What is the Maximum Speed Limit for a Linear Shaft in Reciprocating Motion?

[Sam Safe]

Hi all.
I am not a mechanical engineer but I've been working on an idea which consists of a linear shaft with Reciprocating motion.
Since the device only works with rather a high speed shaft, I wanted to know what are the speed restrictions of a linear shaft?
So let's give it some numbers.
The Shaft is 5m long.
The travel distance is about 2m.

Would I be able to get the shaft up to the speed of 100m/s or higher? in other words that would be approximately 1500 rpm.

Please note that the shaft diameter or the engine's output is not the issue here but I would be glad to read your insights on these matters also.

I simply want to know if there are any mechanical restrictions for a shaft this size.

 

[Tom.G]

I simply want to know if there are any mechanical restrictions for a shaft this size.

Yes. The 'Critical Frequency' (resonant frequency) must be avoided. https://www.google.com/search?source=&q=shaft+critical+speed+calculator
Also search without the word 'calculator.'

EDIT: That is for rotational speed of a shaft. After reading @CWatters response, I see I may have mis-interpreted your description.

 

[CWatters]

The nearest thing I can think of to this is the reciprocating parts of a steam railway engine. I recall reading somewhere that there were issues with them going more than about 500-600 rpm and that this limited how fast trains could go unless the wheels were made bigger.

 

[Sam Safe]

The nearest thing I can think of to this is the reciprocating parts of a steam railway engine. I recall reading somewhere that there were issues with them going more than about 500-600 rpm and that this limited how fast trains could go unless the wheels were made bigger.

Thanks for your reply.
any suggestion on what to search? Because no matter what I search for, I end up with some rotating shaft results.

 

[Tom.G]

Not an expert in mechanics, but here is a possible approach to get things started.

If the motion is strictly axial, find the peak axial force during acceleration/decelleration and keep that below the buckling force of the shaft. Of course any vibration not on-axis will introduce a bending force.

 

[JRMichler]

We need a diagram. Is one end attached to a crankshaft like a connecting rod? If so, the answer will include calculations for shaft bending, shaft peak tension load, shaft peak compression load. and bearing loads. These are all calculated, and the answers are specific to your system.

 

[Sam Safe]

One end of the shaft is connected to a power source and the other end is free.
The mechanism or the engine type are not the issue here and they can change.
When the shaft is moving up there is almost no load on the shaft except for the weight of the shaft.
But when it is moving down there is almost a load of 9000 N in the opposite direction.

As I mentioned before I am not a mechanical engineer and what I am seeking is a general answer to whether it is possible to reach such speeds in a linear shaft? And is there any example in the industry for such a long shaft with that kind of speed?

 

[CWatters]

Google found..
http://www.epi-eng.com/piston_engine_technology/comparison_of_cup_to_f1.htm
..which says..

the peak piston speed (table line 30) for the Cup engine is actually 5% greater than that of the Formula One engine at redline (44.6 m/sec vs. 42.4 m/sec)

So you want your shaft/piston to go about twice as fast?

 

[CWatters]

When the shaft is moving up there is almost no load on the shaft except for the weight of the shaft.

You have to accelerate and stop that shaft. To go from 0 to 100m/s and back to 0 in 2m requires an acceleration of about 5000m/s². If the shaft weighs 10kg the force required is 50,000N.

 

[Sam Safe]

You have to accelerate and stop that shaft. To go from 0 to 100m/s and back to 0 in 2m requires an acceleration of about 5000m/s². If the shaft weighs 10kg the force required is 50,000N.

Thanks for your reply.
But the correct acceleration and force needed would be 2500 m/s² and 25000N and since it is still too high it does not make a difference.

What about 50m/s? The acceleration we need is about 625m/s² and the force would be 6250 N.

Is it possible?

 

[JRMichler]

It's more complex than that. You have a simple crank slider mechanism (google the term). There is a lot more involved that just the acceleration of the rod. Below is a partial list of calculations that need to be done just figure out if this mechanism is possible. It is not a complete list.

