Mechanical Engineering
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# Pendulum Hammer Impact Force Calculation

## Question

Hi all,

I'm a bit embarrassed but I'm extremely rusty with a lot of engineering principles. I've mainly been working in automation and controls within a manufacturing setting and have not done anything like this in ages. Anyways, I have a problem I need to solve and I need to determine the impact force in Gs exerted on the Anvil table by the hammer in the attached image. Some guidance in how to solve this problem/sources of where I can find additional material to refresh on this is greatly appreciated.

Thanks!!

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Gabe, I found the attached article on the 'net. I have not read it through, but I'll bet it has some information for you. The internet also has tons of other information on this machine.

DrD

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By conservation of energy, we can give a pretty good estimate for the speed at which the hammer approaches the underside of the anvil. This assumes good bearings, negligible air friction, etc.

But after that, you have an impact problem and we need to know what appens to the hammer and anvil after impact. Do they stick together? Do they separate, with the anvil moving up while the hammer moves down? If they separate, what is the coefficient of restitution?

Let me also note that force is never measured in g's. A g-value is an acceleration, not a force.

I suggest that you look in a good elementary mechanics text under "Impact." Beer & Johnston is the text I would suggest, but there are many that will do.

DrD

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3 minutes ago, DrD said:

By conservation of energy, we can give a pretty good estimate for the speed at which the hammer approaches the underside of the anvil. This assumes good bearings, negligible air friction, etc.

But after that, you have an impact problem and we need to know what appens to the hammer and anvil after impact. Do they stick together? Do they separate, with the anvil moving up while the hammer moves down? If they separate, what is the coefficient of restitution?

Let me also note that force is never measured in g's. A g-value is an acceleration, not a force.

I suggest that you look in a good elementary mechanics text under "Impact." Beer & Johnston is the text I would suggest, but there are many that will do.

DrD

Thank you for your reply. I will take a look at the source you've suggested.

Thank you also for clarifying my confusion in the force/g mix-up.

To answer your question, in this problem you can negate the friction from the bearing, air drag, etc. The hammer is released from a certain angle above the horizontal plane and it then swings and impacts on the bottom of the anvil. The anvil and hammer then separate, with the anvil traveling straight vertically and the hammer swinging back down and stopped with a brake. The anvil is free to travel upwards until it is stopped at some x distance.

The parameters of this problem are very vague and the goal is to get an estimate of the g-value the anvil will experience in this set up.

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The anvil is supported, but not fixed in the vertical direction? So when it is struck it will be propelled up?

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Just now, JAG Engineering LLC said:

The anvil is supported, but not fixed in the vertical direction? So when it is struck it will be propelled up?

That is correct. Not fixed, however it is limited to some x distance travel in the vertical direction. To clarify what I would like to calculate, it is the max G experienced by the anvil after impact. Does that clarify your question?

This is ultimately a shock test to determine if whatever is placed on the anvil can withstand a high G value. Really only looking to know the max Gs experienced by the anvil. Honestly, the information I have is limited to what I've given, but I may be looking it at incorrectly or trying to figure out an answer that can't be obtained with the information given.

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Here's a video of this type of test being done for reference.

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This looks like a standard military shock test. If that is the case, there should be standards that provide the necessary information in tabular form.

DrD

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Dr D can likely tell you what to do off the top of his head. (TOLD YOU SO, JUST SAW DR D's REPLY) I would need to refresh myself on this. Conservation of momentum may be the best approach. Now that we know the anvil can move, (anvils as used by a blacksmith don't), the g question makes sense but still many issues. If the hammer is one ounce and the anvil a ton, the anvil will not move for all practical applications. Switch the weight values and the anvil will take off like a rocket. Make either out of a compliant material and the answer will once again be different.

You will need to know the mass of the hammer and anvil. If you neglect mechanical friction and air drag, you will arrive a velocity greater than actual. By how much I don't know without running numbers. If you are designing to protect for max impact then that approach will provide some margin. If you must apply a minimum g load as part of a test this would not be a good approach.

From the video the anvil is pretty complicated with springs. The g loading will be one value for the base being struck and less for the spring mounted upper section.

Your first cut would be to use m1 x dv1 = m2 x dv2. ( for greater detail https://www.physicsclassroom.com/class/momentum/Lesson-2/Momentum-Conservation-Principle) Calculate the velocity of the hammer at impact. Measure the weight of the hammer and anvil. From above you get dv2 (speed of anvil) but this too has a wide range due to many variable. Assuming ideal conditions gives you a ballpark number. Depending on how close you need to be will depend on how close you need to mathematically model the system.

