金-刚石线锯切割机设计[含CAD高清图纸和文档全套]
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毕业设计（论文）译文及原稿译文题目：线锯过程中凹凸不平面的损伤情况原稿题目：Roughness Damage Evolution Due to Wire Saw Process原稿出处：Egemen Teomete，International Journal of Precision Engineering and Manufacturing，2011，12(6)：941-947浙江工业大学之江学院毕业设计（论文） 外文翻译线锯过程中凹凸不平面的损伤情况摘要：线锯工艺被被广泛用于硅晶片生产与高收益、低表面损伤的太阳能电池和微电子产业。这个线锯过程是用于机器切割脆性材料从而得到高韧性， 高收益和低表面损伤的。线锯工艺也可用于切割混凝土和岩石，土木工程。在这研究中，通过改变工艺参数进行了试验参数的研究，以确定表面粗糙度损坏。延性材料的穿晶断裂和脆性断裂的晶间破坏的切割表面可以在电子显微镜照片中观察到。涉及粗糙度破坏过程的损伤模型的参数是可以得到的。这个损伤模型预测粗糙度损害令人满意。该模型显示这种粗糙度损伤比率是进给速度与线速度成正比。提高效率的过程在于不增加粗糙度损伤而通过增加进给速度正比线速度的比率。线张力不影响粗糙度损伤。但是，导线的性能影响粗糙度损伤。导线的砂砾半径越小和砂粒间距越短则粗糙度损伤越少。关键词：陶瓷，损伤模型，韧性加工，粗糙度，线锯1 介绍硅晶片用于太阳能电池和微电子学产业可以减少从硅晶体使用内径(ID)锯或线锯。线锯的优势是ID可以看见。这些优点是更高的生产力，更少的晶片表面损伤和较低的切口损失。此外，晶片的直径可以被切成一个线锯高于一个ID。线锯适用切割蓝宝石，碳化硅，锂铌酸，木材，岩石和几乎所有种类的陶瓷，包括泡沫陶瓷。穆勒指出，线锯过程中的成本是占硅晶片生产的总成本的30，这直接影响整个行业。所以有必要来采取优化过程的措施：通过发展模型相关的工艺参数，产品质量和过程效率。20世纪90年代，早期的线锯是在晶圆生产裸钢丝和磨料泥浆过程中开发的，在研磨加工中使用弹性流体动力。研磨颗粒可以是SiC或钻石，用30至60的磨料颗粒的粒度可以是530m体积分数的料浆。平均线直径是180m，切缝损失为200到250m。浆料可以是水性或油性的。油性泥浆使溶液彼此互溶，很难独立，而从晶圆片表面清除油状物是另一个问题。油性泥浆的使用处理也是一个问题。产生的氢气和水性泥浆中硅的相互作用可能会导致爆炸。然而，从环保的角度来看，考虑到高数量的泥浆处理过程，水性通常是优选的。Clark等人说，为了提高生产率和能够削减更硬的陶瓷，开发了镶金刚石线。其适用于磨削加工。在自由磨料线锯中，送丝速度为515米/秒，线张力为2030N。在电线弓中，其结果使得所述导线达到2度到6度的水平。在研磨加工工艺的线锯中，线速度较低的材料去除是不会发生水动力作用的。线锯过程的研究已经持续在三个主要领域：材料去除机制，运动学，进程之间的输入和输出参数的研究。Li等人提出了磨料颗粒的受应力作用是滚动和缩进的线锯的过程。穆勒提出的材料去除机制对于自由磨料加工开发利用断裂力学和流体动力学行为的浆料。材料去除率的定义是作为一个功能电源提供给磨料流体动压效应与流体膜性能。它的计算采用有限元阀夫妇雷诺方程，流体力学与弹性力学方程。刘等人指出，材料去除机理线锯切割岩石是赫兹类破裂，其中破裂的发生是由于拉伸后面滑珠引起的。魏和高从事分析直线的刚度和研究在张力作用下的导线，还有振动特征对线速度，张力，和浆料粘度的研究。当线速度低于25米/秒时，增加线张力和浆粘度而降低振幅和切口损失，对它几乎没有影响。Clark等人监测线锯过程，线速度，送丝速度和线的张力。Clark和Hardin等人还进行了参数研究有关工艺的参数，表面粗糙度和线切割泡沫陶瓷，木材。他们还进行了与一个固定的磨料切片单晶SiC的参数研究，研究金刚石线有关的线速，摇摆频率，下表面和亚表面损伤的进给速度。Meng等人研究了闭环金刚石绳锯切割和浸渍氧化铝陶瓷粉末。硬度各向异性的铌酸锂晶片已经被应用在纳米压痕中。Bhagavat和Kao确定了三个最常见的取向的方法。他们通过切片硅晶体的各向异性来确定的方向。硅片的钢丝锯对光伏及半导体行业有着重大的利益关系。半导体有严格的公差和表面质量要求。从现有的模拟脆性材料压痕损失中可以看出在加工脆性材料时的损坏情况。脆性材料的压痕存在几种的失效模式。Ryu等人研究了硅片，玻璃和碳化硅上的压痕。赵等人观察到在地面上被破坏的光学玻璃表面的压痕。不同的研究人员对延性域磨削脆性材料进行了试验研究。Bifano等人指出在研磨中，当进给量减少到一定量时，磨损机制就可以实现从脆性到韧性转变。在这项研究中，一个线锯损伤模型可以看出线锯过程中粗糙度的损坏。这个损伤模型是基于延性去除模式和脆性损害模式，观察扫描电镜中切割面的图像。过实验测定，用损伤模型来预测损害通是可靠的。第二节提出了这个实验工作。第三节提出了该模型。第四节提出了结果和讨论的研究。在第五部分提出这个结论。2 实验过程线锯的实验是在氧化铝陶瓷上进行的。在线锯切削试验中测量了丝弓角，轴向线速度Vx和进给速率Vz。同时也测量了切断面表面的粗糙度，还得到了扫描电镜成像的切表面。在这些测量中所使用的设备本节介绍及工艺参数。2.1 线锯切割和丝弓角测量图1 单丝，阀芯阀芯线锯机，该线轨道，由虚线标记。（DWT公司，千禧年生产的模型，美国科罗拉多州Springs，美国）实验中使用线锯设备（其模型是千禧年在科罗拉多州斯普林斯应用钻石线技术生产的）。这种阀芯对阀芯的线锯机摇摆运动的线可控制线速度Vx，进料速度Vz和线张力T。张力由紧线滑轮控制，由气压力驱动，而摆动如图1中可以看出。导线的切割长度为300英尺（91.4米）。因此，在每一个方向逆转，300英尺的线是从一个线轴转移到其他的线轴。在切割过程中使用的冷却剂包括水和润滑剂Sawzit（合成润滑剂公司的产品），它们的比例为50/1。线锯实验使用了四种不同的金刚石涂层钢线。平均半包括磨粒的角度DWS2是=71度。这个金刚石粒度的镀层钢丝DWS3是金刚石线锯公司的一个产品。涂金刚石砂砾的钢丝DWS4和DWS5是圣戈班磨料磨具公司的产品。DWS4和DWS5是用镍电镀钢制造的。磨粒被贴到电镀。镍层，而核心依然完整。氧化铝陶瓷样品的抗拉强度=300MP，断裂韧性K=4MPam(1/2)，杨氏模量电子E=370GPa时，硬度H=22GPa，它用于对加工对象物的切削的测试。切割样品的长度是在1520毫米之间，高度7.1毫米。一组测试完成DWS2的线速度变化Vx=1.3，1.8，2.95，3.5米/秒，线张力变化T=13.3，17.8，22.4，26.7牛，和下料速度变化Vz=5，6.35，10.16微米/秒。为了探讨不同特性对表面质量影响，每个线进行了四次试验，在工艺参数Vx=1.35，2，3，4米/秒，Vz=6.35米/秒，T=13.3N下分别使用电线钢丝DWS3，DWS4和DWS5。图2 线钢丝锯弓角测试用一个28562142像素的数码相机（柯达易购DX7630）来测量丝弓角，其角度如图2。图像的线和样品收集过程如图3。氧化铝陶瓷SEM图像的线锯切割表面的（Vx=1.3米/秒，Vz=5微米/秒，T=13N）试验和分析用数字图像处理（Mathworks公司）获得的角度在导线和水平之间。平均稳态丝弓角的测试，达到了稳定状态丝弓角的要求。2.2 表面粗糙度测量和扫描电镜成像切割表面的表面粗糙度的测定使用非接触式的光学轮廓仪，Zygo公司生产的Zygo新查看6000。10倍的镜头用于测量。轮廓的垂直分辨率是3纳米的分辨率，在水平面上为1.1微米，而视野使用0.70.53毫米。在一个探针测量中，需要连续的轮廓测量每个0.70.53毫米，将这些数据结合在一起成为一个数据集。三针测量，是指测量每个0.73毫米尺寸，常应用在每个样品的切割方向的左中右的切割表面。经过测量后，用版本8.1.5Zygo公司开发的MetroPro软件进行数据处理，施加高通滤波，以除去表面的波状起伏。中心线的算术平均偏离就可以获得最佳拟合平面。三次测量的平均值作为表面粗糙度（Ra）的测试值。图3氧化铝陶瓷的线锯切割表面的SEM图像（Vx=1.3米/秒，Vz=5微米/秒，T=13N）扫描电子显微镜（SEM），JEOLJSM-606LV，用于图像的切割面拓扑。