Ring Spinning - flexible shaft couplings for energy management - POLAND 2016
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Transcript of Ring Spinning - flexible shaft couplings for energy management - POLAND 2016
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RING SPINNING – SHAFT ENGINEERING FOR ENHANCED ENERGY
MANAGEMENT
Presenting and communicating author: Debashish Banerjee- CEO- Blackstone
Synergy Consulting Group Limited, Nairobi-00604, Kenya (P.O. Box – 23365)
Ring spinning productivity is the function of the amplitude of torsion deflection around
the coupling points of the shafts that extend in length by more than 30 meters.
The deflection of the shaft along the axis in the lateral coordinates is defined by the
angular displacement and the compensation required to restore the original
coordinates describe the attributing factors to the energy expended. Contemporary
shaft designs have a higher domain of working deflection as described by the
tolerances in microns around the coupling coordinates.
The paper serves to bring in the utility of having flexible rubber coupling with the
resilience and elasticity to extend the creep points in the geometry of the strain curve
and enable the torsion to be compensated by a reactive load. The effect is one of
simulating the spring that restores the original coordinates of the coupling. The
energy conserved in the rubber coupling absorbs the kinetic energy of the angular
deflection and minimizes the loss of transmission speeds across the shaft drive.
Reduction of vibration and improved thermometry conditions around the coupling
point enable the spindle speeds of higher than 20,000 rpm to be seamless with 45%
lower energy consumption.
Introduction
The ring spinning technology has evolved over the decades yielding substantial
increases in the productivity levels through the metallurgical changes brought about
in the ring surface, the profiles in the ring cross-sections, the spindle geometry for
improving on the spinning balloon configuration, the vibration absorption in the
spindles and the tapes as also on the spindle drives and finally on the design of the
shafts and the bearings on the shafts as well.
However, in spite of these phenomenal changes triggered by metallurgy as also the
micro-processed controls on the drives and the synchronization of the lappet, the
ring rail and the ABC rings, the limiting factor yet remains the shaft that provides the
drives to the spindles and the drafting systems when accelerating and with changes
in the dynamic load on the cop build. The limits are imposed by the domain that
defines the coordinates of the coupling points around the shaft joints on changing
torque definition in response to the given acceleration and traction forces caused by
braking and the dynamics of the cop build.
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The paper serves to bring to the fore the implications of the coordinates of the
coupling points on a long shaft and the torque dampening of the traction that reduces
inertia and brings in seamless changes in the dynamics of cop build, twist flow and
resultant ability of the yarn in absorbing a higher air drag caused by the spindle
revolution.
Conceptualization of the designi
Hypothesis-1: The coordinates of a coupling point as illustrated in the diagram-1
need to be explained in a greater detail:
DIAGRAM-1
The direction of the vector is defined by (+) and (-) sense with the clearance in
microns between the two edges assumed to be identical (A1 in magnitude).
The illustration of diagram-1 yields a curve that is essentially sinusoidal in nature
with identical wavelength (as the coupling points are equidistant) and amplitudes
defined by the magnitude of the clearance (herein assumed as identical at all the
nodes as A1).
The resultant sine curve shall have the following configuration as in graph-a for
diagram-1:
GRAPH-a
The simulation is depicting the conditions outlined in the diagram-1.
y = 42.5x4 - 576.1x3 + 2691.x2 - 5068.x + 3145R² = 0.735
-400
-300
-200
-100
0
100
200
300
400
1 2 3 4 5 6
Series1
Poly. (Series1)
A1+ A1+
A1-
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The R2 values indicate a fairly close fit with simulation reliability. The exponential
extrapolation amplifies the jarring collisions of the shaft onto the coupling. The
collisions are fundamentally of two different resolutions – one of high impact and low
frequency and the other of low impact but high frequency; both potentially
contributing to the surface wear of the coupling elements.
