A novel, experimental method is presented for measuring the coefficient of restitution during impact events. These measurements are used to indirectly validate a new model of elastic-plastic contact. The experimental setup consists of a stainless steel sphere that is attached at the bottom of a 2.2 m long pendulum. The test materials are of the form of 1 inch diameter pucks that the sphere strikes over a range of velocities. Digital image correlation is used to measure the displacement and velocity of the ball. From this data the coefficient of restitution is calculated as a function of velocity. This report details the experimental setup, experimental process, the results acquired, as well as the future work.
Measurements are presented from a two-beam structure with several bolted interfaces in order to characterize the nonlinear damping introduced by the joints. The measurements (all at force levels below macroslip) reveal that each underlying mode of the structure is well approximated by a single degree-of-freedom (SDOF) system with a nonlinear mechanical joint. At low enough force levels, the measurements show dissipation that scales as the second power of the applied force, agreeing with theory for a linear viscously damped system. This is attributed to linear viscous behavior of the material and/or damping provided by the support structure. At larger force levels, the damping is observed to behave nonlinearly, suggesting that damping from the mechanical joints is dominant. A model is presented that captures these effects, consisting of a spring and viscous damping element in parallel with a four-parameter Iwan model. The parameters of this model are identified for each mode of the structure and comparisons suggest that the model captures the stiffness and damping accurately over a range of forcing levels.
This memo documents the results and methodology of the high-frequency modal test performed on a solid metal cylinder, provided by Vibrant Corporation, in September 2014 at Sandia National Laboratories. The purpose of this test was to measure mode shapes of the unit (torsion, axial, and bending) as high in frequency as achievable with a Polytec PSV-400 scanning laser Doppler vibrometer.
A cantilever beam is released from an initial condition. The velocity at the tip is recorded using a laser Doppler vibrometer. The ring-down time history is analyzed using Hilbert transform, which gives the natural frequency and damping. An important issue with the Hilbert transform is vulnerability to noise. The proposed method uses curve fitting to replace some time-differentiation and suppress noise. Linear curve fitting gives very good results for linear beams with low damping. For nonlinear beams with higher damping, polynomial curve fitting captures the time variations. The method was used for estimating quality factors of a few shim metals and PZT bimorphs.
To study the rebound of a sphere colliding against a flat wall, a test setup was developed where the sphere is suspended with strings as a pendulum, elevated, and gravity-released to impact the wall. The motion of the sphere was recorded with a highspeed camera and traced with an image-processing program. From the speed of the sphere before and after each collision, the coefficient of restitution was computed, and shown to be a function of impact speed as predicted analytically.
To study the rebound of a sphere colliding against a flat wall, a test setup was developed where the sphere is suspended with strings as a pendulum, elevated, and gravity-released to impact the wall. The motion of the sphere was recorded with a highspeed camera and traced with an image-processing program. From the speed of the sphere before and after each collision, the coefficient of restitution was computed, and shown to be a function of impact speed as predicted analytically.