喜歡這套資料就充值下載吧。。。資源目錄里展示的都可在線預(yù)覽哦。。。下載后都有，，請放心下載，，文件全都包含在內(nèi)，，【有疑問咨詢QQ:1064457796 或 1304139763】

8Fang-Jung Shiou · Chao-Chang A. Chen · Wen-Tu Li 注塑模表面自動(dòng)化磨削和拋光的過程 發(fā)表日期： 2004年3月30日： 2004年7月5日 網(wǎng)上公布： 2005年3月30日?斯普林格-柏林出版社，倫敦有限公司2005年 摘要：本文探討在數(shù)控加工中心中對注塑模上任意一個(gè)自由表面進(jìn)行自動(dòng)化磨削和拋光過程的可能性。作者在本文中已經(jīng)完成了磨削和拋光工具的設(shè)計(jì)和制造。在加工中心的注塑模使用Taguchi正交矩陣方法確定其最佳表面磨削參數(shù)。注塑模的最佳表面參數(shù)為：磨削材料為 ，磨削速度為，磨削深度為，進(jìn)給速度為。通過使用最佳磨削參數(shù)的平磨可使其表面粗糙度從提高到，使用最佳拋光參數(shù)的拋光過程可使其表面粗糙度從提高到，將最佳表面磨削和拋光參數(shù)運(yùn)用到自由表面模腔，其部分表面粗糙度值可從提高到。 關(guān)鍵字：自動(dòng)表面拋光，拋光加工，磨削加工，表面粗糙度，Taguchi方法 1 介紹 塑料是重要的工程材料，由于其具有特定的特點(diǎn)：如耐腐蝕性，抗化學(xué)品的腐蝕，密度低，并且易于制造，在工業(yè)應(yīng)用上已日益取代金屬部件。注射成型工藝在塑料產(chǎn)品中是一個(gè)重要的成形過程。表面加工的質(zhì)量是注塑模的一個(gè)重要要求，因?yàn)樗苯佑绊懰苣z產(chǎn)品的外觀。加工過程中的拋光和研磨被普遍使用來改善工件表面光潔度。 展開磨削已被廣泛應(yīng)用于傳統(tǒng)模具加工行業(yè)。展開磨削的自動(dòng)化表面加工過程的幾何模型將在【1】中介紹。球面磨削加工使自動(dòng)化表面加工系統(tǒng)被提高了【2】。磨削速度，切削深度，進(jìn)給速度，磨具屬性，如研磨材料和磨料粒大小，在球形磨削過程中起主導(dǎo)作用，如圖1所示。注塑模具的最優(yōu)球面磨削參數(shù)尚未被證實(shí)。 近幾年來，一些確定拋光過程最佳參數(shù)的研究已經(jīng)進(jìn)在行了。舉例來說，現(xiàn)在已發(fā)現(xiàn)塑料變形可使工件表面減少使用碳化鎢材料，從而改善其表面粗糙度，表面硬度，抗疲勞強(qiáng)度[ 3-6 ] 。拋光過程是通過加工中心[ 3，4]和車床[ 5 ，6 ] 來完成年的。主要拋光參數(shù)對球或滾子材料的表面的粗糙度具有重大作用，拋光力，進(jìn)給速度，拋光速度，潤滑，其他的拋光途徑，其中包括[ 3 ] 。注塑模的最佳表面拋光參數(shù)是一種組合的油脂潤滑劑，碳化鎢材料，拋光速度，拋光力，進(jìn)給 [ 7 ] 。拋光表面采用最佳球面拋光參數(shù)的滲透速度為2.5微米。通過拋光過程來改善表面粗糙度的概率一般在到 [ 3-7 ] 。 圖1.磨削過程示意圖 圖2 .拋光過程示意圖 本研究的主要目的是提高加工中心注塑模具自由表面的磨削和拋光光潔度。自動(dòng)化表面磨削和拋光過程的流程圖如圖。我們給加工中心設(shè)計(jì)和制造球面磨削工具及其對準(zhǔn)裝置，最佳球面磨削參數(shù)的特定是利用Taguchi正交矩陣方法。四個(gè)因素和三個(gè)相應(yīng)條件，然后挑選Taguchi正交矩陣方法矩陣進(jìn)行實(shí)驗(yàn)。表面研磨的最佳展開球面磨削參數(shù)被應(yīng)用到自由曲面加工過程中。用最佳球面拋光參數(shù)來改善表面粗糙度和光潔度。 2 設(shè)計(jì)球面磨削工具及其對準(zhǔn)裝置 從自由表面的球面磨削過程進(jìn)行的可能性看，球面磨削中心應(yīng)在加工中心的軸，展開磨削的工具及調(diào)節(jié)裝置的設(shè)計(jì)如圖所示。電動(dòng)磨床是安裝在兩個(gè)可調(diào)樞軸螺釘之間。該磨床中心的磨削球借助圓錐曲線溝槽的對齊組件和圓錐形凹線進(jìn)行的良好的排列。排列好的研磨球被兩個(gè)可調(diào)螺釘固定，之后，對準(zhǔn)元件可以被撤銷。球面磨床的中心坐標(biāo)和它的偏差在左右，它是由數(shù)控坐標(biāo)測量機(jī)測量。機(jī)床振動(dòng)導(dǎo)致的力被螺旋型彈簧吸收。球面磨削工具和球面拋光工具的安裝如圖所示，主軸被鎖，不論磨削過程還是拋光過程由主軸鎖定。 圖.4.球面磨床工具及其調(diào)整示意圖 3 矩陣實(shí)驗(yàn)的步驟 3.1 Taguchi正交陣列的結(jié)構(gòu) 用Taguchi正交矩陣[ 8 ]做矩陣實(shí)驗(yàn)要求那些參數(shù)的影響是有效地。為了配合上述球面磨削參數(shù)的要求，在本研究中磨削的材料（直徑10毫米），進(jìn)給速度，磨削深度，電動(dòng)磨床的轉(zhuǎn)速被選定為四個(gè)實(shí)驗(yàn)因素（參數(shù)）并被指定為因子A至D （見表1 ）。并為每個(gè)素設(shè)定了3個(gè)等級來包含它們所涉及的范圍，用數(shù)字1、2、3來標(biāo)識。每個(gè)因素的3個(gè) 表1 .實(shí)驗(yàn)因素和層次 因素 等級 1 2 3 :研磨材料 WA ,PA :進(jìn)給速度 50 100 200 :磨削深度 20 20 80 :轉(zhuǎn)數(shù) 12000 18000 24000 數(shù)值要求在在研究結(jié)果的基礎(chǔ)上來確定。第四個(gè)因素的第三級的磨削過程用正交矩陣來進(jìn)行矩陣實(shí)驗(yàn)。 3.2 數(shù)據(jù)分析 工程設(shè)計(jì)上的問題可以分成越小越好的類型，額定最佳類型，越大越好的類型，標(biāo)記目標(biāo)類型，其中還包括[ 8 ] 。該信號和噪音（）的比例是用來作為優(yōu)化產(chǎn)品或工藝設(shè)計(jì)的目標(biāo)函數(shù)。經(jīng)過磨削參數(shù)的組合，其表面粗糙度值應(yīng)小于原來表面的粗糙度值。因此，球面磨削過程是越小越好類型問題的一個(gè)例子。該比，，是指由下列方程[ 8 ]定義的 ： （1） 結(jié)果： ：觀測表明，質(zhì)量特性是根據(jù)不同的噪聲條件來確定的 n ：多次實(shí)驗(yàn) 每個(gè) 正交矩陣計(jì)算的的比值顯示，每個(gè)因素的主要影響是由不同技術(shù)的分析和方差測試的結(jié)果來決定的 [ 8 ] 。解決越小越好問題的的最佳方法是取的最大值，由公式1來定義的。各個(gè)因素的最大值的選定將對有重大影響，然后就能確定球面磨削的最佳條件。 圖.6.實(shí)驗(yàn)設(shè)置來確定最佳的球面磨削參數(shù) 4 實(shí)驗(yàn)工作及結(jié)果 該材料用于工具鋼的研究[ 9 ] ，這是常用于在汽車部件和家用器具領(lǐng)域的大型注塑模具制品。這種材料的優(yōu)越性在于經(jīng)過加工后，模具可以直接用于其特殊前處理未經(jīng)熱處理的進(jìn)一步加工過程。該產(chǎn)品的設(shè)計(jì)制造使它們可以被要求裝在動(dòng)力架上來測量其動(dòng)力。