瓶底零件加工方案制定與數(shù)控編程仿真含NX三維及CAD圖,瓶底,零件,加工,方案,制定,制訂,數(shù)控,編程,仿真,nx,三維,cad 附錄 1：外文翻譯 在現(xiàn)場為優(yōu)化模具制造工藝銑削仿真 K. Weinert (2). A. Enselmann, J. Friedhoff 多特蒙德大學(xué)，加工技術(shù)部，多特蒙德，德國 1997 1 月 9 日收到 摘要 當銑復(fù)雜曲面的主要 問題是有限的精度時，是由于銑削刀具變形引起切削力和過程的可靠性欠佳引起的。為提高表面質(zhì)量，和保持高的過程可靠性，方法之一是基于計算機的參與分析和進給速率適應(yīng)。而適應(yīng)進給率的目的是為了使他們發(fā)生復(fù)雜曲面半精加工，以避免難以忍受的高刀具載荷。使用高效的開發(fā)方法，用體積模型來仿真切割過程。而最佳的進給率的計算需要從 3 軸銑削的主要技術(shù)方面進行考慮。發(fā)達國家提高效率的做法就是一個被證明了的實際例子。 關(guān)鍵詞：工藝優(yōu)化，銑削仿真，復(fù)雜曲面 1 引言 成形刀的使用是作為一個廣泛的生產(chǎn)技術(shù)的必須刀具，例如注塑或模鍛。使用強大的 CAD / CAM 系統(tǒng)來作為描述和制造的幾何形狀表面的成形工具，是完成從設(shè)計到制造的最快途徑。和侵蝕性技術(shù)相比較，制造這種模具的最經(jīng)濟的方式是直接進行銑削加工。經(jīng)濟銑削過程中最重要的先決條件之一是有良好的切削條件。 優(yōu)化銑削功能強大的 CAM 系統(tǒng)所提供的發(fā)展是帶來顯著的刀具壽命，表面質(zhì)量和經(jīng)濟的加工方面的改善。關(guān)于精密加工存在的主要問題： l 由于不同的約定條件，尤其是在半精加工和過程的可靠性差。 l 由于切削力切削刀具變形引起的輪廓偏差。 出現(xiàn)這些問題，尤其是當使用薄銑刀時。而改善輪廓的質(zhì)量和工藝可靠性的主要理論方法是： l 適應(yīng)進給率，使用接觸條件的分析. l 輪廓偏差以計算機為基礎(chǔ)的輪廓偏差預(yù)測和補償?shù)馁r償 有幾篇論文，在研討精度，工藝可靠性和銑削過程所需的時間時，可顯著改善切削過程中使用不同的模型來確定切削條件。關(guān)鍵的方面是，所有被稱為切削條件的型號。為了 2％的三維問題，參與條件被數(shù)控路徑本身所確定形成，而且是在很寬的范圍的。銑復(fù)雜曲面時，幾乎完全在模具制造業(yè)發(fā)生，參與條件不斷以非?？斓乃俣茸兓蛿?shù)控路徑來計算這些值一般是不可能的。 圖 1 輪廓偏差測量與優(yōu)化策略銑床 在本文中，講述的是銑削過程的模擬方法。此模擬計算對任何特定時間的實際加工零件的幾何形狀的數(shù)控路徑進行控制，使人們有可能以驗證自動生成數(shù)控路徑。但是，尤其是，它允許在復(fù)雜曲面銑削過程的參與條件下進行必要的值計算。仿真是基于離散量模型和方法，降低了計算機模擬過程需要的時間和內(nèi)存空間，文獻一直作為被忽視的一個方面甚至到現(xiàn)在為止。以下各節(jié)描述的輪廓偏差的主要來源，是為適應(yīng)這種高效的仿真模型為基礎(chǔ)的進給率優(yōu)化銑復(fù)雜曲面的方法。 2 輪廓偏差的原因 現(xiàn)在將討論銑復(fù)雜曲面的一個典型的例子。圖 1 所示的工件顯示一個典型的幾何，通常發(fā)生在模具的表面區(qū)域?，F(xiàn)進行優(yōu)化銑削路徑策略。高傾角值和相對平坦的地區(qū)的螺旋銑削領(lǐng)域的圓周銑削表面的精加工。 圖 2 參與的條件分析 使用這些優(yōu)化的銑削策略，正常回火鋼制成的工件被銑削，其中有一個 1600 邏輯模塊和模具使用，總輪廓測量的結(jié)果顯示，平均面積為 0.02 毫米的偏差。而最大偏差，發(fā)生在中空成型，達到 0.04 毫米。 從這里描述的例子得出的結(jié)論，HSC 銑削優(yōu)化的銑削策略可應(yīng)用于大部分地區(qū)使用的工具，而有長度的且比例不超過 5 ，以獲得令人滿意的結(jié)果。另一方面，如果等高品質(zhì)更高的要求，尤其是當使用長，最終沉模輕工具，加工的結(jié)果并不令人滿意。 輪廓變形的主要原因是： l 銑削路徑偏差，是由于有限的動態(tài)的數(shù)控機 CA-數(shù)控機. l 切削力切削工具，工件和機器的變形。 第一個問題提到的 - 由于路徑的偏差。是由于機器的有限動態(tài)能力 - 可避免使用特殊的控制算法，像前瞻和后仰。 輪廓偏差也可能出現(xiàn)由于對切削刀具的變形，工件和機器。而最大的偏差是由刀具的剛度相對較低，尤其是在精銑時，刀具具有高的長度與直徑之比。 在這方面的另一個問題是不理想，而半精加工過程的可靠性。由于約定條件的變化，刀具負載不是在一個恒定的水平。 3 進給速率適應(yīng)算法 一個合適的方法是降低輪廓偏差，同時保持高度工藝可靠性的基礎(chǔ)上，分析當前的約定條件的細節(jié)。以下各節(jié)詳細描述了該算法的發(fā)展。 3.1 預(yù)測的約定條件 輪廓偏差預(yù)測中的第一和最重要的一步是分析的接觸條件。這種分析是必須的， 以確定確切的切割芯片體積和之后所產(chǎn)生的橫截面為 1 函數(shù)的芯片面積。 對于這個問題的一個可行的辦法是對零件表面的幾何表示在任何給定的時間內(nèi)有一個堅實的建模系統(tǒng)反復(fù)的布爾運算。這種方法的缺點是執(zhí)行這項任務(wù)所需的計算數(shù)量龐大。因此，它不適合使用這種方法在實踐中，因為內(nèi)部計算的金額將增加在反復(fù)應(yīng)用布爾運算。 模擬 3 軸銑削的一般問題可以描述如下：設(shè) W 是在三維空間中的線段集定義一個給定的刀具參考點的路徑。此外，讓 f 是一個函數(shù)，代表刀具。此外，讓 f 是一個函數(shù)，代表刀具。 f 映射一個二維的坐標系統(tǒng)為負實數(shù)的起源左右對稱的地區(qū)。典型的例子是平面銑刀， 球頭銑刀， 實數(shù) r 代表刀具的大小。在這兩種情況下的入刀點是用來作為參考點。目的是為了計算削減到堅實的物質(zhì)表面 時，刀具的參考點沿路徑移動，在 M. 首先，我們假設(shè)原料塊是在一個合適的坐標系平行管道與坐標 x 反函數(shù) r 多尺度自回歸 ， y 最小， z 最小和 z 回應(yīng)矩形。表面可描述為刀具表面上所有點的最低沿路徑的每一個位置的刀具，它有除了被截斷點所在的地方以外的材料塊。 F（ X，Y）的精確計算是費時，復(fù)雜的，由于復(fù)雜的數(shù)值不穩(wěn)定，造成詳細幾何所產(chǎn)生的表面。一個確切的做法已由川島[5]實現(xiàn)，并由惠[4]開發(fā)出這個問題的離散解決方案。