Pressure, Force, and Engineering

[WehrdScience]

Hello folks, I have a doozy of a problem, if anyone is willing to assist me I would greatly appreciate it! My son and I are working on a project where we have stacked nine balls on top of each other inside an aluminum tube (vertically). The bottom of the tube has been welded shut with a washer which allows the ball to stick out slightly, but keeps the balls in (the inner diameter of the washer is small than the diameter of the ball). The top of the tube has a threaded bolt that can be tightened to place pressure onto the chain of balls. See attached picture for help and dimensions of everything.

What we would like to know is, if we use a specific diameter wrench and a precise Newton scale (so we know our Force Input and our distance input), how could we accurately find out the Force output of the bolt on the balls? Also, how can we calculate the total pressure of the system, knowing P = F / A, and of course if you help us find out the force applied by the bolt, we were curious which area we should use? The area of the bolt touching the ball? The end of the bolt is rounded but matches the contour of the rounded ball as well…if there is anything we forgot to tell you just ask, we have dimensions for everything!

We have tried calculating this thing from a Mechanical Advantage point of view (which may be too simplistic)...figuring if the diameter of the bolt / pitch length would give us .012m / .0015m = 8...so applying a Force of 5.0 N / .13 m wrench length = 38.5 N Force placed on the chain of balls...it just seems kind of high?

[PLAIN]http://www.odessa.wednet.edu/images/stories/Webmaster/Force-Pressure.jpg

 

[nvn]

WehrdScience: You can use mm, instead of m, for your dimensions. The name Newton is the name of a man, whereas Newton (N) is a unit of force. Always leave a space between a numeric value and its following unit symbol. E.g., 0.012 m, not 0.012m. Also, numbers less than 1 must always have a zero before the decimal point. E.g., 0.13, not .13. See the international standard for writing units[/color] (ISO 31-0[/color]).

It appears you may have made a mistake on the bolt diameter or pitch. An M12 bolt (12 mm diameter) has a pitch of 1.75 mm, not 1.5 mm. The bolt size is written M12. There is also an M10, which has a pitch of 1.5 mm. Which bolt size are you using?

If the wrench length is L1 = 130 mm, and the force you apply to the wrench handle with your hand is F1 = 5 N, then you are applying a torque of T = L1*F1 = 650 N*mm = 0.650 N*m. Could you clarify your bolt size and pitch, and applied torque?

To estimate the force on the balls (output by the bolt), you can use P1 = T/(kt*dn), where P1 = force on balls, and dn = bolt nominal diameter. For an M12 bolt, dn = 12 mm. If your bolt threads are unlubricated, and your bolt head has not contacted the aluminum tube, you can perhaps use kt = 0.18.

 

[WehrdScience]

nvm, thank you for your expedient and informative response. Truth be told, our "bolt" is not a bolt at all, we just used this word for convenience. It is actually a tapered plug with pipe thread:

Pipe Size (inches)...1/2

Threads per Inch TPI - pitch...14

Approximate Length of Thread (inches)...3/4

Approximate Number of Threads to be Cut...10

Approximate Total thread Makeup, Hand and Wrench (inches)...7/16

Nominal Outside Pipe Diameter OD (inches)...0.840

Tap Drill (inches)...23/32

We converted these units into the metric system, which is why the 1/2 " pipe diameter was 1.27 cm for us. We used a macroscope to determine the pitch of these threads, since for metric screw threads pitch refers to the distance between threads...and we found them to be 1.5 mm. Using standard ratios, we realized 14 threads / inch => 14 threads / 25.4 mm, which => 0.551 threads / 1.0 mm...or...1 thread distance / 1.81 mm on average. After measuring in different places, we felt that 1.5 mm was closer to what we really measured than the calculated 1.81 mm. We realize the pipe threads are tapered, but are hoping this small discrepancy will not affect us too much. We threaded the inside of our aluminum tubing to house the tapered plug, and realize, too, that the material of the plug is different than that of the aluminum tubing (and are also hoping this discrepancy will not affect us too much).

We were hoping to calculate torque as you did below (L1*F1)...thank you once again.

 

[Studiot]

If you google hertzian stress for spheres you will find plenty

eg

http://www.scribd.com/doc/9724081/Hertz-Contact-Stresses

 

[nvn]

WehrdScience: From post 1, we did not know you have tapered threads. The last paragraph of post 2 is inapplicable to tapered threads. It appears there is no easy way for you to compute nor measure the output force from a tapered bolt or tapered plug. But at least you now have the formula for input torque.

 

[WehrdScience]

Studiot: Thank you for the link, that helped a LOT.

nvn: thank you for your help as well, it gets us started down the path we needed.

- WehrdScience

 

[Studiot]

Sorry I can't do more but I am away for a few days.