Fault detection, also known as anomaly detection (AD), is at the heart of prediction and health management (PHM), which plays a vital role in ensuring the safe operation of mechanical equipment. Nonetheless, the lack of anomaly data creates a significant obstacle to the AD of the mechanical system. In particular, the complex modulation effects induced by time-varying speeds make AD much more challenging. For rapid and accurate AD, a stable knowledge distillation decoupling net (DecouplingNet) is provided to overcome these difficulties. First, an adversarial network consisting of an encoder, a decoder, and an encoder-discriminator is developed to model normal samples well by imposing constraints on the latent space. Then, a causal decoupling framework is suggested to disentangle equipment state-related information from operating conditions-related features, enabling stable condition monitoring at varying speeds. Finally, feature-based knowledge distillation is employed to boost the efficiency of AD while maintaining the detection accuracy. The proposed method is tested on two experimental scenarios and compared with some typical AD methods. The finding demonstrates that the net outperforms others in terms of accuracy and efficiency when it comes to detecting anomalies in the mechanical equipment that runs under varying speeds.