背后的分立解決方案的初步設(shè)想已描述了若干修改在[9,11,12]前，惠[4] 使用這個簡單的解決辦法，提高使用計算機圖形應(yīng)用程序開發(fā)的算法，像掃描轉(zhuǎn)換， 音量分析以避免計算刀具掃地出門。 我們已經(jīng)制定的，與計算機科學(xué)系在一起的解決方案，多特蒙德大學(xué)，惠[4]和作者[12]所使用的方法是一個類似離散的方法。他們采用一個固定的采樣平面來計算高度場，即從材料塊的上面。和[12]相反，我們的重點在于減少抽樣方法的缺點，也就是已知的簡單實現(xiàn)計算機需要相當長的時間和內(nèi)存空間。這一事實已被忽略，直到現(xiàn)在為止。[8]中所建議的解決方案的細節(jié)描述。圖 3 給出了一個例子。工件表面粗銑（ 4200 路徑，第 18 號第一個奔騰 PC 上的計算時間。數(shù)控路徑模擬為 60 兆赫）。 圖 3 計算所產(chǎn)生表面呈現(xiàn)的圖像 圖 4 截面積和進給率的關(guān)系 由粗銑數(shù)控路徑銑削仿真計算顯示渲染圖像。計算所需的時間計算為 4200 而英特爾電腦計算數(shù)控路徑這一結(jié)果是 18 秒。 3.2 適應(yīng)進給速率的基本方法 圖 4 中的主要思想是描繪進給速率適配。計算是基于截面積的自動加工中心剪切，從接觸條件的分析得出，如上所述。為進給速率適應(yīng)這一因素被修改兩個修正因子，從而為了考慮到切割和傾斜路徑的對稱性技術(shù)的影響。使用的因素是真正的切截面積，無形中增加或減少。稍后將討論的因素和公式，用來計算校正因子。修改后的截面積計算公式： 如果計算截面積模擬通帶調(diào)制器低于指定值最大的進給率。如果模擬通帶調(diào)制器所在的最高和最低值（最小 Amod 和最大 Amod）之間，實際進給率直線下降： 如果修改后的值，Amod 比 Amodmax 高，則進給率不會進一步降低，也就是說， 它保持盡可能低的水平通過 vfmin 定義。如果發(fā)生這種情況，產(chǎn)生一條警告消息，說明事實，說明切割的最大截面面積已超過事實。 3.3 對稱的參與 兩個修正因子的定義是要考慮對稱性和路徑傾斜的切割技術(shù)的影響。第一校正因子溫度? DGES ?框? 工程樣板的對稱性參與的影響（圖 5） 。首先對稱因素 FVM 計算，左側(cè)（進給方向看）和右側(cè)之間的交叉切截面積的比例確定。他的因子描述的 參與情況：無論是在刀尖或只在刀具的圓周對稱的參與。對稱因子定義為： 圖 5 校正因子參與對稱性的定義 在一個完全對稱的參與的情況下的因素δ是設(shè)置為 1 （圖 1） 。對于因素不斷增加的最大的δ，我嘗試介于 1 和可定義的最低值 fsym，最小的值： 這種現(xiàn)象的原因是，在與對稱的接觸在刀尖面積的比較,刀具的圓周參與導(dǎo)致更高的刀具撓度。 3.4 銑床方向的影響 它是一個技術(shù)的事實，明顯高于向上指示的路徑的情況下，向下指示的切割路徑的工具負荷（暴跌切割）是較高的?？紤]到一個路徑傾向δ的校正因子定義如下（圖6）： 在水平對齊的路徑的情況下修正系數(shù)設(shè)置為 1 ，即有不改正。向下對齊的路徑， 無形中增加了計算的切截面積，向上指示的路徑減小。 3.5 加工動力學(xué)方面 考慮到機器的動態(tài)能力（圖 7）的進給率計算，實現(xiàn)在適當?shù)奈恢眠@是必要的。在這種情況下，必須進行減速的長度計算和新的進給率值必須添加到數(shù)控文件在正確的位置。減速的長度被定義為： 圖 6 定義路徑傾斜的校正因子 49 圖 7 減速長度計算 用 am，等于最大的減速機。在此表達的第一項是真正的減速造成的動態(tài)能力有限的機器和值 D （刀具直徑）長度作為一個安全參數(shù)。它是用來確保在削減量超過給定值前計算出最佳的進給率。 4 算法的應(yīng)用 為了表明發(fā)達的銑削進給率的模擬和優(yōu)化的能力，一個典型幾何的一部分已被粉碎。加工的第一步是由 8 毫米直徑的球頭立銑刀粗銑，使用口袋銑削循環(huán)。下一步是使用直徑 6 毫米的球頭立銑刀進行半精加工銑削。這個加工階段的路徑是走直線的形狀。一個問題，往往產(chǎn)生在半精加工這部分，是過程的可靠性低，致使工具損害。銑削切削力這部分記錄。在圖 8 中，在狹窄的領(lǐng)域的一部分區(qū)域可以看出，即一個地區(qū)， 仍然主要是機加工的 8 毫米的刀，導(dǎo)致高刀具載荷的影響 6 毫米刀（頂部） 。 進行比較，優(yōu)化進給率（底部）銑時，切削力記錄。圖 8 顯示了相應(yīng)的力量在 z 方向。約定適應(yīng)的結(jié)果是相對穩(wěn)定的工具載荷，它在穩(wěn)定的切削條件下沒有高力峰產(chǎn)生和一個令人滿意的過程中的可靠性。 5 小結(jié) 銑復(fù)雜曲面的主要問題是由于長，薄的銑刀和過程的可靠性欠佳的有限剛度的輪廓偏差。一個雕刻的 3 軸銑削仿真使用適當?shù)姆椒?，同時實現(xiàn)了高的工藝可靠性，減少輪廓偏差。他算法的開發(fā)是基于一個高效，離散模型分析參與條件允許的容積計算在給定的時間，以便進給率進行優(yōu)化，以確保恒定的刀具載荷的切削條件。通過運用這種方法顯著改善，準確性和過程的穩(wěn)定性方面，可以實現(xiàn)銑復(fù)雜形，復(fù)雜曲面。 6 參考 圖 8 比較傳統(tǒng)銑削切割部隊（頂部） 和銑削進給速率適應(yīng)（ 底部） [1] Altintas, Y.，1996 年，一般的螺旋立銑刀的力學(xué)和動力學(xué)模型，在機械工程研究所紀事， 431 :59 -64 [2] Armarego, E.J.A, Wang. J., et. at., 在 1995 年，計算機輔助面銑刀力量允許對牙齒的運行，機械工程研究所 4411 :43- 48 年鑒預(yù)測切削模型 [3] Bieker, R.,1991 年鋼模具，數(shù)控銑床。 VD-V 出版社，杜塞爾多夫 [4] Hui, K.C., 1994 年，在圖像數(shù)控仿真空間應(yīng)用的固體清掃。計算機視覺， 10:306-316 [5] Kawashima, Y., Itoh, K.. et. al., 1991 年，數(shù)控加工核查靈活使用空間劃分為基礎(chǔ)的實體模型的定量分析方法，計算機視覺， 7:149-157 [6] Spiewak, S.. 1995. 銑切屑厚度的改進模型。史冊的“機械工程研究所。4411:39-42 [7] Weinert, K., Enselmann. A., 1995 年。