types and calculations
DESCRIPTION
Elements of Power CIM Elements of Automation Power What is Work and Power? Work is the energy transferred when a force displaces a mass Power is the rate at which work is done Typically mechanical, electrical, or fluid Work is the energy transferred when a force, F, is applied to an object moving through a distance, d. Power is the rate at which work is done. There are many examples of devices that use power in one form and convert it into another. This presentation will focus on mechanical, electrical, and fluid devices. Project Lead The Way, Inc. Copyright 2008TRANSCRIPT
Types and Calculations
Elements of Power Types and Calculations Computer Integrated
Manufacturing 2013 Project Lead The Way, Inc. Elements of Power CIM
Elements of Automation Power What is Work and Power? Work is the
energy transferred when a force displaces a mass Power is the rate
at which work is done Typically mechanical, electrical, or fluid
Work is the energy transferred when a force, F, is applied to an
object moving through a distance, d. Power is the rate at which
work is done. There are many examples of devices that use power in
one form and convert it into another. This presentation will focus
on mechanical, electrical, and fluid devices. Project Lead The Way,
Inc. Copyright 2008 Mechanical Calculations
Elements of Power CIM Elements of Automation Power Mechanical
Calculations W =F d W = work, measured as ft-lb P = power measured
as ft-lb/s t = time measured as s 1 hp = 550 ft-lb/s Work is
calculated by multiplying force times displacement. It is expressed
as ft-lb. Power is the rate with which work is done and is
calculated as a ratio of work divided by time. It is expressed as
ft-lb/s. If the amount of work remains constant then power and time
are inversely proportional. In other words, if less is power used
then more time is needed. Inversely, if more is power used then
less time is needed. One horsepower is the amount of power required
to displace 33,000 pounds one foot in one minute. To calculate the
work in one second, you would divide by 60 since there are 60
seconds in one minute. Therefore, 33,000 / 60 = 550. So the power
required to displace 33,000 pounds one foot in one minute is equal
to the power required to displace 550 pounds one foot in one
second. Project Lead The Way, Inc. Copyright 2008 Elements of Power
CIM Elements of Automation Power Example If Jessica moves her 112
pound (lb) body up 8 feet (ft) of stairs in 2.3 seconds (s), how
much work did she perform? How much power did she use? ( ) ft-lb 1
hp W =F d W = 112 lb (8 ft) W = 896 ft-lb Php = 390 s 550 ft-lb s
Php = 0.71 hp The units ft-lb/sec is converted into horsepower (HP)
using the conversion factor of 550 as presented previously. W P= t
896 ft-lb P = 2.3 s ft-lb s P = 390 Project Lead The Way, Inc.
Copyright 2008 Elements of Power CIM Elements of Automation Power
Your Turn An escalator moves 84 people per minute from one floor of
a mall to the second floor. The malls floors are 24 ft apart, and
the average passenger weighs 154 lb. How much power does the
escalator need? Write the formula. Then identify and substitute
your unknowns. Project Lead The Way, Inc. Copyright 2008 ( )
Solution F = 154 lb/person 84 people F = 12,936 lb W = F d
Elements of Power CIM Elements of Automation Power Solution F = 154
lb/person 84 people F = 12,936 lb W =F d W = 12,936 lb (24 ft) W =
310,464 ft-lb W P= t 310,464 ft-lb P = 60 s P = 5174 ft-lb s ( )
ft-lb 1 hp P (hp) = 5174 s 550 ft-lb s P (hp) = 9.4 hp Project Lead
The Way, Inc. Copyright 2008 Torque Torque, , is a twisting force
on a shaft
Elements of Power CIM Elements of Automation Power Torque Torque, ,
is a twisting force on a shaft Torque measured as in.-lb or ft-lb =
dFsin A force applied at 90 degrees allows the formula to be
simplified to = dF Examples of torque can be seen in a wrench or an
engine. The Greek letter (Tau), which is usually pronounced so that
it rhymes with now but can also be pronounced so that it rhymes
with law, is used to denote torque. r is the length of the radius,
defined as the distance from the pivot to the point at which the
