Post on 25-Mar-2020
Jeff Shelton – 3 March 2015
V IN
GND
TO COMPUTER
Speed,
Torque, TM
= 0.5 NL
NO LOAD
TSTALL Max Power
T = 0.5 TSTALL
Speed,
Torque, TM
NO LOAD
TSTALL
VIN increase
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Jeff Shelton – 3 March 2015 2
Jeff Shelton – 3 March 2015 3
Images: http://science.howstuffworks.com/transport/engines-equipment/gear2.htm http://robotshop.com
Jeff Shelton – 3 March 2015 4
Images: http://www.carbibles.com/transmission_bible_pg2.html http://robotshop.com
Jeff Shelton – 3 March 2015
Factor SPUR PLANETARY
Size Larger Smaller
Cost Lower Higher
Load Capacity Lower Higher
Operating Speed Lower Higher
Backlash Higher Lower
Efficiency Lower Higher
Noise Lower Higher
Centerline Offset Inline
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Jeff Shelton – 3 March 2015 6
Speed, 𝜔𝑀
Torque, TM
Speed, 𝜔𝐿
Torque, 𝑇𝐿
𝑟 = 1 Motor
Load
Speed, 𝜔𝐿
Torque, 𝑇𝐿
𝑟 < 1 Shallower 𝑇-𝜔 curve
Speed, 𝜔𝐿
Torque, 𝑇𝐿 𝑟 > 1
Steeper 𝑇-𝜔 curve
Unchanged 𝑇-𝜔 curve
Gear ratio (or speed ratio):
𝑟 =𝜔𝑀𝜔𝐿
=NLNM
Torque ratio*:
𝑟 =𝑇𝐿𝑇𝑀
* assuming perfect efficiency
Jeff Shelton – 3 March 2015 Image: https://www.sparkfun.com/products/12497
Jeff Shelton – 3 March 2015 https://www.sparkfun.com/products/12310
Jeff Shelton – 3 March 2015
𝑟 =NL
NM=
𝜔𝑀
𝜔𝐿
𝑟 ⋅ 𝜂 =𝑇𝐿
𝑇𝑀
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Jeff Shelton – 3 March 2015 10
iA LA RA
+
VIN
_
+
VEMF _
JM
TM 𝜃𝑀 , 𝜔𝑀
𝜃𝐿 , 𝜔𝐿 𝑇 disturbance
JL
𝑁𝑀
𝑁𝐿
𝜂
iA LA RA
+
VIN
_
+
VEMF _
JT
TM 𝑇 disturbance𝑟 ⋅ 𝜂
𝜃𝐿 , 𝜔𝐿
𝐽𝑇 = 𝐽𝑀 +𝐽𝐿𝑟2
⇓
𝑟 =𝑁𝐿𝑁𝑀
Jeff Shelton – 3 March 2015
𝐽𝑇
𝐽𝑀𝐽𝐿𝐽𝐺𝑟
𝐽𝑇 = 𝐽𝑀 +𝐽𝐿𝑟2
"reflected inertia"
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Jeff Shelton – 3 March 2015
Sometimes it takes a bit of work to convert inertia values into the proper units…
Jeff Shelton – 3 March 2015
𝐽𝑀)
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Jeff Shelton – 3 March 2015
𝐾𝐸𝐿 =1
2𝐽𝐿𝜔𝐿
2
𝑃 =𝑑
𝑑𝑡𝐾𝐸𝐿 =
𝑑
𝑑𝑡
1
2𝐽𝐿𝜔𝐿
2 = 𝐽𝐿𝜔𝐿 ⋅𝑑
𝑑𝑡𝜔𝐿
𝑃𝐿 =𝐽𝐿𝑟2𝜔𝑀 ⋅
𝑑
𝑑𝑡𝜔𝑀 =
𝐽𝐿𝑟2𝜔𝑀 ⋅ 𝛼𝑀
𝛼𝑀 =𝑇𝑀
𝐽𝑇=
𝑇𝑀𝑟2
𝐽𝑀𝑟2+𝐽𝐿
and 𝜔𝑀 = 𝛼𝑀 ⋅ 𝑡
𝑃𝐿 = 𝐽𝐿𝑟2𝑡 ⋅
𝑇𝑀2
𝐽𝑀𝑟2 + 𝐽𝐿
2
𝐽𝑀 =1
𝑟2𝐽𝐿 or 𝑟 =
