Normal calculation of the carrier harmonic iron losses (CHILs) brought by the pulse width modulated (PWM) voltage source inverter in interior permanent magnet synchronous motors by the time-stepping finite-element analysis (TSFEA) with short time steps is very time-consuming. In this study, a novel method for fast calculation is proposed, where a combination of the frozen differential reluctivity tensor method and the time-harmonic finite-element analysis is proposed to investigate the relationship between PWM voltage harmonics and the corresponding CHILs, with which the CHILs in stator and rotor are fastcalculated with the voltage harmonics in stator and rotor reference frames, respectively. Besides, the eddy current reaction effect in electrical steel sheets on the CHILs at high frequency is considered by an analytical method and validated with the TSFEA. The results reveal that eight parameters are recommended to calculate the CHILs at different operating conditions, which vary with the fundamental current. Consequently, the CHIL map over the entire operating conditions can be fastcalculated using the analytical spectra of the PWM voltages. Experiment on a specimen is conducted to validate the accuracy of the proposed method, which shows it depends on whether the equivalent differential permeability of the silicon steel can be accurately modelled.

An analytical model was developed to predict the tensile behaviour of a corroded steel bar. The model was established based on cross sectional analysis and was validated using experimental data for slotted steel bars and electrochemically corroded steel bars. The model was further used to predict the tensile behaviour of a corroded steel bar. The corrosion mode of the steel bar was supposed to be pitting corrosion and the distribution of the corroded section was supposed to follow a lognormal distribution. A power law between the parameters of the lognormal distribution and the average corrosion rate of the steel bar was used to predict the statistical distribution of the cross section area of a corroded steel bar. Based on these assumptions, the yield strength, ultimate strength and ductility of a corroded steel bar were predicted with different corrosion rates. The predicted behaviours are compared to collected experimental results from various sources. It is found that the numerical results of yield strength and ultimate strength agree well with the collected experimental results. The model slightly underestimates the ductility of the corroded steel bars. The result of the model would be helpful for the prediction of the tensile behaviour of reinforced concrete member subjected to chloride induced corrosion.