Quite often the dynamicist will be faced with having an electric drive motor as a link in the elastic path of a structure such that the motor's characteristics must be taken into account to properly represent the dynamics of the primary structure. He does not want to model it so accurately that he could get detailed stress and displacements in the motor proper, but just sufficiently to represent its inertia loading and elastic behavior from its mounting bolts to its drive coupling. Described here is how the rotor and stator of such a motor can be adequately modeled as a colinear pair of beams

Butler, Thomas G.

English

NASA Technical Reports Server

N91-20513
MODELING AN ELECTRIC MOTOR IN I-D
Thomas G. Butler
BUTLER ANALYSES
INTRODUCTION
Quite often the dynamicist will be faced with having an
electric drive motor as a link in the elastic path of a structure
such that the motor's characteristics must be taken into account
to properly represent the dynamics of the primary structure. He
does not want to model it so accurately that he could get
detailed stress and displacements in the motor proper, but just
sufficiently to represnt its inertia loading and elastic behavior
from its mounting bolts to its drive coupling. This paper
describes how the rotor and stator of such a motor can be
adequately modeled as a colinear pair of beams.
J
I
Figure 1
66 ORIGINAL PAGE IS
OF POOR Q!J,_' !TY
https://ntrs.nasa.gov/search.jsp?R=19910011200 2020-03-19T18:32:35+00:00Z
MODELING AN ELECTRIC MOTOR IN 1 - D
PLAN
Figure 1 shows an assembly drawing of a motor equipped
with a disk brake. The application in which this motor was
incorporated required that the brake be set; consequently, the
electric coupling from the armature to the stator field was not
modeled. The discussion of the modeling will be taken up in four
parts: the rotor, the stator, the brake and the mount.
The overall scheme is to locate grid points at the
bearings, at the concentrations of mass, at the brake, and at the
mating interfaces. Six (6) grid points were assigned to the
rotor and 8 grid points were assigned to the stator. See Table i.
Between the grid points the structure undergoes several changes
of section. Each section is considered separately then the
stiffness for an equivalent prismatic bar is computed for the
sequence of sections between grid points.
One of the intriguing features about finite element
analysis is that parts can occupy the same physical location yet
can still remain disjoint. That feature will be employed here.
The stator is concentric with the rotor so the centroid of the
stator is coincident with the centroid of the rotor. Thus their
individual beam models will be colinear.
EQUIVALENCE
An example of one equivalent bar will be developed for
the rotor and another for the stator. The rotor between the bell
housing and the armature center of gravity has 3 separate sec-
tions: the bearing journal, intermediate shaft and armature.
The three sections are arrayed in line one after the other. This
is an elastic series situation so equivalence is found by summing
compliances (Z). The formulas for equivalent area and equivalent
bending inertia are:
67
MODELING AN ELECTRIC MOTOR IN 1 - D
I ZalLtotal = 1 E1 + A2 E---_+
-I
Since the copper windings are surrounded by a preponderance of
steel it is permissible to assume that the material in the
armature can be represented as steel thus all E's are the same
and the equivalent area becomes:
Aequi v = Ltota I
: 4.889 1 ( .389
1. 37852 +
-i
-i
252 + ....• 3.83122
5.28
Similarly, the computation of the equivalent bending inertias
proceeds with
EIo oivlzzIIIILlLtota I = _ + E2 12 + E3 13
[÷I+÷Ilequiv = Lt°tal 1 3; ÷I
J
equiv
= 4.889[_/_7_6__I .389 + 1.670 + 2._83 _ ]1 37854 2.254 3.8314]
: 2 I _ ,_
equiv"
A
B
Figure 2
Q
I°
-i
-i
= 1.29
68
MODELING AN ELECTRIC MOTOR IN 1 - D
The approach to equivalent properties for the stator is
similar to that for the rotor except that the sections are not
solid, the array is partially in parallel and partially in se-
ries, and it involves distinct materials, as seen in Figure 2.
Note that sections C & D act in parallel; therefore the net
combined stiffness "K" is KCD = KC+ K D, and the net compliance is
ZCD = I/KcD. Section B acts in series with the CD combination,
therefore the net combined compliance is ZBC D = Z B + ZCD.
Section E acts in parallel with the inner combination of BCD,
therefore the net elasticity is obtained by adding stiffnesses.
-i
KBCDE = KE + KBC D = KE + ZBC D and ZBCDE = 1/KBcDE. Finally,
section A acts in series with the combined sections BCDE; i.e.
Zne t = ZA + ZBCDE. The equivalent sectional properties can be
obtained from Zne t. The numerical statistics for the components
of this stator bar example are given in Table 3. Use of these
data in the combining formulas is carried out just for stator
equivalent area as follows.
Karea _ ALE + _) = _/4(7.122- 6.752)x 107
CD C D 2. 689 +
_/4(6.752- 4.582 ) 3 x 107
2.689
"'X 107 ( )= 4 x 2.689 5.132 + 3 x 24.586 = 2.304 X 108 .
zarea = 4 340 x i0 -9
CD
Combining item B in series with the CD combination gives
_area _area _area LB zarea
-BCD -B + -CD ABEal -CD
_ 2.007 + 4.34 x 10 -9= 2.526 x 10 -8
_/4(7.382- 6.52 ) x 107
-i
(area)warea = ZBC D"'BCD = 3.95 x 107
Item E combines in parallel with item BCD.
.area 4(_/4)(5/16)2x 3 x i0'