Calculate rod acceleration, given the input RPM and rod length ratio. Google "piston motion equations".
Calculate force to accelerate the rod.
Calculate external forces on rod (load forces, what the rod is driving).
Calculate force on the connecting rod. It's higher than the total of the above rod forces because of the angle.
Calculate forces on rod bearings.
Calculate peak rod bending moment as a function of crank angle and bearing locations. The connecting rod is pushing at an angle, so it's bending the slider rod.
Calculate rod bending stress.
Calculate rod tensile / compressive stress.
Calculate peak rod stress from tensile and bending stresses.
Calculate forces on connecting rod bearings as a function of crank position.
Calculate bearing loads on crank, stresses in crank and connecting rod.
If any stresses are larger than allowable, redesign as needed. Repeat calculations. Expect to go through this loop several to many times.
Calculate minimum crank inertia.
Calculate foundation forces.
Design foundation.

This is just enough to show proof of concept - whether it can be done or not. If you wanted to actually build, further work is needed. Keep in mind safety. If that heavy rod comes loose at 100 m/sec, or even 50 m/sec, it will go right through a person or concrete block wall.

 

[Nik_2213]

It is so going to wriggle, whip and writhe, and that without resonances. Linear bearings would be essential.

Digs in pre-WW1 'Devices' book...
Aha ! You should not use a simple drive-rod lest it flex. A tube would be better. You may need a tapered truss for rigidity and strength.

Um, IIRC, you may be able to fit truss with lateral dampers, such as an oil-filled tube with a heavy, but porous free-piston...

 

[berkeman]

Thread closed temporarily for Moderation...

 

[berkeman]

Thread re-opened. Thanks for your patience.

 

[JRMichler]

It's time to perform some simple harmonic motion (SHM) calculations, with some preliminary force calculations. All of these calculations are extremely simplified for the purpose of establishing orders of magnitude. The OP originally mentioned 2 meters peak to peak, and 100 meters per second. Plug the knowns into the equations for position, velocity, and acceleration:

Position = 1 cos $\omega$t
Velocity = 1 $\omega$sin$\omega$t
Acceleration = 1$\omega^2$cos$\omega$t

I'm ignoring the negative signs because we only need the peak magnitudes. The peak velocity is 100 m/sec, so the angular frequency is 100 rad/sec^2 = 15.9 per second = 955 RPM on the crankshaft.

The peak acceleration is then $\omega^2$ = 10,000 m/sec^2. Divide 10,000 m/sec^2 by 9.8 = 1020 G's. A more complete analysis would now calculate the effect of rod length ratio (RLR). The RLR will increase the peak acceleration.

If the 5 meter rod with its wrist pin bearing weighs 100 kg, then the force on the wrist pin bearing is 100 X 10,000 = 1E6 Newtons (roughly 200,000 lbs, or 100 tons). The connecting rod needs to be strong enough to carry that force, plus the acceleration forces from its own weight, plus the bending loads due to its own weight and the acceleration perpendicular to the connecting rod. The 9,000 N external load disappears into the noise in this concept calculation. If the connecting rod with wrist pin bearing and big end bearing weighs 900 kg, then the force on the big end bearing and crankshaft is (100 + 900) X 10,000 = 1E7 Newtons (roughly 2,000,000 lbs, or 1000 tons).

Note that the weights for the 5 meter rod and the connecting rod are WAG's. If it was desired to pursue this mechanism, the next step would be to design a concept 5 meter rod based on the above acceleration adjusted for estimated RLR, a concept wrist pin bearing assembly and lubrication system, a concept connecting rod, and a concept big end bearing and lubrication system. Then recalculate forces, and iterate until the concept design converges.

 

[JRMichler]

Now that we know that unbalance forces are roughly 1000 tons at 16 Hz, it's time to look at a foundation for this mechanism. If we arbitrarily choose to make a concrete foundation that weighs 1000 tons (roughly 500 yards of concrete), it would be a cube just under 24 feet on a side. If the mechanism moves vertically, that cube would hop up and down. If the mechanism moved horizontally, the cube would skid and rock back and forth.

A 10,000 ton (5,000 yards of concrete) could be 30 feet thick by 65 feet square. It would not hop up and down, or skid back and forth. But it would be a very effective Earth shaker. An Earth shaker of that size could trigger soil liquefaction. Google earthquake soil liquefaction for some very good examples and photos.