SEM图像的来自中心线的切割表面上，少于一半的样本。由图像可知材料去除的机制是穿晶断裂的。同时，也可以观察到晶间破坏的断裂模式。这两种机制中可以看图3。5INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 6, pp. 941-947 DECEMBER 2011 / 941DOI: 10.1007/s12541-011-0126-4 NOMENCLATURE Fz = Vertical force on a grit Fzg= Force on a single grit Fzs = Total vertical force action on sample y = Yield stress R = Grit radius h = Cut depth for a single particle Vx = Wire speed Vz = Feed speed T = Wire tension Ap = Projected area of the cut trench Lo = Cut length of sample Lg = Distance between cutting particles D = Width of cut trench S = Sliding distance c = Median crack length = Half of the included angle of the grits E = Modulus of elasticity of ingot H = Hardness of the ingot P = Indentation force Kc= Fracture toughness of the ingot w = Distributed wire load on the sample N = Number of cutting particles in the cut length = Wire bow angle 1. Introduction Silicon wafers used in the solar cell and microelectronics industries can be cut from silicon crystals using inner diameter (ID) saw or wire saw. Wire saw has advantages over ID saw. These advantages are higher productivity, less wafer-surface damage, and lower kerf loss.1 Moreover, the diameter of wafer that can be sliced by a wire saw is higher than that obtainable by an ID saw. Wire saws are used to cut sapphire, silicon carbide, lithium niobate, wood, rock, and almost all kinds of ceramics, including foam ceramics.1-3 Moller4 stated that the wire saw process is responsible for 30% Roughness Damage Evolution Due to Wire Saw Process Egemen Teomete1,#1 Dept. Civil Engineering, Dokuz Eylul University, Kaynaklar Campus Buca, Izmir, Turkey, 35160# Corresponding Author / E-mail: eteomete, TEL: +90-232-4127060, FAX: +90-232-4531192 KEYWORDS: Ceramic, Damage model, Ductile regime machining, Roughness, Wire saw The wire saw process is widely used for silicon wafer production with high yield and low surface damage in solar cell and microelectronics industries. The wire saw process is used to machine brittle materials in the ductile regime where high yield and low surface damage are desired. The wire saw process is also used to cut concrete and rocks in civil engineering. In this study, an experimental parametric study was conducted by varying process parameters to determine surface roughness damage. Ductile regime material removal by trans-granular failure and brittle fracture by inter-granular failure are observed in electron micrographs of the cut surfaces. A damage model that relates the roughness damage to process parameters was derived. The damage model predicts the roughness damage satisfactorily. The model shows that the roughness damage is proportional to the ratio of feed speed to wire speed. Improvement in the efficiency of the process without increasing the roughness damage can be attained by increasing the feed speed proportionally to wire speed. Wire tension does not affect roughness damage. Roughness damage, however, is affected by properties of the wire. Wires having smaller grit radius and small grit spacing cause less roughness damage. Manuscript received: May 4, 2010 / Accepted: May 15, 2011 KSPE and Springer 2011 942 / DECEMBER 2011 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 6 of the total silicon wafer-production cost, which directly affects industry. There is a need to optimize the process by developing models relating process parameters to product quality and process efficiency measures.4 Early wire saw processes for wafer production