Iden

tify

ing

mat

eria

l pro

pert

ies

of a

di

elec

tric

mot

or

P. D

i Bar

ba (*

), E.

R. M

ogna

schi

(**)

, M. E

. Mog

nasc

hi(*

), A

. Sav

ini(

*)

(*)

Dep

artm

ent

of E

lect

rica

l Eng

inee

ring

, Uni

vers

ity

of P

avia

,Ita

lye-

mai

l: ev

e.m

ogna

schi

@un

ipv.

it

(**)

Dep

artm

ent

of P

hysi

cs “A

. Vol

ta”,

Uni

vers

ity

of P

avia

, and

IN

FM, U

nità

di P

avia

, Ita

ly

INTR

OD

UCT

ION

Rota

ting

mot

or:

Torq

ueel

ectr

ical

cond

ucti

vity

elec

tric

alpe

rmit

tivi

ty

of t

he lo

ssy

diel

ectr

icm

ater

ial

Cond

ucti

vity

of t

he lo

ssy

diel

ectr

ic:

•dir

ect

mea

sure

men

t: d

iffi

cult

tas

k

•lite

ratu

re: a

ffec

ted

byun

cert

aint

ies

Aim

: to

iden

tify

the

orde

rof

mag

nitu

deof

the

mat

eria

l pr

oper

ties

, sta

rtin

gfr

oma

valu

eof

tor

que.

THE

DEV

ICE

(1/3

)St

ator

: Nom

ex+

elec

trod

esRo

tor:

PVC

(ext

) +

pape

r(in

t)

94 m

m

57 m

mEx

plod

edvi

ew

Cros

s se

ctio

n

PVC

Pape

r

Inne

rai

r re

gion

Air

gap

Nom

exEl

ectr

ode

THE

DEV

ICE

(2/3

)•7

2 co

pper

elec

trod

es.

•Thr

ee-p

hase

pow

er s

uppl

y (f

=50

Hz,

rm

s-va

lue

= 95

0 V)

.

•Asy

nchr

onou

s m

otor

.

•Max

imum

tor

que:

789

μN

m a

t th

e no

min

alsp

eed

of 1

3.1

rad/

s.

•Los

sy d

iele

ctri

c: p

aper

.

Vary

ing

the

hum

idit

yof

the

pap

er(i.

e. v

aryi

ngit

sph

ysic

alpr

oper

ties

), th

e de

velo

ped

torq

uech

ange

s.

THE

DEV

ICE

(3/3

)

Swit

ch-o

n re

spon

se o

f th

e m

otor

Swit

ch-o

ff r

espo

nse

of

the

mot

or

THE

MO

DEL

(1/3

)

Air

gap

: 4 la

yers

, thi

ckne

ss->

250

μm

eac

h.A

ngul

arre

solu

tion

: 0.2

deg

.60

,774

tri

angl

es.

MES

H

THE

MO

DEL

(2/3

)In

the

fre

quen

cydo

mai

n:

Boun

dary

cond

itio

ns:

U =

U0

at t

he e

lect

rode

s

else

wher

e0

=∂∂nU

Tim

e-ha

rmon

ican

alys

is

Max

well

stre

ss

tens

or

0=

⋅∇

J0

=×

∇E (

)D

jE

Ej

Jω

σω

εσ

+=

+=

()

[]

0=

∇+

⋅∇

Ujω

εσ

THE

MO

DEL

(3/3

)

Give

n a

valu

e of

tor

que,

e.g

. aft

er a

mea

sure

men

t on

an

exi

stin

g pr

otot

ype,

it is

inte

rest

ing

to id

enti

fy

the

elec

tric

al p

rope

rtie

s of

the

loss

y di

elec

tric

.

INVE

RSE

PRO

BLEM

Give

n th

e ge

omet

ry o

f th

e m

otor

and

its

elec

tric

su

pply

, fin

d th

e re

lati

onsh

ip a

mon

g st

arti

ng

torq

ue T

(ε,σ

) of

the

mot

or, p

erm

itti

vity

ε an

d co

nduc

tivi

ty σ

of t

he a

ctiv

e m

ater

ial.

RESU

LTS

(1/4

)

RESU

LTS

(2/4

)

ε r=3

.3

RESU

LTS

(2/4

)

ILL-

POSE

DN

ESS

OF

THE

INVE

RSE

PRO

BLEM

!!

ε r=3

.3

RESU

LTS

(3/4

)

Perm

itti

vity

Torq

ue

RESU

LTS

(4/4

)

Perm

itti

vity

D r

adia

l

E ta

ngen

tial

D r

adia

l: ca

lcul

atio

nsat

the

air

gap

, und

er a

nel

ectr

ode.

E ta

ngen

tial

: cal

cula

tion

sin

the

pap

er, b

etwe

en t

wo

adja

cent

ele

ctro

des

εσ

Dn

[Cm

-2]

E t[V

m-1

]T p

[Nm

]3.

31.

9 10

-71.

55 1

0-53.

65 1

051.

12 1

0-3

72.

1 10

-71.

60 1

0-53.

35 1

051.

07 1

0-3

804.

0 10

-72.

20 1

0-51.

80 1

050.

54 1

0-3

400

1.3

10-6

2.60

10-5

5.50

104

1.70

10-4

1000

3.0

10-6

2.70

10-5

2.4

104

0.77

10-4

CON

CLU

SIO

NS

The

perf

orm

ance

of

a di

elec

tric

mot

or is

very

crit

ical

lyde

pend

ent

on t

he p

rope

rtie

sof

the

mat

eria

lswh

ich

the

mot

or is

mad

eof

.

Num

eric

alm

odel

of

the

mot

or t

oge

tin

form

atio

non

the

va

lues

of p

erm

itti

vity

and

cond

ucti

vity

that

give

rise

to

a gi

ven

valu

eof

sta

rtin

gto

rque

.

The

inve

rse

prob

lem

isill

-pos

edN

o un

ique

iden

tifi

cati

onof

m

ater

ial p

rope

rtie

s,

but…

…hel

pin

des

igni

ngth

e op

tim

um m

otor

.