It may be a lot easier and more accurate to use instrumentation. Or as Dr D suggested the info may exist in some spec.

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9 minutes ago, DrD said:

This looks like a standard military shock test. If that is the case, there should be standards that provide the necessary information in tabular form.

DrD

This particular test is MIL-DTL-901e. The information given within the standard is essentially what I have provided. No detailed drawings of the shock machine showing complete dimensions, no information on materials of the hammer/anvil, no spring coefficients, really no information to allow you to fully model this test. That is why I will settle for ballpark numbers. But I appreciate you taking the time to try to assist me in this problem.

7 minutes ago, JAG Engineering LLC said:

Dr D can likely tell you what to do off the top of his head. (TOLD YOU SO, JUST SAW DR D's REPLY) I would need to refresh myself on this. Conservation of momentum may be the best approach. Now that we know the anvil can move, (anvils as used by a blacksmith don't), the g question makes sense but still many issues. If the hammer is one ounce and the anvil a ton, the anvil will not move for all practical applications. Switch the weight values and the anvil will take off like a rocket. Make either out of a compliant material and the answer will once again be different.

You will need to know the mass of the hammer and anvil. If you neglect mechanical friction and air drag, you will arrive a velocity greater than actual. By how much I don't know without running numbers. If you are designing to protect for max impact then that approach will provide some margin. If you must apply a minimum g load as part of a test this would not be a good approach.

From the video the anvil is pretty complicated with springs. The g loading will be one value for the base being struck and less for the spring mounted upper section.

Your first cut would be to use m1 x dv1 = m2 x dv2. ( for greater detail https://www.physicsclassroom.com/class/momentum/Lesson-2/Momentum-Conservation-Principle) Calculate the velocity of the hammer at impact. Measure the weight of the hammer and anvil. From above you get dv2 (speed of anvil) but this too has a wide range due to many variable. Assuming ideal conditions gives you a ballpark number. Depending on how close you need to be will depend on how close you need to mathematically model the system.

It may be a lot easier and more accurate to use instrumentation. Or as Dr D suggested the info many exist in some spec.

I will take a look at the link you suggested and see if I can produce some numbers. I appreciate your response. It definitely would be useful if there were some available values in the spec and if I had access to a machine to use an accelerator to get readings would be ideal, but I don't have access to one.

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Picture of test machine for reference

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Ah, Gabe! I knew I had seen that figure before, but I certainly did not remember the mil-spec designation!

Sadly, really nothing is conserved all the way through the motion. Energy is conserved before the impact and after the impact, but energy is not conserved during the impact. This is where the coefficient  of restitution stuff comes in.

I would strongly suggest that you keep looking for more definition from the military. There has to be a more complete description, because without such, you cannot possibly have a standard test. If everybody has a different test machine, there is nothing standardized or comparable about the results.

DrD

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13 hours ago, DrD said:

Gabe, I found the attached article on the 'net. I have not read it through, but I'll bet it has some information for you. The internet also has tons of other information on this machine.

DrD

I guess I really didn't search hard enough. Thanks for finding this! I noticed in the paper that it refers to it as MIL-DTL-901D and I was looking for 901e. The difference being that the 901e is the most recent updated version, I didn't think to look for 901d. Again, thanks for the help, it's very much appreciated. This definitely will help me.

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For future reference for anyone that comes across this post or is interested in more information. I came across this paper from 1972 by EW Clements: https://apps.dtic.mil/dtic/tr/fulltext/u2/746444.pdf "Shipboard Shock and Navy Devices for its Simulation", which goes into detail and actually measures impact velocities, peak anvil acceleration, and other relevant information.

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Looks like you now have enough reading material to keep you busy for quite a while! I notice that, as usual, the quality of the document from DTIC is dismal; they must have the worst Xerox machines in captivity.

DrD

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4 hours ago, DrD said:

Looks like you now have enough reading material to keep you busy for quite a while! I notice that, as usual, the quality of the document from DTIC is dismal; they must have the worst Xerox machines in captivity.

DrD

The document quality is pretty horrendous 😂

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Gabe, that's just standard US Government quality service (I'm really quite familiar with it all; I used to work for the US Navy as a civilian).

DrD

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