Machine Stiffness Rating: Characterization and Evaluation in Design Stage

Stiffness of mechanical systems of machines with heavy demands on their accuracy, precision and productivity such as machine tools, coordinate measuring machines, and industrial robots presents one of the most important design criteria. However, stiffness evaluation in the general case when force-and-torque load coupling takes place leads to some problems. The problems are associated with physical distinction between translational and rotational stiffness values manifested, in particular, in their different units of measurement. To overcome a majority of the difficulties, a new performance index – the collinear stiffness value (CSV) presenting an equivalent stiffness (compliance) value during simultaneous linear and rotational displacements – is developed and represented in static and dynamic versions. In this presentation, the CSV is used to formulate a new design-related dimensionless criterion: the ratio of the minimal CSV to stiffness value of the drive system, which usually presents a weak point of the modern machines. The CSV-based approach is applied to quantitative formulation of the significant advantage from the stiffness viewpoint of the orthogonal serial-kinematics machines (SKM) compared with the parallel-kinematics machines (PKM): (a) the parameters-of-motion-depending variations of the minimal CSV of the SKM in their workspace are, as a rule, one-two orders of magnitude less than those of the PKMs; (b) the stiffness-limited workspace of the SKM is more than that of the PKM. Application examples are simulated.