As critical components in modern aerospace productions,rolling element bearings(REBs)generally work under varying speed conditions,which brings great challenges to their oper-ating health monitoring.Some novel time-frequency decomposition(TFD)algorithms are estab-lished recently to extract nonlinear features from the non-stationary signals effectively,which are promising for realizing fault diagnosis of REBs under varying speed conditions.However,numer-ous personal experiences must be incorporated and the anti-noise performance of these methods needs to be further enhanced.Given these issues,a synchronous chirp mode extraction(SCME)-based REB fault diagnosis method is proposed for the health monitoring of REBs under varying speed conditions in this study.It mainly consists of following two parts.(a)The shaft rotational frequency(SRF)is initially estimated from the low-frequency band of the vibration signal.Simul-taneously,an adaptive refining strategy is incorporated to obtain a suitable bandwidth parameter.(b)A cycle-one-step estimation frame is constructed to extract synchronous modes from the envel-ope waveform of the vibration signal.Meanwhile,a synchronous mode spectrum(SMS)is gener-ated using the information of the extracted synchronous modes,which is a novel REBs fault diagnosis technique with tacholess and resampling-free.In contrast to the current TFD algorithms,the proposed method needs fewer input parameters and owns a well anti-noise performance because there is no iterative optimization in the procedure of construction of SMS.As a result,the health conditions of REBs are evaluated by detecting the exhibited features in the SMS.Simulations and experiments are conducted to validate the effectiveness of the proposed method in terms of REB fault diagnosis.Analysis results demonstrate that the proposed method outperforms the current TFD algorithm and the conventional order tracking technique for fault diagnosis of REB under varying speed conditions.