Modul 10 Clutches, Brakes, Couplings and Flywheel Part II

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PowerPoint PresentationTeknik Mesin  FTMD ITB MS3111  Elemen
Mesin
Modul 10 Clutches, Brakes, Couplings
and Flywheel Part II
Modul 10 Clutches, Brakes, Couplings and Flywheel Part II
Energy ConsiderationSegment 1
Temperature RiseSegment 2
Friction MaterialSegment 3
FlywheelSegment 5
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and Flywheel Part II
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• In the case of braking action, the kinetic energy must be
absorbed by the brake system.
• For the clutching action, slipping must occur in the clutch until
the driven parts have the same speed as the driver.
• Kinetic energy is absorbed during slippage of either a clutch or
brake, and this energy appears as heat.
• The capacity of a clutch or a brake is limited by two factors:
characteristic of material and ability of clutch/brake to dissipate
heat.
• If the heat generated faster than it is dissipated, we have the
temperaturerise problem.
8.8. Energy Considerations
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To study what happens during a simple clutching/braking operation,
let see the Fig. 161 .
2 1
1 2
The torque is constant.
I1 and I2 have initial angular velocity of 1 and 2
(generaly 1 ≠ 2).
During the clutch operation, both angular velocity change and
eventually become equal.
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Equation of motion for inertia 1 and 2 can be written:
where is angular acceleration and is clutch torque
The instantaneous angular velocities for both inertia can be
determined as follows
1 = −
= 1 − 2 = −
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The clutching operation is completed at the instant when both
angular velocity become equal. Let the time required for entire
operation be t1. Then the Eq. (50) gives the time as
1 = 2 ⇒ = 0 ⇒ 1 = 12(1 −2)
(1 + 2)
Using Eq. (50), the rate of energydissipation during the clucthing
operation is
= = (1 − 2) − 1 + 2 12
(e)
This equation shows that the energydissipation rate is greatest
(maximum) at the start of clutching, when t = 0.
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The total energy dissipated during the clutching operation or
braking cycle is obtained by integrating Eq. (e) from t = 0 to t =
t1. The result is found to be
=
12
Notes:
This is the energy that must be absorbed by clutch or brake.
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In USCS units, if the inertias are expressed in (lbf · in · s2),
then the energy absorbed is in (in · lbf). Using this units, the
heat generated in Btu is.
In SI unit,
energy dissipated is expressed in [Joules].
=
9336 (53)
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and Flywheel Part II
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The temperature rise of the clutch or brake assembly can be
approximated by the classic expression.
8.9. Temperature Rise
× (54)
where = temperature rise, oF = specific heat capacity, [Btu/(lbm ⋅
oF]; use 0.12 for steel or cast iron = mass of clutch or brake
parts, [lbm]
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A similar equation can be written for SI units. It is
Δ =
× (55)
where = temperature rise, oC = specific heat capacity, [J/kg ⋅ oC];
use 500 for steel or cast iron = mass of clutch or brake parts,
[kg]
Notes: The temperature rise equations above can be used to explain
what
happens when a clutch or brake is operated. However, there are so
many variables involved that it would be most
unlikely that such an analysis would even approximate experimental
results.
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If an object is at initial temperature T1 in an environment to
temperature T, Newton’s cooling model is expressed as
− ∞ 1 − ∞
(56)
where = temperature at time , oF 1 = initial temperature, oF ∞ =
environmental temperature, oF = overall coefficient of
heat−transfer,Btu/(in2 ⋅ s ⋅ oF) = lateral surface area, in2. =
mass of the object, lbm = specific heat capacity of the objecy,
Btu/(lbm ⋅o F)
Figure 23 shows an application of Eq. (56). The curve ABC is the
exponential decline of temperature given by Eq. (56).
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Figure 16–23 The effect of clutching or braking operations on
temperature.
At time tB a second application of the brake occurs.
The temperature quickly rises to temperature T2, and a new cooling
curve is started.
For repetitive brake applications, subsequent temperature peaks T3,
T4,…, occur.
