motore - web · 2012. 6. 27. · ~ j c a l c q i { = ; c j { a v { { < pompa a ingranaggi...
TRANSCRIPT
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Pompa aingranaggi
Serbatoio
Attuatorefrizione
Attuatoreselezione
Attuatoreinnesto
Elettrovalvole
Accumulatore
Alimentazione
Scarico
Motoreelettrico
Cambio
Frizione
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RP
valvolafrizione
attuatorefrizione
dischi frizione
sistema dicontrollo
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Va − E = RaIa + LadIadt
E = Kmω
Cm − Cmp = bmω + Jmdωdt
Cm = Iaω
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Va
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La s+Ra
6
6
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E
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1
Jm s+ bm
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ω¾ -
Cmp
ω
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ωbW³U4@-0Sm6I2uE08<?>?>-0DH69-\?>O1S>4@/Q6I2
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Ra
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ω?>O1S>4@/Q6I2\XY4@D@[0O18<[email protected]@-=/1/k2ME08<R@R@Ok2
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Km
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Cmp − Cr − bωpsgn(ωp) = bpωp + Jp
dωp
dt
Cr = (Pl −R)Kp
Qu = Qp − αr(Pl −R)
Qp = ωpKp
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Cmp
ωp
- ¾
1
Jp s+ bp
?
?
ωp¾ - - -
bωpsgn(ωp)
6
6
¾ ¾
-Kp-Qp
Kp¾ ¾
Cr
Qu
- -
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αr
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¾ ¾ ¾
R
¾?
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0 50 100 150 2000
10
20
30
40
50
60
70
80
90
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P0=12
P0=17
P0=22
P0=27
P0=32
P0=37
Vl [cc]
Pl [b
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25S>S>4@A�-0?>-\/`_ 2h6>694V2h698<?>-5b��C-\/`_ 2h6>694V2h698<?>-®S9OV69?>8;:52uO1D�R�8<S>O1[0O18<D@-�E0-0DH69?925/1-°s wax�-./18S>OZ:C4@8</1-|S>R�8<Sm6I25?>-�2�S>O1D@O1Sm69?92'O1D¶R�8<S>O1[0O18<D@-�s`½<xGf�S>OZB@-=:H-jE08</1/1-0eH25?>-°/k2'Ei25A�-0?92��25/1/k2uR@?>-0S>S>O18<D@-UB@O�25/1O1Aj-0DH6I25[0O18<D@-\-U/k2�Ei25A�-0?92 é 25/1/k2uR@?>-0S>S>O18<D@-MB@O�S>Ei2h?9OQE08@bÆ�_ 2h6>694V2h698<?>-�S>OVS>Rr8<Sm6G2tT4@O1D@B@O7:H-0?>S>8uS>O1D@O1Sm69?92MRr-0?>A�-=6>69-0D@B@8u/`_ 4769O1/1OQ[0[08MB@-0/1/k2Uno-B@-0/1/k2qn>n�Ag25?>E0Ok27zh2®T4@-0Sm698\R@4@DH698�S>-dE0OHS>O<:C4@8</1-�?>O1Rr8<?m6I25?>-ZO1DtR�8<S>O1[0O18<D@-ZE0-0DH69?925/1-s waxj¬3D@-0E0-0S>S925?>O18%E08</1/1-0eH25?>--0DT69?925A°p�- /1-�Ei25A�-0?>-)� - é 25/1/k2�R@?>-0S>S>O18<D@-3B@O25/1O1A�-0DH6I25[0O185D@-5fHE08<S>O1E0EGF@µ./k2tB@OQÅ¡-0?>-0D@[i2uB@O�25?>-i2gsYEi254@S92h6I2uBV25/1/1-®R@?>-0S>-0D@[i2°S>4@/1/k2S>O1D@O1Sm69?92B@-0O�p@O1E0EGF@O1-0?>O1D@OZO1D�E08</18<?>-|:<-0?>B@-5fZ2E08<DT6I2h6>698E08<DJ/`_ -0/1-0A�-0DH698?>8<S>S>8TxX{2%S>R�8<Sm6I25?>-�/`_ 2h6>694V2h698<?