I am developing a self adjusting variable pitch propeller tailored by its pitching moments due to aerodynamic loads setting the blade rotation axis in an offset from the aerodynamic center as shown below.
At the moment i am trying to attain static and dynamic stability of the blade due to mass/Inertial effects. I have created a sketch as shown on the following figure, based on my so far understanding on inertial effects which represents a blade airfoil section and the centrifugal force (OR NOT??) acting on a mass particle.
Offset from Pitch Axis x
Offset from longitudinal Axis y
Component along the x-axis: (x/r)*Force
Pitch Moment: y*(x/r)*Force
And now comes the difficult part. I suppose that here i need to consider the theory of three dimensional kinetics of a rigid body and angular momentum, however i am confused on defining the coordinate systems on the blade as well as which exact moments and products of Inertia have to take into account. If i am not wrong, here a fixed coordinate reference system and one that rotates with the twisting of the blade have to be defined. The question is where the coordinate reference system has to be defined; on the blade axis of rotation, C.G, or somewhere else?
Finally i have informed that to compute the blade's dynamic stability, i will need also to consider blade flapping (i.e., motion of the blade out of plane with the rotation of the propeller), and pitching (or twisting) and this is another part i am struggling too!