Distortion in Fourier transform rheology due to frequency error

Fourier transform rheology (FT-Rheology) is a sensitive method to characterize nonlinear rheological properties. To achieve higher precision of FT-Rheology, many random and systematic errors of rheometers have been intensively investigated. Frequency error, the difference between the actual output frequency and set frequency, has never been reported. Therefore, this paper thoroughly investigates the adverse effects of frequency error on FT-Rheology. First, a nonlinear stress response function with frequency error was established and analyzed in both time-domain and frequency-domain. Then, time sweep tests were performed under large amplitude oscillatory shear at different values of frequency error. Because of the pitfalls of Discrete Fourier Transform, FT-Rheology results of nonlinear stress responses with frequency error show the periodic fluctuation and the significant time-length dependence. Finally, a method is provided to compensate for frequency error, and it can eliminate those unreasonable phenomena effectively.