Designing Components for Impact... 1

[MechESteve]

Hello there,

I am trying to design the mechanical interaction and fastening of two components in a bumper system to withstand regular impacts without yielding. I have many methods at my disposal to determine the impact force at the point of contact, but my question here is primarily how to take that information and apply it to engineering an assembly to withstand the forces involved.

I have done some preliminary experimentation with high speed video (to catch 5.8ms compression of the rubber bumper) to calculate the average impact force to be thousands of pounds using: F=dp/dt, dp=momentum, dt=time. The rubber bumper impacts the top of a post that is essentially a vertical cantilevered beam with a flange at it's base bolting it down. My focus is the stress at the connection of the flange and the post which are both 303SS - how do I use impact force in my analysis of this joint?

First I would like to note I am aware that the force I calculated is the average force during the impact, and most certainly not the peak force. I have not been able to find a way to calculate the peak force and have a feeling there isn't, at least an accurate way. Unless someone chimes in with a better idea, I think I will run a full FEA simulation of the impact to determine the peak force - I have only simulated an impact once though and would like to try a different approach.

So lets say I have my average and peak force values determined, how can I use these values? Do I assume the peak value to be a static load? Static FEA simulation? Use Distortion-Energy Theory and also investigate Fatigue life/Strain-Life? Any guidance is appreciated. I don't recall any design problems involving impacts in school and searching the web hasn't yielded what I am looking for just yet.

Thank you,
Steve

 

[rb1957]

if you model the impact then should get good results. you'll need a time history of the applied force. i'd test your bumper, apply a known load get a deflection; now cross-read with your video ... bumper deflection means this much load.

it sounds like this thing is in service already ? is there a problem you're trying to fix, or just trying to understand the structure better ??

Quando Omni Flunkus Moritati

 

[GregLocock]

Yes you can design to the peak force as if it was a static load. This is probably slighyly conservative, if your model is perfect, but since it isn't it is good rnough. What is your failure criterion? yield, low cycle fatigue or what?



Cheers

Greg Locock


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[Sparweb]

Off the top of my head, I think this is a case where the school textbooks coax you into making an energy-transfer problem to solve.
Is it possible to find the kinetic energy of the object before it hits the bumper? KE = 1/2 M v[sup]2[/sup] If you know its mass and velocity...
On the other side of the equation, the kinetic energy of motion is converted into the Strain Energy of deformation. SE = ∫ F(x)*dx
This can be used in conjunction with RB1957's suggestion about the stress-strain of the bumper, to fit a curve that represents the change of force during the exchange of energy from kinetic to strain (assume 100% conversion). The peak force will be the point of maximum compression, therefore a triangular curve (straight line?) Find the area under hte curve - it's the strain energy. If it doesn't match the kinetic energy you started with, adjust the peak force accordingly. If the stress-strain model and the energy model disagree dramatically with each other then there could be another force in action, (or I've overlooked something).


STF

 

[MechESteve]

Thank you guys for the excellent suggestions. This is for a component of a product that is seeing a lot of major changes in its generation and this particular part needs to be broken into two parts (beam and flange) with some improvements to better withstand impacts.

Since my initial post I have found the whole structure is absorbing quite a bit of the impact and I can't just isolate the beam and bumper, so theory will not apply to this problem very well. I have also found my initial numbers from the video were off. I am still very interested in the theory behind this and calculating the peak force so I can apply it to future problems. The mass and velocity are known. From a little research I have found that the behavior of rubber in impacts has a parabolic force/displacement relationship. My assumption is this is for a flat rubber bumper. Using an FEA model to capture the force/deflection relationship is a good idea. I will think about this a little more and try to see if this works in practice. The problem for my particular setup is that the camera I used is fairly low resolution and can't focus close enough to be able to accurately measure/extrapolate the deflection of the bumper.

I have one more experimental approach that I will try tomorrow. I believe I can use F=M*A to find the peak force, if I know M and A_max. F_max=M*A_max
I am borrowing a motion sensor system (APDM Opal) to record the acceleration at impact. The built-in accelerometer peaks at 8G's on each axis and the Opal is only capable of recording at 120Hz (8.3ms). The full compression of the bumper is about 58ms, so I should get 6-7 samples during impact. I will run a few trials to collect as many points as possible. I don't think I will hit 8G's, but if I do I will tilt the sensor 45 degrees on one axis and split the acceleration onto the x and y axis and combine them later, assuming that doesn't saturate too.

On a side note, I wish there was a really low cost and fast data logging system that I could just keep in my tool box... I run into too many situations where I could use one.

Thanks!
Steve

 

[Sparweb]

A "high cost" system to you may be "low cost" to someone else... What are you looking for? If you repeatedly carry out motion and impact studies, you are looking for multi-kHz data collection rates.
Maybe you can live with just one parameter at a time?
Have you priced out the boards from National Instruments?
Extreme low-cost option could be an Arduino, relying on the built-in Analog-to-digital converter. Program it to take measurements from that - connect it to the computer and send a rapid stream of data in through the USB port. I haven't tried to "max it out" before but I've managed some pretty fast data so far. If you can live with low resolution you can probably speed up the data transfer rate, which will be limited by the baud rate of the USB connection. If using a 115kBit connection, and 10-bit ADC, the theoretical maximum speed may be near 10,000 samples per second. The ADC requires less than a millisecond to take a reading so there is some hope of at least 1000 samples per second. But I've never tried...


STF

 

[GregLocock]

There are several cheapish consumer digital cameras around that offer very high frame rates. You'll need bright lights as well.

