Angular contact ball bearings are predominantly used for guiding high speed rotors such as machining spindles. For an accurate modeling, dynamic effects have to be considered, most notably in the bearings model. The paper is based on a dynamic model of angular contact ball bearings. Different kinematic hypotheses are discussed. A new method is proposed for the computation of the stiffness matrix: a complete analytical expression including dynamic effects is presented in order to ensure accuracy at high shaft speed. It is demonstrated that the new method leads to the exact solution, contrary to the previous ones. Besides, the computational cost is similar. The new method is then used to investigate the consequence of the kinematic hypotheses on bearing stiffness values. Last, the relevance of this work is illustrated through the computation of the dynamic behavior of a high speed milling spindle. The impact of this new computation method on the accuracy of a finite element spindle model is quantified.

International audienceThis paper summarises works carried out for defining tool trajectory formats well adapted to High Speed Machining (HSM). Advantages in using native polynomial formats, calculated directly from the CAD model, are highlighted. In particular, polynomial surface formats are presented as a generic format for tool trajectory. Illustrations show that surface formats represent a good compromise between smoothness machining time, and surface quality