A novel vision-based method using inclined sinusoidal fringe for instantaneous rotational speed measurement

Abstract Accurate and stable rotational speed measurement is essential for motion control and condition monitoring. This paper presents a vision-based method utilizing inclined sinusoidal fringes, where rotational angles are encoded as phase shifts and decoded via a dual phase-correlation algorithm. Unlike traditional fringe processing methods that directly rely on gray intensity values and are thus more susceptible to noise and spectral interference, this approach enhances robustness. The first phase correlation step extracts sinusoidal Pearson correlation coefficient curves from the fringe images, while the second correlation calculates inter-frame phase shifts for instantaneous rotational speed estimation. A mathematical imaging model is developed, followed by simulations to evaluate the impact of signal characteristics, noise, and other factors. The proposed method was validated for high accuracy and stability through repeatability tests against a high-precision encoder. The average relative errors obtained from repeated experiments were 0.8796% at 30 rpm, 0.0911% at 600 rpm, and 0.0479% at 1200 rpm. Moreover, at low speeds, the proposed method delivered noticeably smoother speed profiles than the encoder. Furthermore, experiments with dynamic rotational speed on a rotor test platform show that it outperforms conventional encoders, especially at low speeds and during rapid fluctuations. The high sampling rate of the proposed method ensures smooth speed tracking, making it well-suited for dynamic analysis, condition monitoring, and fault diagnosis in rotating systems.