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• A consistency association is established among different conditions signals. • Tool structure and process parameters are introduced to the model structure design. • The model's generalization boundary in tool wear monitoring is studied. • The proposed method is generalized and interpretable on extensive experiments. Cross-conditions tool wear monitoring has a wide application prospect in manufacturing. However, the data distribution discrepancies caused by the inconsistency of process elements restrict the generalization of models under cross-conditions or even similar conditions. The existing methods based on diversity enhancement make it difficult to effectively establish the correlation between the source domain and target domains, which limits the improvement of model generalization. Therefore, this paper details the cause of data distribution discrepancies and proposes a discontinuous physical property-constrained single-source domain generalization network for milling tool wear monitoring. Firstly, a spatial attention mechanism is introduced to weight key signal segments adaptively. Secondly, the generation module is constrained by a standard sample and is used to generate diverse samples with physical properties. Thirdly, extensive recognition experiments on an open dataset and machining experiments with three distribution discrepancy levels were conducted to verify the effectiveness of the proposed method. Finally, feature visualizations provide consistency and interpretability. [ABSTRACT FROM AUTHOR]