數(shù)控功能為 HSC 銑削領(lǐng)域的工具和模具制造，柔性自動化和智能制造（ FAIM ） ，begell 樓公司，紐約， 957-967 附錄2：外文原文 Milling Simulation for Process Optimization in the Field of Die and Mould Manufacturing K. Weinert (2). A. Enselmann, J. Friedhoff University of Dortmund, Department of Machining Technology, Dortmund, Germany Received on January 9. 1997 Abstract When milling sculptured surfaces the major problems are the limited precision due to milling-cutter deflections caused by the cutting force and a unsatisfactory process reliability. One method for improving surface quality while maintaining high process reliability is the computer-based engagement analysis and feed-rate adaptation. The aim of the feed-rate adaptation is to avoid intolerably high tool loads as they occur while semifinishing sculptured surfaces. The method developed uses an efficient, volume model to simulate the cutting process. The calculation of the optimal feed-rate takes the main technological aspects of 3- axis milling into account. The efficiency of the approach developed is demonstrated with a practical example. Keywords: Process Optimisation, Milling Simulation, Sculptured Surfaces 1 Introduction The use of form tools is necessary for a wide range of production technologies, for example injection-moulding or drop-forging. The fastest way from design to manufacturing can be accomplished using powerful CAD/CAM-systems to describe and manufacture the surface geometry of the form-tools. The most economical way to manufacture such moulds is the direct milling process, in comparison with erosive technologies. One of the most important prerequisites for an economical milling process is to have favourable cutting conditions [3]. The development of optimised milling functions offered by powerful CAM-systems leads to significant improvements with regard to tool-life, surface quality and economical machining. Two major problems regarding precision machining exist: l Poor process reliability due to varying engagement conditions especially while semi-finishing and l contour deviations caused by cutting-tool deformations due to cutting forces. These problems arise especially when thin milling tools are used. The main theoretical ways of improving contour quality and process reliability are: l Feed-rate adaptation using an analysis of engagement conditions [12] and l contour-deviation compensation by computer-based contour-deviation prediction and compensation [7]. Several papers have shown, that accuracy, process reliability and the time required for the milling process can be improved significantly when using different models of the cutting process to determine the cutting conditions [l, 7, 121. The crucial aspect is that for all models the cutting conditions have to be known. For 2 and 2 % dimensional problems, the engagement conditions can be determined form the NC paths themselves and are constant over a wide range. When milling sculptured surfaces, which occur almost exclusively in the die and mould manufacturing industry, the engagement conditions constantly vary at a very quick rate