Design of an FDM positioning system and application of an error‐cost multiobjective optimization approach

Abstract

Purpose

As a result of the increased number of applications for additive manufacturing technologies and in addition to the demand for parts produced with high accuracy and better quality, the need for the improvement of positioning and precision equipment in manufacturing has become evident. To address this needed improvement, the main goal of this work is to provide a systematic approach for designing additive manufacturing machines, allowing the identification of the relationship between estimated errors and the cost of equipment. In the same way, this study also intends to indicate a suitable configuration of a machine as a function of final accuracy and total equipment cost.

Design/methodology/approach

To identify the suitable elements of the machine, a numerical model that estimates the final error and relative cost of equipment as a function of cost and tolerance of the machine elements was constructed and evaluated. After evaluating this model by comparing it with first‐generation fused deposition modelling (FDM) machines, an optimisation study was performed that focused on the minimisation of both the total cost and final equipment error. The optimisation problem was defined in accordance with the goal attainment method, which allowed identification of the Pareto optimum of the study. The optimisation results were then compared with current equipment concepts, and possible improvements and restrictions of the optimised concept were described.

Findings

With regard to the evaluation of the numerical model of final error, the general error in the x‐ and y‐direction was observed to have a deviation of 2 μm, while the numerical error in the z‐direction was found to be inferior to that of currently used equipment. The optimisation study also allowed the identification of the machine elements that provide the minimal error and cost for the equipment, identifying an optimal Pareto of the system. In such an optimal case, the average of the final errors for the balanced solution (in which the objective functions have equal importance) was found to be 141 μm. In addition, the cost of this solution was 1.57 times higher than the cheapest solution found. Finally, a comparison between the configuration of commercial FDM machines and the optimum values was found, highlighting the main points that would possibly provide an improvement to the current concepts and an increase in equipment profitability.

Originality/value

Despite the growth of additive manufacturing development, there are still several challenges to overcome to increase the accuracy of the final parts, such as the reduction of mechanical errors. However, in addition to the complexity of this subject, the cost of equipment restricts the development of new solutions. As a result, a systematic approach to identify a suitable configuration of each machine in accordance with the optimal accuracy and cost of equipment is needed.

Citation

Wesley Machado Cunico, M. and de Carvalho, J. (2013), "Design of an FDM positioning system and application of an error‐cost multiobjective optimization approach", Rapid Prototyping Journal, Vol. 19 No. 5, pp. 344-352. https://doi.org/10.1108/RPJ-11-2011-0117