Waterjet and laser etching: the nonlinear inverse problem.

In waterjet and laser milling, material is removed from a solid surface in a succession of layers to create a new shape, in a depth-controlled manner. The inverse problem consists of defining the control parameters, in particular, the two-dimensional beam path, to arrive at a prescribed freeform surface. Waterjet milling (WJM) and pulsed laser ablation (PLA) are studied in this paper, since a generic nonlinear material removal model is appropriate for both of these processes. The inverse problem is usually solved for this kind of process by simply controlling dwell time in proportion to the required depth of milling at a sequence of pixels on the surface. However, this approach is only valid when shallow surfaces are etched, since it does not take into account either the footprint of the beam or its overlapping on successive passes. A discrete adjoint algorithm is proposed in this paper to improve the solution. Nonlinear effects and non-straight passes are included in the optimization, while the calculation of the Jacobian matrix does not require large computation times. Several tests are performed to validate the proposed method and the results show that tracking error is reduced typically by a factor of two in comparison to the pixel-by-pixel approach and the classical raster path strategy with straight passes. The tracking error can be as low as 2-5% and 1-2% for WJM and PLA, respectively, depending on the complexity of the target surface.

On modelling the interaction between two rotating bodies with statistically distributed features: an application to dressing of grinding wheels.

The mechanisms of interaction between bodies with statistically arranged features present characteristics common to different abrasive processes, such as dressing of abrasive tools. In contrast with the current empirical approach used to estimate the results of operations based on attritive interactions, the method we present in this paper allows us to predict the output forces and the topography of a simulated grinding wheel for a set of specific operational parameters (speed ratio and radial feed-rate), providing a thorough understanding of the complex mechanisms regulating these processes. In modelling the dressing mechanisms, the abrasive characteristics of both bodies (grain size, geometry, inter-space and protrusion) are first simulated; thus, their interaction is simulated in terms of grain collisions. Exploiting a specifically designed contact/impact evaluation algorithm, the model simulates the collisional effects of the dresser abrasives on the grinding wheel topography (grain fracture/break-out). The method has been tested for the case of a diamond rotary dresser, predicting output forces within less than 10% error and obtaining experimentally validated grinding wheel topographies. The study provides a fundamental understanding of the dressing operation, enabling the improvement of its performance in an industrial scenario, while being of general interest in modelling collision-based processes involving statistically distributed elements.

Stochastic simplified modelling of abrasive waterjet footprints.

Abrasive micro-waterjet processing is a non-conventional machining method that can be used to manufacture complex shapes in difficult-to-cut materials. Predicting the effect of the jet on the surface for a given set of machine parameters is a key element of controlling the process. However, the noise of the process is significant, making it difficult to design reliable jet-path strategies that produce good quality parts via controlled-depth milling. The process is highly unstable and has a strong random component that can affect the quality of the workpiece, especially in the case of controlled-depth milling. This study describes a method to predict the variability of the jet footprint for different jet feed speeds. A stochastic partial differential equation is used to describe the etched surface as the jet is moved over it, assuming that the erosion process can be divided into two main components: a deterministic part that corresponds to the average erosion of the jet and a stochastic part that accounts for the noise generated at different stages of the process. The model predicts the variability of the trench profiles to within less than 8%. These advances could enable abrasive micro-waterjet technology to be a suitable technology for controlled-depth milling.

Dynamic ultrasonic contact detection using acoustic emissions.

For a non-contact ultrasonic material removal process, the control of the standoff position can be crucial to process performance; particularly where the requirement is for a standoff of the order of <20 µm. The standoff distance relative to the surface to be machined can be set by first contacting the ultrasonic tool tip with the surface and then withdrawing the tool to the required position. Determination of this contact point in a dynamic system at ultrasonic frequencies (>20 kHz) is achieved by force measurement or by detection of acoustic emissions (AE). However, where detection of distance from a surface must be determined without contact taking place, an alternative method must be sought. In this paper, the effect of distance from contact of an ultrasonic tool is measured by detection of AE through the workpiece. At the point of contact, the amplitude of the signal at the fundamental frequency increases significantly, but the strength of the 2nd and 3rd harmonic signals increases more markedly. Closer examination of these harmonics shows that an increase in their intensities can be observed in the 10 µm prior to contact, providing a mechanism to detect near contact (<10 µm) without the need to first contact the surface in order to set a standoff.