1. Drive System Engineering
Presented by:
Ken Zaballos
FIRST Team 1983 – Skunk Works Robotics
Mechanical Engineer
Boeing Research & Technology
777X Wing Assembly Technology Development

2. Today’s Session Drive System Design Process Motor Characteristics
Lift System Case
Lift a load within a given time
Motor Characteristics
Motor Selection
Gearbox Selection
This IS the math!

3. Today’s Case: Lift Systems
ARMS
Arms, Elevators, Drivetrain
The process is the same.
ELEVATORS

4. ELEVATOR LIFT SYSTEM Motor Drivetrain Reduction Load
Chain and sprocket lift system

5. Key Performance Parameters
Drive
Sprocket ? ? ?
Motor
Drivetrain
Reduction
Figure these out when you decide how you want to play the game
? in
KPPs:
40 lbs
44 in
1 second
? lbs

6. Some Terms and Things Force = a push or pull upon an object
Torque = a twisting force that tends to cause rotation.
Voltage = an electromotive force or potential difference
Current = a flow of electrical charge
Friction = the resistance one object encounters when moving over another
Efficiency = the effectiveness of transforming power input to an output force and movement
PMDC = Permanent Magnet Brushed DC Motor

7. First, Understand Motor Characteristics

8. Key Motor Values Stall Torque Stall Current Free Current Free Speed
Torque at the output shaft when it can’t rotate
Stall Current
Current draw when the output shaft can’t rotate
Free Current
Current draw when the output shaft is free
Free Speed
Speed of the output shaft when it is free

9. Motor Data from FIRST (2015)
All 12VDC

10. A FIRST Motor Curve

11. Speed-Torque 𝜔=− 𝜔 𝑓𝑟𝑒𝑒 𝜏 𝑠𝑡𝑎𝑙𝑙 ∙𝜏+ 𝜔 𝑓𝑟𝑒𝑒 𝜔 𝑓𝑟𝑒𝑒 𝜏 𝑠𝑡𝑎𝑙𝑙 Speed (RPM)
𝜔=− 𝜔 𝑓𝑟𝑒𝑒 𝜏 𝑠𝑡𝑎𝑙𝑙 ∙𝜏+ 𝜔 𝑓𝑟𝑒𝑒
𝜔 𝑓𝑟𝑒𝑒
Speed (RPM)
𝜏 𝑠𝑡𝑎𝑙𝑙
Torque (Oz-In)
CONVERT TO SI UNITS FOR CALCULATIONS!

12. Power-Torque P=Torque*Speed P = 𝜏∙𝜔 (𝜏, 𝜔) Power (Watts) Speed (RPM)
Torque (Oz-In)
CONVERT TO SI UNITS FOR CALCULATIONS!

13. Power-Torque ( 𝑷 𝒎𝒂𝒙 , 𝝉 𝒔𝒕𝒂𝒍𝒍 𝟐 ) Max Power Power (Watts) Speed (RPM)
( 𝑷 𝒎𝒂𝒙 , 𝝉 𝒔𝒕𝒂𝒍𝒍 𝟐 )
Power (Watts)
Speed (RPM)
Torque
CONVERT TO SI UNITS FOR CALCULATIONS!

14. Current-Torque 𝑖= 𝑖 𝑠𝑡𝑎𝑙𝑙 −𝑖 𝑓𝑟𝑒𝑒 𝜏 𝑠𝑡𝑎𝑙𝑙 ∙𝜏+ 𝑖 𝑓𝑟𝑒𝑒 𝑖 𝑠𝑡𝑎𝑙𝑙 𝑖 𝑓𝑟𝑒𝑒
𝑖= 𝑖 𝑠𝑡𝑎𝑙𝑙 −𝑖 𝑓𝑟𝑒𝑒 𝜏 𝑠𝑡𝑎𝑙𝑙 ∙𝜏+ 𝑖 𝑓𝑟𝑒𝑒
𝑖 𝑠𝑡𝑎𝑙𝑙
Current (Amps)
Power (Watts)
Speed (RPM)
𝑖 𝑓𝑟𝑒𝑒
Torque
Torque
CONVERT TO SI UNITS FOR CALCULATIONS!

15. Efficiency e = 𝜏∙𝜔 𝑖∙𝑉 Mechanical Power = 𝜔 ∙ τ
Electrical Power = 𝑖 ∙ 𝑉
Efficiency = Mechanical Power / Electrical Power
e = 𝜏∙𝜔 𝑖∙𝑉
Efficiency (%)
Current (Amps)
Power (Watts)
Speed (RPM)
Torque
Torque
CONVERT TO SI UNITS FOR CALCULATIONS!