developed in the 1990s consisted of a bare steel wire and abrasive-carrying slurry, resulting in free-abrasive machining using elasto-hydrodynamic forces.5,6 The abrasive particles can be SiC or diamond. The mean grit size of abrasive particles can be 5 to 30m with a 30% to 60% volume fraction in the slurry. Average wire diameter is 180 m, leading to a kerf loss of 200 to 250 m. The slurry can be water based or oil based. Oil-based slurry causes the wafers to stick to each other, and it is hard to separate them, while removal of the oil from the wafer surface is another problem. Disposal of the oil-based slurry after use is also a problem. Hydrogen gas produced from the interaction of water-based slurry and silicon may cause explosions. However, from an environmental point of view, considering the high amount of slurry disposed of during the process, water-based slurries are generally preferred.4 Clark et al.5 stated that in order to increase the productivity and to be able to cut harder ceramics, diamond-impregnated wire, which leads to fixed-abrasive machining, was developed. In wire sawing with free abrasives, wire speed is between 5 to 15 m/s and wire tension is 20 to 30 N. The feed into the ingot results in a wire bow so that the wire makes 2o to 6o with the horizontal.6 In the fixed-abrasive machining wire-saw process, the wire speed is lower as material removal is not occurring by hydrodynamic action. In multi-wire technology, a single wire is winded to a tension control unit and several guide pulleys, which are grooved with constant pitch. Five to seven hundred parallel wires run together and are collected at a take-up spool. The ingot is sliced into hundreds of wafers as it is fed into the wire web. The wafers in solar-cell industry are cut by running the wire in only one direction at a high speed between 5 to 20 m/s, while the wafers in the micro electronics industry are cut by running the wire in both directions with a lower speed (oscillating the wire from one spool to another).4 Research on the wire saw process has been ongoing in three main areas: material removal mechanisms, kinematics of wires, and parametric studies between the process inputs and outputs. Li et al.7 presented the stresses under an abrasive particle, which is rolling and indenting in a wire saw process. Material removal mechanisms for free-abrasive machining were developed using fracture mechanics and hydrodynamic behavior of slurry by Moller.4 The material removal rate is defined as a function of power supplied to the abrasive by hydrodynamic effect and the hydrodynamic film properties are calculated using the finite element method which couples Reynolds equation of hydrodynamics with the elasticity equation of wire.6 Liu et al.8 stated that the material removal mechanism of bead- impregnated wire-saw cutting of rock is a Hertzian type fracture in which the fracture occurs due to the tensile field behind the sliding bead. Wei and Kao9 worked on stiffness analyses of straight and bowed wires under tension. Vibration characteristics of wire with respect to wire speed, tension, and slurry viscosity was investigated. The increase of wire tension and slurry viscosity decreases vibration amplitude and kerf loss, while the wire speed has almost no affect when it is below 25 m/s.1,10 Process monitoring of the wire saw for forces, wire speed, feed rate, wire bow, and wire tension was developed by Clark et al.5 Parametric studies relating process parameters to forces, and surface roughness and wire