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IM BELOW 100KW FOR CONSTANT
VOLTAGE AND FRECUENCY
EXAMPLE DESIGN
from
The Induction Motor Handbook 2002 by CRC Press LLC
v0.4
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Introduction [1]
100 kW is traditionally considered the borderbetween a small and medium power inductionmachine.
sub 100 kW motors use a single stator androtor stack and a finned frame washed by airfrom a ventilator externally mounted at theshaft end.
It has an aluminum cast cage rotor and, ingeneral, random wound stator coils made ofround magnetic wire with 1 to 6 elementaryconductors (diameter 2.5mm) in parallel and1 to 3 current paths in parallel, depending onthe number of pole pairs.
The number of pole pairs 2p1 = 1, 2, 3, 6. Their design for standard or high efficiency is anature mixture of art and science, at least inthe preoptimization stage.
For the most part, IM design methodologies areproprietary.
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Yes
No
IM Design Algorithm [1]
Design specs
electric &
magnetic loadings
Sizing the electrical &
magnetic circuits
All construction and
geometrical data are known
and slightly adjusted
Verification ofelectric &
magnetic loadings
Computation of
magnetization current
Computation of
Equivalent circuit
electric parameters
Computation of
Loss, slip, efficiency
Computation of power
factor, starting
current, and torque,
breakdown torque
and temperature rise
is performance
satisfactory?
Start
End
Seeking convergence in teethsaturation coefficient
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Rated power: Pn = 5.5kW Synchronous speed: n1 = 1800rpm
Line supply voltage: V1L = 460V
Supply frequency: f1 = 60Hz
Number of phases m = 3
Phase connections: star
Targeted power factor: cosn = 0.83 Targeted efficiency: n = 0.895 (high efficiency motor)
p.u. locked rotor torque: tLR = 1.75
p.u. locked rotor current: iLR = 6
p.u. breakdown torque: tbk = 2.5
Insulation class: F; temperature rise: class B
Protection degree: IP55 IC411 Service factor load: 1.0
Environment conditions: standard (no derating)
Configuration (vertical or horizontal shaft etc.): horizontal shaft
Design specs electric & magnetic loadings
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Sizing the electrical & magnetic circuits
2p 2 4 6 8
.P 0.6 1.0 1.2 1.8 1.6 2.2 2 3
Stack aspect ratio
Dis
From the widely accepted Dis
2L output constant concept [2]:
Stator bore diameterDis p: stator poles pair
f1: stator voltage frecuency
P: stack aspect ratio
Sgap:airgap apparent power
Co: Essons constant
KE = 0,98 0,005p
Pn: rated power
Ln: targeted efficiency
cosJ: targeted power factor
KE: emf coefficientFrom past experiences [1], P is given by the table:
Co is extracted from Essons
constant C0 versus Sgap for low
power IM graph.
nS: synchronous speed
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Essons constant C0 versus Sgap (airgap apparent power) for low power IM [2]
volume utilization factor C0
Be aware that in this chart, C0 is given in J/dm3
, but in Dis equation it is needed in J/m3
[GE]
Sizing the electrical & magnetic circuits
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Sizing the electrical & magnetic circuits
2p 2 4 6 8
. Dis .
Dout0.54 0.58 0.61 0.63 0.68 0.71 0.72 0.74
From optimal lamination concept [1] the ratio of the
internal to external stator diameterDis/Dout, for
standard motors below 100KW is given by the table:
Inner/outer stator diameter ratio
Stator outer diameterDout
Stack length L
The stack length is
obtained from the
stack aspect ratio Pdefinition [2]
Dout
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Sizing the electrical & magnetic circuits
From [3] the number of stator slots can be calculated as:Number of stator slots NS
Ns = 2pqm
p: stator poles pair
q: slots per pole per phase
m: number of phases
Although q may be a fraction, in most IM q is an integer
to provide complete symmetry for the winding. [3]
For small IM, q may be 2 or 3. In general the larger q
gives better performance (space field harmonics and
losses are smaller). [1]
As we are working on 3-phase systems, m=3
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Sizing the electrical & magnetic circuits
Winding Plan
The process to get the winding plan regarding the number of stator slots
for 3-phase IM is presented in [4].
From [3]the coil pitch / pole pitch ratio is normally selected asY / X = 5/6 or7/9
as a practical solution which keeps the 5th mmf harmonic low.
