The Determination of Fan Blade Aerodynamic Loading From a Measured Response

Large-scale cooling system fans often operate under distorted inlet air flow conditions due to the presence of other fans and the prevalent wind conditions. Strain gauge measurements have been used to determine the blade loading as a result of the unsteady aerodynamic forces. However, these measurements are of the blade’s response to the aerodynamic forces and include the deformation as a result of the first natural frequency being excited. When considering the dominant first natural frequency and bending mode of the fan blade, one can approximate the fan blade as a cantilever beam that acts as a single degree-of-freedom system. The response of a single degree-of-freedom system can be calculated analytically for any excitation if the system’s properties are known. The current investigation focuses on using these equations to create an algorithm that can be applied to the measured response of a fan blade to then extract the aerodynamic forces exciting it. This is performed by using a simple non-linear, least-squares optimization algorithm to fit a complex Fourier series to the response and using the coefficients of each harmonic term to determine the Fourier series representing the excitation function. The algorithm was first tested by applying it to the response of a finite element cantilever beam representing a simplified model of the fan blade. Good results were obtained for a variety of excitation forces and as such the algorithm was then applied to the measured response of a full-scale fan blade. The full-scale blade was excited with a shaker where the forcing function could be accurately controlled. Once validated, the algorithm was applied to a set of strain gauge measurements that were recorded at a full-scale fan while in operation. The reconstructed aerodynamic loading showed increased forces when the blade passed beneath the fan bridge as well as when it approached the windward side of the casing.