經(jīng)過簡單加工，然后裝在動(dòng)力架上對3坐標(biāo)加工中心進(jìn)行測量，該加工中心由Yang-Iron公司生產(chǎn)，配備了FUNUC公司數(shù)控控制器。運(yùn)用Hommelwerke T4000設(shè)備對預(yù)加工表面粗糙度的測量，大約為。圖6顯示了實(shí)驗(yàn)開始時(shí)的球面磨削過程，由Renishaw公司生產(chǎn)的觸發(fā)器結(jié)合加工中心刀具參數(shù)來測量和協(xié)調(diào)該制品。該拋光路徑由PowerMILL CAM軟件生成數(shù)控代碼。這些代碼可以同步傳送到數(shù)控加工中心的RS232串行接口中。 表2總結(jié)了表面粗糙度值Ra的測量和用公式1計(jì)算每個(gè)正交矩陣的值，然后進(jìn)行真叫矩陣材料實(shí)驗(yàn)。通過的平均值可以得到每個(gè)級別的4個(gè)因素，在表3中列表，其數(shù)字在表2中列出。其示意圖如圖7所示。 圖 .7 控制因素的影響 表2 . 標(biāo)本表面粗糙度 年限 序號 內(nèi)部陣列 （控制因素） 衡量表面 粗糙度值（） 結(jié)果 A b C D y1（μm） y2(μm) y3(μm) S/N比例(dB) 平均值(μ m) 1 1 1 1 1 0.35 0.35 0.35 9.119 0.35 2 1 2 2 2 0.37 0.36 0.38 8.634 0.37 3 1 3 3 3 0.41 0.44 0.40 7.597 0.417 4 2 1 2 3 0.63 0.65 0.64 3.876 0.640 5 2 2 3 1 0.73 0.77 0.78 2.380 0.760 6 2 3 1 2 0.45 0.42 0.39 7.520 0.42 7 3 1 3 2 0.34 0.31 0.32 9.801 0.323 8 3 2 1 3 0.27 0.25 0.28 11.471 0.267 9 3 3 2 1 0.32 0.32 0.32 9.897 0.320 10 1 1 2 2 0.35 0.39 0.40 8.390 0.380 11 1 2 3 3 0.41 0.50 0.43 6.968 0.447 12 1 3 1 1 0.40 0.39 0.42 7.883 0.403 13 2 1 1 3 0.33 0.34 0.31 9.712 0.327 14 2 2 2 1 0.48 0.50 0.47 6.312 0.483 15 2 3 3 2 0.57 0.61 0.53 4.868 0.570 16 3 1 3 1 0.59 0.55 0.54 5.030 0.560 17 3 2 1 2 0.36 0.36 0.35 8.954 0.357 18 3 3 2 3 0.57 0.53 0.53 5.293 0.543 表3 . 各因素的比值的平均值（分貝） 因素 A B C D 等級1 8.099 7.655 9.110 6.770 等級2 5.778 7.453 7.067 8.028 等級3 8.408 7.176 6.107 7.486 結(jié)果 2.630 0.479 3.003 1.258 等級 2 4 1 3 平均值 .428 其目的在于將磨削過程中的表面粗糙度值減到最小，確定每項(xiàng)因素的最佳等級。由于該函數(shù)為單調(diào)遞減函數(shù)，我們應(yīng)定量增大值。因此，我們能確定每一項(xiàng)因素的最佳等級。其最高值為。因此，基于矩陣實(shí)驗(yàn)，最佳研磨材料是粉紅氧化鋁（,PA），最佳進(jìn)給速度為，最佳磨削深度為，最佳轉(zhuǎn)速為。如表4所示。 表4 .球面磨削的最佳參數(shù) 因素 等級 研磨材料 ,PA 進(jìn)給速度 50mm/min 磨削深度 20um 轉(zhuǎn)數(shù) 18000rpm 表5 .表面粗糙度比的方差分析表 因素 自由度 平方和 均方和 方差比 A 2 24.791 12.396 3.62 B 2 0.692 0.346 C 2 28.218 14.109 4.12 D 2 4.776 2.388 誤差 9 總計(jì) 17 匯集誤差 13 3.424 分析每一項(xiàng)因素的主要原因，進(jìn)一步采用方差分析技術(shù)和F對比檢驗(yàn)，以確定其定義（見表5）根據(jù)F分布表，是指F值在時(shí)，廢品率為，自由度數(shù)為2，匯集誤差為13.F值若大于，對表面粗糙度值有重大影響，因此，進(jìn)給速度和磨削深度對表面粗糙度有重大影響。 表6 .被測樣品經(jīng)實(shí)驗(yàn)測得的表面粗糙度值 年限。序號 實(shí)測值（Ra） 平均值（um） S/N 比 Y1 Y2 Y3 1 0.30 0.31 0.33 0.313 10.073 2 0.36 0.37 0.36 0.363 8.802 3 0.36 0.37 0.37 0.367 8.714 4 0.35 0.37 0.34 0.353 9.031 5 0.33 0.36 0.35 0.347 9.163 平均值 0.349 9.163 通過觀察五個(gè)驗(yàn)證實(shí)驗(yàn)得出了用最佳拋光參數(shù)的可重復(fù)性，如表6所示。該表面粗糙度值被測量是大約.用最佳組合的球面磨削參數(shù)可使表面粗糙度大概提高了約78 ％ 。表面用最佳拋光參數(shù)進(jìn)一步拋光。通過拋光后，表面粗糙度值可能達(dá)到。圖8顯示的是用30倍的的顯微鏡對拋光后的表面粗糙度進(jìn)行觀察。拋光后預(yù)加工表面的粗糙度改進(jìn)大約為。 從Taguchi正交矩陣實(shí)驗(yàn)獲得的最佳磨削參數(shù)應(yīng)用到表面光潔度的自由曲面的模具插入評價(jià)表面粗糙度的改善。 1個(gè)香料被選定為測試載體。數(shù)控加工的模具，亞塞特為測試對象，模擬銑床 CAM軟件。模具插入進(jìn)的地面與最優(yōu)球面磨削參數(shù)取自田口的矩陣實(shí)驗(yàn)。拋光與最佳球拋光是地面的參數(shù)，以進(jìn)一步改善表面粗糙度的測試對象（見圖9 ） 。表面粗糙度模具插入測量儀器與霍梅爾有限公司 t4000設(shè)備。平均表面粗糙度值在未加工表面平均值;工件表面的平均值為，以及對拋光表面的平均值為。通過實(shí)驗(yàn)后表面粗糙度的改進(jìn)，工件表面大約為（ 2月15日-0 45 / 2 15 = 79 1 ％ ，拋光表面大約為（ 2月15日-0 07 / 2月15日= 96 7 ％ ）。 圖. 8 用30倍的模具顯微鏡觀測比較加工前工件表面和加工后工件表面 圖. 9磨削和拋光模具中插入一個(gè)香水瓶 5 結(jié)論 這篇文章中，在一個(gè)加工中心對注塑模表面自動(dòng)化磨削和拋光過程的最佳參數(shù)已經(jīng)研究出來。掛接球面磨削工具（和其對齊元件）的設(shè)計(jì)和制造方法 。最佳球面磨削參數(shù)是通過Taguchi的矩陣實(shí)驗(yàn)來確定的。最佳球面磨削參數(shù)是注塑模pds5是研磨材料粉紅氧化鋁（,PA）的組合，進(jìn)給速度，拋光深度的，轉(zhuǎn)速。利用最佳磨削參數(shù)來進(jìn)行表面磨削可以使表面粗糙度從提高到。模具的自由表面加工運(yùn)用最佳表面研磨和拋光參數(shù)，測量的表面粗糙度有很大的提高，磨削表面大概為，拋光表面大概為。 