Frequency of a spring?

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I need to calculate the frequency of a flat spring. I need to make reed valves for a pulse jet engine.

I read online to use Hooks's Law but this is not working. F = force. x = the amount spring moves. k = spring constant.

I have a flat spring made of .010" spring steel. Spring is .375" wide by 1.250" long.

I have no clue what k is for flat spring steel?

It seems to me Hooke's law does not tell me the frequency of a spring.

If I tie a string to the ceiling that hands down 6' with weight on the end I can get the weight swinging and count the swings per min. No matter how much the weight is changed Hz is the same. If I change the distance of the swing Hz stays the same.

If string is shortened to 3' frequency changes. Now I can do math to calculate frequency if string is 1.250" long.

I don't think my experiment & math applies to metal that is spring steel.

If I cut a sample piece of spring steel, clamp it in the vise, flip the end it is too fast for me to count the Hz I can hear is buzz like a tuning fork.

NEXT the pulse jet engine is 40" long I can use the formula to find the frequency of a tube to get Hz of the tube. It has been 7 years since I worked on this project I don't remember the frequency of the pulse jet engine body which is a tube closed on the valve end.

If the frequency of the tube is 180 Hz the spring steel reed valves also need to be 180 Hz also.

I could probably use some type of electric device that listens to tuning forks to listen to my valve to tell me what the Hz is if there is suck a thing?

After a lot of trial and error I have an engine that runs very well but maybe it could be better. Watch the YouTube video of my engine running. I have run this engine for many hours the valves have no damage and no signs of getting hot. This engine produces 20 lbs of thrust running on propane or gasoline. A mix of 80% gas + 20% diesel engine produces 24 lbs of thrust. Running on methanol 34 lbs thrust. Methanol + 5% water = 34 lbs thrust.

 

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  • #2
ZapperZ
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I need to calculate the frequency of a flat spring. I need to make reed valves for a pulse jet engine.

I read online to use Hooks's Law but this is not working. F = force. x = the amount spring moves. k = spring constant.

I have a flat spring made of .010" spring steel. Spring is .375" wide by 1.250" long.

I have no clue what k is for flat spring steel?

I don't quite understand the problem here. Are you unable to measure the spring constant of your spring, or are you saying that you do not know how to find the spring constant of your spring?

And once you find the spring constant, do you know how to find the natural frequency of the mass-spring system?

Zz.
 
  • #3
berkeman
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I could probably use some type of electric device that listens to tuning forks to listen to my valve to tell me what the Hz is if there is suck a thing?
There are cell phone apps for that... :smile:
 
  • #4
sophiecentaur
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Is there a mass attached to the spring or is it just like a reed, vibrating due to its own mass and its spring constant?
I tried google and eventually found a search term that gives a number of hits that are sort of relevant. I used the terms "cantilever vibration" and this link was one that has what you need to know. There is a formula that gives the natural vibration frequency in terms of the dimensions of the spring and the Modulus of the material. Have a look at it an see if it makes sense.
 
  • #5
sophiecentaur
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But there's nothing in the physics that requires this, as long as F is linear with x.

Again, have you done the experiment? If you have, how far did you stretch the spring? Can the graph of F versus x be represented by a straight line? If it can, then that entire range of x can be used during oscillation.

Now, there may have been other non-physics reason why your teacher do not want you to have the mass oscillate with large amplitudes, especially if the mass is simply resting on a hook. A large oscillation may cause the mass to dislodge off the hook. But this has nothing to do with the physics.

Zz.
The OP is talking about a reed valve, which is, at its simplest, just a cantilever which vibrates. Its period is not 2π√(m/k) but a more complicated formula - found in the link I gave above. It would not behave linearly, I suspect, because of the valve action on the fluid it regulates. (more like a relaxation oscillator) We'd need much more detail from the OP. I don't quite see how the original post contains stuff about a coil spring and a mass . . . . . ? Perhaps the teacher hasn't caught onto what the OP actually has in mind.
 
  • #6
ZapperZ
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The OP is talking about a reed valve, which is, at its simplest, just a cantilever which vibrates. Its period is not 2π√(m/k) but a more complicated formula - found in the link I gave above. It would not behave linearly, I suspect, because of the valve action on the fluid it regulates. (more like a relaxation oscillator) We'd need much more detail from the OP. I don't quite see how the original post contains stuff about a coil spring and a mass . . . . . ? Perhaps the teacher hasn't caught onto what the OP actually has in mind.

I agree that we went off on a tangent, but I was replying to arman777 since Post #5.

