Stepped Shaft torsional stiffness/rigidity calculator?

[sprintcar]

About 2 years ago I made a spreadsheet to calculate shaft stiffness and the L3/D4 values along with total weight and mass moment of inertia. Works fine.

I'm going from straight shafts to stepped shaft design with different diameter/length segments for bearing fits, etc. Here's where I'm having a brain cramp and need a bit of assistance.

To calculate overall shaft torsional stiffness, are the individual shaft segments summed and averaged, or is this a series spring calculation? A non-calculus solution is preferred.

If anyone has an existing spreadsheet, it would be appreciated!
Thanks

"If A equals success, then the formula is: A = X + Y + Z, X is work. Y is play. Z is keep your mouth shut."
-- by Albert Einstein

 

[zekeman]

If the angular deflection of a shaft for torque, T, is
TL/JG; then for a series of steps you sum the deflections to get
T/G*(summation of Li/Ji)
Since J=pi*d^4/32; then this becomes
T/G/(pi*32)*(summation of Li/di^4)
Stiffness is the reciprocal of the deflection per unit torque
so this becomes
stiffness=T/deflection=G/(pi*32)*(summation of di^4/Li)

 

[GregLocock]

The easy way to remember is that it is springs in series, so you use total compliance = sum (each compliance)

where compliance =1/stiffness

Does your ss use Holzer's method? I only ever used it twice, but it is a good way of understanding MDOF resonances.


Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.