maxon formelsammlung e
TRANSCRIPT
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VCC
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Formulae
HandbookJan Braun
maxon academy
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Selection process
When performing a system analysis WKH UVW VWHS LV WR GHVFULEH WKH GULYH DV D ZKROH LQ LWV
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IHDVLELOLW\RIDVROXWLRQDQGWRJHWDSLFWXUHRIWKHERXQGDU\FRQGLWLRQVDQGUHVWULFWLRQV See chapterA.1: Overview, system analysis
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DFFXUDF\"See chapter A.2: Motion of the load
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QRWLQFOXGHDmechanical transformation.
Mechanical drivesWUDQVIRUPPHFKDQLFDOSRZHULQWRPHFKDQLFDOSRZHU)RUWKHVHOHFWLRQRIWKH
GULYHWKHORDGNH\GDWDDUHFRQYHUWHGWRWKHRXWSXWRI WKHPRWRURU JHDUVKDIWSee chapter A.3:
Mechanical drives.
7KHVWHSIRUWKHgearhead selectionFDQEHVNLSSHGLIQRPD[RQJHDUKHDGLVXVHG*HDUKHDGVDUH
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7KHSXUSRVHRIWKLVVWHSLVWRGHWHUPLQHLIDQGZKLFKmaxon gearheadFDQEHXVHG7KHNH\GDWD
IRUWKHPRWRUVHOHFWLRQFDQWKHQEHFDOFXODWHGIURPWKHJHDUKHDGUHGXFWLRQDQGHIFLHQF\See
chapter 3.4: maxon gearhead
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motors7KHXVHIXOOLIHFRPPXWDWLRQDQGEHDULQJV\VWHPVDOVRKDYHWREHFRQVLGHUHG See chapter
6.5: Motor selection
7KHselection of the windingLVPDGHRQWKHEDVLVRIDFRPSDULVRQRIWKHDSSOLHGPRWRUYROWDJH
ZLWKWKHVSHHGDQGDFRPSDULVRQRIWKHDYDLODEOHFXUUHQWZLWKWKHWRUTXHUHTXLUHPHQWV See chapter
6.5: Motor selection
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Step 1
SystemOverview
Step 2
Load
Step 3
Drive
Step 4
Gearhead
Step 5 + 6Motor type
Winding
Step 7
SensorController
v(t),F(t)
Ambientconditions
Communicaton
Power
Gear
Motor
Controlle
r
Load
Start
drive selection
Overview, system analysis,
preselection of controller & sensor
Chap. A.1
Motion of the load
Chap. A.2
Mechanical drive design
Chap. A.3
ec an ca
trans ormat on
Use ofgearhead?
Motor type selection
Chap. 6.5
Winding selection
Chap. 6.5
Verification of controller & sensor
Chap. A.3
Drive selected
Gearhead selection
Chap. 3.4
No
No
Yes
Yes
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Foreword
This Formulae Handbook lists the most important formulae in relation to all components of
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Numerous illustrations and the clear descriptions of the symbols on the respective page help the
reader to understand the formulae.
Roughly speaking, it is a collection of the most important formulae from the maxon catalog, as
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for engineers, professors, lecturers and students, as a perfect supplement to the above mentioned
book.
