Maxon dc motor sizing made easy presentation english version march 2010

1. Drive selection: What is it all about?
maxon Seminar at Electromate, March 2010 © by maxon motor ag, 2010

Drive Selection:
What is it all about?
The context of motor selection
Application and situation analysis
Extracting key load parameters

Seminar at Electromate
© 2010, maxon motor ag, Sachseln, Switzerland

Systematic selection process: Step 1

Step 1
overview
situation

power

communication
ambient
condition

step 2 step 3 step 4 step 5+6 step 7+8
load drive gear- motor type sensor
head winding controller
Book: Chapter 3
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DC motor sizing made easy


Gain an overview
mechanics

operating mode power

motion profile
control concept

control accuracy working points

boundary conditions

Drive system as a black box
environment
temperature, atmosphere
impacts, vibration
electrical power … boundary conditions
current dimensions
task voltage service life
set values …
commands
emissions
electro magnetic
heat
noise
…
mechanical power
force, torque
quality, accuracy velocity, speed
resolution
mech. play
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Mechanical drive concept
Drive design: linear – rotation
Drive elements and coupling with load
relative position of motor and load
– e.g. bridge a distance with a belt

Mechanical drive concept: Bearing
Support of all the forces
– Eccentric drive, cam, pump

– rack guidance

– pulley bearings of conveyors, cranes
and belt drives

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Operating modes
continuous (S1) load

time
short term (S2)

working cycles

intermittent (S3)

Control concept
Controlled variable
– torque, current
– speed, velocity feedback sensor
– position
Controlled range, accuracy?
– position resolution
– speed stability
What kind of communication?
– communication with higher level host system
– set value range: 0 … 5 V or -10 … +10 V
– inputs and outputs (homing, temperature monitoring, ….

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Task and control accuracy

gearhead,
command controller motor load
drive

control loop

sensor

The accuracy of control is the combined result of all
components in a drive system!
– resolution, precision
– signal amplification, control parameter
– phase shifts, time shifts, backlash, mech. play

Particular boundary conditions
dimensions
– length, diameter
service life
– specific depending on load cycle, ambient conditions and application
– given as service hours or numbers of working cycles
– limited by the weakest component
temperature, atmosphere
– can influence the achievable power and service life
noise, vibration
– specific depending on load cycle, mounting and ambient conditions,
application
– influences on service life
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Systematic selection process: Step 2
Step 1
overview
situation

power

communication
ambient
condition

Book: Chapter 4

Working points
Pair of
– torque and speed
– force and velocity
standard representation: (x,y) = (M,n) or (F,v)
speed n
velocity v
deceleration acceleration

dwell torque M
force F

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Working point and motion profile
n
1 2 3 4 1

t

n extreme
working point
2
4 3 1 M

(M1,n1) acceleration friction and acceleration
(M2,n2) const. speed friction only
(M3,n3) deceleration friction helps during deceleration
(M4,n4) dwell depending on friction

Motion profiles
general parameters
– duration ∆ttot
– max. velocity vmax
– distance ∆s
symmetrical triangular profile
– for fast motions
– minimum acceleration
3/3 profile
– minimum power
– thermally advantageous

Book: P. 24/25
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Operating modes
continuous operation (S1)
– acceleration and deceleration can be neglected
– constant load
– duration: longer than all thermal time constants of the system
in thermal equilibrium: constant temperatures
typically: several minutes up to hours
Tmax

temperature

load

time

Operating modes
short term operation (S2)
– very short operation time
only elements with a correspondingly short time constant can heat
up
– long dwell times
drive can cool down completely
Tmax

temperatur

load

time
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Operating modes
cyclic operation (general case)
– load profile to be repeated permanently with relatively short dwell
times
duration of a cycle: typically up to several seconds
– thermal equilibrium is reached on average only
temperature variations
– effective load (RMS) is an important key parameter

MRMS =
1
t tot
(t1M1 + t 2M2 + t 3M3 + ...
2
2
2
)
Tmax
temperature

load
time

Operating modes
intermittent operation (S3) ON - OFF M t on
RMS = ⋅ Mon
– special case of cyclic operation t on + t off

temperature
• winding
• housing

1s 10s 100s 1000s 10000s 10s 100s 1000s Time
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Friction forces
difficult to evaluate
– many influencing factors: state of
the interface layer normal force FN

