maxon formelsammlung e

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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

HQYLURQPHQW7KHREMHFWLYHLVWRREWDLQDQ overviewRIWKHV\VWHPWRGHWHUPLQHWKHWKHRUHWLFDO

IHDVLELOLW\RIDVROXWLRQDQGWRJHWDSLFWXUHRIWKHERXQGDU\FRQGLWLRQVDQGUHVWULFWLRQV See chapterA.1: Overview, system analysis

7KHJRDORI0RWLRQRIWKHORDGLVWRGHQHWKHNH\UHTLUHPHQWVUHJDUGLQJIRUFHVWRUTXHVDQG

YHORFLWLHV VSHHGV RIURWDWLRQ+RZ ORQJ PXVW WKH\ EHDSSOLHG" :KDW LVWKH UHTXLUHGFRQWURO

DFFXUDF\"See chapter A.2: Motion of the load

7KHPHFKDQLFDOGULYHGHVLJQFDQEHVNLSSHGLIWKHORDGLVGULYHQGLUHFWO\DQGWKHGULYHV\VWHPGRHV

QRWLQFOXGHDmechanical transformation.

Mechanical drivesWUDQVIRUPPHFKDQLFDOSRZHULQWRPHFKDQLFDOSRZHU)RUWKHVHOHFWLRQRIWKH

GULYHWKHORDGNH\GDWDDUHFRQYHUWHGWRWKHRXWSXWRI WKHPRWRURU JHDUVKDIWSee chapter A.3:

Mechanical drives.

7KHVWHSIRUWKHgearhead selectionFDQEHVNLSSHGLIQRPD[RQJHDUKHDGLVXVHG*HDUKHDGVDUH

W\SLFDOO\XVHGZKHQHYHUKLJKWRUTXHVDUHUHTXLUHGDWORZVSHHGV

7KHSXUSRVHRIWKLVVWHSLVWRGHWHUPLQHLIDQGZKLFKmaxon gearheadFDQEHXVHG7KHNH\GDWD

IRUWKHPRWRUVHOHFWLRQFDQWKHQEHFDOFXODWHGIURPWKHJHDUKHDGUHGXFWLRQDQGHIFLHQF\See

chapter 3.4: maxon gearhead

2QWKH EDVLV RI WKHWRUTXHDQG VSHHGUHTXLUHPHQWV WKHQH[WVWHS LVWR VHOHFW VXLWDEOHtypes of

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


3/60


4/60

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

SURIHVVLRQDOOD\RXW DQGLOOXVWUDWLRQVZHUHGRQH E\3DWULFLD*DEULHODQG%HQL$QGHUKDOGHQ8UV

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have read the manuscript and have given valuable suggestions for improvements. I also received

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DJHQWVPD\QRWEHKHOGOLDEOHIRUERGLO\LQMXU\RUSHFXQLDU\RUSURSHUW\GDPDJH


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Content 5

A. Drive selection 6

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1. Mass, force, torque 9 )RUFHVLQJHQHUDO

7RUTXHVLQJHQHUDO

0RPHQWVRILQHUWLDRIYDULRXVERGLHVZLWKUHIHUHQFH

WRWKHSULQFLSDOD[HVWKURXJKWKHFHQWHURIJUDYLW\6

2. Kinematics

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3. Mechanical drives 0HFKDQLFDOWUDQVIRUPDWLRQ

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7UDQVIRUPDWLRQRIPHFKDQLFDOGULYHVURWDWLRQ

PD[RQJHDU

4. Bearing

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5. Electrical principles

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6LPSOHOWHUV

6. maxon motors

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7. maxon sensor

8. maxon controller

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6HOHFWLRQRISRZHUVXSSO\

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9. Thermal behavior

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6KRUWWHUPRSHUDWLRQ

10. Tables PD[RQ&RQYHUVLRQ7DEOHV

7\SLFDOFRHIFLHQWVRIIULFWLRQIRUUROOLQJVWDWLFDQGNLQHWLFIULFWLRQ

11. Symbol list for the Formulae Handbook 56


6/60

PD[RQ)RUPXODH+DQGERRN

A. Drive selectionA.1 Overview, system analysis

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Mechanical design

JS

p

mR

d1

J2

d2

J1

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Set value

Actuator

Output

SensorFeedback

Measurement

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Verify the power components

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Determine the boundary conditions

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d

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Cost considerations

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7/60



A.2 Motion of the load

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EHH[SHFWHG

Operating points

123

4

1 32 4 1

Time t

Velocity v

Speed n

Force F, torque M

Velocity v

Speed n

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pointsYDOXHSDLUVRIWRUTXHDQGVSHHGRI

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Mechanical play of the drive

-1500 -500-1000

-0.2

-0.4

0.2

0.4

0 500 15001000

0

Test torque mNm

Twisting angle

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Key data

Force F

Torque M

Fmax

/Mmax

FRMS

/MRMS

tmax

ttot

Time t

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QDOO\EHFDOFXODWHGIURPWKHRSHUDWLQJSRLQWV

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8/60


7KHcontroller and sensorYHULFDWLRQLQYROYHVFKHFNLQJZKHWKHUWKHSUHVHOHFWLRQPDGHGXULQJ

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Motion controller

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Sensor

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9/60


1. Mass, force, torque1.1 Forces in general

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Typical component forces in a drive system

Fa

m

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[F] = kg m/s = kgm/s = N

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= m a = m t

v

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F* = m g

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FR

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Symbol Name SI

$ &URVVVHFWLRQ P

F )RUFH 1

Fa $FFHOHUDWLRQIRUFH 1

F* :HLJKWRIDERG\ 1

FH 'RZQKLOOVORSHIRUFH 1

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FR )ULFWLRQIRUFH 1

F6 6SULQJIRUFH 1

Symbol Name SI

a $FFHOHUDWLRQ PV

g *UDYLWDWLRQDODFFHOHUDWLRQ PV

k 6SULQJFRQVWDQW 1P

m 0DVV NJ

p 3UHVVXUH3DN/mbar 3D

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10/60


Calculating the total load force consisting of component forces

F1

F2

Fx

FL

$GGLWLRQRIIRUFHVDFWLQJLQWKHVDPHGLUHFWLRQ FL = F + F + ...+ F

F1

F2

Fx

FL

$GGLWLRQRIIRUFHVDFWLQJLQRSSRVLWH

GLUHFWLRQVFL = F))

F1

F2

FL

$GGLWLRQRISHUSHQGLFXODUIRUFHV F1

+ F2

2

FL

=2

Symbol Name SI

FL /RDGIRUFHRXWSXW 1

F / F / Fx 3DUWLDOIRUFHV 1


11/60


1.2 Torques in general

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r

M 7RUTXHIRUFH[OHYHUDUP

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Typical component torques in drive systems

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Calculating the load torque consisting of component torques

M1

M2

Mx

ML

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VDPHGLUHFWLRQ0L000

M1

M2

Mx

ML

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RSSRVLWHGLUHFWLRQV0L000

Symbol Name SI

F )RUFH 1

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- 0RPHQWRILQHUWLD NJP

0 7RUTXH 1P

0L /RDGWRUTXH 1P

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06 7RUTXHVSLUDOVSULQJ 1P0 7RUTXHIRUDFFHOHUDWLRQ 1P

000x 3DUWLDOWRUTXHV 1P

km 7RUVLRQFRHIFLHQWVSULQJFRQVWDQW 1P

Symbol Name SI

r 5DGLXV P

r./ 0HDQGLDPHWHUEHDULQJ P

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W 'XUDWLRQ V

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$QJXODUYHORFLW\FKDQJH UDGV

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Symbol Name maxon

Q 6SHHGFKDQJH USP


12/60


Body type Illustration Mass, moments of inertia

Circular cylinder, disc 21

121

Pr2K

Jx= Pr2

Jy=J

z= P(3r2+ K2)

Hollow cylinder

P(ra

2Ui

2) K

JxP(r

a

2 + ri

2)