and in general it is impossible to calculate these values from the NC paths. Fig. 1 Contour deviations measured when milling with optimised strategies In this paper, a method for simulation of the milling process is presented. This simulation calculates the actual geometry of the machined part at any given time during the processing of the NC paths and makes it possible to verify the automatically generated NC paths. But especially, it allows the calculation of the necessary values of the engagement conditions during the milling process of sculptured surfaces. The simulation is based on a discrete volume model and our method diminishes the time and memory space the computer requires for the simulation process, an aspect which has been neglected in the literature up to now. The following sections describe the main sources of contour deviations and a method for optimising the milling of sculptured surfaces by an adaptation of feed-rates based on this efficient simulation model. 2 Causes of contour deviations A typical example of the milling of sculptured surfaces will now be discussed. The workpiece depicted in figure 1 displays a typical geometry with surface regions that commonly occur in moulds and dies. The milling was done by optimised milling path strategies. The finishing of the surfaces was performed by circumferential milling of areas with high inclination values and helicoidal milling of relatively flat areas. Fig. 2 Analysis of engagement conditions Using these optimised milling strategies, the workpiece made of normal tempered steel which has a final strength of 1600 Nlmm2 and is used for moulds, was milled directly.The results of the total contour measurement showed a mean area deviation of 0.02 mm. The maximum deviation,which occurred in hollow mouldings, amounted to 0.04 mm. The example described here leads to the conclusion, that the HSC-milling with optimised milling strategies can be applied to most parts using tools having a length-todiameter ratio that does not exceed 5 in order to get satisfactory results. On the other hand, if an even higher contour quality is demanded, especially when using long, thin tools for the final die-sinking, the machining results are not satisfactory. The main causes of contour deformations are: l Milling-path deviations due to the limited dynamic ca pabilities of the NC-machine and l Deformation of cutting tool, workpiece and machine by the cutting forces. The first problem mentioned - path deviations due to. The limited dynamic capabilities of the machine - can be avoided using special control algorithms, like look-ahead and feed-forward. Contour deviations also occur due to deformations of the cutting-tool, the workpiece and the machine. The biggest deviation is caused by the relatively low stiffness of the cutter, especially in the case of finish-milling, by cutters with a high length-to-diameter ratio. Another problem in this area can be an unsatisfactory process reliability while semi-finishing. Due to changing engagement conditions the tool load is not at a constant level. 