I added the following variables to the Test13.fst Outlist: LSShftMxa, RootMxc1, RootMxc2, RootMxc3. I summed the blade in-plane moments with the expectation that the value would equal (or exceed) the rotor torque. Instead, the rotor torque exceeded the sum of the moments by about 10%. The shape of the difference curve does not look like any of the other root moments. What mechanism is the source of the difference?
Jim J
Dear Jim,
The sum of the in-plane root bending moments should not exactly equal the rotor torque. Since the blade root is offset of the shaft axis by a distance of HubRad, the in-plane shear forces at the blade root also contribute to the torque within the low-speed shaft. The inertia of the hub about the shaft, which is accelerating and decelerating, also has a small effect on the shaft torque.
Without blade precone, the exact equation is:
LSShftMxa = [ RootMxc1 + RootMxc2 + RootMxc3 ] - [ HubRad*( RootFyc1 + RootFyc2 + RootFyc3 ) ] - [ (HubIner/1000)( LSSTipAxaPi/180 ) ]
The 1st bracketed term is the sum of the in-plane root bending moments. The 2nd bracketed term is the shaft moment caused by the sum of the in-plane shear forces, which are offset of the shaft by a distance of HubRad (in Test13, HubRad = 1.75m). The 3rd bracketed term includes the inertia of the hub (in Test13, HubIner = 34600kg*m^2). (The factors of 1/1000 and Pi/180 are unit conversions from N to kN and degrees to radians, respectively.)
I also reran Test13 with LSShftMxa, RootMxc1, RootMxc2, RootMxc3, RootFyc1, RootFyc2, RootFyc3, and LSSTipAxa all output. If only the 1st bracketed term on the right hand side of the equation above is used, the average mismatch error between the left and right sides is 10%, as you stated. When the 2nd bracketed term is included with the 1st, the average mismatch error is reduced to 0.1%. When all terms are included, the average mismatch error is reduced to 0.01%–This very small mismatch is most likely due to numerical round-off.
I hope that helps!
Best regards,
Mystery solved - thanks Jason.
Jim J