses of paper can be estimated with high precision, thus allowing us to design the fusing apparatus, paper handling mechanism, and paper cooling system more efficiently than before.

- Note1 Roll mark: a phenomenon in which streaks appear on the image areas that are in contact with the paper transport belt when the paper temperature is too high at the time of printout output
- Note2 Paper blocking: a phenomenon in which stacked printouts become adhered to each other
- Note3 Heat sink: the heat dissipating component of the paper cooling system
- Note4 Finite difference method: one of the discretization methods used in numerical analysis to solve differential equations