Loss parameter identification of a welded ring core lamination of NO‐electrical steel

Lamination packaging processes such as welding lead to a significant material degradation of non‐oriented (NO) electrical steel sheets. Increase in iron loss and decrease in permeability are the results of the deterioration. For an efficient modeling of a drive train, the accurate parameterization of the iron loss is of upmost importance. For this reason, the iron loss model is expanded to include the influences of welding procedure. Its influence can be classified into changes in the grain size diameter dG$$ \left({d}_{\mathrm{G}}\right) $$ and residual stresses σ$$ \left(\sigma \right) $$ . In this study, a locally varying iron loss model for the simulation of effects of weld‐packaging on the electromagnetic properties of non‐oriented (NO) electrical steel sheets is presented. Packaging technologies such as interlocking, welding, clinching and gluing are typically utilized for the manufacturing of electric steel stacks of electric machines. Understanding the micro‐structural changes due to the macro‐structural degradation accruing to weld‐packaging helps in the accurate understanding of its influence on the performance and achievable range of the electric vehicle. Five (5) electric steel probes are annealed for the modeling of the local varying iron loss model at five different temperatures and electromagnetically measured to determine its magnetization and loss values. This will help in determining the grain size dependency of the different loss parameters. The annealed probes are measured under mechanical stresses showing also the residual stress dependency.


| INTRODUCTION
A prerequisite for the manufacturing of a mechanically stable magnetic core of an electrical ac machine is the firm connection of the electrical steel sheets.The current states of the art in mechanical packaging of electrical machines are interlocking, welding, clinching and gluing.Each packaging technology deteriorates the electromagnetic properties of the electrical steel sheet differently. 1 Effects of this deterioration are evident in the increased iron loss and decreased magnetizability of the material.Welding is one of the most utilized packaging technologies due to the ease of its incorporation into the manufacturing process.][4] This heat dissipation gives rise to thermal degradation and local changes in the micro-structure of the utilized electrical steel sheets.This thermal degradation leads to increases in residual stress in and around the weld-area due to villari effect.This will deteriorate the magnetizability and iron loss of the material. 5,6Increased grain sizes result in increased iron loss at high frequencies.It can also lead to improvement of the magnetizability of the material, but the increases in residual stress results in an overall deterioration of the weld-packaged core.
In this study, a local changing loss parameter identification is introduced.This will enhance the understanding of the influence of local degradation due to weld-packaging on the different iron loss components associated with the non-oriented (NO) electrical steel.This will enable an application-dependent improvement of the deterioration effects of welding.Beginning with the calculation of the local residual stress and grain size distribution associated with the weld-packaging on the basis of equivalent heat source, to the electromagnetic measurements of the mechanically loaded and unloaded annealed probes, an iron loss model that maps the changes in material properties with the changes in electromagnetic properties of electrical steel.The modeling of the equivalent heat source with the same weld parameters as with the manufactured core, will enable the validation of the extended iron loss identification procedure using the characterized results of a manufactured ring core.

| EXPERIMENTAL APPROACH
For the annealing process, samples of non-oriented (NO) electrical steel strips of grade 280-30AP of 180 mm Â 60 mm dimensions are prepared.Three (3) samples of the same geometry are annealed with the same annealing temperature to ensure the repeatability of the process.The different probes are annealed at temperatures of 800, 900, 1000, 1100 and 1200 C. The measured average grain sizes of the annealed samples are 80, 97, 140, 237, and 277 μm, respectively, with the average grain size of the unannealed sample being 78 μm.The individual rings are cut to the aforementioned dimensions with the laser cutting process.Ring core samples of inner D inner and outer D outer diameters of 48 mm and 60 mm respectively are manufactured with the spot-weld packaging procedure for the validation of the model.The measured specific iron loss and magnetization values illustrate the electromagnetic properties of the ring core.The equivalent heat source are modeled using a laser beam power of 100 W, working pressure of 1 mbar (vacuum), weld speed and weld diameter of 0:135 m= min and 600 μm respectively.The manufacturing of the ring cores for the model validation is done with a multi-mode disc-laser with a focal length of 400 mm.

