adding ordinary lubricant, effectively changing dry friction into viscous damping –
with the important difference that HF excitation can easily be removed or changed.
The consequence is depicted in the stability diagram of Fig. 7.12, showing that the
interval of belt speeds causing self-excited oscillations shrinks and eventually
vanishes as the frequency X of the HF excitation is increased.
In this example the HF excitation is applied tangentially to the surface. However,
using a HF-modulated normal force also reduces the effective friction, and may
significantly reduce or remove friction-induced oscillations (Cochard et al. 2003).
7.7.2 Displacement Due to HF Excitation
and Asymmetric Friction
Thomsen (2000) and Fidlin and Thomsen (2001) analyzed a device where the
biasing effect of HF excitation is used to make a slider propel itself controllably
inside a stator (Fig. 7.7(a)). The slider is sandwiched between two friction layers of
differing friction properties, and driven by an internal HF resonator. Inertia forces
from the resonator make the slider oscillate back and forth at small amplitude and
high frequency. With the resonator aligned askew to the friction layers, friction
forces are less when the resonator presses against the layer of least friction, so the
slider moves a bit longer in one direction than in the other during each vibration
period – effectively in one direction with a small overlay of HF vibrations. The
internal resonator might be realized using piezoelectric ceramics, as with traditional
ultrasonic motors (Ueha and Tomikawa 1993). Compared to these, the driving
principle considered here does not rely on the establishment of traveling waves,
thus circumventing the need for two vibration exciters (source and absorber) and
complicated electronics.
Fig. 7.12 Ranges of belt speeds v b producing self-excited oscillations, as a function of excitation
frequency X. (–,–) Analytical prediction; (○, □) numerical simulation. Parameters: as in Fig. 7.11,
and a = 0.01
7.7 Specific Systems and Results – Some Examples
437
with the important difference that HF excitation can easily be removed or changed.
The consequence is depicted in the stability diagram of Fig. 7.12, showing that the
interval of belt speeds causing self-excited oscillations shrinks and eventually
vanishes as the frequency X of the HF excitation is increased.
In this example the HF excitation is applied tangentially to the surface. However,
using a HF-modulated normal force also reduces the effective friction, and may
significantly reduce or remove friction-induced oscillations (Cochard et al. 2003).
7.7.2 Displacement Due to HF Excitation
and Asymmetric Friction
Thomsen (2000) and Fidlin and Thomsen (2001) analyzed a device where the
biasing effect of HF excitation is used to make a slider propel itself controllably
inside a stator (Fig. 7.7(a)). The slider is sandwiched between two friction layers of
differing friction properties, and driven by an internal HF resonator. Inertia forces
from the resonator make the slider oscillate back and forth at small amplitude and
high frequency. With the resonator aligned askew to the friction layers, friction
forces are less when the resonator presses against the layer of least friction, so the
slider moves a bit longer in one direction than in the other during each vibration
period – effectively in one direction with a small overlay of HF vibrations. The
internal resonator might be realized using piezoelectric ceramics, as with traditional
ultrasonic motors (Ueha and Tomikawa 1993). Compared to these, the driving
principle considered here does not rely on the establishment of traveling waves,
thus circumventing the need for two vibration exciters (source and absorber) and
complicated electronics.
Fig. 7.12 Ranges of belt speeds v b producing self-excited oscillations, as a function of excitation
frequency X. (–,–) Analytical prediction; (○, □) numerical simulation. Parameters: as in Fig. 7.11,
and a = 0.01
7.7 Specific Systems and Results – Some Examples
437