wear for cutting foam ceramics and wood were conducted by Clark et al.2 Hardin et al.11 conducted a parametric study for slicing single crystal SiC with a fixed-abrasive diamond wire, relating wire speed, rocking frequency, and down-feed rate with surface and subsurface damage. Closed-loop diamond- impregnated wire saw cutting of Al2O3 and TiC ceramics was studied by Meng et al.12 Hardness anisotropy of Lithium Niobate wafers has been investigated using nano-indentation.13 Bhagavat and Kao14 determined the direction of approach for three most commonly sliced orientations of silicon considering crystal anisotropy. Damage evolution due to wire sawing of silicon wafers is of significant interest as the photovoltaic and semiconductor industries have strict tolerances for surface quality. The process-induced damage on brittle materials can be modeled starting with existing damage models of indentation of brittle materials. There exist several models for the failure mechanisms in brittle materials due to indentation.15-20 Ryu et al. studied indentation on silicon wafer, glass and silicon carbide.21 Zhao et al. observed the indentation damage modes on ground surface of optical glass.22 Ductile regime grinding of brittle materials has been investigated experimentally by different researchers.23-28 Bifano et al.24 stated that when the feed is decreased below a certain amount in grinding, a transition of wear mechanism from brittle to ductile mode can be achieved. In this study, a damage model for wire saw process induced roughness damage is developed. The damage model is based on ductile mode material removal and brittle mode damage, as observed in SEM images of cut surfaces. The damage model predicts the experimentally measured damage successfully. The experimental work is presented in section 2. The model is presented in section 3. The results and discussion of the study are presented in section 4. The conclusions are presented in section 5. 2. Experimental Process Wire saw experiments were conducted on alumina ceramic. The wire bow angle, wire axial speed, Vx and feed rate, Vz were measured during the wire saw cutting tests. The surface roughness of cut surfaces was also measured. The SEM imaging of cut surfaces was obtained. The equipment used in these measurements and the process parameters are presented in this section. 2.1 Wire Saw Cutting and Wire Bow Angle Measurement A wire saw machine (Millennium model produced by Diamond Wire Technology in Colorado, Springs) was used in the experiments. This spool-to-spool wire saw machine with rocking motion of the wire can be controlled by the wire speed, Vx, down-INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 6 DECEMBER 2011 / 943 feed speed, Vz, and wire tension, T. The tension was controlled by wire tension pulleys powered by air pressure, while the rocking motion was controlled by wire guide pulleys as can be seen in Fig. 1. The cut length of the wire was 300 ft (91.4 m). Thus, at every direction reversal, 300 ft of wire was transferred from one spool to the other. A coolant consists of water-to-lubricant Sawzit (Product of Synthetic Lubricants, Inc.) ratio of 50/1 was used during cutting tests. Four different diamond grit coated steel wires were used in the wire saw experiments. The average half-included angle of the grits on DWS2 was =71o. The diamond-grit-coated steel wire DWS3 was a product of Well Diamond Wire Saws Inc. Diamond-grit-coated steel wires DWS4 and DWS5 were products of Saint-Gobain Abrasives