In real-world applications, large-scale outdoor Li- DAR point cloud registration faces significant challenges, including data sparsity, occlusions, and reliance on expensive ground-truth pose labels. To address these issues, this paper proposes an unsupervised registration framework based on spherical projection consistency. Specifically, both the input point cloud and its spatially transformed counterpart are projected into range images, and their spatial consistency is exploited as a supervision signal. Furthermore, a multi-scale patch-topatch feature fusion module is introduced to effectively integrate features from point clouds and range images, thereby enhancing feature discriminability. In addition, a dynamic masking strategy is applied in the range image domain to mitigate the impact of sparsity variations and further strengthen the spatial consistency of the supervision signal. Extensive experiments on the KITTI and NuScenes datasets demonstrate that the proposed method outperforms state-of-the-art unsupervised approaches, validating its effectiveness and robustness in large-scale outdoor scenarios.