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For ultra-precision machining it is curcial that machine components are operated outside – and better below – resonance frequencies of the machining system. As a core component the tool and/or work holding spindle is predomonantly responsible for the resulting surface finish of the machined part.

Beside the shaft bending critical the bearing stiffness need to have such a value that the exciting frequency – predominantly the turning frequency – is always below any resonance frequency. These resonance frequencies are a function of the shaft mass, its moments of inertia as well as the actual bearing stiffness.

In this paper the stiffness as a function of static parameters as well as speed is described. The changein stiffness not only results from a dynamic drag, but also from a change in bearing gap size with speed. This physical model leads to a theoretical speed dependent resonance and stability map of a spindle system and can be used to optimize spindle systems for robust and safe dynamics.

The test methods and set up to measure speed depending resonance frequencies is descibed that is used to check every production spindle in Levicron. Measurement reslts are finally compared with the calculated values and an used for an error-budget.


  • Description of the properties of aerostatic bearings with speed and temperature
  • Rigid-mode model of a shaft-bearing system
  • Solution of the equations of motion for the mathematical system
  • Derivation of a resonance and stability map for motor spindles
  • Description of a measurement set-up
  • Measurement results and comparison with theoretical model
  • Error-Budgeting and assesment of the theoretical model



Publisher: Elsevier Science
Journal / Issue: Journal of the ASPEN / Issue 40, April 2015, 7-13
Author: Dr. Ralf Dupont
Date: April 2014

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