>-¶O1D�R�8<S>O1[0O18<D@-¶E0-0DH69?925/1-5b/O E08<S±´�R�8<S>S>O1p@O1/1-3O1D@S>-0?>O1?>-/k2�n>n>n°- /k2�nÂc Ag25?>E0Ok27b��C- BV25/1/k2¶Rr8<S>O1[0O18<D@-�E=-0DT69?925/1-�E0O�S>O�:C4@8</1-�S>Rr8<Sm6I25?>-D@-0/1/k2MR�8<S>O1[0O18<D@-�B@-0Sm69?92's{¾HxGfTp@OQS985e<DV2tE08</1/1-0eH25?>-®/k2MEi25A�-0?92 é 25/1/k2UR@?>-0S>S>O18<[email protected]@O25/1O1A�-0DH6I25[0O185D@-°-°/k2P� 25/1/18gS>Ei25?>O1E08@b�·o-0?M?>O1R�8<?m6I25?>S>O�O1D¶R�8<S>O1[0O18<D@-°E0-0DH69?925/1-|S>O8<R�-0?92jE08<A�-MS>-tE0O�S>O�69?>8a:h25S>S>-uO1DRr8<S>O1[0O18<D@-MS>O1D@O1Sm69?927b�C-�S>O®B@-0E0O1B@-B@OqO1D@S>-0?>O1?>-�/k2¶Ã\Lå¬D@-=E0-0S>SI25?>O18�E08</1/1-0eH25?>-'/1-�Ei2hA�-0?>-KÎ-
�Î25/1/18ÄS>Ei25?>O1E08¸- /k2 é 25/1/k2�R@?>-0S>S>O18<D@-3B@O\25/1O1Aj-0DH6G2h[0O18<D@-5fqE08<S±´tO��VD@-3E08<?>S92:H-0?>B@OqR�8<S>S>8<D@8�S>E08<?>?>-0?>-'�VD@8�25B)25?>?>OQ:h25?>-�23E08<DH6I2h6>698¶E08<D*/k2 RV25?>-=69-�B@-0Sm69?92-j/`_ 2h6>694V2h698<?>-°R@4���S>E08<?>?>-0?>-|�VD@8�25/1/`_ -0Sm69?>-0Ag2'B@-0Sm69?92JsY¿TxGb|·�-0?tO�D@8<Sm69?>OZS>E08<R@O?>O1S>4@/Q6I2UO1DT4769O1/1-lE08<D@S>O1B@-0?925?>-�/k2\R�8<S>S>O1p@O1/1OQ6I¹.B@OVO1D@S>-0?>O1?>-q/k2MÃ\LÄf<?>O1S>4@/Q69-0?9¹UT4@O1D@B@O25S>S>-0DT69-'D@-0OlA�8TB@-0/1/1OZ�VS>O1E0OW-gS>O1A|4@/k2h6>OQ:COd25DV25/1O1[0[i2h69O�O1D¸S>-0e<4@OQ698@b Æ�_ 2h6>694V2h698<?>-R@4���E08<S±´o-0S>S>-0?>-�S>-0A�R@/1OQ�VEi2h698|E08<Aj-tO1D�voO1e@b@¾7bQwa½Cbn±/oA�8TB@-0/1/18gAg2h69-0Ag2h69OQE08gE08<S>?>4@OQ698'S>Oo?>OQX{¹'25/1/18�S>EGF@-=Ag2�S>-0A�R@/1OQ�VEi2h698gB@-0/1/k2
S>-0/1-0[0O18<D@-5f�O1/1/Q4@S>69?92h698�O1D�voO1e@b�¾7bQwa½CbtÉ.D¶e<-0D@-0?>O1E08�-0/1-0A�-0DH698�S>8<e<e<-=6>698�25B¶4@DV2R@?>-0S>S>O18<D@-
PB@OQ:<-0?>S92�BV2
0S>4@p@O1S>E0-�4@DV2XY8<?>[i2
FRV25?>Od25/1/k2'R@?>-0S>S>O18<D@-�Rr-0?u/k2
S>4V2g25?>-i2AB@O�E08<DT6I2h6>698@fVe<-0D@-0?>O1Ei25A�-0DH69-tS>O�FV2�T4@O1D@B@O�EIF@-
F = APblK\R@R@/1O^]
Ei25D@B@8'6I25/1-�-0T4V25[0O18<D@-|e<-=D@-0?925/1-|25/oS>O1Sm69-0Ag2gO1/1/Q4@Sm69?92h698gO1D¶voO1e@b�¾7bQwa½Cf¡/k2�XY8<?>[i2Fpsx
-0S>-0?>E0OQ6I2h6I2gBV25/1/k2�R@?>-0S>S>O18<D@-°D@-=/1/k2�Ei25A�-0?92gB@O�S>O1D@O1Sm69?92Psx
S>4@/1/`_ -0/1-0A�-0DH698A�8<p@O1/1-5f7B@O�25?>-i2
Asx = Asel + Abic
1 + sgn(xs)
2B@8a:<-5yAsel
¬ /`_ 25?>-i2ÄB@-0/1/`_ -0/1-0Aj-0DT698Ä?>8<S>S>8@fAbic
/{_ 25?>-i2ÄB@-0/\p@O1E0EIF@O1-0?>O1D@8JE08<? ]?>O1S>R�8<D@B@-0DH69-%-
xsO1D@B@O1Ei2º/18�S>R�8<Sm6I25A�-0DH698�B@-0/1/`_ 2h6>694V2h698<?>-JBV25/1/k2)R�8<S>O1[0O18<D@-
ñ�� ï&�����C�{�{�W���C�q�<���J�������C���a�l���C�q�<�V�¶ðo�Y�
1
1 2
2
B
BB
BA
A
A
A
Xs
voO1e<4@?92q¾7bQwa½Cy��CEIF@-0Ag2®S>-0A�R@/1OQ�VEi2h698qB@-0/1/`_ 2h6>694V2h698<?>-oB@OHS>-0/Q-0[0O18<D@-�S>-0D@[i2�/k2qRV25?m69-D@-0E0-0S>S925?>Ok2�25/1/`_ OQD@S>-0?>O1A�-0DH698|B@-0/1/k2|Ã\LÄbE0-0DH6I?925/Q-5fV¬
Fpsx= PsxAsx
25DV25/18<eH25A�-0DH69-UD@-0/1/k2°Ei25A�-0?92|B@O�B@-0Sm69?92Fpdx
= PdxAdx
E08<D 25?>-i2Adx = Asel + Abic
1− sgn(xs)2Æ�2°XY8<?>[i2j4769O1/1-UEIF@-u25e<O1S>E0-tS>4@/1/`_ 2h6>694V2h698<?>-jsY-0/1-0A�-=DT698j?>8<S>S>8Txl?>O1S>4@/Q6I2°T4@O1D@B@O`y
Fu =(
Fpsx− Fpdx
