G-load for an impact (shop cart hitting an immovable stop)

[DTM]

TL;DR Summary

A cart holding a 3,000 lbs load is pushed on casters around the shop floor. It is accidently pushed into an immovable stop. What is the impact load on the cart?

I'm designing a cart holding a 3,000 lbs load that will be pushed around the shop floor. One structural load I am concerned about is if the operator pushes the cart into a rigid stop, how much load will that impart to the cart? I realize calculating the g-load is a very complicated problem depending not just on the initial velocity, but the stiffness of the entire system. So I think I'd like to make a good conservatives assumption for the max deceleration during the impact. In the past I've used a 2g impact loads for similar but smaller equipment. However a 2g load in this situation is an enormous load that may be overly conservative. What do you think is a reasonable g-load? What do heavy shop cart manufactures use for a "crashing" g-load.

I'm assuming an initial velocity is a typical walking speed of 3mph or 4.4 ft/s, which is conservative as they usually go slower than this.

Edit: The 3,000 lbs mass on the cart is bolted to the cart.
Thank you.

 

[erobz]

Nothing is immovable in reality, lets talk about the properties of what it is going to hit worst case?

 

[DTM]

Nothing is immovable in reality, lets talk about the properties of what it is going to hit worst case?

I would say worst case, I imagine they could hit a step in the foundation around a building column. I would say that is easily 10x more ridged than the cart and load. So for the purpose of calculations we can assume the thing they hit is immovable, and the cart and load will stretch/flex as it comes to a stop.

I believe auto makers make the same assumption when they crash cars into an "immovable wall". It's a big steel plate with tons of concrete behind it. The car crushes so much more than the wall moves, for all intents and purposes it can be considered immovable.

 

[erobz]

I would say worst case, I imagine they could hit a step in the foundation around a building column. I would say that is easily 10x more ridged than the cart and load. So for the purpose of calculations we can assume the thing they hit is immovable, and the cart and load will stretch/flex as it comes to a stop.

I believe auto makers make the same assumption when they crash cars into an "immovable wall". It's a big steel plate with tons of concrete behind it. The car crushes so much more than the wall moves, for all intents and purposes it can be considered immovable.

Ok, so you want to then consider the cart as elastic. My point was that something has to be elastic if you want to calculate a force other than $\infty$

 

[jack action]

If you assume the kinetic energy ($\frac{1}{2}mv^2$) is absorbed by the deformation of the cart ($\frac{1}{2}kx^2 = \frac{1}{2}Fx$), then you get the maximum impact force:
$$F= \frac{mv^2}{x}$$
Or:
$$\frac{a}{g}= \frac{v^2}{xg}$$
Where $x$ is the amount of deformation for the cart on impact.

According to this, you need a cart deformation of 3.5" to get only a 2g load. I don't think it is conservative at all unless you have big pneumatic wheels.

More info

 

[DTM]

Ok, so you want to then consider the cart as elastic. My point was that something has to be elastic if you want to calculate a force other than $\infty$

Yes. Agreed, the cart must be elastic as it can't stop instantly or that would take infinite force. The cart would actually not be too hard to calculate the elasticity of, but the part ON the cart (The 3000 lbs load) is actually a complicated machine that I think might be very difficult to calculate the elasticity of. Now that you got me thinking more, maybe the stiffness of the cart alone would be enough to show I could go from 3mph to zero in an amount of time that would limit my g-load to under a certain amount. I'll try that.
Thx.

 

[hutchphd]

I don't think it is conservative at all unless you have big pneumatic wheels.

Absolutely. And because the cart itself will flex the g-load will be different for different parts of the cart/load. The OP should realize that making a "scientific" guess is still just making a guess. The margin for error is still huge and the design needs to allow for that. Or real data is required.

 

[erobz]

Absolutely. And because the cart itself will flex the g-load will be different for different parts of the cart/load. The OP should realize that making a "scientific" guess is still just making a guess. The margin for error is still huge and the design needs to allow for that. Or real data is required.

Well, trying to calculate the strain energy assuming not excessive deflection, should be better than "I think it will stop in $0.1~\rm{s}$, or $0.01 ~\rm{s}$, etc...?

I was under the impression that everything in science is really "just a guess"- albeit a "scientific one".

 

[hutchphd]

What does that mean? A scientific guess without good data is simply speculation.