3 Algorithm for feed-rate adaptation A suitable method for decreasing contour deviations while maintaining a high degree of process reliability is the federate adaptation based on an analysis of the current engagement conditions. The following sections describe in detail the algorithm developed. 3.1 Prediction of engagement conditions The first and most important step in contour-deviation prediction is the analysis of the engagement conditions. This analysis is necessary to determine the exact cutting chip volume and afterwards the resulting cross-sectional area of the chip as a function of the pressure-angle cp for all positions of the NC-data (Fig. 2). The analysis itself is performed by a simulation of the 3-axis milling process. A possible solution for this problem is the geometric representation of the surface of the part at any given time by repeated Boolean operations in a solid modeling system. The disadvantage of this method is the enormous number of calculations needed to perform this task. Therefore, it is not suitable to use this method in practice because the amount of internal calculations will increase during repeated application of Boolean operations. The general problem of simulation 3 axis milling can be described as follows: Let .W be a set of line segments in 3d space defining the path of the reference point of a given cutter. Furthermore, let f be a function that represents the cutter. f maps a symmetric region around the origin of a 2d coordinate system into negative real numbers. Typical examples are flat-end cutters, and ball-end cutters, The real number r represents the size of the cutter. In both cases the origin is used as the reference point. The aim is to calculate the surface which is cut into the solid material when the reference point of the cutter is moved along the paths in M. First we assume the block of raw material to be a parallel piped rectangle with coordinates xminv .rmar, ymins yma, zmin and zmwr in a suitable coordinate system. The surface can be described as the minimum of all points on the cutter surface at every location of the cutter along the path, which in addition have to be clipped where the points lie outside of the block of material. The exact calculation of F(x. y) is time consuming, complicated and numerically unstable due to the complex, detailed geometry of the resulting surface. An exact approach has been implemented by Kawashima [5]. Hui [4] has developed a discrete solution of this problem. The initial idea behind the discrete solution has been described in several modifications before [9, ll, 121. Hui [4] improves on this straightforward solution by using algorithms developed for computer graphics application, like scan conversion, to avoid analytic calculations of the volume swept out by the cutter. The solution we have developed, together with