Correction of machining operations with the Total Inertial Steering

Abstract

The Total Inertial Steering approach proposed in this paper can perform an optimum correction of the geometric deviations of the manufactured part with respect to its digital model, from the measured points on its surfaces. In the case of production by machine tool numerical control, there exist a link between the tool offsets and deviations of measured points. An incidence matrix which represents this link is obtained. In most cases, this matrix is not square and therefore not invertible, because there are more measured points as correctors to adjust. The Gauss pseudo-inverse is used to calculate the values of corrections to be made to compensate for measured deviations. Tolerances associated with the surfaces must also be taken into account in the incidence matrix. However, when the same cutting tool machine two surfaces with different point values, the resulting solution favors the one with the highest number of points, at the expense of the other surface which can remain not conform towards its tolerance. This paper proposes a strategy to rebalance the correction surfaces, and this regardless of the number of points and tolerance of each surfaces. A relatively simple tutorial example is given in the paper to enable tracking calculations.