11 DOI 10.1007/s00170-004-2328-8 ORIGINAL ARTICLE Int J Adv Manuf Technol (2006) 28: 6166 Fang-Jung Shiou Chao-Chang A. Chen Wen-Tu Li Automated surface finishing of plastic injection mold steel with spherical grinding and ball burnishing processes Received: 30 March 2004 / Accepted: 5 July 2004 / Published online: 30 March 2005 Springer-Verlag London Limited 2005 Abstract This study investigates the possibilities of automated spherical grinding and ball burnishing surface finishing pro- cesses in a freeform surface plastic injection mold steel PDS5 on a CNC machining center. The design and manufacture of a grinding tool holder has been accomplished in this study. The optimal surface grinding parameters were determined using Taguchis orthogonal array method for plastic injection molding steel PDS5 on a machining center. The optimal surface grind- ing parameters for the plastic injection mold steel PDS5 were the combination of an abrasive material of PA Al 2 O 3 , a grind- ing speed of 18 000 rpm, a grinding depth of 20 m, and a feed of 50 mm/min. The surface roughness R a of the specimen can be improved from about 1.60 mto0.35 m by using the optimal parameters for surface grinding. Surface roughness R a can be further improved from about 0.343 mto0.06 mbyusingthe ball burnishing process with the optimal burnishing parameters. Applying the optimal surface grinding and burnishing parame- ters sequentially to a fine-milled freeform surface mold insert, the surface roughness R a of freeform surface region on the tested part can be improved from about 2.15 mto0.07 m. Keywords Automated surface finishing Ball burnishing process Grinding process Surface roughness Taguchis method 1 Introduction Plastics are important engineering materials due to their specific characteristics, such as corrosion resistance, resistance to chemi- cals, low density, and ease of manufacture, and have increasingly F.-J. Shiou (a117) C.-C.A. Chen W.-T. Li Department of Mechanical Engineering, National Taiwan University of Science and Technology, No. 43, Section 4, Keelung Road, 106 Taipei, Taiwan R.O.C. E-mail: shioumail.ntust.edu.tw Tel.: +88-62-2737-6543 Fax: +88-62-2737-6460 replaced metallic components in industrial applications. Injec- tion molding is one of the important forming processes for plas- tic products. The surface finish quality of the plastic injection mold is an essential requirement due to its direct effects on the appearance of the plastic product. Finishing processes such as grinding, polishing and lapping are commonly used to improve the surface finish. The mounted grinding tools (wheels) have been widely used in conventional mold and die finishing industries. The geometric model of mounted grinding tools for automated surface finish- ing processes was introduced in 1. A finishing process model of spherical grinding tools for automated surface finishing sys- tems was developed in 2. Grinding speed, depth of cut, feed rate, and wheel properties such as abrasive material and abrasive grain size, are the dominant parameters for the spherical grind- ing process, as shown in Fig. 1. The optimal spherical grinding parameters for the injection mold steel have not yet been investi- gated based in the literature. In