摘要
本文通过对自动化车床 1 0 0次刀具故障的记录进行数理统计分析 ,研究了自动化车床连续加工单一零件时刀具的检测及更换模型 .首先利用概率大样本场合的 D检验方法证明了刀具的故障发生规律服从正态分布 [1] ,继而求出系统工序的寿命分布函数 [2 ] ,列出以合格零件单位期望损失为目标 ,关于检测间隔和刀具定期更换间隔为变量的多目标函数方程 ,最后利用计算机进行列举比较求解 ,从而得出取得最大经济效益的系统工序的最优检测间隔以及最优刀具更换策略 .由于刀具的故障发生服从正态分布 ,我们对模型进行了改进 ,采取有规律的不等间隔的检查方式 ,结果取得了相对于等检查间隔的更优解 .本文利用算法较好地解决了问题 ,得到了问题的优化解 .对于问题 1 ,解得换刀间隔和检查间隔分别为369和 1 8,单位合格零件损失 4 .61 5元 ,采用不等间隔的损失为 4 .4 0 5元 ;对于问题 2 ,由于情况复杂 ,解得换刀间隔和检查间隔分别为 30 6和 2 8,单位合格零件损失 9.2 68元 ,采用不等间隔的损失为 9.0 4 7元 。
Through statistical analysis of more than1 0 0 times breakdown of cutting tools on the automatic machine tool,the checking and replacing model has been studied for cutting tool to machine only one part continuously.In this paper,by using of the D inspection method for the large- scale sample situation in the probability theory,it has been proved thatthe occurring law of cutting tool′s breakdown accords with the normal distribution.After figuring out the life- span distribution function of the system process,the multi- objective function equation has been obtained in which the unit expected loss of the qualified part is taken as objective and the checking interval as well as the regular replacement interval for cutting tool are variables.By means of enumeration and comparison methods to look for the solution on the microcomputer, the optimum checking interval and the optimum replacing strategy forthe cutting tool have been given which could bring outthe optimal economic profitin the system process.Since the occur- ring law of cutting tool′s breakdown accords the normal distribution,the improved model has been presented by adopting the regular unequal interval checking method and the better results than these of equal interval checking method are obtained. By using the algorithm mentioned above,the function has been solved fairly and the opti- mum solution has been got.In this paper two study cases are described.For case1 ,the inter- vals of replacing and checking are 369and 1 8respectively,the loss of unit qualified part is 4.61 5Yuan and it will be down to4.40 5Yuan if the unequal interval is adopted.For case2 , under complicated conditions,the intervals of replacing and thecking are30 6and2 8respective- ly,the loss of unit qualified part is 9.2 68Yuan and it will change to 9.0 4 7Yuan when using unequal interval.These results provide a more advantage proof for the improved model using the unequal interval checking method
出处
《数学的实践与认识》
CSCD
2000年第1期16-25,共10页
Mathematics in Practice and Theory
