Domain generalization techniques are often used to address the distribution differences between training and testing data. Existing studies are mostly based on the assumption that the label spaces of the training and testing data are consistent. However, as complex industrial equipment operates, unknown faults may emerge in the testing data. This scenario is referred to as open-set domain generalization (OSDG), where traditional domain generalization diagnosis models tend to fail. Therefore, an auxiliary-feature-embedded causality-inspired dynamic penalty network (ACDPN) is proposed for OSDG diagnosis. A label reconstruction strategy and a memory dynamic penalty term are designed to enhance the model's sensitivity to low-probability unknown classes. The dynamic penalty helps balance the model's learning of known classes with its attention to unknown classes. To enhance the model's generalization performance for diagnosing known classes, a causal loss under causal intervention is constructed to extract domain-invariant causal features. Meanwhile, auxiliary features that can reflect the physical characteristics of the signals are extracted to jointly drive the classification predictions of the diagnosis model, enhancing the model's decision-making ability. In the target domain decision stage, a dual-path optimal matching strategy and a multi-class similarity quantification strategy are incorporated to enhance the model's diagnosis performance and quantitatively predict the categories of unknown faults, thereby increasing the practical engineering value of OSDG diagnosis. Comparative experiments, ablation studies, and model interpretability analysis experiments are conducted on two multi-domain datasets, and the results demonstrate the effectiveness and superiority of the proposed method in OSDG scenario.