Effect of height to width ratio on the dynamics of ultrasonic consolidation

The purpose of this paper is to focus on the changing dynamics of the ultrasonic consolidation (UC) process due to changes in substrate geometry. Past research points to a limiting height to width ranging from 0.7 to 1.2 on build features.

Resonances of a build feature due to a change in geometry are examined and then a simple non‐linear dynamic model of the UC process is constructed that examines how the geometry change may influence the overall dynamics of the process. This simple model is used to provide estimates of how substrate geometry affects the differential motion at the bonding interface and the amount of energy emitted by friction change due to build height. The trends of changes in natural frequency, differential motion, and frictional energy are compared to experimental limits on build height.

The paper shows that, at the nominal build, dimensions of the feature the excitation caused by the UC approach two resonances in the feature. In addition trends in regions of changes of differential motion, force of friction, and frictional energy follow the experimental limit on build height.

This paper explores several aspects of the UC process not currently found in the current literature: examining the modal properties of build features, and a lumped parameter dynamic model to account for the changes in of the substrate geometry.