# Simple Dynamic Model

## Main Question or Discussion Point

Gday fellow engineers,

I have what I think is a rather trivial problem but would appreciate feedback on it. What I am working on is a mechanical model measuring the force of an object (eg a paddle pop stick or something else) along one axis of motion once a force is applied to it, causing it to bend. A force is created by a voice coil actuator that is couped to a translating beam that produces the force to the object. The actuator is fixed on a linear bearing along the axis of motion, and at the base of the actuator, is a load cell that is rigidly attached.

Along this axis, we need the load cell to measure the total force resulting to the object. The question is, how do we define exacly what the force that the load cell will be measuring under this current setup? We need this information to be able to purchase the correct capacity load cell and also to understand exacly what the load cell is measuring. Our understand is that the load cell would measure two components of force. The first component would be the force attributable to the inertia caused by the mass of the translating beam PLUS the force caused to the object. However, how does the mass of the actuator effect the load cell measurements?

I understand it's difficult to visualise the problem, so I have attached a free body diagram. The force we are after is that highlighted in bold. Any help making this clearer for me would be much appreciated.

James

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If I understand the problem correctly (and I'm not necessarily saying that I fully understand what the goal is here), the load cell will measure the applied force as well as any resulting force due to the acceleration of the moving part of the actuator (as well as any acceleration the non-moving part will experience if the load cell deflects at all: Forces act in both directions in equal amounts, also don't forget any effects due to gravity). This second force can be calculated using Newton's law: F=m*a (mass times its acceleration). However the question I have is: why would you place the load cell at the attachment point and not inbetween the actuator and the object? Or even better, use an actuator with force feedback data.
I think the problem you will encounter is that the value of the acceleration of the actuator is not constant so you may end up with a fairly nasty integral if you use this approach.
Maybe if you could post some more information about what you are doing (and why you are doing it this way) and your ultimate goal/measurand, there might be some follow-on info that would help. Also, have you considered using a simple spring with linear potentiometer as a source for your force data?

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I may as well describe the purpose of the actual model. The model is a spinal cord injury machine that dislocates the spine of both neonatal and adult rats using a very sophisticated control system so that mechanical parameters can be accurately matched to pathophysiological outcomes. The direction of injury occurs in only one axis of motion and the free body diagram I have attached accurately describes the mode of operation.

The linear actuator we have has a force constant of 31.11N/A with maximum static thrust of about 100N, or 10kg. The load cell previously attached to the model was only rated at 2kg, and was not sufficent for the model and is most likely broken.

Therefore our goal is to replace this load cell with one that is capable of the job. The question is how to choose a load cell of the right capacity, and also one that deflects minimally. My logic is that all we have to look at is the maximum force that the actuator will apply, which is 100N. Therefore, an equal an opposite force will be applied to the load cell and so the maximum capacity load cell we need is 100N (we are thinking of getting a 20kg load cell to be extra safe) as there will never be loads applied above this value. Does this logic seem correct?

We were then going to install an accelerometer on the model in order to separate the inertial force component from the total force component as measured from the load cell (i.e. this will include the force caused by botht he moving part of the actuator and the applied force from the spine).

How does this logic sound? We were initially going to purchase a cantilever type load cell but upon my reseach I read that these deflect up to 0.5mm at full load with a low natural frequency. Hence, I have been looking at these from sensotec:
http://content.honeywell.com/sensing/sensotec/pdf_catalog08/008609-1-EN_Model_41.pdf
What do you guys think?

Any feedback on what we are doing would be appreciated.

p.s. We thought of putting the load cell in between the actuator and the object (spine) but it is just not practical to do it this way due to the method in which the model attaches to the spine (i.e through a prong assembly).
Cheers,
Jamie

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I would still recommend you look into coming up with a way to insert the transducer inbetween the actuator and the "target". But if there really is no way to do that, you should be ok with what you are describing. Note however that just because a cell has a maximum rated value doesn't mean it can handle loads higher than those wihout damage. The spec sheets will usually have ranges for the measurement and for ultimate loads. The measurement range is usually just the linear range...
The range that the cell can measure should be determined by what loads you are expecting. If you will only use a force from say 1-10N, then it doesn't make sense to have a transducer that measures up to 100N since that will give you bad resolution over the measurement range. So the first question you need to answer is what you are expecting from your experiment.
Also, what is the acceleration of your actuator? Is this a fast/dynamic event? If not, your acceleration may not be a big deal. So the next question would be regarding uncertainty/accuracy.
Bottom line I believe is that you need to know more about the results that you expect in order to make a better call on what transducer to select (both static and dynamic capabilities).
I would also recommend that you take a look at the http://www.mcmaster.com" [Broken] regarding available transducers.
Are you also considering the data aquisition system in all of this?

P.S. have you considered doing numerical (or even spreadsheet) modeling of your setup to approximate what you will see and the sensitivity of the various parameters?

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