Thank you)LUVWO\ , ZRXOG OLNH WR WKDQN 'U 8UV .DIDGHU ZKR HQFRXUDJHG PH WR WDFNOH WKLV ERRN 7KH
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have read the manuscript and have given valuable suggestions for improvements. I also received
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Content 5
A. Drive selection 6
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1. Mass, force, torque 9 )RUFHVLQJHQHUDO
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2. Kinematics
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4. Bearing
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5. Electrical principles
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7. maxon sensor
8. maxon controller
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9. Thermal behavior
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11. Symbol list for the Formulae Handbook 56
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A. Drive selectionA.1 Overview, system analysis
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Mechanical design
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Determine the boundary conditions
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A.2 Motion of the load
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Operating points
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1. Mass, force, torque1.1 Forces in general
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Calculating the total load force consisting of component forces
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1.2 Torques in general
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Body type Illustration Mass, moments of inertia
Circular cylinder, disc 21
121
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1.3 Moments of inertia of various bodies with reference
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Body type Illustration Mass, moments of inertia
Hollow sphere34
52
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ra
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ra
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HP High power versionK Plastic version
L Low-cost version
M Sterilizable version for medical application
S Spindle drive with axial bearing
V Reinforced version
Z Low backlash version
Operating ranges of gearheads
PD[RQJHDUKHDGVDUHGHVLJQHGIRUDQRSHUDWLQJOLIHRIDWOHDVWKRXUVDWWKHJLYHQPD[LPXP
FRQWLQXRXV WRUTXH DQG PD[LPXP LQSXW VSHHG UDWLQJV 2SHUDWLRQ EHORZ WKHVH OLPLWV ZLOO
VLJQLFDQWO\LQFUHDVHRSHUDWLQJOLIH,IWKHOLPLWVDUHH[FHHGHGWKHXVHIXOOLIHRIWKHJHDUKHDG
PD\EHUHGXFHG
Load speed nL
Short-term operation
Max. load speed
(determined by gearhead input speed)
Continuous operation
MG,cont
Load torque ML
MG,max
nmax,L
nmax,L
nmax,in
nmax,L
=iG
nmax,in
iG
nmax,in
3.4 maxon gear
Symbol Name SI
0*FRQW 0D[FRQWLQXRXVWRUTXHJHDUKHDG
FDWDORJYDOXH 1P0*PD[ ,QWHUPLWWHQWO\SHUPLVVLEOHWRUTXH
JHDUKHDGFDWDORJYDOXH 1P
i* 5HGXFWLRQUDWLRJHDUKHDGFDWDORJYDOXH
Symbol Name maxon
nmax,in 0D[LPXPLQSXWVSHHG USP
nmax,L 0D[LPXPORDGVSHHG USP
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Sintered sleeve bearings Ball bearings
r
Operating
modes
&RQWLQXRXVRSHUDWLRQ 6XLWDEOHIRUDOOW\SHVRIRSHUDWLRQ
(VSHFLDOO\ IRU VWDUWVWRSRSHUDWLRQVDQG
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Speed
range
,GHDODERYHDSSUR[USP
UDQJHIRUK\GURG\QDPLF OXEULFDWLRQ
:LWKVSHFLDOPDWHULDOSDLULQJDQG
OXEULFDWLRQHYHQDWORZHUVSHHGV
8SWRDSSUR[USP
,QVSHFLDOFDVHVXSWRUSP DQGKLJKHU
Radial /
axial load
