Multiball-independent static modeling of linear ball guides considering raceway surface topography and variable load deformation

Accurate analysis of linear ball guide stiffness influencing factors requires establishing micro-geometric and load-deformation models. Existing methods assume identical ball contact states and use Hertzian contact theory for 2D models, unable to represent 3D contact characteristics like feeding-induced variations. This paper proposes a multiball-independent contact analysis method, establishing a static mechanical model considering raceway topography and load-induced micro-deformations. Individual ball contact states are independently analyzed to build the multiball-independent model. Raceway topography is introduced as a variable, with curve-fitting functions characterizing micro-topography. With 5 µm amplitude and 90 mm wavelength topography under 13 kN total load, slider deformation fluctuates between 13.92 µm and 14.31 µm during stroke. Finite element and theoretical comparisons show average absolute deviation below 10 %, confirming the model’s accuracy in analyzing raceway topography’s effect on stiffness.