Journalof

Mechanisms,
Transmissions,
and
Automation in
Design

Optimal Design of Cooling Fans for Industrial Electric a baffle system to the cooler surfaces of the end caps. By a
Motors combination of convection and conduction, the heat is
dissipated to the outside. The one external fan blows air over
the frame of the motor. Heat is conducted through the frame
J. K. Woodard, Jr.' and G. E. Johnson1 (which is in direct contact with the stator) and then removed
through forced convection induced by the external fan.
Various industrial electric motors use a combination of inter- In recent years as the electrical efficiency of motors has im-
nal and external fans to remove internally generated heat. In proved, the power drawn by the cooling fans has become a
recent years as the electrical efficiency of motors has im- large percentage of the total motor losses. In some cases the
proved, the power drawn by the cooling fans has become a fans can consume 2 percent of the energy input to the motor
large percentage of the total motor losses. This paper presents and this may represent 20 percent of the losses [1, 2]. In the
an optimization approach to the selection of the cooling fan past it was only important to cool the motor, and the fans
dimensions. The design objective is to obtain minimum power selected would most likely produce more airflow than was ac-
input to the fans while maintaining adequate cooling capacity. tually needed. With the need today for increased motor effi-
To illustrate the method, the cooling fan design for a 30 hp, ciency, it is desirable to design the fans so that they work
3600 rpm, a-c motor is considered. The optimal fan dimen- together as an optimum system.
sions result in a 70 percent reduction in fan power.
Nomenclature Development of the Optimization Model
A = area, mm 2 The fans are basic bidirectional centrifugal fans. The
C = constants parameters chosen for optimization are the widths and
Z)[ = diameter of external fan, mm diameters of the fans. The objective will be to minimize the
D2 = diameter of internal fan, mm power drawn by the cooling fans which will in turn lead to a
h = convective heat transfer coefficient, W/mm 2 °C higher motor efficiency. The objective function is [3]
P = power drawn by fans, W
-C^W^D^ + C 2W2D2* (1)
Q = air flow rate, mVmin
q = heat energy rate, W The design constraints require that fan dimensions be
R = thermal resistance, °C/W bounded by zero at the low extreme and by suitable limits dic-
T = temperature, °C tated by enclosure geometry at the other. In addition, the fans
W\ = width of external fan, mm must produce adequate airflow to cool the motor.
W2 = width of internal fan, mm The development of the heat transfer constraint requires
several assumptions. First, the rotor and stator are lumped
Subscripts
a = ambient
E = end caps
F = frame
5 = heat source

Introduction and Background

The major inefficiencies in an industrial electric motor are
core losses and resistance heating losses in the rotor and
stator. It is essential to remove the heat created by these losses
to prevent high temperature of the insulation system and even-
tual motor failure. One method used for heat removal involves
a combination of internal and external fans.
In a totally enclosed fan cooled motor, there are three fans
driven from the motor shaft (see Fig. 1). Two of these fans are
inside the motor enclosure. They circulate air over the ends of
the rotor and stator to remove heat. The air is then directed by

Department of Mechanical and Materials Engineering, Vanderbilt Univer-

sity, Nashville, TN 37235.
Contributed by the Design Automation Committee for publication in the
JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN. Fig. 1 Motor components: (1) stator, (2) rotor, (3) shaft, (4) frame, (5) end
Manuscript received at ASME Headquarters, November 4, 1985. cap, (6) external fan, (7) fan cover, (8) internal fan, (9) internal fan baffle

