Single-domain generalized deep metric learning (SDG-DML) faces the dual challenge of both category and domain shifts during testing, limiting real-world applications. Therefore, aiming to learn better generalization ability on both unseen categories and domains is a realistic goal for the SDG-DML task. To deliver the aspiration, existing SDG-DML methods employ the domain expansion-equalization strategy to expand the source data and generate out-of-distribution samples. However, these methods rely on proxy-based expansion, which tends to generate samples clustered near class proxies, failing to simulate the broad and distant domain shifts encountered in practice. To alleviate the problem, we propose CenterPolar, a novel SDG-DML framework that dynamically expands and constrains domain distributions to learn a generalizable DML model for wider target domain distributions. Specifically, \textbf{CenterPolar} contains two collaborative class-centric polarization phases: (1) Class-Centric Centrifugal Expansion ($C^3E$) and (2) Class-Centric Centripetal Constraint ($C^4$). In the first phase, $C^3E$ drives the source domain distribution by shifting the source data away from class centroids using centrifugal expansion to generalize to more unseen domains. In the second phase, to consolidate domain-invariant class information for the generalization ability to unseen categories, $C^4$ pulls all seen and unseen samples toward their class centroids while enforcing inter-class separation via centripetal constraint. Extensive experimental results on widely used CUB-200-2011 Ext., Cars196 Ext., DomainNet, PACS, and Office-Home datasets demonstrate the superiority and effectiveness of our CenterPolar over existing state-of-the-art methods. The code will be released after acceptance.