Quantitative measurements of contact stiffness

The differential UFM approach is based on three main assumptions  

It is possible to identify a threshold amplitude, defined as the amplitude at which the contact breaks, and pull-off occurs, for part of the ultrasonic cycle. It can be identified as the amplitude at which the inflection occurs in the normal deflection signal. 

The threshold amplitude depends on the applied normal force. 

The cantilever vibration at the ultrasonic working frequency is negligible. 

Therefore the difference in threshold amplitude at different values of normal force is equal to the difference in indentation Ah - h2 — h.  

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Fig. 13.5. Quantitative measurements of contact stiffness by UFM (a) theoretical calculation of the UFM response on Si (1) and Ge (2) surface, using the engineering parameters ESi = 164 GPa, EGe = 121 GPa, surface energy in an ambient environment y = 1 N m-1, and the manufacturer s data for cantilever stiffness kc = 2.8 nN nm-1 and tip radius Rt = 10 nm (b) experimentally measured UFM response of a silicon surface (c) schematic illustration of the differential UFM approach to the measurement of contact stiffness (Kolosov and Yamanaka 1993), from the threshold amplitude values (ai and a2) for two different normal force values (Fi and P2), the contact stiffness Seff is given by Seff = (F2 — -Fi)/(a2 — ) (d) experimental stiffness measurements... 

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