Inc. The DWS4 and DWS5 were manufactured by nickel electroplating on steel. The grits were affixed into the electroplated nickel layer, while the core remains intact. Alumina ceramic samples having tensile strength of fr=300 MPa, fracture toughness KIC =4 MPam1/2, Youngs modulus of E=370 GPa,29 and hardness of H=22 GPa20 were used in the cutting tests. The cut length of the samples was between Lo =1520 mm and the height was Hs =7.1 mm. A group of tests were done with DWS2 with the wire speed varied over Vx=1.3, 1.8, 2.95, 3.5 m/s, the wire tension varied over T=13.3, 17.8, 22.4, 26.7 N, and the down feed varied over Vz=5, 6.35, 10.16 m/sec. In order to explore the effect of different wires characteristics on surface quality, twelve tests were done with process parameters Vx=1.35, 2, 3, 4 m/s, Vz=6.35 m/sec, and T=13.3 N using the wires DWS3, DWS4, and DWS5; four tests were conducted with each wire. A megapixel digital camera (Kodak Easy Share DX 7630) of 2856 2142 pixels was used to measure the wire bow angle seen in Fig. 2. The images of the wire and sample were collected during the test and analyzed using Matlab (Mathworks) to obtain the angle between the wire and the horizontal. The average of the steady state wire bow angles, , was attained to the test as the steady state wire bow angle of that test. 2.2 Surface Roughness Measurements and SEM Imaging The surface roughness of the cut surfaces were measured by using an optical non-contact profilometer, Zygo New View 6000, manufactured by Zygo Corporation. A 10x lens was used for the measurements. The profilometer had a vertical resolution on the order of 3 nanometer; the resolution in the horizontal plane was 1.1 m, while the field of view used was 0.70.53 mm. In a stitch measurement, the profilometer takes continuous measurements each 0.70.53 mm and stitches them together into one data set. Three stitch measurements, each of 0.73 mm dimensions, were applied in the direction of cutting for each sample on the left-middle-right of the cut surface. After the measurements were taken, the data was processed using the software MetroPro Version 8.1.5 developed by Zygo Co. A high pass filtering was applied to remove the surface waviness. Arithmetic average deviation from the centerline (best fit plane) was obtained. The average of three measurements was taken as surface roughness (Ra) of the test. A Scanning Electron Microscope (SEM), JEOL JSM-606LV, Fig. 1 Single wire, spool-to-spool wire saw machine. The wire track is marked by the dashed line. (DWT Inc., Millennium Model, Colorado, Springs, USA) Fig. 2 Wire bow angle in wire saw tests Fig. 3 SEM image of a wire saw cut surface of alumina ceramic(Vx=1.3 m/sec, Vz= 5 m/sec, T=13 N) 944 / DECEMBER 2011 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 6 was used to image the cut-surface topology. The SEM images were taken from the lower half of the sample, on the center line of the cut surface. It is seen from the images that the material removal mechanism is the trans-granular failure. Inter-granular failure, in which grain boundary failure results in grain dislodgement in a brittle mode, is also observed. Both mechanisms can be seen in Fig. 3. 