【正文】 mum tool geometry and machining conditions to produce the best possible surface quality within the constraints. The constrained optimization problem is stated as follows: Minimize Ra using the model given here: where xil and xiu are the upper and lower bounds of process variables xi and x1, x2, x3, x4 are logarithmic transformation of cutting speed, feed, radial rake angle and nose radius. The GA code was developed using MATLAB. This approach makes a binary coding system to represent the variables cutting speed (S), feed rate ( f ), radial rake angle (α) and nose radius (r), . each of these variables is represented by a ten bit binary equivalent, limiting the total string length to 40. It is known as a chromosome. The variables are represented as genes 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 9 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 10 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. 11 中文翻譯 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 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。它可用于各種各樣的制造工業(yè)，包括航空航天和汽車這些以 質(zhì)量為首要因素的行業(yè)，以及在生產(chǎn)階段，槽孔，精密模具和模具這些更加注重尺寸精度和表面粗糙度產(chǎn)品的行業(yè)內(nèi)。它也影響著芯片冰壺和修改芯片方向人流。實(shí)驗(yàn)顯示，這項(xiàng)工作將被用來測(cè)試切削速度，進(jìn)給速度，徑向前角和刀尖半徑與加工反應(yīng)。所進(jìn)行的若干實(shí)驗(yàn)是用來決定該中心復(fù)合設(shè)計(jì)的。 因?yàn)槎算娺^程介入多數(shù) f參量，重大參量的聯(lián)合只能通過塑造得到。該模型是銑操作進(jìn)行實(shí)驗(yàn)鋼標(biāo)本。他們還優(yōu)化了車削加工用表面粗糙度預(yù)測(cè)模型為目標(biāo)函數(shù)。 一般二階多項(xiàng)式的回應(yīng)是，作為提供以下資料： 如 Y2型是估計(jì)響應(yīng)的基礎(chǔ)上的二階方程。眾多的制約因素和月票數(shù)目，使加工優(yōu)化問題更加復(fù)雜化。 遺傳算法（ GA ）表格一類是自適應(yīng)啟發(fā)式原則的基礎(chǔ)上得出的，從動(dòng)態(tài)的人口自然遺傳學(xué)。加文來根據(jù)類別的非傳統(tǒng)的搜索和優(yōu)化技術(shù)。有效性選定的模型用于優(yōu)化工藝參數(shù)，是經(jīng)過檢驗(yàn)的幫助下統(tǒng)計(jì)測(cè)試，如 F檢驗(yàn)，卡方檢驗(yàn)等 [10] 。 13 3 方法論 在這項(xiàng)工作中，數(shù)學(xué)模型已經(jīng)開發(fā)使用的實(shí)驗(yàn)結(jié)果與幫助響應(yīng)面方法論。上述模式并沒有考慮到對(duì)刀具幾何形狀對(duì)表面粗糙度的影響。數(shù)學(xué)模型已經(jīng)研制成功，可用在計(jì)算切削速度，進(jìn)給速度和軸向切深。對(duì)主軸速度，切削深度和進(jìn)給速度對(duì)切削力和表面粗糙度的影響進(jìn)行了研究。 2回顧 12 建模過程與優(yōu)化，是兩部很重要的問題，在制造業(yè)。因此，發(fā)展一個(gè)很好的模式應(yīng)當(dāng)包含徑向前角和刀尖半徑連同其他相關(guān)因素。因此，測(cè)量表面光潔度，可預(yù)測(cè)加工性能。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。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。此外，表面光潔度還影響到機(jī)械性能，如疲勞性能，磨損，腐蝕，潤滑和導(dǎo)電性。此外，研究人員 [ 1 ]也指出，在不影響表面光潔度情況下，刀尖半徑發(fā)揮著重要作用。數(shù)學(xué)模型的進(jìn)一步利用，尋找最佳的工藝參數(shù)，并采用遺傳算法可促進(jìn)更大發(fā)展。切削性能的立銑刀則被評(píng)定采用方差分析。曼蘇爾和艾布達(dá)萊特基地 [ 5 ]已開發(fā)出一種表面粗糙度模式，為年底銑 EN32M（半自由切削碳硬化鋼并改進(jìn)適銷性）。表明表面粗糙度及各項(xiàng)參數(shù)，即切削速度，飼料和切削深度之間的關(guān)系?？紤]到上述情況，已試圖在這方面的工作，以發(fā)展一個(gè)表面粗糙度的模型與工具幾何形狀和切削條件，在此基礎(chǔ)上的實(shí)驗(yàn)結(jié)果，然后再優(yōu)化，在端銑操作中，它為選拔這些參數(shù)給定了限制。參數(shù)，即本 B0中， B1， B2的， B3的， B4的，B12的， b23的， b14等 ，要估計(jì)由最小二乘法。因此，決定使用遺傳算法作為優(yōu)化技術(shù)。搜索過程模擬自然的評(píng)價(jià)生物的動(dòng)物，和