Torsional Stiffness 2

[TonyCro]

(newbi - please be gentle!)

I trying to calcule the torsional stiffness of rotor, the construction is a simple rolled bar with 6 arms welded down the rotor body.

Is there an equation for the Polar moment for this type of rotor construction?

Help
TonyCro

 

[gwolf]

You should calculate the polar moment of the rotor body alone, calculate the polar moments of each of the arms ABOUT THE ROTOR CENTROID NOT THE ARM CENTROID, and add them all up.

 

[Drej]

Not easy. Especially if the cross section geometry is complex - not sure which category yours falls into without more information. There are simplifications you can make, but the way I always do it is to import the geometry into FE software, mesh it (roughly) and then apply a torque T to the rotor. The torsional stiffness is energy/rad (SI units Nm/radian). Pick two points along the cross section and measure the difference in angle turned through (delta R) having applied the torque. Then the stiffness k of that portion of the shaft is:

k = T/(delta R)

There are books which give you equations for the stiffness, ranging from simple bars through to complex crankshafts. Names (authors) I can think of are Kerr Voss and Bicera. I do have access to these at work, but I'm on holiday today - sorry.

Cheers,

-- drej --


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[Philrock]

Draw the cross section in SolidWorks or AutoCad. Either program can directly tell you all the significant structural properties of the cross section, including the polar moment of inertia.

 

[arto]

Grampa's "Advanced Strength of Materials" by Den Hartog [McGraw-Hill, 1952] has lotsa good Torsion stuff in Chapter 1 - might be helpful.

 

[TonyCro]

excellent, many thanks everybody. I'll be cranking on Autocad shortly to try it!

Thanks
TonyCro

 

[ccw]

Hi TonyCro,
if the information is at all critical, and construction is feasible, then make a physical model and measure the stiffness. Even better, make several and measure the stiffness. I think you will find variance among physical models and even more variance between Acad SolidWorks and the physical models, particularly when welded construction is involved.

 

[GregLocock]

As soon as the cross section gets weird I've given up on analytical approaches, and just build an FEA model.

To a first approximation I'd just smear the ribs out over the rest of the shell and use the equation for a tube, but, IF the stress flow argument holds that will overestimate the torsional rigidity of the shaft.



Cheers

Greg Locock

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[EddyC]

TonyCro,

Be forewarned about using AutoCAD to calculate your polar moment of inertia. If your cross section is a closed section (tubular or box type), the value that AutoCAD calculates is correct. If your section is open (I, C, plate, L), the value calculated by AutoCAD can be much higher than the actual. This discrepancy is due to the fact that AutoCAD neglects open cross section warping. In addition, Roark's Formulas For Stress & Strain is a usual source for hand methods to calculate moments of inertia.