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Home New Research | About New Research | Exec Summary | Abstract

PART - II

Chapter 6

Practical Application

An Attempt to use the General Equation to Estimate Rotor-spun Yarn CSP From HVI Data

On the basis of published data (15), an attempt was also made to modify the general equation to use it to predict rotor yarn CS from HVI data. Unlike in the case of SITRA data, these data do not exhibit a marked increasing trend of fibre-tenacity with increasing fibre-length – Figure II – 6 - x. The data covered cottons that spun NE 10.1 yarns ranging in CS from 1232 to 2807 at T.M. of 5.3. The modified equation (16) gave estimates of CS of acceptable accuracy over a range of yarn count – Table II – 6 –vii.

The modification of the general equation to predict rotor yarn CS from HVI length, uniformity ratio, tenacity and micronaire seems a distinct possibility.

Cotton	XX S-4			ZZ F 414
Effective length, mm	32.3			27.1
% fibres shorter than 12-mm	19.8			19.7
% fibres longer than 24-mm	56.1			37.8
Stelo g/t at zero gauge	35.42			43.40
Stelo g/t at 1/8-inch	19.29			21.43
Fibre fineness, millitex	130			150
Cost index	100			84
T.M.	CSP at NE
	30	50	30		50
3.25	2144	1853	1639		1297
3.75	2307	2044	2121		1781
4.25	2300	2056	2278		1974
4.50	2270	2034	2288		2000
4.75	2231	2001	2273		1998

Table II – 6 – i Comparing CS 0f two cottons:
one long and fine but weak and another short and coarse but strong

cotton	L mm	H mtex	Z g/t	F g/t	S %	B %	NE C	TM M	OBS CS	ERR %
% DCH %G11	L mm	H mtex	Z g/t	F g/t	S %	B %	NE C	TM M	OBS CS	ERR %
100 0	37.2	88	41.32	22.46	25.7	49.6	30	4.6	2719	0.2
75 25	34.4	100	41.23	22.06	23.6	45.8	30	4.6	2498	-0.5
50 50	31.7	115	41.15	21.59	21.4	41.9	30	4.6	2318	-2.5
25 75	29	136	41.06	21.19	19.3	38	30	4.6	2034	0.3
0 100	26.2	166	40.97	20.79	17.2	34.2	30	4.6	1838	-0.5

Table II – 6 - ii: Application Of Equation To Estimate
CSP Of Yarns From Mixings Of Disparate Cottons

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%-AGE IN MIX OF		NOIL 10 %						NOIL 18 %
%-AGE IN MIX OF		NE 30				NE 40		NE 30				NE 40
VL	G 11	OBS C S	% ERR	RATIO CS C/K		OBS C S	% ERR	OBS C S	% ERR	RATIO C/K		OBS C S	% ERR	RATIO CS 18 %/ 10 %
				OBS	EST					OBS	EST			OBS	EST
				OBS	EST					OBS	EST			OBS	EST
100	0	2965	-0.6	1.090	1.082	2809	1.6	3078	-0.7	1.132	1.122	2898	2.3	1.038	1.045
75	25	2715	-1.4	1.087	1.077	2520	1.1	2816	-1.3	1.127	1.118	2627	1.0	1.032	1.039
50	50	2390	1.3	1.031	1.072	2242	0.7	2507	0.5	1.082	1.114	2288	3.1	1.042	1.042
25	75	2189	0.6	1.076	1.066	1982	0.0	2306	-1.7	1.134	1.111	2050	1.3	1.021	1.044
0	100	1985	-2.3	1.080	1.061	1720	0.2	2093	-3.3	1.139	1.107	1829	-1.0	1.034	1.047