Jy

= Jz

=K2

21

41

3PU

a

2 + ri

2 +

Circular cone

m =

Jx=

Jy=J

z= P(4r

2 + h2)

31

103

803

Pr2

r2 K

Truncated circular cone

10

3

P(r22 + r

2r1+ r

12) K

31

JxP

r25r

15

r23

r13

Circular torus

41

m = 22r2 5

Jx

=Jy

=81P(452 + 5r2)

Jz

= P(452 + 3r2)

Sphere3

4

52

m = r3

Jx

= Jy

= Jz

= Pr2

1.3 Moments of inertia of various bodies with reference

to the principal axes through the center of gravity S

Symbol Name SI

-x 0RPHQWRILQHUWLD

ZLWKUHIHUHQFHWRWKHURWDWLRQD[LVx NJP

-y 0RPHQWRILQHUWLD

ZLWKUHIHUHQFHWRWKHURWDWLRQD[LVy NJP

-] 0RPHQWRILQHUWLD

ZLWKUHIHUHQFHWRWKHURWDWLRQD[LV] NJP

R 5DGLXVFLUFXODUWRUXVDURXQG]D[LV P

Symbol Name SI

h +HLJKW P

m 0DVV NJ

r 5DGLXV P

ra 2XWHUUDGLXV P

ri ,QQHUUDGLXV P

r 5DGLXV P

r 5DGLXV P

'HQVLW\ NJP


13/60


Body type Illustration Mass, moments of inertia

Hollow sphere34

52

P(ra3

Ui

3

)

Jx

= Jy

= JzP

ra

5U

i

5

ra

3U

i

3

Cuboid

m =DEF

Jx

=121

P (E2+F2)

Thin rod yym $O

12

1J

x= J

zPO2

Square pyramid

31

201

201

43

PDEK

JxP(D2 + E2)

JyP(E2 + K2)

Arbitrary rotation body

21

m =x1 f2(x) G[

Jx=

x1f4(x) G[

x2

x2

Steiner's theorem

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HQFHWRDSDUDOOHOD[LVRIURWD

tionx DWDGLVWDQFHRIrsWRD[LVs

WKURXJKWKHFHQWHURIJUDYLW\6

Jx= mr

s

2 + Js

Symbol Name SI

$ &URVVVHFWLRQ P

-s 0RPHQWRILQHUWLDZLWKUHIHUHQFH

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-x 0RPHQWRILQHUWLD

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-y 0RPHQWRILQHUWLD

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-] 0RPHQWRILQHUWLD ZLWKUHIHUHQFHWRWKHURWDWLRQD[LV] NJP

a /HQJWKRIVLGHa m

b /HQJWKRIVLGHb m

Symbol Name SI

c /HQJWKRIVLGHc m

h +HLJKW P

l /HQJWK P

m 0DVV NJ

ra 2XWHUUDGLXV P

ri ,QQHUUDGLXV P

rs 'LVWDQFHRID[LVs IURPFHQWHURIJUDYLW\6 m

'HQVLW\ NJP

x 3RLQWRQWKH[D[LV P

x 3RLQWRQWKHxD[LV P


14/60


2. Kinematics2.1 Linear equations of motion

Uniform movement

s

t

v

Velocity v

Time t

9HORFLW\

YVWFRQVWDQW

>Y@PV

v =W

V

VYW

Constant acceleration from a standing start

s

t

v

Velocity v

Time t

$FFHOHUDWLRQ

DYWFRQVWDQW

>D@PV

YDW

VDt22

1

)UHHIDOO

YJW

h = g t22

1

Constant acceleration from initial speed

s

t

Velocity v

Time t

vstart

vend

vend = vstart+ a W

VYVWDUW

WDW22

1

Symbol Name SI

a $FFHOHUDWLRQ PV

g *UDYLWDWLRQDODFFHOHUDWLRQ PV

h 'URSKHLJKW P

V 'LVWDQFH P

Symbol Name SI

WW 7LPHGXUDWLRQ V

YY 9HORFLW\YHORFLW\FKDQJH PV

vend 9HORFLW\DIWHUDFFHOHUDWLRQ PV

vstart 9HORFLW\EHIRUHDFFHOHUDWLRQ PV

Remarks:

7KHVKDGHGDUHDVUHSUHVHQWWKHGLVWDQFHVWUDYHOHGGXULQJWLPHSHULRGW


15/60


2.2 Rotary equations of motion

General

1m

1m

1 rad =1m

1m57.2958

1rad

2 rad 360

&RQYHUVLRQ EHWZHHQ UDGLDQ

DQGGHJUHHV7KH XQLW rad LV IUHTXHQWO\

RPLWWHG

1 rad 2

360

UDG

&RQYHUVLRQEHWZHHQ

DQJXODUYHORFLW\DQGVSHHG

of rotation

QQ30

30

Uniform movement

t

,n

Angular velocity,

Speed n

Time t

$QJXODUYHORFLW\

WFRQVWDQW[] = rad/s

t

6SHHGRIURWDWLRQ

n = WFRQVW

[n] = /min USP

Q30

t

Constant acceleration from a standing start

t

Angular velocity,

Speed n

Time t

, n$FFHOHUDWLRQ

WFRQVWDQW

[] = /s = rad/s

t

Qt30

t22

1

Qt2

1

30

Constant acceleration from initial speed

t

end

, nend

start

, nstart

Angular velocity,

Speed n

Time t

end

startt

nend

= nstart

t30

start

Wt221

Qstart

Wnt2

1

30

30

Symbol Name SI

WW 7LPHGXUDWLRQ V


$QJOHRIURWDWLRQ UDG

$QJXODUYHORFLW\FKDQJH UDGV

end $QJXODUYHORFLW\DIWHUDFFHOHUDWLRQ UDGV

Symbol Name SI

start $QJXODUYHORFLW\EHIRUHDFFHOHUDWLRQ UDGV

Symbol Name maxon

QQ 6SHHGRIURWDWLRQFKDQJH USP

nend 6SHHGDIWHUDFFHOHUDWLRQ USP

nstart 6SHHGEHIRUHDFFHOHUDWLRQ USP

Remarks:

7KHVKDGHGDUHDVUHSUHVHQWWKHDQJOHRIURWDWLRQWUDYHOHGGXULQJWLPHSHULRGW

$QJOHRIURWDWLRQ= 1XPEHURIUHYROXWLRQV1XPEHURIUHYROXWLRQV


16/60


3UROH General Symmetrical

Suitability 7UDYHORYHUORQJGLVWDQFHDWOLPLWHGYHORFLW\

Diagram

vmax

ta

s

tb

tc

ttot

s

vmax

ta

tb

ta

ttot

Task:

7UDYHODGLVWDQFHRIV

in time Wtot

vmax

=

2

V

WWRW

WaW

c

amax

=

vmax

Wa

vmax

=(W

WRWW

a)

