Development of an Improved Model for Piezo-Electric Driven Ink Jets

Numerical modeling and experimentation are used at Xerox Office Group to design, optimize, and verify the fluid dynamic behavior of phase-change ink jets, including the individual jets in a print head. A typical model of an ink jet is based upon lumped-parameter (no spatial variation) assumptions. While quite accurately predicting the main Helmholz resonant frequency (a key performance measure), a lumped-parameter model does not predict other parasitic frequencies that occur in a typical ink jet. As printer performance improves by increasing the jetting frequency, understanding and controlling these other resonant frequencies becomes critical. This paper documents the improvement of an existing lumped-parameter model by incorporating one-dimensional transmission line elements which substantially increases the ability of the model to predict the frequency response of an ink jet. The first part of the paper describes the application of lumped-parameter elements and of transmission line theory to the modeling of ink jets. The existing lumped-parameter model and the improved model are then used to simulate a Xerox Phaser® 350 ink jet. The model predictions are compared with experimental data obtained with an impedance meter.