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impact force estimate/calculation
4

impact force estimate/calculation

impact force estimate/calculation

(OP)
I have an application of a trolley hoist traveling on a monorail track. Though it's not supposed to be run into the trolley stop at the end of the rail, sometimes operators do it anyway. I've been asked to determine the force produced if this occurs.

A moving object hitting an immoveable object generates a theoretically infinite force. Is there a way to estimate a force assuming virtually zero deflection? Or is it best to assume a very small deflection, say 0.01"?

Open to suggestions.

RE: impact force estimate/calculation

Force = mass x velocity, per Mr. Newton

RE: impact force estimate/calculation

Quote:


Force = mass x velocity, per Mr. Newton  




Accelleration, not velocity!

You need to decide the maximum deflection that will be acceptable, and work back from that to get the force for a given volcity.

You might well end up having to accept a bigger deflection than you first thought!

Remember that there will be some deflection in the trolly as well as the stop.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
 

RE: impact force estimate/calculation

You might want to search this site for similar threads - I believe that subject has been beaten to death a few times.

RE: impact force estimate/calculation

I think you want to work this problem the other way around.  I'm assuming that there is a bumper on the trolley.  So calculate the force needed to deflect the material to either to yield or ultimate.  Once you know this, you can calculate the max acceleration or velocity the trolley can travel before damage (F=ma).  The way that you are attempting is more of kinematic / kinetic study that will lead to conservation of energy equations, but you will still need to know the deflection.

Tobalcane
"If you avoid failure, you also avoid success."
"Luck is where preparation meets opportunity"  

RE: impact force estimate/calculation

The building or support columns are going to be the most flexible item in that system.  

You can certainly feel it through the building when that happens.  At the top of a column, it's going to a matter of how many quarter inches of movement, not tenths.

RE: impact force estimate/calculation

Don't forget that the mass hanging on the hoist chain below the trolley reacts as a pendulum, i.e. on a different time constant than the trolley+hoist...

RE: impact force estimate/calculation

You'll want to figure in the stiffness of the two parts. All things being equal, KE_cart = PE_deformed shape. Or, in other words: 0.5*m*v^2 = 0.5*k*x^2.

How to figure the stiffness? Well, I don't know what the parts look like, but perhaps they could be idealized. If you really want to get fancy, an explicit FEA model will give you the most accurate results.

RE: impact force estimate/calculation

^^ per my last post.
1. cart = trolley hoist
2. When considering the PE, be sure to consider combined stiffness of the two parts (think two springs in series).
3. an implicit FEA solver can probably handle this sort of impact these days with enough horsepower.
 

RE: impact force estimate/calculation

I think that the operators need more safety training on hoist operation.

RE: impact force estimate/calculation

It's not simply F=m*a. Search. I remember commenting on at least 2 threads on the exact topic.  

peace
Fe

RE: impact force estimate/calculation

(OP)
Thanks. I have been searching. There are so many to be found searching keywords such as "Impact", "Shock", and "Collision" that I haven't yet been able to sift thru all of them.

RE: impact force estimate/calculation

the cart's momentum (m*v) applies a force to the stop depending on the time of the impact (m*v/t) ...

1) test it if an accelerometer on the cart or a load cell on the stop

2) add a soft (comfy?) cushion to the stop (to increase t)

3) train the operators

RE: impact force estimate/calculation

F=Ma
is not the way you do this, since you only know V, the velocity and mass, m. You don't know a and you don't have clue for the time of impact. Guessing at a is a non-starter.

Also since I assume you haven't destroyed the trolley or stop, we have stresses that are less than the yield.
As a few others have said, the problem is mainly linear motion and the energy equation yields.

1/2*m*v^2=1/2* k*x^2=F^2/2k
and

F=v*square root(k*m)


which  assumes constant k implying (since you haven't previously destroyed the trolley or stop) we have stresses that are within the elastic limit


In this all you have to do is get k, the "spring constant".

I would do it empirically by a controlled experiment allowing the trolley to move at a very low known velocity and get the deflection, x by simple visual means.
Then for the experiment
use the energy equation to get k

k=mv^2/x^2

and then the force equation above to get F,namely

F=v*square root(k*m)

 

RE: impact force estimate/calculation

Doh!

What was I thinking?!?!?  A failed attempt at a quick answer I guess.  When I was thinking of a quick estimation I short-cutted it too much.

mass * velocity squared / your assumed small deflection

F = m * V^2 / (2 * 0.005), or maybe 0.002/0.003
(rough estimation but good enough for your purpose I suppose)

{that's where my mind went, when I was thinking of getting rid of the inch squared, I threw away the whole V squared, and then when I was thinking of an assumed deflection of 0.005 x 2 being equal to your proposed 0.01, I threw away the whole bottom term.  Haste makes waste, I learn again.}

RE: impact force estimate/calculation

Although the approach proposed by Zekeman is conservative as it does not take into account friction effects that are involved in the process and considers the impact as fully elastic, I think is quite appropriate for your case.