2QO\VPDOOEHDULQJORDGV +LJKHUORDGV
3UHORDGHGEDOOEHDULQJV
$[LDOORDGLQJXSWRWKHYDOXHRIWKH
SUHORDG
Additional
operatingcriteria
7\SLFDOLQVPDOOEUXVKHG'&PRWRUV
XSWRDSSUR[PPGLDPHWHUDQG LQVSXUJHDUKHDGV
1RWVXLWDEOHIRUURWDWLQJORDG
1RWVXLWDEOHIRUYDFXXP
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1RWVXLWDEOHIRUORZWHPSHUDWXUHV
&
7\SLFDOLQ'&PRWRUVDERYHPP
GLDPHWHUDQGLQSODQHWDU\JHDUKHDGV 3UHORDGHGEDOOEHDULQJVRIIHUDYHU\
ORQJOLIHDQGVPRRWKRSHUDWLRQ
7\SLFDOLQEUXVKOHVV'&PRWRUV
Bearing
play
$[LDOW\SLFDOO\PP
5DGLDOW\SLFDOO\PP
$[LDOW\SLFDOO\PP
QRD[LDOSOD\LISUHORDGHG
5DGLDOW\SLFDOO\PP
&RHIFLHQW
of friction
K\GURG\QDPLFOXEULFDWLRQ
Lubrica-
tion
+\GURG\QDPLFOXEULFDWLRQRQO\DW
KLJKVSHHGV
6KDIWEHDULQJPDWHULDOYHU\LPSRUWDQW
SRUHVL]HRIWKHVLQWHUHGEHDULQJDQG
YLVFRVLW\RIWKHOXEULFDQWDWRSHUDWLQJ
WHPSHUDWXUHDUHFULWLFDO
6SHFLDO6LQWHUHGLURQEHDULQJVZLWK
FHUDPLFVKDIWIRUKLJKUDGLDOORDGV DQGORQJRSHUDWLQJOLIH
7HPSHUDWXUHUDQJHIRUVWDQGDUG
OXEULFDWLRQW\SLFDOO\&
6SHFLDOOXEULFDWLRQSRVVLEOHIRUYHU\
KLJKRUYHU\ORZRSHUDWLQJWHPSHUDWXUHV
6HDOLQJSRVVLEOHEXWKLJKHUIULFWLRQ
VKRUWHUOLIHDQGORZHUVSHHGOLPLW
Costs (FRQRPLFDO 0RUHH[SHQVLYH
4. Bearing4.1 Comparison of characteristics of sintered sleeve bearings and ball bearings
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5. Electrical principles5.1 Principles of DC (Direct Current)
Electric power
8QLW
[3] 9$9$
:-V
3RZHU
P = U I = R I2 =
R
U2
3RZHUORVV
3V= R I
Power adjustment
$WRL = RiWKHPD[LPXPSRZHULVGUDZQIURPDYROWDJHVRXUFH
1.0
0.8
0.6
0.4
0.2
0.0
0.01 0.1 1 10 100
RL/Ri
P/P
max
I Ri
Linear source Consumer loada
b
U0
Ukl
RL
I
Pmax
=4 Ri
U0
2
4
I2
Ri
=Ohm's law
V RU
A+
_
I 85,
I =R
U
R =I
U
Symbol Name SI
I &XUUHQW $
3 3RZHU :3max 0D[LPXPSRZHU :
3V 3RZHUORVVHV :
R (OHFWULFDOUHVLVWDQFH
Symbol Name SI
Ri ,QQHUUHVLVWDQFHYROWDJHVRXUFH
RL /RDGUHVLVWDQFH 8 9ROWDJH 9
80 6RXUFHYROWDJH 9
8kl 7HUPLQDOYROWDJH 9
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Electrical time constant
100
%
60
40
20
00
el2
el4
el3
el5
el
Uin
Uout
t
63%
7KHHOHFWULFDOWLPHFRQVWDQW
GHVFULEHVWKHUHDFWLRQWLPHRIWKHFXUUHQWZKHQVZLWFKLQJ
RQRURIIDYROWDJH
[el])$V9V
[el]+9V$V
&XUUHQWFKDQJHZLWK
LQGXFWLYHORDG
el=R
L
9ROWDJHFKDQJHZLWK
FDSDFLWLYHORDG
el= R C
Pull-up / pull-down
+V
Ru
Logic
Pull-up
Pull-up:UHODWLYHO\KLJKLPSHGDQFHUHVLVWRU &RQQHFWVVLJQDOOLQHZLWKKLJKHUYROWDJHSRWHQWLDO
3XOOVWKHOLQHXSWRWKHKLJKHUSRWHQWLDOLIQRH[WHUQDO
YROWDJHDFWLYHO\SXOOVWKHOLQHWRDORZHUSRWHQWLDO
Logic
Rd
Pull-down
Pull-down:UHODWLYHO\KLJKLPSHGDQFHUHVLVWRU
&RQQHFWVVLJQDOOLQHZLWKORZHUYROWDJHSRWHQWLDO
3XOOVWKHOLQHGRZQWRWKHORZHUSRWHQWLDOLIQRH[WHUQDO
YROWDJHDFWLYHO\SXOOVWKHOLQHWRDKLJKHUSRWHQWLDO
Open-collector output
Logic
Collector
Emitter
Base
Ru
+V
Open
Collector
Output
Iout
Uout
Open-collector output (OC):
2XWSXWRIDQLQWHJUDWHGFLUFXLWZLWKDELSRODUWUDQVLVWRU
ZLWKDQRSHQFROOHFWRURXWSXW
8VXDOO\WKHRXWSXWVDUHXVHGLQFRPELQDWLRQZLWK
DSXOOXSUHVLVWRUZKLFKUDLVHVWKHRXWSXWYROWDJHWRD
KLJKHUSRWHQWLDOLQWKHLQDFWLYHVWDWH
8out9 Iout Ru
Hall sensorsXVXDOO\KDYHDQRSHQFROOHFWRURXWSXW
ZLWKRXWSXOOXSUHVLVWRU7KHUHIRUHLWLVLQWHJUDWHGLQWRWKH
PD[RQFRQWUROOHUV
Symbol Name SI
& &DSDFLWDQFH )
Iout 2XWSXWFXUUHQW $
L ,QGXFWDQFH +R (OHFWULFDOUHVLVWDQFH
Rd 3XOOGRZQUHVLVWDQFH
Ru 3XOOXSUHVLVWDQFH
Symbol Name SI
t 7LPH V
8in ,QSXWYROWDJH 9
8out 2XWSXWYROWDJH 9+V 6XSSO\YROWDJH 9
el (OHFWULFDOWLPHFRQVWDQW V
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Series resistor circuits
R2
U
+
I
U1
U2
R1
,FRQVWDQW
888 +...
R = R + R + ...
=U
2
U1
R2
R1
Parallel resistor circuits
R2
U
+
I
I1
I2
R1
8FRQVWDQW
I = I + I +...