𝐽𝐿
𝐽𝑀
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Jeff Shelton – 3 March 2015
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Images: http://electrolift.com/the-worm-gear-advantage.php http://www.longwaymotor.com/imagefile/pro/125013500416790.jpg
Jeff Shelton – 3 March 2015
𝐾𝑇 𝑖𝐴 𝑇𝑀
iA LA RA
+
VIN
_
+
VEMF _
JM
TM
TL
q,
+ VM -
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Jeff Shelton – 3 March 2015
𝐾𝑇 𝑖𝐴 𝑇𝑀 1
𝐿𝐴𝑠 + 𝑅𝐴
iA LA RA
+
VIN
_
+
VEMF _
JM
TM
TL
q,
+ VM -
𝑉𝑀
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Jeff Shelton – 3 March 2015
𝐾𝑇 𝑖𝐴 𝑇𝑀 1
𝐿𝐴𝑠 + 𝑅𝐴
𝑉𝑀
−𝐾𝐸𝑀𝐹
𝑉𝐼𝑁
𝜔
iA LA RA
+
VIN
_
+
VEMF _
JM
TM
TL
q,
+ VM -
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Jeff Shelton – 3 March 2015
𝐾𝑇 𝑖𝐴 𝑇𝑀 1
𝐿𝐴𝑠 + 𝑅𝐴
𝑉𝑀
−𝐾𝐸𝑀𝐹
𝑉𝐼𝑁
𝜔
𝑇𝐿
𝑇𝑜𝑢𝑡
iA LA RA
+
VIN
_
+
VEMF _
JM
TM
TL
q,
+ VM -
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Jeff Shelton – 3 March 2015
𝐾𝑇 𝑖𝐴 𝑇𝑀 1
𝐿𝐴𝑠 + 𝑅𝐴
𝑉𝑀
−𝐾𝐸𝑀𝐹
𝑉𝐼𝑁
𝑇𝐿
𝑇𝑜𝑢𝑡 1
𝐽𝑀𝑠 + 𝑏𝑀 𝜔
Ω 𝑠 =𝐾𝑇
𝐿𝐴𝐽𝑀𝑠2 + 𝑏𝑀𝐿𝐴 + 𝑅𝐴𝐽𝑀 𝑠 + 𝑅𝐴𝑏𝑀 + 𝐾𝐸𝑀𝐹𝐾𝑇
⋅ 𝑉𝐼𝑁 𝑠
iA LA RA
+
VIN
_
+
VEMF _
JM
TM
TL
q,
+ VM -
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𝜏 = 𝐽𝜔 + 𝑏𝜔
Jeff Shelton – 3 March 2015
−𝐾𝐸𝑀𝐹
𝑉𝐼𝑁
𝑇𝐿
𝑇𝑜𝑢𝑡 1
𝐽𝑀𝑠 + 𝑏𝑀 𝜔
𝐾𝑇𝑅𝐴
𝑇𝑀 𝑉𝑀
Ω 𝑠 =𝐾𝑇
𝑅𝐴𝐽𝑀 𝑠 + 𝑅𝐴𝑏𝑀 + 𝐾𝐸𝑀𝐹𝐾𝑇⋅ 𝑉𝐼𝑁 𝑠
iA LA RA
+
VIN
_
+
VEMF _
JM
TM
TL
q,
+ VM -
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Jeff Shelton – 3 March 2015
−𝐾𝐸𝑀𝐹
𝑉𝐼𝑁
𝑇𝐿
𝑇𝑜𝑢𝑡 1
𝐽𝑀𝑠 𝜔
𝐾𝑇𝑅𝐴
𝑇𝑀 𝑉𝑀
Ω 𝑠 =𝐾𝑇
𝑅𝐴𝐽𝑀 𝑠 + 𝐾𝐸𝑀𝐹𝐾𝑇⋅ 𝑉𝐼𝑁 𝑠
iA LA RA
+
VIN
_
+
VEMF _
JM
TM
TL
q,
+ VM -
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Jeff Shelton – 3 March 2015
Time, t
Spe
ed,
𝜔𝑠𝑠
Ω 𝑠 =𝐾𝑇
𝑅𝐴𝐽𝑀𝑠+𝐾𝐸𝑀𝐹𝐾𝑇⋅ 𝑉𝐼𝑁 𝑠 ⇒
Ω 𝑠
𝑉𝐼𝑁 𝑠=
𝐺 0
𝜏𝑀𝑠+1
𝐺 0 =𝐾𝑇
𝐾𝐸𝑀𝐹𝐾𝑇=
1
𝐾𝐸𝑀𝐹
𝜏𝑀 =𝑅𝐴𝐽𝑀
𝐾𝐸𝑀𝐹𝐾𝑇
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Jeff Shelton – 3 March 2015
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Jeff Shelton – 3 March 2015
KT 1
LA s + RA
KEMF
-
+ 1 JL s + B
Power Amplifier (Driver)
VCMD VM
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Jeff Shelton – 3 March 2015
RB
RA VCMD
Bipolar Unipolar
RB
RA
VCMD VA
VM
𝑉𝐴𝑉𝑀
=𝑅𝐴
𝑅𝐴 + 𝑅𝐵
𝑉CMD =𝑅𝐴