force is being applied. This is why r can be changed to d for
distance, not diameter. F is the force applied. sin is a
trigonometric function, relating the sides of a right triangle,
which would be formed if a vertical line were drawn from the lever
to the ending line. For a 90 degree angle, sin = 1, which is why
that part of the equation is reduced with simplification. r = 90 F
Project Lead The Way, Inc. Copyright 2008 Elements of Power CIM
Elements of Automation Power Finding Torque 116 pounds of force is
applied at the end of a lever 2.4 feet long. The force is applied
at an angle of 90 to the lever. What is the torque produced? 90 116
lb 2.4 ft pivot Project Lead The Way, Inc. Copyright 2008 Torque
Calculation 116 lb 2.4 ft 90 pivot d= 3 ft =dFsin F=100 lb
Elements of Power CIM Elements of Automation Power Torque
Calculation 90 116 lb 2.4 ft pivot d= 3 ft =dFsin F=100 lb =2.4 ft
116 lb sin90 =278 ftlb Project Lead The Way, Inc. Copyright 2008
Elements of Power CIM Elements of Automation Power Power
Calculations Using the previous problem, how much power will be
generated if the force is applied at a rate of 42 rpm? Convert rpm
to rad/s =42 1 60 2 1 =4.40 P=1222 ftlb sec1 hp 550ftlb s
Converting torque to horsepower is not as straightforward as
ft-lb/sec. The angular velocity is measured in radians per seconds
so must convert rpm into rad/sec to use the power formula. P= P=278
ftlb P= 2.2 hp P=1222ftlb Convert hp Project Lead The Way, Inc.
Copyright 2008 Elements of Power CIM Elements of Automation Power
Your Turn A shaft has a force of 32 pounds applied 5.2 feet from
the pivot point. What is the resulting torque? How much power is
generated if the torque is produced at 2,850 rpm? Project Lead The
Way, Inc. Copyright 2008 Solution F=32 lb =dFsin r=d = 5.2 ft =5.2
ft 32 lb sin90
Elements of Power CIM Elements of Automation Power Solution F=32 lb
=dFsin r=d = 5.2 ft =5.2 ft 32 lb sin90 =166 ftlb Rate of rotation=
2,850 rpm Convert rpm to rad/s =2,850 1 60 2 1 =298 P=49,637 ftlb
s1 hp 550ftlb s P= P=166 ftlb 298 P= 90 hp P=49,637ftlb Convert to
horsepower Project Lead The Way, Inc. Copyright 2008 Electrical
Work and Power
Elements of Power CIM Elements of Automation Power Electrical Work
and Power Commonly measured as watt (W) Also measured as joule or
horsepower A joule is a measurement of electrical work in the
International System of Units (SI).One watt is equal to one joule
per second. Project Lead The Way, Inc. Copyright 2008 Electrical
Calculations
Elements of Power CIM Elements of Automation Power Electrical
Calculations Electrical power is determined by the formula P = IV P
= power Measured as watt (W) and horsepower (hp) Students should
know that kW means for kilowatt, or 1000 W. Note that power can
also be expressed as a function of electrical resistance measured
in ohms. Apply the equation V = IRfor two alternate equations: P =
(I^2)R or P = (V^2)/R 1 hp = W 1 W = hp V = voltage measured as
volt (V) I = current measured as ampere (A) Project Lead The Way,
Inc. Copyright 2008 Electrical Calculations
Elements of Power CIM Elements of Automation Power Electrical
Calculations A house is wired such that a typical circuit can allow
15 A. Which two appliances can be used simultaneously without
blowing a circuit? P = IV Hair dryer (1500 W, 110 V) Microwave
(1600 W, 120 V) Toaster (400 W, 110 V) Coffee maker (250 W, 120 V)
Dishwasher (1300 W, 120 V) Flat iron (72 W, 110 V) 13.6 A 13.3 A
3.6 A 2.1 A 10.8 A 0.65 A The hairdryer and microwave must be used
alone. All other combination of two appliances would work. Project
Lead The Way, Inc. Copyright 2008 Elements of Power CIM Elements of
Automation Power Your Turn Assume that a shop is wired so that a
typical circuit is 20 amps. Which appliances can be used
simultaneously? P = IV 1 hp = W 7 A 1.7 A 16 A 3.3A 2.1 A 7.3 A
Band saw (1 hp, 110 V motor) CNC laser (200 W, 120 V) Laser
engraver (3500 W, 220 V) Light (each) (400 W, 120 V) Computer (250
W, 120 V) 3D printer (1600 W, 220 V) If more than one light is
used, then the combinations would change. This activity gives you
practice in applying electrical power calculations; however in
practice heavy machinery often requires a dedicated circuit.
