# Presentation: 034346

**Static and Dynamic Modeling**
** ****of Piezoelectric Drivers**
** ****in Drop on Demand Printing**
- Abed M. Khaskia
- Mallett Technology

**Contributors**
- Georgios Karles, Henry Dante  and M. Subbiah
- Philip Morris, USA
- and
- David Power
- Mallett Technology, Inc.

## Overview

**Introduction**
**Purpose**
**Device Analysis**
**Devices Modeled**
**Finite Element Analyses**
**Results **
**Conclusions    **

## Introduction

- Ink jet printers have evolved in the SOHO market with high resolution and image quality
- Two technologies are used, bubble jet and piezoelectric
- Our focus is on piezoelectric technology for industrial applications that did not advance as the SOHO market
- Industrial applications require higher printing speed, defect free printing for longer times and not very high resolution
- Ink variability is important in order to meet regulations without compromising the performance required

## Purpose

- Use FEM to study the effect of ink variables and print speed on print quality
- Obtain deformations, modes of vibrations and the effect of ink damping
-  Couple structural to fluid behavior in order to predict drop formation

##  Device Analysis

- Print head performance is affected by device geometry, all material properties including the ink’s and by electric pulse applied
- Traditionally devices were analyzed using lumped mechanical models
- There were also few finite element based analyses

##   Devices Modeled

- Cylindrical tube and rectangular print head

## Finite Element Analyses

**Cylindrical Tube**
- 3-D quarter symmetry model. Coupled Field elements for piezoelectric PZT-4. 3-D Solid for Glass and Fluid element for ink using Super-element
-  Analysis performed are static to validate material behavior. Modal to capture model shapes and frequencies in open and closed circuit. Transient dynamics under a square pulse that allow capturing tube true behavior
**    **

## Finite Element Analyses

**Print Head**
- 3-D full model. Coupled Field elements for piezoelectric PZT-4. 3-D Solid for substrate and Fluid element for ink using Super-element
-  Analysis performed are static to validate material behavior
**    **

##     Cylindrical Tube Results

**Static under 80 volt. Max def of .02 micron**

**1****st**** modes for closed and open circuit with frequency of 15Khz**

##     Cylindrical Tube Results

**Transient analysis results under 80 volt 40 microsecond square pulse**

- No ink no damp

- Ink damp

- No ink damp

- Ink
-  no damp

## Print Head Results

**    **

**Static def under 80 volt. Max def is 0.22 micron**

## Conclusions

- FEM can be used to study the dynamic response of piezoelectric ink jet devices
- Modeling illustrates the effect of materials, device geometry and ink variables on final drop formation
- Ink damping, mass and bulk modulus affect device response
-  Piezoelectric material properties should be validated in terms of values and orientation
- Future work will incorporate the ink’s surface tension in order to predict drop formation. This requires better structural – fluid coupling

## Conclusions

- Current work incorporates FSI between piezoelectric model and ink model

## Conclusions

- Current work incorporates FSI between piezoelectric model and ink model – drop formation