Increased Productivity Example #1



A.C. Motor Design
__________

AC Motor Design Example

Figure 1 is a case study of re-engineering -- an A.C. motor design simulation that was reapplied as an optimization program and fully tested in about an hour. The original program had been used for trial and error design calculations by a west coast manufacturer. Restructuring this mature engineering model into a design optimization program, only required introducing a FIND statement that defined a constrained optimization problem with 12 unknown parameters and 7 constraints. A FIND statement invokes a solution technique or solver that consists of automatic differentiation with a numerical algorithm. The solver involved in this case is a nonlinear programming algorithm called THOR. Figure 2 (part of output) is a report automatically generated by the solver, THOR, summarizing the iteration steps. This partial summary shows initial guesses of the parameters and the final results.

This case study illustrates the economic benefits of AD based software for reapplying existing application software in a higher-productivity mode. The existing engineering simulation model was used "as is". It was automatically elevated to optimization by the hidden differential arithmetic. There was no mathematical analysis or algorithm design required. Because this was a re-engineering of an existing program, no debugging was necessary, and since the optimization solvers are interchangeable, different algorithms could be substituted to verify solution correctness.

Increased Productivity Example #1 Source Code:



Figure 1. Calculus Code ... A.C. Motor (Optimal) Design

global all
problem acmotor 
  dimension cns(7) 
  dynamic botm, bnd 
  call input 
  call design 
  print *, '---------------initial design---------------' 
  call output
  Find coiltrns, ! number of turns per coil 
&     EPDIAM,     ! Separating diameter 
&     STASLOTW,   ! Stator slot opening width 
&     ROTSLOTW,   ! Rotor slot opening width 
&     AIRGAP,     ! Air gap 
&     STATOOTW,   ! Stator tooth width 
&     STABAKIR,   ! Stator back iron 
&     ROTTOOTW,   ! Rotor tooth width 
&     ROTBAKIR,   ! Rotor back iron 
&     STASLOTO,   ! Stator slot opening depth 
&     ROTSLOTO,   ! Rotor slot opening depth 
&     SLIP        ! Slip 
&   in DESIGN; by thor(TCON); 
&   with bounds BND; and lowers BOTM; 
&   holding CNS; to maximize EFF 
  print *, '----------------optimized design-----------------' 
  call output 
end 