 

[berkeman]

the part ON the cart (The 3000 lbs load) is actually a complicated machine

If the complicated machine could get damaged by a very abrupt stop of the cart, and if you think it's possible/likely to happen occasionally, maybe consider putting a safety bumper mechanism on the leading end of the cart. Something like a bumper with shock absorbers that will spread out the impact time to lower the peak acceleration.

Is this cart powered? 3000 pounds is a lot for a single person to be pushing around a shop floor, it seems.

 

[erobz]

What does that mean? A scientific guess without good data is simply speculation.

"What is good data" is speculation in and of itself. I just mean, use the best model one can (presumably with the best data you have). I think strain energy is better than the alternative "guess a time for it to stop" is all I'm saying. There is theory that is developed for impact loading using strain energy.

 

[hutchphd]

My grandpa (a civil engineer) used to remind me that a little knowlege is a dangerous thing: a theory that may be better than a bad theory is not a good theory.

 

[erobz]

My grandpa (a civil engineer) used to remind me that a little knowlege is a dangerous thing: a theory that may be better than a bad theory is not a good theory.

I'm not going to argue with that, but that's not the theory's fault. Application is seldom straightforward (easy).

 

[hutchphd]

I am not blaming the theory. I am worrying about a (false) sense of security obtained by its (possibly) improper application. Bad engineering is worse than no engineering.

 

[erobz]

I am not blaming the theory. I am worrying about a (false) sense of security obtained by its (possibly) improper application. Bad engineering is worse than no engineering.

As an engineer seeing what its like in the trenches... a very large portion of "real world" problem solving is completed with a tenuous grasp on an application of a theory...or most times...no theory at all.

 

[DTM]

If the complicated machine could get damaged by a very abrupt stop of the cart, and if you think it's possible/likely to happen occasionally, maybe consider putting a safety bumper mechanism on the leading end of the cart. Something like a bumper with shock absorbers that will spread out the impact time to lower the peak acceleration.

Is this cart powered? 3000 pounds is a lot for a single person to be pushing around a shop floor, it seems.

The machine is complicated, but pretty robust. It's been tipped over on it's side (about a 4 foot fall) by shippers and survived. So I think it could handle a 2g shock load pretty easily. But the bumpers is not a bad idea. As for pushing around 3,000 lbs machine, we do it by hand all day long. On 4, 8" hard casters, it's surprising easy on a nice hard shop floor. We do it all day long.

 

[Tom.G]

With the Center-Of-Gravity that far above the impact point at the wheels, load inertia will likely raise the rear wheels of the cart as the load keeps moving.

Paging @jrmichler to suggest the needed bumper deceleration characteristics to avoid the rear cart wheels coming down on the operators foot.

Cheers,
Tom

 

[256bits]

The machine is complicated, but pretty robust. It's been tipped over on it's side (about a 4 foot fall) by shippers and survived. So I think it could handle a 2g shock load pretty easily. But the bumpers is not a bad idea. As for pushing around 3,000 lbs machine, we do it by hand all day long. On 4, 8" hard casters, it's surprising easy on a nice hard shop floor. We do it all day long.

It's not so surprising what one can do just by trying.

 

[256bits]

they could hit a step in the foundation around a building column. I would say that is easily 10x more ridged than the cart and load. So for the purpose of calculations we can assume the thing they hit is immovable, and the cart and load will stretch/flex as it comes to a stop

You should have collision guards around columns for their own protection.

TL;DR Summary: A cart holding a 3,000 lbs load is pushed on casters around the shop floor. It is accidently pushed into an immovable stop. What is the impact load on the cart?

I'm assuming an initial velocity is a typical walking speed of 3mph or 4.4 ft/s, which is conservative as they usually go slower than this.

Can the operator not see over the machine where they are going?
If manipulating in tight spaces, the 3mph is a bit excessive.
Perhaps a half day hands on training course expressing the importance of safety within the workplace.
Cuz if they keep on running into hard solid objects, imagine what running into and over a human would do with 3000 pounds coming at them.

 

[DTM]

You should have collision guards around columns for their own protection.Can the operator not see over the machine where they are going?
If manipulating in tight spaces, the 3mph is a bit excessive.
Perhaps a half day hands on training course expressing the importance of safety within the workplace.
Cuz if they keep on running into hard solid objects, imagine what running into and over a human would do with 3000 pounds coming at them.

The machine on the cart is about 4.5 feet tall. If someone is moving it from the assembly department to the shipping department, I can see them accidently hitting something low on the ground. For example if they are going around a building column and cut it too close. They're usually pretty careful, but I can see an accident happening and I don't want the cart to fail catastrophically dumping the machine over and potentially landing on another person.