the Department of Computer Science, University of Dortmund, is a discrete approach similar to the methods used by Hui [4] and Yazar [12]. Like Yazar [12], we calculate the height field with respect to a fixed sampling plane when looking at the block of material from the top. In contrast to [12], our emphasis lies on diminishing the disadvantages of the sampling approach, i.e. the considerable time and memory space required by the computer for known straightfoward implementations. This fact has been neglected in the literature up to now. The details of the proposed solution are described in [8]. An example is given in figure 3. The resulting surface of the workpiece by the simulation of the NC paths for rough milling (4200 paths, 18 s computing time on a Pentium PC. 60 MHz. Fig. 3 Rendered image of the resulting surface calculated Fig. 4 Relation between cross-sectional area and feed-rate as calculated by the milling simulation of the NC paths for rough milling is displayed as a rendered image. The computing time necessary to calculate this result for 4200 NC paths is 18 seconds on a Pentium PC. 3.2 Basic method of feed-rate adaptation In figure 4 the main idea of the feed-rate adaptation is depicted. The calculations are based on the crosssectional area of cut Ach, derived from the analysis of engagement conditions, described above. For feed-rate adaptation this factor is modified by two correction factors, in order to take into account the technological influences of symmetry of cut and inclination of path. The factors are used to virtually increase or decrease the real crosssectional area of cut. The factors and the formulas used to calculate the correction factors are discussed later. The modified cross-sectional area is calculated by the formula: If the calculated cross-sectional area Amod is below a specified value the maximum feed-rate is used. If Amod lies between the maximum and minimum values (.4mod,min and Am,d,mm), the actual feed-rate is decreased linearly: If the modified value Amod is higher than Amod,max. The feed-rate will not be further reduced, i.e. it remains on the lowest possible level defined by vjm,,,. If this occurs, a warning message is generated, indicating the fact that the maximum cross-sectional area of cut has been exceeded. 3.3 Symmetry of engagement To take the technological influences of cutting symmetry and path inclination into account two correction factors are defined. The first correction factor C ~ dGes~crib~es the influence of symmetry of engagement (Figure 5). First a symmetry factor f v m is calculated, defining the ratio between cross sectional area of cut on the left side (viewed in feed-direction) and on the right side. This factor describes the engagement situation: whether it is a symmetrical engagement at the tool tip or only at the circumference of the cutter. The symmetry factor is defined as: Fig. 5 Definition of correction factor for symmetry of engagement In case