R
1=
R1
1+
R2
1+ ...
R1+R
2
R1 R
2
R =
=I2
I1
R1
R2
5.2 Electrical resistive circuits
Symbol Name SI
I 7RWDOFXUUHQW $
I, I 3DUWLDOFXUUHQWV $
R (TXLYDOHQWUHVLVWDQFH
Symbol Name SI
R, R 3DUWLDOUHVLVWDQFHV
8 7RWDOYROWDJH 9
88 3DUWLDOYROWDJHV 9
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Voltage divider, no-load
R2
U
+
I
U2
R1
U1
R1+R
2
R2
U2 = U
=U
2
U1
R2
R1
R2
U2
I =R
1+R
2
U
=
Voltage divider, under load
R2
U
+
I
IR2
R1
UL
RL
IL
Rx
R1
+
Rx
UL = URx+R
1
RL
R2
Rx
=R
L+R
2
R2
IL
= I R
L+R
2
RL
IR2
= I R
L+R
2
Potentiometer
0
U
+
A
RL
1
UL
R0
S
E
x
A: Start
S: Wiper
E: End
x R0
RL
R =(x R
0) + R
L
1RORDGR
UL
= UR + (1 x) R
0
8QGHUORDG
xU
L= U
RL
R0
(x
x2
) +1
Winding resistance
7HPSHUDWXUHGHSHQGDQFH RT= Rmot &X7
Symbol Name SI
I 7RWDOFXUUHQW $
IL /RDGFXUUHQW $
IR &XUUHQWWKURXJKUHVLVWRU5 $
R (TXLYDOHQWUHVLVWDQFH
R 5HVLVWDQFHSRWHQWLRPHWHU
R, R 3DUWLDOUHVLVWDQFHV RL /RDGUHVLVWDQFH
Rmot 7HUPLQDOUHVLVWDQFHPRWRUFDWDORJYDOXH
R[ (TXLYDOHQWUHVLVWDQFHRIRDQGRL
Symbol Name SI
RT 5HVLVWDQFHDWWHPSHUDWXUHT
8 7RWDOYROWDJH 9
88 3DUWLDOYROWDJHV 9
8L /RDGYROWDJH 9
7 7HPSHUDWXUHGLIIHUHQFH .
x 3RWHQWLRPHWHUSRVLWLRQ
Symbol Name Value
&X 5HVLVWDQFHFRHIFLHQWFRSSHU .
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Alternating quantities
t
T
[f] = V+]
[] = / s =
rad / s
f =T1
I
Ohm's law
V ZU
A~
~
I8t=,t
I(t) =Z
U(t)
Z =I(t)U(t)
Resistances
Reactance
~
XL
,QGXFWLYH XL/I/
~
XC
&DSDFLWLYH XC=
&1
2I&1
=
Impedance (AC resistance)
)RUVHULHVFRQQHFWLRQRIRDQGL, orRDQG& R2 + X2Z =
5.3 Principles of AC (Alternating Current)
Symbol Name SI
& &DSDFLWDQFH )
I &XUUHQW $
L ,QGXFWDQFH +
R (OHFWULFDOUHVLVWDQFH
T 3HULRG V
8 9ROWDJH 9
Symbol Name SI
X 6WDQGVIRUX& orXL
X& 5HDFWDQFHFDSDFLWLYH
XL 5HDFWDQFHLQGXFWLYH
Z ,PSHGDQFH
f )UHTXHQF\ +]
t 7LPH V $QJXODUIUHTXHQF\ UDGV
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General
&XWRIIIUHTXHQF\ f&
fC
=2 R C
1
orf
C
=2 L
R
3KDVHVKLIWU
in
Uout
FRV
/RZSDVVOWHUVLQWHJUDOHOHPHQW
$OORZIUHTXHQFLHVWRSDVVYLUWXDOO\XQDIIHFWHGEHORZWKHLUFXWRIIIUHTXHQF\f&
+LJKHUIUHTXHQFLHVDUHGDPSHQHG
$SSOLFDWLRQVPD[RQFRQWUROOHULQSXWVFRPPXWDWLRQVLJQDOPHDVXUHPHQWRIPD[RQPRWRUV
R
Uin
C Uout
L
Uin
R Uout
URI
Uout
Uin
Uout
I
UL
Uin
1.0
Uin
Uout
0.707
90
f = fC
45
0
0.1
f/fC
100.2 0.5 1 2 5
0.1
0.5
0.2
Uin
Uout
1 + ( f / fC)2
= 1
Uout
= Uin
R2 +X
c
2
Xc
Uout
= Uin
R2 +XL
2
R
6LPSOHOWHUV
Symbol Name SI
& &DSDFLWDQFH )
I &XUUHQW $
L ,QGXFWDQFH +
R (OHFWULFDOUHVLVWDQFH 8& 9ROWDJHRYHUFDSDFLWDQFH 9
8in ,QSXWYROWDJH 9
8L 9ROWDJHRYHULQGXFWDQFH 9
Symbol Name SI
8out 2XWSXWYROWDJH 9
8R 9ROWDJHRYHUUHVLVWDQFH 9
X& 5HDFWDQFHFDSDFLWLYH
XL 5HDFWDQFHLQGXFWLYH f )UHTXHQF\ +]
f& &XWRIIIUHTXHQF\ +]
3KDVHVKLIW
+LJKSDVVOWHUGHULYDWLYHHOHPHQW
$OORZIUHTXHQFLHVWRSDVVYLUWXDOO\XQDIIHFWHGDERYHWKHLUFXWRIIIUHTXHQF\f&
/RZHUIUHTXHQFLHVDUHGDPSHQHG
R
Uin
L Uout
Uout
I
UC
Uin
UR
I
Uout
Uin
C
Uin
R Uout
0.707
f = fC
1.0
Uin
Uout
90
45
0
0.1
f/fC
100.2 0.5 1 2 5
0.1
0.5
0.2
Uin
Uout
1 + ( fC
/ f)2
=1
Uout= UinR2 +X
C
2
R
Uout
= Uin
R2 +XL
2
XL
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6. maxon motors6.1 General
What is special about maxon motors?
7KHheartRIWKHPD[RQPRWRULVWKHself-supporting ironless copper winding
2XWVWDQGLQJIHDWXUHVRIWKHPD[RQ'&PRWRUV
