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We studied consecutive impact loading on woven high-modulus polyethylene rope, which is used in robotics fields. An impact tester was developed to conduct the experiments. Five consecutive impact loads (five drops) were applied to the rope and the stiffness of the loading part that corresponds to each drop was evaluated. The stiffness of the woven ropes was affected strongly by consecutive impact loading. The change in stiffness is undesirable in some applications such as in robotic fields. Therefore, we have proposed a method that can optimize changes in stiffness by applying a preload before impact testing (preload treatment). The experimental results show that preload is an efficient way to reduce changing rope stiffness. We have also proposed an empirical equation that can estimate the rope stiffness after arbitrary preload treatment, and this equation is a function of the number of drops and the static preload level. The equation can be used to determine the preload treatment conditions to stabilize the stiffness of the woven ropes before they are used in engineering fields.

Woven synthetic-fiber ropes such as high-modulus polyethylene (HMPE), polyester, polyamide and aramid were developed decades ago and they have emerged as potential materials to replace steel-wire ropes because they offer advantages of light weight, high strength, a high flexibility and a low friction coefficient. They have been used in many applications, such as in offshore mooring systems, climbing mountaineering ropes, and recently, in robotics fields in artificial muscles [

Although synthetic-fiber ropes have been used in many applications, their mechanical behavior is complicated, mainly because of the polymeric nature of the fibers that are used in their manufacture and the construction geometry of the ropes (either in twisting or braiding) [

Flory et al. [

Therefore, the stiffness of the synthetic-fiber ropes that are used in offshore mooring lines has been studied extensively, particularly for large-diameter ropes under cyclic loading. However, no specific research has investigated the stiffness of synthetic-fiber rope because of the constant consecutive loading of large- or small-diameter ropes. Small-diameter synthetic-fiber rope is used in the robotic fields [

In summary, because of the lack of research that deals with consecutive impact loading and methods to optimize stiffness changes of synthetic-fiber rope, the main purpose of this research has been to study the effect of consecutive impact loading and to optimize changes in the rope stiffness. Consecutive impact loading is represented in terms of the number of drops. A preload method was used to determine its effect on the stiffness of a fiber rope. We proposed an empirical equation for stiffness by considering the number of drops and the preload level based on experimental data, and we discuss the pre-treatment of rope before using it in a robotics application.

HMPE, which is normally used in robotic fields, was used in this study. This rope has an MBL of 1765 N under a static loading, a linear density of 1760 dtex, and 8 strands in braided construction. Tex is a unit that is used commonly in textile engineering to measure the linear mass density of fibers and yarns, and it equates to the mass in grams per kilometer (1 tex = 10 dtex). A photograph and the properties of this rope are shown in

An impact tester as shown in

Material | High Modulus Polyethylene (HMPE) |
---|---|

Fiber | IZANAS |

Fiber Model | DB-60 |

MBL (Static) (N) | 1765 |

Construction | 1760 dtex, 8 strands braid |

Diameter (mm) | 2 |

Supplier | Fiber: Toyobo, Rope: Hayami Industry |

ponents with the first being the drop mass that is used to generate an impact load. The mass moves along linear guides that are mounted on side poles of the tester. The second part that is located on the side of the drop mass is the steel disk that is used to fix the fiber rope at the bottom end. The disk is used to reduce the stress concentration of the ropes at a fixed point. The third component is the rotating winch on the right of the tester that is used to lift and release the drop mass by connecting it with a rope. The fourth component is a load cell (Kyowa, LUK-A-10 KN) that is used to measure the impact load by mounting on top of the tester. The fiber rope is fixed to this load cell directly. The fifth component is the draw-wire displacement sensor (Tokyo Sokki Kenkyujo, DP-500E) that is used to measure the rope elongation.

Impact testing was performed by releasing a 5.1-kg drop mass from 1.2 m. Impact testing was carried out under two conditions, with the first being for virgin rope and the other being for rope after preload treating. Ropes were cut to 1.8 m and were subjected to five consecutive impact loads. Impact load simulates most severe load that will apply to the robots. Preload treatment was performed by applying a deadweight on the rope for 1 h and the preload levels used in the experiment are presented in

A normalized stiffness of the ropes that were subjected to consecutive impact loading was calculated by using Equation (1), which was proposed by Francois and Davis [

where K is the non-dimensional stiffness of the rope from impact loading, E is the longitudinal elastic modulus of the rope (MPa), A is cross-sectional area of the virgin rope

The obtained parameters were the load and displacement with respect to time for each impact test. We investigated the relationship between load and displacement.