V

Vamax

=(W

WRWW

a) W

a

7UDYHODGLVWDQFHRIV at a

OLPLWHGYHORFLW\RIvmax

vmax

2

V+

WaW

c

WWRW=

vmax

Waamax

=

vmax

a

max

=

WWRW=

VW

a

vmax

Wa

7UDYHODGLVWDQFHRIV at a

OLPLWHGDFFHOHUDWLRQRIamaxv

max= a

max W

a

WWRW

=V

Waa

max W

a

&RPSOHWHPRWLRQLQWKHWLPH

WtotDWPD[LPXPYHORFLW\vmax

2V

Wa

vmax

vmax

WaW

c

Wb

amax

amax

=

vmax

V(WWRWW

a) v

max

Wa

&RPSOHWHPRWLRQLQWKHWLPHWtotDWPD[LPXPDFFHOHUDWLRQ

amaxv

max= a

max W

a

VDmax

(WWRWW

a) W

a

0RWLRQDWOLPLWHGYHORFLW\vmax

DQGOLPLWHGDFFHOHUDWLRQamax

7\SLFDOOLQHDUPRWLRQSUROHV

Symbol Name SI

amax 0D[LPXPDFFHOHUDWLRQ PVvmax 0D[LPXPYHORFLW\ PV

V 'LVWDQFH P

Symbol Name SI

Wa 7LPHD VWb 7LPHE V

Wc 7LPHF V

Wtot 7RWDOWLPH V


17/60


3/3 Trapezoidal Triangle

2SWLPL]HGIRUPLQLPXPSRZHU

DWJLYHQVDQGW0RVWDGYDQWDJHRXVIURPDWKHUPDO

SRLQWRIYLHZ

2SWLPL]HGIRUOLPLWHGDFFHOHUDWLRQRUIRUFH

DWJLYHQVDQGW2SWLPL]HGIRUPLQLPXPWLPHUHTXLUHPHQW

DWJLYHQVDQGamax

vmax

s

ttot

s

ttot

vmax

vmax

= 1.5

amax

= 4.5

WWRW

V

W2WRW

V

vmax

= 2

amax

= 4

WWRW

V

W2WRW

V

vmax

amax

= 2 v

2

max

WWRW= 1.5

V

V

vmax

amax

=

v2

max

WWRW= 2

V

V

2

3

2

amax

amax

vmax

=

WWRW=

V V

V amax Va

max

amax

vmax

=

WWRW= 2

V

V amax

3

2 W

WRW v

max

amax

3 vmax

V

WWRW

2

1

amax

= 2vmax

V

WWRW

WWRW v

max

92

3

1vmax

= amax

ttot a

maxt

tot

V amax

t2tot a

maxt2

tot

vmax

= amax

WWRW

V amax

W2WRW

2

1

41

amax

v2

max

WWRW= 3

amax

vmax

V2amax

v2

max

amax

vmax

V

WWRW2

Symbol Name SI

amax 0D[LPXPDFFHOHUDWLRQ PVvmax 0D[LPXPYHORFLW\ PV

Symbol Name SI

V 'LVWDQFH PWtot 7RWDOWLPH V


18/60


3UROH General Symmetrical

Suitability /RQJURWDWLRQDWOLPLWHGVSHHGof rotation

Diagram

nmax

ta

tb

tc

ttot

nmax

ta

tb

ta

ttot

Task:

7UDYHODQDQJOHRI

in time Wtot

2W

WRW

Wa+ W

c

n

max=

30

max

=

2W

WRW

Wa+ W

c

Wa

nmax

=

(WWRWW

a)

30

max

=

(WWRWW

a

) Wa

7UDYHODQDQJOHRI

DWDOLPLWHGVSHHGRInmax

nmax

2W

WRW=

+

30

W

a+ W

c

ta

max

=nmax

30

nmax

+ Wa

WWRW=

30

max

=

nmax

Wa

30

7UDYHODQDQJOHRI at a

OLPLWHGDQJXODUDFFHOHUDWLRQ

ofmax

max W

a

+ Wa

WWRW=

nmax

= max

30

&RPSOHWHPRWLRQLQWKHWLPH

WtotDWPD[LPXPVSHHGnmax

2=

WaW

c+W

b

30 n

PD[

max

= nmax

Wa

30

(WWRWW

a

)30

nmax

max

= nmax

Wa

30

&RPSOHWHPRWLRQLQWKHtimeWtotDWPD[LPXPDQJXODU

DFFHOHUDWLRQmax

max(WWRWWa)Wa

max W

anmax

=30

0RWLRQDWOLPLWHGVSHHG

ofnmaxDQGOLPLWHGDQJXODU

DFFHOHUDWLRQRImax

7\SLFDOURWDU\PRWLRQSUROHV

Symbol Name SI

max 0D[LPXPDQJXODUDFFHOHUDWLRQ UDGV

Wa 7LPHD VWb 7LPHE V

Wc 7LPHF V

Wtot 7RWDOWLPH V

Symbol Name SI

$QJOHRIURWDWLRQ UDG

Symbol Name maxon

nmax 0D[LPXPVSHHGLQORDGF\FOH USP


19/60


3/3 Trapezoidal Triangle

2SWLPL]HGIRUPLQLPXPSRZHU

DWJLYHQDQGW0RVWDGYDQWDJHRXVIURPDWKHUPDO

SRLQWRIYLHZ

2SWLPL]HGIRUOLPLWHGDQJXODUDFFHOHUDWLRQ

RUWRUTXHDWJLYHQDQGWDQGIRUPLQLPXPWLPHUHTXLUHPHQW

DWJLYHQDQGmax

nmax

ttot

ttot

nmax

WWRW

nmax

= 1.5 30

max

= 4.5 t2

tot

ttot

nmax

= 2 30

max

= 4 t2

tot

nmax

WWRW= 1.5

30

max

= 2

n2

max2

302

nmax

WWRW= 2

30

max

=

n2

max

2

302

2

3

max

max

WWRW=

2

1nmax

= max

max

30

max

W

WRW= 2

nmax

= max

30

3

2W

WRW n

max 30

max

= 3 nmax

WWRW

30

2

1= WWRW nmax

30

max= 2

nmax

W

WRW

30

9

2

max t2

tot PD[t2

tot

3

1nmax

= max W

WRW

maxW

WRW30

max t2

tot4

1

nmax

=30

2

1

max W

WRW

ttot

nmax

= 2 30

max

= 4 t2

tot

max

n2

max

=30

max

nmax

WWRW= 2

30

Symbol Name SI


Wtot 7RWDOWLPH V $QJOHRIURWDWLRQ UDG

Symbol Name maxon

nmax 0D[LPXPVSHHGLQORDGF\FOH USP


20/60

Notes


21/60


3. Mechanical drives3.1 Mechanical transformation

Symbol Name SI

F )RUFH 1


0 7RUTXH 1P

0L /RDGWRUTXH 1P

0in ,QSXWWRUTXH 1P

3mech 0HFKDQLFDOSRZHU :3mech,in 0HFKDQLFDOLQSXWSRZHU :

3mech,L 0HFKDQLFDORXWSXWSRZHU :

v 9HORFLW\ PV

Symbol Name SI

vL /RDGYHORFLW\ PV

(IFLHQF\

$QJXODUYHORFLW\ UDGV

L $QJXODUYHORFLW\ORDG UDGV

in $QJXODUYHORFLW\LQSXW UDGV

Symbol Name maxon

n 6SHHGRIURWDWLRQ USP

&ODVVLFDWLRQ Output power/transformation, general

Rack and pinionSpindle

Ball screw

Trapezoidal screw

Conveyor belt

Crane

Eccentric drive

Crankshaft

Linear

Rover

Output power, linear motion

[:]PV1

3mechY)

