Existing contrastive learning methods for anomalous sound detection refine the audio representation of each audio sample by using the contrast between the samples' augmentations (e.g., with time or frequency masking). However, they might be biased by the augmented data, due to the lack of physical properties of machine sound, thereby limiting the detection performance. This paper uses contrastive learning to refine audio representations for each machine ID, rather than for each audio sample. The proposed two-stage method uses contrastive learning to pretrain the audio representation model by incorporating machine ID and a self-supervised ID classifier to fine-tune the learnt model, while enhancing the relation between audio features from the same ID. Experiments show that our method outperforms the state-of-the-art methods using contrastive learning or self-supervised classification in overall anomaly detection performance and stability on DCASE 2020 Challenge Task2 dataset.