Stiffness Computation and Identification of Parallel Kinematic Machine Tools

This paper deals with the stiffness computation and model identification of parallel kinematic machine tools (PKMs). Due to their high dynamic abilities, PKMs are subjected to high inertial and cutting loads while machining. These loads generate structure deflection, and it results in a low level of accuracy compared with serial machines. The aim of this paper is to present a compact and predictable model of PKM. This model could be useful to optimize part positioning in the workspace or adapt machining strategies in order to minimize the influence of structure deflections. The proposed model takes into account legs' and joints' compliances. Considering the geometry of most of parallel architectures, the legs are modeled as beams. The focus, here, is particularly on joints' models. In literature, when the compliance of joints is considered, it is most of the time modeled with a constant stiffness. In this paper, a different approach is proposed, based on a technical analysis of the joints. Models proposed are applied to an existing PKM: the Tricept. The parameters of this model (i.e., the stiffness of the joints) are then identified; thanks to experimental stiffness measurements done on an ABB 940 Tricept robot. This robot is used in the industry for machining operations, such as grinding or drilling. A discussion about identifiable parameters is performed so as to best fit with experimental measurements. Finally, this model is used to define a static workspace where the machined parts are within the tolerances for a given operation.