纤维绳索强力与直径、线密度数学模型分析

Mathematical models of diameter and linear density with breaking strength for chemical fibre ropes

以ISO1346-2012中聚丙烯8股绳索为例,分别对该绳索的直径和断裂强力、线密度和断裂强力进行了指数函数拟合,并进行修正检验。通过对修正前后函数的极差和方差等比较,结果显示,修正后的函数比修正前函数的准确度有明显提高。用相同的方法对现有ISO标准中的其它材质和规格绳索进行分析,分别建立了其它材料绳索的直径和断裂强力以及线密度和断裂强力的数学模型。该直径-强力与线密度-强力模型的建立,对进行软件设计以及数据库的建立有重要辅助作用,对标准中未规定的产品的设计和技术指标的建立也具有重要的指导和参考意义。

Chemical fiber technology has been developing fast in the past two decades, especially the high strength fiber. Chemical fiber ropes play a more and more extensive role in the production of all fields in the world, with the advantage of high strength and light weight. The high strength fiber ropes have been widely applied in the areas of load lifting, deep sea mooring and gradually replaced traditional wire rope. The International Standardization Organization sets rules for the diameter, breaking strength and linear density of ropes made by all kinds of chemical fibers, guiding the applications of ropes. However, the key indicator values of ropes of other sizes are not clear in ISO standards. Diameter and breaking strength values of polypropylene 8-strand rope in ISO1346 -2012 were analyzed as an example, and mathematical model was fitted and revised. The exponential function RN = k · Fx of diameter and breaking strength was given in ISO 1346 -2012, every value of diameter-breaking strength was taken into the function and got the corresponding “x”. The x value was optimized, and the ones with the probability less than 5 % were removed, so as to get the function model of diameter and breaking strength of polypropylene 8-strand rope. The revised model was obviously more accurate. Chemical ropes of other materials and specifications in other ISO standards were also analyzed in the similar way. The corresponding mathematical models of diameter-breaking strength and linear density-breaking strength were also obtained. Function models were established for rope indicators, when there are standards in the future. The models in the meanwhile it could set up or update the models paper are innovative and helpful in the following aspects ： Firstly, various chemical materials and rope structures are included. The models refer to most of rope sizes：8-strand, 12-strand and double braid rope structures of the exiting fiber-polypropylene, polyester, polyamides, ultra high molecular weight polyethylene and the multiple materials. This will greatly enlarge the types of rope standards. Secondly, calculate the key indicators of continuous size of the rope. The fitted models contain all continuous size of the rope, making it possible to calculate the specified indicator values when other indicators are decided. That will be helpful in the design and production of ropes. Finally, direct the database and specific software design. Some rope database and software are made to test or design the rope structure, diameter, breaking strength and other factors. The models established in the paper will play an important supporting role in this respect.