+LJKHIFLHQF\/RZSRZHUFRQVXPSWLRQ
9HU\ORZPRPHQWRILQHUWLD+LJKHVWDFFHOHUDWLRQ
/RZLQGXFWDQFH/RQJVHUYLFHOLIH
/LQHDUFKDUDFWHULVWLFV*RRGFRQWUROODELOLW\
&RPSDFWGHVLJQ*RRGYROXPHSRZHUUDWLR
1RPDJQHWLFFRJJLQJ
/RZHOHFWURPDJQHWLFLQWHUIHUHQFH
+LJKUHOLDELOLW\
maxon DC motor (brushed permanent-magnet energized DC motors)
RE program
+LJKSRZHUGHQVLW\
+LJKTXDOLW\'&PRWRUZLWK1G)H%PDJQHW
+LJKVSHHGVDQGWRUTXHV
5REXVWGHVLJQPHWDODQJH
PP
A-max program
*RRGSULFHSHUIRUPDQFHUDWLR
'&PRWRUZLWK$O1L&RPDJQHW $XWRPDWHGPDQXIDFWXULQJSURFHVV
PP
RE-max program
+LJKSHUIRUPDQFHDWORZFRVWV
&RPELQHVUDWLRQDOPDQXIDFWXULQJDQG
GHVLJQRIWKH$PD[PRWRUVZLWKWKHKLJKHU
SRZHUGHQVLW\RIWKH1G)H%PDJQHWV
$XWRPDWHGPDQXIDFWXULQJSURFHVV
PP
Properties of the two brush systemsGraphite brushes
:HOOVXLWHGIRUKLJK
FXUUHQWVDQGSHDNFXUUHQWV
:HOOVXLWHGIRUVWDUWVWRSDQG
UHYHUVHRSHUDWLRQ
/DUJHUPRWRUVIURPDSSUR[:
+LJKHUIULFWLRQKLJKHUQRORDGFXUUHQW
1RWVXLWHGIRUORZFXUUHQWV
+LJKHUDXGLEOHQRLVH +LJKHUHOHFWURPDJQHWLFHPLVVLRQV
0RUHFRPSOH[DQGKLJKHUFRVWV
Precious metal brushes
:HOOVXLWHGIRUORZHVW
FXUUHQWVDQGYROWDJHV
:HOOVXLWHGIRUFRQWLQXRXVRSHUDWLRQ
6PDOOHUPRWRUV
9HU\ORZIULFWLRQORZDXGLEOHQRLVH
/RZHOHFWURPDJQHWLFHPLVVLRQV
&RVWHIIHFWLYH
1RWVXLWHGIRUKLJKFXUUHQWVDQG SHDNFXUUHQWV
1RWVXLWHGIRUVWDUWVWRSRSHUDWLRQ
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maxon EC motor
%UXVKOHVV'&PRWRUV%/'&PRWRUV
0RWRUEHKDYLRUVLPLODUWREUXVKHG'&PRWRU 'HVLJQVLPLODUWRV\QFKURQRXVPRWRUSKDVHVWDWRUZLQGLQJURWDWLQJSHUPDQHQWPDJQHW
3RZHULQJRIWKHSKDVHVDFFRUGLQJWRWKHURWRUSRVLWLRQE\DFRPPXWDWLRQHOHFWURQLFV
maxon EC range
3RZHURSWLPL]HGZLWKKLJKVSHHGV
XSWRUSP
5REXVWGHVLJQ
9DULRXVW\SHVHJVKRUWORQJVWHULOL]DEOH
/RZHVWUHVLGXDOLPEDODQFH
PP
EC-max range
$WWUDFWLYHSULFHSHUIRUPDQFHUDWLR
5REXVWVWHHOKRXVLQJ
6SHHGVXSWRUSP
5RWRUZLWKRQHSROHSDLU
PP
EC-4pole range
+LJKHVWSRZHUGHQVLW\WKDQNVWRSROHURWRU
.QLWWHGZLQGLQJV\VWHPPD[RQ ZLWKRSWLPL
]HGLQWHUFRQQHFWLRQRIWKHSDUWLDOZLQGLQJV 6SHHGVXSWRUSP
+LJKTXDOLW\PDJQHWLFUHWXUQPDWHULDOWR
UHGXFHHGG\FXUUHQWORVVHV
0HFKDQLFDOWLPHFRQVWDQWVEHORZ
PLOOLVHFRQGV
PP
PD[RQ(&DWPRWRU
$WWUDFWLYHSULFHSHUIRUPDQFHUDWLR
+LJKWRUTXHVGXHWRH[WHUQDO
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([FHOOHQW KHDWGLVVLSDWLRQ DW KLJKHU VSHHGV
UHVXOWLQJIURPWKHWRRSHQGHVLJQ
6SHHGVRIXSWRUSP
PP
maxon EC-i range
+LJKO\G\QDPLFGXHWRLQWHUQDO
PXOWLSROHURWRU
0HFKDQLFDOWLPHFRQVWDQWV
EHORZPLOOLVHFRQGV
6SHHGVRIXSWRUSP
PP
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Electronic commutation
Commutation type Rotor position determination
Block commutation ZLWK+DOOVHQVRUV VHQVRUOHVV
Turning angle
Block-shaped phase currents
0 36060120180 240300+
+
+
U
U
U
1-2
2-3
3-1
1
0
1
0
10
60 120 180 240 300 3600
Signal sequence diagram
for the Hall sensors (HS)
Supplied motor voltage
(phase to phase)
HS 1
HS 2
HS 3
0 60 120 180 240 300 360
EMF
EMF
Legend
Star point
Time delay 30
Zero crossing of EMF
Sinusoidal commutation :LWKHQFRGHUDQG+DOOVHQVRUV+6
0 36060 120 180 240 300
Turning angle
Sinusoidal phase currents
EC motor with HS Encoder
Comparison of DC and EC motors
DC motor (brushed)
6LPSOHRSHUDWLRQDQGFRQWURO
HYHQZLWKRXWHOHFWURQLFV
1RHOHFWURQLFSDUWVLQWKHPRWRU
2SHUDWLQJOLIHOLPLWHGE\EUXVKV\VWHP
0D[VSHHGVOLPLWHGE\EUXVKV\VWHP
EC motor (brushless)
