For the design of a cantilever, assuming a Hookean material is used below its proportionality limit, stress will be proportional to strain. From this we can conclude that its behavior will be linear.
However, how can we apply this knowledge towards helical springs? Is it possible to design a helical spring whose linearity approaches or equals the cantilever?
Thanks,
Thadman
However, how can we apply this knowledge towards helical springs? Is it possible to design a helical spring whose linearity approaches or equals the cantilever?
Thanks,
Thadman
Assuming a cylindrical, uniform, helical spring, whose coils have not started to close, which supports a surface. Would the spring force be linear across the contact surface?
I picked up the seventh edition of Roark's formulas for Stress and Strain. It appears to be rather trivial to calculate the fundamental resonance for a helical spring (f
=1/2sqrt(k/m), where k=spring constant and m=mass). However, calculating the mass normalized modes does not appear to be trivial.
How should we approach solving this problem?
=1/2sqrt(k/m), where k=spring constant and m=mass). However, calculating the mass normalized modes does not appear to be trivial.How should we approach solving this problem?
noah katz said:
I've searched google and have purchased several engineering texts (>$300! academia is EXPENSIVE!). I have been trying to schedule meetings with a few of the professors in the engineering department, however they are very busy with research and have limited time to answer my questions. However, I do have a meeting tomorrow, we'll see if I'm able to reach any resolution.
Let me be more explicit,
Assuming a cantilever (left end fixed, right end free), an equation exists which defines all of the natural frequencies.
F(x)=(K
/2pi)*sqrt(EIg/wl^4)Where K
= 3.52 for the 1st mode (n=1), 22 for the second mode (n=2), 61.7 for the third mode (n=3), 121 for the fourth mode (n=4), 200 for the fifth mode (n=5), etc.Nodal position wrt length = .783 for the 2nd mode (n=2), .504/.868 for the third mode (n=3), .358/.644/.905 for the fourth mode (n=4), .279/.5/.723/.926 for the fifth mode (n=5), etc
How can we define a similar equation for a helical spring?
The application is abstract, purely inquisitive (ie personal interest). I'm sorry if I offended you. I'm simply trying to gain a more complete understanding of the behavior of systems. I take great pride in being able to visualize and understand systems that I am interested in. Loudspeakers use a variety of springs in their construction. My interest in the helical spring simply arose as a tangent off of my interest in the springs in loudspeakers (surround, suspension, etc).
If we acquire a complete understanding of the system, qualitative logic can be exploited.
For example, the electric field within a uniformly charged sphere is 0 due to symmetry.
However, if we were to observe a charged rod of uniform cross section with an arbitrary length, it can only approach infinite linearity (with regards to the field), it will never achieve it.
I find (as demonstrated in example 1) systems which equal a value (rather than approach it) deeply fascinating.
Why do I post on this forum? I feel this community is highly educated, open-minded, and mature. Intelligent discussion benefits the community, ideas/concepts become more accessible to those with an incomplete understanding and those ideas/concepts reach a higher resolution through debate.
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I'm sorry, as I assure you that was not my intention.
Regardless, are you aware of any texts or resources that describe the behavior of Helical (as well as other types of springs) in fine detail?
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My suggestion would be to spend some time learning an FEA program and how to set up good FEA simulations. You would want a program that can do nonlinear analysis if you want to look at nonlinear force vs deflection curves. This would also let you calculate modal frequencies. It doesn't give you an analytical expression that you can optimize, but you can learn some things about a given geometry. You can also set up an iterative optimization where the program modifies the geometry to try to optimize the output.
There aren't any FEA programs I can afford
I sent Comsol an email and they offered me a 1 year license for $1500. Linux is always as an option, however I currently have a mac and have never used Linux before. The Mechanical Engineering department offers Ansys in their labs, however I'm currently AAE. I would have to change majors or receive special permission from the ME department Regardless, I've been having difficulty finding texts which correspond to multiphysics software packages (ie Ansys for Dummies). Are you aware of any introductory tutorials?
I would start from the proposition that as far as their resonant properties go, a cantilever is basically an organ pipe, and a helical spring a Helmholtz oscillator.
By inspecting the elecro mechanical analogues of these you are bound to find how close this is to being true as a first order approxmation at least.
rcw.
By inspecting the elecro mechanical analogues of these you are bound to find how close this is to being true as a first order approxmation at least.
rcw.
"I would start from the proposition that as far as their resonant properties go, a cantilever is basically an organ pipe, and a helical spring a Helmholtz oscillator.
By inspecting the elecro mechanical analogues of these you are bound to find how close this is to being true as a first order approxmation at least."
I don't see either analogy as particularly relevant or useful..
An organ pipe is a 1/4-wave acoustic resonator, and a Helmholtz oscillator is a single-DOF oscillator.
A multicoil spring is neither.
By inspecting the elecro mechanical analogues of these you are bound to find how close this is to being true as a first order approxmation at least."
I don't see either analogy as particularly relevant or useful..
An organ pipe is a 1/4-wave acoustic resonator, and a Helmholtz oscillator is a single-DOF oscillator.
A multicoil spring is neither.
The book I had in school was 'building better products with finite element analysis' by Adams and Askenazi. I just flipped through it and it has some good information, but I'm not sure how highly I would recommend it. I had that coupled with a professor and tutorials written for a specific software package we were using (cosmos, I think...). Don't worry about multiphysics until you can do basic mechanical analysis. If you can use ansys, the software user manual is massive and generally helpful.
If you want to do it bad enough, you will figure out a way - linux, or begging some ME professor. Or make friends with the lab people.
If you want to do it bad enough, you will figure out a way - linux, or begging some ME professor. Or make friends with the lab people.
The deflection of a cantilever beam will be linear as long as the deflection is small. Since you could model a helical spring as an assembly of very short cantilever beams connected end to end in a spiral pattern then the helical spring would also be linear in the axial direction for small local deflections.
Both the cantilever beam and the helical spring have evenly distributed mass and stiffness along their lengths. Therefore, the lateral vibratory deflection of the cantilever beam and the axial vibratory deflection of a helical spring (with one end fixed and the other end free) will both be quarter wavelength in shape, a quarter sine wave and its odd harmonics.
Think of the cantilver beam as a yard stick clamped to a table and the helical spring as a slinky hung from one end. Play with those two mechanical systems to physically prove to yourself what the vibration characteristics are and how the fundamental mode shape can be described by a quarter sine wave.
I don't have the text at home, I use it at work all the time, but go to the technical library and find a copy of Blevins' text Formulas for Natural Frequency and Mode Shape, I believe both systems are in his tables.
http://www.amazon.com/Formulas-Natu...=sr_1_1?ie=UTF8&s=books&qid=1253583948&sr=8-1
This is the "Roark" of vibration problems. If you plan on doing any vibration or dynamics work it is a must have textbook. I think I have had Blevins and Roark on my desk for almost all of the 30 years I have been an engineer, they are extremely useful for figuring out where a big complicated FE model went wrong.
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