Transcript Document

Simple Machines
Simple Machines
Effort
Load
Work done = Force x
distance moved (in direction
of the force)
In this case the effort move
the same distance as the
load
The effort force is equal to
the load force (weight of
load)
Simple Machines
•Force multipliers
• Work done = Force x distance moved (in direction of the force)
• Work done by effort = work done on load
• F x d (effort)= F x d (Load)
• The further the distance moved by the effort force
compared to the distance moved by the load means that
a smaller effort force can move a larger load force
Simple Machines
Effort
Load
In the case of a lever
the effort force moves
further than the load
so the less effort can
lift a larger load
Simple Machines
Diameter 200mm
Driver pulley
20 RPM
Diameter 400mm
Driven pulley
10 RPM
Simple Machines
A wheel and axle
assembly used as
a hoist the effort
force again moves
further than the
load force
100mm
400mm
Load
Effort
Simple Machines (equations)
The mechanical advantage (MA) of a system
=
load /effort
The velocity ratio (VR)
=
Distance moved by effort/ distance moved by load
Simple Machines (equations)
• In the case of the hoist shown in the diagram the
effort moves a distance of 400π (Circumference of wheel)
• And the load moves by 100π (circumference of the axle)
• The velocity ratio = 400π/100π
•= 4
Simple Machines (equations)
• The efficiency (η) of the for a system for any set of
values is found by the equation
• η = (MA x100)/VR x 100
• The limiting efficiency
• =100/(VR x a) (a = gradient of graph)
Simple Machines (equations)
• The Law of the machine (in the form of y = mx + c)
E= aW + b
Where W is the weight (load force)
• E is the Effort Force
• a and b are found by plotting the graph of load against
effort
Simple Machines
W = aE + b
E kN
(y)
b is where the line
crosses the y axis
(a) is the
gradient of
the graph
(0.31)
W kN (x)
Simple Machines
MAmax ≈ 3.24
MA
W kN
Maximum (ideal)
MAmax is found
by plotting MA
against W (load)
and estimating
the value for MA
where the line is
horizontal
Simple Machines
F
Friction
effort
W kN
Plotting the graph of
Friction effort against
the load (W) shows that
the friction effort
decreases with
increasing load
The efficiency of the
system increases with
increasing load
Simple Machines
• Friction effort is calculated using the
equation
• F = E- (W/MAmax)
Simple Machines
Simple Machines
Simple Machines
• Limiting efficiency 1 ÷ (a x VR)
• = 1 ÷ (0.31 x4)
• 80.6%
• A machine can never reach limiting
efficiency because of friction losses in the
system
Simple Machines
A
C
0.3m
D
0.8m
B
0.2m
0.6m
Simple Machines
• In the above belt drive system, the input
power is 10kW at a speed of 480 rpm and the
efficiency is 85%
• Power output = η x 10000
• = 0.85 x 10000 = 8500W
• =8.5kW
Simple Machines
• Calculate the speed at pulley D
• Speed at A = 480/60 = 8 rev/sec
• Speed at B = 8 x (8/3) = 21.3 rev/sec
• Speed at C= 21.3rev/sec
• Speed at D =21.3 X (6/2) = 63.9 rev/sec
Simple Machines
• Calculate the output torque at D
• Torque = power/ (2π x number of turns (per sec))
• = 8500/ (2π x 63.9)
• 21.17Nm
Simple Machines
• The ratio of tensions in the output belt is 5:1.
• Calculate the effective tension in the belt and show
that the maximum tension the belt is subjected to
is less than 400N.
• Effective tension = ( T1 – T2)
• = torque/ radius of pulley D
• =21.17/0.1
• (T1 - T2)= 211.7N
Simple Machines
•T1/T2 = 5/1
•T1 - T2 = 5-1 = 4
•T2 = 211.7/4 = 52.93N
•T1 = 52.93 x 5
•= 264.63 N
Simple Machines
•If higher speeds or greater power
transmission is required vee belts used
with vee grooves in the will be more
effective because they provide a larger
surface area which will give a better
grip to prevent slip.