/RQJRSHUDWLQJOLIHDQGKLJKVSHHGVZLWK
SUHORDGHGEDOOEHDULQJV
1RFRPPXWDWRUDUFLQJ
,URQORVVHVLQWKHPDJQHWLFUHWXUQ
1HHGVHOHFWURQLFVIRURSHUDWLRQ PRUHFDEOHVDQGKLJKHUFRVWV
(OHFWURQLFSDUWVLQWKHPRWRU+DOOVHQVRUV
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6.2 Power consideration of the DC motor: in general
Motor as energy converter
PJ= Rmot,mot2
PL
= n M30
Pel= U
mot,
mot
3RZHUEDODQFHPRWRU
3el3L3-
30
U
mot I
mot= n M + R
mot I
mot
2
Umot
> UN
Umot
= UN
Torque M
n0
MH
PL
PL
Power P
Speed n,QWKHVSHHGWRUTXHGLDJUDPWKHRXWSXWSRZHU
LVHTXLYDOHQWWRWKHDUHDRIWKHUHFWDQJOHEHORZ
WKHVSHHGWRUTXHOLQH7KLVUHFWDQJOHLVODUJHVWDWKDOIWKHVWDOOWRUTXHDQGKDOIWKHQRORDG
VSHHG
7KHSRZHUFXUYHLVDSDUDERODZKRVH
PD[LPXPYDOXHLVSURSRUWLRQDOWRWKHVTXDUH
RIWKHPRWRUYROWDJH
Symbol Name SI
Imot 0RWRUFXUUHQW $
0 7RUTXH 1P
0H 6WDOOWRUTXH 1P
3 3RZHU :
3el (OHFWULFDOLQSXWSRZHU :
3- -RXOHSRZHUORVV :3L 0HFKDQLFDORXWSXWSRZHU :
Rmot 7HUPLQDOUHVLVWDQFHPRWRU
FDWDORJYDOXH
Symbol Name SI
8mot 0RWRUYROWDJH 9
8N 1RPLQDOYROWDJHPRWRU
FDWDORJYDOXH 9
Symbol Name maxon
n 6SHHGRIURWDWLRQ USPn 1RORDGVSHHG USP
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6.3 Motor constants and diagrams
Motor constants
7KHspeed constant knDQGWKHtorque constant kMDUHWZRLPSRUWDQWFKDUDFWHULVWLFYDOXHVIRU
WKHHQHUJ\FRQYHUVLRQ
Speed constant kn7KHVSHHGFRQVWDQWknFRPELQHVWKHVSHHGn ZLWKWKHYROWDJH
LQGXFHGLQWKHZLQGLQJ8ind(0)
n = kn8ind
Torque constant kM7KHWRUTXHFRQVWDQWk0OLQNVWKHSURGXFHGWRUTXH0ZLWKWKH
HOHFWULFDOFXUUHQW I.
Information:PD[RQXQLWP1P$
0N0,mot
Dependence between kn and kMPD[RQXQLWV
30 000k
n k
M=
Vrpm
AmNm
[ ]
s Vrad
= 1A
Nm
Speed-torque line
'HVFULEHVWKHPRWRUEHKDYLRULHSRVVLEOHRSHUDWLQJSRLQWV
Q0DWDFRQVWDQWYROWDJH8mot
Umot>U
N
Torque M
n0
MH
nUmot=U
N
Speed n
M
MR
I0
IA
Motor current Imot
nNn8mot
0H= k0,$
0R = k0,
0
QQN
Q8
mot0
PD[RQXQLWV
6SHHGWRUTXHJUDGLHQW
M
n
30 000=
kM
2
Rmot
MH
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Symbol Name SI
Imot 0RWRUFXUUHQW $
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Symbol Name SI
8mot 0RWRUYROWDJH 9
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Symbol Name maxon
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Voltage equation, motor
Imot
+
Umot
Uind
Lmot
Rmot
EMF
W
LU
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Kmax
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Efficiency K
Speed n
MH
30 000
Umot,
mot
Q(005
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M,
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max
=IA
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1
2
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(0) (OHFWURPRWLYHIRUFH 9
I 1RORDGFXUUHQW $
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Imot 0RWRUFXUUHQW $
k0 7RUTXHFRQVWDQWFDWDORJYDOXH 1P$
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Symbol Name SI
8mot 0RWRUYROWDJH 9
L &XUUHQWFKDQJH $
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Angular acceleration: Start with constant current
ML, n
L
n0
n0
nL
MH
t Time t
lmot
= constant
Torque M
Speed n
Speed n
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JR-
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Angular acceleration: Start with constant terminal voltage