Hypothesis-2: with varying magnitudes of tolerances between the shaft edges as
illustrated in diagram-2:
DIAGRAM-2:
Conditions:
a) Magnitude: A2 < A3<B1
b) Vector sequence +/+/- (identical sequence as in diagram-1)
c) Graphical illustration-B linked to diagram-2 is as follows:
GRAPH-b:
The entropy in the system is augmented owing to the varying
magnitudes keeping the vector sequencing identical. Inherent volatility
y = 17.80x4 - 282.9x3 + 1532.x2 - 3261.x + 2210R² = 0.367
-400
-300
-200
-100
0
100
200
300
400
1 2 3 4 5 6 7
Series1
Poly. (Series1)
A2 +
A3+ B1-
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lowers the R2 values on an exponential extrapolation of the coordinate
simulation of the shaft.
Hypothesis-3:ii random variation in the vector sequence as also the magnitudes
DIAGRAM-3
Conditions:
a) Magnitude C1<D1 and overall conditions C1>A1 and D1<A2
b) Vector sequencing -/+/- and is different from the illustrations-1 and 2
c) The graphical illustration yields the following:
GRAPH-c:
i) The R2 of 1 indicates that with a pattern of wild volatility, the graph
becomes a close fit
ii) The entropy energy in the system is high thereby causing a higher
probability of surface damages on the coupling after the bearing
resolution
d) The domain coordinates of the degree of freedom provided in the
hypotheses -1 through 3 cause varying degrees of abrasion on the
surfaces of the couplings owing to the nature of the collisions. Hence, it
is vital to describe the conditions prevailing around the geometric
configuration of the coupling points in order to map the degrees of
damage
y = 149.5x4 - 1808.x3 + 7610.x2 - 12917x + 7290R² = 1
-400
-300
-200
-100
0
100
200
300
400
500
1 2 3 4 5
Series1
Poly. (Series1)
C1- C1+ D1-
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Critical derivatives on the conceptualization of the faults in the existing shaft design:
A) The entropy in the system is a function of the geometric configuration around the
coupling nodes and is defined to a large extent by the quality of bearing resolution of
the impacting torque.
B) The collisions around the joints describe a domain that determine the wear
characteristics and are not identical between the nodes along the length of the shaft.
C) The structural vibrations within a system are caused by the domain characteristics
of the colliding impact and in turn define the transmission quality onto the drafting
and the spindles as the cop building happens during a cycle.
D) The energy function of the machinery is fundamentally a derivative of the wave
characteristics of the nodal points and gets aggregated over the length of the shaft to
influence the rotor shaft.
E) Containing the amplitude of the wave describes the reduction of the energy in a
continuous shaft and therein is the onus of the present paper.
F) The mechanism for containing the amplitudes would be influenced to a large
extent by the damping of the collisions and restricting the degrees of freedom
through the domain coordinates of the abrasion characteristics.
Enabling factors for solving the issues in the design deficiency:
A) Introduction of the flexible couplings effectively changes the configuration of the
coordinates during the shaft distortion in response to the torque generation as
illustrated in the diagram-4:
DIAGRAM-4
The introduction of the flexible couplings brings in a change in trajectory of the shaft
element in as much as there is a compensation of the impacting force and a
paradigm shift in the coordinates of the said element.
The dotted line in the illustration describes the mirror-image of the impacting
coordinates of the shaft element that can effectively bring down the domain
configuration and the corresponding degree of freedom.
The vector sequencing becomes irrelevant as also the original tolerances between
the two shaft elements since the mirror-image creation of the impact lower the
A11 A22
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tolerance bandwidth of the distortion thereby causing a sharp reduction in the twist
angle of the shaft itself.
GRAPH-d
The axial shift happens owing to the compensation by the flexible coupling. The
distortion in the shaft in response to torque are compensated real time and the
coordinates change on a mirror-mode thereby providing the buffer for the impact and
settling at lower amplitude points.
With the lowering of the amplitude, the general entropy in the system reduces but the
predictability of the coordinates depreciates in reliability as is reflected by the R2
values in the equation. The exponential extrapolation clearly converges onto
significantly lowered amplitude thereby realizing the energy gains in the system.
