A 3D shell-based intelligent tire framework for lateral force estimation using axially distributed acceleration measurements

Lateral tire force is crucial for vehicle stability and handling performance yet remains difficult to estimate accurately. Conventional methods rely on onboard measurements and infer tire forces indirectly through vehicle and tire dynamics models, making them highly sensitive to modeling errors. Intelligent tires offer a more direct route by reconstructing forces from internal acceleration measurements; however, existing ring-model-based approaches neglect widthwise deformation variations and thus perform reliably only under pure side slip. This study proposes a physics-based lateral-force estimation framework integrating a three-dimensional shell-based analytical model with axially distributed sensing strategy. The shell formulation captures coupled circumferential–axial–radial deformation of the tire, and closed-form kernel functions are derived through circumferential mode expansion and axial shape-function solutions. These relationships establish a linear observation matrix mapping distributed contact excitations to global multi-axis acceleration responses, enabling an efficient least squares inverse scheme for real-time force estimation. Tire-bench experiments with an intelligent-tire prototype achieve normalized errors below 6% and fast convergence across varying loads, speeds, and slip conditions. Comparative validation against ring-based estimators using acceleration data generated by finite element simulations shows markedly higher robustness under combined-slip conditions with slip angles up to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mn>15</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>°</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . Co-simulations using CarSim–Simulink inversely reveal that vehicle-dynamics-based observers, established using a UKF with linear and brush tire models, both suffer sharp accuracy loss or divergence beyond <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mo>±</mml:mo> <mml:mn>1</mml:mn> <mml:mo>.</mml:mo> <mml:msup> <mml:mrow> <mml:mn>5</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>°</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . The proposed intelligent-tire-based estimator, grounded in three-dimensional shell-based tire analytical model and spatial sensing strategy, offers a reliable, interpretable, and scalable foundation for next-generation vehicle control.