recent years, some research has been carried out in de- termining the optimal parameters of the ball burnishing pro- cess (Fig. 2). For instance, it has been found that plastic de- formation on the workpiece surface can be reduced by using a tungsten carbide ball or a roller, thus improving the surface roughness, surface hardness, and fatigue resistance 36. The burnishing process is accomplished by machining centers 3, 4 and lathes 5, 6. The main burnishing parameters having signifi- cant effects on the surface roughness are ball or roller material, burnishing force, feed rate, burnishing speed, lubrication, and number of burnishing passes, among others 3. The optimal sur- face burnishing parameters for the plastic injection mold steel PDS5 were a combination of grease lubricant, the tungsten car- bide ball, a burnishing speed of 200 mm/min, a burnishing force of 300 N, and a feed of 40 m 7. The depth of penetration of the burnished surface using the optimal ball burnishing parameters was about 2.5 microns. The improvement of the surface rough- ness through burnishing process generally ranged between 40% and 90% 37. The aim of this study was to develop spherical grinding and ball burnishing surface finish processes of a freeform surface 62 plastic injection mold on a machining center. The flowchart of automated surface finish using spherical grinding and ball bur- nishing processes is shown in Fig. 3. We began by designing and manufacturing the spherical grinding tool and its alignment de- vice for use on a machining center. The optimal surface spherical grinding parameters were determined by utilizing a Taguchis orthogonal array method. Four factors and three corresponding levels were then chosen for the Taguchis L 18 matrix experiment. The optimal mounted spherical grinding parameters for surface grinding were then applied to the surface finish of a freeform surface carrier. To improve the surface roughness, the ground surface was further burnished, using the optimal ball burnishing parameters. Fig. 1. Schematic diagram of the spherical grinding process Fig. 2. Schematic diagram of the ball-burnishing process Fig. 3. Flowchart of automated surface finish using spherical grinding and ball burnishing processes 2 Design of the spherical grinding tool and its alignment device To carry out the possible spherical grinding process of a freeform surface, the center of the ball grinder should coincide with the z-axis of the machining center. The mounted spherical grinding tool and its adjustment device was designed, as shown in Fig. 4. The electric grinder was mounted in a tool holder with two ad- justable pivot screws. The center of the grinder ball was well aligned with the help of the conic groove of the alignment com- ponents. Having aligned the grinder ball, two adjustable pivot screws were tightened; after which, the alignment components could be removed. The deviation between the center coordi- nates of the ball grinder and that of the shank was about 5 m, which was measured by a CNC coordinate measuring machine. The force induced by the vibration of the machine bed is ab- sorbed by a helical spring. The manufactured spherical grind- ing tool and ball-burnishing tool were mounted, as shown in Fig. 5. The spindle was locked for both the spherical grinding process and the ball burnishing process by a spindle-locking mechanism. 