| MEASUREMENT RESULTS
The measured iron loss values of the annealed samples under different mechanical stresses are evaluated and analyzed in this section.Figures 1 and 2 depicts the iron loss of the annealed samples under no stress influence at lower (50 Hz) and higher (1000 Hz) frequencies.Observation of the high dependency of the iron loss on the micro-structural changes is seen.At low frequency, at first a slight deterioration of the losses is observed.This is due to positive effects of grain size on the hysteresis loss component and deterioration effect on the excess loss component.With increased microstructural degradation, a combination of the deterioration of both hysteresis loss and excess loss components leads to a significant increase in the iron loss.At high frequency, where the excess loss has a significant percentage of the total iron loss, an evenly distribution of the deterioration dependent on the grain size is observed.The influence of the micro-structure (grain size) on the iron loss is evident on the domain wall movements which are dependent on the size of the grains. 7The increase in the average grain sizes during weld-packaging is due to thermal energy dissipation associated with the procedure.The Equation (1) depicts the equivalent mathematical equation of the local changing permeability.
Figures 3 and 4 depicts the magnetization and the specific iron loss of the magneto-mechanical coupled sample annealed at a temperature of 800 C. It can be seen that the deterioration of the magnetizability is visibly observed at F I G U R E 3 Magnetizability at 1000 Hz.
][10] This is due to increased mobility of grains at low stress values due to domain wall smoothness.A continued increase in the mechanical stress results in an increase of the specific iron loss with reference to the results of a sample loaded with 50 MPa.The decrease in magnetizability results in the increase of the required magnetic field strength for the attainment of specific flux density rapidly at very high mechanical stress values.Whereas at a frequency of 1000 Hz, the measured deterioration of the magnetic field strength at a stress of 100 MPa is 21% in comparison to characterization results at an unloaded state (0 MPa), the loading of a stress of 200 MPa results in the deterioration of the magnetizability by almost 75%.

| FEM SIMULATION
The electromagnetic simulation is premised upon the modeled equivalent heat source, with which the residual stress and micro-structural (grain size) distributions are simulated.The residual stress and micro-structural (grain size) distributions alongside the reference geometry and the material model forms a closed simulation loop, with which the electromagnetic analysis of the effects of welding can be achieved.The modeling of the equivalent heat source is realized from the temperature profile of the weld-packaging procedure and the welding parameters (beam power, degree of absorption, welding speed, focal diameter, etc.).To incorporate the effect of temperature changes, the equivalent heat source is modeled as a thermal load.The use of laser of efficiency 60%, a laser power of 328 W will result in an effective 200 W thermal load.The entire equivalent heat source comprises of two loads.The electromagnetic simulation of a ring core (reference) model with a local varying material (stress and grain size values) model will enable the characterization of the deterioration effect of weld-packaging.The Simufact software is used in the simulation of the residual stresses.
Initially, a single weld spot was simulated, revealing maximum stresses of approximately 700 MPa just above the weld spot.Subsequently, the stress distribution on a laminated core is simulated using a lamination stack of 30 lamellas.The spot welds are evenly distributed statistically to ensure an equal distance between all points on average.In Figure 5 is the simulated stress distribution inside the ring core shown.It depicts first an overall increase in the stress values and later a decrease with increasing distance from the weld-point.A 3D-FEM simulation should provide a complete representation of the electromagnetic field distribution within the sample.Due to its high time consumption, a 2D-simulation with an analytic solution to the eddy current problem as a prerequisite is presented.The analytical solution of the eddy current problem enables the understanding of electromagnetic field distribution in the radial direction of the core.The 2D-simulative investigation of the effect of weldpackaging on the electromagnetic properties of a laminated core is then achieved by solving the magneto-static vector potential formulation of the finite element method.This formulation involves the impression of current by defining a current density in the winding system.The determination of a vector potential A