) s{¾7bǽ<x25/1/12�T4V25/1-Mp@O1S>8<e<DV2|R�-0?Q�jS>856>69?925?>?>-M/1-UXY8<?>[0-M?>-0S>O1Sm69-0DH69O�B@8a:C4769-u2he</1O�2h6>69?>OQ69O
:CO1S>E08<S>8b-tE08<4@/18<A°p@Ok25D@8
bcs
Fattriti = b xs + bcssgn(xs)
ñ�òK<%ï&�����C�{�Y�J���C�{�Y� (@�V�*(����Y� �3���Tó��{�W�7�i�a���7�;�r�h�l���ML��C�Y��,T�Y����� ñ�îL�-=6>69-0D@B@8�69476>698�25S>S>O1-0A�-MS9O�8h6969O1-=D@-tO1/¡S>-0e<4@-0DT69-uS>O1Sm69-0Ag2|B@O�-0T4V25[0O18<D@O`y
Fpsx= PsxAsx
Fpdx= PdxAdx
msdxs
dt= Fu −K(xs)− Fattriti
Fattriti = b xs + bcssgn(xs)B@8a:<-5yPsx
?925R@R@?>-0S>-0DH6I2�/k2°R@?>-0S>S>O18<D@-tD@-0/1/k2°Ei25A�-0?92|B@O�S>O1D@O1Sm69?927zPdx
?925R@R@?>-0S>-0DH6I2�/k2°R@?>-0S>S>O18<D@-tD@-0/1/k2°Ei25A�-0?92|B@O�B@-0Sm69?927zAsx(xs)
?925R@R@?>-0S>-0DH6I2�/`_ 25?>-i2°D@-0/1/k2°Ei25A�-0?92|B@O�S>O1D@O1Sm69?92�XY4@D@[0O18<D@-B@-0/1/k2°R�8<S>O1[0O18<D@-UB@-0/1/`_ 2h6>694V2h698<?>-5z
Adx(xs)?925R@R@?>-0S>-0DH6I2�/`_ 25?>-i2°D@-0/1/k2°Ei25A�-0?92|B@O�B@-0Sm69?92|XY4@D@[0O18<D@-MB@-0/1/k2R�8<S>O1[0O185D@-MB@-0/1/`_ 2h6>694V2h698<?>-5z
K(xs)?925R@R@?>-0S>-0DH6I2�/`_ O1DH69-0?925[0O18<D@-\XY?92|/`_ 2h6>694V2h698<?>-U-t/1-MS>4@Rr-0?m�VE0O�B@OE08<DH6I2h6>698�2|�VD@-tE08<?>S92jB@-0/1/`_ 2a69694V2h698<?>-5z
Fattriti?925R@R@?>-0S>-0DH6I2�/`_ 2h6>69?>O^698°:CO1S>E08<S>8�-ME08<4@/18<A|p@O125D@8|S>4@/�A�85698|B@O69476>69O�e5/1O�-0/1-0A�-0DH69O�O1De<O18CE08@z
ms
?925R@R@?>-0S>-0DH6I2j/k2|Ag25S>S92°B@-0/1/1-MRV25?m69O�O1D�A�8a:CO1A�-0DH698°E08<D@D@-0S>S>-E08<D�/`_ 2h6>694V2h698<?>-UB@O�S>-0/1-0[0O18<D@-5z
íU25/1/1-\-0T4V25[0O18<D@O�R@?>-0E0-=B@-0DT69O�¬MSm6I2h698jE=?9-02h698j4@D�A�8TB@-0/1/18|·Wêtë|f7A�8<Sm69?I2a6I8O1D�voO1e@b@¾7bQw;¾7bO BV2D@856I25?>-jEIF@-j/18S>EIF@-0Ag2�¬jp@O1B@O1A�-0D@S>O18<DV25/Q-5f�O1D7X{2h6>69OZ/k2':h25?>Ok25p@O1/Q-j· ¬
4@DV2gAg2h69?>O1E0-t-�?925R@R@?>-0S>-0DH6I2'S>Ok2j/k2�R@?>-0S>S>O18<D@-�D@-0/1/k2jEi25A�-0?92�B@O�B@-0Sm69?92gEGF@-�O1DT4@-0/1/k2|B@O�S>O1D@O1Sm69?927b
P =
[
Psx
Pdx
]
�_ -0/1-0A�-0DT698As
?925R@R@?>-0S>-0DH6I2U/k2�Ag2h69?>O1E0-dB@OT69?925SmXY8<?>Ag25[0O18<D@-dBV25/CEi25A�R�8\O1B@?9254C]/1O1E08j25/�Ei25A�Rr8jA�-0E0Ei25D@O1E08@f@E08<DH69O1-0D@-tE0O18C¬M/1-t25?>-0-tB@-0e</1O�2h6>694V2h698<?>O`b
As =[
Asel + Abic1+ sgn(Xs)
2−(Asel + Abic
1− sgn(Xs)2
)]
ñ�� ï&�����C�{�{�W���C�q�<���J�������C���a�l���C�q�<�V�¶ðo�Y�
P
Ql
As- -
ATs
¾ ¾
Fu - ¾
1
mss+b
?
?
xs¾ - - -
bcs sgn()
6
6
¾ ¾
- -6
1s
6
K(xs)
6
xs
¾ ¾ 0
xs
voO1e<4@?92t¾7bQw;¾7yZL�8CB@-0/1/18u·Wêtë B@-0/VS9OQS>69-0A�2tB@Or2h6>694V25[0O18<D@-�B@-0/1/k2US>-0/1-0[0O18<[email protected]@-0/1/k2Ag25?>E0Ok27bÆ�2¶XY8<?>[i2Ä4769O1/1-
FuE08<S±´M856>69-0DT476I2ÄB@-0/1/`_ -0T4V25[0O18<D@-Js{¾7bǽ<x|¬�T4@-0/1/k2�EGF@-�X{2
S>R�8<Sm6I25?>-t/`_ 2h6>694V2h698<?>-t2°:<-0/18CE0OQ6I¹xs69?925A�OQ69-U/k2°B@O1DV25A�OQEi2
[
1
mss+b
]
Æ�2 Ag2h69?>O1E0-gB@-0/1/1-�:H-0/18TE0OQ6I¹ B@OqS>Rr8<Sm6I25A�-0DT698¶A�8</Q69OQR@/QOQEi2h6I2�R�-0?|/k2 Ag2h69?>O^]E0-�69?925S>R�8<Sm6I2)B@-0/1/1-�25?>-0-
As
