Generalized capstan problem: Bending rigidity, nonlinear friction, and extensibility effect
Generalized capstan problem: Bending rigidity, nonlinear friction, and extensibility effect
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DOI：
10.1016/j.triboint.2007.11.005
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发表时间：
2008-06
影响因子：
6.2
通讯作者：
J. Jung;N. Pan;T. Kang
中科院分区：
文献类型：
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作者：
J. Jung;N. Pan;T. Kang
本研究建立了一个包含延伸率和泊松比的绞盘问题的理论模型。研究了几种情况下重要参数对张力传递效率的影响。结果表明，杆件的可伸长性与杆件的抗弯刚度和系统的摩擦性能的影响相竞争，从而提高了张力比。在没有摩擦修正的情况下（n=1，简单的Amonton定律），较大的初始应变产生较大的拉伸比。这种效应在高半径比时更加显著。但是，当初始张力T0增大时，修正摩擦定律的作用可能会压制杆伸长的作用。泊松比的影响也倾向于增加拉伸比。但这一数额几乎可以忽略不计，因为最大降幅至多为7.8%。我们还通过求解控制方程和迭代λavg的值来计算整个杆的平均应变。整个棒的计算应变是初始应变的2.6倍。但这一贡献导致最多1.078倍的半径比初始杆半径。因此，仅考虑延伸率对拉伸比增加的影响就足够了。我们还提出了建立模型的几个先决条件。介绍并澄清了对这一模式的三个主要关切。
A theoretical model of the capstan problem including the extensibility and the Poisson's ratio of the rod is established in this study. Several cases were examined to investigate the effects of important parameters on the tension transmission efficiency. As a result, the rod extensibility turned out to enhance the tension ratio, competing with the effects of rod bending rigidity and the frictional behaviors of the system. In case of no frictional modification (n=1, the simple Amonton's law), larger initial strain renders greater tension ratio. This effect becomes more remarkable at high radius ratio. However, the effect of the modified frictional law may oppress the effect of rod extensibility if the initial tension T0grows larger. The effect of Poisson's ratio also tends to increase the tension ratio. But the amount was almost negligible since the maximum decrease was at most 7.8%. We also calculated the average strain throughout the rod by solving the governing equation and iterating the value of λavg. Calculated strain throughout the rod was up to 2.6 times larger than initial strain. But this contribution leaded to at most 1.078 times larger radius ratio than the initial rod radius. Thus, it is well enough to consider only the extensibility effect on the increase of the tension ratio. We also presented several prerequisites to establish the model. Three major concerns about this model were introduced and clarified.