Transformation, general

Pmech,in

Pmech,L

=

inM

invLF

L=

Special design

Cyclo gear

Harmonic Drive

Gearhead

Spur gearhed

Planetary gearhead

Bevel gear

Worm gear

Wolfrom gear

Belt

Toothed belt

Chain drive

RotationOutput power, rotary motion

[:] = s1P

30

P

mech0Q0

Transformation, general

Pmech,in

Pmech,L

=

inM

inLM

L=

Designations in the formulae

7KHORDGVLGHYDULDEOHVDWWKHRXWSXWDUHLGHQWLHGE\WKHLQGH[L

7KHLQSXWVLGHYDULDEOHVXVXDOO\WKHPRWRUDUHLGHQWLHGE\WKHLQGH[in


22/60


Spindle drive

JS

p

6SHHGRIURWDWLRQp

nin

= vL

60

7RUTXH2

Min

= p

FL

$GGLWLRQDOWRUTXHIRUFRQVWDQWDFFHOHUDWLRQ

VSHHGFKDQJHQinGXULQJSHULRGWa

M

LQ-

in-

S

mLP

S

42p2

30

Wa

Qin

3OD\

SRVLWLRQHUURU2p

inV

L

Belt drive/conveyor belt/crane

mB

J2

d2

d1

J1 6SHHGRIURWDWLRQ

60

d1

vL

nin=

7RUTXHF

L

2 Min =

d1


VSHHGFKDQJHQin GXULQJSHULRGWa

Wa

QLQ

+

304M

LQ= J

LQ+ J

1+

J2

d2

2

mL

+ mB

d1

2d1

2

JX

dX

2

d1

2

+

J1

d1

3OD\

SRVLWLRQHUURU

2

d1

inV

L

Symbol Name SI


-in 0RPHQWRILQHUWLDLQSXW

PRWRUHQFRGHUEUDNH NJP

-6 0RPHQWRILQHUWLDVSLQGOH NJP

-X 0RPHQWRILQHUWLDGHHFWRUSXOOH\X NJP

- 0RPHQWRILQHUWLDGULYLQJHQG NJP

- 0RPHQWRILQHUWLDGHHFWRUSXOOH\ NJP

0in ,QSXWWRUTXH 1P

0LQ 7RUTXHIRUDFFHOHUDWLRQ 1P

dX 'LDPHWHUGHHFWRUSXOOH\X md 'LDPHWHUGULYHSXOOH\ P

d 'LDPHWHUGHHFWRUSXOOH\ P

m% 0DVVEHOW NJ

Symbol Name SI

mL 0DVVRIWKHORDG NJ

m6 0DVVVSLQGOH NJ

p 6SLQGOHOHDGSLWFK P

vL /RDGYHORFLW\ PV

VL 0HFKDQLFDOSOD\RXWSXW P

Wa $FFHOHUDWLRQWLPH V

in 0HFKDQLFDOSOD\LQSXW UDG

(IFLHQF\

Symbol Name maxonnin ,QSXWVSHHG USP

Qin 6SHHGFKDQJHLQSXW USP

3.2 Transformation of mechanical drives, linear


23/60


Rack-and-pinion drive

p

JP, z

mz

6SHHGRIURWDWLRQ nin = pz

vL60

7RUTXH2

Min=p z F

L



Min,

= Jin

+ JP

+p2 z2

Wa

Qin

mL

+ mZ

42 30

3OD\

SRVLWLRQHUURU2

p z

in= V

L

Rover

JW

mF

d

6SHHGRIURWDWLRQ60

nin=

d

vL

7RUTXH Min =F

L

2

d



mL

+ mF

4

Wa

QLQ

MLQ

=d2

30J

LQ+ J

W+

3OD\

SRVLWLRQHUURU

2

d

in= s

L

Symbol Name SI




-3 0RPHQWRILQHUWLDSLQLRQ NJP

-: 0RPHQWRILQHUWLD

DOOZKHHOVWRJHWKHU NJP

0in ,QSXWWRUTXH 1P


d 'LDPHWHUGULYHZKHHO P

mF 0DVVURYHU NJmL 0DVVRIWKHORDG NJ

mZ 0DVVJHDUUDFN NJ

p 3LWFK P

Symbol Name SI

vL /RDGYHORFLW\ PV

] 1XPEHURIWHHWKSLQLRQ

VL 0HFKDQLFDOSOD\RXWSXW P



(IFLHQF\

Symbol Name maxon

nin ,QSXWVSHHG USP



24/60


Eccentric drive

e

JE

6LQXVRLGDOYHORFLW\FXUYHRIWKHORDG

DVVXPSWLRQFRQVWDQWPRWRUVSHHGnin

vL

(t) = nin

e sin nin

t30 30

$QJOHGHSHQGHQWSHULRGLFDFFHOHUDWLRQIRUFHIRUORDG

SLVWRQVDQGURGVmL

30nin

2

e cos

Fa)

aFRVP

L

$QJOHGHSHQGHQWWRUTXHVGXHWRGLIIHUHQWORDGFRQGLWLRQV

0inH)LVLQ)aFRV

0inH)LVLQ)aFRV

$YHUDJHWRUTXHORDG

eF F

2 L1 L2

2 2 2 2 +

a2a1+Min,RMS= +FF

$GGLWLRQDOWRUTXHIRUDFFHOHUDWLRQRIWKHHFFHQWULFGLVF


30

Wa

QLQ

MLQ

-LQ-

E

Symbol Name SI

FL /RDGIRUFHVWKDOIF\FOH 1

FL /RDGIRUFHQGKDOIF\FOH 1

Fa $FFHOHUDWLRQIRUFH 1

Fa 3HULRG LFDFFHOHUDW LRQIRUFHD VD

IXQFWLRQRIWKHDQJOHRIURWDWLRQ 1

Fa $FFHOHUDWLRQIRUFHVWQGKDOIF\FOH 1

Fa $FFHOHUDWLRQIRUFHVWQGKDOIF\FOH 1



-( 0RPHQWRILQHUWLDHFFHQWULFGLVF NJP

0LQ506 506WRUTXH 1P0LQ 7RUTXHIRUDFFHOHUDWLRQ 1P

0in 7RUTXHVWKDOIF\FOH 1P

Symbol Name SI

0in 7RUTXHQGKDOIF\FOH 1P

e (FFHQWULFLW\ P

mL 0DVVRIWKHORDG NJ

vLW 6LQXVRLGDOYHORFLW\FXUYHRIWKHORDG PV

t 7LPH V


$QJOHRIURWDWLRQ UDG

(IFLHQF\

Symbol Name maxon

nin ,QSXWVSHHG USPQin 6SHHGFKDQJHLQSXW USP


25/60


Gearhead

iG J

1

J2

6SHHGRIURWDWLRQ nin = nL i*

7RUTXHiG

Min

ML

=



30 30

Wa

QLQ

=

MLQ

= JLQ+ J

1+

JL

+ J2

iG

QLQ

Wa

JLQ

+ JG

+J

L

iG

2 2

3OD\SRVLWLRQHUURU in

L

L*

5HGXFWLRQUDWLR

SODQHWDU\JHDUKHDG z1iG

z1+ z

3=

Belt drive

mR

d1

J2

d2

J1

6SHHGRIURWDWLRQd1

d2

nin

= nL

7RUTXHd2

d1

ML

Min=



MLQ

=m

Rd

2

1

2

ta

nin

+ Jin

+ J1

+J

L+ J

2d1

4 302d2

2

d1

2

dx

Jx

+

3OD\SRVLWLRQHUURU in L2

= d

1d

Symbol Name SI

-* 0RPHQWRILQHUWLD

JHDUKHDGWUDQVIRUPHG NJP



-L 0RPHQWRILQHUWLDORDG NJP

-x 0RPHQWRILQHUWLDGHHFWRUSXOOH\X NJP

- 0RPHQWRILQHUWLDGULYLQJHQG NJP

- 0RPHQWRILQHUWLDRXWSXW NJP

0in ,QSXWWRUTXH 1P


0L /RDGWRUTXH 1Pdx 'LDPHWHUGHHFWRUSXOOH\X m

d 'LDPHWHUGULYHSXOOH\ P

d 'LDPHWHUORDGSXOOH\ P

Symbol Name SI

i* 5HGXFWLRQUDWLRJHDUKHDGFDWDORJYDOXH

mR 0DVVEHOW NJ

] 1XPEHURIWHHWKVXQZKHHO

] 1XPEHURIWHHWKLQWHUQDOJHDU



L 0HFKDQLFDOSOD\RXWSXW UDG

(IFLHQF\

Symbol Name maxon

nin ,QSXWVSHHG USPnL /RDGVSHHG USP


3.3 Transformation of mechanical drives, rotation


26/60


,GHQWLFDWLRQV\VWHPIRUPD[RQJHDUKHDGV

A22GP

Gearhead design type

GS Spur gearheadGP Planetary gearhead

KD Koaxdrive

Diameterin mm

Version

A Metal version

B Version with enlarged internal gear

C Ceramic version

HD Heavy Duty for applications in oil

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


27/60


Sintered sleeve bearings Ball bearings

r

Operating

modes

&RQWLQXRXVRSHUDWLRQ 6XLWDEOHIRUDOOW\SHVRIRSHUDWLRQ

(VSHFLDOO\ IRU VWDUWVWRSRSHUDWLRQVDQG

ORZVSHHGDSSOLFDWLRQV

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

DSSOLFDWLRQVRXWJDVVLQJ

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


28/60

Notes


29/60


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


30/60


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


31/60


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


32/60


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 .