XY8<?>D@O1S>E0-�/1-�R�8<?m6I2h69-Ä25S>S>8<?>p@OQ69-�D@-0/tE08<A�R@/1-0S>S>8BV25/1/`_ 2h6>694V2h698<?>-\BV25/1/1-UB@4@-u-0/1-=6>69?>8;:525/Q:<8</1-UB@O�B@-0Sm69?92�-MB@O�S>O1D@O1Sm69?927b
Ql =
[
Qsx
Qdx
]
R��-S.�m� T.§\£\�¡� ¢d£\¨W©���£Wª7¢«¤\��¥ ¥ �VUo¨d¥ Ud¢d¥ �&¤\�|�C��¥ ���¡� ¢d£\�Æ�-\:h25/Q:<8</1-\B@O�S>-0/1-0[0O18<D@-\S>8<D@8°B@O1S>R�8<S>OQ69OQ:COrR@?>8<R�8<?>[0O185DV25/1OrO1DgR�8<?m6I2h6I27fCE0O18T¬.XY8<? ]D@O1S>E08<D@8u4@DV2uT4V25DH69OQ6I¹MB@OrR�8<?m6I2h6I2MB@O1?>-=6>6I25A�-0DH69-�R@?>8<R�8<?>[0OQ8<DV25/1-�25/1/k2UE08<?>?>-0DH69-EGF@-t/1-t25/1O1Aj-0DH6I27b�Æ�_ -0T4V25[0O18<D@-tEi25?92h6>69-0?>O1Sm69O1Ei2°B@-0/1/1-U:h25/Q:H8</1-U¬5y
Q = KmI2√
4P
B@8a:<- 4P = Pl − Psx8
Pl − Pdx¬�/k23B@OQÅ¡-0?>-0D@[i2¶B@OqR@?>-0S>S>O18<D@-25OqEi25R@O
B@-0/1/k2 :525/Q:<8</k23E0O18C¬�/k2¶R@?>-0S>S>O18<D@-�2¶A�8<DT69-�A�-0D@8�/k23R@?>-0S>S>O18<D@- 23:525/1/1-5bI¬
/k2�E08<?>?>-0DH69-�EGF@-�25/1O1A�-0DH6I2'O1/�B@OQS9Rr8<S>OQ69OQ:<8-Km
4@DV2E08<Sm6I25DT69-jEi25?92h6>69-0?>O1Sm69O1Ei2
ñ�ò!>Jï&�����C�{�Y�J���C�{�Y� (@�V�*(����Y� �3���Tó��{�W�7�i�a���7�;�r�h�l���q�{�����C�=�;� ñrñB@-0/1/k2g:525/Q:<8</k27b°É.DÄRr8<S>S>O1p@O1/1-°A�8CB@-0/1/18�·Wêtë EIF@-jB@-0S>E0?>OQ:<-�O1/�XY4@D@[0O18<DV25A�-0DH698B@-0/1/k2:525/Q:<8</k2�¬gO1/1/14@Sm69?92h698�O1D¸voO1e@b�¾7bQwi¿@fZB@8;:H-
Cm?925R@R@?>-0S>-0DT6I23/k2�Ei25RV25E0OQ6I¹
O1B@?9254@/1O1Ei2�B@O�E08<A�R@?>-0S>S>O18<D@-tB@-0/�S>O1Sm69-0Ag2|B@O�2h6>694V25[0O185D@-5b
[
1− sgn(I)2
1+ sgn(I)2
]′
−Qr
Qv
[
1− sgn(I)2
1+ sgn(I)2
]
Pl
R- ¾
KmI2√∆P
?
?
Q
¾ -
¾ -
C−1m
1s
6
6
6
[
Pa
Pb
]
- ¾
voO1e<4@?92|¾7bQwi¿@ydL�8CB@-0/1/18j·Wêtë�B@-0/1/1-U:525/Q:<8</1-UB@O�S>-0/1-0[0O18<D@-tB@-0/1/k2°Ag25?>E0Ok27b
ÐgÑ�W ÓÕÔ�æ�Ø®Ú=Ú0Ô�æ�Ø®Ú=Ú=ØX.MátÚ0.°ÔuÚ=Ø ØPæ�Ø®èuÚ=Û�átÖ�Ö�àáMÖ�Ôt×oÛ�æ�ÛÛ0ÞÞ�ØM��Ö�Ô
·o-0?|Ei25R@O1?>-'O1/WE08<?>?>-=6>6983XY4@D@[0O18<DV25A�-0DH698¶B@-0/qp@/18TE0E08¶B@OqO1D@D@-0Sm698¶¬�D@-0E0-0S>S925?>O18Ei25R@O1?>D@-�O1/lS>O1e<D@OQ�VEi2h698@b%L�-0DH69?>-O1/lp@/18CE0E08¶B@OqS>-0/1-0[0O18<D@-�B@-=:H-S>8</18¶A°4@8;:H-0?>S>OR�-0?�S>-0/1-0[0O18<DV25?>-M/k2|Ag25?>E0Ok27fC-0S>S>8gB@-=:<-5y
]gB@O1S>O1D@S>-0?>O1?>-M/12|Ag25?>E0Ok2°R@?>-0E0-=B@-0DT69-5z]gS>O1D@E0?>8<D@O1[0[i25?>-MO1/�R@?>O1Ag25?>OQ8°-0B�O1/�S>-0E08<D@BV25?>O18jB@-0/�Ei25A°p@O18E08<D�O�DC4@8;:CO�?925R@R�8<?m69O�B@O�Ei25A°p@O18@z]gO1D@e<?925DV25?>-U/k2|DT4@8;:52jAg25?>E0Ok27z
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Attuatore innesto
Albero primario Albero secondario
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xs [mm]
Ev1 Ev2
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ωprim
ωsec
R�-0?�/1-MB@OQ:<-0?>S>-tAg25?>E0-5bE08<R@R@Ok27fZ8</Q69?>-jEGF@-'?>O1B@4@?>?>-�/k2�B@OQÅ¡-0?>-0D@[i2 B@Od:<-0/18CE0OQ6I¹7f�X{2 ?>4@856I25?>-g/`_ -0/Q-0A�-0DT698í�?>O1S>R�-=6>69825BÄK«E08<S±´lBV2�O1A�Rr-0B@O1?>-°/`_ 2i:525D@[i25A�-0DH698�B@O�K�:<-0?>S>8�O1/ZE08<A�R@/1-G6I8O1D@e<?925DV25A�-0DT698�B@-0/1/k2�Ag25?>E0Ok27b ³U4V25D@[email protected]@4@- -0/1-0A�-0DH69O.í -0B�¼«S>8<D@8%25/1/12Sm69-0S>S92�:<-0/18CE0OQ6I¹7fT/k2tS>4@R�-0?m�VE0O1-Uí S>Or?