Abstract
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.
Highlights
The dynamic behavior of a high speed rotor needs to be studied during its design
Numerical models contribute to choosing the optimum set of operating conditions in high speed machining (HSM) in order to maximize the productivity while ensuring workpiece quality and spindle health [1]
The following high precision bearing has been retained for the study: SNFA VEX70/NS9CE3. It corresponds to a hybrid angular contact ball bearing that can be found in high speed and high power spindles
Summary
The dynamic behavior of a high speed rotor needs to be studied during its design. The dynamic stability is one of the most important criteria. Its model, associated with a finite element model, enables the building of a global model of the rotor [3,4] In this process, the accuracy of the bearing stiffness values is crucial. The balls are made of ceramic instead of steel, which decreases the dynamic effects on the balls and the subsequent load on the outer race at high speed due to centrifugal forces. The mechanical model of the bearing aims at obtaining the relation between the global loads f and global displacement d, and the stiffness values. The dynamic effects on the balls are taken into account during local and global equilibriums. A new complete analytical expression of the stiffness matrix, taking into account the dynamic effects on balls, is detailed. The present method can be refined with radial ring expansions [13]
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