Abstract: Looseness faults are widely present in mechanical equipment, and the diagnosis of looseness faults under variable speed conditions still poses certain challenges. To achieve looseness fault diagnosis under variable speed operating conditions and tackle this challenge, an innovative adaptive time-frequency modal decomposition method that effectively handles non-stationary signals and enhances the accurate diagnosis of looseness is proposed in this paper. The research method begins by introducing the basic steps of time-frequency modal decomposition, involving temporal truncation through window functions and obtaining time-frequency distribution using Fourier transform. The concept of fault characteristic orders is introduced, and filtering is performed through time-frequency windows to ultimately obtain time-domain waveforms for each order mode. To enhance the adaptability of the method, we introduce fusion metrics, including signal-to-noise ratio and cross-correlation coefficient, for optimizing the selection of window width parameters. By defining and calculating the energy proportion of each order, fault feature analysis of vibration signals was completed, and feature extraction and diagnosis of looseness faults were achieved. The parameter of the window width for time-frequency modal decomposition is optimized and selected, and the nonlinear correlation characteristics between the window width and the decomposition output are studied to achieve adaptive time-frequency modal decomposition. Experimental validations are conducted on both bearing seat looseness faults and rotating component looseness faults. In the bearing seat looseness fault experiment, a comprehensive analysis of time-domain waveforms, time-frequency plots, and the output of adaptive time-frequency modal decomposition successfully achieves accurate diagnosis of the looseness fault. In the rotating component looseness fault experiment, effective diagnosis of the rotating component looseness fault is achieved through the processing of variable speed bearing vibration signals. Based on the proposed method, the fault features in the experimental signals were effectively extracted. In the experiment on bearing seat looseness faults, a comprehensive analysis of time-domain waveforms, time-frequency plots, and the output of adaptive time-frequency modal decomposition allowed us to successfully capture the characteristic information related to the looseness fault. Experimental results verified the effectiveness of the method, looseness faults caused by bearing seat looseness, and rotating parts looseness faults were both diagnosed by the proposed adaptive time-frequency modal decomposition algorithm. The experimental results show that the proposed method can achieve modal decomposition of non-stationary signals and has effective diagnostic capabilities for looseness faults. Overall, this research demonstrates the effectiveness of the adaptive time-frequency modal decomposition method in diagnosing looseness faults under variable speeds and strong noise backgrounds. The method is not only applicable to different types of looseness faults but also exhibits adaptability by optimizing parameters under varying noise intensities. This innovative approach expands the application potential in the field of signal decomposition, providing a powerful tool for the health monitoring of mechanical equipment.