Analysing Stresses from only G forces

[WannaBeME]

I am in a course this semester, Mechanical Engineering Design, and the bulk of the course is a semester long project that you must design/analyze/build. It's a relatively small device that won't exceed about (6x5x4)inches in volume. One requirement is that it must withstand (4.5±2) G's while it is placed on a machine that will test this by shaking it. My group is at the point where we had what we thought was a solid final design, and when we consulted our client (a professor, just not the professor to the course) his concerns were mainly that it would not hold up to the vibrations and topple over. Here's a pic.

The point of concern is the left tube, the one with the piston inside. The plate it is on is an aluminum base plate with a bored hole to seat the tube. The tube will have an adhesive on the bottom of the surface to attach to the aluminum, as well as some type of epoxy of caulking around the top of the aluminum to ensure it's sealed and also does not come out during the vibrations test.

Vibrations is a senior level course at my college, so no one in my group has an idea how to analyze this device with only give the acceleration it might experience. We recognize the point of concern at where the caulking would be, and that the biggest stress will occur from the lid as it is at the top and relatively heavy being aluminum and will cause the maximum bending stress. During the testing I would leave the piston at the lowest position trying to keep the center of gravity as low as possible. Is that something practical to calculate? And is a roll center something that is possible to calculate on this tube as well?

My main question is how we should approach analyzing this device, especially when it comes to vibrations. We are all thinking that this small device does not have anything truly to calculate aside from vibrations, and we have searched up and down for an idea on how to do that. This is a course where we learn about fatigue/shaft design/load&stress analysis for design/etc. so having a nice couple pages of calculations is expected.

Any help is really appreciated, even if it's just pointing us in the right direction.

 

[Vadar2012]

So this device isn't going to operate at all, it's just going to be put onto a machine that shakes it, and it just has to withstand that?

How is this device attached to the shaking machine? This will let us tell you how to improve the design to reduce its tipping potential.

 

[WannaBeME]

Well it has to operate, but not under the given conditions. It will be attached to the shaking machine with bolts. Here is another picture to give a better visualization of the device. The tubes are made of PMMA, or plexiglass, and the base plate/lids/etc. are made of aluminum. The shaft part connecting the piston to the knob is stainless steel.

 

[AlephZero]

If your OP contains all the information you have about the shake test, you can't really do a study of vibrations and resonance, because you don't know what frequency (or frequency range) it will be tested at. If you haven't studied vibration or fatigue yet, quite likely you are not supposed to worry about them.

The first thing to check is that the steady loads and stresses caused by the maximum acceleration of 6.5g won't cause any problems. This is the same as stressing the structure loaded by its own weight, with the weight acting in whatever direction(s) (vertical or horizontal) it will be shaken.

For a shake test at more than 1g, the structure must be fixed to the shaker table (not just standing on it) otherwise it will go into free flight or slidie around. Maybe your design needs to include some features to bolt it to the table, or you need to say how should will be clamped down, or whatever.

EDIT: I started typing this before I saw your second post about bolting it to the table.

 

[WannaBeME]

If your OP contains all the information you have about the shake test, you can't really do a study of vibrations and resonance, because you don't know what frequency (or frequency range) it will be tested at. If you haven't studied vibration or fatigue yet, quite likely you are not supposed to worry about them.

The first thing to check is that the steady loads and stresses caused by the maximum acceleration of 6.5g won't cause any problems. This is the same as stressing the structure loaded by its own weight, with the weight acting in whatever direction(s) (vertical or horizontal) it will be shaken.

For a shake test at more than 1g, the structure must be fixed to the shaker table (not just standing on it) otherwise it will go into free flight or slidie around. Maybe your design needs to include some features to bolt it to the table, or you need to say how should will be clamped down, or whatever.

EDIT: I started typing this before I saw your second post about bolting it to the table.

Sorry, I forgot to paste the link to the picture. Thank you for the help. I am not sure why I thought with only an acceleration I could not analyze the static load on certain areas. Yeah I was not sure if you could analyze vibrations with just an acceleration though. Thanks again for the help!

Oh and we are studying fatigue right now, so maybe my group could analyze points at the maximum acceleration in two directions. One more question though, when analyzing static loads, I am assuming we should find the center of gravity and place the acceleration acting through that point?

 

[AlephZero]

I am assuming we should find the center of gravity and place the acceleration acting through that point?

You need to find the forces on each part separately from its own CG. For example if the shaking is horizontal, you want to find the force on each vertical tube separately so you can find the forces and moments between the tubes and the base plate.

Your CAD system should be able to do most of the grunt work finding the weights, if you define the density of the material for each part.

 

[Vadar2012]

Yeah, for some reason it seems a little too simple. Can't you just treat it as a couple of cantilevers and calculate the loads at the restraints. That will tell you how strong the connection has to be to withstand the g force that is applied to it. I'm guessing this is what your professor was getting at.

Personally, I'd just do a simple FEA model of it, and apply a range of forces to it, say in the transverse direction at the top of the tubes. This will allow you to do vibrational and statics analyses. Although, I'm guessing this is beyond your course.

Therefore, in terms of the simple g forces, you can easily calculate the resultant forces at the restraints (the maximum) and design it accordingly. This will also allow give you the values you need to construct your goodman diagram (fatigue analysis). You can also calculate the "bearing" forces applied to the plate by the bolts and determine if you've allocated strong enough bolts and a thick enough plate.

 

[WannaBeME]

Great, thanks a lot. I'm not sure why but with it being such a small/compact device and having to perform an unfamiliar function (to experiment with capillary flow), me and my group were getting caught up in that rather than being able to analyze it as we have in statics/strength of materials. I asked a few other groups and they were also stumped as to what to calculate. Now it seems insane this stuff was simply overlooked. Good thing we're just students I suppose. lol

Aside from treating them as cantilevers, and just calculating stresses in that manner, is it possible to find a roll center on such a device? I would love to throw something in there that I know would be unique in that no other groups did the same.

I'm hoping for my group to begin manufacturing next week, and when finished I'll be sure to let you all know if it fell to pieces.

 

[Vadar2012]

Just use the CAD program to give you the centre of mass. You can use this to calculate its' tipping potential if you see it useful. This is the force required to tip it over. The program will give you a dot with coordinates. It usually gives it to you measured from the 0,0,0 global coordinates. This is dependant on what densities you give materials of the components that you drew it with. So hopefully you've drawn the assembly in such a manner that allows you do designate densities properly.

I was just looking at the picture again. Is the base made from a solid plate, or is that sheets welded together to form a box?

 

[WannaBeME]

Just use the CAD program to give you the centre of mass. You can use this to calculate its' tipping potential if you see it useful. This is the force required to tip it over. The program will give you a dot with coordinates. It usually gives it to you measured from the 0,0,0 global coordinates. This is dependant on what densities you give materials of the components that you drew it with. So hopefully you've drawn the assembly in such a manner that allows you do designate densities properly.

I was just looking at the picture again. Is the base made from a solid plate, or is that sheets welded together to form a box?

Thanks for your help! It's actually a solid piece, in this design it's a 3/4" thick aluminum plate. We've actually done a slight redesign which only needs a 1/2" thick plate, where both tubes are sitting similar to the one on the left, and the lid will extend out with holes to use long screws to screw to the base plate. Just for piece of mind that they will hold.