In an actual industrial environment, the complex working environment of mechanical equipment may lead to new faults in the target domain, called the open-set domain adaptation problem. Recently, open-set adaptive fault diagnosis has been extensively employed. However, most studies not only require pre-set fixed thresholds to identify unknown class features but also ignore the learning of discriminable features under specific tasks, which affects the diagnostic performance. Hence, this paper proposes a complementary weighted dual adversarial network combined with supervised contrastive learning (CWDAN-SCL) to address the open-set cross-different working fault diagnosis of bearings. Specifically, a novel complementary weighted adversarial learning strategy is designed using supervised classification and uncertainty measurement to effectively control the participation of target domain features in the domain adaptation process and achieve the alignment of shared class fault features between the source and target domains. Moreover, an adaptive unknown fault separation module is designed using an adversarial learning method to construct a hyperplane between shared and unknown class fault features in the target domain to identify unknown class faults accurately. Additionally, a supervised contrastive loss term is designed based on contrastive learning and label knowledge to improve the aggregation of fault features of the same class and enhance the model's generalization ability in target domain diagnosis tasks. Subsequently, the efficacy and advancement of the proposed method are substantiated through experimentation on two datasets. The experimental results illustrate that the average diagnostic performance of the proposed method is 91.73 %. This study contributes a dependable diagnostic approach for ascertaining the health status of rotating machinery equipment.