33/60


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 +


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


34/60


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


35/60


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


36/60


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

PXOWLSROHURWRU

([FHOOHQW KHDWGLVVLSDWLRQ DW KLJKHU VSHHGV

UHVXOWLQJIURPWKHWRRSHQGHVLJQ

6SHHGVRIXSWRUSP

PP

maxon EC-i range

+LJKO\G\QDPLFGXHWRLQWHUQDO

PXOWLSROHURWRU

0HFKDQLFDOWLPHFRQVWDQWV

EHORZPLOOLVHFRQGV

6SHHGVRIXSWRUSP

PP


37/60


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


38/60


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


39/60


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

n0

PD[RQXQLWV

Symbol Name SI

Imot 0RWRUFXUUHQW $

I$ 6WDUWLQJFXUUHQW $

I 1RORDGFXUUHQW $

k0 7RUTXHFRQVWDQWFDWDORJYDOXH 1P$

0 7RUTXH 1P

0H 6WDOOWRUTXH 1P0R )ULFWLRQWRUTXH 1P


8ind ,QGXFHGYROWDJH 9

Symbol Name SI

8mot 0RWRUYROWDJH 9

8N 1RPLQDOYROWDJHPRWRUFDWDORJYDOXH 9

Symbol Name maxon

kn 6SHHGFRQVWDQWFDWDORJYDOXH USP/9


Q0 6SHHGWRUTXHJUDGLHQWPRWRU

FDWDORJYDOXH USPP1P


40/60


Voltage equation, motor

Imot

+

Umot

Uind

Lmot

Rmot

EMF

W

LU

PRW= L

PRW + R

PRW I

PRW+ U

LQGR

PRW I

PRW+ U

LQG

'HULYHGIURPWKLVWKHVSHHGRIURWDWLRQDVD

IXQFWLRQRIWKHORDGVSHHGWRUTXHOLQH

0

QQN

Q8

mot 0Q

00

0

Q

PD[RQXQLWV

(IFLHQF\FXUYHI0

n0

Umot

= UN

Kmax

Torque M

Efficiency K

Speed n

MH

30 000

Umot,

mot

Q(005

)(with0

RN

M,

0)

max

=IA

I0

1

2

Symbol Name SI

(0) (OHFWURPRWLYHIRUFH 9

I 1RORDGFXUUHQW $

I$ 6WDUWLQJFXUUHQW $

Imot 0RWRUFXUUHQW $


Lmot 7HUPLQDOLQGXFWDQFHPRWRUFDWDORJYDOXH +

0 7RUTXH 1P

0H 6WDOOWRUTXH 1P

0R )ULFWLRQWRUTXH 1PRmot 7HUPLQDOUHVLVWDQFHPRWRUFDWDORJYDOXH

8N 1RPLQDOYROWDJHPRWRUFDWDORJYDOXH 9

8ind ,QGXFHGYROWDJH 9

Symbol Name SI

8mot 0RWRUYROWDJH 9

L &XUUHQWFKDQJH $

W 7LPHFKDQJH V

(IFLHQF\

max 0D[LPXPHIFLHQF\DW8NFDWDORJYDOXH

Symbol Name maxon

kn 6SHHGFRQVWDQWFDWDORJYDOXH USP9



FDWDORJYDOXH USPP1P


41/60


Angular acceleration: Start with constant current

ML, n

L

n0

n0

nL

MH

t Time t

lmot

= constant

Torque M

Speed n

Speed n

$FFHOHUDWLRQ

JR-

L

kMI

mot

JR-

L

M

5DPSWLPHWRORDGVSHHG

W30

Q

kMI

PRW

JR-

L

30

Q

M

JR-

L

Angular acceleration: Start with constant terminal voltage

nL

ML, n

Ln

0

MH

n0

tm

Umot

= constant

Time t

Torque M

Speed n

Speed n

$FFHOHUDWLRQPD[LPXP

max

=J

R+ J

L

MH

5DPSWLPHWRORDGVSHHG

Wm

' ln

1M

H

ML

+ MR

n0

1M

H

ML

+ MR

n0n

L

0HFKDQLFDOWLPHFRQVWDQWZLWKORDGLQHUWLD

m

'

= kM2

(JR

+ JL) R

mot

Symbol Name SI

Imot 0RWRUFXUUHQW $

-L 0RPHQWRILQHUWLDORDG NJP

-R 0RPHQWRILQHUWLDURWRUFDWDORJYDOXH NJP


0 7RUTXH 1P

0H 6WDOOWRUTXH 1P

0L /RDGWRUTXH 1P

0R )ULFWLRQWRUTXH 1P

Rmot 7HUPLQDOUHVLVWDQFHPRWRUFDWDORJYDOXH t 7LPH V

8mot 0RWRUYROWDJH 9

Symbol Name SI



W $FFHOHUDWLRQWLPH V

m 0HFKDQLFDOWLPHFRQVWDQWFDWDORJYDOXH V

m 0HFKDQLFDOWLPHFRQVWDQW

ZLWKDGGLWLRQDO-L V

Symbol Name maxon


nL /RDGVSHHG USP

Q 6SHHGFKDQJH USP

6.4 Acceleration


42/60


Motor type selection

Speed n

Short-term operation

Max. permissible speed

Continuous

operation

MRMS

Torque MM

maxM

NM

H

0RWRUW\SHVHOHFWLRQ

EDVHGRQWKHUHTXLUHGWRUTXHV0N!05060H!0max

5RRWPHDQVTXDUHORDG506

MRMS

=ttot

1(t

1 M

12 + t

2 M

22 + ... + t

n M

n

2)

Remark:

