# Simulation Technology for Paper Curl Formed by Transportation Path

In multifunction devices and printers, paper that has been heated and strained during the fusing process may curl after being passed through the fusing unit and the subsequent transportation path. When there is significant paper curl, such problems as a paper jam or stapling error may occur. Fuji Xerox is striving to prevent such problems from occurring.

As the mechanism of the paper curl phenomenon is not fully understood, there is an urgent need to clarify that mechanism and develop a simulation technology that can predict the amount of paper curl. Fuji Xerox has developed a simulation technology that can predict the amount of paper curl by establishing methods of calculating and analyzing the paper properties, and creating a physical model of paper deflection based on the calculation and analysis results.

The basic mechanisms of the curling of paper that occurs in multifunction devices and printers are categorized below.

Contraction curl | Curl formed due to contraction that occurs within the sheet, which is non-uniform in the thickness direction. (This curl can be predicted using this analysis.) |
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Paper path curl | Curl formed by the geometry of the paper path after fusing. When the moisture level decreases and the fiber bonds together, the paper hardens. When paper hardens in the deflected shape, the shape is maintained, resulting in paper curl. (This curl can be predicted using this analysis.) |

Fuser nip curl | Curl formed due to heat stress and strain added to the paper when it is transported through the fusing unit. (Paper is passed through the actual fusing unit for measurement.) |

Fig. 1 shows where these curls are formed after paper passes through the fusing unit.

Fig. 1: Where the curls are formed

Conducting this analysis made it possible to measure the parameters necessary for the calculations that could not previously be measured (e.g., changes in mechanical properties according to paper temperature and moisture content, paper temperature and moisture content inside a device, contraction non-uniformity in the thickness direction, amount of curl formed after paper passes through the fusing unit).

The time history of the viscoelasticity of paper^{Note1} (ii in Fig. 2) is consequently calculated from the changes in temperature and moisture content of paper in the transportation path, and the curl that forms due to the difference in contraction between the sides of paper (iii in Fig. 2) is calculated from moisture content changes in the paper.

Given the time history of paper viscoelasticity, the placement of the roller, and the shape of the guide in the transportation path, deflection curvature history (v in Fig. 2) can also be estimated. Then, the fuser nip curl (iv in Fig. 2) value measured beforehand as the initial value is used to periodically update the deflection rate to the latest value for calculating the amount of curl, by ignoring the influence of gravity. Lastly, the influence of gravity is also included as a factor in predicting the amount of curl.

By using this simulation technology, the amount of curl can be accurately predicted before creating a device.

- Note1
- Indicator of the vulnerability of paper to deflection

Fig. 2: Flow of calculating the amount of curl