By Keith Frankie - Mechanical Engineer at TriAxial Design and Analysis, Inc.
When performing a drop test the ground contact time can be an important result. Longer contact times mean lower average acceleration and thus lower impact forces.
As with other parameters of the test, such as impact velocity, knowing these “intermediate” results can be very helpful in confirming that the test is proceeding in a fashion similar to what hand calculations predict.
As an example the specimen’s stiffness can be estimated with a simple linear study. The impact event can then be modeled as a simple ‘mass on a spring’. From this the ground contact time can be calculated and then compared to the SW drop test impact time.
We’ll use a bouncing rubber ball as a reference while explaining several methods to retrieve ground contact time. (Here is the sldprt for the ball in a zip file ball)
The ball is a simple 1 inch rubber ball (generic material ‘rubber’ from the SW material library) dropped from 0.1m (centroid). Velocity on impact can be hand calculated as v=(2gh)^1/2 = 1.31 m/s.
By definition ground contact begins at the start of the drop test. Remember that the default drop test plot animation includes 10 “fake” frames of free fall before impact.
A first pass approximation of the contact time is usually made by observing the test animation and taking note at which result step the specimen last touches the ground. Having a visual picture of the part’s behavior during impact certainly helps provide a sanity check against the more numerical results we’ll see later. Sometimes it can be hard to gauge exactly when contact ends.
A more robust method of checking contact times is to look at the .OUT file that SW writes while solving the simulation. Every time a plot is generated SW records which nodes are in contact with the ground. Simply look for the last entry with contact and the first entry without contact.
If it’s clear which node will be the last to loose contact with the surface a sensor can be placed there. A split feature is used here to create a vertex on the bottom, middle, and top of the ball.
A graph of vertical motion vs. time can be created at both the top and bottom point. A plot of velocity gives the clearest indication of the takeoff time. In the plot below the blue line shows velocity at the top. Initial speed can clearly be read as -1.31 m/s, which matches the calculated value. Takeoff occurs when velocity at the contact point becomes non zero at 1524 µs.
Let’s do some hand calculations as a sanity check. We’ll model the system as a mass on a spring.
According to the drop test the center of the ball will move down a maximum of 0.67mm during impact. Because of the ball’s geometry the effective stiffness of the ball varies throughout the impact event. We’ll simplify to an “average” displacement of .010 in, a little less than half of the maximum displacement.
We’ll run a static test on half the ball to determine the approximate stiffness of the structure. On the cut “half face” we’ll apply a forced displacement of .010 in. On the bottom we’ll use a virtual wall to simulate the ground.
This static study solves quickly. Querying reaction forces we see a load of 1.22 lbs is required to squish the ball. This converts to 5.43 N per .254 mm, or 21.4 kN/m.
Now we can model the system as a simple oscillator consisting of a mass on a spring. The natural frequency can be calculated as f = 1/2 π *(k/m)^1/2 . Substituting in our values we get 353.7 Hz. Half of a cycle is 1.41 ms. Since our theoretical model doesn’t account for the changing stiffness of our ball we know it’s not totally accurate, but it indicates we haven’t made any egregious errors with our FEA study.
Since solve time can be lengthy when testing real parts it’s rare to run the model much past the initial impact. With this simple (4k DOF) model it’s fun to run through a few bounces. Displacement results look as expected, with decreasing rebound height at each bounce.
Keith Frankie is a Mechanical Engineer at TriAxial Design and Analysis, Inc. with a BSME from UC Berkeley. He is a Certified Solidworks Expert (CSWE) with additional certifications in Simulation, Advanced Sheet Metal, Advanced Drawing Tools, and Advanced Weldments. In his 10 year career as a mechanical engineer he has worked on a wide variety of projects in both the commercial and defense sectors. He is active in the leadership of the San Diego chapter of the American Society of Mechanical Engineers (ASME). He can be reached at TriAxial Design and Analysis (619) 460-0216 or email@example.com