$PRWRUW\SHHJ5(LVGHQHGE\LWVVL]HWKHPHFKDQLFDORXWSXWSRZHUWKHEHDULQJV\VWHP

RIWKHVKDIWWKHFRPPXWDWLRQV\VWHPXVHGDQGWKHSRVVLEOHFRPELQDWLRQVZLWKJHDUKHDGVDQGVHQVRUVPD[RQPRGXODUV\VWHP

Winding selection

)RUDQRSWLPXPPDWFKEHWZHHQWKHHOHFWULFDODQGPHFKDQLFDOSRZHUFRPSRQHQWVRIWKHPRWRU

Speed-torque line

high enough for all

operating points

n0,theor

Safety

factor

~ 20%n

max

Deceleration Acceleration

Mmax

Speed n

Torque M

knVSHFLHVWKHZLQGLQJ

6HOHFWZLQGLQJZLWK

knN

n,theor=

Umot

n0,theor

Umot

nmax

+

=0

Q0

max

PD[RQXQLWV

ZKHUHnmax0max LVWKHH[WUHPHRSHUDWLQJSRLQW

DQGQ0 WKHDYHUDJH VSHHGWRUTXHJUDGLHQW

RIWKHVHOHFWHGPRWRUW\SH

Recommendation:$GGDVDIHW\IDFWRURIDSSUR[WR kn WRFRPSHQVDWHIRUWROHUDQFHVDQGORDG

FKDQJHVEXWGRQRWVHOHFWWRRODUJHDYDOXHIRUknDVWKLVZRXOGOHDGWRODUJHFXUUHQWV

5HTXLUHGPD[LPXPPRWRUFXUUHQW Imot

= I0

+k

M

Mmax

6.5 Motor selection

Symbol Name SI

Imot 0RWRUFXUUHQW $

I 1RORDGFXUUHQW $


0...n 7RUTXHDWRSHUDWLQJSRLQWV...n 1P

0 7RUTXH 1P

0H 6WDOOWRUTXH 1P

0N 1RPLQDOWRUTXHPRWRUFDWDORJYDOXH 1P

0506 506WRUTXH 1P0max 0D[LPXPWRUTXHLQORDGF\FOH 1P


8mot 0RWRUYROWDJH 9

Symbol Name SI

tn 'XUDWLRQRIRSHUDWLQJSRLQWV...n V

ttot 7RWDOWLPHRSHUDWLQJF\FOH V

Symbol Name maxon

kn 6SHHGFRQVWDQWFDWDORJYDOXH USP9

kn,theor 5HTXLUHGVSHHGFRQVWDQW USP9


nmax 0D[LPXPVSHHGLQORDGF\FOH USPn,theor 5HTXLUHGQRORDGVSHHG USP


FDWDORJYDOXH USPP1P


43/60


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

+LJKQXPEHURIFRXQWV

+LJKVSHHGV

/RZVSHHGV

/LQHGULYHULQWKHFDVHRIORQJ

FDEOHVURXJKDPELHQWFRQGLWLRQV

SRVLWLRQLQJDSSOLFDWLRQV

/RZSRVLWLRQLQJDFFXUDF\RU

SRVLWLRQLQJZLWKJHDUKHDG,

+LJKSRVLWLRQLQJDFFXUDF\ ,

,QGH[FKDQQHOIRUSUHFLVLRQKRPLQJ

'XVWGLUWRLO

,RQL]LQJUDGLDWLRQ

([WHUQDOPDJQHWLFHOGV

0HFKDQLFDOO\UREXVW

5HFRPPHQGHG :LWKUHVWULFWLRQV 2SWLRQDORQUHTXHVW 1RWUHFRPPHQGHG


44/60


Counts per turn from position resolution

5HTXLUHGFRXQWVSHUWXUQNof the

HQFRGHUIRUDVSHFLHGSRVLWLRQLQJDFFXUDF\RI

1 L360

Remark:%\HYDOXDWLQJWKHTXDGFRXQWVTFDIRXUWLPHVKLJKHUUHVROXWLRQLVDFKLHYHG7KLVLV

UHFRPPHQGHGIRUDVXIFLHQWO\DFFXUDWHSRVLWLRQLQJ

Measurement resolution, motor speed

Example:

0HDVXUHPHQWUHVROXWLRQ4

TFPV&RXQWVSHUWXUQNHQFRGHU

&37

Q =Q N

4

Q =Q N

4=

1ms

qc

CPTCPT

qc=

PLQ

qc

qc= rpm

Comment:7KHDFKLHYDEOHVSHHGVWDELOLW\LVPXFKKLJKHUWKDQWKHDERYHPHDVXUHPHQW

UHVROXWLRQGXHWRWKHPDVVLQHUWLDVDQGIHHGIRUZDUGLIDSSOLFDEOH

Symbol Name SI

N &RXQWVSHUWXUQ &37

i 5HGXFWLRQUDWLRPHFKDQLFDOGULYH4 4XDGFRXQWVSHUSXOVH TF,03

4 0HDVXUHPHQWUHVROXWLRQ TFPV

Symbol Name SI

3RVLWLRQUHVROXWLRQ

Symbol Name maxon

Q 0HDVXUHPHQWUHVROXWLRQPRWRUVSHHG USP


45/60


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

Counterclockwise

(ccw)

Quadrant IVBraking operation

Counterclockwise

(ccw)

Quadrant I

Motor operation

Clockwise (cw)

1-Q operation

2QO\PRWRURSHUDWLRQ

4XDGUDQW,RU4XDGUDQW,,,

'LUHFWLRQUHYHUVDOYLDGLJLWDOVLJQDO

7\SLFDODPSOLHUIRU(&PRWRUV

%UDNLQJLVQRWFRQWUROOHGIULFWLRQ

RIWHQVORZ

4-Q operation

&RQWUROOHGPRWRURSHUDWLRQ

DQGEUDNLQJRSHUDWLRQLQERWK URWDWLRQGLUHFWLRQVDOOTXDGUDQWV

$PXVWIRUSRVLWLRQLQJWDVNV

8.2 Selection of power supply

Required supply voltage at given load (nL, ML)

VCC

0

QQ

L0

L+ 8

max (maxon units)

Q0,81

81

Notes:

,QWKHFDVHRID4VHUYRDPSOLHUWKHSRZHUVXSSO\KDVWREHDEOHWRDEVRUEWKHNLQHWLFHQHUJ\

JHQHUDWHGIRUH[DPSOHLQDFDSDFLWRUZKHQWKHORDGLVGHFHOHUDWHG

:KHQDVWDELOL]HGSRZHUVXSSO\LVXVHGWKHRYHUFXUUHQWSURWHFWLRQKDVWREHGHDFWLYDWHGIRU

WKHRSHUDWLQJUDQJH

7KHIRUPXODLQFOXGHVWKHPD[LPXPYROWDJHGURS8RIWKHFRQWUROOHUDWPD[LPXPFRQWLQXRXV FXUUHQW

Achievable speed at given voltage supply

nL(V

CCU

max) (maxon units)

0

Q0

LUN

n0,UN

Symbol Name SI

0 7RUTXH 1P

0L /RDGWRUTXH 1P8N 1RPLQDOYROWDJHPRWRUFDWDORJYDOXH 9

V&& 6XSSO\YROWDJH 9

8max 0D[LPXPYROWDJHGURSRIWKHFRQWUROOHU 9

Symbol Name maxon


nL /RDGVSHHG USPn81 1RORDGVSHHGPRWRUDW8NFDWDORJYDOXHUSP


FDWDORJYDOXH USPP1P


46/60


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

,PP,max

=2 L

tot f

PWM

VCC

,PP,max

=4 L

tot f

PWM

VCC

&DOFXODWLRQLtot Ltot = Lint + /mot + Lext

7KHHIIHFWLYHPRWRULQGXFWDQFHLQWKHFDVHRIVTXDUH3:0H[FLWDWLRQRQO\DPRXQWVWRDSSUR[

RIWKHFDWDORJYDOXHLmot.

7KHFDWDORJYDOXHLmotLVGHQHGDWDIUHTXHQF\RIN+]ZLWKVLQXVRLGDOH[FLWDWLRQ.

$WDFXUUHQWULSSOHRI,33INWKHPRWRUFDQVWLOOEHORDGHGWRDSSUR[RIWKH

QRPLQDOFXUUHQWINFDWDORJYDOXH

$WDFXUUHQWULSSOHRI,33!INLWLVUHFRPPHQGHGWRXVHDQH[WHUQDOPRWRUFKRNH

LQDFFRUGDQFHZLWKWKHIRUPXODEHORZ

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

motL

ext=

3 IN

fPWM

VCC L

int0.3 L

mot

Lext 1RDGGLWLRQDOPRWRUFKRNHUHTXLUHG

Lext > $GGLWLRQDOPRWRUFKRNHUHFRPPHQGHG

PWMDC

motorLmot

Lext

Lint

DC amplifier

PWM

PWM

PWM

EC

motorLmot

1/2Lext

1/2Lint

1/2Lint

1/2Lint

1/2Lext

1/2Lext

EC amplifier

Symbol Name SI

f3:0 3:0IUHTXHQF\ +]

IN 1RPLQDOFXUUHQWPRWRUFDWDORJYDOXH $Lext ,QGXFWDQFHDGGLWLRQDOH[WHUQDO

PRWRUFKRNH +

Lint ,QGXFWDQFHEXLOWLQFKRNHFRQWUROOHU +

Symbol Name SI

Lmot 7HUPLQDOLQGXFWDQFHPRWRUFDWDORJYDOXH +

Ltot 7RWDOLQGXFWDQFH +V&& 6XSSO\YROWDJH 9

,33 &XUUHQWULSSOHSHDNWRSHDN $

,33PD[ 0D[LPXPFXUUHQWULSSOHSHDNWRSHDN $


47/60


9. Thermal behavior9.1 Basics

Heat sources

Iron losses in EC

motors and motorswith iron core winding

5HPDJQHWL]DWLRQORVVHV

PV, magn

=30 n M

magn

(GG\FXUUHQWORVVHV

3V,eddyFRQVWQ

Joule power losses

in windingTemperature T

Resistance R

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

Efficiency1-stage3-stage

5-stage

Torque M

30

PV,R = nmot Mmot (1G )

30

P

V,R= n

L M

L

G

1G

Stall torque reduced through temperature rise

)LUVWDSSUR[LPDWLRQFDOFXODWHGIURPYROWDJHDQGLQFUHDVHG

ZLQGLQJUHVLVWDQFH

7HPSHUDWXUHGHSHQGHQFHRIk0QRWFRQVLGHUHGM

HT= k

M I

AT= k

MR

TW

Umot

Storing heat

4FP7&th7 43 vW

:LQGLQJ&WK: = c&XP: 6WDWRU&WK6 = cFePmot *HDUKHDG&WK* = cFeP*

Symbol Name SI

&th +HDWFDSDFLW\ -.