Please read the reference book for a more detail explanation of the
graph.
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When a disk brake has a rhythm such as discussed above, then the
rate of heat transfer is described by another Newtonian
equation:
= − ∞ = + − ∞ (57)
where
= overall coefficient of heat−transfer,Btu/(in2 ⋅ s ⋅ oF)
= radiation component of ,Btu/(in2 ⋅ s ⋅ oF), Fig. 24(a)
= convective component of ,Btu/(in2 ⋅ s ⋅ oF), Fig. 24(a)
= ventilation factor, Fig. 24(b)
= disk temperature, oF ∞ = ambient temperature, oF)
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Figure 16–24 (a) Heattransfer coefficient in still air. (b)
Ventilation factors.
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The energy E absorbed by the brake stopping an equivalent rotary
inertia I in terms of original and final angular velocities ωo and
ωf is given by Eq. (50) and Eq. (49) with I1 = I and I2 =0
The temperature rise T due to a single stop is
Tmax has to be high enough to transfer E Btu energy in t1
seconds.
= 1
Δ =
(59)
For steady state, rearrange Eq. (53) as
Crossmultiply, add Tmax to both sides of Eq. (57) and
letting
Tmax – Tmin = T, and rearrange, we obtain
∞ Δ
− ∞ − ∞
Example 5
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From Fig. 24 (b) with air speed of 25 ft/s we find fv = 4.8, and
so we have
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Answer
Answer
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and Flywheel Part II
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8.10. Friction Material A brake or friction clutch should have the
following lining material characteristics to a degree that is
dependent on the severity of service:
• A high and uniform coefficient of friction.
• Imperviousness to environmental conditions, such as
moisture.
• The ability to withstand high temperatures, together with good
thermal conductivity and diffusivity, as well as high specific heat
capacity
• Good resiliency.
• Compatible with the environment
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Table 16–2 gives area of friction surface required for several
braking powers.
Table 16–3 gives important characteristics of some friction
materials for brakes and clutches.
The manufacture of friction materials is a highly specialized
process, and it is advisable to consult manufacturers’ catalogs and
handbooks, as well as manufacturers directly, in selecting friction
materials for specific applications.
Selection involves a consideration of the many characteristics as
well as the standard sizes available.
Table 16–4 lists properties of typical brake linings. Table 16–5
includes a wider variety of clutch friction materials,
together
with some of their properties.
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Material Fabrication Field of Application
Wovencotton lining
As a fabric belt which impregnated with resin and polymerized
Mostly in heavy machinery; usually in rolls up to 50 ft length.
Thickess frm 1/8 in to 1 in; width up to 12 in.
Wovenasbestos lining
Similar to cotton lining and may contain metal particles. Not as
flexible as cottong lining.
Widely used as a brake material in heavy machinery. Comes in
smaller range of sizes.
Moldedasbestos lining
Contain asbestos fiber and friction modifiers; thermoset polymer is
used, with heat, to form a rigid/semi0rigid molding.
Principal use is in drum brakes.
Moldedasbestos pads
Used both for clutches and brakes.
Sinteredmetal pads
Made of a mixture of copper and/or iron particles with friction
modifiers; molded under high pressure and the heated to a high
temperature to fuse the material.
Pads are used in both brakes and clutches for heavyduty
applications.
Cermet pads Similar to the sinteredmetal pads and have a
substantial ceramic content.
Pads are used in both brakes and clutches.
Table of several common friction material
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and Flywheel Part II
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8.11. Miscellaneous Clutches and Coupling Squarejaw clutch as
shown in Fig. 25 (a) in one form of positivecontact clutch.
These clutches have the following characteristics:
1. They do not slip
2. No heat is generated
3. They cannot be engaged at high speeds
4. Sometimes they cannot be engaged when both shafts are at
rest
5. Engagement at any speed is accompanied by shock.
The greatest differences among the various types of positive
clutches are
connected with the design of the jaws (ractchedshaped,
spriralshaped, gear
toothshaped).
Although positive clutches are not used to the extent of the
frictionalcontact
types, they do have important applications where synchronous
operation is
required.