Combination ABDE, ABEF, ADEF, BDEF, BC, CD, CE or any subset
Project Lead The Way, Inc. Copyright 2008 Fluid Power Operated by
compressed fluid Low load-carrying capacity
Elements of Power CIM Elements of Automation Power Fluid Power
Operated by compressed fluid Low load-carrying capacity Requires
mechanical stops if not used with servomotors Two types: hydraulic
and pneumatic Pneumatic systems are operated by air or other
compressed gas. Advantages of pneumatic power: - light weight -
compressed air is readily available Disadvantages of pneumatic
power: - low efficiency - low stiffness - low accuracy Hydraulic
systems are operated by the action of water or other fluids of low
viscosity. Advantages of hydraulic power: - provides a large amount
of power - moves high loads at reasonable speeds - moderate noise
level - Usually more efficient Disadvantages of hydraulic power: -
more expensive - less accurate - requires an energy storage system,
such as pumps or accumulators - susceptible to leakage Project Lead
The Way, Inc. Copyright 2008 Fluid Power Definitions
The use of a fluid to transmit power from one location to another
Hydraulics The use of a liquid flowing under pressure to transmit
power from one location to another Pneumatics The use of a gas
flowing under pressure to transmit power from one location to
another Fluid Calculations p= F A
Elements of Power CIM Elements of Automation Power Fluid
Calculations p = Pressure, measured in pounds per square inch (psi)
F = Force, measured in pounds A = Area of the base of the fluid
container p=F A F A piston has the geometric shape of a circle so
how is area calculated? A The area of a circle is r2 If the piston
diameter is 4 in. then what is the area? 12.6 in.2 Project Lead The
Way, Inc. Copyright 2008 A = Area to which force is being
applied
Elements of Power CIM Elements of Automation Power F = Force being
applied A = Area to which force is being applied The area is
defined as a circle for a piston. Project Lead The Way, Inc.
Copyright 2008 Elements of Power CIM Elements of Automation Power
Your Turn 62 pounds of force is applied to a inch pneumatic
cylinder. How much pressure is created in the cylinder? An accepted
industry standard is that a 1 inch cylinder means the cylinder has
a diameter of 1 inch. Project Lead The Way, Inc. Copyright 2008
Solution r = D r = (0.75 in.) r = 0.375 in. A = r2
Elements of Power CIM Elements of Automation Power Solution r = D r
= (0.75 in.) r = in. A = r2 A = (0.375 in.)2 A = 0.44 in.2 p=F A
p=62 lb 0.44 in.2 p=140 psi Project Lead The Way, Inc. Copyright
2008 Elements of Power Your Turn CIM Elements of Automation Power A
hydraulic pressure of 175 psi is applied to a piston that has a
3.75 inch diameter and 8 inch stroke. What is the power produced by
the piston that moves its full stroke in 2.25 s? Project Lead The
Way, Inc. Copyright 2008 ( ) Solution p= F A F=pA F=175 psi (11.0
in.2) F=1932 lb A = r2
Elements of Power Solution CIM Elements of Automation Power A = r2
A = (1.875 in.)2 A = 11.0 in.2 W r = D r = (3.75 in.) r = in. P= t
1288 ft-lb P= p=F A 2.25 s P= 572 ft-lb F=pA s ( ) F=175 psi (11.0
in.2) ft-lb 1 hp P (hp) = 572 F=1932 lb s 550 ft-lb s P (hp) = 1.04
hp W =F d W = 1932 lb (8 in.) W = 15,455 in.-lb W = 1288 ft-lb
Project Lead The Way, Inc. Copyright 2008 Image Resources
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