With an optical interferometer, the free vibration spectra and the local vibration amplitude of four rectangular atomic force microscope cantilevers made of silicon have been examined experimentally in a spectral range of 100 kHz to 10 MHz. A good agreement with the flexural wave theory of elastic beams was found. Coupling to torsional vibrations was also observed. When the sensor tip of the cantilever is in contact with a sample surface the resonances are shifted in frequency and the vibration amplitudes along the cantilever change. A method is presented to calculate this frequency shift using a linear approximation for the tip–sample interaction forces, and the results are compared with the frequency shift calculated from the point-mass model. The measured resonance frequencies of a surface-coupled cantilever do not correspond as well to the theoretical ones as in the free case even if the elastic-beam model is used. The reason for the disagreement is found to be the geometry of the commercial cantilevers and the nonlinearity of the tip-sample interaction force.
The demands on modern machine parts, i.e., bearings, are increasing constantly. To ensure that highly clean steel is used, a number of different test methods are commonly used. In the field of test methods the ultrasonic immersion testing has reached a dominant position. This paper will give a short comparison of the ASTM E 588-03 and the SEP 1927 standards and will point out some experiences the authors have made using ultrasonic testing as a tool to increase steel cleanliness and using ultrasonic testing and blue fracture testing as complementary test methods. To be able to use ultrasonic testing as a powerful tool, a number of side aspects like the geometry of the test piece, the structure of it, or the frequency of the used ultrasonic-probe are important. This will be demonstrated by showing results from testing and incoming inspection.
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