Moderator's note: that discussion has been moved to https://www.physicsforums.com/threads/hooks-law.959131/

Zz.
 
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  • #7
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I don't quite understand the problem here. Are you unable to measure the spring constant of your spring, or are you saying that you do not know how to find the spring constant of your spring?

And once you find the spring constant, do you know how to find the natural frequency of the mass-spring system?

Zz.

I don't know how to measure spring constant?

I have to make my own spring from spring steel, how can i find k if spring is not make yet?

Spring Hz has to hatch the Hz of the engine.

I need a way to make a spring the correct Hz?

There use to be online calculators for Hz of a closed 40" tube can not find 1 anymore?
 
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  • #9
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I don't know how to measure spring constant?
That's easy: measure the force required to bend the spring by a given amount. You will find that for sufficiently small deflections the relationship between force and deflection is linear; the constant of proportionality is the spring constant.

What's not easy is calculating the natural frequency from that constant. If you were working with a mass attached to a spring of negligible weight, there would be simple and beautiful differential equation (google for "harmonic oscillator differential equation") for the frequency; but if the mass of the spring is a significant fraction of the total mass of the reed valve, the equation becomes hairy and ugly and intractable. You might find it in some handbook of engineering formulas... maybe... but I wouldn't count on it.
 
  • #10
sophiecentaur
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I have to make my own spring from spring steel, how can i find k if spring is not make yet?
What spring are we actually discussing here? Is it a common helical spring or is it a leaf type reed spring? If you want results for a leaf spring then make one and measure the displace for a given load (a graph) and then work back from that to find the Modulus. Otherwise, use the available information about steel (the place you buy the steel from can tell you the grade it it).
I need a way to make a spring the correct Hz?
I reckon that an arbitrary choice of modulus value from a list of 'typical' steel grades will give you an accurate value to work with because there will be many other variables involved in your final design of a reed valve and the dimensions of the spring will need to be adjusted somewhere down the line. You can't rely on making just one spring and for it to work as you expected.
 
  • #12
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What spring are we actually discussing here? Is it a common helical spring or is it a leaf type reed spring? If you want results for a leaf spring then make one and measure the displace for a given load (a graph) and then work back from that to find the Modulus. Otherwise, use the available information about steel (the place you buy the steel from can tell you the grade it it).

I reckon that an arbitrary choice of modulus value from a list of 'typical' steel grades will give you an accurate value to work with because there will be many other variables involved in your final design of a reed valve and the dimensions of the spring will need to be adjusted somewhere down the line. You can't rely on making just one spring and for it to work as you expected.

This is a picture of reed valves made from spring steel these are flat springs. If you flip the tip end of the spring with your finger it does exactly like a tuning fork it goes back and forth at a certain Hz.. The engine runs at 291 Hz so the spring Hz needs to be 291 also.

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  • #13
sophiecentaur
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This is a picture of reed valves made from spring steel these are flat springs. If you flip the tip end of the spring with your finger it does exactly like a tuning fork it goes back and forth at a certain Hz..
Right. So the coil spring with a mass hanging on it is not relevant.
Without the extra shaping near the anchor point, it would be fairly simple to calculate the frequency. As it is, you are in much deeper water if you expect to calculate the characteristic. The result will be somewhere between the simple rectangular case (a high frequency) and treating it as a short length of much more 'bendy' reed ( about 2/3 of the width, loaded by a long, massive piece that doesn't flex significantly but will have significant angular momentum, as well as linear movement. At what actual level are you treating this problem? You have to expect to do some experimental measurements.
Also, I wouldn't expect the natural frequency of the reed to be exactly the same as the engine frequency because the motion is truncated each time the valve closes. It's probably not as critical, actually because there will never be any 'resonance' with only a half cycle involved each time.
 
  • #14
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Here is instruction and animation video how a pulse jet engine runs. With spark plug on continuous spark air & fuel goes into the engine at the same time. Fuel air mixture ignites in the combustion chamber then blows out the exhaust. Internal air pressure goes from 0 to 9 psi in .003436 / 2 = .001718 seconds as exhaust blows out the exhaust pipe. About 1/2 way down the exhaust pipe internal air pressure drops to 0. As exhaust continues out the end of the exhaust pipe it sucks a vacuum inside the engine negative air pressure is about -8 psi that allows fuel & air to flow into the engine again. Once the engine starts the cycle continues automatic and the spark plug is turned off. Each new fuel air mixture is ignited by the hot burning gasses in the exhaust pipe. Engine starts very easy at 25% thrust then is throttled up to 99% throttle. This engine will not tolerate being over throttled on a test stand more than 100.8% but as the engine picks up speed on a airplane or missile ram air allows the engine to burn more fuel at 400 mph engine thrust has doubled and tripled. A speed indicator automatically increases fuel as the engine goes faster.

