截齿切削厚度与截割比能耗的算法及误差分析

Algorithm behind cutting thickness and specific energy of conical picks and its error analysis

为给出截齿切削厚度和截割比能耗的准确算法,通过分析滚筒半径、最大切削厚度和截齿位置角三者间的数学关系,提出切削厚度和截割比能耗的准确算法,对比分析准确算法与近似算法间的误差变化范围。通过研究截齿截割速度、采煤机牵引速度和滚筒转速三者间的几何关系,获得截齿截割速度的准确算法、截割速度大小与方向的变化规律。结果表明:当滚筒半径为0.3 m、最大切削厚度为50 mm,截割位置角为10°时,切削厚度两种算法误差率为32.0%,截齿截割一周平均切削厚度误差率为6.0%,截割比能耗误差率为33.4%;截齿截割速度两种算法误差最大值等于采煤机牵引速度大小。该研究为截齿截割参数和截割比能耗的准确计算提供了参考。

This paper proposes an accurate algorithm behind cutting thickness and specific energy of conical picks.The study consists of achieving the accurate algorithm of cutting thickness and the specific energy of conical picks by analyzing the mathematical relationship among the drum radius,the maximum cutting thickness and the position angle of the conical picks;obtaining the error range of different algorithms by comparing and analyzing the error range between the accurate algorithm and the approximate algorithm;and identifying the accurate algorithm for the conical picks and the changing rules controlling the cutting speed and direction by analyzing the geometric relations among the cutting speed of the conical picks,the haulage speed of the shearer,and the rotation speed of the drum.The results show that,in the presence of the drum radius(0.3 m),the maximum cutting thickness(50 mm),and the cutting position angle(10°)the error rates are 32.0%,6.0%,and 33.4%respectively for the cutting thickness by the two algorithms,for the average cutting thickness the picks,and for the specific energy of the cutting ratio.The maximum error produced by the two algorithms in cutting speed of picks is equal to the haulage speed of shearers.This study could provide a reference for further calculation of cutting parameters and specific energy of conical picks.