# Coil Compression Spring Reaction to a Pulse

• Quester
In summary, the pulse has no observable effect on the spring when it is at rest, but when the spring is subjected to a brief, violent pulse, the pulse appears to propagate the length of the spring relatively quickly.

#### Quester

TL;DR Summary
How does a coil spring react to a low amplitude pulse applied to one end?
I am trying to understand the reaction of a steel coil compression spring when pulsed. The spring I am interested in has the following physical characteristics:

k (spring constant in pounds per inch) = 2.88
d (wire diameter in inches) = .043
n (number of active coils) = 29
D (mean diameter of the coil in inches) = .430
Lf (spring free length is inches) = 6.55

The spring is mounted to a fixed plate on one end and a moveable plate on the other. The spring is at rest. It is compressed to a length of 3.75" and held there by the moveable plate. In this condition, the spring is exerting a force of about 8.064 pounds on the plates. If it matters, the moveable plate weighs 19 ounces.

The moveable plate is subjected to a pulse that accelerates the plate at a rate of 29,400 ft/sec^2 for a period of .8 milliseconds (by a force of about 1,091 pounds applied to the moveable plate).

Intuitively, it seems to me that the spring will not have time to react to the pulse, so the presence of the spring has no practical effect on the acceleration of the moveable plate. However, I actually have no idea how to determine the length of time it would take the pulse to propagate the length of the spring.

I will appreciate any and all responses. Just to be clear, I am not looking for a lengthy explanation here. I would like to be pointed in the right direction and a link to some of that information would be greatly appreciated.

Your best approach is to get a copy of the SMI Handbook of Spring Design: https://smihq.org/store/ListProducts.aspx?catid=550000. Then read about spring surge. Another approach is to search coil spring surge.

BTW, the book by Wahl is THE ultimate source for spring theory and calculations, but very few people need more information than is in the SMI Handbook.

Dr.D and Quester
jrmichler said:
Your best approach is to get a copy of the SMI Handbook of Spring Design: https://smihq.org/store/ListProducts.aspx?catid=550000. Then read about spring surge. Another approach is to search coil spring surge.

BTW, the book by Wahl is THE ultimate source for spring theory and calculations, but very few people need more information than is in the SMI Handbook.

Thank you for your prompt response. The handbook looks very interesting. Apparently, I cannot order it because I am not a member and I cannot become a member since I do not meet their membership requirements. I will continue to search and see if I can get a copy through some other venue.

Your suggestion of "surge" is probably going to be helpful. I had tried several variations like "coil spring propagation" and "coil spring pulse delay" with no joy. Maybe "surge" will prove to be the magic word! I do know a little about spring delay because I used mechanical reverberators years ago in audio amplifier design.

Mechanical springs, by A.M. Wahl. Cleveland, O., Penton Pub. Co., 1944.
This work is in the Public Domain and is available from the HathiTrust Digital Library;
http://hdl.handle.net/2027/uc1.\$b76475

Quester
Baluncore said:

I appreciate your attempt to help, but I'm not having any luck at that link, either. If I log in as a guest, it will allow me to download one page at a time. I am not a member of any HathiTrust partner institutions.

Thanks for trying!

Quester said:
Summary:: How does a coil spring react to a low amplitude pulse applied to one end?

Intuitively, it seems to me that the spring will not have time to react to the pulse, so the presence of the spring has no practical effect on the acceleration of the moveable plate. However, I actually have no idea how to determine the length of time it would take the pulse to propagate the length of the spring.
Ideal springs act instantaneously.
A real spring has mass so that has to be considered in practice.

You could start off with lumped model of spring-mass, and determine the differential equation.

Around page 222 they give an explanation.

outlines a torsional spring - you could adapt for a linear system.

Lnewqban and Quester
Thank you 256bits. I will study that lab problem It looks promising.

Thanks to everyone's help, I have found a lot of information on how to compute the lowest resonant frequency of compression coil springs and I have been able to use quite a few of the various formulas and calculators to get consistent results using different approaches.

However, I am still lost in my quest of understanding the dynamics of what I see as being the response of the spring to a very short, violent pulse.

