Transfer learning techniques can reduce the distribution difference between source and target domain features. However, in cross-device scenarios, existing research is often difficult to measure and reduce the differences in the conditions of data between different devices, resulting in the knowledge obtained by the model in the source domain cannot be migrated to the target domain. Additionally, in real-world failure diagnostic scenarios, decision-makers usually need to understand why the model classifies a specific type of fault. Due to the complexity of deep learning models, they are often seen as " black boxes," making it difficult to explain their internal workings. To address these issues, an interpretable fault diagnosis method based on conditional metric transfer learning is proposed. Firstly, Hilbert envelope spectrum analysis is used to convert time-domain signals into frequency-domain signals. Secondly, a deep twin convolutional neural network and classifier are built to extract high-dimensional features from both source and target domain data in the frequency domain and perform classification training. Then, the interpretable Conditional Kernel Bures is embedded into the loss function of unsupervised learning to enhance feature adaptation and model interpretability under conditional distribution. Finally, the SHAP method from game theory is used to conduct post-event interpretable analysis of the model diagnosis results based on the envelope spectrum. Tests were conducted on 12 cross-equipment bearing fault diagnosis tasks across three types of mechanical equipment, evaluating the proposed method against other related methods. The results show that the proposed method could effectively improve the accuracy of cross-equipment mechanical fault diagnosis, achieving an average diagnostic accuracy of 99. 47% . It also identifies which frequency points played a crucial role in the model′s decision-making process.