Dynamics of the Distribution
Mechanism with Rocking Tappet with Roll
Florian Ion Tiberiu Petrescu
Bucharest Polytechnic University, Romania
E-mail: petrescuflorian@yahoo.com
Relly Victoria Virgil Petrescu
Bucharest Polytechnic University, Romania
Submission: 01/09/2015
Revision: 18/09/2015
Accept: 21/11/2018
ABSTRACT
In this paper the
authors present shortly an original method to make the dynamic synthesis of a
mechanism with rotary cam and rotated tappet with roll, used with priority at
the distribution mechanisms from the heat engines with internal combustion.
This type of distribution can improve the changes of gases, and may decrease
significantly the level of vibration, noises, and emissions. As long as electricity
and heat are produced by burning fossil fuels is pointless to try to replace
all thermal engines with electric motors, as loss of energy and pollution will
be even larger. However, it is well to continuously improve the thermal
engines, to reduce thus fuel consumption. At the heat engine with internal
combustion a great loss of power is realized and by the distribution mechanism,
reason for the improvement of the
functionality of this mechanism. The dynamic synthesis of this type of
distribution mechanism can be made shortly, by the Cartesian coordinates, but
to determine these coordinates some trigonometric parameters of the mechanism
are necessary. Dynamics and forces of this distribution mechanism are presented
as well. The dynamic coefficient D is also introduced.
Keywords: Distribution mechanism, Rotary cam, Rotating tappet
with roll, Cam dynamics, Cam dynamic synthesis, Forces, Velocities, Powers,
Efficiency, Dynamic coefficient
1. INTRODUCTION
Mechanisms with rotary cam and rotating tappet with
roller (Module F) are presented, as it is shown in Figure 1. They have a unique
kinematic and dynamic due primarily of the mechanism geometry, which forces to
study them in greater detail if need to determine the kinematic and dynamic
precision of these mechanisms. Typically the study of this type of mechanism is
made approximately, considering being enough for both, kinematic and dynamic to
study the center of the coupling B (the center of the roll). This approximation
has a great weakness, because it neglects dynamic kinematics, the forces
transmission, and precision of the mechanism, which leads to a dynamic study
inadequate.
In this paper the authors present shortly an original
trigonometric method to make the dynamic synthesis of a mechanism with rotary
cam and rotated tappet with roll, used with priority at the distribution
mechanisms from the heat engines with internal combustion.
This type of distribution can improve the changes of
gases, and may decrease significantly the level of vibration, noises, and
emissions.
As long as produce electricity and heat by burning
fossil fuels is pointless to try to replace all thermal engines with electric
motors, as loss of energy and pollution will be even larger. However, it is
well to continuously improve the thermal engines, to reduce thus fuel
consumption.
At the heat engine with internal combustion a great
loss of power is realized and by the distribution mechanism, and for that
reason needs to improve the functionality of this mechanism.
The synthesis of this type of distribution mechanism
can be made shortly, by the Cartesian coordinates, but to determine these
coordinates some trigonometric parameters of the mechanism are necessary as
well.
Why to study today this type of mechanism? The first
human revolution was produced by the mechanisms with cams used in the automatic
looms introduced in England in 1719 by John Kay. The second human revolution
was produced in 1866 when the German engineer Nikolaus August Otto has invented
his engine in four times with gas, a heat engine with internal combustion with
distribution having all valves in the known today form of mushrooms. Cam
mechanisms can transmit high forces and loads with a high reliability and
dynamic. For this reason they are irreplaceable in various fields in which they
are used. Distribution mechanisms with cam, follower and valve are
irreplaceable in internal combustion engines.
This work study
the dynamics of the distribution mechanism module F, with rotation cam and
rotating tappet with roll Figure 1.
Figure
1: Mechanism with rotating cam and rotating tappet with roll
Internal combustion engines in four-stroke (Otto,
Diesel) are robust, dynamic, compact, powerful, reliable, economic, autonomous,
independent and will be increasingly clean (WANG, 2011).
Magnetic motors (combined with the electromagnetic)
are just in the beginning, but they offer us a good perspective, especially in
the aeronautics industry.
The Otto engines or those with internal combustion in
general, will have to adapt and to hydrogen fuel.
In some countries (USA, Brazil, Germany) producing
alcohol or vegetable oils, for their use as fuel (KARIKALAN, 2013).
In the future, aircraft will use ion engines,
magnetic, laser or various micro particles accelerated. Now, and the life of
the jet engine begin to end.
Recently it was announced that occurred in Germany car that runs on salt water. This means that we will not put in tank oil or water but salt water.
If Otto engine production would stop right now, they will still working until at least about 40-50 years to complete replacement of the existing fleet today.
