Whirl frequency of a high speed spindle subjected to different pre-load mechanisms

Pre-loading, both in terms of application method and actual applied force, significantly affects the stiffness and natural frequency of a high speed spindle system. The gyroscopic moment at high speed leads to whirling of the spindle, and the whirl frequency is not equal to the system’s natural frequency. To discover the relationship between pre-load and whirl frequency, theoretical and experimental research was undertaken. Two numerical models of the angular contact ball bearings, based on rigid and constant pre-load mechanisms, were established. The shaft is considered as a set of Timoshenko beam elements, and gyroscopic moment and centrifugal force are both considered. Adding bearing stiffness in the form of springs to this finite element system produced a spindle-bearing coupled model. Iteration was used to deduce the interactions among bearing groups. The exact whirl frequency of a spindle subjected to different pre-load mechanisms has been calculated. To validate the proposed theory, frequency analysis was carried out on a Siemens CAT40 spindle. Experimental results agreed with theoretical calculations. The result shows that speed had a great influence on bearing stiffness and spindle whirl frequency. Adopting a reasonable pre-load method and pre-load force improved the spindle critical frequency.

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