【正文】 s 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] 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。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。在過去，雖然通過許多人的大量工作，已開發(fā)并建立了表面光潔度預(yù)測模型，但影響刀具幾何方面受到很少注意。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)。 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。目前已發(fā)現(xiàn)的壓力和摩擦法對芯片 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。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 13 線圖。結(jié)果已得到驗(yàn)證，通過比較優(yōu)化的加工條件得到了應(yīng)用遺傳算法。 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。這些算法并不強(qiáng)勁。傳統(tǒng)方法的優(yōu)化和搜 14 索并不收費(fèi)，以及點(diǎn)多面廣的問題域。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)。許多方法已經(jīng)被國內(nèi)外文獻(xiàn)報(bào)道，以解決加工參數(shù)優(yōu)化問題。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。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。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)測任何加工操作。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)的加工操作中及競爭激烈的市場中發(fā)揮了關(guān)鍵作用。由于這些過程涉及大量的參數(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)。這些參數(shù)對表面粗糙度 的 建立，方差分析 極具意義 。 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。 1 導(dǎo)言 端銑是最常用的金屬去除作業(yè)方式，因?yàn)樗軌蚋焖偃コ镔|(zhì)并達(dá)到合理良好的表面質(zhì)量。然 而，除了切向和徑向力量，徑向前角對電力的消費(fèi)有著重大的影響。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(jìn)給速度） ，表面精整生產(chǎn)過程中端銑中碳鋼的影響。分別對鋁合金 L65的 3向銑削過程（面，槽和側(cè)面）進(jìn)行了切削試驗(yàn)，并對其中的切削力，表面粗糙度，凹狀加工平面進(jìn)行了測量。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。 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。 （蘇瑞等人 [ 9 ]已開發(fā)出一種表面粗糙度預(yù)測模型，將軟鋼用響應(yīng)面方法，驗(yàn)證生產(chǎn)因素對個(gè)別工藝參數(shù)的影響。一階線性模型，發(fā)展了，從上述的功能關(guān)系用最小二乘法，可派代表作為如下： 在估計(jì)響應(yīng) y1的基礎(chǔ)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(jìn)給速度，徑向前角和刀尖半徑 ,∈是實(shí)驗(yàn)誤差和 b值是估計(jì)相應(yīng)的參數(shù)。他們傾向于獲得局部最優(yōu)解。 優(yōu)化中的應(yīng)用遺傳算法 大部分的研究人員一直使用傳統(tǒng)的優(yōu)化技術(shù)，為解決加工問題。旨在促進(jìn)數(shù)學(xué)模型與加 工的反應(yīng)及其因素，是要促進(jìn)優(yōu)化加工過程。 自從世紀(jì)之交的相當(dāng)多的嘗試已找到了最佳值的加工參數(shù)。這些參數(shù)對表面粗糙度的影響已進(jìn)行了響應(yīng)面分析法（丹參）。調(diào)查顯示銑刀與左手螺旋角一般不太具有成本效益比。生產(chǎn)過程的特點(diǎn)是多重性的動態(tài)互動過程中的變數(shù)。 對于制造業(yè)，建立高效率的加工參數(shù)幾乎是將近一個(gè)世紀(jì)的問題，并且仍然是許多研究的主題。 車削過程對表面光潔度造成的影響歷來倍受研究關(guān)注，對于加工過程采用多刀，用機(jī)器制造處理，都是研究員需要注意的。該模型 取得的 優(yōu)化 效果 已得到證實(shí)， 并通過了 卡方檢驗(yàn)。 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 4 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 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