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Apparatus for the determination of friction forces in miniaturized rolling element guideways

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Apparatus for the determination of friction forces in miniaturized rolling element guideways

Due to internal pre-loads or external loads, rolling-element bearings often exhibit non-linear correlations between friction force and displacement. High-precision positioning therefore requires the exact knowledge of the friction behaviour for different external loads, displacements and displacement velocities. At PTB, a novel device has been developed which allows force displacement curves of miniaturized rolling element guideways to be recorded, see Fig. 1. The driving force of up to 100 mN is generated in a defined way by an electromagnetic drive. The displacements of up to 3 mm are determined with high resolution by an interferometer. The displacement of the carriage, the action line of the driving force and/or of the force measurement and the measurement of the carriage displacement lie on one axis, see Figure 2. This axis runs through the centre of gravity of the bearing carriage and the virtual centre of the internal friction forces of the bearing. By this, the Abbe error is minimized and only uniaxial forces occur.


Figure 1: Photo of the experimental set-up for the determination of friction forces	Figure 2: Photo of micro-linear bearing and drive; displacement: measurement axis of the displacement and active line of the force, collinear (red line)

This facility allows the carriage of a linear bearing to be axially moved in two different modes of operation: In the mode of operation "positioning , the path signal is used as feedback for a positioning control so that almost any temporal displacement curves can be passed through. In the operating mode "force specification , almost any temporal force curves can be applied to the carriage. Results of the measurement are the respective curves of force and displacement.

Figure 3 and Figure 4 show typical curves of friction force and displacement in positioning operation. The measurements were performed on a micro-linear bearing developed at PTB which is equipped with 4 ruby spheres (diameter: 200 µm) rolling on hard metal surfaces. In the case of large displacements, the two superimposed periods show a highly reproducible, wavy curve of the friction force. This behaviour indicates the great influence of the topography of the contacting surfaces.

With decreasing displacement amplitude, the local maxima disappear and the energy losses become smaller, see Figure 4. Finally, the relation in the case of displacements of less than one micrometer can be realized by simple models. A pure rolling motion of the spheres does then no longer occur in the bearing. This behaviour allows such bearings to be used also as safety couplings in measuring devices [2].
Knowledge of the friction behaviour allows the linear bearing in the case of small displacements to be positioned by means of simple PI control with nanometer resolution. The knowledge of the curve of the friction forces in the case of large displacements helps to develop control algorithms for the displacement with constant velocities.


Figure 3: Friction force displacement diagram for sinusoidal movements with amplitudes from 8 µm to 30 µm, 1Hz	Figure 4: Friction force displacement diagram for sinusoidal movements with amplitudes from 1 µm to 8 µm, 1Hz

[1] R. Meeß, F. Löffler: Design and Evaluation of a Rolling Friction Apparatus for Micro Linear Bearings; Friction, Wear and Wear Protection, Aachen, 9.-11. April, 2008

[2] R. Meeß, S. Bütefisch, F. Löffler: Linear ball bearings as a safety clutch for micro-tactile sensors European Society for Precision Engineering and Nanotechnology, 10th Anniversary International Conference, Zurich, 18th-22nd May, 2008

Contact person:

R. Meeß, AG 5.54, E-Mail: rudolf.meess@ptb.de