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)

db@blackstonesynergy.com

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.

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-

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-

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-

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

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)

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

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