The high cost of collecting and processing high-quality motor fault data samples has resulted in the collection of newly unlabeled data samples. Domain adaptation has emerged as a promising approach to process and recognize new unlabeled data with the help of existing data. This has led to a surge of interest in domain adaptation in the field of fault diagnosis. In the field of electric machine fault diagnosis based on domain adaptation, two issues require attention. A conflict arises in the gradients of multiple tasks when employing the conventional domain adaptation framework. And, the existing methods rarely study the migration task between complex states. In light of the aforementioned issues, this paper puts forth AMDA motor fault diagnosis method based on multi-task alignment, with the aim of providing a solution to the aforementioned problems. The AMDA method employs a feature extractor comprising a multi-task one-dimensional convolutional layer, a batch normalization layer, and a pooling layer, to extract the higher-order features of the source and target domains. Subsequently, a combination of an adversarial-based approach and a distributional difference metric-based approach is utilized to reduce the distributional differences of data features. Finally, a multi-task learning approach based on gradient alignment is introduced to balance and optimize the three tasks: fault classifier, domain discriminator, and distributional difference metric. By reducing the conflicting gradients among the tasks, this approach ultimately enables the development of a domain adaptation fault diagnosis model for acoustic signals of electric motors based on multitask learning. Cross-operational state fault diagnosis tests are conducted under multiple test setups using the proposed AMDA method, and the test results demonstrate that the AMDA method effectively accomplishes the migration task between stable operational state (Stable), start operational state (Start), and European driving cycle state (NEDC) in the acoustic signal. Based on cross-operational state electric motor fault diagnosis tests, the highest diagnosis accuracies reach 91.49%. Furthermore, the performance of AMDA method is significantly higher than that of other methods in the two comparison tests, which offer valuable insights for research and engineering applications.