【導(dǎo)讀】附錄。conditions.Nomenclature. dofDegreeoffreedom. fFeedrate,mm/min. rNoseradius,mm. SCuttingspeed,m/min. YMachiningresponse,μm. Greekletters. Responsefunction. αRadialrakeangle,degree. ∈Experimentalerror. 1Introduction

　　

【正文】 It is known as a chromosome. The variables are represented as genes (substrings) in the chromosome. The randomly generated 20 such chromosomes (population size is 20), fulfilling the constraints on the variables, are taken in each generation. The first generation is called the initial population. Once the coding of the variables has been done, then the actual decoded values for the variables are estimated using the following formula: where xi is the actual decoded value of the cutting speed, feed rate, radial rake angle and nose radius, x(L) i is the lower limit and x(U) i is the upper limit and li is the substring length, which is equal to ten in this case. Using the present generation of 20 chromosomes, fitness values are calculated by the following transformation: where f(x) is the fitness function and Ra is the objective function. Out of these 20 fitness values, four are chosen using the roulettewheel selection scheme. The chromosomes corresponding to these four fitness values are taken as parents. Then the crossover and mutation reproduction methods are applied to generate 20 new chromosomes for the next generation. This processof generating the new population from the old population is called one generation. Many such generations are run till the maximum number of generations is met or the average of four selected fitness values in each generation bees steady. This ensures that the optimization of all the variables (cutting speed, feed rate, radial rake angle and nose radius) is carried out simultaneously. The final statistics are displayed at the end of all iterations. In order to optimize the present problem using GA, the following parameters have been selected to obtain the best possible solution with the least putational effort: Table 7 shows some of the minimum values of the surface roughness predicted by the GA program with respect to input machining ranges, and Table 8 shows the optimum machining conditions for the corresponding minimum values of the surface roughness shown in Table 7. The MRR given in Table 8 was calculated by where f is the table feed (mm/min), aa is the axial depth of cut (20 mm) and ar is the radial depth of cut (1 mm). It can be concluded from the optimization results of the GA program that it is possible to select a bination of cutting speed, feed rate, radial rake angle and nose radius for achieving the best possible surface finish giving a reasonably good material removal rate. This GA program provides optimum machining conditions for the corresponding given minimum values of the surface roughness. The application of the geic algorithmic approach to obtain optimal machining conditions will be quite useful at the puter aided process planning (CAPP) stage in the production of high quality goods with tight tolerances by a variety of machining operations, and in the adaptive control of automated machine tools. With the known boundaries of surface roughness and machining conditions, machining could be performed with a relatively high rate of success with the selected machining conditions. 6 Conclusions The investigations of this study indicate that the parameters cutting speed, feed, radial rake angle and nose radius are the primary actors influencing the surface roughness of medium carbon steel uring end milling. The approach presented in this paper provides n impetus to develop analytical models, based on experimental results for obtaining a surface roughness model using the response surface methodology. By incorporating the cutter geometry in the model, the validity of the model has been enhanced. The optimization of this model using geic algorithms has resulted in a fairly useful method of obtaining machining parameters in order to obtain the best possible surface quality. References 1. Chung SC (1998) A force model for nose radius worn tools with a chamfered main cutting edge. Int J Mach Tools Manuf 38:1467–1498 2. Perez CJL (2020) Surface roughness modeling considered uncertainty in measurements. Int J Prod Res 40(10):2245–2268 3. Davies R, Ema S (1989) Cutting performance of end mills with different helix angles. Int J Mach Tools Manuf 29:217–227 4. Guven Y, Bayoumi AE (1993) Determination of process parameters through a mechanistic force model of milling operations. Int J Mach Tools Manuf 33:627–641 5. Mansour A, Abdalla H (2020) Surface roughness model for end milling: a semifree cutting carbon case hardening steel (EN32) in dry condition. J Mater Process Technol 124:183–191 6. Alauddin M, Hasmi MSJ (1995) Computer aided analysis of a surface roughness model for end milling. J Mater Process Technol 55:123–127 7. Hasmi MSJ, (1996) Optimization of surface finish in end milling inconel 718. J Mater Process Technol 56:54–65 8. Jain RK, Jain VK (2020) Optimum selection of machining conditions in abrasive flow using neural works. J Mater Process Technol 108:62–67 9. Suresh PVS, Venkateswara Rao P, Deshmukh SG (2020) A geic algorithmic approach for optimization of surface roughness prediction model. Int J Mach Tools Manuf 42:675–680 10. Montgomery DC (1996) Introduction to statistical quality control. Wiley, New York11. Goldberg DE (1999) Geic algorithms. AddisonWesley, New Delhi 選擇最佳工具，幾何形狀和切削條件 利用表面粗糙度預(yù)測(cè)模型端銑 收到日期： 2020年 10月 14日 /接受： 2020年 1 月 22日 /網(wǎng)上公布： 2020年 1 月 12日 施普林格出版社，倫敦有限公司 2020年 ? ? 摘要： 刀具幾何形狀 對(duì) 工件表面 質(zhì)量產(chǎn)生 的影響 是人所共 知的 ， 因此，任何成型面 端銑 設(shè)計(jì) 應(yīng)包括刀具的幾何形狀。在當(dāng)前的工作中，實(shí)驗(yàn)性研究 的 進(jìn)行 已 看到刀具幾何（徑向前角和刀尖半徑）和切削條件（切削速度和進(jìn)給速度） ，對(duì)加工性能， 和 端銑中碳鋼 影響效果 。第一次和第二次 為建立 數(shù)學(xué)模型，從加工參數(shù) 方面 ，制訂了表面粗糙度預(yù)測(cè)響應(yīng)面方法（丹參） ，在此基礎(chǔ)上的實(shí)驗(yàn)結(jié)果。該模型 取得的 優(yōu)化 效果 已得到證實(shí)， 并通過(guò)了 卡方檢驗(yàn)。這些參數(shù)對(duì)表面粗糙度 的 建立，方差分析 極具意義 。 通過(guò) 嘗試也取得了優(yōu)化表面粗糙度預(yù)測(cè)模型，采用遺傳算法（ GA ） 。在加文的程式 中實(shí)現(xiàn)了 最低值，表面粗糙度及各自的 值 都達(dá)到了 最佳條件。 關(guān)鍵詞 端銑；遺傳算法；塑造；徑向