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An analysis is given from which equations can be derived that relate the variations of twist factor, tension, and yam path through a false-twist friction spindle. The solution of these (differential) equations leads to predictions about the dependence of over-all twist factor and tension ratio on, among other parameters, the ratio of yam speed to spindle speed, the angle of wrap, and the input tension. These are compared with the early experimental results of Arthur and Weller and with more recent results. The equations also yield the variation of twist factor and tension over the spindle surface and could be used to estimate wear. The early part of the analysis would have general application in any situation in which a yarn is moving over a surface.
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J. J. Thwaites (1970) studied this question.
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