Motor Engineering
New Magnetic Parameters to Characterize Cold-Rolled Motor Lamination Steels and Predict Motor Performance

by K. Blazek, Ispat Inland Research Department and
C. Riviello, A. O. Smith Electrical Products Company

For several years, Ispat Inland Inc. and A. O. Smith Electrical Products Company have been jointly working on a project to use computer modeling to predict the operating parameters for motors and their dependence on cold-rolled motor lamination (CRML) magnetic properties.

Predicting Motor Operating Parameters

One analytical computer program, RMxprt by Ansoft Corporation, has been used to closely predict the operating characteristics of a commercial single-phase induction motor using many different CRML materials, both semi-processed and fully-processed. RMxprt uses two lamination material property curves as the basis for calculating the motor performance. The first curve is a plot of the core loss as a function of the induced field, B, from 0 to 2 Tesla. The second is the induced field as a function of the applied field from 0 to 2 Tesla. This second plot can be calculated from plots of the permeability as a function of the induced field. These two curves were obtained by determining the core loss and permeability from 0.05 Tesla to 2 Tesla in increments of 0.05 Tesla via Epstein testing. This resulted in a total of 40 determinations; hence, these curves were designated as 40-point curves. Previously published work from this joint effort demonstrated the irrelevance of the 1.5 Tesla permeability indicating CRML's influence on motor performance [1].

Figure 1. Efficiency as a function of 1.5 Tesla permeability for a single-phase induction motor. CLICK for larger graphic.

This conclusion is supported by additional work conducted in this research shown in Figure 1. As part of the initial work, the predictive capability of the models was verified by building motors of various CRML materials and comparing the measured motor performance to the predicted performance.

Since the 1.5 Tesla permeability was not relevant to motor performance, the question is raised - what are the relevant material properties of CRML that could predict motor performance? In an attempt to determine the important variables, all available CRML materials for which 40-point curves were available were inserted into a model developed for a single-phase induction motor, and the efficiency, stator current, and torque produced were calculated for each material. There were more than 100 materials used. This provided a broad database of motor performance versus CRML magnetic properties and allowed a simple linear regression analysis of the efficiency as a function of the two traditional magnetic parameters - 1.5 Tesla core loss and permeability, as well as many newly developed magnetic parameters. This analysis led to the development of two new magnetic parameters that are capable of predicting motor performance - the integrated average core loss (IACL) and integrated average permeability (IAP). The IAP and IACL are the integrated average of the permeability and core loss respectively over the range of induced field from 0 to 2 Telsa.

Predictor Equations for Efficiency, Stator Current, and Torque

Single-Phase Induction Motor

Multiple linear regression analyses were performed on the efficiency, stator current, and torque of a single-phase induction motor as used in residential air-conditioning units. The following independent variables were considered in the analysis for 145 different lamination steels: silicon content, aluminum content, manganese content, 1.0 Tesla core loss, 1.0 Tesla permeability, 1.5 Tesla permeability, 1.5 Tesla core loss, thickness, IAP, and IACL. Fully processed, semi-processed, and un-annealed materials were included.

The result for the efficiency was as follows:

Three-Phase Induction Motor

Identical multiple linear regression analyses were performed on the efficiency, stator current, and torque of a three-phase induction motor as used in the condenser fan of an air-conditioning unit for the same 145 different lamination steels. The result for the efficiency was as follows:

Correlation of IACL and IAP with Motor Performance

It has been shown that the 1.5 Tesla core loss and IACL are the only magnetic properties that are highly correlated with efficiency. Therefore, the 1.5 Tesla core loss is highly correlated with the IACL, which will be demonstrated later in this paper. The two aforementioned analyses also indicate that the IACL is highly correlated with the efficiency. Thus, the 1.5 Tesla core loss alone may be used as the sole magnetic parameter to specify CRML materials for use in motors. The IAP may be used as a second parameter as an indication of the permeability of a CRML, but its effect on motor efficiency is negligible compared to the IACL.

The direct link of the IACL and IAP of a CRML material with the efficiency of a motor constructed from such a material will have large implications on the future design efforts of motor manufacturers. Presently, whenever a new material is being considered for use in an existing motor design, several prototype motors must be made using the new material. This entails punching the laminations of the proposed CRML material, annealing the laminations, and then constructing the motors. The motors must then be tested on a dynamometer to determine the efficiency and other operating parameters. The results are then compared to motors made with the currently used CRML material to determine if the new CRML material is acceptable. This must be done even when the same CRML material is used but is of a different thickness. This entire process is time consuming and can take several months to a year to complete.