– varies upon time: ageing effects
moving
– typical coefficients of friction from direction
tables (book p. 30/31) body
tion
brica
r, lu
laye
face is
friction force FN in te r bas
FR = µ ⋅ FN

estimation formula for ball bearings:
MR = 0.5 ⋅ µR ⋅ F ⋅ d

Acceleration of mass inertias

additional force / torque ∆v
Fa = m ⋅ a = m ⋅
necessary ∆t
– basic equations for ∆ω π ∆n
translation / rotation Mα = J ⋅ α = J ⋅ = J⋅
∆t 30 ∆t
mass inertias
– translation: mass m
– rotation: moment of mass inertia JX
with respect to axis x
Jx = r 2 ⋅ dm
m 2
– example cylinder: Jx = ⋅r
2
Book: P. 40ff
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Constant forces, preloading forces
Example spring preload

Example gravity
speed n
velocity v
deceleration acceleration

dwell torque M
without gravity
force F
with gravity

Determination of forces / torques
simple measurements
– precision needed: 5-10%
– e.g. by means of pulleys and spring balances

estimation of friction torques by means of friction
coefficients µR

using a motor for torque determination
– by means of a current measurement and the torque constant kM
– in original conditions
– Suitable current measuring tool
M = kM ⋅ I

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Key load data for characterization
average effective load (RMS)
maximum load

duration of a load cycle
duration of the maximum load

max. velocity or speed

required position resolution
required speed accuracy

Load characterization
dominating constant load
– typically in cases of high friction
– maximum forces exceed RMS load by less than 20%
– maximum forces applied during short terms only
=> selection based on RMS load is sufficient
dominated by peak load
– typically in cases of highly dynamic drives with high acceleration
– RMS value of load very small (< 50 % of maximum load)
=> selection based on maximum load values
general case without domination of one load type
Remark: Acceleration and friction in the mechanical drive
are not taken into consideration yet!
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Systematic selection process: Steps 3 & 4
Step 1
overview
situation

power

communication
ambient
condition

Book: Chapters 5&6

Mechanical transformation
by means of drive
elements
– also in series
characteristic variables
– reduction i
– efficiency η
– mass inertias
– backlash
transformation equations
bearings

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Screw drives
speed
60
nin = ⋅ v out
p
torque
p Fout
Min = ⋅
2π η
torque for acceleration
mout + mS p 2 π ∆nin
Min,α = Jin + JS + ⋅
η 4π 30 ∆t α
2

Spindle drives
spindel type: trapezoidal, metric, ball screws
spindle type has influence on
– efficiency, heating
– possible working cycles, ON time
– costs
– accuracy, play, backlash
– maximum load
– life
– application: actuators or positioning units

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Gearhead stage
speed
nin = nout ⋅ iG

torque
Mout
Min =
iG ⋅ ηG
torque for acceleration

Jout + J2 π ∆nin
Min,α = Jin + J1 + ⋅
iG ⋅ ηG
2
30 ∆t α

maxon gear
operation at high torques and low speeds
2 standard types:

GS: spur gearhead GP: planetary gearhead
lower power density high power density
material options
– plastic: lower power, lower costs
– ceramic: higher power, longer life
bearing options
– ball bearing: standard for larger planetary gears
– sleeve bearing: standard for GS and small GP

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Most important gearhead data
reduction - absolute reduction
efficiency
– as a function of torque
gearhead limits
– max. continuous torque (output)
– intermittent torque (short-term = 1s)
– max. input speed
– temperature (lubrication)
backlash
load on bearings

