Wind power is increasingly seen as a global, sustainable, and eco-friendly energy option. However, one significant obstacle to further wind energy investment is the high failure rate of wind turbines. The gearbox plays a pivotal role in turbine performance. In recent years, there has been a surge in the focus on gearbox fault diagnosis, reflecting its criticality and prevalence in the industry. Time synchronous averaging (TSA) is a primary technique to identify faults in wind turbine gearboxes using mechanical vibration signals. Generally, implementing TSA requires a device that is capable of recording the phase information of a rotary shaft. Nevertheless, there are situations in which the installation of such a device poses difficulties. For instance, gearboxes that are in use cannot be halted to allow for the installation of a device, and sealed gearboxes provide challenges while being inserted into the device. This research presents an innovative technical way to improve the TSA method without requiring a phase signal. The proposed method has the advantage of extracting the shaft rotation angle signal from the measured acceleration signal, even in non-stationary conditions where the rotational speed varies over time. The effectiveness of the proposed method is validated through measured datasets from wind turbine gearboxes with actual faults and a dataset from a gear system with variable rotational speeds.