RE: impact force estimate/calculation

(OP)
I know we're trying to hit an unknown target. This is even worse than the problems about dropping a mass onto a spring.

Thanks for your help.

RE: impact force estimate/calculation

zekeman points out the key that a lot of people miss when discussing impact... what was the duration of the event... that is why you can't simply do F=ma.

Here is  a link to a vendor that put out a nice little white paper on the subject.

http://www.brushwellman.com/alloy/tech_lit/julycom7_99.pdf

-Dustin
Professional Engineer
Pretty good with SolidWorks

RE: impact force estimate/calculation

This subject has been discussed on several older threads.  The closest solution appears to be modeling the materials as springs, and using the calculated spring constant to determine the deflection.  Given the deflection, you can then use the kinetic energy to solve for the deflection in the stored spring energy.

TTFN

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RE: impact force estimate/calculation

Kenetic energy of the moving crane equals the elastic energy stored in the deflection of the crane stop/crane body.   

RE: impact force estimate/calculation

"what was the duration of the event... that is why you can't simply do F=ma."

I don't think you need to know the duration (or pulse like 0.001 sec half sine wave) unless there is something that is frequencies sensitive that you want to avoid shock amplification.  

 

Tobalcane
"If you avoid failure, you also avoid success."
"Luck is where preparation meets opportunity"  

RE: impact force estimate/calculation

F = d/dt(m*v), which requires a time element.  An impact that takes 100ms is substantially less forceful than an impact that takes 11ms.  That's why the legacy military shock waveform was a specific shape with an 11-ms duration.

In fact, if you want a tolerable approximation, I would just use an 11-ms half-sine or sawtooth as a starting point.

TTFN

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RE: impact force estimate/calculation

Impulse = change in momentum
F*t = m*(v2 - v1), assuming no mass change
F = force
t = time during which force acts
m = mass of the moving object
v1 = velocity, initial
v2 = velocity, final

Yes, time is a factor.

Ted

RE: impact force estimate/calculation

I would agree with he both of you, but how are we defining duration are we talking about shock frequency coupling with the Fn of anything on the trolley or are you saying duration is time from Vo to final V just before impact?  If Fn of anything on the trolley is close to the shock frequency then we would have a problem, but this is not what the OP was asking, hence my post.  The latter would give you the force, but I've never heard of this quantity as "duration", but I could be wrong.   

Tobalcane
"If you avoid failure, you also avoid success."
"Luck is where preparation meets opportunity"  

RE: impact force estimate/calculation

You should look at building codes, AISC Design Guide 7, AISE Technical report 13, ASCE 7, etc.  For instance, ASCE 7 says "The lateral force on crane runway beams with electrically powered trolleys shall be calculated as 20 percent of the sum of the rated capacity of the crane and the weight of the hoist and trolley."  etc.

RE: impact force estimate/calculation

If you want to do the complex analysis, then there is no simple duration, although one could probably still come up with some equivalent "rms" force or somesuch.  But for some analyses, such as that suggested in the OP, then a simple force profile and a time duration will provide some sort of answer.

TTFN

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RE: impact force estimate/calculation

You don't need to know deflection or duration. Use Zekeman's equation  F(max)=v*square root(k*m)

Determine k statically:
- put the trolley in contact with the barrier
- apply a measured force (preferrably at the CG) to a rigid part of the trolley, pushing towards the barrier
- measure the deflection at the same point
- use k=F/x

There are a number of assumptions in this method, mostly concerning the location and magnitude of compliances in the system but the results should be close enough for your purpose.
 

Engineering is the art of creating things you need, from things you can get.

RE: impact force estimate/calculation

(OP)
Regarding the comment from IFRs: the building codes as well as crane and hoist specs limit the travel speed for estimating lateral forces, and we design our equipment accordingly. The hoist in question is in use by one of our customers and we'd like to convince them to put energy-absorbing bumpers on the trolley.

RE: impact force estimate/calculation

(OP)
Thanks for your help. I managed to come up with a value (rather large) which I believe has convinced the end user to install shock-absorbing bumpers. Who knows what operators will do despite what the manual says?

RE: impact force estimate/calculation

"convinced the end user to install shock-absorbing bumpers" ... brillant ! ... it is truly a good analysis that convinces the end user to do the right solution all along !

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