>Ok25/1/QOQD@-i2tE08<Dg/1-.S>4@R�-0?m�VE0O¡K -0B�¼¸E08<S±´�EIF@-O1/�Ag25D@O1E0856>698K R�8<S>S92�E08<DH69O1DC4V25?>-j/k2S>4V2�E08<?>S92�-0BJO1D@e<?925DV25?>-jOdB@-0DH69OWB@-0e</1O-0/1-0A�-0DT69O@í�-0Bg¼®f<O1D|A�8TB@8MBV2ME0?>-i25?>-®4@D�E08</Q/1-0eH25A�-0DH698\XY?92M/`_ 25/Qp�-0?>8UR@?>O1Ag25?>OQ8-g/`_ 25/1pr-0?>8S>-0E08<D@BV25?>O18@b é 8<A�-�R�-0?u/k2S>-0/1-0[0O18<D@-5f�/`_ -0/1-0A�-0DH698�A�8<p@O1/Q-|B@-0/1/`_ 2h6m]694V2h698<?>-5fVE08</1/1-0eH2h698|E085D�O1/�S>O1D@E0?>8<D@O1[0[i2h698<?>-�sY-0/1-0A�-0DT698j?>8<S>S>8�B@-0/1/12jvoO1e@b@¾7bQwJ=HxGf¬MS>8<e5e<-=6>698j25/1/k2tB@OQÅ¡-0?>-0D@[i2°B@O�XY8<?>[0-Ue<-0D@-0?92h69-UD@-0/1/1-\Ei25A�-0?>-UB@-0Sm69?92°-US>O1D@O1Sm69?927fS>O�FV2�T4@O1D@B@O�EIF@-j/k2gXY8<?>[i2�4769O1/Q-°¬
Fu = Fpsx− Fpdx
B@8;:<-Fpsx
= PsxAsx
-Fpdx
= PdxAdx
b é 8<D%O1/WA�85698 B@-0/1/`_ O1D@D@-0Sm6983O1DH69-0?925e<O1S>E08<D@8325D@EGF@-'/`_ -0/1-0A�-0DC]698\� -�/12�?>-i25[0O18<D@-�:CO1D@E08</k25?>-�B@-0/�E08<DH6I2h6>698�XY?92�/1-S>4@R�-=?>�VE=O\í -0B�¼�B@-0/1/k2voO1e@bC¾7bQwJ=7b�Æ�_ -0/1-0A�-0DT698]��e5-0D@-0?92°4@DV2uXY8<?>[i2�sYE04@?m:52°p@/14�v�O1e@bC¾7bǽ<½<xdEIF@-\69-0D@B@-2:CO1D@E08</k25?>-�O1/�Ag25D@O1E0856>698K O1DÄR�8<S>O1[0O18<D@-jE0-0DT69?925/1-5bÆ�2�?>-i25[0O18<D@-j:CO1D@E08</k25?>-¬XY4@D@[0O18<D@-B@-0/1/18�S>Rr8<Sm6I25A�-0DH6I8Ä-B@-0/1/k2¶B@OQÅ¡-0?>-0D@[i2�e<O1?>O`fdO1D7X{2h6>69Oq/k2¶?>-i25[0OQ8<D@-O1D@O1[0Ok2�25/¡E08<DH6I2h6>698°XY?92°/1-\B@4@-MS>4@R�-0?m�VE0O�-\69-0?>A�O1DV2�T4V25D@B@8|/k2�B@OQÅ¡-0?>-0D@[i2°XY?92�Oe<O1?>OrB@-0OV:525?>O�-0/1-=A�-0DT69Or¬.4@e<4V25/1-5fCBV2h698�EIF@-U2uB@OQÅ¡-0?>-0D@[i2ue<O1?>O^Iue</1OV-0/1-0A�-0DH69OrK�fí«-0Bļ�B@-0/1/k2'voO1e@b¡¾7bQwJ=g?>O1S>4@/Q6I25D@8�25/1/1OQD@-i2h69O{bMN�25/1-�XY8<?>[i2g:CO1-0D@-°O1D@B@O1Ei2h6I2gE08<DFsinc
(
xi,4ω
) b�n±D@8</Q69?>-5f�25/1/18�S>R�8<Sm6I25A�-0DH698�B@-0/1/`_ 2h6>694V2h698<?>-°S>O�8<R@R�8<D@e<8<D@8e</1O2h6>69?>OQ69Oo:CO1S>E08<S>8�-|E08<4@/18<A|p@O125D@8@f�O1D@B@O1Ei2h69OoE08<D
Fattriti = bxi + k sgn(xi)bjn±D
6I25p�-0/1/1-�¾7bǽMS>8<D@8uO1D@B@O1Ei2h69O@OV:h25?>Or?925R@Rr8<?m6IO@B@OV69?925SmXY8<?>Ag25[0O18<D@-qXY?92MO1/VDT4@A�-0?>8uB@Oe<O1?>O�B@-0/¡R@?>O1Ag25?>OQ8u-UB@-0/¡S>-0E08<D@BV25?>O18|2�S>-0E08<D@BV2|B@-0/¡?925R@Rr8<?m698°O1D@S>-0?>OQ698@bd³U4V25DC]B@84@DV2Ag2h?9E=Ok2'?>O1S>4@/Q6I2gO1D@e<?925DV2h6I27f�O1/oR@?>O1Ag25?>OQ8'-0BÄO1/oS>-0E08<D@BV25?>O18@f�69?925A�OQ69-�O1/?925R@R�8<?m698MB@O7Ei25A°p@O18@f5e<O1?925D@8M25/1/1OQD@-i2h69O{z<Ag2\T4V25D@B@8MS>O@B@-0E0O1B@-®B@O7-=Å¡-=6>694V25?>-®4@DEi25A|p@Ok25Aj-0DT698uB@O¡?925R@R�8<?m698@f7O�e<O1?>O�B@-0O¡B@4@-M25/1p�-0?>O�?>O1S>4@/Q6I25D@8�B@O1S925E0E08<R@R@Ok2h69O`fTO1DT4V25DT698|-0?925D@8j25/1/1OQD@-i2h69OrE08</�:H-0E0EIF@O18j?925R@Rr8<?m698|B@O¡Ei25A°p@O18@bd³U4@-0Sm6I2°B@OQÅ¡-0?>-0D@[i2B@OVe<O1?>O7B@-=:�_ -0S>S9-0?>-U25D@DT4@/1/k2h6I2\R�-0?dRr8569-0?d-=Å¡-=6>694V25?>-�4@DV2MEi25A°p@Ok2h6I27b�n±/VE08<A�R@OQ698