&WK* +HDWFDSDFLW\JHDUKHDG -.

&WK6 +HDWFDSDFLW\VWDWRU -.

&WK: +HDWFDSDFLW\ZLQGLQJ -.

c 6SHFLFKHDWFDSDFLW\ -NJ.

I$7 6WDUWLQJFXUUHQWDWWHPSHUDWXUHT: $Imot 0RWRUFXUUHQW $


0 7RUTXH 1P

0*FRQt 0D[LPXPFRQWLQXRXVWRUTXHJHDUKHDG

FDWDORJYDOXH 1P

0HT 6WDOOWRUTXHDWWHPSHUDWXUHT: 1P

0L /RDGWRUTXH 1P

0magn 7RUTXHIRUUHYHUVDORIPDJQHWL]DWLRQ 1P

0mot 0RWRUWRUTXH 1P

m 0DVV NJ

m* 0DVVJHDUKHDG NJ

mmot 0DVVPRWRU NJ

m: 0DVVZLQGLQJ NJ3- -RXOHSRZHUORVVHV :

3V 3RZHUORVVHV :

3V,eddy (GG\FXUUHQWSRZHUORVVHV :

Symbol Name SI

3V,magn 3RZHUORVVHVIRUUHYHUVDORIPDJQHWL]DWLRQ :

3V,R )ULFWLRQSRZHUORVVHV :

4 6WRUHGKHDW -


R7: :LQGLQJUHVLVWDQFHDWFXUUHQWWHPST:

T 7HPSHUDWXUH &T: :LQGLQJWHPSHUDWXUH &

t 7LPH V

8mot 0RWRUYROWDJH 9

7 7HPSHUDWXUHGLIIHUHQFH .

(IFLHQF\

* *HDUKHDGHIFLHQF\

Symbol Name maxon


nL /RDGVSHHG USP

nmot 0RWRUVSHHG USP

Symbol Name Value&X 5HVLVWDQFHFRHIFLHQWFRSSHU .

c&X 6SHFLFKHDWFDSDFLW\FRSSHU -NJ.

cFe 6SHFLFKHDWFDSDFLW\LURQ -NJ.


48/60


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

Thermalo+HDWRZ

/RVVHV

Symbol Name Unit

4 6WRUHGKHDW -

3V 3RZHUORVVHV :-V

7: 7HPSHUDWXUHGLIIHUHQFHZLQGLQJDPELHQW .

76 7HPSHUDWXUHGLIIHUHQFHVWDWRUDPELHQW .

T$ $PELHQWWHPSHUDWXUH &.

Rth 7KHUPUHVLVWDQFHZLQGLQJKRXVLQJ

FDWDORJYDOXH .:

Rth 7KHUPUHVLVWDQFHKRXVLQJDPELHQW

FDWDORJYDOXH .:

&WK: +HDWFDSDFLW\ZLQGLQJ -.

&WK6 +HDWFDSDFLW\VWDWRU -.

Electrical o&XUUHQWRZ

&XUUHQWVRXUFH

Symbol Name Unit

4 (OHFWULFFKDUJH &

I &XUUHQW $&V

8 9ROWDJHSRWHQWLDOGLIIHUHQFH V

8 9ROWDJHSRWHQWLDOGLIIHUHQFH V

*1' *URXQG V



& (OHFWULFDOFDSDFLWDQFH F

& (OHFWULFDOFDSDFLWDQFH F

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 &

Tend (QGWHPSHUDWXUH &Tstart 7HPSHUDWXUHDWVWDUW &

T6 6WDWRUWHPSHUDWXUH &

T: :LQGLQJWHPSHUDWXUH &

Symbol Name SI

t 7LPH V

7max 0D[LPXPWHPSHUDWXUHFKDQJH .

7W 7HPSHUDWXUHFKDQJHDVD IXQFWLRQRIWLPHt .

th 7KHUPDOWLPHFRQVWDQW V


49/60


&RQWLQXRXVRSHUDWLRQLVFKDUDFWHUL]HGE\DWKHUPDOHTXLOLEULXP$IWHUVHYHUDOVWDWRUWLPHFRQVWDQWVWKHWHPSHUDWXUHGLIIHUHQFHEHWZHHQWKHURWRUDQGVWDWRUVWD\VFRQVWDQWDVWKHLUWHPSHUDWXUHVGRQRWLQFUHDVHIXUWKHU

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

= 7S7

A=

Rth1

+ Rth2

7W

Gearhead: Housing temperature

PV, G

TG

Rth,G

TG

TA

PV, G

7* = T*7$ = RWK*39*

RWK*: HJHVWLPDWHGZLWKRWK of

PRWRUVZLWKWKHVDPHVL]H

9.2 Continuous operation

Symbol Name SI

Imot 0RWRUFXUUHQW $

3- -RXOHSRZHUORVVHV :

39* 3RZHUORVVHVJHDUKHDG :

R7$ :LQGLQJUHVLVWDQFHDWWHPSHUDWXUHT$

Rth,* 7KHUPUHVLVWDQFHJHDUKHDGDPELHQW .:


FDWDORJYDOXH .:


FDWDORJYDOXH .:

T 7HPSHUDWXUH &T$ $PELHQWWHPSHUDWXUH &

T* *HDUKHDGWHPSHUDWXUH &


Symbol Name SI

T6 (QGWHPSHUDWXUHVWDWRU &


T: (QGWHPSHUDWXUHZLQGLQJ &

t 7LPH V

7* 7HPSHUDWXUHGLIIHUHQFHJHDUKHDGDPELHQW .



6 7KHUPWLPHFRQVWDQWVWDWRUFDWDORJYDOXH V

: 7KHUPWLPHFRQVWDQWZLQGLQJ

FDWDORJYDOXH V

Symbol Name Value



50/60


Permissible nominal currentIN

IN

MN

nN

Speed n

Torque M

Motor current Imot

Continuous

operation

Short-term

operation

Max. permissible speed

7HPSHUDWXUHGHSHQGHQFHXQGHUVWDQGDUGPRXQWLQJ

FRQGLWLRQVIUHHDLUFRQYHFWLRQDW&PRXQWHGKRUL]RQWDOO\RQSODVWLFSODWH

Tmax

TA

IN,TA

= IN

T

max25C

7HPSHUDWXUHGHSHQGHQFHXQGHUPRGLHGPRXQWLQJ

FRQGLWLRQV

Tmax TAI

N,TA= I

N

Tmax

25C

Rth1 + Rth2R

th1+ R

th2,mod

DeterminingRth2,mod

TW

TA

TS

Rth2, mod

Rth1

TS

PV

PV

PV

Motor under original conditions

,QVWDOODWLRQIDVWHQLQJDLUFLUFXODWLRQ

Separate measurement during

continuous operation$WDQ\PRWRUFXUUHQWImot

6WDWRUWHPSHUDWXUHT6 $PELHQWWHPSHUDWXUHT$

1Cu

Rth1

RTA

Imot

2

Rth2,mod

7S

R

TA I

mot

2 (1Cu

7S)

Symbol Name SI

Imot 0RWRUFXUUHQW $

IN 1RPLQDOFXUUHQWPRWRUFDWDORJYDOXH $

I17$ 1RPLQDOFXUUHQWDVDIXQFWLRQRIT$ $

0 7RUTXH 1P

0N 1RPLQDOWRUTXHPRWRUFDWDORJYDOXH 1P

3V 3RZHUORVVHV :



FDWDORJYDOXH .:


FDWDORJYDOXH .:Rth,mod 7KHUPUHVLVWDQFH

KRXVLQJDPELHQWPRGLHG .:

T$ $PELHQWWHPSHUDWXUH &

Symbol Name SI

Tmax 0D[SHUPLVVLEOHZLQGLQJWHPSHUDWXUH

FDWDORJYDOXH &



76 7HPSHUDWXUHGLIIHUHQFH

VWDWRUDPELHQW .

