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Hoop Stress Question

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  • Hoop Stress Question

    Lets say I've got a 36" solid rod with an axis of rotation through the center of the rod and perpindicular to the length. I want to know, in terms of tension, what kind of force it expierences.

    I thought I worked up an equation for it, but the numbers I'm getting seem to be a little bit askew. I googled it but didn't come up with the formula I wanted.

    Basically I need to spin a rod very fast. Like I said, the axis of rotation is perpindicular to the length of the rod and in the center. I need to get as high a tangential velocity as possible without blowing something up to give you all a little background for this machine. I'm in the intitial design process trying to decide if it is even feasible to get the velocity I need in a mechanical system.

    Alright well I've said enough. Let me know if you've got a handy dandy equation ...

  • #2
    Originally posted by Fasttrack
    Lets say I've got a 36" solid rod with an axis of rotation through the center of the rod and perpindicular to the length.
    So, is this a rod shaped propeller?

    Is there a hole in the material, or other shape that would degrade the strength.?


    • #3
      Hoop stress part answer?

      First thing to do is to define hoop stress.

      Will this help?


      • #4
        Nope - Say its an 18" long rod with a diameter of 1/2" and welded to a hub. I figured on 36 because I will have another rod on the otherside for balance but they will be attached via a hub.

        Not exactly a propellor, more of a centrifuge. I need to accelerate an electronic package I've designed to very very high speeds.

        OT - "will this help" Not very much. I used the term "hoop stress" in order to help give a mental picture of what is going on and, mainly, attract the engine guys here who know about designing flywheels and etc
        Last edited by Fasttrack; 05-16-2008, 11:24 PM.


        • #5
          Look for flywheel formulas. Same thing. Many high energy density flywheels use in ride through power supplies are drum shaped.
          Free software for calculating bolt circles and similar: Click Here


          • #6
            Well I guess thats another question, am I better off with a solid flywheel or just a rod? Obviously a rod is much cheaper to produce and easier to work with. Like I said, this project will really be pushing the envelope for me. Evan -what do you think about spining an 18" radius at 2000 (or higher!) rpm? Can it be done?


            • #7
              Do the math

              The forces are huge as are the mechanics and physics!!



              Also check Machinery's Handbook.


              I've reached my limit here.


              • #8
                Here are some hints. The optimum shape for a disc flywheel is the one below. It results in constant stress on the material because of the thickness distribution. This will apply equally to an arm as it does to a disc.

                Unfortunately the above shape is a pain to make. Fortunately a close approximation is both easy and nearly as good.

                Free software for calculating bolt circles and similar: Click Here


                • #9
                  I guess I'm not as good at reading between the line. So... what are the other dimension of this 36" rod. what size is the hole thru it?

                  Ok you answered that will I was typing no hole but a hub... So your making a centrifuged.

                  oldtiffie's Your fast with the wickedpeda...
                  Wow... where did the time go. I could of swore I was only out there for an hour.


                  • #10
                    Just calculate the centrifugal "force" and compare it to the tensile strength of the material used for the arm or disc. If the shape approximates the upper one the tension will be linearly distributed with radius. The number of gees times the density will tell you when the limit is reached. For a safety margin then back it off by 50%.

                    BTW, is this homework?
                    Last edited by Evan; 05-16-2008, 11:45 PM.
                    Free software for calculating bolt circles and similar: Click Here


                    • #11
                      I'd think about using a flat bar instead of a round... and balanced off end for whatever your load (package) is so it did not shake it self apart. Not really knowing how big the package is but what about modifying a lawn mower blade to hold it... you could cut the grass while you give it a whirl.
                      Wow... where did the time go. I could of swore I was only out there for an hour.


                      • #12

                        The maximum speed of the flywheel is dependent on the material available and the quantity of money avilable. The earlier post shows the classic high speed solid flywheel design. The Swiss used them in an energy storage system to drive passenger busses many years ago. Look at the speeds produced in the modern jet engine and they use high alloy forged wheels. Define the velocity required for your project and then some valid numbers can be calculated, along with the energy required to accelerate the mass.


                        • #13
                          Wow thanks for all the replies guys. Alright, here it goes.

                          1) Evan - thats what I was curious about, how the force of tension is distributed through the radius of the part. Cost becomes an issue when we start talking about flywheels in large diameters since it requires a rather large blank of material. Plus, it requires a big lathe! Nope, its not homework. I'm begining an "advanced" physics lab next semester where we essentially pick a project and then present our results to the entire faculty. Kind of intimidating! Anyway, my plan is pretty ambitious at this point but should be interesting. Most students end up doing something sort of lame, like measuring the effect of acceleration on newtonian and non-newtonian fluids. It's like the college equivalent of the "volcanoe experiment".

                          2) Does anyone know how tension is distributed in a round, square, rectangular, etc bar? something like 1/2 r^2 ? I can't remember now...

                          3) It definitely needs to be balanced! I'd like to spin this just as fast as possible.

                          4) I don't know for sure what speed I need, or rather I have some wiggle room. The faster the better. The minimum speed is 36,000 inches per minute. This an 18" radius wheel spinning at 2000 rpm and the package on the outside.

                          Some more details:
                          The "package" is fairly light, figure an absolute max of 150 grams. I will need to run at least three wires to the package. A reference, a voltage, and a signal. The signal wire needs to be shielded as it will be transmitting a high frequency to a series of digital flip-flops. The faster the velocity, the lower frequency signal required (which means cheaper components and less noise) and the more accurate the data. This is a tricky procedure at best, since I have to deal with accuracies of the electronics and the effect that enormous accelerations will have on the components.
                          Last edited by Fasttrack; 05-17-2008, 12:01 AM.


                          • #14
                            Roark's Formulas for Stress and Strain has a formula for the maximum tensile stress in a rod rotating about a pivot at one end

                            s (psi) = numerator/denominator
                            numerator = W*L*(w**2)
                            denominator = (2)*(386.4)*A
                            W = weight of rod, lb.
                            L = length of rod, in.
                            w = rotational velocity (radians/sec) = pi*(RPM)/30
                            A = rod cross-section area, in**2

                            So here L is the radial length from the pivot, half the length of your rod which is pivoted at its center instead of its end.
                            Allan Ostling

                            Phoenix, Arizona


                            • #15


                              A bit of academic regimen/rigour is required here instead of perhaps pulling numbers and opinions out of the air.

                              I'd guess that the OP has a good grip on math and physics.

                              He should be able to derive his specific application from the general case/principles involved by substituting his own values as regards inputs and limitations.

                              As "fly-wheels" has come to the fore, try these:



                              As in all flywheels, there will be potentially considerable dynamic fores not the least of which may be those of:

                              - gyro-scopic action/s:

                              Last edited by oldtiffie; 05-17-2008, 01:17 AM.