63 Fig. 4. Schematic illustration of the spherical grinding tool and its adjust- ment device 3 Planning of the matrix experiment 3.1 Configuration of Taguchis orthogonal array The effects of several parameters can be determined efficiently by conducting matrix experiments using Taguchis orthogonal array 8. To match the aforementioned spherical grinding pa- rameters, the abrasive material of the grinder ball (with the diam- eter of 10 mm), the feed rate, the depth of grinding, and the revolution of the electric grinder were selected as the four experi- mental factors (parameters) and designated as factor A to D (see Table 1) in this research. Three levels (settings) for each factor were configured to cover the range of interest, and were identi- Fig. 5. a Photo of the spherical grinding tool b Photo of the ball burnishing tool Table 1. The experimental factors and their levels Factor Level 123 A. Abrasive material SiC Al 2 O 3 ,WA Al 2 O 3 ,PA B. Feed (mm/min) 50 100 200 C. Depth of grinding (m) 20 50 80 D. Revolution (rpm) 12 000 18 000 24 000 fied by the digits 1, 2, and 3. Three types of abrasive materials, namely silicon carbide (SiC), white aluminum oxide (Al 2 O 3 , WA), and pink aluminum oxide (Al 2 O 3 , PA), were selected and studied. Three numerical values of each factor were determined based on the pre-study results. The L 18 orthogonal array was se- lected to conduct the matrix experiment for four 3-level factors of the spherical grinding process. 3.2 Definition of the data analysis Engineering design problems can be divided into smaller-the- better types, nominal-the-best types, larger-the-better types, signed-target types, among others 8. The signal-to-noise (S/N) ratio is used as the objective function for optimizing a product or process design. The surface roughness value of the ground sur- face via an adequate combination of grinding parameters should be smaller than that of the original surface. Consequently, the spherical grinding process is an example of a smaller-the-better type problem. The S/N ratio, , is defined by the following equation 8: =10 log 10 (mean square quality characteristic) =10 log 10 bracketleftBigg 1 n n summationdisplay i=1 y 2 i bracketrightBigg . (1) where: y i : observations of the quality characteristic under different noise conditions n: number of experiment After the S/N ratio from the experimental data of each L 18 orthogonal array is calculated, the main effect of each factor was determined by using an analysis of variance (ANOVA) tech- nique and an F-ratio test 8. The optimization strategy of the 64 smaller-the better problem is to maximize ,asdefinedbyEq.1. Levels that maximize will be selected for the factors that have a significant effect on . The optimal conditions for spherical grinding can then be determined. 