Abstract-Two new models for specific power losses in cold-rolled motor lamination steel are described together with procedures for coefficient identification from standard multifrequency Epstein or single sheet tests. The eddy-current and hysteresis loss coefficients of the improved models are dependent on induction (flux density) and/or frequency, and the errors are substantially lower than those of conventional models over a very wide range of sinusoidal excitation, from 20 Hz to 2 kHz and from 0.05 up to 2 T. The model that considers the coefficients to be variable, with the exception of the hysteresis loss power coefficient that has a constant value of 2, is superior in terms of applicability and phenomenological support. Also included are a comparative study of the material models on three samples of typical steel, mathematical formulations for the extension from the frequency to the time domain, and examples of validation from electrical machine studies.Index Terms-Brushless permanent-magnet (BLPM) motor, cold-rolled motor lamination steel, core loss, electric machine, Epstein test, finite-element analysis (FEA), interior permanentmagnet (IPM) motor, iron loss.

IntroductionTorque calculation of a rotating machine in a finite element solution (FEA) may seem straightforward however there can be considerable error. The most common method for calculating torque uses a Maxwell stress tensor integral. However, unless the mesh is well meshed the results will be poor. Even with a good mesh there are errors and [1] recommends that several integral paths at different radii in the air-gap is used and an average taken. Several methods exist to calculate the torque with the aim to minimize the error and produce a good calculation, and these were recently addressed in [2] [3]. These varied in their approaches and use techniques such as the Virtual Work and Maxwell Stress Filter methods. Many methods have been implemented in commercial software (e.g., PC-FEA from the SPEED Laboratory, University of Glasgow). These techniques rely on a good mesh which is one that exhibits geometrical symmetry in terms of the airgap, poles and slots; automatic mesh generators now address this [4]. The air-gap should also be multilayer and ideally, as rotation takes place, the shape of the elements should stay constant. Alternatively, an early paper [5] addresses a technique which uses the change in stored energy to calculate the torque and this method is addressed in this paper. Example Machine, FEA and Method An example machine is used to test the method (Fig 1) using PC-FEA. This is a brushless permanent magnet 6-pole 3-phase machine. The results are compared to other methods already implemented in the software and tests conducted under different loadings and step angles, and irregular meshing. While intuitively, it may seem reasonable to reduce the step angle, many methods rely on differences in stored energy or coenergy, and these differences become small at small step angle so that numerical errors occur. It can be convenient to break the torque down into different components, such as the mean torque (which can be obtained from current/flux-linkage loops), instantaneous torque (which can be obtained from Maxwell stress) and cogging torque (which can be obtained from the Virtual Work method, which uses the change in system coenergy assuming the there is either no or constant electrical excitation). The Virtual Work method will be described and fundamental explanations put forward to highlight the limitations of the method. The Energy Difference method can be simply noted as: mechanical work done = input energy during step -increase in stored energy where work done = torque * step angle This neglects the copper and iron losses. The advantage to this method is that it is general, and valid for both cogging and load torques. Results Fig 2 shows the results for the torque calculation using different methods including the Energy Difference (TqE). The other methods use an averaged Maxwell stress using two integrals with two fur-