Operating range diagram

recommended gear input speed
output defines max. output speed
speed
n
nmax,out = max,in
i

continuous intermittent
operation operation

output
torque M
Mcont Mmax

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Step 1
overview
situation

power

communication
ambient
condition

Book: Chapter 7&8

DC motor designs
DC motors BLDC motors

conventional,
with iron core slotless

slotted
external rotor

slotted
coreless
internal rotor

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Step 1
overview
situation

power

communication
ambient
condition

Book: Chapter 9

Controller: The Heart of the Drive System
Communication
Power Supply – Host, Master
– cont. current – I/O
– max. current controlled quantity
– voltage Controller power
digital – analogue
Sensor
…
– measured
quantity
– resolution Motor
– motor type Gearhead, mech. drive
– power – reduction ratio
– backlash
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Motion Control System
Application
Program Cycle (e.g. 5 ms)
11001..
command
Path
Generator
Pos Position Set Value
t
Position/Speed Actual
Control loop Position
I Motor with Encoder
Current Set Value
and Drive
t Current Actual
Control loop Current
PWM
Clock Clock
duty
(e.g. 1 kHz) (e.g. 10 kHz) Driver, Power
cycle
Amplifier PWM (e.g. 50 kHz)

Sensors
Set value Output

Actuator
Measurement
Feedback

DC Tacho Incremental Encoder Resolver
IxR Hall Sensor

Speed ∆Pos/∆t Position
Direction

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2. DC and BLDC Motors with Permanent Magnets

DC and BLDC Motors with
Permanent Magnets
Design, design variants
Commutation: Graphite and precious metal brushes
Brushless commutation


DC motor designs
conventional, slotted
e.g. Dunker motor

coreless
e.g. maxon

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Coreless maxon DC motor (RE 35)
self-supporting press ring
commutator- winding shaft
plate ball bearing

brushes

el. connections

flange
housing
(magn. return)
ball bearing commutator
permanent magnet
press ring (in the centre)

Advantage coreless: no cogging
no soft magnetic teeth to interact with the permanent
magnet
smooth running even at small speeds
less vibration and noise

any rotor position can be controlled in a simple way
no nonlinear control behaviour

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Advantage coreless: no iron losses
no iron – no iron losses
constant magnetization
high efficiency, up to above 90%
low no load current, typical < 50 mA

no saturation effects in the iron core
Even at the highest currents the produced torque
remains proportional to the motor current.
stronger magnets = stronger motors
compact design
small rotor inertia

Advantage coreless: small inductance
less brush fire
– commutation: open and close a contact on an inductive load
higher live expectancy
less electromagnetic emissions
easier to suppress interferences:
– capacity between connections
– ferrite core at motor cable

but fast reaction of the current
– problems in combination with pulsed supply (choke needed)

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maxon DC motor: Variants
RE-Motor with
NdFeB magnet
graphite brushes
ball bearing

A-max-Motor with
AlNiCo magnet
precious metal brushes
sintered sleeve bearing

Commutation process _
+
+
1 4
1 5
2 5
2 6
3 6
1 3 7
7
2 4 7
6 4 1
3 5 1
5 4 5 2
6 2
6 3
7 3
7 4

_ 1 4

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DC commutation systems
graphite
graphite brush with 50%
copper
copper reduces contact and
brush resistance
graphite acts as lubricant
spring

precious metal
bronze brush body with plated silver (with
palladium) contact area
silver copper commutator
small contact and brush resistance (50mΩ)
CLL for extended service life

Precious metal brushes: CLL
the problem
arc production
commutator
wears off

after
short circuit

commutator
solution
- capacitors between neighbouring C
commutator segments C
- energy is deviated into capacitor: C
no arcs produced
CLL disc

RS
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DC commutation: pros and cons
graphite precious metal
well suited for high currents and well suited for smallest currents
current peaks and voltages
well suited for start-stop and well suited for continuous
reversed operation operation
bigger motors smaller motors
very low friction and noise
higher friction, higher no-load low electromagnetic emission
currents favourable price
not well suited for small currents
more audible noise and not well suited for high currents
electromagnetic emission and current peaks
more expensive not well suited for start-stop
operation

maxon DC motor: service life
service life life influencing factors
no general statement possible the electric load: higher currents
average conditions: 1'000 - = higher electric wear (arcing)
3'000 hours speed: higher speed = higher
under extreme conditions: less mechanical wear
than 100 hours
type of operation: reversed
under favourable conditions:
operation = reduced service life
more than 20'000 hours
temperature
humidity with graphite brushes
use graphite brushes and CLL (with precious metal
ball bearings for extreme brushes) enhances service life
operating conditions
load on shaft (bearings)