For this purpose, the pole pitch is measured as slots [3]
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P F
Sizing the electrical & magnetic circuits
Number of turns per phase W1 From [3] the number of turns per phase canbe calculated as:
W1
V1ph: voltage per phase
KE: emf coefficient
Kf: form factor
Kw1: stator winding factor
f1: stator frecuency
J: pole flux
Kq1: spread factor
Ky1: chording factor
q: slots per pole per phase
Y: coil pitch
X: pole pitch
For star phase
connection:
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The airgap flux density is recommended in the
intervals [1]
2p 2 4 6 8
.Bg [T] 0.5 0.75 0.65 0.78 0.7 0.82 0.75 0.85
P F
Sizing the electrical & magnetic circuits
Number of turns per phase W1
From [2] the pole flux J can be calculated as:
W1 Ei: flux density shape factor
X: pole pitch
L: stack length
Bg: flux density in the airgap
Dis: bore stator diameter
p: pole pair
Both the flux density shape
factorEi and the form factor
Kfare dependent of the
magnetic saturation
coefficient of teeth 1+Ksd
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Form factor Kfand flux density shape factor i versus teeth saturation [2]
Initially the theeth saturation is stimated (by example 1+Ksd = 1,4) then after some
computations the 1+Ksd is verified. If it is found near the stimation value, then the
design process continue, else the values are reset and the process start again [GE]
Sizing the electrical & magnetic circuits
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If there are two distinct coils per slot in a double layer
winding, ncs must be an even number.
Sizing the electrical & magnetic circuits
Number of conductorsper slots ncs
From [2] the number of conductors per slotscan be calculated as:
ncs
a1: numer of current paths in parallel
W1: number of turns per phase
p: pole pair
q: slots per pole per phase
Ifncs is adjusted to a even number, then the numberof turns per phase W1 and the airgap flux density Bgmust be recalculated.
P F
i.e. ifncs was adjusted to an even number, consequently W1=pqncs/a1 must be
adjusted, and so it must be made with Bg (Bg=BgW1/W1)
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Sizing the electrical & magnetic circuits
Stator wire gauge
diameter dCo
For star phase connections I1L = I1ph:
Pn: rated power
L: targeted efficiency
V1L: rated line voltage
cosn : targeted power factor
For high efficiency the recommended
current densities are found in [1]
2p 2, 4 6, 8
.Jcos[A/mm2]
4 7 5 8
From [1] the wire gauge diameter can becalculated as:
ACo: magnetic wire cross section
I1n: rated stator current
Jcos: current density
a1: numer of current paths in parallel
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Sizing the electrical & magnetic circuits
Stator wire gauge
diameter dCo
The value ofdCo calculated must be adjustedto a standardized bare wire diameter.
ACo: magnetic wire cross section
Ifdco > 1.3mm, in low power IMs, it may be used a few
conductors in parallel ap
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Standardized magnetic
wire diameter table [1]
Sizing the electrical & magnetic circuits
If the number of conductors in parallel
ap > 4, the number of current paths inparallel a1 has to be increased.
If, even in this case, a solution is not
found, use is made of rectangular cross
section magnetic wire.
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Sizing the electrical & magnetic circuits
Stator slot sizingThe are several stator slot and teeth forms. For small IMs,trapezoidal or rounded semiclosed shape is recommended [1]
bos
hoshwStator tooth is rectangular,
and variables assigned
from past experience are:
From [2] the airgap can be calculated as:
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Sizing the electrical & magnetic circuits
Stator slot sizing Assuming that all the airgap flux passes through thestator teeth:
bts
Bg: flux density in the airgap
Xs: pole pitch
L: stack length
Bts: flux density in the stator tooth
bts: average width of stator tooth
KFe: influence of lamination
insulation thickness.
For 0.5 mm thick lamination KFe 0.96 [1]
And with Bts normally between 1.5 and 1.65 T [1]
From technological limitations, the tooth width should not be under 3.5mm. [1]
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Sizing the electrical & magnetic circuits
Stator slot sizing For geometrical dimensions the slot lower width canbe calculated as [1]:
bs1
bs2hs
The useful slot areaAsu may be expressed as:
then
now
where Kfill is a slot fill factor.
With Kfill = 0.35 to 0.4 below 10KW
and Kfill = 0.4 to 0.44 above 10KW
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Verification of electric & magnetic
loadingsNow we proceed in calculating the teeth saturation factor1 + Kst by
assuming that stator and rotor tooth produce same effects in this respect.
Fmts: stator tooth magnetomotive force
Fmtr: rotor tooth magnetomotive force
Fmg: airgap magnetomotive force
Hts: stator magnetic field intensity
If this value is only slightly larger
than that of stator tooth, we may
go on with the design process.However, ifFmtr
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Bibliografical References
[1] The Induction Machine Handbook. CRC Press LLC. 2002. Chapter15
[2] The Induction Machine Handbook. CRC Press LLC. 2002. Chapter14
[3] The Induction Machine Handbook. CRC Press LLC. 2002. Chapter 4
[4] Gustavo Espitia. Bobinado de Motores AC. Notas de clase. Uninorte, 2009.