Preload (N) | |
---|---|

172 | 0.097 |

220 | 0.124 |

363 | 0.206 |

607 | 0.344 |

Stiffness | Case 1 | Case 2 | Case 3 | Average |
---|---|---|---|---|

K1 | 4.4 | 3.8 | 3.5 | 3.9 |

K2 | 19.5 | 15.2 | 12.9 | 15.9 |

K3 | 24.1 | 20.0 | 17.7 | 20.6 |

K4 | 27.4 | 24.9 | 22.1 | 24.8 |

K5 | 27.7 | 26.1 | 24.3 | 26.0 |

consecutive impact loading and preload treatment on stiffness, so we take the average of the stiffness for the three cases as a representative rope stiffness. The stiffness results indicate that consecutive impact loading affects the HMPE rope significantly by changing the stiffness with respect to the number of drops. These phenomena occurred because of the nature of the viscoelastic ropes and their construction geometry. Northolt et al. [

According to the results of virgin rope that was subjected to consecutive impact loading, the rope stiffness was changed by the number of drops. The stiffness changed significantly after the first drop (second to fifth drops). This inconsistence of stiffness causes a number of problems in practical applications, for example, in robotic fields, because the transfer function of the robot system is changed by this inconsistence. Based on this problem, we propose a so-called preload treating method to minimize the change in rope stiffness. Preload treatment was applied at 0.097, 0.124, 0.206 and 0.344 of the rope MBL for 1 h prior to conducting impact testing. When the rope was subjected to preloading, its construction geometry changed notably when the preload value was high because of a rearrangement of fibers and strands that move toward to rope axis as depicted in

N. drop | Stiffness | Preload level | |||
---|---|---|---|---|---|

0.097 | 0.124 | 0.206 | 0.344 | ||

1 | K1 | 10.6 | 13.3 | 17.3 | 19.7 |

2 | K2 | 18.1 | 20.8 | 23.5 | 26.1 |

3 | K3 | 21.2 | 21.1 | 23.5 | 25.7 |

4 | K4 | 21.3 | 22.3 | 23.2 | 25.4 |

5 | K5 | 24.1 | 23.2 | 23.3 | 26.7 |

y-axis is impact load and right y-axis is the ratio of impact load to MBL.

An empirical equation is usually needed to compare results from experimental data, discuss trends in results and estimate results at the outer range of the experimental data. Many proposed empirical equations exist for the stiffness for woven synthetic-fiber ropes based on experimental parameters and researchers’ concepts. Recently, Liu et al. [

where

Inspired by Equation (2) and based on the experimental data from our research, we found that the stiffness of the synthetic-fiber rope depends on two main parameters, namely, the number of drops and the preload level. The stiffness increases as the preload level and/or the number of drops increases and it becomes stable as the preload level and the number of drops becomes large. An empirical equation of the stiffness in this research is proposed as follows:

where

In Equation (3), the stiffness is dimensionless because the preload level

substituting the preload level

ropes exhibits fewer changes because they have already changed during preload treating, and so their errors are smaller than those of virgin rope and the errors decrease while the preload level increases.

Parameters | a | λ | μ | α | γ | φ |
---|---|---|---|---|---|---|

Value | 25.9768 | 45.3700 | 1.3113 | 1.0376 | 0.6921 | 0.9919 |

N. drop | Stiffness | Nopreload | Preload level | |||
---|---|---|---|---|---|---|

0.097 | 0.124 | 0.206 | 0.344 | |||

1 | K1 | 7.67 | 11.8 | 12.8 | 15.4 | 18.6 |

2 | K2 | 18.6 | 21.0 | 21.5 | 22.7 | 24.1 |

3 | K3 | 23.0 | 24.2 | 24.4 | 25.0 | 25.5 |

4 | K4 | 24.8 | 25.3 | 25.4 | 25.7 | 25.9 |

5 | K5 | 25.5 | 25.8 | 25.8 | 25.9 | 25.9 |

To discuss the detail of the effect of consecutive impact loading in terms of the number of drops on the stiffness of the HMPE rope, the relationship between stiffness and number of drops with a variation in preload levels at 0, 0.1, 0.2, 0.5, 0.8 and 0.9 of the MBL was calculated by using Equation (3) with the parameters in

Equation (3) is the empirical expression for stiffness in which only the preload and number of drops is considered. This empirical expression provides the basis for understanding the effect of preload and number of drops on the HMPE rope and it will be useful for future research by taking additional parameters into account, such as density, diameter and braiding angle of the rope. There is a possi- bility that a suitable procedure exists (level of preload and number of drops) for preload treatment to stabilize the rope stiffness.

We investigated changes in the stiffness of HMPE rope subjected to consecutive impact loading and studied the effect of preload treatment on the rope stiffness. Based on these research results, we could derive useful conclusions:

² Consecutive impact loading affects the properties of virgin HMPE rope by changing the stiffness from the first to the next drops because of a rearrangement of rope structure such that all fibers or strands move towards to the rope axis.

² The construction geometry of the rope is changed by preload treatment.

² It was found that the rope stiffness becomes stable and hardened by preload treatment when the maximum of impact loading is around 1/3 of preload level (0.344 of MBL). This treatment is useful to stabilize response of woven synthetic-fiber rope in robotic.

² An empirical expression for stiffness is proposed by considering the number of drops and preload level. Results from experimental data and empirical equation agree reasonably well. Suitable preload-treatment can be estimated by using this equation.

² The stiffness of virgin rope becomes stabilize when the rope experiences six consecutive impact loadings (six drops) as depicted in

This paper is based on results from a project commissioned by the New Energy and Industrial Technology Development Organization (NEDO).

Sry, V., Mizutani, Y., Endo, G., Suzuki, Y. and Todoroki, A. (2017) Consecutive Impact Loading and Preloading Effect on Stiffness of Woven Synthetic-Fiber Rope. Journal of Textile Science and Technology, 3, 1-16. https://doi.org/10.4236/jtst.2017.31001