mBCDE = 4.53
+ 3.958 x 107 : 4.162 x 107 .
69
MODELING AN ELECTRIC MOTOR IN 1 - D
-I
zarea (.area_BCDE = _BCDE) = 2.403 x 10 -8
And now section A can be combined in series
result.
with the current
zarea = LA _area _ 0.62
net AA_a + _BCDE (7.52- _ 2/852 ) x 107
= 2.567 x 10 -8 = Lt°tal
EalAequi v"
Eal
Aequi v = zare a = 19.347.
Ltotal net
+ 2.403 x 10 -8
Similar calculations yield equivalent area
Iequi v as was shown for the rotor bar example.
COLLATERAL
moment of inertia
These operations were performed for the rest of the rotor
and stator. This completes the complement of properties for
equivalent prismatic bars. It will be mentioned, only in pass-
ing, that the mass can be well modeled automatically (except for
torsional inertias) by calling for COUPMASS. The assignment of
torsional mass moment of inertia per grid point must be manually
determined and entered as CMASS2 elements. The next topic
concerns the mating of the rotor to the stator at the bearings.
This motor was designed with ball bearings which can absorb
thrust. Therefore, the two bearings link the rotor and stator
without connecting any rotations. This was represented as
Multi-Point-Constraints (MPC's) in all 3 translations, between
the two rotor bearing points, numbers 2 & 4 and the corresponding
stator points, numbers 30 & 33.
brake.
The topic that needed particular study was the disc
The following discussion will refer to Figure 3.
70
MODELING AN ELECTRIC MOTOR IN 1 - D
< i
/
5 hp:
Figure 3
Two shoes bind on the brake disc to hold the rotor shaft. When
the brake is actuated, the load path from shaft to stator is all
that is of concern. How the brake force is exerted is extraneous
to the finite element modeling of the braked condition (if
stresses are of no concern). The as-braked load path is from the
shaft at the aft end of the brake disc into the hub, into the
disc and out of the forward shoe to the brake bracket via the pad
then into the resolver bell. Thus there is no contribution to
the stiffness of this load path from the after shoe. The model-
ing starts by incorporating the hub into the bar of the rotor
shaft. The stator bar begins with the disc and connects in
series with the forward pad. Then the shoe is a series component
in the equivalent bar extendinq from the resolver bell through
the actuator bracket and the shoe. It was difficult to get
material properties for the asbestos pad so it was assumed that
the asbestos could be reasonably represented by limestone.
Finally, consideration must be given to the connection of
this one dimensional model to the outside world. The drive shaft
will connect throught a keyway into a power shaft of a reduction
gear or similar; so this poses no difficulty in linking 1 - D to
71
MODELING AN ELECTRIC MOTOR IN 1 - D
1 - D. With the stator bell it is a different matter. The motor
casing attaches at either end bell or through feet along its
length to a 2 - D or 3 - D parent. In this model it is through
the forward bell. If MPC's or rigid elements are chosen to make
this connection at the forward bell one must review the MPC used
to tie the ball bearings together. The ball bearing MPC must
retain the stator degrees of freedom as independent, so that they
will be available to be picked up for further tying to the
mounting bolts. If instead of constraints, bar connections are
used, then consideration must be exercised so as not to short
circuit the forward bell elasticity with an overly stiff
representation. Nor should the bars be so limber as to introuce
wobble into the connnection.
SUMMARY
are:
The statistics for this 1 - D model of an electric
Grid Points - 6 in the rotor, 8 in the stator = 14.
Bars - 5 in rotor, 8 in stator = 13
MPC - 3
Torsional Mass Elements CMASS2 - 14
motor
An exploded plot of these 2 colinear elements in Figure 4 il-
lustrates the connections at bearings, brake, and externals.
Mount
U
I
o o 0_o--o
I I
U Brg n Brg
Drive I l
JJ44o o--0 .o '0'
0--0--0
I
V Brake
o
Figure 4
72
MODELING AN ELECTRIC MOTOR IN 1 - D
CONCLUSION
It has been shown that the necessary characteristics of
an electric motor can be incorporated into a dynamic model by
means of a lean bar model without having to resort to a full
blown three dimensional model.
73
MODELING AN ELECTRIC MOTOR IN 1 - D
TABLE OF GRID POINTS
ROTOR
GP LOCATION
Drive Shaft Coupling Keyway
Center Line of Bell Housing with Bearings
Center of Gravity of Rotor Armature
Bearing at Brake End
Center of Gravity of Resolver
Center Line of Brake Disc
STATOR
30
31
32
33
34
35
36
37
Center line of Bell Housing with Bearings
Center of Gravity of Stator Coil
Center Line of Outer Resolver Bell
Bearing at Brake End
Resolver End Bell
Brake Housing
End Cover
Brake Shoe Plate
Table i
74
MODELING AN ELECTRIC MOTOR IN 1 - D
TABLE OF COMPONENT STATISTICS
ROTOR COMPONENT STATISTICS
DESCRIPTION DIAMETER LENGTH MATERIAL
1/2 Bearing Journal 1.3875 0.389 Steel
Intermediate Shaft 2.25 1.670 Steel
1/2 Armature 3.831 2.830 Steel/Copper
Total 4.889 Steel
Table 2
STATOR BAR COMPONENT STATISTICS
ITEM DESCRIPTION DIAMETER
0D/ID
LENGTH MATERIAL
A Bell
B Shell
7.5 / 2.85
Square Round
7.38/2.85
0.62 Aluminum
2.007 Aluminum
C Stator Shell 7.1216.75 2.689 Aluminum
D
E
Stator
4 Bolts
Total
6.75/4.58
5
1-6
2.689 Steel/Copper
4.53 Steel
4.889 Aluminum
Table 3
75


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