APPENDIX B

 

B.1 TORQUE CALCULATIONS

This section consists of the torque calculations for motor and gearing requirements. The initial calculations were determined using revised weights and measurements from the 1999-2000 teams design. These calculations were then updated as the design progressed and changed. The calculations take into consideration the length, center of gravity, and weight for each part of the arm. These calculations are somewhat approximated but accurate enough for motor and gear selection.

 

Weights (lbs)

Lengths (in)

A

15.0

a

5

B

4.00

b

25.5

C

3.00

c

33.0

 

 

x

15.50

 

 

y

14.56

 

 

 

 

Weights (lbs)

Lengths (in)

B

4.00

b-x

10.0

C

3.00

c-x

17.5

 

 

 

 

Shoulder

Motor

494.0

lb-in

Elbow

Motor

214.0

lb-in

 

 

 

 

 

Application Factor =

1.5

 

Load =

3.3 lbs

 



 

B.2 GEAR RATIO CALCULATIONS FOR FIRESTORM 18V DRILL MOTOR

Necessary Dimensions:

 

1st Stage

Gear

Material

# of Teeth

Diameter (mm)

Sun

Metal

18

14

Planet (3)

Metal

15

12

Ring

Metal

48

34

 

 

 

2nd Stage

Gear

Material

# of Teeth

Diameter (mm)

Sun

Metal

21

16

Planet (3)

Plastic

12

10

Ring

Plastic

45

34

 

 

3rd Stage

Gear

Material

# of Teeth

Diameter (mm)

Sun

Metal

12

10

Planet (3)

Metal

18

15

Ring

Metal

48

34

 

 

 

 

 

Important Equations:

 

1.

where:

 

2.

where:

3.

 

1st Stage Calculations:

From motor literature operational speed of motor: 10702rpm

 

(since ring = 0)

 

 

2nd Stage Calculations:

 

*arm becomes sun2 in the next set of calculations

 

 

 

3rd Stage Calculations:

 

*arm2 becomes sun3 in the next set of calculations

 

 

 

Gear Ratio:

 

57.6 : 1

 

 

Power loss in Gear Train of Firestorm 18V drill:

 

Input power from motor:

 

where:

T = Motor torque in Nm

n = Motor speed in RPM

 

 

The resultant force between the sun and planet gears, Fs, can be calculated at each mesh assuming 2% losses per mesh. A free body diagram of the gear train is displayed in Figure B.2. From static analysis of this diagram the relationship between the force Fs and the force transferred to the arm, Fa. The relationships for Fs and Fa are as follows:

 

where:

Ts = Torque in the sun gear

rs = Sun gear radius

 

Figure B.2 Planetary Gear Train Free Body Diagram

 

We calculate that 1.24Nm is transferred to the 2nd sun gear, 3.63Nm is transferred to the 3rd sun gear, and that the output torque is 13.5Nm. Since the output speed is 185.74 rpm, the power at the exit of the gearbox is 263 Watts.

 


Table of Contents

Appendix A
Appendix C