Simulation model of wax diffusion and cleaning in printer belts

Abstract

A belt that transports toner is one of the vital components of a printer. Since toner is fused to the paper at a high temperature, wax releases from the paper and penetrates into the rubber top layer of the belt. When the rubber becomes saturated with wax, the wax remains on top of the belt. The formed layer of wax has negative impact on the image forming unit leading to bad printing quality. Thus, a wax cleaner is installed. To determine optimal functioning of the cleaner, time consuming and inefficient experiments have to be carried out. Thus, an efficient simulation tool to predict wax build-up and cleaning may replace the experiments. Simulation is based on a mathematical model that describes the influx of wax as a convection/diffusion process. The standard numerical discretization methods to calculate the evolution in time of the wax concentration are not applicable. Saturation is reached after ten thousands of rounds. In this article, we propose a combination of an analytical and a numerical method to tackle the problem, where we discretize the second-order differential operator that generates the evolution of the wax concentration. The simulations show an adequate fit with results from measurement. The wax build-up in the belt up to saturation is described realistically. Our study reveals that the contact resistance between belt and cleaner is the most important parameter that influences the effectiveness of the cleaner.