DC Motor Selection Study

Sojourner F17 | By Zach Oyog

[1]

DC Motor Calculations and Comparisons:

The objective of this study is to compare different dual-shaft micro metal gear motors and replace the current dc micro metal gearmotors on the Sojourner Rover [9].  The criteria include motor dimensions like that of the current motors, high stall torque, low stall current, dual-shaft design. Since the rover will need six motors, the current draw must be as low as possible while maintaining a good speed-torque ratio. All the motors selected for the tradeoff study are micro gear dc motors, they were chosen because of their relatively low mass and volume.

Discussion:

The micro gear motors chosen from Spring ’17 were ideal due to their compact size and low power consumption, i.e. current draw [9]. However, the current sojourner rover design requires a slip differential for each motor, color sensors, a proximity sensor, and a phone mount/solar panel mount module which creates additional weight. The reason for replacing current N20 motors is the need of Hall Effect sensors, the sensors require a dual shaft motor design for a magnetic disk to rotate at the same speed as the main shaft.

Another concern when deciding on the gear-motor is the amount of current drawn at the stall torque, also known as stall current. The current draw needs to be as low as possible while maintaining enough torque and enough speed. Due to the low current requirement, a low ratio of the load torque to the stall torque will yield a low ratio of current drawn compared to the stall current. Meaning the motor needs to have a high stall torque compared to the load torque and a relatively low stall current.

An alternative to the Pololu gear-motor is the DF Robotics motor, this motor has the same dimensions as the current N20 gear-motor and Pololu gear-motor. Unlike the Pololu model, the DF Robotics model includes an attached Hall Effect rotary encoder, but the encoder is much larger than the Pololu which would require a redesign of the suspension motor mounts. Another issue with the DF Robotics model is that the stall current is not given but instead a current rating at 170mA [3]. However, a stall current was measured from a forum community member albeit for a model like that of the 210:1 DF Robotics model at 480mA [12].

Motor Characteristics:

Manufacturer Specified Characteristics
Values: Motor 1 Motor 2 Present Motor Used
Voltage (V) 6 6 5
No Load Speed (rpm) 45 75 30
No Load Current (mA) 40 60 Not Given/ Unknown
Stall Current (mA) 360 ~480 Not Given/ Unknown
Stall Torque (Kgf*cm) 2.9 2.8 Not Given/Unknown
Price ($) 16.95 12.19 0

 

 

 

 

 

 

 

(1) Pololu 250:1 Micro Metal Gearmotor LP 6V [2]

Voltage: 6V

No load speed (): 45 rpm

No load current (): 40mA

Stall current (): 360mA

Stall torque ():  40oz-in (2.9kgf-cm)

Price: $16.95

(2) DF Robotics 210:1 Micro Metal Gearmotor LP 6V w/ encoder [3]

Voltage: 6V

No load speed (Nnl): 75 rpm

No load current (Inl): 60mA

Stall current (Istall): 480mA [?]

Stall torque (Tstall):  2.8kgf-cm

Price: $12.19

(3) Current Motor: N20 Micro Metal Gearmotor LP 6V [9] [10] [11]

Voltage: 5V

No load speed (Nnl): 30 rpm

No load current measured (Inl): 14.7mA

Armature current measured (Ia): 16.9mA
Note: torque values were not listed, rough calculations unsing measured current values were made to compensate for missing information.

Price: $0.00 (current motors)

Equations:
Constants and known values:
Mass per motor: mr=mt6=.075 [kg] where mt=.450 kilograms [4]
Radius: r=1.3cm [5]
Acceleration due to gravity: g=9.81 ms2

Torque load: TL=(r*g)*mr [N*cm]  [5]

Motor torque constant:  KT=TstallIstall= TLIa [N*cmmA]   where Ia=armature current [mA]. [6]

Mechanical Power: Pmo=ωL*TL [mW]

Electrical Power: Pe=Pmo+Ploss=Pmo where Ploss=loss of power due to friction    Pe =V*Ia [mW]

Angular velocity: ωL= 2πNL60 [rads]

Linear Velocity: vL= ωL*r[cms] [7]

Methodology:
After calculating the torque load equation for allocated mass per motor, mr , the armature current can be found by manipulating the motor torque constant equation. The angular velocity can also be derived from relating the mechanical power to the electrical power, to allow this comparison the power losses, Ploss, from friction and the iron core have been negated.

Load torque required to rotate the wheel,
TL=(r*g)*mr
TL=.9565 [N*cm] = 1.355 [Oz-in] = .09757 [Kgf-cm]

Theoretical values at  TL
Motor Motor Torque Constant
[N*cm/mA]
Current
[mA]
Angular Velocity
[rad/s]
Linear Velocity [cm/s]
1 0.07846 12.191 6.373 8.285
2 0.05721 16.719 10.488 13.34
3 0.0560 16.9 8.834 11.48

Conclusion:

Each of the selected motors have sufficient torque to ensure that the rover has enough traction with the maze surface, and the current draw is low enough to stay in accordance with the preliminary power budget [8]. The information missing from the datasheet was calculated from the voltage and measured current at both no load and with a load mass load. Due to the missing stall current information for the DF Robotics model, the Pololu motors would be the best option in terms of current consumption.

Resource:

  1. https://www.pololu.com/category/60/micro-metal-gearmotors
  2. https://www.pololu.com/product/1094/specs
  3. http://www.robotshop.com/en/6v-2101-75rpm-micro-metal-gearmotor-encoder.html#
  4. http://arxterra.com/sojourner-preliminary-documentation-fall-2017/#toggle-id-20
  5. https://www.pololu.com/product/1096/faqs
  6. https://www.precisionmicrodrives.com/tech-blog/2013/09/23/torque-calculations-gearmotor-applications
  7. http://www.engineeringtoolbox.com/motion-formulas-d_941.html
  8. http://arxterra.com/sojourner-preliminary-documentation-fall-2017/#toggle-id-19
  9. http://arxterra.com/mini-pathfinder-spring-2017-motor-trade-off-study/
  10. http://arxterra.com/spring-2017-mini-pathfinder-motor-no-load-current-and-voltage-test/
  11. https://www.ebay.com/itm/131747528794?_trksid=p2060353.m2749.l2649&ssPageName=STRK%3AMEBIDX%3AIT
  12. https://www.dfrobot.com/forum/viewtopic.php?f=12&t=3086&p=12385&hilit=Stall+current#p12385