| ANALYTIC CALCULATION OF THE EDDY CURRENT LOSS
The eddy current loss of a weld-packaged ring core can be analytically calculated using an equivalent electric circuit model. 11The model consists mainly of the induced voltage sources and resistors.The induced voltage U ind can be calculated from the lamination area A ring , the angular frequency ω and flux density B. The calculation is done according to Equation 3 and at a frequency of 1000 Hz.
To effectively estimate the behaviors of the eddy current, the lamination resistor is subdivided into resistance along the lamination thickness R thickness and along its width R width .The sum total of these two resistances is the lamination resistance R lam .This subdivision will enable the accurate application of the Kirchhoff's node rule.The total lamination resistance is calculated using Equation (4).Whereas the lamination area A lam described the area of the eddy current path inside the ring, the lamination length l lam describes the length of the flow.The qualitative description of the global eddy current loss using resistors is premised upon the dependency of this iron loss component to the physical (thickness d) and electrical (conductivity ρ el ) properties of the steel sheets. 12 In Figure 6 is the depiction of the eddy current path for both the lamination core and also the connection.Connection resistance R con ð Þ is the resistance emanating due to the welding process and describes resistance between the ring probes.It is dependent on the radius of the welded area r weld , penetration depth d weld and the connection length l weld .The penetration depth can be influenced by the type of utilized laser and the weld parameters.The ellipse modeling of the area is due to the uniformity in the welded area.With the usage of multi-mode disc-laser and welding at room pressure, the penetration depth is measured to be 0.366 mm.
To ensure a good mechanical stability of the ring core, rings are welded many times.The different resistances accruing to the welded area can be summarized through the assertion of parallel connections between them.This leads to the calculation of the total resistance according to Equation (11).
The application of the equivalent circuit diagram in Figure 7 will result in a comprehensive calculation of the eddy current loss of a welded ring core.Two welding methodology is used to analyze this analytic model.Ring core welded only at the outer ring side and ring cores welded at both the inner and outer sides.Figure 8 depicts the calculated eddy current of ring core welded at the outer side.For the inner side is an assumption of a very high connection resistance, thereby not enabling a current flow.The loss emanating from a glued ring core consisting of 30 steel sheets equates to the loss of a one-side welded ring core consisting of 30 steel sheets.This shows that the one-sided welding of ring cores does not increase the eddy current loss component of iron loss.This is because the global eddy current path cannot be increased with a one-sided connection of the ring core.In Figure 9 is the depiction of the calculated eddy current loss of ring cores welded at both sides.It can be observed that loss emanating from a glued ring core consisting of 30 steel sheets is approximately the same as the loss emanating from a bothside welded ring core consisting of only nine steel sheets.This shows a significant increase in the global eddy current loss due to increases in global eddy current path.
The validation of the analytic model is achieved with the comparison of the calculated and measured eddy current loss.For this comparison a method of extracting the measured eddy current loss component is presented. 13First, the iron loss parameters of the glued ring core (reference sample) is extracted from the measured loss using Equations ( 12)-( 14).Then the loss parameters of the one-side welded ring core is equally extracted.
The different between these losses results in the exact increases of the hysteresis P hyst,increase , excess P excess,increase and nonlinear P NL,increase loss components due to welding and are calculated using Equations ( 15)-( 17)).Finally, the eddy current loss of a both-sides welded ring core P eddy,bothÀsides is calculated with the subtraction of the hysteresis, excess and nonlinear (NL) loss components (see Equation ( 18)).
The validation with a both-sides welded ring core is premised upon the evidence of the eddy current loss increases due to welding of both sides of the ring core (inner and outer sides).Figures 10 and 11 depicts the normal and gravimetric eddy current loss of the measured ring core and the calculated ring core at a frequency of 1000 Hz, respectively.
With these results, it can be postulated that a 2D-FEM simulation the complete characterization of the electromagnetic behavior of the welded ring cores because the eddy current losses calculated on the basis of the ring core geometry almost correlate with the eddy current losses measured from the welded ring sample.The iron loss model will be introduced into the FE simulation using Equation (20).

| VALIDATION OF THE MODEL
Ring cores welded with the same parameters of laser power of 328 W, a focal position of 0 mm and atmospheric working pressure of 1 bar of the equivalent heat source are prepared for the validation of the material model.The grain size and residual stress distribution are simulated with these welding parameters.In Figure 14 is the measured and simulated iron loss result of welded as well as glued ring probes shown.An observation of an increase in the iron loss due to welding can be seen in the measured and simulated results.This is in part due to high increases of the residual stress and also due to changes in the grain size distribution emanating from the weld-packaging process.At low flux densities, an improvement of the electromagnetic properties can be observed.This is due to measurement inaccuracy attributed to this flux density range.Figure 15 depicts the measured and simulated percentage degradation of the welded ring probes.The percentage degradation is calculated according to Equation (21).A maximum percentage degradation of 10% was measured as well as simulated using the material model.The results of the simulated ring core can be seen to be in good agreement with the measured ring probe.The absolute deviation of the simulated values to the measured values can be observed to be under 5%.The differences are due to the sensitivity of the different measurement procedures of the ring probes and the SST-probes.ΔP Fe % ½ ¼ 100 Á P fe,welding À P fe,glued À Á Figure 16 depicts the deviation of the simulated values from the measured one for both the glued sample and the welded sample.The deviations are calculated using Equation (21).At low flux density, a higher value of deviation of the simulated result from the measured result is observed.This is due to measurement inaccuracies at this flux density range.The Deviation values are calculated with the Equation (22).Interpolation methodology (calculation of the reluctivity values) of the material model are some of the reasons for the deviations of the simulated result from the measured result.
The extrapolation of the reluctivity values is achieved the Froehlich-Kennelly approximation.A better agreement of the results is achieved for the higher flux density range due to the efficiency of the measurement setup at high flux density.These validation results show that modeling of the effects of weld-packaging on the electromagnetic properties with a local varying material model is a better approach of calculating the electromagnetic properties of a weldpackaged geometry.