3. Roughness Model Derivation Ductile material removal and brittle fracture is observed in SEM images. The proposed model is shown in Fig. 4. The material removal occurs in a ductile mode as seen in SEM images, while the damage occurs due to median cracking as in Fig. 4. As discussed by Evans and Marshall,15 removal of plastically deformed material in the cutting zone reduces residual stress. This reduces the tendency of lateral crack formation in brittle materials. Fu et al.30 derived the force on a single grit in ductile mode material removal as presented in Eq. (1), where y is yield stress, R is cutting particle radius, and h is cut depth for a single particle. zzgyFFRh= (1) The mass continuity of the cutting process gives us Eq. (2). ogzxpoggLDhsLdVolddShhVVdtAdtLDdtLL= (2) Volume is the total amount of material removed, Ap is the projected area of the cut trench, Lo is the cut length of sample, Lg is the distance between cutting particles, D is width of cut trench that can be taken as diameter of wire, S is sliding distance, Vx is the axial speed of wire, and Vz is the feed of wire. The force on a single grit, Fzg, can be obtained in terms of process parameters by using Eq. (1) and Eq. (2). zzgygxVFRLV= (3) The damage resulting from wire saw cutting is correlated with median crack depth. Lawn et al.16 derived the median crack length using fracture mechanics principles. The median crack length is presented in Eq. (4). Lawn et al.16 calibrated the indentation coefficients 0.032 and 0.017 in Eq. (4) using indentation data of soda-lime glass and noted that they are applicable to all brittle materials. 2132230.0320.017(cot)cEPcHK=+ (4) Inserting Eq. (3) in place of P=Fzg in Eq. (4) gives us Eq. (5). 221323230.0320.017(cot)ygzcxRLEVcHKV=+ (5) Fig. 4 Wire saw roughness damage model: ductile material removal and brittle fracture The damage due to the wire saw process is presented in terms of the process parameters in Eq. (5). The damage is a function of the half of the included angle of the grits, ; the modulus of elasticity of ingot, E; the hardness of the ingot, H; the fracture toughness of the ingot, Kc; and wire properties, feed speed, and wire speed. 4. Results and Discussion Decreasing feed rate in grinding below a threshold yields ductile regime grinding of brittle materials.23-28 In ductile regime machining of brittle materials, the material removal takes place with plastic deformation of the grains.23,24,26-28,31 While the material removal is in ductile mode, brittle fracture is still observed in ductile regime grinding.24,28 The material removal and damage formation in the wire saw process is analogous to ductile regime grinding as seen from SEM images of wire saw processed surfaces. A damage model is derived for roughness damage induced by wire saw process. The model is compared to experimental data in Fig. 5. The model has a good performance in predicting roughness damage due to the wire saw process. The damage model states that if the feed-speed-to-wire-speed ratio (Vz/Vx) is increased, the roughness damage will increase, while if this ratio is kept constant, roughness damage will be constant. The two experiments marked in Fig. 5 have different feed speeds and wire speeds but a very close (Vz/Vx) ratio, and their roughnesses are also very close to each other. In a wire saw process, if efficiency should be increased by increasing the feed speed, in order to keep the level of damage constant, the wire speed should be increased proportionally to the feed speed. In order to explain the effect of wire tension on roughness damage, the change of forces with wire tension should be considered. The total force and distributed force acting on the sample by the wire due to wire bow and tension is presented in Eq. (6) and Eq. (7), respectively. The total force, Fzs, is distributed on the cutting grits as cutting forces per grit, Fzg, by Eq. (8). The N=Lo/Lg is the number of cutting particles in the cut length, Lo, and, INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 6 DECEMBER 2011 / 945 Lg, is the distance between cutting grits. 