To address problems of large distribution difference in rolling bearing vibration data under different working conditions, difficulty in obtaining labeled vibration data under certain working conditions, the non-sharing of data among different users and the small amount of single user data, which lead to the low accuracy of the established diagnosis model, a federated feature transfer learning framework and a fault diagnosis method of rolling bearing under different working conditions based on the federated multi-representation adaptation are proposed. The time domain vibration data of rolling bearings are transformed by wavelet transform and the time-frequency spectrum can be obtained. The priori labeled public data are used as the source domain and the multi-user unlabeled privacy silos data are used as the target domain. A multi-representation feature extraction architecture is introduced to improve the original residual network, multi-representation features of source domain and target domain are extracted, and multi-user local models are constructed respectively. To enhance the security of the federated framework and reduce the communication overhead, the deep neural network model compression idea is used to improve the parameter transfer strategy in the federated transfer learning framework. A federated global model for rolling bearing fault diagnosis under different working conditions is formulated on the server side. On two bearing datasets, experimental results show that the proposed method can integrate soils data knowledge without multi-user sharing data, and establish an effective fault diagnosis model of rolling bearings under different working conditions, the average fault diagnosis accuracy canreach 97. 6% , which is at least 3. 2% higher than the single user modeling. which has high accuracy and strong generalization.