ANALYSIS OF TEMPERATURE-DEPENDENT NATURAL FREQUENCIES OF SPINDLES WITH POSSIBLE APPLICATION IN MEDICINE
ANALYSIS OF TEMPERATURE-DEPENDENT NATURAL FREQUENCIES OF SPINDLES WITH POSSIBLE APPLICATION IN MEDICINE

Summary/Abstract: The calculus of natural frequencies plays an important role in modal analysis of spindlebearing systems, especially is micro-milling or micro-grinding applications in medicine (surgery and dentistry). Each natural frequency is associated with spindle mass, and therefore material, on which the heating generated in bearings causes axial and radial expansion. Because the radial expansion is limited by the housing and bearings, the most important thermal deformation becomes the axial one. The natural frequency changes caused by temperature evolution due to heating sources in a spindle is analyzed. The heating interval is split in an equal number of intervals, each limit of interval representing a simulation. A predictor is proposed in order to construct a function that shows the dependency of natural frequencies of temperature. The continuous space in an interval is covered by this predictor. The result of predictor is compared with a nonlinear universal approximator known for its capability in prediction, a feedforward neural network. In this preliminary application, the spindle has a predefined shape and the heating sources are placed in predefined locations of spindle - the location of angular contact bearings that are the major sources of heat in the assembly. The spindle is modeled as connected regular geometric bodies - hollow cylinders and hollow truncated cone. The truncated cone is approximated by connected sections of hollow cylinders. The user can see in a graphical interface the changes of natural frequencies with the temperature for didactic scope or a possible optimization of the lifetime of the spindle-bearing assembly. The further development will investigate the possibility of implementation online of simulation using finite elements method.

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