Perhaps my goal will become clearer if I change my original given condition to be:

"The moveable plate is subjected to a pulse that accelerates the plate at a rate of 350,000 ft/sec2 for a period of 60 microseconds (by a force of about 12,000 pounds applied to the moveable plate)."

Any help will be appreciated.

It helps to visualize what's happening before looking for a mathematical solution. I like to use the ESP method - Exaggeration of System Parameters. Think of two cases:

Case 1: The plate is displaced slowly. In this case, the spring force is proportional to the displacement times the spring constant.

Case 2: The plate is displaced almost instantaneously - much faster than the spring can possibly respond. The end turns will compress solid, then a wave will travel down the length of the spring. You can see this for yourself by playing with a Slinky toy (highly recommended to improve understanding).

Now for some calculations. Calculate the velocity reached at the end of the force pulse. You can ignore the spring force for this calculation because it is small compared to the acceleration force. Calculate the distance traveled at the end of the force pulse. Now compare the time to travel that distance to the period of one cycle of the surge frequency, while thinking of Cases 1 & 2 above.

Given the velocity at the end of the force pulse, the spring preload, and the spring constant, calculate how far the plate travels until the velocity decreases to zero. Then think about surge pulses traveling back and forth, and recognize that this calculation is an approximation.

BTW, your numbers for force and duration look very similar to the numbers I came up with when I calculated that the best way to provide a force impulse of defined force and duration to a load cell was to shoot it with a gun of specified caliber and muzzle velocity. The experiment was successful, the oral report well received, after which we found that the professor's hobby was target shooting.

256bits
Thank you for your response, jr. I do often use the consideration of extremes to try to "box in" something with which I have little or no experience.

Last edited:
It's not that simple. The sudden start causes a spring surge. The spring surge is bouncing while the plate is moving, so the spring force on the plate cannot be calculated easily. Any calculations are only a rough approximation. Did you calculate the spring surge frequency for the case of both ends fixed? When one spring end is connected to a mass such that the spring mass natural frequency is lower than the spring surge frequency, the surge frequency is for both ends fixed.

If the purpose of the spring is stop the plate, then the real test is to try and see if it works. The calculations tell whether your choice of spring should do the job, the test tells if it will do the job.

Make sure that the spring is not overloaded when compressed to solid height, because the individual coils are compressing that far during spring surge. Also, if you can find a high speed video, you would find it very interesting to video the spring at 1000 to 2000 frames per second.

256bits
"Did you calculate the spring surge frequency for the case of both ends fixed?"

I calculated the lowest natural frequency for both ends fixed per the example beginning on page 232 of Mechanical Springs by Wahl.

"If the purpose of the spring is stop the plate, then the real test is to try and see if it works."

I wasn't clear in my explanation. The plate is stopped just prior to the spring becoming solid. The spring itself does not stop the plate. Also, I know the spring performs as intended, because the application is repeated millions of times the world over every day.

However, there are many people (most, actually) who believe that the spring plays a material role in slowing the plate. I, and a few others, think that the role of the spring in slowing the plate is minor.

The purpose of my attempted analysis is to test my personal theory that the spring does not even have time to materially oppose the plate until a significant amount of time after the initial pulse. I don't care whether that is true or not, but I would like to have my theory either disproven or deemed reasonable. Either way, I gain understanding. Once I have some understanding of the system, I can (hopefully) engage is some intelligent discussion about it with others.

The actual design purpose of the spring is to absorb energy from the moving plate so that once the plate has expended all its energy by being stopped, the spring can then return the plate to its original position, ready to begin a new cycle. A person is capable of cycling the system at up to 7 cycles per second. The system handles that rate with total reliability.

256bits
Quester said:
Also, I know the spring performs as intended, because the application is repeated millions of times the world over every day.
Now you have me VERY curious (and probably others too).
I hope (beg) you to enlighten us as to the application, even if it is after you get a satisfying, or even unsatisfying, conclusion to this thread.

Thanks,
Tom

jim mcnamara
I will be happy to tell all in the end. For now, I'll just say that your intuition in Post #11 is in the right arena, just looking at it from a different direction. Think internal instead of external.

Here is a sketch of a rough model of the situation (note the two stops on the moveable plate):