Symbol Name maxon


nN 1RPLQDOVSHHGPRWRUFDWDORJYDOXH USP

Symbol Name Value



51/60


5HSHWLWLYHZRUNF\FOHVRIVKRUWGXUDWLRQW\SLFDOO\RQO\DIHZVHFRQGVFDQEHDVVHVVHGZLWKWKH

VDPHIRUPDOLVPDVFRQWLQXRXVRSHUDWLRQ

TemperatureT

90.00

80.00

70.00

60.00

50.00

40.00

30.000.1 1 10 100 1000

On

(1s)

Averageend temparture,

winding

10000Time t

Off

(3s)

On

Time constant

winding 9s

Off

Average temperature rise during intermittent operation

8VHHIIHFWLYHFXUUHQWYDOXH506DVPRWRU

ORDG(R

th1+ R

th2R

TAI

RMS

2

7W

=1

Cu(R

th1+ R

th2R

TAI

RMS

2

Rth2

7S

=(R

th1+ R

th2)7

W

Intermittent operation

Temperature T

Time t

Current I IonIRMS

TW,avf

TS,

Tmax

ton

toff

506FXUUHQWtonI

RMS= I

on

ton

+ toff

%DVLFUHTXLUHPHQWI506,17$

0D[LPXPORDGFXUUHQWIRUDJLYHQWLPHF\FOH

Tmax

TA

Ion,

N

Tmax

25C

ton t

off

ton

2))GXUDWLRQIRUDORDGRIIonGXULQJton

toff

Ion

2

Tmax

7A

Tmax

25CIN2

1 ton

9.3 Cyclic and intermittent operation (continuously repeated)

Symbol Name SI

I &XUUHQW $


I17$ 1RPLQDOFXUUHQWDVDIXQFWLRQRIT$ $

Ion &XUUHQWGXULQJ21SKDVH $

I506 506FXUUHQW $



FDWDORJYDOXH .:

Rth 7KHUPUHVLVWDQFHKRXVLQJDPELHQW FDWDORJYDOXH .:

T 7HPSHUDWXUH &

T$ $PELHQWWHPSHUDWXUH &

Symbol Name SI


FDWDORJYDOXH &


T:DY $YHUDJHHQGWHPSHUDWXUHZLQGLQJ &

t 7LPH V

toff 2))WLPH V

ton 21WLPH V



Symbol Name Value



52/60


+LJKEULHIRQHWLPHRYHUORDGRIWKHPRWRU7KHRSHUDWLRQGXUDWLRQLVVRVKRUWWKDWWKHWHPSHUDWXUH

RIWKHWKHUPDOO\LQHUWVWDWRUGRHVQRWLQFUHDVHVLJQLFDQWO\WKLVFRUUHVSRQGVWRDQ21WLPHRI

DSSUR[6 Z

2QO\WKHKHDWLQJRIWKHZLQGLQJZKLFKFRUUHVSRQGVWRWKHKHDWLQJRIDVLPSOHERG\ VHHFKDSWHUKDVWREHWDNHQLQWRDFFRXQW

140

1 10 100 10000

120

100

80

4020

60

0.1 s

10000

Temperature T

Stator

Temperature

difference

Winding

Time t

TW,

Rth1

TS,

TW

TA

Rth2

T6 = T$

7: = Rth3-

Rth1

RTA

Imot

2

7W

=1Cu Rth1 RTA Imot

2

Overload factor K

4XDQWLFDWLRQRIWKHRYHUORDG

Meaning:

.TmaxLVQRWUHDFKHGGXULQJVKRUWWHUPRSHUDWLRQ

.!/LPLWPD[LPXP21WLPHton

Tmax

25CK =

Tmax

TS

R

th1

Rth1+

R

th2

Imot

IN

0D[LPXPSHUPLVVLEOHRYHUORDGDWJLYHQ21WLPHton

1K =

1 exp ton

W

0D[LPXP21WLPHtonDWJLYHQRYHUORDGIDFWRU.K2

ton

W ln

K2 1

0D[LPXPPRWRUFXUUHQWImotDWJLYHQ

RYHUORDGIDFWRU.

Tmax

TS

Imot

= K IN

T

max25 C

Rth1

+ Rth2

Rth1

9.4 Short-term operation

Symbol Name SI

Imot 0RWRUFXUUHQW $


. 2YHUORDGIDFWRU

3- -RXOHSRZHUORVVHV :


Rth 7KHUPUHVLVWDQFHZLQGLQJKRXVLQJ .:

FDWDORJYDOXH

Rth 7KHUPUHVLVWDQFHKRXVLQJDPELHQW .:

FDWDORJYDOXH

T 7HPSHUDWXUH &T$ $PELHQWWHPSHUDWXUH &


FDWDORJYDOXH &

Symbol Name SI

T: (QGWHPSHUDWXUHZLQGLQJ &



t 7LPH V

ton 21WLPH V


6 7KHUPWLPHFRQVWDQWVWDWRU

FDWDORJYDOXH V

: 7KHUPWLPHFRQVWDQWZLQGLQJ

FDWDORJYDOXH V

Symbol Name Value



53/60


10. Tables10.1 maxon Conversion Tables

Power 3>:@

% $ R]LQV R]LQUSP LQOEIV IWOEIV 1PV: mW NSPV P1PUSP

:1PV

mW

R]LQV

IWOEIV

NSPV

Torque 0>1P@

% $ R]LQ IWOEI 1P:V 1FP P1P NSP SFP

1P

P1P

NSP

R]LQ

IWOEI

Moment of inertia ->NJP]

% $ R]LQ R]LQV OELQ OELQV 1PVNJP P1PV JFP NSPV

JFP 6

NJP1PV

R]LQ 5

OELQ

Mass P>NJ@ Force )>1@

% $ R] OE JUJUDLQ NJ g %$ R] OEI 1 NS p

NJ 1

g NS

R] R]

OE

OEI

JUJUDLQ 6 SGO

Length O>P@

% $ in ft \G 0LO m FP mm P

m

FP

mm

in

ft

Angular velocityZ>V

]Angular acceleration >V]

% $ V+] rpm UDGV % $ min V UDGV USPV

UDGV S S V

S

rpm

SUDGV S S

S

Linear velocity Y>PV]

% $ LQV LQUSP IWV IWUSP PV FPV PPV m rpm

PV

LQV

IWV 5

Temperature 7>.@

% $ )DKUHQKHLW &HOVLXV .HOYLQ

.HOYLQ )

&HOVLXV )

)DKUHQKHLW & .

General Information

4XDQWLWLHVDQGWKHLUEDVLFXQLWVLQWKH

,QWHUQDWLRQDO6\VWHPRI8QLWV6,

4XDQWLW\ %DVHXQLW 8QLWVLJQ

/HQJWK meter m

0DVV NLORJUDP NJ

7LPH VHFRQG V

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