4 Experimental work and results The material used in this study was PDS5 tool steel (equiva- lent to AISI P20) 9, which is commonly used for the molds of large plastic injection products in the field of automobile com- ponents and domestic appliances. The hardness of this material is about HRC33 (HS46) 9. One specific advantage of this ma- terial is that after machining, the mold can be directly used for further finishing processes without heat treatment due to its special pre-treatment. The specimens were designed and manu- factured so that they could be mounted on a dynamometer to measure the reaction force. The PDS5 specimen was roughly ma- chined and then mounted on the dynamometer to carry out the fine milling on a three-axis machining center made by Yang- Iron Company (type MV-3A), equipped with a FUNUC Com- pany NC-controller (type 0M) 10. The pre-machined surface roughness was measured, using Hommelwerke T4000 equip- ment, to be about 1.6 m. Figure 6 shows the experimental set-up of the spherical grinding process. A MP10 touch-trigger probe made by the Renishaw Company was also integrated with the machining center tool magazine to measure and determine the coordinated origin of the specimen to be ground. The NC codes needed for the ball-burnishing path were generated by PowerMILL CAM software. These codes can be transmitted to the CNC controller of the machining center via RS232 serial interface. Table 2 summarizes the measured ground surface roughness value R a and the calculated S/N ratio of each L 18 orthogonal ar- ray using Eq. 1, after having executed the 18 matrix experiments. The average S/N ratio for each level of the four factors can be obtained, as listed in Table 3, by taking the numerical values pro- vided in Table 2. The average S/N ratio for each level of the four factors is shown graphically in Fig. 7. Fig. 6. Experimental set-up to determine the op- timal spherical grinding parameters Table 2. Ground surface roughness of PDS5 specimen Exp. Inner array Measured surface Response no. (control factors) roughness value (R a ) ABCD y 1 y 2 y 3 S/N ratio Mean (m) (m) (m) (dB) y (m) 1 1 1 1 1 0.35 0.35 0.35 9.119 0.350 2 1 2 2 2 0.37 0.36 0.38 8.634 0.370 3 1 3 3 3 0.41 0.44 0.40 7.597 0.417 4 2 1 2 3 0.63 0.65 0.64 3.876 0.640 5 2 2 3 1 0.73 0.77 0.78 2.380 0.760 6 2 3 1 2 0.45 0.42 0.39 7.520 0.420 7 3 1 3 2 0.34 0.31 0.32 9.801 0.323 8 3 2 1 3 0.27 0.25 0.28 11.471 0.267 9 3 3 2 1 0.32 0.32 0.32 9.897 0.320 10 1 1 2 2 0.35 0.39 0.40 8.390 0.380 11 1 2 3 3 0.41 0.50 0.43 6.968 0.447 12 1 3 1 1 0.40 0.39 0.42 7.883 0.403 13 2 1 1 3 0.33 0.34 0.31 9.712 0.327 14 2 2 2 1 0.48 0.50 0.47 6.312 0.483 15 2 3 3 2 0.57 0.61 0.53 4.868 0.570 16 3 1 3 1 0.59 0.55 0.54 5.030 0.560 17 3 2 1 2 0.36 0.36 0.35 8.954 0.357 18 3 3 2 3 0.57 0.53 0.53 5.293 0.543 Table 3. Average S/N ratios by factor levels (dB) Factor A B C D Level 1 8.099 7.655 9.110 6.770 Level 2 5.778 7.453 7.067 8.028 Level 3 8.408 7.176 6.107 7.486 Effect 2.630 0.479 3.003 1.258 Rank2413 Mean 7.428 The goal in the spherical grinding process is to minimize the surface roughness value of the ground specimen by determin- ing the optimal level of each factor. Since log is a monotone decreasing function, we should maximize the S/N ratio. Conse- quently, we can determine the optimal level for each factor as being the level that has the highest value of . Therefore, based 65 Fig. 7. Plots of control factor effects on the matrix experiment, the optimal abrasive material was pink aluminum oxide; the optimal feed was 50 