Rotational Doppler effect is an important phenomenon when the vortex electromagnetic wave carrying orbital angular momentum is used to detect a rotating target. Compared with the traditional plane wave case, rotational Doppler effect enables the vortex electromagnetic wave to detect the spin motion along the rotation axis of target. However, there are still some blind zones when the integer orbital angular momentum beams are used to detect specific spinning objects. To expand the application scope of detection scheme based on the rotational Doppler effect, according to the time-frequency analysis, in this paper we study the method of estimating the rotation speed of spinning objects under the normal incidence and oblique incidence of fractional orbital angular momentum beams. Firstly, based on the ideal scattering point model, the echo models are derived under the normal incidence and oblique incidence of integer orbital angular momentum beam and fractional orbital angular momentum beam, respectively, as well as theoretical time-frequency curves. Then taking the three-dimensional practical object for example, the echo under the incidence of fractional orbital angular momentum beams and its time-frequency graph are achieved by using the momentum method and short-time Fourier transform. The time-frequency ridge and its fluctuation period are extracted from the time-frequency graph, thereby estimating the spinning speed of target. The results show that the fractional orbital angular momentum beams can be used to estimate the rotation speed of spinning objects effectively, whether it is normal incidence or oblique incidence, thereby solving the problem about the detection blind zone of integer orbital angular momentum beams, and improving the applicability in detecting spin motion.