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Mechanics for Motors and Generators: Lesson 5 on Torque, Speed, and Power, Summaries of Mechanics

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

  • How does torque change with position in circular motion?
  • How is torque represented?
  • How is power calculated in rotating systems?
  • How can you convert power, torque, and speed units from SI to English units?
  • What are the definitions of torque and angular speed?

Typology: Summaries

2021/2022

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6/17/2015
1
LESSON 5: MECHANICS FOR
MOTORS AND GENERATORS
ET 332a
Dc Motors, Generators and Energy Conversion
Devices
1
Learning Objectives
After this presentation you will be able to:
Explain how torque and speed is represented.
Convert power, torque and speed units from
SI to English Units
Perform simple mechanical calculations.
Identify common mechanical loads for
electrical machines.
2
pf3
pf4
pf5
pf8
pf9
pfa

Partial preview of the text

Download Mechanics for Motors and Generators: Lesson 5 on Torque, Speed, and Power and more Summaries Mechanics in PDF only on Docsity!

LESSON 5: MECHANICS FOR

MOTORS AND GENERATORS

ET 332a

Dc Motors, Generators and Energy Conversion Devices

1

Learning Objectives

After this presentation you will be able to:

 Explain how torque and speed is represented.

 Convert power, torque and speed units from

SI to English Units

 Perform simple mechanical calculations.

 Identify common mechanical loads for

electrical machines.

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 = T∙

P = power (Watts, W)

T = torque (N-m)

= angular speed (rad/sec)

W = T∙

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

18,650W

ω

P

T

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

P T

In a linear motion system

P F v

Where: F = force in Newtons (N) v = velocity in meters/second (m/s) T = torque in N-m = angular velocity (rad/s)

Since power is conserved T F v

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

P 58,434W

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

5252 P

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)