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Figure 16–25 (a) Squarejaw clutch; (b) overload release clutch
using a detent.
Squarejaw Overloadrelease clutch
Devices such as linear drives or motoroperated screwdrivers must
run
to a definite limit and then come to a stop.
An overloadrelease type of clutch required for theses application.
Fig.
25 (b) is a schematic drawing illustrating the principle of the
operation
of such clutch.
This clutches are usually springloaded so as to release at a
predetermined torque.
The clicking sound which is heard when the overload point is
reached is
considered to be a desible signal.
Both fatigue and shock must be considered in obtaining the stress
and
deflections of the various portions of postive clutches. In
addition, wear
must generally be considered.
An overrunning clutch or coupling
permits the driven member of a
machine to “freewheel” or
of power increases the speed of the
driven mechanism.
The driving action is obtained by wedging the rollers between
the
sleeve and the cam flats.
There are many varieties of overrunning clutches available,
and
they are built in capacities up to hundreds HP.
Since no slippage is involved, the only power loss is that due
to
Plain shaft coupling Light duty toothed coupling
BOSTFLEX throughbore coupling Threejaw coupling
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and Flywheel Part II
8.12. Flywheel A flywheel is an inertial energystorage device. It
absorbs mechanical
energy by increasing its angular velocity and delivers energy by
decreasing its velocity.
A flywheel is used to smooth out variations in the speed of a shaft
caused by torque fluctuations.
Piston comp., punch presses, rock crusher, etc. all have
timevarying loads. The prime mover (ex.: internal combustion
engine) introduce torque
oscillations to the transmission shaft. Other systems may have both
smooth torque sources and loads such as an
electrical generator driven by a steam turbine no need flywheel. If
the source of driving torque or the load torque have a
fluctuating
nature (see Fig. 1628) then a flywheel is usually needed.
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Figure 16–28
Relation between torque and crank angle for a one cylinder,
fourstroke–cycle internal combustion engine.
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Note:
Ti is considered positive and To negative.
Values of Ti and To may depend on the angular displacement and/or
their angular velocities.
In many case (ex. induction motor), its characteristic depends upon
only the speed of the motor. Generally, motor manufacturers publish
the torquespeed characteristics of their various motors.
The equation of motion for the flywheel represented in Fig. 161
is
i, i
Figure 16–1
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When the input and output torque functions are given, Eq. (a) can
be solved for
the motion of the flywheel using wellknown techniques for solving
linear or non
linear differential equation.
We can simplify this by assuming a rigid shaft, giving i = = o
.
Thus, Eq. (a) becomes
= (, ) − (, ) (b)
When the two torque functions are known and the starting values of
the
displacement and velocity are given, Eq. (b) can be solved.
Here, we are not really interested in the instantaneous values of
these terms at all.
Primary, we want to know the overall performance of the flywheel
(what should its
moment of inertia?, how do we match the power sources to the load?,
what are the
resulting performance?, etc.)
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To gain insight into the problem, a hypothetical situation is
diagrammed in Fig. 24.
1 cycle
1 2
3 4
Energy released back to system
The work input to the flywheel is the area of the rectangle between
1
and 2 , or.
Figure 16–27
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The work output of the flywheel is the area of the rectangle
between 3 and 4 , or.
= × (4 − 3) (d)
Three conditions possible (assume: no friction losses)
If > ⇒ 4 < 1; load uses more energy than has been delivered
to the flywheel If = ⇒ 4 = 1; the gains and the losses are equal If
< ⇒ 4 > 1; load uses less energy than has been delivered to
the flywheel
These relation can also be written in terms of kinetic
energy.
At = 1 the flywheel has a velocity of 1 rad/s, and so its kinetic
energy is
1 = 1
2 1
2 (e)
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At = 2 the velocity is 2 rad/s, and so its kinetic energy is
2 = 1
2 2
2 (f)
Notes:
Many of the torque displacement functions encountered on practical
engineering situations are so complicated that they must be
integrated by approximate methods.
