Evaluate extrapolation suitability of the polynomial Fourier model

Determine whether the polynomial Fourier series model for load-, velocity-, and temperature-dependent transmission errors in cycloidal drives remains suitable when extrapolating beyond the load-torque, velocity, and lubricant-temperature ranges used for parameter identification.

Background

The model is validated using Sobol quasi-random measurements whose load torque, velocity, and temperature remain within the minimum and maximum bounds of the identification data. Consequently, the reported validation results establish interpolation performance within the identified operating domain but do not establish behavior outside that domain. Assessing extrapolation is important because the quadratic dependence of Fourier amplitudes, phases, and offset on the operating variables may produce inaccurate or physically implausible predictions beyond the measured range.