TABLE II – 6 – iii Accuracy of estimates of combed yarn CS
by Modified equation

** Yarn of this count was not spun.

COTTON	FQI	T.M.	% ERROR
COTTON	FQI	T.M.	100s	90s	80s	70s	50s	40s	30s	20s
Suvin	369.4	3.6	5.3		-4.7	1.6	0.7	3.2	5.7	1.8
	369.4	4.0	-3.6		-3.5	6.8	3.6	0.6	5.2	-0.2
	369.4	4.4	-3.2		2.5	1.4	5.8	1.1	6.9	-0.3
DCH 32	341.9	3.8	**		2.3	-0.3	1.3	2.4	6.5	5.2
	341.9	4.2	**		0.0	-0.2	1.7	1.4	4.9	5.7
	341.9	4.6	**		1.3	1.9	2.4	1.3	5.2	7.6
MCU 5	280.2	3.9	**	-2.2	0.7	0.9	0.1	-2.6	-0.7	-2.2
	280.2	4.3	**	-1.7	-0.6	-2.7	-2.4	-0.3	-0.2	-4.5
	280.2	4.6	**	0.2	0.2	-4.1	2.3	0.5	1.9	-4.3
LK	215.0	4.0	**	**	**	11.0	8.8	1.7	3.6	7.3
	215.0	4.4	**	**	**	6.5	4.9	1.9	8.2	3.2
	215.0	4.9	**	**	**	7.9	8.0	2.5	10.5	8.9
S 6	157.0	4.0	**	**	**	4.9	12.5	-0.8	3.1	5.4
	157.0	4.5	**	**	**	7.9	5.9	7.3	5.0	-0.5
	157.0	5.0	**	**	**	13.9	10.0	10.3	8.5	3.1
Mech	144.3	4.1	**	**	**	**	5.8	7.5	11.3	5.5
	144.3	4.6	**	**	**	**	4.5	9.4	4.4	5.5
	144.3	5.0	**	**	**	**	7.0	8.4	9.2	8.7
LRA	163.1	4.2	**	**	**	**	**	20.1	14.2	17.2
	163.1	4.7	**	**	**	**	**	15.5	19.8	13.3
	163.1	5.1	**	**	**	**	**	16.3	18.5	15.8
RCH	107.4	4.3	**	**	**	**	**	**	-4.2	-7.9
	107.4	4.8	**	**	**	**	**	**	-5.3	-8.8
	107.4	5.3	**	**	**	**	**	**	-5.0	-4.2
V797	76.4	4.4	**	**	**	**	**	**	2.6	4.8
	76.4	4.8	**	**	**	**	**	**	1.7	-3.0
	76.4	5.3	**	**	**	**	**	**	5.8	3.4

II – 6 - iv % ERROR IN ESTIMATES OF CSP SITRA FORMULA

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COTTON	UHML	ML	TEN	EST EL	EST A	H	EST G	EST(1+r)	EST Z	EST F	Q
suvin	35.8	30.6	33.8	38.9	35.8	97	0.343	0.857	39.9	23.0	4.27
DCH	34.6	29.1	32.9	37.6	34.9	103	0.357	0.863	40.0	22.5	4.29
mcu5	32.2	26.6	31.6	35.0	33.1	117	0.382	0.880	40.8	22.1	4.32
LK	29.9	25.1	31.7	32.5	31.3	141	0.399	0.895	42.8	22.5	4.36
S-6	28.8	23.7	26.5	31.3	30.6	151	0.415	0.916	37.6	19.3	4.38
Mech	25.8	20.7	23.7	27.9	28.8	143	0.454	0.995	38.9	18.7	4.43
LRA	24.8	20.3	24.9	26.7	28.3	137	0.460	1.011	41.9	20.0	4.45
RCH	24	19.4	22.7	25.8	28.0	165	0.473	1.056	40.7	19.0	4.46
V797	23	18.5	19.4	24.6	27.8	183	0.487	1.116	37.6	17.2	4.46

Table – II – 6 - v Estimates of Conventional Fibre Test Data
from HVI Data SITRA Cottons

EST: estimated; EL: effective length; H: fibre fineness, millitex;
Z: zero-gauge Stelo level fibre-bundle tenacity;
G: gauge-length parameter of tenacity; F: Stelo level 1/8-in gauge tenacity;
Q: floating fibre index, a function of HVI UHML and ML

COTTON	L	H	Z	F	S	B	G	A	Q	f
DCH	39.3	118	41.1	23.7	26.3	50	0.341	34.0	4.303	0.636
MCU5	34.8	114	41.5	21.0	28.1	42.6	0.422	31.4	4.359	0.592
VL	34.0	109	39.0	21.5	22.9	52.3	0.369	34.6	4.291	0.645
S4	32.3	130	35.4	19.3	19.8	56.1	0.378	36.5	4.261	0.67
MCU7	30.0	146	44.0	23.5	24.2	48.7	0.390	32.7	4.328	0.616
JYOTI	28.1	157	42.1	20.2	23.3	36.6	0.455	29.8	4.401	0.562
F414	27.1	150	43.4	22.1	19.7	37.8	0.420	30.7	4.376	0.580
SOM	26.7	132	34.0	17.8	22.1	34.7	0.403	29.4	4.413	0.553
J34(K)	26.7	148	41.3	20.0	21.9	33.9	0.451	29.2	4.418	0.550
J34	25.4	142	42.8	20.8	25.7	27	0.449	27.1	4.490	0.503
CJ	25.4	168	44.1	22.7	24.9	29.2	0.413	27.6	4.470	0.515
CO2	23.9	171	35.3	15.6	29.9	15.8	0.507	25.0	4.584	0.446