<^� ï&�����C�{�{�W���C�q�<���J�������C���a�l���C�q�<�V�¶ðo�Y�B@-0/7?>Ok25/1/QOQD@-i25A�-0DH698\B@-0/1/1-W:<-0/18TE0OQ6I¹\S>R�-=6>6I2M25/CS>O1D@E0?>8<D@O1[0[i2h698<?>-5bZ¼�S>S>8U69?925S>A�-=6>69-4@DV2jE08<R@R@Ok2|B@O�2h6>69?9O^6I8
Csinc = Fsync(xi,∆ω)K4syncsgn(4ω)
EGF@-t?>Ok25/1/QOQD@-i2°/1-U:<-0/18CE0OQ6I¹7f7B@8;:H-5yCsync
?925R@R@?>-0S>-0DH6G2�/k2jE08<R@R@Ok2jB@O�S>O1D@E0?>8<D@O1[0[i25[0O18<D@-MXY?92j/`_ 25/1p�-0?>8jS>-0E08<D@BV25?>O18g-/`_ 25/1p�-0?>8|R@?>O1Ag25?>OQ8@z
K4sync?925R@R@?>-0S>-0DH6I2uO1/@RV25?925A�-=69?>[email protected]?92h6>69-0?>O1[0[i2M/k2U69?925SmXY8<?>Ag25[0O18<D@-qBV25/1/k2
XY8<?>[i2Fsinc
25/1/k2�E08<R@R@Ok27b³U4@O1D@B@Oo/k2gS>OQ694V25[0O18<D@-�EIF@-|S>O�:CO1-0D@-j2'E0?>-i25?>-°¬|T4@-=/1/k2gO1D@B@O1Ei2h6I2gO1D¶voO1e@b¡¾7bǽ;I7fB@8a:<-j/`_ 25/1p�-0?>8�R@?>O1Ag25?>OQ8@f¡E08<DÄO1D@-0?>[0Ok2
Jp?>4@856I22':<-0/18CE0OQ6I¹
ωp-0BĬjS>8<e<e<-=6>698
25/1/k2tE08<R@R@Ok2 −Csync A�-0DT69?>-\O1/�S>-0E08<D@BV25?>O18°R@?>-0S>-0DH6G2CfVO1D@-0?>[0Ok2 Js E08<R@R@Ok2 Csync:H-0/Q8CE0OQ6I¹ωsb
ps ωω CsincCsinc
�C-0E08<D@BV25?>O18 ·�?>O1Ag25?>O18
voO1e<4@?92|¾7bǽ;I7yd·�?>O1D@E0O1R@O18°B@O�XY4@D@[0O18<DV25A�-0DH698jB@-0O�S>O1D@E0?>8<D@O1[0[i2h698<?>O`bÆ�-M-0T4V25[0O18<D@O�EIF@-ue<8;:<-0?>DV25D@8�O1/�S>O1Sm69-0Ag2|B@OQ:<-0DH6I25D@8�T4@O1D@B@O
Jpωp = −Csync − bpωp
Jsωs = Csync − bsωs
4ω = ωp − ωs
í\8a:<-bp?925R@R@?>-0S>-0DT6I2./`_ 2h6>69?>OQ698q:CO1S>E08<S>8@bon±/TR@?>8<p@/1-0Ag2®¬l25DV25/1O1[0[i2h698�E08<D�B@8;:CO1[0Ok2
B@OoRV25?m69O1E08</k25?>O�D@-0/1/`_ 25?m69O1E08</Q8_8 ¾#:`b�L�-=6>69-0D@B@8�69476>69825S>S>O1-0A�-5f¡/1-°-0T4V25[0O18<D@OoEIF@-
ñ�ò!>Jï&�����C�{�Y�J���C�{�Y� (@�V�*(����Y� �3���Tó��{�W�7�i�a���7�;�r�h�l���q�{�����C�=�;� <�îe<8a:<-0?>DV25D@8�O1/¡S>O1Sm69-0Ag2|S>8<D@8@y
Fpsx= PsxAsx
Fpdx= PdxAdx
Fu = Fpsx− Fpdx
F = Fu − Fb(xi)− Fsinc(
xi,4ω
)
− Fattriti
Fattriti = b xi + k sgn(xi)
Jpωp = −Csinc sgn(4ω)− bp ωp
Jsωs = Csinc sgn(4ω)− bs ωs
4ω = ωp − ωs
Csinc = Fsinc(xi,∆ω)K4sinc sgn(4ω)
N�?925A�OQ69-o6I25/1Oh-0T4V25[0O18<D@O<¬�Sm6I2h698�E0?>-i2h698�4@DMA�8CB@-0/1/18q·Wêtë)A�8<Sm69?92h698qO1DtvoO1e@b0¾7bǽCw<bé 8<A�-|R�-0?MO1/oA�8TB@-0/1/18'B@-0/1/k2gS>-0/1-0[0O18<D@-5f�O1/oA�8TB@-0/1/18'B@-0/1/`_ OQD@D@-0Sm698�?>O1S>4@/Q6I2gp@O1B@O^]A�-0D@S>O18<DV25/1-5bZn±/�R@?>8CB@856>698|69?92|/1-MAg2h69?>O1E0O
P-Ai
E08<D
P =
[
Psx
Pdx
]
-Ai =
[
Ainn + Abic1+ sgn(Xi)
2−(
Ainn + Abic1− sgn(Xi)
2
) ]
XY8<?>D@O1S>E0-U/k2uXY8<?>[i2�4769O1/1-\e<-0D@-0?92h6I2�B@-0/1/`_ 2h6>694V2h698<?>-5b��_ -0/1-0A�-0DH698K?925R@R@?>-0S>-0DH6I2
/1-°XY8<?>[0-jB@O1Rr-0D@B@-0DT69O�BV25/1/k2gR�8<S>O1[0O18<D@-°EGF@-jA�8TB@-0/1/k2g/k2'XY8<?>[i2Fgiri
-0BÄOZXY-0D@8h]A�-0D@OoB@OZpV2a6969476I27f¡EIF@-|S>Oo:h25D@D@8T4@O1D@B@OZ2'S>856>69?925?>?>-°25/1/k2jXY8<?>[i2'4769O1/1-5bUn±D7�VD@-5f/`_ -0/1-0A�-0DT698 1
meqs+b
?925R@R@?>-0S>-0DH6G2 /`_ 2h6>69?>OQ698-g/k2�B@O1DV25AjO1Ei2B@8;:C476I2325/1/1-jAg25S>S>-O1DA�8;:CO1A�-0DT698°D@-0/�S>O1Sm69-0Ag2°E08<D@D@-0S>S>-�E08<D�/`_ O1D@D@-0Sm698@bÆ�-M:525/Q:<8</1-tB@O�O1D@D@-0Sm698�S985D@8gB@O1S>R�8<S>OQ69OQ:CO�R@?>8<R�8<?>[0O18<DV25/QO�O1D�R@?>-0S>S>O18<D@-5frE0O18C¬