Using the aforementioned results, computer motor models can be utilized to establish equations relating the IAP and IACL to motor efficiency, stator current, and other variables for a specific motor design. A material being considered for use in the motor can then be tested to determine the IACL and IAP, or these values can be provided by the producer of the CRML material. The effect of the material on motor performance can be predicted without constructing test motors. This process will only take minutes instead of months.

Also, in the future, CRML steels could be sold and specified based on some type of efficiency index. This index could be a normalized version of an equation such as equations (1) or (4). This would be possible since the equations for efficiency are obviously of the same form for different types of motors. Only the coefficients for the equations vary and, hence, the relative ranking of efficiency for any motor will be the same regardless of the type of motor in which the material is used.

Magnetic Parameters to be Used for Mill Qualification of CRML

Figure 2. Correlation between 1.0 Tesla and 1.5 Tesla core loss Ð Ispat Inland Commercial CRML. CLICK for larger graphic.

The IAP and IACL were selected as the parameters to be used to specify CRML for motor applications because they were highly correlated with motor efficiency. However, it is impossible for the mill to obtain these numbers for each coil processed in the mill due to the lengthy process of obtaining 40-point curves and their further processing to obtain the IACL and IAP. Therefore, other parameters were investigated that could be measured in the mill that would be indicative of the IAP and IACL. There was a high correlation between the 1.5 Telsa core loss and the IACL (r-squared of 0.9746 for linear regression). Therefore, it was obvious that the 1.5 Tesla core loss could be used to predict a value for the IACL.

Figure 3. Correlation between 1.5 Tesla core loss and 1.0 Tesla permeabilityÐ Ispat Inland Commercial CRML. CLICK for larger graphic.

While conducting the study, it appeared there was a strong correlation between the 1.0 Tesla permeability and the IAP. This was evaluated on the same data set as above. There was a high correlation between the 1.0 Telsa permeability and IAP (r-squared of 0.9833 for a linear transgression). It is obvious that the 1.0 Tesla permeability has an excellent correlation with the IAP; therefore, these two parameters can be used for mill testing of coils. The only drawback is that testing would now have to be done at two different induced field values instead of a single value.

Mill-tested Epstein packs from all Ispat Inland's commercial CRML grades were retested at 1.0 Tesla and 1.5 Tesla to see if there were strong correlations between the 1.5 Tesla core loss and either the 1.0 Tesla core loss or the 1.0 Tesla permeability. The information was gathered to see if only 1.0 or 1.5 Tesla measurements could be used in the mill to expedite testing. The plots for the correlations found are shown for all grades in Figures 2 and 3.

Figures 2 and 3 indicate that, indeed, the 1.0 Tesla core loss can be substituted for the 1.5 Tesla core loss. What is more important is that the 1.0 Tesla permeability is highly correlated with the 1.5 Tesla core loss. This means that by measuring the 1.5 Tesla core loss, the IACL and IAP have been essentially determined. The 1.5 Tesla core loss is highly correlated to the IACL, and it was shown earlier that there was a high correlation between the 1.0 Tesla permeability and the IAP.

Since Figures 2 and 3 were only semi-processed materials, it was necessary to verify the results for other types of CRML materials other than just semi-processed. This was done on the original database consisting of semi-processed, fully-processed, and un-annealed CRML materials. The correlation between the 1.0 Tesla permeability and the 1.5 Tesla core loss is not as high as expected based on the correlations observed in the commercial semi-processed material mentioned above. The r-squared value was only 0.6804. It was surmised that the reason for the poor correlation was that fully processed materials were included, and they did not follow the same trend as semi-processed CRML. If these fully processed materials are eliminated from the plot, then the r-squared value increases to 0.7976. This means that the correlation between the 1.0 Tesla permeability and the 1.5 Tesla core loss is good for only semi-processed materials; therefore, the 1.0 T permeability must be obtained to know the IAP for fully processed CRML.

Directionally Averaged Magnetic Properties

Figure 4. IACL as a function of angle to the rolling direction, W/kg. CLICK for larger graphic.

The entire discussion to this point has been concerned with magnetic properties that are obtained from Epstein frame samples consisting of one-half of the material being cut from the longitudinal or rolling direction of the CRML coil and the other half being cut in the transverse direction (L&T Epstein packs). It is obvious that magnetic fields in a motor are traveling at all angles to the rolling direction since these fields rotate around the center of the stator. Therefore, the proper magnetic properties to use in the design of a motor should be the directionally averaged properties from 0 to 360 degrees to the rolling direction of the CRML coil.