model design 
  f1 = 231258.0438 / coiltrns 
  q1 = sepdiam * pi / 56 : q2=sepdiam * pi / 69 : q3=sepdiam * pi / 28 
  c1 =q1/((q1-staslotw)+(staslotw *(.7 -(.036 * staslotw/ airgap)))) 
  c2 =q2/((q2-rotslotw)+(rotslotw *(.7-(.036 * rotslotw/airgap))))
  crnol = f1 * airgap * c1 * c2 / (6.96 * coiltrns * q3) 
  q4 = (statorod - stabakir - stabakir - sepdiam - .1) / 2 - .01 
  q5= (sepdiam+q4+.1) * pi / 56 - statootw - .016 : a3=q4 * q5 
  z1 = 7000 * a3 
  q6 = coiltrns * 2 / z1 : z3= - 2 : z4=32+z3 : q7=1.26**z3 * 162 
  q8=64 / 1.26**z3 : z5=stacklen+stacklen+pi * statorod / 14 
  rdc =z5 * coiltrns * 28 * q7 / 12000 
  v1 = (sepdiam - .06 - rotorid - rotbakir - rotbakir) / 2 
  v2 = (sepdiam - .06 - v1) * pi / 69 - rottootw 
  a4 = v1 * v2 : r2 = (.0133 / a4) * (stacklen / 12000) * u1 
  rrot= (56 * coiltrns)**2 * r2 / 138 : r4 = rrot 
  g3 = 3.2 * (q4 / (3 * q5)+.03 / (staslotw+q5)+stasloto / staslotw) 
  g4 = 3.2 * (v1 / (3 * v2)+.03 / (rotslotw+v2)+rotsloto / rotslotw) 
  g5 = (1 / c1+1 / c2 - 1)**2 * .26 / airgap 
  g6= (g3+g5 * q1) / 56+(g4+g5 * q2) / 69 
  xleak = xc * pi * coiltrns**2 * (.05+g6 * stacklen) ! leakage reactance 
  crstal = 115 / (sqrt(((rdc+r4)**2)+xleak**2))       ! stall current 
  crfl= 115 / (sqrt(((rdc+r4 / slip)**2)+xleak**2))   ! full load current 
  storq = 1.5792 * (crstal**2) * r4                   ! stall torque 
  rtorq = 1.5792 * (crfl**2) * r4 / slip              ! running torque 
  p8=rtorq * (1 - slip) * 1.264944649 : p6= (crstal**2) * (rdc+r4) 
  p7 = (crfl**2) * r4 / slip 
  flux = (1.4 * f1 / (statootw * stacklen) / 6450     ! flux density 
  b7 = (sqrt(crfl**2+crnol**2) * flux / crnol) / 1.4 : b2 =.13 * b7**1.9
  b3 = (((statorod**2 - sepdiam**2) * pi / 4) - 56 * a3) * 0.28 * stacklen 
  feloss = b3 * b2                                    ! iron losses 
  culsta = (b7 * crnol) / flux)**2 * rdc        ! stator copper losses 
  eff = .5 * p8 / (p7+feloss / 2+culsta)        ! efficiency - maximize this 
  rac =13225 / feloss                           ! a.c. resistance 
  xmag =115 / crnol                             ! magnetizing reactance 
  culrot = crfl * crfl * rrot / staslotw        ! rotor copper losses 
  cns(1) = statorod - .1 - sepdiam     ! stator o.d. > = separation diam+.1 
  cns(2) = sepdiam - rotorid+.1        ! separation diam > = rotor i.d. - .1 
  cns(3) = ((sepdiam * pi / 69) - .035) - rottootw   ! rotor tooth geometry 
  cns(4)=.5*(sepdiam - rotorid) -.025 -rotbakir ! rotor back iron geometry 
  cns(5) = storq - 60                           ! stall torque > = 60 
  cns(6) = 19 - flux                            ! flux density < = 19 
  cns(7) =.05 - slip                            ! slip < = 5 percent 
end

As this example illustrates, the benefits of multiple - parameter optimization in practical engineering calculation can often be dramatic. Because of the large number of parameters, something on the order of a billion to a trillion computer cases would have been necessary to achieve this result if using the original program. The bottom line benefit is dramatically reduced cost, higher engineering productivity, and immediate results to meet tight schedules.

Increased Productivity Example #1 Solver Output:



Figure 2. (Partial) Output Report ... A.C. Motor (Optimal) Design


---- Thor Summary, Invoked At Acmotor[29] For Model Design
---- Convergence Condition After 35 Iterations
     o
     o
     o
Loop Number......     [Initial]         35
Unknowns

coiltrns        2.900000e+01    3.214302e+01
sepdiam         4.000000e+00    5.010000e+00
staslotw        6.000000e-02    6.570807e-02
rotslotw        3.500000e-02    3.500000e-02
airgap          8.000000e-03    8.000000e-03
statootw        1.350000e-01    1.687119e-01
stabakir        1.500000e-01    3.955060e-01
rottootw        1.100000e-01    8.885508e-02
rotbakir        4.700000e-01    9.700004e-01
stasloto        3.500000e-02    2.500000e-02
rotsloto        1.500000e-02    0.000000e+00
slip            3.000000e-02    5.000000e-02 

Objective 
Eff             4.020854e-01    7.312523e-01 

Inequality Constraints 
cns ( 1)        1.010000e+00    0.000000e+00
cns ( 2)        1.225000e+00    2.235000e+00
cns ( 3)        3.712132e-02    1.042519e-01
cns ( 4)        6.750000e-02    7.249963e-02
cns ( 5)       -7.555936e+00    6.415480e-04
cns ( 6)        1.258933e+01    1.437190e+01
cns ( 7)        2.000000e-02    0.000000e+00 

--- End Of Loop Summary

AC Motor design is another increased productivity example do to using Calculus (level) programming .

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<a href=""><img style="float:left; width:100px" src="http://fortranCalculus.info/image/ac-motor.jpg"/> <strong>AC Motor design</strong> </a> simulated & tweaked 12 parameters in one run!

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