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Brushless DC motor
names: EC motor, BLDC motor
motor behavior similar to DC motor
– design similar to synchronous motor (3 phase stator winding,
rotating magnet)
– the powering of the 3 phases according to rotor position

main advantages: higher life, higher speeds
slotless windings
– similar advantages as coreless DC motors
– no magnetic detent, less vibrations

the more attractive, the smaller the costs and size of
electronics

maxon EC motor / brushless DC motor
magn. return:
preloaded
laminated iron stack
ball bearings
PCB with
Hall sensors

control
magnet
shaft

housing

3 phase knitted balancing rings
maxon winding rotor
el. connections winding
and Hall sensors (permanent magnet)

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maxon EC motor design variants
slotless

slotted
external rotor
features in common
– rotating permanent magent
made of NdFeB
– 3 phase winding in the stator
(3 winding connections)
– preloaded ball bearings
slotted
– electronic commutation
internal rotor

maxon EC motor: Coreless design
design with coreless maxon winding
– internal rotor with 1 or 2 pole pair

maxon EC motor
– many types: e.g. short – long,
sterilisable, integr. electronics, …
– typically for high speeds
maxon EC-max
– Philosophy: reliable EC motor at
reasonable price
maxon EC-powermax
– Philosophy: the strongest possible motor

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maxon EC motor: Slotted design
maxon EC-i
– Philosophy: strong EC Motor at
attractive price
– dynamic motor, high cogging torque
– slotted winding, internal rotor
– several magnetic pole pairs
flat maxon EC motor
– Philosophy: flat EC Motor at an
attractive price
– slotted winding, external rotor
– more than 4 magnetic pole pairs
– relatively high torque but limited speed
and dynamics

DC and EC motor: Comparison
maxon motor family RE (DC) EC EC-max
(20 – 45 mm) EC-powermax EC-flat EC-i

40 000 min-1 5 W/cm3 2 mNm/cm3 10 ms

max. speed power density torque density mech. time const.
(min-1) (W/cm3) (mNm/cm3) (ms)

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Interaction of rotor and stator
current distribution in phases
– 3 phases 3 phases
– 6 possible current distributions
winding
– 6 winding magnetic field directions
rotated by 60°
– commutation every 60°

field produced
by winding

Electronic commutations systems
common goal: Applying the current to get the maximum torque
perpendicular magnetic field orientation of
- rotor (permanent magnet)
- and stator (winding)
knowledge of rotor position with respect to winding

block comm.-Typ sine

rotor position
sensorless hall sensors encoder (+ HS)
feedback

DECS external DES
DEC family
electronics
EPOS

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Block commutation
rotor position from Hall
sensor signals
φ north

control magnet south

Hall sensor
1 1 0 0 0 1 1
0 1 1 1 0 0 0
0 0 0 1 1 1 0
0° 60° 120° 180° 240° 300° 360°
EC-max and EC flat:
rotation angle φ
Power magnet is probed directly

Block commutation
power stage EC motor
controller + (MOSFET) (magnet, winding, sensor)

phase 1 HS2
commutation
logics

phase 3

HS3
HS1
_ phase 2

rotor position feedback

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Multipole EC motor: commutation

15°

Sensorless block commutation
rotor position detection without (Hall) sensors
measuring the back EMF
star point R R
zero crossing of back EMF EMF
time delay 30°
R
difficult at low speeds
EMF
flyback pulse

0° 60° 120° 180° 240° 300° 360°

special starting procedure sensorless commutation
similar to stepper motor only for continuous
operation at high speeds

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Sensorless block commutation
virtual star point
virtual star point in the electronics
star or delta configuration
controller for
sensorless operation

EMF
~1
kΩ

R
R
~1kΩ R R
R
kΩ

R
~1

Y ∆

Sinusoidal commutation
winding current
rotor position
must be known very accurately
typical 2'000 points per rev.
500 pulse encoder
(Hall sensors for start: absolute rotor
position)
resolver as an alternative
0° 60° 120° 180° 240° 300° 360°
rotation angle φ
phase currents
sinusoidal
120° phase shift Sinusoidal commutation for
similar to synchronous motor with smooth running even at the
variable frequency lowest speeds

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3. Motor Data and Operating Ranges

Motor data and operating
ranges of DC motors
Motor behaviour: speed-torque line, current
Motor data and operating ranges