mm/min; the optimal depth of grinding was 20 m; and the optimal revolution was 18 000 rpm, as shown in Table 4. The main effect of each factor was further determined by using an analysis of variance (ANOVA) technique and an F ratio test in order to determine their significance (see Table 5). The F 0.10,2,13 is 2.76 for a level of significance equal to 0.10 (or 90% confidence level); the factors degree of freedom is 2 and the degree of freedom for the pooled error is 13, according to F-distribution table 11. An F ratio value greater than 2.76 can be concluded as having a significant effect on surface roughness and is identified by an asterisk. As a result, the feed and the depth of grinding have a significant effect on surface roughness. Five verification experiments were carried out to observe the repeatability of using the optimal combination of grinding pa- rameters, as shown in Table 6. The obtainable surface roughness value R a of such specimen was measured to be about 0.35 m. Surface roughness was improved by about 78% in using the op- Table 4. Optimal combination of spherical grinding parameters Factor Level Abrasive Al 2 O 3 ,PA Feed 50 mm/min Depth of grinding 20 m Revolution 18 000 rpm Table 5. ANOVA table for S/N ratio of surface roughness Factor Degrees Sum Mean F ratio of freedom of squares squares A 2 24.791 12.396 3.620 B 2 0.692 0.346 C 2 28.218 14.109 4.121 D 2 4.776 2.388 Error 9 39.043 Total 17 97.520 Pooled to error 13 44.511 3.424 F ratio value 2.76 has significant effect on surface roughness Table 6. Surface roughness value of the tested specimen after verification experiment Exp. no. Measured value R a (m) Mean y (m) S/N ratio y 1 y 2 y 3 1 0.30 0.31 0.33 0.313 10.073 2 0.36 0.37 0.36 0.363 8.802 3 0.36 0.37 0.37 0.367 8.714 4 0.35 0.37 0.34 0.353 9.031 5 0.33 0.36 0.35 0.347 9.163 Mean 0.349 9.163 timal combination of spherical grinding parameters. The ground surface was further burnished using the optimal ball burnishing parameters. A surface roughness value of R a = 0.06 m was ob- tainable after ball burnishing. Improvement of the burnished sur- face roughness observed with a 30 optical microscope is shown in Fig. 8. The improvement of pre-machined surfaces roughness was about 95% after the burnishing process. The optimal parameters for surface spherical grinding ob- tained from the Taguchis matrix experiments were applied to the surface finish of the freeform surface mold insert to evalu- ate the surface roughness improvement. A perfume bottle was selected as the tested carrier. The CNC machining of the mold in- sert for the tested object was simulated with PowerMILL CAM software. After fine milling, the mold insert was further ground with the optimal spherical grinding parameters obtained from the Taguchis matrix experiment. Shortly afterwards, the ground surface was burnished with the optimal ball burnishing parame- ters to further improve the surface roughness of the tested object (see Fig. 9). The surface roughness of the mold insert was meas- ured with Hommelwerke T4000 equipment. The average surface roughness value R a on a fine-milled surface of the mold insert was 2.15 m on average; that on the ground surface was 0.45 m Fig. 8. Comparison between the pre-machined surface, ground surface and the burnished surface of the tested specimen observed with a toolmaker microscope (30) 66 Fig. 9. Fine-milled, ground and burnished mold insert of a perfume bottle on average; and that on burnished surface was 0.07 monaver- age. The surface roughness improvement of the tested object on ground surface was about (2.150.45)/2.15 = 79.1%, and that on the burnished surface was about (2.150.07)/2.15 = 96.7%. 