16. Efficiency e = 𝜏∙𝜔 𝑖∙𝑉 Efficiency (%) Current (Amps) Power (Watts)
Speed (RPM)
Torque
Torque
CONVERT TO SI UNITS FOR CALCULATIONS!

17. Efficiency e = 𝜏∙𝜔 𝑖∙𝑉 NEVER DESIGN TO THE RIGHT OF PEAK POWER!
Peak Efficiency
e = 𝜏∙𝜔 𝑖∙𝑉
Efficiency (%)
Current (Amps)
Power (Watts)
Speed (RPM)
Smoke!
Torque
Torque
CONVERT TO SI UNITS FOR CALCULATIONS!

18. Motor Data from FIRST (2015)
Not necessarily at a usable current

19. MOTOR PRIORITIES Rank motors by power @ 30 amps Eliminate weak motors
Make
Name
Max Power (w)
30A
30A
30 A
Stall Torque (oz-in)
Stall Torque (N-m)
Free Speed (rpm)
Free Current (A)
Stall Current (A)
Vexpro
775Pro
346.3
237.5
0.16
14590
100.2
0.71
18700
0.7
134
BaneBots
RS-775 Motor
266.6
236.6
0.26
8682
110.9
0.78
13000
1.8
86.7
AndyMark
CIM
337.1
223.3
0.51
4197
343.4
2.42
5310
2.7
133
RS-550 Motor
245.7
221.2
0.17
12697
68.9
0.49
19300
1.4 85
VEX
Mini CIM Motor
227.2
203.2
0.47
4109
198.3
1.40
6200
1.5 86
9015 Motor
179.4
178.2
0.20
8639
60.6
0.43
16000
1.2
63.8
BAG Motor
146.6
118.4
0.29
3929
56.6
0.40
14000 41
Snow Blower Motor
29.6
-49.2
14.87
-32
1600.0
11.30
100 5 24
Denso
Window Motor
23.3
-64.2
15.57
-39
1501.1
10.60 84 21
RS775-5 Motor
36.9
-75.8
0.34
-2131
35.0
0.25
5700
0.6 22
RS Motor
-106.2
17.79
-57
18.6
Throttle Motor
18.0
0.63
-20317
18.4
0.13
5300 1 7
Eliminate weak motors

20. Back to the Lift Design

21. How much power do we need?
Hint: Convert to SI units! ?
𝒑𝒐𝒘𝒆𝒓= 𝒘𝒐𝒓𝒌 𝒕𝒊𝒎𝒆 ? ?
𝒘𝒐𝒓𝒌=𝒇𝒐𝒓𝒄𝒆∙𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆
KPPs:
40 lbs = N
44 in = m
1 seconds
𝒑𝒐𝒘𝒆𝒓= 𝒇𝒐𝒓𝒄𝒆∙𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒕𝒊𝒎𝒆
𝒑𝒐𝒘𝒆𝒓= 𝟏𝟕𝟕.𝟗𝑵∙𝟏.𝟏𝟏𝟖𝒎 𝟏 𝒔𝒆𝒄
44in
𝒑𝒐𝒘𝒆𝒓=𝟐𝟐𝟔 𝒘𝒂𝒕𝒕𝒔
40 lbs
We need a motor that can deliver AT LEAST 226 watts.

22. We Choose … Make Name Max Power (w) Power @ 36A Stall Torque (oz-in)
Stall Torque (N-m)
Free Speed (rpm)
Free Current (A)
Stall Current (A)
BaneBots
RS-775 Motor
266.8
256.5
110.9
0.783
13000
1.8
86.7

23. Max Motor Torque (Design)
𝜏 𝑚𝑜𝑡𝑜𝑟 = Torque at max allowed current
𝑖 𝑚𝑎𝑥 = Maximum allowed current draw
𝜏 𝑠𝑡𝑎𝑙𝑙 = Stall torque
𝑖 𝑓𝑟𝑒𝑒 = Motor free current
𝑖 𝑠𝑡𝑎𝑙𝑙 = Motor stall current
𝑖= 𝑖 𝑠𝑡𝑎𝑙𝑙 −𝑖 𝑓𝑟𝑒𝑒 𝜏 𝑠𝑡𝑎𝑙𝑙 ∙𝜏+ 𝑖 𝑓𝑟𝑒𝑒
𝜏 𝑚𝑜𝑡𝑜𝑟 = 𝜏 𝑠𝑡𝑎𝑙𝑙 ∙( 𝑖 𝑚𝑎𝑥 − 𝑖 𝑓𝑟𝑒𝑒 ) 𝑖 𝑠𝑡𝑎𝑙𝑙 − 𝑖 𝑓𝑟𝑒𝑒
The Algebra is left to the student as an exercise!