2 sinzsFT= (6) 2 sinoTwL= (7) 2 sin2 sinzggoTTFLNL= (8) The increase of wire tension, T, decreases the wire bow as seen in Fig. 6. As tension, T, increases, the wire bow decreases and the distributed load on the sample w, remains constant due to Eq. (7), as seen in Fig. 7. The increase of tension, T, decreases the bow angle and the force on a single grit, Fzg, remains constant due to Eq. (8); thus, the surface roughness does not change with respect to tension, T, as seen in Fig. 8. The surface roughness is independent of tension. The damage model relates the roughness damage with wire properties approximately, as in Eq. (9). The roughness is expected to increase with the increase in the radius, R, of abrasive grits and T (N) Fig. 7 Variation of distributed load w as a function of wire tension T (Vx =1.8 m/sec, Vz = 5 m/sec) T (N) Fig. 8 Variation of surface roughness with respect to wire tension T (Vx =1.8 m/sec, Vz = 5 m/sec) Vx(m/s) Fig. 9 Variation of surface roughness as a function of wire speed Vx. The tests were carried out with 3 different wires. (Vz = 6.35 m/sec, T=13N) the spacing between the abrasive grits, Lg. c (RLg)2/3 (9) Vz/Vx*10-6 Fig. 5 Comparison of wire saw roughness damage model with respect to experimental results T (N) Fig. 6 The variation of normalized wire bow angle by cut length /Lo as a function of wire tension T (Vx=1.8 m/sec, Vz= 5 m/sec) 946 / DECEMBER 2011 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 6 Four roughness tests with different wire speeds but the same feed speed and tension were done with three different wires. The roughness versus wire speed for each wire is presented in Fig. 9. For the same wire speed, the increase of (R.Lg)0.6 yields a higher roughness as seen in Fig. 9. Thus, the prediction of the model about the increase of roughness with grit radius and spacing is verified experimentally. 5. Conclusions Wire saw process is widely used to slice brittle materials including silicon wafers in semi-conductor and photo-voltaic industries; almost all kinds of ceramics in different engineering applications; concrete and rocks in civil engineering with high yield and low surface damage. The surface damage occurred due to wire saw process decreases the quality of the cut surface and has to be removed by post processes including grinding, and polishing which increase the production cost. In this study an experimental parametric work was conducted for wire saw process with different process parameters. The process induced roughness damage is modeled according to direct observations on the cut surfaces obtained by the process. The results obtained in this study are presented below. 1. The SEM images of the cut surfaces showed that the material removal occurs in the ductile mode, while there is brittle fracture, which is analogous to the ductile regime grinding of brittle materials. 2. In the literature, there has not been an analytical roughness damage model relating the process parameters with the damage for wire saw process. A roughness damage model relating process parameters to the wire-saw induced roughness damage was derived. The mode of ductile regime cutting and brittle fracture damage on the cut surfaces observed by SEM, have one to one correspondence in the damage model. Experimental study validated the derived model. The damage model in this work is a contribution to the science and technology as being the only analytical roughness damage model for wire saw process. 