DC motor as an energy converter
electrical in mechanical energy
– speed constant
– torque constant PJ = R ⋅ I2
– speed-torque line

Pel = U ⋅ I π
Pmech = n ⋅M
30

applies to DC and EC motors
– "EC" = "brushless DC" (BLDC)

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Characteristic motor data
describe the motor design and general behaviour
independent of actual voltage or current

strongly winding dependent values (electromechanical)
– terminal resistance (phase to phase) R
– terminal inductance (phase to phase) L
– torque constant kM
– speed constant kn
almost independent of winding (mechanical)
– speed-torque gradient ∆n/∆M
– mechanical time constant τm
– rotor mass inertia JMot

Winding resistance
resistance increases from left to right
low resistance winding high resistance winding

thick wire, few turns thin wire, many turns
low rated voltage high rated voltage
high rated and low rated and starting
starting currents currents
high specific speed low specific speed
(min-1/V) (min-1/V)
low specific torque high specific torque
(mNm/A) (mNm/A)

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Torque and current: torque constant
current direction towards brush forces:
force on current leading
force conductor in a magnetic field
torque:
sum of all forces at the
distance to the rotating axis
influencing parameters:
geometry
field density design
winding number
magnetic
force field M = kM ⋅ I

current direction towards flange current I application

Speed constant kn
Speed n and induced voltage Uind
– law of induction: changing flux in a conductor loop
– induced voltage proportional to speed n = k n ⋅ Uind
– basically the inverse of kM, but in different units
Speed constant kn
n0 = k n ⋅ U
– mostly used for calculating no-load speeds n0
– unit: min-1 / V
Generator constant ke
– inverse of kn: motor as a generator (e.g. DC-Tacho). How much
voltage is produced per rpm?
– units: mV / min-1
V / 1000 min-1

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Motor as an electrical circuit
U I applied motor voltage U:
_ +
U = L ⋅ ∂I + R ⋅ I + EMF ≅ R ⋅ I + Uind
∂t
EMF R L
Uind = U − R ⋅ I

n M
EMF: induced voltage Uind = U−R⋅
kn kM
(winding) resistance R
winding inductance L ⎛ 30'000 R ⎞
n = kn ⋅ U − ⎜ ⋅ ⎟ ⋅M
• voltage losses over L can be ⎜ π kM ⎟
2
neglected in DC motors ⎝ ⎠
∆n
n = kn ⋅ U − ⋅M
∆M

Speed-torque line
speed n ∆n
n = kn ⋅ U − ⋅M
∆M

n0 U > UN
n0 = k n ⋅ U

∆n
U = UN
∆M

MH torque M
IA current I

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Speed-torque gradient
by how much is the speed reduced ∆n, if the output motor torque is
enhanced by ∆M? ∆n 30'000 n
= ⋅R = i

speed n ∆M π ⋅ kM
2
MiH

M1, n1 strong motor:
• flat speed-torque line, small ∆n/∆M
n0 ∆n M2, n2 • not sensitive to load changes
• e.g. strong magnet, bigger motor
∆M

weak motor:
• steep speed-torque line, high ∆n/∆M
• sensitive to load changes
• e.g. weak magnet, smaller motor
MH torque M

Winding series
numerous winding variants adjust
n electrical input power (voltage,
at U constant
current of power supply)
mechanical output power
thick wire (speed, torque)

thin wire

M
speed-torque gradient
basically constant for the winding series
constant filling factor: a constant amount of copper fills the air gap

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Values at nominal voltage
describe the special working points: at rated voltage UN
at rated current IN

No-load operating point
– resulting no-load speed n0
n – resulting no-load current I0

rated working point
– resulting rated speed nN
– resulting rated torque MN

Motor at stall
– resulting stall torque MH
– resulting starting current IA
M

Current characteristics
current and torque
• are proportional, torque
constant kM
IA mechanical M = kM ⋅ I
losses
• no-load current corresponds
n0 to the friction torque
• starting current corresponds
to the stall torque
U MH
IA = =
R kM
I0

MR MH torque M

I0 IA current I

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Maxon dc motor sizing made easy presentation english version march 2010

Maxon dc motor sizing made easy presentation english version march 2010

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