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8/8/2019 Resumen Handbook Motores

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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]



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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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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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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


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


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


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]



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If there are two distinct coils per slot in a double layer

winding, ncs must be an even number.


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


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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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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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]


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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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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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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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.

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