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:
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1st Stage
|
Gear |
Material |
# of Teeth |
Diameter (mm) |
|
Sun |
Metal |
18 |
14 |
|
Planet (3) |
Metal |
15 |
12 |
|
Ring |
Metal |
48 |
34 |
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2nd Stage
|
Gear |
Material |
# of Teeth |
Diameter (mm) |
|
Sun |
Metal |
21 |
16 |
|
Planet (3) |
Plastic |
12 |
10 |
|
Ring |
Plastic |
45 |
34 |
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3rd Stage
|
Gear |
Material |
# of Teeth |
Diameter (mm) |
|
Sun |
Metal |
12 |
10 |
|
Planet (3) |
Metal |
18 |
15 |
|
Ring |
Metal |
48 |
34 |
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Important Equations:
����������� 1.
����������� where:
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����������� 2.
����������� where:
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����������� 3.�
����������� 1st Stage Calculations:
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����������������������� From motor literature
operational speed of motor: 10702rpm
����������������������� ��� (since ring = 0)
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����������� 2nd Stage Calculations:
����������������� arm becomes sun2 in the next set of calculations
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����� 3rd
Stage Calculations:
����������������� arm2 becomes sun3 in the next set of calculations
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����� Gear Ratio:
57.6 : 1
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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.
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