224/Vol. 108, JUNE 1986 Transactions of the ASME

Copyright © 1986 by ASME
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 together and considered to be a constant temperature heat The mathematical model representing the objective function
source. This is a reasonable assumption since the rotor and and the constraints is nonlinear and multivariable. To find the
stator are in close proximity; they are made of the same optimum fan dimensions, a nonlinear programming approach
material; and usually they generate about the same amount of based on conjugate directions and exterior penalty functions
resistive heat [1]. Tests have also verified that the temperatures was used [5, 6].
are approximately the same. Second, the heat escapes through
a combination of convection and conduction only. Heat Results
transfer through radiation is not considered. Only in extreme The program was set up to analyze a General Electric 30 hp
cases do motors operate at a temperature high enough for (22 kW), 3600 rpm, a-c motor. The original design has an ex-
radiative heat transfer to be significant. Third, there is no con- ternal fan with a diameter of 135 mm and a width of 50 mm.
duction of heat between the frame and end caps. This assump- The two internal fans have a diameter of 175 and a width of 28
tion can be justified since the area of contact between the mm. The power required to drive the three fans is 210 W. The
frame and end caps is small relative to the surrounding con- abovementioned fan dimensions provide a feasible starting
vective heat transfer surfaces (conductive area is approxi- point for the optimization. The final optimal design identified
mately 2 percent the size of convective area). Fourth, there is by the computer program reduced the fan power to 52 W. This
no conduction of heat along the motor shaft. This assumption is an improvement of 75 percent. Results are given in Table 1.
is valid if the driven equipment's temperature is approximately
the same as the motor's. For other cases this assumption Table 1 Values of fan dimensions and fan power consump-
would not hold and conduction along the shaft would have to tion before and after optimization
be considered. In most cases the driven equipment is at a lower
Variable Starting point Optimal design
temperature than the motor, and conduction along the shaft is
beneficial. Last, the amount of heat that has to be removed Dt (mm) 135 130
from the motor is constant. It is a function of load and can be Wx (mm) 50 56
D2 (mm) 175 160
calculated [1] or determined by test. The maximum load is 1^2 (mm) 28 0.03
used for analysis. P(W) 210 52
The total amount of heat that must be removed from the
motor (qT) is divided between the heat flow through the end
Discussion and Conclusions
caps (qE) and heat flow through the frame (qF). Each of these
quantities of heat must travel through a series circuit to reach The most interesting result is the reduction of the internal
the outside. The series for qE consists of: fan width (W2) to 0.03 mm which is approximately equal to its
1 Forced convection across the rotor and stator surfaces lower bound of zero. The impression given is that the
which heats the air. The convective heat transfer coefficient algorithm is trying to converge to this lower bound, but this
across these surfaces (hs) is a function of the internal fan turned out to be incorrect. Some small internal fan width is re-
dimensions. quired in order to satisfy the heat transfer constraint. To
2 Forced convection across the interior surface of the end verify this conjecture, the program was rerun with W2 initially
cap which cools the air. The convective heat transfer coeffi- set equal to zero. The algorithm converged to the same design
cient across this surface (hE) is a function of the internal fan that is summarized in Table 1.
dimensions. From a practical standpoint, a 0.03-mm-width fan is not
3 Conduction through the end cap. realistic because it is well below normal manufacturing
4 Free convection on the outer surface of the end cap. The tolerances. The smallest practical value is 3 mm. Therefore a
heat flow through the end caps is expressed as decision had to be made to set W2 = 0 or round it up to 3 mm.
With the internal fans completely removed, a test motor
f 2hsAE(Ts-Ta) , demonstrated a higher efficiency, but it had localized "hot
L2 + hsAERE+(hs/hE)) spots" on the rotor. These hot spots were eliminated by in-
The series for qF consists of: stalling a 3-mm-width fan to create a slight amount of flow.
1 Conduction through the frame. The fan power with a 3-mm-width internal fan is 64 W
2 Forced convection across the outer surface of the frame. which is a 70 percent decrease in power compared to the
The convective heat transfer coefficient across this surface original fan geometry. This provides a 0.60 percent increase in
(hF) is a function of the external fan dimensions. motor efficiency, a major improvement in the motor industry
The heat flow through the frame is expressed as where a 0.10 percent difference in motor efficiency can in-
fluence a customer's choice of motor.
qF=
\RF + l\/haFAF))- (3) Acknowledgments
qE and qF combine to give the total heat transfer rate from the The authors would like to acknowledge Mr. R. E. Davidson
motor. and Mr. G. M. Rosenberry of the General Electric Co. for
their assistance and contributions to the completion of this
/ 2h*AF 1 \ work.
qT= (Ts-Ta){ £_£ + 1(4)
" \2 + hsAERE+(hs/hE) RF + (l/hFAF)J
References
The heat transfer constraint requires that during the optimiza-
1 Levi, E., Polyphase Motors —A Direct Approach to Their Design, Wiley,
tion, qT has to be equal to or greater than the total heat New York, 1984.
generation rate within the motor. 2 Werninck, E. H., ed., Electric Motor Handbook, McGraw-Hill, London,
As stated, hs and hE are functions of the internal fan 1978, p. 345.
dimensions and hF is a function of the external fan dimen- 3 Shepherd, D. G., Principles of Turbomachinery, McMillan, New York,
1956, p. 34.
sions. The flow rate of the fan is [3] 4 Baumeister, T., et al., (ed.), Mark's Standard Handbook for Mechanical
Q = C,WD2. (5) Engineers, (8th edition), McGraw Hill, 1978, pp. 4.59-4.70.
5 Johnson, G. E., and Townsend, M. A., "An Acceptable Point Algorithm
The flow rate is divided by the flow areas to arrive at the flow for Design Optimization," Appendix C in Optimum Design of Mechanical
velocity. The flow velocity is used to calculate the heat transfer Elements (2nd edition), by R. C. Johnson, Wiley Interscience, NY, 1980, pp.
488-507.
coefficients based upon standard formulas for forced convec- 6 Fiacco, A. V., and McCormick, G. P., Nonlinear Programming: Sequen-
tive heat transfer [4]. tial Unconstrained Minimization Techniques, Wiley, New York, 1968.

Journal of Mechanisms, Transmissions, and Automation in Design JUNE 1986, Vol. 108/225

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