of a completely symmetrical engagement the factor dceo is set at 1 (figure 1). The factor is increased continuously to the maximum G G ~ ~for, s~ym~me, try values between 1 and a definable minimum value fsym,min: The reason for this behaviour is that an engagement only at the circumference of the cutter leads to higher cutter deflections in comparison with a symmetrical engagement in the area of the tool tip. 3.4 Influence of milling direction It is a technological fact, that the tool load for downward directed cutting paths (plunge cutting) is remarkably higher than in the case of an upward directed path. To take this into account a correction factor for the path inclinationδis defined as follows (figure 6): In the case of a horizontally aligned path the correction factor is set to 1, i.e. there is no correction. Downward aligned paths virtually increase the calculated crosssectional area of cut and upward directed paths decrease it. 3.5 Aspects of machining dynamics In order to achieve the calculated feed-rate at the appropriate position it is necessary to take into account the dynamic capabilities of the machine (figure 7). In this case the deceleration length must be calculated and the new feed-rate value must be added to the NC-file at the correct position. The deceleration length is defined by: Fig. 6 Definition of the correction factor for path inclination Fig. 7 Calculation of the deceleration length with a,,, equal to the maximum deceleration of the machine. The first term in this expression is the real deceleration length caused by the limited dynamic capabilities of the machine and the value D (cutter diameter) is used as a safety parameter. It is used to ensure that the calculated optimal feed-rate is reached before the volume to be cut exceeds a given value. 4 Application of the algorithm In order to show the capability of the developed milling simulation and optimisation of the feed-rate , a part with a typical geometry has been milled. The first step of machining is the rough milling by an 8-mm-diameter ball-end cutter, using pocket-milling cycles. The next step is the semi-finish milling using a 6-mm-diameter ball-end cutter. The paths for this machining stage are generated in a rectilinear shape. A problem, often arising while semi-finishing this part, is the low process reliability, causing tool damages. While milling this part the cutting forces are recorded. As can be seen in figure 8, the volume in a narrow area of the part, i.e. an area that remains mostly unmachined by the 8 mm cutter, causes high tool loads that affect the 6 mm cutter (top). For comparison, the cutting forces are recorded when milling with optimised feed-rates (bottom). Figure 8 shows the corresponding forces in z-direction. The results of federate adaptation are relatively steady tool loads without high force peaks resulting in stable cutting conditions and a satisfactory process reliability. 5 Summary Major problems in millin