A NURBS curve-based method for quantifying high-speed train wheel wear

To support real-time wheel-rail matching monitoring for high-speed trains, this study proposes a unified representation of wheel tread wear over a complete reprofiling cycle. Measured wheel profiles showed dominant hollow wear, mainly in segments BC, CD and DE near the nominal rolling circle. Cubic Non-Uniform Rational B-Spline (NURBS) curves were used to represent worn tread profiles segment by segment. For BC and CD, common control vertices and knot vectors enabled NURBS weight factors to describe profile evolution across mileage stages. For DE, wear was classified as mild, moderate or severe; wear width was represented by intermediate control points and wear depth by NURBS weight factors. Contact-geometry analysis showed good agreement between NURBS-fitted and measured profiles, with normal fitting errors below 0.35, 0.10 and 0.05 mm for BC, CD and DE, respectively. Among the tested regression models, the quadratic polynomial model gave the highest accuracy, with DE wear-depth error below 0.005 mm and wear-area errors for BC, CD, and DE below 0.15 mm2. The method provides a parametric basis for tread evolution characterisation and maintenance decision-making.