V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed,...

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Jeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL Speed, Torque, T M NO LOAD T STALL V IN increase 1

Transcript of V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed,...

Page 1: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

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

1

Page 2: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015 2

Page 3: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015 3

Images: http://science.howstuffworks.com/transport/engines-equipment/gear2.htm http://robotshop.com

Page 4: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015 4

Images: http://www.carbibles.com/transmission_bible_pg2.html http://robotshop.com

Page 5: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

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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Page 6: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

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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

Page 7: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015 Image: https://www.sparkfun.com/products/12497

Page 8: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015 https://www.sparkfun.com/products/12310

Page 9: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015

𝑟 =NL

NM=

𝜔𝑀

𝜔𝐿

𝑟 ⋅ 𝜂 =𝑇𝐿

𝑇𝑀

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Page 10: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

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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

Page 11: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015

𝐽𝑇

𝐽𝑀𝐽𝐿𝐽𝐺𝑟

𝐽𝑇 = 𝐽𝑀 +𝐽𝐿𝑟2

"reflected inertia"

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Page 12: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015

Sometimes it takes a bit of work to convert inertia values into the proper units…

Page 13: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015

𝐽𝑀)

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Page 14: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

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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Page 15: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

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Page 16: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015 16

Images: http://electrolift.com/the-worm-gear-advantage.php http://www.longwaymotor.com/imagefile/pro/125013500416790.jpg

Page 17: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015

𝐾𝑇 𝑖𝐴 𝑇𝑀

iA LA RA

+

VIN

_

+

VEMF _

JM

TM

TL

q,

+ VM -

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Page 18: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

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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Page 19: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

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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Page 20: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

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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Page 21: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

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 -

21

𝜏 = 𝐽𝜔 + 𝑏𝜔

Page 22: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

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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Page 23: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

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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Page 24: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

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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Page 25: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015

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Page 26: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015

KT 1

LA s + RA

KEMF

-

+ 1 JL s + B

Power Amplifier (Driver)

VCMD VM

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Page 27: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

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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Page 28: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015

Current Amplifier (Driver) Current Measurement

Commanded Current (voltage)

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Page 29: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015

VCMD

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Page 30: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015

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Page 31: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

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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Page 32: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015

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Page 33: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015

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Page 34: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015

Commutation Brushes

Power Brushes Head (Table)

N S Channel

(Guide way)

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Page 35: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015

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Commutation Brushes

Power Brushes Head (Table)

N S Channel

(Guide way)

Page 36: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015

Shaft (Rotor) Angle

I1

I2

I3

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Page 37: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

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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Page 38: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015 38

Image: http://electronics.howstuffworks.com/brushless-motor.htm

Page 39: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015 39

Image: http://www.rcuniverse.com/magazine/reviews/1344/BrushlessMotors7.jpg

Page 40: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015

Shaft (Rotor) Angle

I1

I2

I3

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Page 41: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015

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Page 42: V IN GND TO COMPUTER Torque, TM V increaseJeff Shelton – 3 March 2015 V IN GND TO COMPUTER Speed, Torque, T M = 0.5 NL NO LOAD T STALL Max Power T = 0.5 T STALL

Jeff Shelton – 3 March 2015

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