Analytical and numerical investigation of reaction forces in fixturing of the rigid workpiece with polyhedral geometry

Reaction forces are generated at the locating points of the machining fixture by application of the external forces. They are considered as one of the important input parameters in different stages of fixture design procedure; including fixture planning, unit design, and verification. In the present study, an agile tool is proposed for calculation of the reaction forces based on the minimum norm principle. For validation of the results, finite element analysis is performed in Abaqus® software on a rigid workpiece with polyhedral geometry. Reaction forces are calculated from the numerical analysis and compared to the theoretical predictions. The worst-case error value equal to 3.9% is obtained for the theoretical predictions of the normal-to-surface components of reaction forces in comparison to the numerical results. Theoretical predictions of the tangential components of reaction forces are not accurate which seems to be a shortcoming for the model; however, their effects are negligible by considering that the intensity of these forces are low in comparison to the normal components. Effects of the influence parameters including the coefficient of friction and intensity of the clamping forces are also investigated on the results. It was concluded that the theoretical predictions of the normal components of reaction forces agreed well to the numerical data and results that were published at the previous studies. Agreement between the theoretical predictions, results of the previous studies and the finite element results confirmed the accuracy of the suggested model in calculation of the reaction forces in fixturing of the polyhedral workpieces.