Determining The Force Transducer Parameters Algebraically Based on The Transfer Function in Frequency Domain of The Sinusoidal Dynamic Measurement System

Abstract This paper presents an algebraic method for determining the equivalent stiffness and damping coefficients of force transducers from sinusoidal dynamic calibration data, and compares it with conventional Lorentzian curve fitting. The novelty lies in using the system's transfer function algebraically to directly represent the transducer's dynamic behavior, thereby avoiding the model-form error inherent in the Lorentzian approximation and improving identifiability particularly for the damping coefficient, whose small magnitude makes it highly sensitive to fitting inaccuracies. Furthermore, the method includes a systematic frequency-point selection strategy and a comprehensive uncertainty analysis that explicitly accounts for correlations between the input quantities, aspects not addressed in previous algebraic identification studies. The method solves the idealized single-degree-of-freedom transfer function directly from the amplitude ratio at two frequency points, eliminating iteration, initial guesses, and convergence checks. Uniqueness was proven through the Jacobian determinant, and the normalized condition number ranged from 1.34 to 18.5, confirming that the method is well-conditioned. The method was applied experimentally to two force transducers with capacities of 5 kN and 20 kN. Nonlinear fitting of the same transfer function served as a consistency check, with stiffness agreeing within 1% and damping within 1.7%–14.02%, well within the expanded uncertainty. Independent validation on unused data achieved an adjusted coefficient of determination of approximately 0.99. The algebraic method yielded smaller damping uncertainty than the Lorentzian method and executes in less than 1 ms per frequency pair, making it suitable for practical calibration.