The purpose of this effort was to develop a finite element code for the analysis and design of permanent magnet electric motors. These motors would drive electromechanical actuators in advanced rocket engines. The actuators would control fuel valves and thrust vector control systems. Refurbishing the hydraulic systems of the Space Shuttle after each flight is costly and time consuming. Electromechanical actuators could replace hydraulics, improve system reliability, and reduce down time

Campbell, C. Warren

English

NASA Technical Reports Server

N94- 2_ 411
1993
NASA/ASEE SUMMER FACULTY FELLOWSHIP PROGRAM
MARSHALL SPACE FLIGHT CENTER
THE UNIVERSITY OF ALABAMA IN HUNTSVILLE
FINITE ELEMENT BASED ELECTRIC MOTOR DESIGN OPTIMIZATION
Prepared by:
Academic Rank:
Institution and
Department:
MSFC Colleague(s):
C. Warren Campbell, Ph.D., P. E.
Associate Professor
The University of Alabama in Huntsville
Department of Civil and Environmental Engineering
Charles S. Cornelius
Rae Ann Weir
NASA/MSFC:
Laboratory:
Division:
Branch:
Propulsion Lab
Component Development Division
Control Mechanisms and Propellant
Delivery Branch
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https://ntrs.nasa.gov/search.jsp?R=19940019938 2020-06-16T16:51:49+00:00Z

I. INTRODUCTION
The purpose of this effort was to develop a finite element
code for the analysis and design of permanent magnet electric
motors. These motors would drive electromechanical actuators in
advanced rocket engines. The actuators would control fuel
valves and thrust vector control systems. Refurbishing the
hydraulic systems of the Space Shuttle after each flight is
costly and time consuming. Electromechanical actuators could
replace hydraulics, improve system reliability, and reduce down
time.
The organization of the code is shown in Figure i.
motor preprocessor is a routine that does the following:
The
I)
2)
3)
4)
Receives data on the motor geometry, materials,
windings, and currents
Generates the meshes and elements for the motor for
different rotor positions
Renumbers the nodes for minimal storage using the
minimum degree ordering algorithm
Dynamically allocates storage for coefficient arrays
for the finite element analysis
The finite element model calculates the magnetic vector
potential and stores the results in a file that can be accessed
by the postprocessor.
The postprocessor will do the following:
I)
2)
3)
Calculate flux densities and field intensities
Calculate torques and back emfs for the motor
Plot the results
The optimizer will take torques and information from the
postprocessor and calculate a general objective function with
internal penalty function constraints. Constraints could
include magnitude of current densities, motor weight and
volume, and cogging torque. Based on previous values of the
objective function, the optimizer will select motor geometry for
the next iteration. Optimization will continue until the motor
design is optimized.
The optimization will begin with an initial motor design
and will proceed toward an improved design. Care must be taken
in the design of the mesh. Sometimes in finite element
structural optimization, a mesh is generated which gives an
accurate solution to the initial design, but as optimization
proceeds, the mesh becomes too coarse for an accurate solution.
Then the "optimized" design is invalid.
Clearly, the code will be very long running. Consider using
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cogging as a constraint. For each value of the objective
function the finite element code must find several solutions for
different positions of the rotor.
The finite element code developed in this effort was based
on the models in Silvester and Ferrari (3). The sparse matrix
algorithms were taken from George and Liu (1). The optimizer
will be an adaptation of code available from Numerical Recipes
in C by Press, et al.(2).
II. APPROACH
The objective of this effort was to develop a finite
element code with optimization that could run on a 386- or 486-
class machine with up to 15,000 nodes in a two-dimensional
problem. Since motors are very long compared to airgap widths
and since we will not use rotor or stator skewing of magnets or
teeth, the problem can be assumed to be two-dimensional.
Also, these goals should be achievable without making users buy
thousands of dollars of software.
Because of the ambitious goals for this project, as many of
the routines as possible were based on existing code. At the
beginning, I did not realize that the code in Silvester and
Ferrari (3) was learning code in which coefficient arrays were
dimensioned to the maximum number of nodes, that is A(maxnod,
maxnod). For a 15,000 node problem (the goal for this effort),
the coefficient array alone would require 15,000 by 15,000 = 225
Megawords of storage! For 4-byte words, this is a gigabyte of
storage. Clearly, sparse matrix methods are required.
The need for sparse matrix methods significantly slowed the
progress of the effort. Even though George and Liu is an
excellent reference for solutions of finite element problems and
though it has Fortran subroutines in the text, progress was
extremely slow. This is because the routines in the text are
spaghetti code that are extremely hard to debug andunderstand.
The code uses variables that perform several functions and have
values that change in mysterious ways at different places in the
program. For these reasons, direct application of the routines
would make the code difficult to understand, debug, and
maintain. For these reasons, algorithms presented in George and
Liu were used to write new code that was understandable,
structured, and maintainable.
Borland C and C++ was chosen as the development language
for many good reasons. The Borland package is
inexpensive(~$300), well documented, and well written. It
permits tracing line by line through the code viewing values of
any variable at any point. It also allows the setting of
breakpoints. The code can be executed to the breakpoints where
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each variable of interest can be examined. This capability
minimizes debugging effort. C was chosen because of its power.
Desirable features include dynamic memory allocation, ability to
implement data structures easily while writing readable code,
and accessibility of computer graphics capabilities. Dynamic
memory allocation means that large arrays can be created as
needed, used, and then the memory deallocated for other uses.
In C this is done cleanly without impact to any of the desirable
features of the code. The same thing can be done in Fortran
using equivalence statements, but the process can cause
unexpected and untraceable errors in the code.
A strategy was found to be very useful for code
development. The first step was to take simple test problems
and use Mathcad (a mathematical spreadsheet easy to use and
understand) to calculate values of the variables at every point
in the execution of a program. With the line-by-line tracing
ability of Borland C, values of the variables in the code and
those calculated with Mathcad could be compared.
I also adapted an array dynamic allocation strategy from
Press, et al. (3). C normally dimensions arrays from 0 to n -
1, where n is the array dimension. By the Numerical Recipes
approach, arrays can be allocated from nlow to nhighwhere nlow
and nhighare any values with nhigh > nlow. This is very useful
in translating Fortran code with arrays dimensioned from 1 to n.
III. SUMMARY
In the first year of this task, work was done on the
preprocessor and on the finite element solver. Next year the
goal will be to add a nonlinear equation solver, a motor
preprocessor, post processor, and optimizer.
IV. ACKNOWLEDGEMENT
Thanks are due to Charlie Cornelius and Rae Ann Weir whose
support and encouragement were invaluable.
V. REFERENCES
1. George, Alan, and Liu, Joseph W., Computer Solution of
Larue Sparse PositiveDefinite Systems, Prentice-Hall, Englewood
cliffs, NJ, 1981.
2. Press, William H., et al., Numerical Recipes
Cambridge University Press, New York, 1990.
i_ C,
3. Silvester, P. P., and Ferrari, R. L., Finite Elements for
Electrical Enuineers , 2nd Edition, Cambridge University Press,
New York, 1990.
VI-4 _


Finite element based electric motor design optimization

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