Planning Freeform Extrusion Fabrication Processes with Consideration of Horizontal Staircase Effect

An algorithm has been developed to estimate the “horizontal” staircase effect and a technique is proposed to reduce this type of geometrical error for freeform extrusion fabrication processes of 3D “solid” parts. The adaptive rastering technique, proposed in this paper, analyzes the geometry of each layer and changes the width of each line of the raster adaptively in order to reduce the staircase error and increase the productivity simultaneously. For each line, the maximum width that results in a staircase error smaller than a predefined threshold is determined for decreasing the fabrication time or increasing the dimensional accuracy, or both. To examine the efficacy of the proposed technique, examples are provided in which staircase errors and fabrication times are compared between uniform and adaptive rastering methods for each part. The results show a considerable improvement in accuracy and/or fabrication time for all parts studied when using the adaptive rastering technique. Introduction One of the main challenges facing additive manufacturing processes is the geometrical errors caused by approximating complex shapes by lines of deposited material. In the additive manufacturing literature, this problem is commonly referred to as the staircase effect, which is typically considered only in the vertical direction. An obvious method to decrease this type of error is using finer lines. However, this will result in prolonged fabrication time. Approaches to reduce the horizontal staircase effect include printing outer contours, which follow the boundary of every layer, and machining the part after fabrication. These methods might be suitable for polymeric and metallic materials. However, for ceramics the former method may result in lower mechanical strength and the latter method is difficult and expensive. The reason that printing outer contours may considerably reduce the strength of the part is that it may introduce gaps between the outer contours and deposited lines of material in the inner regions and, since ceramics are very sensitive to voids and flaws, the part loses its strength. In many freeform extrusion fabrication machines, the bottleneck in achieving higher productivity is the maximum attainable travel speed [1]. When the travel speed is set to its maximum value, productivity could be further increased by increasing the feed rate. However, at a constant travel speed, higher material feed rates result in larger lines and, thus, larger staircase errors, creating a compromise between productivity and accuracy. Another approach is setting the travel speed at its maximum value and adaptively changing the feed rate depending on changes in geometry of the part. In other words, when there is no abrupt change in the geometry, higher feed rates are used to decrease the fabrication time; however, lower feed rates are used to build steep slopes and delicate features with fine lines. This concept has been employed in “adaptive slicing” methods to reduce the “vertical” staircase effect. Figure 1 shows a simple example where a hemisphere is adaptively sliced to increase the dimensional accuracy. A brief review of adaptive slicing methods is provided in the following paragraphs.