| CONCLUSIONS
To efficiently analyze and evaluate the effects of weld-packaging, the development of a model, that encompasses the changes in the electromagnetic properties of the utilized electric steel due to welding, is required.For this purpose, a locally varying material model is presented.The model depicts the local variations in the electromagnetic property due to packaging effect.These variations are in part due to the increases in the residual stresses and also to changes in the average grain sizes in and around the weld area.The calculation and estimation of the grain size distributions and also the residual stress distributions is realized using an equivalent heat source.This source contains information about the welding process.This calculation is premised on the accurate modeling of the mode and degree of diffusion of the thermal energy.The reproduction of the accurate electromagnetic properties by the material model is realized through the electromagnetic measurements of samples annealed with temperatures of 800, 900, 1000, 1100, and 1200 C. The electromagnetic characterization of the annealed probes depicts a general deterioration of the properties with increasing grain sizes and residual stresses.It can be observed that increasing grain size leads to an exponential increase in iron loss.At high grain sizes, the effects of residual stresses become increasingly degrading on the electrical steel sheet.The analytic modeling of the effect of welding on the electromagnetic properties shows that a one-sided welding of the ring probes does not increase the eddy current loss.With a relative deviation of the analytic model of 5% at high flux densities, it can be concluded that the result represents a realistic behavior of the eddy current in a welded sample.
The model was validated with the characterization of a welded ring probe.It shows increases in the iron losses due to weld-packaging.This can be attributed to the dependencies of the hysteresis loss component and excess loss components to the residual stress and average grain size changes due to weld-packaging of the electrical steel sheet.The results of the simulated ring core can be seen to be in good agreement with the measured ring probe due to a maximum percentage degradation of 10% observed using the material model.The absolute deviation of the simulated values to the measured values can be observed to be under 5% with differences due to the sensitivity of the different measurement procedures of the ring probes and the SST-probes.At low flux densities, a higher value of deviation of the simulated result from the measured result is observed.This is due to measurement inaccuracies at this flux density range.A more visible deterioration of the iron loss is observed for both simulated and measured ring cores at flux densities higher than 0.8 T.

! 4
, whose r Â A ! ¼ B ! ensures a divergence free magnetic field, that is r Á B ! ¼ 0. During pre-processing, the modeling of weld-packaging procedure's Iron loss at 1000 Hz. equivalent heat source, with which the residual stress and micro-structural change distributions is determined, is achieved together with the ring core geometry to be simulated.The accurate simulation of the weld-packaging process involves the mapping of the magnetization and iron loss models with the local distribution of the grain size and residual stress, to account for the local degradation of the material occasioned by the procedure.This micro-macro mapping represents the complete material model, that accounts for the deterioration due to weld-packaging.This enables the simulation of a ring core geometry with local varying material properties.The simulated geometry has dimensions of outer D outer and inner D inner diameters of 60 mm and 48 mm respectively.The material 280-30AP has a thickness of 0.3 mm.For good comparison during the verification phase, the height of the core is determined to consist of 30 electrical sheets amounting to 9.9 mm with the inclusion of the isolation coatings.During post-processing, the iron loss components are determined through the application of the iron loss model using the local values from the flux densities distributions.

8
Eddy current loss of one side welded ring core at 1000 Hz.

9
Eddy current loss of both sides welded ring core at 1000 Hz.

5
Iron loss increases due to welding.

5 F I G U R E 1 6
Deviation of the simulation from the measurement.
Figures 12 and 13 depicts the percentage deviation of the calculated values to the measured eddy current loss and is calculated using Equation (19).rel: deviation in % ¼ P fe,calculated À P fe,measured P fe,measured :