XY8<?>D@O1S>E08<D@8'4@DV2gR@?>-0S>S>O18<D@-°B@O�4@S>E0OQ6I2gR@?>8<R�8<?>[0O18<DV25/1-�2h/�:h25/18<?>-�B@-0/1/k2jE08<?>?>-0DT69-B@OZO1D@e<?>-0S>S>8@b°íU25/1/`_ 25DV25/QO1S>O�B@-0/1/k2g?>O1R�8<Sm6I2gB@-0/1/`_ -0/1-=6>69?>8a:h25/Q:<8</12gO1D3XY4@D@[0O18<D@-°B@-0/^]/k2�E08<?>?>-0DT69-jB@Od-0E0E0OQ6I25[0O18<D@-�sYA�8<Sm69?92h6I2�O1DÄvoO1e@b�¾7bǽ5¾Hx\¬�Rr8<S>S>O1p@O1/1-|D@856I25?>-jEIF@-O1/�B@O1S>R�8<S>OQ69OQ:<8|?>O1S>4@/Q6I2°S>47²�E0O1-0DH6I-=A�-0DT69-u/1O1D@-i25?>-U-tE08<D�4@D�_ O1Sm69-0?>-0S>O�S>47²�E0O1-0DT69-G]A�-0DT69-upV25S>S927b�N�?925S>E04@?925D@B@8'T4@O1D@B@O�/`_ O1Sm69-0?>-0S>O�-�/k2jD@8<D R�-0?mXY-=6>6I2�/1O1D@-i25?>O^6I¹7fVS>O
<`� ï&�����C�{�{�W���C�q�<���J�������C���a�l���C�q�<�V�¶ðo�Y�
P
Q
Ai- -
ATi
¾ ¾
- ¾
1
meqs+b
?
?
xi¾ - - -6
1s
6
K
6
¾ ¾ 0
xi
Cp
ωp
- ¾
1
Jps+bp
?
?
ωp¾ -
¾ -
FsincK4sinc
6
6
Csync
- ¾
6xi
- ¾
1
Jss+bs
?
?
ωs¾ -
Cs
ωs
voO1e<4@?92�¾7bǽCw<yoL�8TB@-0/1/18\·WêtëºB@-0e</1OT2h6>694V2h698<?>OHB@OTO1D@[email protected]@-0OTS>O1D@E0?>8<D@O1[0[i2h698<?>O`b
ATi =
[
Ainn + Abic1+ sgn(Xi)
2−(Ainn + Abic
1− sgn(Xi)2
)]
ñ�ò!>Jï&�����C�{�Y�J���C�{�Y� (@�V�*(����Y� �3���Tó��{�W�7�i�a���7�;�r�h�l���q�{�����C�=�;� <¡ñ
−15 −10 −5 0 5 10 15
−400
−300
−200
−100
0
100
200
300
400
Spostamento [mm]
For
za [N
]
Reazione vincolare A−BSgancio marcia
voO1e<4@?92|¾7bǽ<½Cy é 4@?m:52jR�8<S>O1[0O18<D@-G]ÂXY8<?>[i2°?>-0S>O1Sm69-0DH69-�25/�A�85698@b
0 200 400 600 800 1000 1200 1400 1600 18000
10
20
30
40
50
60
Corrente [mA]
Pre
ssio
ne [b
ar]
Risposta della valvola di innesto
voO1e<4@?92|¾Cbǽ5¾7y é 4@?m:52jE08<?>?>-0DH69-G]±R@?>-0S>S>O18<D@-uR�-0?�/`_ -0/1-=6>69?>8;:525/^:H8</12�B@O�O1D@D@-0Sm698@b
<�< ï&�����C�{�{�W���C�q�<���J�������C���a�l���C�q�<�V�¶ðo�Y�FV2jEIF@-t/k2|R@?>-0S>S>O18<D@-tB@O�4@S>E0OQ6I2°:525/1-5y
Pout = Pin
(
Iv − IoffImax − Ioff
)
B@8a:<-5yPout
?925R@R@?>-0S>-0DH6I2�/k2°R@?>-0S>S>O18<D@-tB@O�4@S>E0OQ6I2|BV25/1/k2°Rr8<A�RV27zPin
/k2°R@?>-0S>S>O18<D@-tAg25S>S>O1Ag2°-0?>8<eH25p@O1/1-5zIv/k2°E08<?>?>-0DH69-uB@O�-0E0E0OQ6I25[0O18<D@-MB@-0/1/k2�:525/Q:<8</k27z
Ioff/k2°E08<?>?>-0DH69-uB@O�85Å¡S>-=6iz
ImaxO1/�:525/18<?>-MAg25S>S>O1A�8°B@-0/1/k2°E08<?>?>-0DT69-tB@O�-0E0E0OQ6I25[0O18<D@-MB@-0/1/k2:h25/Q:H8</k2Cb
Æ�2'S>8</k2g-0T4V25[0O18<D@-|R@?>-0E0-=B@-0DT69-jR�-0?Q��D@8<D¶?>O1S>R�-0E0EIF@Ok2'O1/�E08<A�R�8<?m6I25A�-0DH698gB@-0/S>O1Sm69-0Ag27bt�C-|E08<S±´dD@8<D3XY8<S>S>-5f¡:H8<?>?>-0p@pr-|B@O1?>-�EGF@-°4@DV2g:525?>Ok25[0O18<D@-uB@OoE08<?>?>-0DH69-25/1/`_ -0/1-=6>69?>8;:h25/Q:<8</12JR@?>8TB@4@E0-�4@D�_ O1A�A�-0B@Ok2a6I2Ä:h25?>Ok25[0O18<D@-3B@-0/1/12¸R@?>-0S>S>O18<D@-¶D@-0/^]/`_ 2h6>694V2h698<?>-5fHE08<S92tO1A�R�8<S>S>O1p@OQ/Q-qBV2h6I2t/k2MB@OQDV25A�O1Ei2UB@-0/VS>O1Sm69-0Ag27b�·�-0?dB@-0S>E0?>OQ:H-0?>-25/®A�-0e</1O18¶O1/qE08<A�R�8<?m6I25A�-0DH698�B@-0/�S>O1Sm69-0Ag2�¬T4@O1D@B@O�D@-0E0-0S>S925?>O18JO1DH69?>8CB@4@?>?>-4@DS>O1Sm69-0Ag2°B@-0/�R@?>O1A�8�8<?>B@O1D@-MEIF@-MB@8a:C?>-0p@pr-t69-0D@-0?>-MO1D�E08<D@S>O1B@-0?925[0O18<D@-U69476>69-/1-|B@O1DV25A�O1EIF@-|O1D¶e<O18CE08ÄsYA�8a:CO1A�-=DT698�B@-0/1/k2'S>Rr8</1-=6>6I2�B@-0/1/k2':h25/Q:<8</k27f�:h25?>Ok25[0O18h]D@-�B@O�R@?>-0S>S>O18<D@-u/14@D@e<8�O�E08</1/1-0eH25A�-0DH69O�O1B@?9254@/1OQE0O�-0B¶25/1/`_ OQDH69-0?>D@8jB@-0/1/k2jEi25A�-0?92B@-0/1/`_ 2h6>694V2h698<?>-;xGzCXY8<?>D@-0D@B@8�4@DV2|?>O1S>R�8<Sm6I2|E08<A�-MO1D@B@O1Ei2h698|O1D�voO1e@b@¾7bǽh¿@b
