Acoustic signals offer a promising non-contact approach for robust fault diagnosis in rotating machinery, a critical component of industrial systems. In this study, we propose a novel Multi-Domain Alignment Transformer (MDAT) that integrates knowledge from multiple source domains and leverages Transformer Encoder in the frequency domain to extract invariant global features. To address cross-domain discrepancies, our method combines two complementary alignment strategies—a statistical metric-based approach and a classifier alignment strategy—to enhance generalization across varying operating conditions. The proposed approach was rigorously evaluated on a bearing failure simulation test bench, where non-contact acoustic signals were acquired under diverse rotational speeds. We collected acoustic signals of bearings in seven health conditions and validated the proposed method experimentally. Experimental results demonstrate that MDAT achieves an average fault identification accuracy of 98.91%, outperforming both no-transfer models and classical multi-source domain adaptation methods, thereby underscoring its practical relevance and superior diagnostic performance for industrial fault diagnosis.