In full energy crisis since 1970 until today, production and sale of cars equipped with internal combustion heat engines has skyrocketed, from some millions
yearly to over sixty millions yearly now, and the world fleet started from tens of millions
reached today the billion. As
long as we produce electricity and heat by burning fossil fuels is pointless to
try to replace all thermal engines with electric motors, as loss of energy and
pollution will be even larger.
However, it is well to continuously improve the thermal engines, to
reduce thus fuel consumption. Planet supports now about one billion motor vehicles in
circulation. Even if we stop totally production of heat engines, would still
need minimum 50 years to eliminate total the existing car park in the current
rate.
2. FORCES, VELOCITIES, POWERS, EFFICIENCY OF MECHANISM
Speeds and forces transmitted by the mechanism can be watched in Figure
2.
Figure 2:
Forces and velocities of the mechanism
Forces and speeds (relations of the system 1).
|
(1) |
Where FM
and vm mean the force of entry (input force) and entry velocity
(input velocity); both perpendicular to OA in A (green color on the Figure 2).
Force Fm can be
broken down into two components: Fa (blue) and Fn (red);
(The velocity Vm as well).
Component Fa is a force to slip between elements tangential to the two profiles contact in point A, it produces slippage between the two profiles (the cam and roller tappet). This component gives a moment to roll center B (M=Fa.rb), moment which can produce the rolling of roll (This is advantageous because it always changes the focal point of the roll, which is thus reduced wear and uniformity throughout the surface of the roller).
Component Fn is the main one, which is transmitted to the
roller and then to the tappet. It is
perpendicular to Fa and tangent to the right n-n passing through the
points A and B. When the follower rises (as shown in figure 2) force Fn
presses the roller, so it is directed from A to B.
Force Fn (red) shall
be forwarded radial to the center roll where can be broken down into two
components, in two directions: one direction is along tappet from B to D, and
the other direction is perpendicular on the pushrod (DB) in B.
Component Fc (mustard color) presses the follower along it,
thus compressing it, and component Fu (mauve color) perpendicular in
B on DB, produces tappet rotation around tappet pivot D, as it is up to the
single part useful.
All speeds decompose like forces.
Relations linking forces and those of speeds are given in the system (1). As can be seen there are two angles of pressure, a and d.
Instantaneous yield mechanism
(see the relationship 2), is the ratio between utile (output) power and
consumption (input) power, so using the last two relations of the system (1) we
obtain the expression instantly mechanical efficiency of the mechanism (2).
(2)
Instantly mechanical efficiency is the square of the product of the cosines of the two pressure angles a and d, or is the fourth power of the pressure d angle amplified with a variable, .
3. DETERMINATION OF THE TRANSFER FUNCTION OF THE MOVEMENT
Next is determined the function of motion transmitting (the transmissivity function or coefficient) to the rotating cam mechanism and rotating follower with roller (F module), function denoted by D (PETRESCU, 2013).
Between helpful velocity (vu)
and known velocity (v2) of the tappet occurs a difference, which
must be embedded in the transmission coefficient D, or the transmission
function D (PETRESCU, 2015a).
Write the tappet reduced velocity vB2r
in the form known (3).
(3)
Absolute speed tappet in B (relation 4) is obtained by multiplying the reduced speed (3) with w.
(4)
See
this velocity in its dynamic form (actual 5), together with an inserted
coefficient of motion transmission, D:
(5)
Useful speed obtained from system 1 (and
figure 2) may be writhed in the form 6.
(6)
Two speeds (5-6) equaling gets the
expression of transmission (dynamic) coefficient D (relation 7).
(7)
Considering classical variant (without
dynamic input), when , the dynamic coefficient D takes the simplified value (8).
(8)
4. DYNAMICS OF MODULE F
For
the dynamic calculations one uses the below original relations (9-11) obtained
by a double integration of the Newton equation (PETRESCU, 2014).
(9)
(10)
Determining
DX
it can calculating then X with expression (11).
(11)
Where
s is the theoretical tappet movement law and x is the real (dynamic) tappet
movement law; K is the elastic constant of the system and k is the elastic
constant of the valve spring; x0 is the valve spring pretension; is the valve mass
reduced at the valve axis; is the tappet mass reduced at the valve axis.
Then
changing the rotation moving of the tappet into a translation moving of the
valve (see the Figure 3, and relations 12-13).
Figure 3: Converting the rotation moving
of the tappet into a translation moving of the valve. Simplified diagram.
(12)
(13)
5. DYNAMIC ANALYSIS OF THE MODULE F
The
dynamic analysis begins with the classical law sine (see diagram of the figure
4, and the profile of the figure 5), to can be compared with the known law
dynamic module C classic (AMORESANO, 2013; PETRESCU, 2015b).
It uses a drive shaft rotation speed of n=5500 [r/min], the theoretical maximum displacement both the valve and the tappet, h=10 [mm] (CHOI, 1994).
