In order to facilitate the computation of the stiffness matrix for angular contact ball bearings under arbitrary load and operating conditions, a five-degree-of-freedom stiffness calculation model grounded in the theory of the bearing quasi-static method without raceway control hypothesis is proposed. On the basis, the above model innovatively integrates explicit and implicit differentiation techniques to analytically determine the stiffness matrix of ball bearings. Recognizing the potential for parameter uncertainties in bearing design and manufacturing, the action mechanism of interval uncertainty on bearing stiffness change is further studied by using Chebyshev polynomial method, and the influence of multiple structural parameters uncertainties inside bearings on their stiffness changes are discussed. The results demonstrate that the proposed method effectively calculates the stiffness matrix of ball bearing with interval uncertain parameters. As the axial load increases, bearing stiffness exhibits a typical exponential growth trend, while a rise in rotational speed leads to a modest decline trend in stiffness. Additionally, key parameters such as the ball diameter, inner and outer raceway contact diameters, and inner and outer contact curvature radii play significant roles in bearing stiffness.