Theoretical study into the aerodynamic imbalance of a propeller blade and the correcting masses to balance it

This paper reports the theoretically investigated aerodynamic imbalance of the propeller blade, as well as correcting masses for balancing it. It has been established that the aerodynamic forces acting on the propeller blade can be balanced by the adjustment of masses. This is also true for the case of compressed air (gas) provided that the blades are streamlined by laminar flow. That makes it possible to use rotor balancing methods to study the aerodynamic forces acting on the propeller blade. The rotating blade mainly generates torque aerodynamic imbalance due to a lift force. A much smaller static component of the aerodynamic imbalance is formed by the drag force acting on the blade. The correcting mass located in the propeller plane balances both static and torque components of the aerodynamic imbalance in its correction plane. A second correcting mass (for example, on the electric motor shank) balances the torque component of aerodynamic imbalance in its correction plane. The calculations are simplified under the assumption that the equilibrium of aerodynamic forces is perpendicular to the chord of the blade. For approximate calculations, one can use information about the approximate location of the pressure center. The aerodynamic forces acting on the blade can be determined on the basis of the correcting masses that balance them. The accuracy in determining the aerodynamic forces could be improved by measuring a lift force. The computational experiment has confirmed the theoretical results formulated above. The experiment further proves the possibility of applying the devised theory for propellers whose rotation speed changes with a change in the angles of blade installation. The findings reported here could be used both for devising methods of propeller balancing and for constructing methods to study the aerodynamic forces acting on the blade.

Robust balancing for rotating machines

The balancing of rotors divides broadly into two categories: balancing in situ and balancing in a balancing machine. In the latter case, the most common practice is to arrange balance corrections on the rotor such that the net excitations of each of the four in-plane rigid-body modes of the free rotor is zero by deploying balance corrections on two independent planes. In a small proportion of cases, the net excitations of the first pair of flexural modes are also zeroed using a third correction plane. This paper proposes that, when rotors are balanced in a balancing machine (not similar to the machine stator), substantially more utility can be gained from the balancing operation by combining a suitably weighted account of the specific balancing requirements of the machine with knowledge of the expected machine characteristics than can be achieved by ignoring this knowledge. A single cost function is established based on a numerical model of the machine. Then, depending on circumstances, either the expected value of this cost function or its worst possible value can be minimized. The methods proposed require that relatively detailed knowledge of the distribution of residual unbalance be obtained experimentally. The paper briefly discusses some practical methods for how such information might be extracted. The definition of the cost function as a matrix quadratic form provides potentially valuable information about the necessary number and the optimal location of balance planes on a given rotor, and methods for determining an optimal set of balance planes are outlined.