【正文】 orce, surface roughness and concavity of a machined plane surface were measured. The central posite design was used to decide on the number of experiments to be conducted. The cutting performance of the end mills was assessed using variance analysis. The affects of spindle speed, depth of cut and feed rate on the cutting force and surface roughness were studied. The investigation showed that end mills with left hand helix angles are generally less cost effective than those with right hand helix angles. There is no significant difference between up milling and down milling with regard tothe cutting force, although the difference between them regarding the surface roughness was large. Bayoumi et al. [4] 3 have studied the affect of the tool rotation angle, feed rate and cutting speed on the mechanistic process parameters (pressure, friction parameter) for end milling operation with three mercially available workpiece materials, 11 L 17 free machining steel, 62 353 free machining brass and 2024 aluminium using a single fluted HSS milling cutter. It has been found that pressure and friction act on the chip – tool interface decrease with the increase of feed rate and with the decrease of the flow angle, while the cutting speed has a negligible effect on some of the material dependent parameters. Process parameters are summarized into empirical equations as functions of feed rate and tool rotation angle for each work material. However, researchers have not taken into account the effects of cutting conditions and tool geometry simultaneously。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。因此，測(cè)量表面光潔度，可預(yù)測(cè)加工性能。在過(guò)去，雖然通過(guò)許多人的大量工作，已開(kāi)發(fā)并建立了表面光潔度預(yù)測(cè)模型， 但影響刀具幾何方面受到很少注意。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。鑒于銑削運(yùn)行在今天的全球制造業(yè)中起著重要的作用，就必要優(yōu)化加工參數(shù)。 12 2回顧 建模過(guò)程與優(yōu)化，是兩部很重要的問(wèn)題，在制造業(yè)。 迪維斯等人 [ 3 ]調(diào)查有關(guān)切削加工性能的五個(gè)銑刀具有不同螺旋角。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。目前已發(fā)現(xiàn)的壓力和摩擦法對(duì)芯片 工具接口減少，增加進(jìn)給速度，并與下降的氣流角，而切削速度已微不足道，對(duì)一些材料依賴參數(shù)，工藝參數(shù)，歸納為經(jīng)驗(yàn)公式，作為職能的進(jìn)給速度和刀具旋轉(zhuǎn)角度為每個(gè)工作 材料。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。為選擇適當(dāng)?shù)慕M合，切割速度和伺服，增加金屬去除率并不犧牲的表面質(zhì)量，多此進(jìn)行了模型建造并繪制隨層等高線圖。上述模式并沒(méi)有考慮到對(duì)刀具幾何形狀對(duì)表面粗糙度的影響。結(jié)果已得到驗(yàn)證，通過(guò)比較優(yōu)化的加工條件得到了應(yīng)用遺傳算法。 3 方法論 在這項(xiàng)工作中，數(shù)學(xué)模型已經(jīng)開(kāi)發(fā)使用的實(shí)驗(yàn)結(jié)果與幫助 響應(yīng)面方法論。 之間的關(guān)系，表面粗糙度及其他獨(dú)立變量可以發(fā)生情況如下： 其中 c是一個(gè)常數(shù)，并為 A ， B ， C和 D的指數(shù) 為方便測(cè)定常數(shù)和指數(shù) ，這個(gè)數(shù)學(xué)模型，必須由線性表演對(duì)數(shù)變換如下： 常數(shù)和指數(shù) c，為 A,B,C和 D都可以由最小二乘法。有效性選定的模型用于優(yōu)化工藝參數(shù)，是經(jīng)過(guò)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] 。這些算法并不強(qiáng)勁。加文來(lái)根據(jù)。眾多的制約因素和月票數(shù)目，使加工優(yōu)化問(wèn)題更加復(fù)雜化。傳統(tǒng)方法的優(yōu)化和搜索并不收費(fèi)，以及點(diǎn)多面廣的問(wèn)題域。 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。這個(gè)數(shù)學(xué)模型已被作為目標(biāo)函數(shù)和優(yōu)化進(jìn)行了借助遺傳算法 響應(yīng)面分析法（丹參）是一種有益建模和分析問(wèn)題的組合數(shù)學(xué)和統(tǒng)計(jì)技術(shù)的方法，在這幾個(gè)獨(dú)立變量的影響力供養(yǎng)變或反應(yīng)。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)。許多方法已經(jīng)被國(guó)內(nèi)外文獻(xiàn)報(bào)道，以解決加工 參數(shù)優(yōu)化問(wèn)題。該模型是銑操作進(jìn)行實(shí)驗(yàn)鋼標(biāo)本。分別制定了一階方程涵蓋的速度范圍為 3035米 /分，一類二階方程涵蓋速度范圍的 2438米 /分的干切削條件。 因?yàn)槎算娺^(guò)程介入多數(shù) f參量，重大參量的聯(lián)合只能通過(guò)塑造得到。上下銑方面切削力與右手螺旋角，雖然主要區(qū)別在于表面粗糙度大，但不存在顯著差異。所進(jìn)行的若干實(shí)驗(yàn)是用來(lái)決定該中心復(fù)合設(shè)計(jì)的。表面光潔度一直是一個(gè)重要的因素，在機(jī)械加工性能預(yù)測(cè)任何加工操作。實(shí)驗(yàn)顯示，這項(xiàng)工作將被用來(lái)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)。獲得最佳切削參數(shù)，是在制造業(yè)是非常關(guān)心的，而經(jīng)濟(jì)的加工操作中及競(jìng)爭(zhēng)激烈的市場(chǎng)中發(fā)揮了關(guān)鍵作用。它也影響著芯片冰壺和修改芯片方向人流。由于這些過(guò)程涉及大量的參數(shù)，使得難以將關(guān)聯(lián)表面光潔度與其他參數(shù)進(jìn)行實(shí)驗(yàn)。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)。這些參數(shù)對(duì)表面粗糙度 的 建立，方差分析 極具意義 。 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 works for modeling and optimizing the machining conditions. The results have been validated by paring the optimized machining conditions obtained using geic 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 4 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 Methodology In 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 geic algorithms. Mathematical formulation Response 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 firs