Higher-order approximation in accuracy computations of machine tools and robots

Second and higher-order approximations for machine accuracy calculations are necessary when the precision of the error estimation obtained on the basis of the first order approximations is poor or when first order approximations are not influencing the output accuracy of the machine. This latter case is widely present in the calculations of the functional accuracy of machines, in particular when estimating the machine tool set-up errors or when calculating the influence of machine setting displacements. In the case of machining operations, the second order approximation for the normal position error of the real surface relative to the nominal one is shown to depend on the second fundamental form of the nominal surface. As a real world application, the setting of a grinding machine for a crowned conic surface grinding operation is calculated.