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A lesson from ET 332a, Dc Motors, Generators and Energy Conversion Devices, focusing on mechanics for motors and generators. It covers topics such as speed definitions and unit conversions, force and torque, circular motion and torque, work and power, and English-SI unit conversions. Students will learn how to explain torque and speed representation, convert power, torque, and speed units, perform mechanical calculations, and identify common mechanical loads for electrical machines.
What you will learn
Typology: Summaries
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ET 332a
Dc Motors, Generators and Energy Conversion Devices
1
2
SPEED DEFINITIONS AND UNIT
CONVERSIONS
3
Angular speed (radians/second)
dt
d
= angular speed (radians/sec)
= arc length (radians)
Standard for motors and generators Revolutions per minute (RPM)
rad/sec used in calculations
Conversions
rad/sec to RPM RPM to rad/sec
2
60 n n 60
FORCE AND TORQUE
4
Torque
Force
r
Lever arm
Perpendicular
Torque – ”twisting force
Units SI (N-m)
English (ft-lb)
Definitions
Torque =(applied force)∙(perpendicular distance)
T F(rsin())
Vector representation
CIRCULAR MOTION AND TORQUE
7
Torque changes with position in circular motion
0 deg 180 deg
90 deg
270 deg
rotation
F
r
F
F
F
F
d
d =0 T = 0 at 90 and 270
deg = 0o
d=r and T = max at 0 180 deg = 90o
WORK AND POWER
8
Energy dissipates and work occurs when a force acts on
a mass
Force = (Mass)(Acceleration of gravity) = Weight
Lifting a weight requires work and dissipates energy
Work = (Force)(Distance) Linear Systems
W (Joules) = F (Newtons) X D (Meters)
D
Mass (M)
F
Power is how fast work is done
Rate of energy consumption
Power = Work/Time
P (Watts) = W (Joules)/ t (seconds)
9
WORK AND POWER IN ROTATING SYSTEMS
Work in rotating system
P = power (Watts, W)
T = torque (N-m)
= angular speed (rad/sec)
T = torque (N-m)
= angular distance (m)
Power in rotating system
10
ENGLISH-SI UNIT CONVERSIONS
English Units Power = Horsepower (HP) Torque = (lb-ft)
SI Units Power = Watts or Kilowatts (W, kW) Torque = Newton-Meters (N-m)
Mechanical Power Conversion- Watts to Hp
Conversion factor: 1 hp = 746 watts
P(W) P(hp) 746 W/hp hptoWatts
Wattstohp 746 W/hp
P(W) P(hp)
13
UNIT CONVERSION EXAMPLES
Example 1: A motor develops 25 Hp at the shaft at a
speed of 1750 rpm. Find the torque (N-m) developed
and the power output in Watts
Make power unit conversion. HP=25 hp
P 746 W/hpHP 746 W/hp 25 hp 18 , 650 W
Find torque by converting n in rpm to in radians /second
1750 rpm 183.17 rad/s 60
2 π ω
101.8N-m 183.17rad/s
ω
14
UNIT CONVERSION EXAMPLES
Example 2: A generator delivers 50 kW of power at
170 rad/s. What horsepower and torque (ft-lb) should
the drive engine have.
Convert power in watts to hp. Remember 50 kW = 50,000 W
hp W/hp
, W
W/hp
P HP 67 746
50000
746
To find torque in lb-ft, convert the speed into rpm
n 170 rad/s 1624. 2 rpm 2
60
2
60
Now you can find torque
with these two equations n
. P T
704 or n
5252 P T
216.7lb-ft 1624.7rpm
525267 hp T
216.7lb-ft 1624.2rpm
T 7.0450,000W
MECHANICS FOR MOTORS AND GENERATORS
15
Power is conserved in a lossless mechanical system. (Need consistent units)
In a rotational motion system
In a linear motion system
Where: F = force in Newtons (N) v = velocity in meters/second (m/s) T = torque in N-m = angular velocity (rad/s)
16
MECHANICS FOR MOTORS AND GENERATORS
Example 3: A small electric locomotive develops 620
N-m of torque at 900 rpm as it moves at a speed of 15
mph. Determine the power, in horsepower, and Watts
this requires. Also compute the force opposing the
locomotive.
Compute rotational power
900 rpm 60
2 π P T 620 N- m
Convert to horsepower
. hp 746 W
hp , W 746 W
hp HP P 783
1 58434
1
19
MECHANICS FOR MOTORS AND GENERATORS
Example 4 continued
Remember the torque definition T Fd
Where d is distance to center of rotation (half the diameter)
1062.5lb-ft 12 in/ft
15in T 850 lb
5 in
0 in d 1 2
3
Find the speed from n
T Solve this for n, speed in rpm
n T
5252 P
n
1
5252 P
T
. rpm n
n 1062.5lb-ft
5252 5.409hp
2674
MECHANICAL LOADS FOR MOTORS
20
Constant Speed - motor must maintain constant speed
over wide range of torque loading.
Examples: machine tools (lathes, Mills etc) rolling mills (steel production)
21
MECHANICAL LOADS FOR MOTORS
Constant Torque - motor works against constant
force. Weight of load does not change.
Examples: Hoisting, conveyors
22
MECHANICAL LOADS FOR MOTORS
Constant Power - Mechanical characteristic of the
load change (size, weight). Torque and speed change
Example: Winding operations (cable, wire)
