The success of deep neural networks usually relies on massive amounts of manually labeled data, which is both expensive and difficult to obtain in many real-world datasets. In this paper, a novel unsupervised representation learning network, UMA-Net, is proposed for the downstream 3D object classification. First, the multi-scale shell-based encoder is proposed, which is able to extract the local features from different scales in a simple yet effective manner. Second, an improved angular loss is presented to get a good metric for measuring the similarity between local features and global representations. Subsequently, the self-reconstruction loss is introduced to ensure the global representations do not deviate from the input data. Additionally, the output point clouds are generated by the proposed cross-dim-based decoder. Finally, a linear classifier is trained using the global representations obtained from the pre-trained model. Furthermore, the performance of this model is evaluated on ModelNet40 and applied to the real-world 3D Terracotta Warriors fragments dataset. Experimental results demonstrate that our model achieves comparable performance and narrows the gap between unsupervised and supervised learning approaches in downstream object classification tasks. Moreover, it is the first attempt to apply the unsupervised representation learning for 3D Terracotta Warriors fragments. We hope this success can provide a new avenue for the virtual protection of cultural relics.