When reed valves are tuned to 291 Hz to match the frequency of the engine high speed camera shows the reed valves open and close 291 times per second. The reed valves look like rockers on a rocking chair as they open & close.

NOTE the engine does not run at exactly 291Hz it fluctuates plus & minus 2, 3 & 4 Hz = 287 to 295 Hz about 94% of the time. Sometimes it fluctuates from 286 to 297 and some times 1% of the time as much as 284 to 299 Hz but this is not much of a problem for the reed valves. If valve Hz does not match engine Hz fairly close engine will fire before valves have completely closed.

Argus Reed Valves only need to open .186" where a STOP prevents the reed valve from opening more than .186".

https://en.wikipedia.org/wiki/Pulsejet#Valved_pulsejets
 
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  • #15
sophiecentaur
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Where are you going with this now?
Do you have the engine without the valves or is it all at the planning stage at the moment? If you use the link I gave at the top, you can design a reed that will oscillate at any frequency you want. The length and width are presumably fixed by the port size so you just need to choose a grade of steel (read around for the best choice) and that will lead to the thickness of a simple rectangular reed. You can adjust the natural frequency in the same way that they tune harmonica reeds - shave off the reed at the end to increase frequency and shave off at the base to lower the frequency.
If, as you say, you want to restrict the movement, the period of the reed will not be the inverse of the frequency. It's going to have to be more suck it and see than you seem to be hoping but that's no problem for a practical project like this one.
 
  • #16
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Where are you going with this now?
Do you have the engine without the valves or is it all at the planning stage at the moment? If you use the link I gave at the top, you can design a reed that will oscillate at any frequency you want. The length and width are presumably fixed by the port size so you just need to choose a grade of steel (read around for the best choice) and that will lead to the thickness of a simple rectangular reed. You can adjust the natural frequency in the same way that they tune harmonica reeds - shave off the reed at the end to increase frequency and shave off at the base to lower the frequency.
If, as you say, you want to restrict the movement, the period of the reed will not be the inverse of the frequency. It's going to have to be more suck it and see than you seem to be hoping but that's no problem for a practical project like this one.

I did not see the link above. That will be helpful. Like a tuning fork reed valve Hz does not change with shorter or longer stroke. I want to build a larger engine.
 
  • #17
Mister T
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I could probably use some type of electric device that listens to tuning forks to listen to my valve to tell me what the Hz is if there is suck a thing?

All you have to do is play that same buzzing noise on your phone (using an app) while listening to the piece of metal vibrate. Adjust the frequency of the buzz on your phone, matching it by ear. Humans are quite good at this skill, especially when we learn how to listen for the beats.
 
  • #18
sophiecentaur
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If you already have some working reed valves, you can use the same design and just increase the number of ports. Presumably the engine will have a bigger cross sectional area so there should be room for them. I think you just to need some hands on with this problem. See if you can make a replacement working valve for the existing engine first.
 
  • #19
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If you already have some working reed valves, you can use the same design and just increase the number of ports. Presumably the engine will have a bigger cross sectional area so there should be room for them. I think you just to need some hands on with this problem. See if you can make a replacement working valve for the existing engine first.

I was thinking the same thing but not sure that will really work I don't want to waste a lot of machine time building something that does not work. The way I originally designed the best working reed valve was to make sure 8 psi vacuum will suck them open. Metal thickness has to be .010" thick for the valve to not, chips, crack, break off, or bend.

I already have several good running engines, 5 lbs of thrust up to 100 lbs of thrust. Time to build a larger engine.



'
 
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  • #20
sophiecentaur
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I don't want to waste a lot of machine time building something that does not work.
I think you need a bit more confidence with this project.
So why not try making a design that you already know will work? Have you not made reeds before, for your existing engines? I don't understand the back story of this.
You can buy 10thou shim material so you only need to make up a stamp (or you could even use a chisel on a block of hardwood) to mimic the shape you know will work. It strikes me that you expect to do some calculations and end up with a working engine. That is just not realistic; you need to progress from a point that is achievable now. You won't find anyone who will give you the right dimensions for your reeds. There is very little machine time needed for the actual reed cutting. Making the ports the right size and shape is far more time consuming.
Also,
 