 

[jrmichler]

With the Center-Of-Gravity that far above the impact point at the wheels, load inertia will likely raise the rear wheels of the cart as the load keeps moving.

The cart with the load has a center of mass, and is supported by four wheels. Simplifying to a two dimensional problem results in a free body diagram as follows:

Since we want to know the acceleration that causes the rear wheels to raise, the force on those wheels is zero. Adding the necessary dimensions, and taking the sum of moments about the front wheels, we can calculate the acceleration. Knowing the velocity and acceleration, we calculate the stopping distance and force.

The next step is to go to a catalog of industrial shock absorbers, such as https://www.acecontrols.com/us/products/automation-control.html. There are other manufacturers, but this is the one that came to mind first. You will need to know the moving mass, the velocity, and the duty cycle. Shock absorbers are sized by kinetic energy, momentum, and energy dissipated per time.

 

[DTM]

If you assume the kinetic energy ($\frac{1}{2}mv^2$) is absorbed by the deformation of the cart ($\frac{1}{2}kx^2 = \frac{1}{2}Fx$), then you get the maximum impact force:
$$F= \frac{mv^2}{x}$$
Or:
$$\frac{a}{g}= \frac{v^2}{xg}$$
Where $x$ is the amount of deformation for the cart on impact.

According to this, you need a cart deformation of 3.5" to get only a 2g load. I don't think it is conservative at all unless you have big pneumatic wheels.

More info

Looking at this line of thinking, and putting these equations into a spreadsheet, I've come across a common engineering dilemma regarding impacts. The stronger you make it, the stiffer it is, the higher force of the impact, and the stronger it needs to be. I've come to the conclusion that crashing a 3,000 lbs object, even at 3mph, into a ridged object, will result in yielding of something. This makes it obvious why cars need "crumple zones" So now I'm looking at going from fairly quick and easy elastic FEA, to elastic-plastic FEA which is far from quick and easy. If I go this route, I think I need to prove that the crash will damage and permanently deform the cart, but even in that condition, the cart will not tip enough to make the machine dump over. This may be more easy to build and test then to do an analysis I'm confident in.
Thanks all for the thoughts and discussion.

 

[DTM]

The cart with the load has a center of mass, and is supported by four wheels. Simplifying to a two dimensional problem results in a free body diagram as follows:
View attachment 325946

Since we want to know the acceleration that causes the rear wheels to raise, the force on those wheels is zero. Adding the necessary dimensions, and taking the sum of moments about the front wheels, we can calculate the acceleration. Knowing the velocity and acceleration, we calculate the stopping distance and force.

The next step is to go to a catalog of industrial shock absorbers, such as https://www.acecontrols.com/us/products/automation-control.html. There are other manufacturers, but this is the one that came to mind first. You will need to know the moving mass, the velocity, and the duty cycle. Shock absorbers are sized by kinetic energy, momentum, and energy dissipated per time.

I like this analysis, and I can see if the rear of the cart did hop up, that would be one way of dissipating the kinetic energy over a longer period of time and lowering the impact load. However, the exact geometry of this cart/machine is actually lower than shown in the sketch and I think this is unlikely. I will do the analysis and find out though.
I do like the shock absorbers idea.

 

[erobz]

The cart is going to tip if you lose a caster in the impact...I would look there. How much force causes a caster failure?

 

[berkeman]

In some places I've worked, we were required to pull carts instead of push them, to avoid the types of collisions you are talking about. Can such a rule be implemented at your workplace, to better protect the cart and machine (and people)?

EDIT/ADD -- Hmm, I wish I could remember where it was that pulling the carts was required. Searching now for Push versus Pull seems to universally turn up Pushing as better, since it is easier on your back...

https://lni.wa.gov/safety-health/_docs/PushDontPull.pdf

 

[DTM]

The cart is going to tip if you lose a caster in the impact...I would look there. How much force causes a caster failure?

Very good point. The caster may be the weak point. We may need to test one to see what kind of load causes failure and what that failure looks like. Thank you.

 

[DTM]

In some places I've worked, we were required to pull carts instead of push them, to avoid the types of collisions you are talking about. Can such a rule be implemented at your workplace, to better protect the cart and machine (and people)?

EDIT/ADD -- Hmm, I wish I could remember where it was that pulling the carts was required. Searching now for Push versus Pull seems to universally turn up Pushing as better, since it is easier on your back...

https://lni.wa.gov/safety-health/_docs/PushDontPull.pdf

Interesting thoughts. We'll have some discussions EHS and the assembly department.