It would also be noisy. The 65 foot square concrete base would be a big speaker radiating noise at 16 Hz and 32 Hz (the second harmonic is from the effects of RLR). Low frequency noise carries a long distance. Between the ground shaking, possible soil liquefaction, and noise, you would make lots of enemies. Some of whom would be very expensive lawyers.

If we knew more about what the OP really wants to accomplish, it's possible that a practical mechanism could be proposed.

 

[Sam Safe]

Now that we know that unbalance forces are roughly 1000 tons at 16 Hz, it's time to look at a foundation for this mechanism. If we arbitrarily choose to make a concrete foundation that weighs 1000 tons (roughly 500 yards of concrete), it would be a cube just under 24 feet on a side. If the mechanism moves vertically, that cube would hop up and down. If the mechanism moved horizontally, the cube would skid and rock back and forth.

A 10,000 ton (5,000 yards of concrete) could be 30 feet thick by 65 feet square. It would not hop up and down, or skid back and forth. But it would be a very effective Earth shaker. An Earth shaker of that size could trigger soil liquefaction. Google earthquake soil liquefaction for some very good examples and photos.

It would also be noisy. The 65 foot square concrete base would be a big speaker radiating noise at 16 Hz and 32 Hz (the second harmonic is from the effects of RLR). Low frequency noise carries a long distance. Between the ground shaking, possible soil liquefaction, and noise, you would make lots of enemies. Some of whom would be very expensive lawyers.

If we knew more about what the OP really wants to accomplish, it's possible that a practical mechanism could be proposed.

Thanks @JRMichler for taking the time and your detailed answer.

From what understood so far since I am not using this for soil liquefaction (lol) and the fact that it should be mobile, the use of a steel(or any other metal) shaft is out of question.

Since my goal is to use a conventional engine to the shaft moving, the only possible solution that comes to my mind is using a super-light super-strong material for the shaft. The first thing that came up to my mind was carbon fiber. I know that carbon fiber has a lot of tensile strength but I'm not sure about the compressive strength. Besides I am not sure if it is the right material for this application due to its fragility.

I know that carbon fiber shafts are already being used in race cars and etc. but those are rotating shafts and are completely different than this linear reciprocating shaft.

So if I wanted to choose a material for this to work what be my best bet?

 

[JRMichler]

Don't be offended by what I'm saying in this post, but this is getting beyond what PF is all about. You clearly are in way over your head on this mechanism, and need to start thinking in terms of bringing an engineer into this project. What you have here is beyond the capabilities of most mechanical engineers. You need somebody that understands how to design, build,and test high speed mechanisms. And do it safely.

Much as I would like to continue this, it's time for me to cut it off before a moderator closes the thread. I'm sorry. I really like these sort of challenging problems. It's why I have 19 patents.

FYI, a consultant that knows his/her stuff will charge mid five figures just for a concept design, and will into six figures for a fully engineered system with parts drawings. That's just for the engineering of the first prototype. Manufacturing, assembly, testing, and modifications will cost considerably more. You can count on several rounds of modifications.

 

[Sam Safe]

Don't be offended by what I'm saying in this post, but this is getting beyond what PF is all about. You clearly are in way over your head on this mechanism, and need to start thinking in terms of bringing an engineer into this project. What you have here is beyond the capabilities of most mechanical engineers. You need somebody that understands how to design, build,and test high speed mechanisms. And do it safely.

Much as I would like to continue this, it's time for me to cut it off before a moderator closes the thread. I'm sorry. I really like these sort of challenging problems. It's why I have 19 patents.

FYI, a consultant that knows his/her stuff will charge mid five figures just for a concept design, and will into six figures for a fully engineered system with parts drawings. That's just for the engineering of the first prototype. Manufacturing, assembly, testing, and modifications will cost considerably more. You can count on several rounds of modifications.

Not offended my friend.
And as I said before your help was much appreciated.

I am not trying to design, build or test anything here and as I mentioned from the start I wanted to know if it is possible or not and why! and even if I had a six figure to spend I wouldn't until at least I knew if there is a high chance that is possible.

So once again I thank everyone who participated in answering to this thread.
It was a great help for me.

 

[CWatters]

9000N at 100m/s is 900,000 Watts. Allowing for some losses were talking over a megawatt or the wrong side of 1000HP. Ok so that's not a very accurate figure but hey ho.

What's the application? Perhaps there is a better way?