ñ�ò!>Jï&�����C�{�Y�J���C�{�Y� (@�V�*(����Y� �3���Tó��{�W�7�i�a���7�;�r�h�l���q�{�����C�=�;� <`>
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
10
20
30
40P
re
ssio
ne
[b
ar]
PEc1
PEc1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
500
1000
1500
Tempo [s]
Co
rre
nte
[m
A]
Ec1Ec1
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.84500
5000
5500
6000
6500
7000
Tempo [s]
[giri
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]
Giri primario Giri secondario
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
4500
5000
5500
6000
6500
7000
Tempo [s]
[giri
/min
]
Giri prim. simulati Giri sec. simulati Giri prim. sperimentaliGiri sec. sperimentali
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Ë�>?>O1S>4@/Q6I2�XY4@D@[0O18<D@-MB@-0/1/`_ -0D@-0?>e<Ok2°BV2|B@O1S>S>O1RV25?>-5bdÆ�2|Sm69?92h69-0e<Ok2°¬tT4@-0/1/k2°B@O�X{25?®Ei2a]/k25?>-®R@O!Gj/1-0DH6I25A�-0DT69-®/`_ -0D@-0?>e<Ok2UB@O1S>S>O1RV2h6I2UD@-0/1/`_ 4@/Q69OQAg2\RV25?m69-�B@OVEi25A°p@Ok2h6I27f<E08<S±´BV23?925/1/1-0DH6I25?>-�/k2�B@O1S>E0-0S923B@-0Ole<O1?>OW-g?>O1B@4@?>?>-g/1-g8<S>E0O1/1/k25[0OQ8<D@O�XY?92 OWB@4@-�25/1p�-0?>OB@-0/qEi25A°p@O18 -'T4@O1D@B@OW/k2 ?>4@A�8<?>8<S>OQ6I¹B@-0/lEi25A|p@OQ8 Sm6I-=S9S>8@bijU4@-0Sm6I23Sm69?92h69-0e<Ok2R�-0?>A�-=6>69-0?>-0p@p�-°B@O�-=Å¡-=6>694V25?>-�4@D3Ei25A°p@O18�Ag25?>E0Ok2jD@-0/1/18�Sm69-0S>S>8'69-0A�R�8gAg2�B@O?>O1B@4@?>?>-°/18gSm69?>-0S>Su25/�Ei25A°p@O18@f�R�-0?>A�-=6>69-0D@B@8�Ag25eH25?>O�E08<D¶4@/Q69-0?>O18<?>O�-=:<8</14@[0O18<D@OB@O�A�O1e</QOQ8<?92h?>-|25D@EIF@-jO1/�69-0A�Rr8B@OZEi25A°p@Ok2h6I27bun±DÄvoO1e@bi'CbÇÀ�:<-0D@e<8<D@8�E08<D7XY?>8<DC]6I2h69OZ/`_ 25D@BV25A�-0DT698�B@-0/1/k2'E08<?>?>-0DH69-jB@O�O1D@D@-0Sm698B@4@?925DH69-j/`_ 2h6>694V25/1-°Sm69?92h69-0e<Ok2'B@OE08<DT69?>8</1/18sY?>8<S>S>8Txq-tE08<DO1/�E08<DH69?>8</1/18j25R@Rr-0DV2jB@-0S>E0?>OQ6>6983sYp@/14rxGb
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
200
400
600
800
1000
1200
1400
1600
Tempo [s]
Cor
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e [m
A]
EC1 simulata EC1 sperimentale
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Ë »
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
−10
−5
0
5
10
Po
siz
ion
e [m
m]
Pos. in. a.Pos. in. e.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
4500
5000
5500
6000
6500
7000
Tempo [s]
[giri/m
in]
Giri prim. a.Giri prim. e.Giri sec. a. Giri sec. a.
voO1e<4@?92�'Cb &7y K\D@BV25A�-0DH698Ä[email protected]/1E04@D@O®RV25?925A�-=69?>O®Ei25?92h6>69-0?>O1Sm69O1E0O®B@4@?925DH69-�4@DV2Ei25A|p@Ok2h6I2�R�-0?�B@4@-tSm69?92h69-0e<O1-MB@O�E08<DH69?>8</1/18@b