One simplest integration routine is Simpson’s rule. This
approximation can be handled on any computer and is short enough to
use on the smallest programmable calculators.
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Example 1.
The crankshaft of a punch press rotates at 60 rpm, causing holes to
be punched in a steel part at the rate of 60 punches per
minute.
The crankshaft torque requirement is shown in Fig. 25. The press is
driven (through suitable speed reducers) by a 1200rpm motor.
Neglecting any “flywheel effect”, what motor power is required to
accommodate the peak crankshaft torque? Figure 25
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Assumption: 1. Friction losses are negligible 2. No energy is
stored as rotational kinetic energy (no flywheel) 3. The motor
delivers maximum torque continuously
Solution: 1. Neglecting friction losses motor power = crankshaft
power out, and the 20 : 1
speed reduction (1200 rpm/60 rpm) is associated with a 20 : 1
torque increase. Hence, the motor torque required is 10 kN·m/20 =
500 N·m.
2. Motor delivers the torque continuously. The work capacity
corresponding to 1 revolution of the shaft is 2 x 500 N·m = 1000
J.
3. In 1 second, the motor shaft turns 20 revolutions (1200 rpm),
the work capacity is 20x1000 J = 20 kJ.
This is equivalent to 20 kW or 62.8 kW or 84.2 hp (a big motor
??)
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Example 2.
For the punch press in Example 1 determine the motor power capacity
required if we use a flywheel.
The energy required for the press is represented by the area under
the actual crank torque versus the crank angle curve of Fig. 26,
which
is = 2 kN·m or 6283 Joules.
Figure 26
Assumption: Friction losses are negligible
Solution:
1. Fig. 26 shows that average torque requirement during the actual
punch stroke is 6
kN and that the punch stroke lasts for /3 rad. (The energy involved
is this area
under the curve is 2 kN·m or 6283 J).
By using the flywheel that permits the motor to deliver a constant
torque over the
entire 2 rad, we can reduce the torque requirement to 1 kN·m
resulting a total
energy of 2 kN.m (kJ)
This is shown in Fig. 26 as “uniform torque supplying equal
energy”.
2. Since, at the same shaft speed, motor torque and motor power are
proportional,
thus the 10:1 reduction (20 2) in motor torque corresponds to a
like reduction
in power rating required.
Hence, the motor power required is 62.8 kW/10 = 6.28 kW or equal to
8.4 hp (a
small motor).
Example 3.
Continuing with the previous problem, we choose to design a
flywheel that rotates at 1/3 motor speed and that limits motor
speed fluctuation to the range of 900 rpm to 1200 rpm. The flywheel
is to be made of steel and have the geometric proportions as shown
in Fig. 27.
Figure 27
To simplify the calculation, assume that the inertia contributed by
the hub and arms is negligible. Determine the required flywheel
polar moment of inertia, I, and the diameter, d.
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Assumption and decisions:
1. Friction losses are negligible.
2. The inertia contributed by the hub and arms is negligible.
Decisions:
1. The flywheel rotates at 1/3 motor speed.
2. Motor speed fluctuation is limited to 900 to 1200 rpm.
3. The flywheel is made of steel.
4. Geometric proportions for the flywheel are shown in Fig.
27.
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Solution:
1. Fig. 26 shows that during the actual punch stroke, energy
provided by the motor is represented by an approximate rectangle 1
kN·m x /3 rad. Thus, the motor provides 1000 N x /3 = 1047 J of the
total of 6283 J required. The flywheel must provide the remaining
(6283 – 1047) = 5236 J.
2. The flywheel inertia must be such that
5236 = 1
2. The moment of inertia for a hollow cylinder is
1
5236 = 1
2 13.33 2 − 10 2 ⇒ = 13.80 kg ⋅ m2
=
From wich we find = 688 mm Comment:
If the inertia contributed by the hub and arms is included in the
analysis, we would find that a smaller d is required.
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Thank You Lecturers
Institut Teknologi Bandung
Modul 10 Clutches, Brakes, Couplings and Flywheel Part II