𝑅𝐴 + 𝑅𝐵𝑉𝑀 ⇒ 𝑉𝑀 =
𝑅𝐴 + 𝑅𝐵𝑅𝐴
𝑉CMD
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Jeff Shelton – 3 March 2015
Current Amplifier (Driver) Current Measurement
Commanded Current (voltage)
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Jeff Shelton – 3 March 2015
VCMD
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Jeff Shelton – 3 March 2015
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Jeff Shelton – 3 March 2015
Electric Motors
DC Motors
Permanent Magnet
Series Wound
Compounded
Shunt Wound
Separately Excited
Brushed
Brushless
Stepper
AC Motors
Reluctance
Hysteresis
Synchronous
Induction
Wound Rotor
Squirrel Cage
Permanent Magnet
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Jeff Shelton – 3 March 2015
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Jeff Shelton – 3 March 2015
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Jeff Shelton – 3 March 2015
Commutation Brushes
Power Brushes Head (Table)
N S Channel
(Guide way)
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Jeff Shelton – 3 March 2015
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Commutation Brushes
Power Brushes Head (Table)
N S Channel
(Guide way)
Jeff Shelton – 3 March 2015
Shaft (Rotor) Angle
I1
I2
I3
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Jeff Shelton – 3 March 2015
Electric Motors
DC Motors
Permanent Magnet
Series Wound
Compounded
Shunt Wound
Separately Excited
Brushed
Brushless
Stepper
AC Motors
Reluctance
Hysteresis
Synchronous
Induction
Wound Rotor
Squirrel Cage
Permanent Magnet
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Jeff Shelton – 3 March 2015 38
Image: http://electronics.howstuffworks.com/brushless-motor.htm
Jeff Shelton – 3 March 2015 39
Image: http://www.rcuniverse.com/magazine/reviews/1344/BrushlessMotors7.jpg
Jeff Shelton – 3 March 2015
Shaft (Rotor) Angle
I1
I2
I3
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Jeff Shelton – 3 March 2015
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Jeff Shelton – 3 March 2015
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