nL
ML, n
Ln
0
MH
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tm
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= constant
Time t
Torque M
Speed n
Speed n
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m
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8mot 0RWRUYROWDJH 9
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Symbol Name maxon
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6.4 Acceleration
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Motor type selection
Speed n
Short-term operation
Max. permissible speed
Continuous
operation
MRMS
Torque MM
maxM
NM
H
0RWRUW\SHVHOHFWLRQ
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Winding selection
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Speed-torque line
high enough for all
operating points
n0,theor
Safety
factor
~ 20%n
max
Deceleration Acceleration
Mmax
Speed n
Torque M
knVSHFLHVWKHZLQGLQJ
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5HTXLUHGPD[LPXPPRWRUFXUUHQW Imot
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M
Mmax
6.5 Motor selection
Symbol Name SI
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7. maxon sensor
maxon incremental encoder
360e 90e
Channel A
Channel B
Signal edges (quadcounts)
Index channel I
Recommended applications QUAD MEnc MR EASY MILE Optical
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Counts per turn from position resolution
5HTXLUHGFRXQWVSHUWXUQNof the
HQFRGHUIRUDVSHFLHGSRVLWLRQLQJDFFXUDF\RI
1 L360
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Measurement resolution, motor speed
Example:
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Q =Q N
4
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8. maxon controller8.1 Operating quadrants
Operating quadrants
n
M
n
M
n
M
n
M
n
M
Quadrant II
Braking operationClockwise (cw)
Quadrant IIIMotor operation
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(ccw)
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Quadrant I
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1-Q operation
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8.2 Selection of power supply
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VCC
0
QQ
L0
L+ 8
max (maxon units)
Q0,81
81
Notes:
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Achievable speed at given voltage supply
nL(V
CCU
max) (maxon units)
0
Q0
LUN
n0,UN
Symbol Name SI
0 7RUTXH 1P
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8.3 Size of the motor choke with PWM controllers
Calculation of current ripple
PWM scheme 1-Q 2-level (4-Q) 3-level (4-Q)
0D[LPXP
FXUUHQWULSSOH
SHDNWRSHDN,
PP,max=
4 Ltot
f
PWM
VCC
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tot f
PWM
VCC
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tot f
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VCC
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RIWKHFDWDORJYDOXHLmot.
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Calculation, additional external motor choke
PWM scheme 1-Q and 3-level (4-Q) 2-level (4-Q)
5XOHRIWKXPE Lext
=6 I
N f
PWM
VCC L
int0.3 L
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PWM