The flexible couplings have the following advantages and claims over the empirical
structure that is metallic on the following features:
Feature-1: The impact caused by the absorption of the angular torque thereby
providing a mirror-image of the displacement coordinates bring down the amplitude
of the distortion in the first place and help lower energy as also improve on the
transmission quality of the drives.
Feature-2: Sequential vectors are irrelevant in the context of the flexible couplings
since mirror–images of the impacting distortion nullify the vector.
y = -0.009x4 + 0.002x3 + 3.828x2 - 44.94x + 166.5R² = 0.108
-200
-150
-100
-50
0
50
100
150
200
250
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Series1
Poly. (Series1)
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Fetaure-3: The magnitude of the tolerance gap around the coupling point is also
rendered irrelevant owing to the compensation factors that are brought into play by
the flexible couplings at the nodes.
Feature-4: The aggregation of the nodal distortion culminating into the rotor shaft
yields a curve with significant reduction in amplitude and area of the energy curve
thereby precluding the causal links of high energy consumption in drives emanating
from the main shaft including the ones for the drafting and the spindles.
Feature-5: With the building cop, the weight of the driven component increases and
thus has a damping effect as well thereby causing the magnitude and the matrices of
the coordinates to describe a narrower domain and hence further reduction in the
energy density of the ring spinning machine.
The key determinant for the energy performance of the shaft engineering dynamics
is essentially the distortion angle and the coordinates of the domain described by the
coupling geometry as described in the literature.
The entropy of change around the structure caused by the distortion angle increases
with increasing rotational speed and the concomitant disturbances in the shaft
metallurgy as well as the particle drift within the structure. The radius of the torque
and the quantum of particles described in the distortion model define the angle f and
hence the domain boundaries of the degree of freedom.iii
SHAFT Distortion
angle 1 with
flexible couplings SHAFT Distortion
angle with
regular metallic
couplings
N1 N2
N3 N4
A0
A1
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The angular torque is determined by the particle displacement within the shaft
structure caused by the differential radial forces on a centrifugal mode originating
from the geometric nucleus as also the congruence with the rotational nucleus of the
body.
The rigidity of the body and the spatial configuration of the particles shall determine
the effective twist angle and that in turn shall describe the coordinates of the domain
of collisions. The flexible couplings serve to reduce the impacting domain by creating
a mirror-image of the impact and creating space on a reversal mode so as to buffer.
In the process, the volumes of particles described by the nomenclature N1, N2, N3
and N4 shall reduce in disparity owing to the compensating forces of the flexible
couplings. In the conventional design, owing to the hilf ( high impact low frequency)
collisions, the volume disparities in N1~N4 increase manifold while the lohf (low
impact and high frequency) collisions, the line of equilibrium ( A0-A1) caused by the
N1~N4 shift change in configuration quite too often. The flexible couplings cause the
equilibrium axis itself to gravitate between closely matching coordinates thereby
altering the shape of the distortion and hence retain the primary facets of the torque
values.
The energy savings in the model can be calculated along the following lines:
1) The amplitude of the wave = a and the m- mass of the aggregates of the nodal
points ( for instance in a 30 meter long shaft with 15 coupling points, the domain
described by each nodal point being dn, then the m= dn describes the total affected
mass causing the distortion of the wave .
2) The kinetic energy of the wave = ½ ma2 since instantaneous amplitude is an
indicating measure of the acceleration apart from describing the flexing points.
3) The area described by the wave inclusive of the two vectors shall now be the total
energy measure that can be changed and saved upon.
On equivalent conditions, the savings potential with identical background mechanical
indicators of vibration and thermometry is to the tune of 45%.
i Vardhman textiles trials on vibration at Arisht Spinning Mills – G5/1 RF and Com4 compact Rieter iiPT Indorama technologies trials in Indonesia yielding the curve
iii Spin Knit, Kenya trials on the worsted ring spinning frame