5 Conclusion In this work, the optimal parameters of automated spheri- cal grinding and ball-burnishing surface finishing processes in a freeform surface plastic injection mold were developed suc- cessfully on a machining center. The mounted spherical grinding tool (and its alignment components) was designed and manu- factured. The optimal spherical grinding parameters for surface grinding were determined by conducting a Taguchi L 18 matrix experiments. The optimal spherical grinding parameters for the plastic injection mold steel PDS5 were the combination of the abrasive material of pink aluminum oxide (Al 2 O 3 ,PA),afeed of 50 mm/min, a depth of grinding 20 m, and a revolution of 18 000 rpm. The surface roughness R a of the specimen can be improved from about 1.6 mto0.35 m by using the optimal spherical grinding conditions for surface grinding. By applying the optimal surface grinding and burnishing parameters to the surface finish of the freeform surface mold insert, the surface roughness improvements were measured to be ground surface was about 79.1% in terms of ground surfaces, and about 96.7% in terms of burnished surfaces. Acknowledgement The authors are grateful to the National Science Coun- cil of the Republic of China for supporting this research with grant NSC 89-2212-E-011-059. References 1. Chen CCA, Yan WS (2000) Geometric model of mounted grinding tools for automated surface finishing processes. In: Proceedings of the 6th International Conference on Automation Technology, Taipei, May 911, pp 4347 2. Chen CCA, Duffie NA, Liu WC (1997) A finishing model of spherical grinding tools for automated surface finishing systems. Int J Manuf Sci Prod 1(1):1726 3. Loh NH, Tam SC (1988) Effects of ball burnishing parameters on surface finisha literature survey and discussion. Precis Eng 10(4):215 220 4. Loh NH, Tam SC, Miyazawa S (1991) Investigations on the sur- face roughness produced by ball burnishing. Int J Mach Tools Manuf 31(1):7581 5. Yu X, Wang L (1999) Effect of various parameters on the surface roughness of an aluminum alloy burnished with a spherical surfaced polycrystalline diamond tool. Int J Mach Tools Manuf 39:459469 6. Klocke F, Liermann J (1996) Roller burnishing of hard turned surfaces. Int J Mach Tools Manuf 38(5):419423 7. Shiou FJ, Chen CH (2003) Determination of optimal ball-burnishing parameters for plastic injection molding steel. Int J Adv Manuf Technol 3:177185 8. Phadke MS (1989) Quality engineering using robust design. Prentice- Hall, Englewood Cliffs, New Jersey 9. Ta-Tung Company (1985) Technical handbook for the selection of plas- tic injection mold steel. Taiwan 10. Yang Iron Works (1996) Technical handbook of MV-3A vertical ma- chining center. Taiwan 11. Montgomery DC (1991) Design and analysis of experiments. Wiley, New York