Hertzian impact: experimental study of the force pulse and resulting stress waves

Ball impact has long been used as a repeatable source of stress waves in solids. The amplitude and frequency content of the waves are a function of the force-time history, or force pulse, that the ball imposes on the massive body. In this study, Glaser-type conical piezoelectric sensors are used to measure vibrations induced by a ball colliding with a massive plate. These measurements are compared with theoretical estimates derived from a marriage of Hertz theory and elastic wave propagation. The match between experiment and theory is so close that it not only facilitates the absolute calibration the sensors but it also allows the limits of Hertz theory to be probed. Glass, ruby and hardened steel balls 0.4 to 2.5 mm in diameter were dropped onto steel, glass, aluminum, and polymethylmethacrylate plates at a wide range of approach velocities, delivering frequencies up to 1.5 MHz into these materials. Effects of surface properties and yielding of the plate material were analyzed via the resulting stress waves and simultaneous measurements of the ball's coefficient of restitution. The sensors are sensitive to surface normal displacements down to about +/-1 pm in the frequency range of 20 kHz to over 1 MHz.