These properties have been derived for all of Ispat Inland's commercial CRML products. They have been obtained by making up Epstein packs that consist of all material being cut from one angle to the rolling direction of the coil and then measuring 40-point core loss and permeability curves for each angle. The angles to the rolling direction investigated were 0, 11.25, 22.5, 33.75, 45, 56.25, 67.50, 78.75, and 90 degrees. Symmetry was assumed for the remaining three quadrants, and plots of the IACL and IAP are shown in Figures 4 and 5, respectively.

Figure 5. IAP as a function of angle to the rolling direction. CLICK for larger graphic.

Similar plots could be made for the core loss and permeability at any value of induced field from 0 to 2 Tesla as well. Directionally averaged values for both core loss and permeability were obtained at each point in the 40-point curves. Figures 4 and 5 also contain the values of the IACL and IAP for an L&T Epstein pack and the directionally averaged IACL and IAP. The L&T values and directionally averaged values are not necessarily the same. Figures 4 and 5 show that the IACL is about the same for either method for this example, but that there is a slight difference in IAP. Larger differences in the L&T value compared to the directionally averaged value of the core loss or permeability may exist at a specific B field value than observed in the IACL or IAP.

The 40-point curves from which the IACL and IAP values were derived for both the L&T Epstein pack and the directionally averaged properties are shown in Figures 6 and 7 respectively. It is obvious from these figures that there is only a slight difference between the L&T and directionally averaged curves as well as the IACL and IAP values. Therefore, it is possible to use the L&T values of IACL and IAP in evaluating the performance of a motor with this type of material.

Figure 6. 40-point curves of core loss vs. B for an L&T Epstein Pack and directionally averaged value. CLICK for larger graphic.

Figure 7. 40-point curves of permeability vs. B for an L&T Epstein Pack and directionally averaged value. CLICK for larger graphic.

Similar analyses for all of Ispat Inland's CRML grades show there is no significant difference in these two curves. Therefore, as a general rule, it can be stated that the L&T values can be used in lieu of the directionally averaged values for Ispat Inland's CRML materials. This most likely is the case for other materials as well, but this should be verified on a case by case basis.

Conclusions

The following conclusions can be reached from the above work:

• One material characteristic commonly used today, 1.5 Tesla permeability, is not effective in predicting motor efficiency.
• The IACL and IAP are excellent predictive parameters of the efficiency of motors, and these parameters are considered the best parameters for specifying motor laminations.
• Very accurate predictor equations for motor efficiency can be derived as a function of only IACL and IAP with the IACL capable of closely predicting the efficiency independently. These predictor equations can eventually replace testing of prototype motor on a dynamometer.
• The stator current can be predicted reasonably well, but it is a function of additional magnetic parameters beyond the IACL and IAP as well as the thickness.
• IACL is closely correlated with the 1.5 Tesla core loss, and the IAP is closely correlated with the 1.0 Tesla permeability. The IAP is also strongly correlated with the 1.5 Tesla core loss for semi-processed materials; therefore, the 1.5 Tesla core loss alone can be used to specify semi-processed CRML materials for motors.
• Directionally averaged magnetic properties should be used in motor models and predictor equations for motors due to the rotational fields in a motor. For all cases studied, the directionally averaged IACL and IAP are almost the same as the L&T properties. They can, therefore, be used in lieu of the directionally averaged properties.
• CRML materials can eventually be specified based on an efficiency index rating instead of core loss and permeability values.

The above work also leads to the conclusion that CRML users should begin to select materials for their applications based on the IAP and IACL and the associated 40-point curves. Engineering design models and predictor equations should use these curves and parameters as input. The 1.5 Tesla core loss is the only parameter that should be used for specifying a material since it is highly correlated with the IACL. This parameter can be used by the CRML consumer for qualifying material for approval based on mill testing. If a parameter related to permeability is desired, the 1.0 Tesla permeability should be specified since it is highly correlated with the IAP.

References

1. K. E. Blazek and T. A. Bloom, "A Paradigm Shift in the Magnetic Test Criteria for Motors," 21st Annual Conference on Properties and Applications of Magnetic Materials, May 13-15, 2002, Illinois Institute of Technology, Chicago, IL, U.S.