 

[TonyStewart]

When I was Test Engineering Mgr at Unisys in the 80's we made 6ft tall cabinets on caster wheels for servers filled with 8" disk drives. Part of the design was pass this test and several different heavy duty casters failed this test before ones were found to withstand the forces, although they did not with as much as your cabinet. It was equivalent to an inclined ramp slip into an end-stop.

After hundreds of drop tests with different objects and accelerometers, I discovered a formula for calculating the average g level of any drop test due any height due to gravity compared to the compression stop distance. The best case was an elastic stop for constant g.

The formula is ;
shock = a [g] = drop height / stop height. and the time duration is controlled by mass.

The equivalent drop height for this speed is;
h = (v^2)/(2g)

where h is the drop height, v is the velocity of the object, and g is the acceleration due to gravity (approximately 32.2 ft/s^2).

Plugging in the value of v = 4.4 ft/s, we get:

h = (4.4^2)/(2 x 32.2) = 0.34 feet = 4 inches

Thus if the caster & bearings collapse by 40 thou, the shock level is 4.000/0.04 = +100 g's (pretty harsh) but it still has to roll after ....

If you go on an amusement ride free-fall from 10 stories and the smooth ride stops in the same distance as they do in Amusement parks then the shock level after the cart is pushed over the edge on the track a=10/10 = +1 g. First -1g during freefall then + 1g during brake time. (which is pretty smooth) ( ok a= sqrt {1x+1y} during transition)

 

[bdrobin519]

TL;DR Summary: A cart holding a 3,000 lbs load is pushed on casters around the shop floor. It is accidently pushed into an immovable stop. What is the impact load on the cart?

I'm designing a cart holding a 3,000 lbs load that will be pushed around the shop floor. One structural load I am concerned about is if the operator pushes the cart into a rigid stop, how much load will that impart to the cart? I realize calculating the g-load is a very complicated problem depending not just on the initial velocity, but the stiffness of the entire system. So I think I'd like to make a good conservatives assumption for the max deceleration during the impact. In the past I've used a 2g impact loads for similar but smaller equipment. However a 2g load in this situation is an enormous load that may be overly conservative. What do you think is a reasonable g-load? What do heavy shop cart manufactures use for a "crashing" g-load.

I'm assuming an initial velocity is a typical walking speed of 3mph or 4.4 ft/s, which is conservative as they usually go slower than this.

Edit: The 3,000 lbs mass on the cart is bolted to the cart.
Thank you.

Possibly a elastic or absorbable mechanism with surrounding bumpers. I have the same problem at work but 3000 lbs. doesn't seem to roll by itself. Actually there's an idea, adjustable brakes to resist the inertia.

 

[256bits]

The machine on the cart is about 4.5 feet tall. If someone is moving it from the assembly department to the shipping department, I can see them accidently hitting something low on the ground. For example if they are going around a building column and cut it too close. They're usually pretty careful, but I can see an accident happening and I don't want the cart to fail catastrophically dumping the machine over and potentially landing on another person.

But not careful enough if they are clipping.
Then a half day course on safety at the workplace is definitely in order.
The idea is to prevent, and at the very least minimize the chances of, accidents from ever occurring,
If you are worried what would happen to the machine and anyone around if it bangs into something, then STOP ever the operators from being careless.

Make reports if the machine does clip a column and follow up.
Have a discussion with the individuals involved on why the clipping occurred and what can be done to prevent occurrences in the future. Move the machine only on clear pathways. Line the floor with yellow paint to make a path on which the machine can be moved. Make sure the path is always clear and no one else puts anything on the path even for a second. Have a horn on the machine and a flashing light to cause attention to the machine when being moved. Perhaps you have a forklift running around the place. One would not want a forklift hitting the machine either.

Have a maintenance schedule to be applied to the machine and its carriage.
Are the bolts tight and secure so the machine is tight on its platform.
Check the wheels and bearings for wear and even running.
One wheel falling off will tilt the machine, and could even tilt it over if at 'high speed'.

Make a log book, for the operator to sign when moving and from where and to destination.
Have a check off for any occurrences - ie wobbly wheel, path not clear, ...
A reason for this is to
- a fall back reference ie 99 days without occurrence type of thing.
- an emphasis on the being safe being put into the minds of the operators.

You are right to attempt a "what would happen in a collision", and this could be used to show to the operators what could happen when not full attention is given to the task at hand.