FedAC is an adaptive clustered federated learning framework designed to address the challenges of data heterogeneity in federated learning (FL). The framework integrates global and intra-cluster knowledge by decoupling neural networks into submodules, each with distinct aggregation methods. It introduces a low-rank cosine model similarity metric for efficient online model similarity measurement and includes a cluster number fine-tuning module to dynamically adjust the cluster count during training. Extensive experiments on the CIFAR-10 and CIFAR-100 datasets demonstrate that FedAC achieves superior performance compared to state-of-the-art methods, with test accuracy improvements of 1.82% and 12.67%, respectively, under different non-IID settings. The framework's effectiveness is validated through ablation experiments, showcasing its flexibility and robustness in handling complex, heterogeneous environments.FedAC is an adaptive clustered federated learning framework designed to address the challenges of data heterogeneity in federated learning (FL). The framework integrates global and intra-cluster knowledge by decoupling neural networks into submodules, each with distinct aggregation methods. It introduces a low-rank cosine model similarity metric for efficient online model similarity measurement and includes a cluster number fine-tuning module to dynamically adjust the cluster count during training. Extensive experiments on the CIFAR-10 and CIFAR-100 datasets demonstrate that FedAC achieves superior performance compared to state-of-the-art methods, with test accuracy improvements of 1.82% and 12.67%, respectively, under different non-IID settings. The framework's effectiveness is validated through ablation experiments, showcasing its flexibility and robustness in handling complex, heterogeneous environments.