Once you have the pictures digitising the data is mainly an exercise in pixel counting if you want to do it manually.

If you get accelerometer data at the same time then you will learn far more, but you may be spending time that is better spent on repeat tests - impact is not a very repeatable test in general, and getting to a rough understanding of several tests may be better than a perfect model of one. (in the real world in controlled conditions peak forces can vary from 4 to 7 in the same nominal test)



Cheers

Greg Locock


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[MechESteve]

The data I captured at 128Hz was, as expected, insufficient to capture the full impact and is likely averaging the peak values, which were right around 2G's. The data did provide some interesting facts and having a 3-axis accelerometer was helpful to see things I didn't expect. My next step for this impact testing is to borrow a high bandwidth accelerometer and a digital storage oscilloscope in the next couple weeks. I am shooting for a 1kHz sample rate.

SparWeb,
I am looking for a extremely low-cost option. I usually need to perform one or two tests a year that need some type of data logging, which is not frequent enough to justify spending "too much" on a data logging system. I have been looking at Arduino sketches recently (much easier than learning how to write to an SD card from scratch in C), but from what I have found online, 1kHz is pushing the reliable data limit. The bottleneck is writing the data.

NI's lowest cost DAQ is the USB-6008 @ $169, but the basic software to just record data and copy it over to Excel is $1035 (NI LabVIEW SignalExpress Development System).
DataQ Instruments makes comparable DAQ: DI-149 @ $59. If you bundle the DAQ and the software, total cost is $244. I would say this is my very upper limit of what I consider a low cost system for what I am doing. Compared to what is out there though, I haven't seen anything less than this.

GregLocock,
I used a consumer (higher end of the spectrum ~$1k) camera to capture the 1200fps video, along with a 500W halogen work light 6 inches from the impact area I filmed. To analyze the video, I used Tracker, an Open Source Video Analysis and Modeling tool, designed to be used for physics education. The software was excellent.

The 128Hz system allowed me to stream the sensor data live and repeat the impacts over and over again so I can see the variance. I recorded multiple impacts and analyzed the "worst" of the recordings.

Thank you!
-Steve

 

[IRstuff]

Impacts are usually so short that you can buffer all the data and write to nonvolatile memory after the event. 60 seconds at 1kHz for 3 channels amounts to barely 360 kB of data. You trigger the recorder, trigger the event, and at the 60 second mark, the record stops and copies to SD card.

TTFN
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[rotw]

You can also Build your own data acquisition system. In the past I have made a card by myself for RS232 acquisition for other type of measurements. I've tried tried 8 bits resolution of conversion but appeared very poor so I went for a 12 bits resolution and that was enough and I think 1 kHz was doable if I remember well. Why don't you use an evaluation version of LabView, is that possible ?

I've made also an uncertainty analysis which was quite useful to capture the total uncertainty of the measured signal and how it spreads to other dependent variables. That's how I figured out the total uncertainty resulting from taking many samples, doing calibration and choosing the resolution of the converter (10 bits ADC was still not sufficient).

If you are interested I can share, but the card can not be easily duplicated because I have programmed a microcontroller.

What is the output signal from your motion sensor ?

 

[bcd]

Don't know if this option is viable, but in the old days before FEA and high speed digital cameras, Engineers would put a piece of clay or soft lead next to the bumper and measure its height after the impact. Then you know exactly how much the bumper deflected. Then compress the bumper in press at various laods to create a load / deflection curve. Match the results and you will get your equivalent static design load.

 

[avantibngrant]

If you know the stress strain curve of the bumper, convert it to a force vs deflection curve for the bumper using the frontal area and the length. Then use an energy balance of kinetic energy (1/2mv^2) = area under the force versus deflection curve. This is easier to do if the curve is linear. This will give you a D value and a peak value. Average force with be an equivalent area rectangle height with length D.
I have done this before to estimate bumper loads on a vehicle barrier.

Regards

Neil

 

[hendersdc]

From Roark's 7th addition section 16.4:

For Vertical Impact:

di/d = Sigmai/Sigma = 1 + sqrt(1 + 2*h/d)

For Horizontal Impact:

di/d = Sigmai/Sigma = sqrt(v^2/(g*d))

Where:

di = deformation due to impact
d = deformation due to static load
Sigmai = stress due to impact
Sigma = stress due to static load
h = drop height
v = velocity at impact
g = acceleration due to gravity

These formulas basically give you a way to relate the results of a static FEA or hand calcs to the force and deformation that may be seen during impact. I have applied these formulas in the past to model impact of a round object on a spherical plastic lens for a small handheld device and found them to be fairly accurate if not a little conservative. In my case I did a static FEA of the impactor sitting on the lens with the only force being its own weight. Using the deformation and stresses found from the FEA I applied the formulas using the test drop height and found the deformation and stresses due to impact. The lens was protecting an LCD. During testing the impactor was dropped from increasing heights until failure which is where my opinion of the formulas being a little conservative comes from though I can't remember exact values.

In your case the static calcs would need to include the weight of the unit being dropped, not just the bumper.

Doug

 

[avantibngrant]

Doug, very interesting. Thanks for the idea. I ahve been threatening myself to buy the Roark's book. Sound like it would be useful. If I understand well, if you get stress and deflection at a given point for static loading, you just use the ratios given to get the impuse deflection and stresses. Would that be average values or peak?

Regards
Neil

 

[hendersdc]

I believe these would give you the peak values though it is not explicitly stated. Certainly from my own testing the deformation seems to relate well to the peak. I would definitely recommend getting Roark's, it is my go-to book for hand calcs.

Doug