PWM
EC
motorLmot
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1/2Lint
1/2Lint
1/2Lint
1/2Lext
1/2Lext
EC amplifier
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9. Thermal behavior9.1 Basics
Heat sources
Iron losses in EC
motors and motorswith iron core winding
5HPDJQHWL]DWLRQORVVHV
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magn
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Joule power losses
in windingTemperature T
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25C TW
Rmot
RTW 3- = R7: Imot
R7: = Rmot >&X T: &@
Friction losses: in the bearings and in the brushes (brushed DC motors)
Losses in the
gearhead40%
60%
80%
100%
MG, cont
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5-stage
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30
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30
P
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L M
L
G
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Analogy to electrical circuit:
Power loss PV
Thermal Electrical Current I
Rth1
Rth2
TW
TW
TS
TS
TA
U1
U2
Cth,W
R1
R2
C1
C2
GND
Cth,s
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Symbol Name Unit
4 6WRUHGKHDW -
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8 9ROWDJHSRWHQWLDOGLIIHUHQFH V
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R (OHFWULFDOUHVLVWDQFH
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& (OHFWULFDOFDSDFLWDQFH F
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Heating of a simple body Cooling of a simple body
Tstart
Tend
Tmax = 100%
th
Time t
Temperature T
Heating
63%
Tend
Tstart
Tmax = 100%
th Time t
Temperature T
Cooling63%
th
t
7W =7end
1[ ]
th
t
7W =7start
Symbol Name SI
T 7HPSHUDWXUH &
T$ $PELHQW7HPSHUDWXUH &
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T6 6WDWRUWHPSHUDWXUH &
T: :LQGLQJWHPSHUDWXUH &
Symbol Name SI
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Motor: Winding and stator temperature
Temperature T140
1 10 100 1000 10000
Stator
Temperature
difference
Winding
TW,
TS,
Rth1
Rth2
TW
TS
TA
Time t
0
120
100
80
40
20
60
Heating of the winding in accordancewith the thermal time constant
of the winding W
Heating of the stator in accordancewith the thermal time constant
of the stator s
Thermal equilibriumafter several stator time
constants
7: = T:7$ = Rth + Rth3-
Rth1
RTA
Imot
2
7W
=1
Cu R
th1 R
TA I
mot
2
Rth2
7S
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+ Rth2
7W
Gearhead: Housing temperature
PV, G
TG
Rth,G
TG
TA
PV, G
7* = T*7$ = RWK*39*
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9.2 Continuous operation
Symbol Name SI
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T* *HDUKHDGWHPSHUDWXUH &
T6 6WDWRUWHPSHUDWXUH &
Symbol Name SI
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T: :LQGLQJWHPSHUDWXUH &
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t 7LPH V
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Symbol Name Value
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Permissible nominal currentIN
IN
MN
nN
Speed n
Torque M
Motor current Imot
Continuous
operation
Short-term
operation
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