24. Calculate Max Motor Torque (Design)
𝑖 𝑚𝑎𝑥 = 30 amps (a design choice)
𝜏 𝑠𝑡𝑎𝑙𝑙 = 0.78 Nm (from motor data)
𝑖 𝑓𝑟𝑒𝑒 = 1.8 amps (from motor data)
𝑖 𝑠𝑡𝑎𝑙𝑙 = 86.7 amps (from motor data)
𝜏 𝑚𝑜𝑡𝑜𝑟 = 𝜏 𝑠𝑡𝑎𝑙𝑙 ∙( 𝑖 𝑚𝑎𝑥 − 𝑖 𝑓𝑟𝑒𝑒 ) 𝑖 𝑠𝑡𝑎𝑙𝑙 − 𝑖 𝑓𝑟𝑒𝑒
𝜏 𝑚𝑜𝑡𝑜𝑟 = 0.78∙(30−1.8) 86.7−1.8 =0.26𝑁𝑚

25. Calculate Torque on the Output Shaft
𝝉 𝒔𝒉𝒂𝒇𝒕
Sprocket:
#25, 16T
0.26 Nm ?
2.88 Nm ?
P.D.
𝜏 𝑠ℎ𝑎𝑓𝑡 = 𝐹 𝑙𝑜𝑎𝑑 ∙ 𝑃.𝐷. 2
𝜏 𝑠ℎ𝑎𝑓𝑡 =40𝑙𝑏𝑠∙ 1.273𝑖𝑛 2
𝜏 𝑠ℎ𝑎𝑓𝑡 =25.46𝑖𝑛𝑙𝑏𝑠
𝑭 𝒍𝒐𝒂𝒅
𝝉 𝒔𝒉𝒂𝒇𝒕 =𝟐.𝟖𝟖𝑵𝒎
44in
16T, #25 Chain (Design Choice)
40 lbs

26. What is a Gear Reduction?
A gearbox REDUCES speed
A gearbox INCREASES torque
Motor Drives Small Gear

27. Ratios in gear trains 𝝎𝟐 𝝎𝟏 = 𝒏𝟐 𝒏𝟏 = 𝒅𝟏 𝒅𝟐 = 𝑵𝟏 𝑵𝟐 F t1 ,w1 r1 r2
t1 = r1 * F
v = r1 * w1
t2 = r2 * F
v = r2 * w2
t2 = (r2 / r1) * t1
w2 = (r1 / r2) * w1
Increases Torque
Reduces Speed

28. Find Required Gearbox Reduction
0.26 Nm
2.88Nm ?
𝝉 𝒔𝒉𝒂𝒇𝒕 =𝝉 𝒎𝒐𝒕𝒐𝒓 ∙𝑹 𝒈𝒆𝒂𝒓𝒃𝒐𝒙
𝑹 𝒈𝒆𝒂𝒓𝒃𝒐𝒙 = 𝝉 𝒔𝒉𝒂𝒇𝒕 𝝉 𝒎𝒐𝒕𝒐𝒓
Gearbox
Reduction?
𝑹 𝒈𝒆𝒂𝒓𝒃𝒐𝒙 = 𝟐.𝟖𝟖𝑵𝒎 𝟎.𝟐𝟔𝑵𝒎
𝑹 𝒈𝒆𝒂𝒓𝒃𝒐𝒙 =𝟏𝟏.𝟏
40 lbs
THIS WOULD BE A BIG MISTAKE!