Table – I –6 - vi Conventional Fibre Test Data
on Cottons Comparable to those in Table – A - viii

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Cotton	OBS CS FOR NE10.1	% ERROR IN ESTIMATE FOR YARN COUNT NE (T.M.)
Cotton	OBS CS FOR NE10.1	10.1 (5.3)	20.2 (5.1)	32.4 (4.9)
1-A	2549	-3.4	-4.3	-5.9
1-B	2546	0.9	-0.2	-3.4
2-A	2807	-3.2	-2.7	-0.5
3-A	2404	0.8	1.9	-4.5
3-B	2384	-1.0	4.4	1.8
3-C	2401	3.7	7.6	1.5
4-A	2256	1.8	2.8	-3.8
5-A	2065	-1.8	-3.6	-2.3
6-A	1723	4.8	-4.7	0.0
7-A	1232	2.1	**	**

Table I –6 - vii Percentage Error in Estimate of CS Of Rotor-Yarns
By General Equation Modified To Accept HVI Cotton Test Data

** Cotton 7-A could not be spun to these counts.
Source of fibre and yarn data:
Zhang Hongwei pp 44-46, ITB (1/2003)


Figure II – 6 – i CS – C plot of yarns from S-4 and F 414 cottons	Figure II – 6 – ii CS – M plot of yarns from S-4 and F 414 cottons


Figure II – 6 – iii CS – C plot of yarns from Karnak and Interspecies cottons	Figure II – 6 – iv CS – M plot of yarns from Karnak and Interspecies cottons


Figure –II –6 - v Fibre Length Distribution of Two Cottons


Figure II – 6 - vi Increasing Trend In Fibre-Tenacity With Length: SITRA Data Cottons: Suvin, DCH32, MCU5, S-6, LK, MECH, LRA, RCH, V797	Figure II – 6 - vi Increasing Trend In Fibre-Tenacity With Length: SITRA Data Cottons: Suvin, DCH32, MCU5, S-6, LK, MECH, LRA, RCH, V797


Figure II – 6 –vii Lack of trend between tenacity by manual method and fibre length Cottons: DCH, VL, MCU5, MCU7, S-4, F414, Jyoti, Somnath, J34(1), J34(2), CJ, CO2~~	Figure II – 6 – vii Lack of trend between tenacity by manual method and fibre length Source Brown, J.J., Howell, N.A., Fiori, L. A., Sands, J. E. and Little. H. W., Tex. Res. J, 27, 332-339 (1957).

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Figure II – 6 – vii Lack of trend between tenacity by manual method and fibre length
Cottons: American El Paso, twelve US cottons ranging in staple from 7/8-in to 13/32-in, three Ugandan, two Brazilian, three Pakistani Source Lord, E., The Characteristics of Raw Cotton, Vol. I, Part I, Manual of cotton Spinning, The Textile Institute, Butterworths, Manchester and London, 1962, 310

Figure II – 6 – viii Adjusted SITRA HVI Fibre-tenacity and Manually Tested Tenacity of Similar Cottons VS Length
Adjusted: Tenacity values after correcting for length related bias
Manual: Data from ATIRA Spinnings in which tenacity was determined
by manual testing and did not incur the bias

Figure II – 6 - ix Comparing Errors in Estimates of CSP

NOTE: With The SITRA equation errors are on either side, positive and negative, in the first half of the plot, but positive errors predominate in the second half of the plot; with the Modified General Equation there is hardly any bias.

Figure II – 6 –x Plot of Fibre-tenacity VS Length: ITB Data
Source of Data: Zhang Hongwei, Relationship Of Cotton Fibre HVI Properties

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PART - II

Conceptual Framework and Methodology Used to Derive the Algebraic Expressions

Chapter 1	Concept and Structure of a General Equation
Chapter 2	The Algebraic Expression 0f the General Equation : The First Attempt
Chapter 3	Improved Algebraic Expressions And Their Interpretation
Chapter 4	Implications of the General Equation
Chapter 5	Appraisal
Chapter 6	Practical Application
APPENDIX II - 1	Derivation of the algebraic expressions in the general equation for Brown’s data
APPENDIX II - 2	Regression equations for estimating Uster frequencies of thin and thick places in yarn
APPENDIX II - 3	Estimating yarn CS from the ATIRA expressions for the general equation.
APPENDIX II - 4	Cross-Checking Applicability Of Model To Viscose Yarns
APPENDIX II - 5	Procedure for Adjusting SITRA HVI Test Data To Use In The Modified General Equation For Estimating CS Of Ring-spun Yarns of optimum twist