## Measuring “Force Output” of the (SI) Single Impact Air Knocker Series

###### David Strong

Recently one of our sales team reps was working with a potential customer on a Single Impact (SI) vibrator application.  At some point in the conversation the issue of force output of the unit came up and there was some comparison with an unknown competitor’s model.

I’ve written at least a couple of blogs talking about documenting the performance of piston vibrators, both air cushioned and impact piston pneumatic vibrators.  One of the big questions is what is a meaningful “number” for the force output and how do we arrive at that number.  For an air cushioned piston vibrator, as mentioned before it’s pretty easy, data can be collected and calculations made.  Impact units such as the 1200 VMS present a few more wrinkles but again, I think we’ve got a reasonable method of documenting the vibrators performance.  The single impact vibrator adds at least a couple more levels of complexity to the problem.

Impulse, Force of Impact, Energy of Impact, Kinetic energy, Potential energy or “force output”, where to start, how to mathematically model the unit and what data can we capture to fill in the blanks.  With our current instrumentation we can accurately collect data on acceleration of something to which we mount the vibrator as well as the resulting displacement of that vibrator – mounting plate assembly.

In the past folks here have mentioned that it made sense to look at the kinetic energy generated by the unit, a reasonably sensible approach; we have a moving mass that strikes some non-moving plate to which the vibrator is connected. Or they’d calculated force output based on the assumption of a sinusoidal wave form.  I’ve never been a big fan of the equation that was used, it really seemed to me to pertain more to a rotating vibrator such as a ball vibrator and not something that has a reciprocating piston.  The form of the equation is very similar to the generic equation for a rotating off balanced mass and that makes me a bit less confident in that approach.

Our old piston vibrator force output data sheet had an interesting note on the bottom of the table.  “The data for the impact type vibrators is lower than the actual PEAK IMPACT FORCE developed.  The actual impact is neglected in the calculations since it provides astronomically high data not at all indicative of the actual EFFECTIVE FORCE OUTPUT…”  This makes a lot of sense and I’ve seen this when recording the acceleration data on the impact piston.   During testing for the 1300 SI, with a very high sample rate, I was recording acceleration values 1600-1700 g’s and above.  With the known mass of the vibrator and mounting plate we’d calculate a force output above 115,000 lbf and I know that’s not right!   You can view the video of a portion of the testing on the Cleveland Vibrator Youtube channel.  You can see the set up and the display of the CoCo-80 as we monitor the acceleration of the assembly.

I spent some time researching various physics sites trying to look for a good approach to document the force output of the SI units.  I ran across a number of interesting discussions by what appear to be some pretty smart folks.  The more I read the more you could see variables enter into the problem.  How rigid is the surface that is being impacted?  How long or short is the time period of the impact?  Discussions about the differences between work, force and energy, with colliding objects, somethings we probably only touched on in my too long ago physics classes.

Traditionally, the Sales Team has likened the SI vibrator to a sledge hammer.  The single impact of the piston is good for keeping moist material moving while reducing the possibility of packing which can happen with continuous vibration.  So I investigated some “hammer physics”, that research yields that the force acting to decelerate the hammer can expressed by the equation F = (m * U2/2x ) where U is the impact speed and X is the distance required to slow the speed of the hammer to zero after striking an object.  I might be able to work with that, equal and opposite forces concept, unfortunately I have no way of knowing the speed of the piston at impact, I can measure the deflection of the mounting plate as it reacts to the impact but that still leaves me with an unknown.  Additionally the characteristics of the hopper and hopper wall struck by the piston of the SI vibrator would influence the results of the above equation.  A thicker hopper wall would deflect less than a thin one, therefore the distance to reduce the speed of the piston to zero would vary with wall thickness and the force to counter act the pistons force would vary as well.

Some place along the way while looking at various physics forums and topics of impacting objects, someone mentioned that “pressure” is a force per unit of area.  This got me thinking a bit about “what do I know” and “what can I measure” in an effort to characterize the performance of the unit.  I do know the inlet air pressure and the diameter of the piston with its surface area.  I also know the weight of the piston and the distance the piston strokes during operation.  For now I’m thinking a decent way to look at the “force” of the impacting piston might be in terms of “potential” energy.  Looking at the piston as it drops from the top of the body to the mounting plate, then using the operating pressure and surface area of the piston head and “adding” that calculated weight to the piston’s weight to arrive at some “force” output for the vibrator. For example, if I do that calculation we get a potential energy at 80 psi of 1033 in-lbs of force.  This seems like a much more reasonable number than the 115,000 lbf due to the instantaneous impact of the piston due to the huge acceleration value generated by the  steel on steel strike.

Admittedly this is still a work in progress.  I’d like to determine a way to derive the “force” of the vibrator based on what I can record and observe, but I’m not there yet.  I can’t find any support documents to explain how the catalog data for the SI family of vibrators was derived back in the day.  So I can’t really say it’s spot on or way off.  What I do know is that Cleveland Vibrator Company has a trial policy for its complete line of industrial vibrators.  Sometimes the best avenue is to get a unit on trial, install it and try it.  The Cleveland Vibrator Sales Team will be happy to assist in making the best vibrator choice given the end users conditions.  There are a lot of years of application and practical experience behind the complete line of Cleveland Vibrator products, give our Sales Team a call and tap into that knowledge base.

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#### David Strong

David Strong joined Cleveland Vibrator in 1996 after graduating from Cleveland State University with a degree in Mechanical Engineering. Job focus over the years with Cleveland Vibrator has included design and engineering of fabricated vibratory equipment and systems as well as research and development of pneumatic vibrators. David views engineering as a creative problem solving endeavor and has worked with a wide range of customers and industries to successfully solve a variety of material handling challenges. Combining the technical aspects of the engineering degree with a Master Degree in Fine Arts, David a flexible, right and left brain thinker who is always looking forward to that next design challenge or customer application. When not working or thinking about vibration at Cleveland Vibrator you’ll find David working in his basement “Guitar factory” as a Luthier want to be. Even there it’s all about the vibration, just of strings and wood and not bulk material.