The existing deep transfer learning-based intelligent fault diagnosis studies for machinery mainly consider steady speed scenarios, and there exists a problem of low diagnosis efficiency. In order to overcome these limitations, an unsupervised domain-share convolutional neural network (CNN) is proposed for efficient fault transfer diagnosis of machines from steady speeds to time-varying speeds. First, a Cauchy kernel-induced maximum mean discrepancy based on unbiased estimation is developed for improving the efficiency and robustness of feature adaptation. Secondly, an unsupervised domain-share CNN is constructed to simultaneously extract the domain-invariant features from the source domain and the target domain. Finally, adjustable and segmented balance factors are designed to flexibly weigh the distribution-adaptation loss and cross-entropy loss to improve diagnosis accuracy and transferability. The proposed method analyzes raw vibration signals collected from bearings and gears under different rotating speeds. Results of case studies show that the proposed method can achieve higher diagnosis accuracy, faster convergence, and better robustness than the reported methods, which demonstrates its potential applications in machine fault transfer diagnosis from a steady speed condition to a time-varying speed condition.