Interferometric angular velocity measurement of rotating blades: theoretical analysis, modeling and simulation study

Doppler radar can only measure the radial velocity of a moving object. If an object is moving along a curved path, when its radial velocity decreases, the angular velocity must increase. Thus, if the angular velocity can be measured, the problem caused by little or no radial velocity can be solved. In this paper, we provide detailed theoretical analysis and establish the mathematical model of the interferometric frequency shifts of rotating blades. We first analyze the instantaneous frequency of a SINC function, which comprises a pair of sinusoidals and a train of strong spectrum lines. Then, we utilize the convolution theory in time-frequency domain to calculate the interferometric frequency shifts of rotating blades. Simulation results manifest that some important parameters and features of rotating blades, such as blade length, rotating rate and blade number, can be accurately estimated from the time-varying interferometric frequency signatures.