Predicting
Motor Operating Parameters
One analytical computer program, RMxprt by Ansoft Corporation, has
been used to closely predict the operating characteristics of a commercial
singlephase induction motor using many different CRML materials, both
semiprocessed and fullyprocessed. 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 40point 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 singlephase
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 40point
curves were available were inserted into a model developed for a singlephase
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
SinglePhase
Induction Motor
Multiple linear regression analyses were performed on the efficiency,
stator current, and torque of a singlephase induction motor as used
in residential airconditioning 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, semiprocessed, and
unannealed materials were included.
The result for the efficiency was as follows:
Ê 
Ê 
1. 
Efficiency (%)
= 0.391584 x IACL + 0.000038 x IAP + 90.279626 rsquared = 0.91333
The rsquared value for efficiency as a function of IACL alone
is 0.9121. Including the IAP only increases rsquared by 0.00123
to 0.91333. This clearly shows that the only significant magnetic
parameter for predicting the efficiency of a motor is the IACL.
The effect of permeability is not significant.
A similar analysis conducted on the torque yielded the following
result:

2. 
Torque (n*m) =
0.152289 x (1.0 Tesla Core Loss) + 0.061846 x (1.5 T Core Loss)
+ 0.000009 x (1.5 T Permeability) + 7.51189
rsquared = 0.406022
This indicates that the torque is not predictable from the
magnetic parameters of the CRML.
The result of the linear regression analysis for the stator
current follows:

3. 
Stator Current (A)
= 0.073011 x (1.5 Tesla Core Loss) + 0.091629 x (1.0 Tesla Core
Loss) Ð 10.499422 x (Thickness, in) + 14.195776 rsquared = 0.797142
This indicates that stator current is more predictable from the
magnetic properties than the torque, and it is also not dependent
upon the 1.5 Tesla permeability. The core loss values in all of
these equations are in units of W/kg. 
ThreePhase
Induction Motor
Identical multiple linear regression analyses were performed on the
efficiency, stator current, and torque of a threephase induction motor
as used in the condenser fan of an airconditioning unit for the same
145 different lamination steels. The result for the efficiency was
as follows:
Ê 
Ê 
4. 
Efficiency (%)
= 0.78113 x IACL + 0.000025 x IAP + 84.742159
rsquared = 0.929163
The rsquared value for efficiency as a function of IACL alone
is 0.9281. Including the IAP only increases the rsquared value
by 0.001063. This again shows that the only significant magnetic
parameter for predicting the efficiency of a motor is the IACL.
The effect of permeability is not significant.
A similar analysis conducted on the torque yielded the following
result:

5. 
Torque (n*m) =
0.000007 x (1.5 T Permeability) Ð 1.983952 x (Thickness, in)
+ 9.322411
rsquared = 0.509127
This again indicates that the torque is not predictable from
the magnetic parameters of the CRML.
The result of the linear regression analysis for the stator
current follows:

6. 
Stator Current (A)
= 0.012166 x IACL Ð 0.000023 x IAP 0.024565 x (1.5 T core loss) Ð 0.000025
x (1.5 T perm) + 0.138196 x (1.0 T core loss) Ð 0.00001 x (1.0
T perm) + 2.062222 x (thickness, in) + 1.985033
rsquared = 0.948638
This indicates that stator current is also predictable from
the magnetic properties and is related to the all the variables
studied except for composition.

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 40point 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 (rsquared 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 (rsquared 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.
Milltested 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 semiprocessed materials, it was necessary
to verify the results for other types of CRML materials other than
just semiprocessed. This was done on the original database consisting
of semiprocessed, fullyprocessed, and unannealed 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 semiprocessed material mentioned above. The rsquared
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 semiprocessed CRML. If these fully
processed materials are eliminated from the plot, then the rsquared
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 semiprocessed 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 onehalf 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 40point 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 40point 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 40point 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. 40point curves of core loss vs. B for an L&T Epstein Pack and
directionally averaged value.
CLICK for
larger graphic. 
Figure
7. 40point 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 semiprocessed
materials; therefore, the 1.5 Tesla core loss alone can be used to
specify semiprocessed 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 40point 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 1315, 2002, Illinois Institute
of Technology, Chicago, IL, U.S.
About
the Authors

Ken Blazek is a staff scientist in the Research Department
at Ispat
Inland Steel. He has a B.S. in Material Science and an M.S.
and PhD in Metallurgical Engineering.


Craig Riviello serves as global manager of Materials Engineering
at A.
O. Smith Electrical Products Company. He has a B.S. in Mechanical
Engineering and an M.S. in Material Science and Engineering.