29. Mechanical Efficiency
Friction (primary source of inefficiency)
Gear meshing (center-center distance)
Gear form accuracy
Lubrication
Cleanliness
Bearings
Rules of thumb*
Sprocket (chain) = 95%
Spur gear stage = 95%
Planetary Stage = 75%
Depends on the number of planets, lubrication, quality
Worm gear = 60%
*-YOUR ASSUMPTIONS MAY VARY
Involute gear form

30. Find Required Gearbox Reduction (considering mechanical efficiency)
𝝉 𝒔𝒉𝒂𝒇𝒕 =𝝉 𝒎𝒐𝒕𝒐𝒓 ∙𝑹 𝒈𝒆𝒂𝒓𝒃𝒐𝒙 ∙𝜺
0.32 Nm
2.88Nm ?
𝑹 𝒈𝒆𝒂𝒓𝒃𝒐𝒙 = 𝝉 𝒎𝒐𝒕𝒐𝒓 𝝉 𝒅𝒆𝒔𝒊𝒈𝒏∙ 𝜺
Stage 1
Stage 2
Sprocket
Carriage
Gearbox
Reduction?
𝜺=𝟕𝟓%∙𝟕𝟓%∙𝟗𝟓%∙𝟖𝟎%=𝟒𝟑%
𝑹 𝒈𝒆𝒂𝒓𝒃𝒐𝒙 = 𝟐.𝟖𝟖𝑵𝒎 𝟎.𝟐𝟔𝑵𝒎∙𝟒𝟑%
𝑹 𝒈𝒆𝒂𝒓𝒃𝒐𝒙 =𝟐𝟓.𝟖
Vexpro
planetary
gearbox
Pick the nearest BIGGER
reduction you can make.
40 lbs
2 stages :1and 9:1 = 27:1
2 stages :1and 7:1 = 28:1
(more durable)

31. Is this good enough? No? Design is all about tradeoffs Finally,
Decrease Gearbox Load (can be difficult)
Increase Gearbox Power (use bigger motor or add a motor)
Live with the low speed…
Risk failure
Design is all about tradeoffs
Finally,
Design for one motor (torque and speed)
Then, add another motor!
Factor of Safety = 2!

32. Important things to consider
Motors are 12VDC
Batteries are only 12VDC once during a match!
Circuits are limited to 20, 30 and 40 amps.
Motor Controller (PWM)
Pulse Wave Modulation – understand how it works
PID control
Proportional-Integral-Differential – understand how it works and practice tuning them.
Mechanical efficiency of the things you build
Accuracy and quality play huge roles
Typically, make your system go FAST!

33. Important Equations Speed at a given torque Current at a given torque
𝜔 𝑚𝑜𝑡𝑜𝑟 =− 𝜔 𝑓𝑟𝑒𝑒 𝜏 𝑠𝑡𝑎𝑙𝑙 ∙𝜏+ 𝜔 𝑓𝑟𝑒𝑒
Speed at a given torque
𝑖= 𝑖 𝑠𝑡𝑎𝑙𝑙 −𝑖 𝑓𝑟𝑒𝑒 𝜏 𝑠𝑡𝑎𝑙𝑙 ∙𝜏+ 𝑖 𝑓𝑟𝑒𝑒
Current at a given torque
Power output
P = 𝜏∙𝜔
e = 𝜔∙𝜏 𝑖∙𝑉
Motor efficiency
𝜏 𝑑𝑒𝑠𝑖𝑔𝑛 = 𝜏 𝑠𝑡𝑎𝑙𝑙 ∙( 𝑖 𝑚𝑎𝑥 − 𝑖 𝑓𝑟𝑒𝑒 ) 𝑖 𝑠𝑡𝑎𝑙𝑙 − 𝑖 𝑓𝑟𝑒𝑒
Torque at Design current
𝑅 𝑔𝑒𝑎𝑟𝑏𝑜𝑥 = 𝜏 𝑠ℎ𝑎𝑓𝑡 𝜏 𝑑𝑒𝑠𝑖𝑔𝑛∙𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦
Gearbox reduction
𝜔 𝑠ℎ𝑎𝑓𝑡 = 𝜔 𝑚𝑜𝑡𝑜𝑟 𝑅 𝑔𝑒𝑎𝑟𝑏𝑜𝑥
Output Shaft Speed
𝑡 𝑙𝑖𝑓𝑡 = 𝜔 𝑠ℎ𝑎𝑓𝑡 ∙𝜋∙𝑃.𝐷. ℎ 𝑙𝑖𝑓𝑡
Time to lift

34. Useful Websites www.andymark.com (robot marketplace)
(robot marketplace)
(motors and gearboxes)
(electronics)
(technical and social)
(raw material)
(everything else)

35. THE END GOOD LUCK! WE’LL SEE AT THE COMPETION, or sooner if you want some help!