The phase angle is ju=jc=60 [degree]; core radius has value r0=24 [mm]. Roll radius has been adopted the value rb =20 [mm]; b=20[mm];
d=50[mm].
Valve
spring adjustments are: k=60 [N/mm] şi x0=30 [mm].
The
yield has a high value, h=12.0%.
Figure 4: Dynamic analysis of
the module F. Law Sine, n=5500 [rot/min], ju=60 [deg], r0=24 [mm], rb=20
[mm].
Dynamic
is better (in general) compared with that of the module classic, C, in
conditions in that the real movement of the valve, s, almost doubled!
Figure 5: Cam profile of the
module F. Law Sine, ju=60 [deg], r0=24 [mm], rb=20 [mm].
For
the law cosine lifting is higher as compared with the law sine. See the Figure
6-7.
Figure 6: Dynamic analysis of
the module F. Law Cosine, n=5500 [rot/min], ju=60 [deg], r0=24 [mm], rb=20
[mm].
Figure 7: Cam profile of the
module F. Law Sine, ju=60 [deg],
r0=24 [mm], rb=20 [mm].
In the Figure 8 one
can see the dynamic analysis of the original law denominated by the authors
C4P1-0, and in the Figure 9 the corresponding profile.
Figure 8: Dynamic analysis of
the module F. Law C4P1-0, n=5500 [rot/min], ju=45 [deg], r0=6 [mm], rb=3
[mm].
Opening of the valve
is less, but the yield mechanism has increased.
Figure 9: Cam profile of the
module F. Law C4P1-0, ju=45 [deg],
r0=6 [mm], rb=3 [mm].
In
the Figure 10 one can see the dynamic analysis of the original law denominated
by the authors C4P3-2, and in the Figure 11 the corresponding profile.
Figure 10: Dynamic analysis of the
module F. Law C4P3-2, n=40000 [rot/min], ju=85 [deg], r0=10 [mm], rb=3
[mm].
Figure 11: Cam profile of the
module F. Law C4P3-2, ju=85 [deg],
r0=10 [mm], rb=3 [mm].
This last presented
law, allow the increase of the drive shaft rotation speed to the 40000 rot/min.
6. DISCUSSION
The distribution
mechanisms work with small efficiency for about 150 years; this fact affects
the total yield of the internal heat engines. Much of the mechanical energy of
an engine is lost through the mechanism of distribution. Multi-years the yield of the distribution mechanisms was only 4-8%.
In the past 20
years it has managed a lift up to the value of 14-18%; car pollution has decreased and people have better
breathing again.
The paper
presents an original method to increase the efficiency of a mechanism with cam
and follower, used at the distribution mechanisms.
This paper treats
only module F: with rotary cam
and rotating tappet with roller.
The
distribution mechanism with rotation cam and rotating tappet with roll, allow
us the increasing the rotation speed of the drive shaft and the increasing of
the mechanical yield of the couple cam-tappet.
This
type of distribution mechanism allow and the construction of a compact motor
(engine), which may work with high power producing a level of noxious gases
lowest and a fuel consumption decreased as well.
Even
the higher accelerations produced by these conditions may by increased by the
valve spring adjustments.
These
adjustments may be provided for some special dynamic calculation with an
improved dynamic system, new created by authors.
The
secret is appropriate increase in those two values: k and x0.
As long as we produce electricity and heat by burning fossil fuels
is pointless to try to replace all thermal engines with electric motors, as
loss of energy and pollution will be even larger.
However, it is well to continuously improve the thermal engines,
to reduce thus fuel consumption.
At the heat engine with internal combustion a great loss of power
is realized and by the distribution mechanism, reason for that we must try to
improve the functionality of this mechanism.
7. BENEFITS
The main advantage is that the F module supports a much higher
speed compared to classic module C (An engine with high rotation speed can be
more compact, more powerful and more economical, and without nuisance).
In addition at this mechanism (cam module F) and efficiency is
higher.
8. CONCLUSIONS
At the heat engine with internal combustion a great loss of power
is realized and by the distribution mechanism, reason for that to improve the
functionality of this mechanism.
The dynamic synthesis of this type of distribution mechanism can
be made shortly, by the Cartesian coordinates, but to determine these
coordinates trigonometric parameters of
the mechanism are necessary as well. The paper presents shortly an original
trigonometric method to make the synthesis of a mechanism with rotary cam and
rotated tappet with roll, used with priority at the distribution mechanisms
from the heat engines with internal combustion.
This type of distribution can improve the changes of gases, and
may decrease significantly the level of vibration, noises, and emissions.
The main
advantage is that the F module supports a much higher speed compared to classic mode (An engine with high rotation speed can be more compact, more powerful and more economical, and without nuisance).
In addition at this mechanism (cam
module F) and efficiency is higher.
9. AUTHORS’ CONTRIBUTION
All the authors
have contributed equally to carry out this work.
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