Mechanics Research Communications 37 (2010) 129

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Mechanics Research Communications

journal homepage: www.elsevier .com/locate /mechrescom

Letter

Comment on He, J.H. et al., Quasistatic model for two-strand yarnspinning [Mech. Res. Commun. (2005), doi:10.1016/j.mechrescom.2004.05.010]

The first theoretical study on identifying the location of the con-vergence point in Siro spinning was presented by Emmanuel andPlate (1982). Their model was unsolvable due to the fact that thenumber of independent equations is less than that of the depen-dent variables. The theory was not improved until He et al.(2005) proposed a novel model. He combined static model withkinematic equations (conservation theorem) to the system, induc-ing new unidentified variables (u1, u2, x1 and x2) in the conserva-tion equations. Yu et al. (2005) tried to make the model closed viamaterial mechanics approach. However the initial problem wasnot solved.

Actually, in force equilibriums, the other torque equation in thehorizontal direction presented as below is lost by He et al. (2005)

m1 sin a1 �m2 sin a2 � f1 cos a1R1 þ f2 cosa2R2 ¼ 0 ð5aÞ

Furthermore, in the steady state, the convergence point mustobey angular momentum conservation

q1x1R21 cos a1 þ q2x2R2

2 cosa2 ¼ qxR2 ð10Þ

q1x1R21 sin a1 ¼ q2x2R2

2 sin a2 ð11Þ

0093-6413/$ - see front matter � 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.mechrescom.2009.09.001

where x1, x2 and x are rotation angular velocities of two strandsand resultant yarn.

Therefore, self-closed solutions of the 10 variables f1, f2, m1, m2,a1, a2, u1, u2, x1 and x2 can be theoretically obtained by the 10equations (3), (4), (5), (5a) and (6)–(11). No any empirical orsemi-empirical inputs are needed.

References

Emmanuel, A., Plate, D.E.A., 1982. An alternative approach to two-fold weaving yarnPart II: the theoretical model. J. Textile Inst. 73 (3), 107.

He, J.H., Yu, Y.P., Pan, N., et al, 2005. Quasistatic model for two-strand yarn spinning.Mech. Res. Commun. 32, 197–200.

Yu, Y.P., Liu, W.Y., Chen, L.D., et al., 2005. A new static model for Sirofil spinning. In:International Conference on Advanced Fibers and Polymer Materials, Shanghai,China, pp. 1277–1280.

Wen-yan LiuDepartment of Civil Engineering,

Suzhou Dengyun Institute of Science and Technology,1058 Ma’an shan Xilu Road,

Suzhou 215300, ChinaE-mail address: w.y.liu@163.com

Available online 27 September 2009