  • #21
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I think you need a bit more confidence with this project.
So why not try making a design that you already know will work? Have you not made reeds before, for your existing engines? I don't understand the back story of this.
You can buy 10thou shim material so you only need to make up a stamp (or you could even use a chisel on a block of hardwood) to mimic the shape you know will work. It strikes me that you expect to do some calculations and end up with a working engine. That is just not realistic; you need to progress from a point that is achievable now. You won't find anyone who will give you the right dimensions for your reeds. There is very little machine time needed for the actual reed cutting. Making the ports the right size and shape is far more time consuming.
Also,

I think I should tell you my history. I graduated from college 1975 with an engineering degree. I worked factory maintenance, electronic technician, tool and die maker, design engineer, then plant engineer. Retired at age 55, I have a machine shop with, bridgeport mill, lathe, surface grinder, welders, saws, lots of tools. I got interested in jet engine & rocket engines in college been building them 45 years. I have to do my own research & development to learn what works. I have been hand cutting reed valves with new sharp aviation snips. I could build a die to stamp out reed valves by the 1000s but not until I know for sure they work. I am only building 1 engine so really don't need more reed valves that it takes to make 1 engine. There was a period of time about 35 years I did not get to work on pulse jet engines I was too busy at my job. I have forgotten a lot of what I learned in college because I never needed it at work. Now I need that information I'm not finding what I need. I watched a lot of MIT physics professor videos. I talked to the people on the rocket & jet engine forum they tell me I can not build a pulse jet engine but I am the only person on the forum that has built one, all those guys know is math and theory, they refuse to believe I built an engine that runs. I talked to a guy last night that worked in the USA military secret research lab building & testing pulse jet engines after WWII ended he said, test they did for several year showed reed valve Hz does not need to match the Hz of the engine reeds operate like a 1 way valve in a cage. Reed valves in the German V1 were 250 Hz but the engine ran at 45 Hz. I was already on the right track and didn't know it. YOU are right I just need to make more reed valves like I already have. Here is a photo of reed valve cage for 100 lb thrust engine that I designed & built.

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  • #22
sophiecentaur
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That's useful and interesting information. A shame you didn't give us the history of your project before. I'm not sure exactly what you want from PF, though. There's no chance that any PF member will hand you a design for a reed valve - just like that. There are many sources of basic spring calculations (for instance my link in #4) and that's pretty much all you can expect from here; you have so much more experience than you are likely to find on PF. What more can we do for you?
 
  • #23
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That's useful and interesting information. A shame you didn't give us the history of your project before. I'm not sure exactly what you want from PF, though. There's no chance that any PF member will hand you a design for a reed valve - just like that. There are many sources of basic spring calculations (for instance my link in #4) and that's pretty much all you can expect from here; you have so much more experience than you are likely to find on PF. What more can we do for you?

I was hoping for a way to calculate the Hz of a reed valve made of .010" spring steel but as it turns out looks like that is not needed. I like physics it is very interesting I took physics classes in college. I built my own physics test area in the work shop to test things this is very interesting. Seeing it is better than reading about it.
 
  • #24
sophiecentaur
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Seeing it is better than reading about it.
But only when it's available for being seen. Learning the theory gives you far more future capability than just learning by doing. There is just not time or money to work every Engineering problem out by building something and altering things.
PS I like the sound of your workshop!!
 
  • #25
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From my 2 cycle outboard race days reeds were carefully monitored and played with type, thickness, reed stop length and reed max opening as well as reed cage landing surface texture for holding oil for a reed landing cushion. Stock engines were required to use SS modified engines used fibre reeds of different materials.

Although for 2 cycle engines this software may provide information on reed frequency. Purchase required for the software.

May or may not not relate to the reed material you are using?

Not discussed what frequency formula used for the calculations. Maybe if purchased?


Reed valve theory and performance

http://torqsoft.net/reed-petal-design.html

From the program:

“The stiffness of the reed petals in a high performance reed valve induction two-stroke engine has a dramatic effect on the power output. The stiffness not only influences the amount that the reeds open but also the natural frequency of the reeds. Three main factors influence the stiffness.

  1. Reed Petal Material
  2. Thickness
  3. Free Length
The Reed Petal Design Programme calculates the natural reed frequency, reed deflection and tip ratio. These values provide a valuable indicator as to the direction that reed development should proceed for optimal performance.

Here at TorqSoft we have found that the natural frequency of the reeds should be between the values of 0.75 to 1.25 times the fundamental frequency of the engine peak power speed. Hence if an engine gives its peak power at 12000 revs/min its fundamental frequency is 200 hz. Therefore the natural frequency of the reeds should be between 150 hz and 250 hz”.
 
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