【正文】 第3和第4 ，獲得了來自下列轉化方程：凡x1是編碼的價值切削速度（ s ）和x2是編碼值的進給速度（f） ， x3就是編碼值的徑向前角（ α ）和x4是編碼值的刀尖半徑（r） 。范圍值的每一項因素是定于三個不同層次，即低，中和高如表1所示。4 實驗細節(jié)為在此基礎上的實驗數(shù)據(jù)發(fā)展模式，周密籌劃的試驗是必不可少的。這將產(chǎn)生新的后代的解決方案，并分享一些特點，從父母雙方。GA開始有(個體)的人口隨機被創(chuàng)造的串。操作更方便和計算效率是兩個主要景點的遺傳算法的方法。 。加文不同于傳統(tǒng)優(yōu)化技術在以下幾個方面：，用編碼的參數(shù)集，而不是參數(shù)本身。他們傾向于獲得局部最優(yōu)解。大部分的研究人員一直使用傳統(tǒng)的優(yōu)化技術，為解決加工問題。一階線性模型，發(fā)展了，從上述的功能關系用最小二乘法，可派代表作為如下：在估計響應y1的基礎上，一階方程，Y是衡量表面粗糙度對對數(shù)的規(guī)模x0=1（虛擬變量）的x1,x2,x3和x4分別為對數(shù)變換切削速度，進給速度，徑向前角和刀尖半徑,∈是實驗誤差和b值是估計相應的參數(shù)。旨在促進數(shù)學模型與加工的反應及其因素，是要促進優(yōu)化加工過程。 （蘇瑞等人[ 9 ]已開發(fā)出一種表面粗糙度預測模型，將軟鋼用響應面方法，驗證生產(chǎn)因素對個別工藝參數(shù)的影響。自從世紀之交的相當多的嘗試已找到了最佳值的加工參數(shù)。 瀚斯曼等人[ 7 ] ，還使用了丹參模式來評估工件材料表面粗糙度對加工表面的影響。這些參數(shù)對表面粗糙度的影響已進行了響應面分析法（丹參）。不過，研究人員也還有沒有考慮到的影響，如切削條件和刀具幾何同步，而且這些研究都沒有考慮到切削過程的優(yōu)化。調查顯示銑刀與左手螺旋角一般不太具有成本效益比。分別對鋁合金L65的3向銑削過程（面，槽和側面）進行了切削試驗，并對其中的切削力，表面粗糙度，凹狀加工平面進行了測量。生產(chǎn)過程的特點是多重性的動態(tài)互動過程中的變數(shù)。因此通過努力，在這篇文章中看到刀具幾何（徑向前角和刀尖半徑）和切削條件（切削速度和進給速度） ，表面精整生產(chǎn)過程中端銑中碳鋼的影響。對于制造業(yè)，建立高效率的加工參數(shù)幾乎是將近一個世紀的問題，并且仍然是許多研究的主題。然而，除了切向和徑向力量，徑向前角對電力的消費有著重大的影響。車削過程對表面光潔度造成的影響歷來倍受研究關注，對于加工過程采用多刀，用機器制造處理，都是研究員需要注意的。1 導言端銑是最常用的金屬去除作業(yè)方式，因為它能夠更快速去除物質并達到合理良好的表面質量。該模型取得的優(yōu)化效果已得到證實，并通過了卡方檢驗。 besides these studies have not considered the optimization of the cutting process.As end milling is a process which involves a large number f parameters, bined influence of the significant parameters an only be obtained by modelling. Mansour and Abdallaet al. [5] have developed a surface roughness model for the end milling of EN32M (a semifree cutting carbon case hardening steel with improved merchantability). The mathematical model has been developed in terms of cutting speed, feed rate and axial depth of cut. The affect of these parameters on the surface roughness has been carried out using response surface methodology (RSM). A first order equation covering the speed range of 30–35 m/min and a second order equation covering the speed range of 24–38 m/min were developed under dry machining conditions. Alauddin et al. [6] developed a surface roughness model using RSM for the end milling of 190 BHN steel. First and second order models were constructed along with contour graphs for the selection of the proper bination of cutting speed and feed to increase the metal removal rate without sacrificing surface quality. Hasmi et al. [7] also used the RSM model for assessing the influence of the workpiece material on the surface roughness of the machined surfaces. The model was developed for milling operation by conducting experiments on steel specimens. The expression shows, the relationship between the surface roughness and the various parameters。 namely, the cutting speed, feed and depth of cut. The above models have not considered the affect of tool geometry on surface roughness.Since the turn of the century quite a large number of attempts have been made to find optimum values of machining parameters. Uses of many methods have been reported in the literature to solve optimization problems for machining parameters. Jain and Jain [8] have used neural networks for modeling and optimizing the machining conditions. The results have been validated by paring the optimized machining conditions obtained using genetic algorithms. Suresh et al. [9] have developed a surface roughness prediction model for turning mild steel using a response surface methodology to produce the factor affects of the individual process parameters. They have also optimized the turning process using the surface roughness prediction model as the objective function. Considering the above, an attempt has been made in this work to develop a surface roughness model with tool geometry and cutting conditions on the basis of experimental results and then optimize it for the selection of these parameters within the given constraints in the end milling operation.3 MethodologyIn this work, mathematical models have been developed using experimental results with the help of response surface methodology. The purpose of developing mathematical models relating the machining responses and their factors is to facilitate the optimization of the machining process. This mathematical model has been used as an objective function and the optimization was carried out with the help of genetic algorithms. Mathematical formulationResponse surface methodology (RSM) is a bination of mathematical and statistical techniques useful for modelling and analyzing the problems in which several independent variables influence a dependent variable or response. The mathematical models monly used are represented by:where Y is the machining response, ? is the response function and S, f , α, r are milling variables and ∈ is the error which is normally distributed about the observed response Y with zero mean.The relationship between surface roughness and other independent variables can be represented as follows， where C is a constant and a, b, c and d are exponents.To facilitate the determination of constants and exponents, this mathematical model will have to be linearized by performing a logarithmic transformation as follows:The constants and exponents C, a, b, c and d can be determined by the method of least squares. The first order linear model, developed from the above functional relationship using least squares method, can be represented as follows:where Y1 is the estimated response based on the firstorder equation, Y is the measured surface roughness on a logarithmic scale, x0 = 1 (dummy variable), x1, x2, x3 and x4 are logarithmic transformations of cutting speed, feed rate, radial rake angle and nose radius respectively, ∈ is the experimental error and b values are the estimates of corresponding parameters.The general second order polynomial response is as given below:where Y2 is the estimated response based on the second order equation. The parameters, . b0, b1, b2, b3, b4, b12, b23, b14, etc. are to be estimated by the method of least squares. Validity of the selected model used for optimizing the process parameters has been tested with the help of statistical tests, such as Fte