3. The model states that the roughness damage is proportional to the ratio of feed speed to wire speed. If the efficiency of the process should be increased without increasing the roughness damage, the feed speed should be increased proportionally with respect to wire speed. 4. Wire tension does not affect surface quality. There is no need to apply high wire tension which will decrease the life of the wire. 5. Wire properties have a marked effect on roughness damage. Wires with smaller grit radius and spacing lead to smaller roughness damage. Wires of high grit density with small grits are beneficial for surface quality. The results of the damage model can be directly used by the engineers and technicians working on the wire saw process in the industry. ACKNOWLEDGEMENT This work is supported by US-National Science Foundation NSF. This work is a part of the authors PhD study in Iowa State University, Iowa, USA. REFERENCES 1. Zhu, L. and Kao, I., “Galerkin Based Modal Analysis on the Vibration of Wire-Slurry System in Wafer Slicing Using a Wiresaw,” Journal of Sound and Vibration, Vol. 283, No. 3-5, pp. 589-620, 2005. 2. Clark, W. I., Shih, A. J., Lemaster, R. L. and McSpadden, S. B., “Fixed Abrasive Diamond Wire MachiningPart II: Experiment Design and Results,” International Journal of Machine Tools and Manufacture, Vol. 43, No. 5, pp. 533-542, 2003. 3. Ge, P. Q., Zhang, L., Gao, W. and Liu, Z. C., “Development of Endless Diamond Wire Saw and Sawing Experiments,” Materials Science Forum, Vol. 471-472, pp. 481-484, 2004. 4. Moller, H. J., “Basic Mechanisms and Models of MultiWire Sawing,” Advanced Engineering Materials, Vol. 6, No. 7, pp. 501-513, 2004. 5. Clark, W. I., Shih, A. J., Hardin, C. W., Lemaster, R. L. and McSpadden, S. B., “Fixed Abrasive Diamond Wire MachiningPart I: Process Monitoring and Wire Tension Force,” International Journal of Machine Tools and Manufacture, Vol. 43, No. 5, pp. 523-532, 2003. 6. Bhagavat, M., Prasad, V. and Kao, I., “Elasto-Hydrodynamic Interaction in the Free Abrasive Wafer Slicing Using a Wiresaw: Modeling and Finite Element Analysis,” Journal of Tribology Transactions of the ASME, Vol. 122, No. 2, pp. 394-404, 2000. 7. Li, J., Kao, I. and Prasad, V., “Modeling Stresses of Contacts in Wire Saw Slicing of Polycrystalline and Crystalline Ingots: Application to Silicon Wafer Production,” Journal of Electronic Packaging, Vol. 120, No. 2, pp. 123-128, 1998. 8. Liu, B. C., Zhang, Z. P. and Sun, Y. H., “Sawing Trajectory and Mechanism of Diamond Wire Saw,” Key Engineering Materials, Vol. 259-260, pp. 395-400, 2004. 9. Wei, S. and Kao, I., “Analysis of Stiffness Control and Vibration of Wire in Wiresaw Manufacturing Process,” Proceeding of ASME Manufacturing Science and Engineering Division, pp. 813-818, 1998. 10. Wei, S. and Kao, I., “Vibration Analysis of Wire and Frequency Response in the Modern Wiresaw Manufacturing Process,” Journal of Sound and Vibration, Vol. 231, No. 5, pp. 1383-1395, 2000. 11. Hardin, C. W., Qu, J. and Shih, A. J., “Fixed Abrasive Diamond Wire Saw Slicing of Single-Crystal Silicon Carbide Wafers,” Materials and Manufacturing Processes, Vol. 19, No. 2, pp. 355-367, 2004. INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 6 DECEMBER 2011 / 947 12. Meng, J. F., Li, J. F., Ge, P. Q. and Zhou, R., “Research on Endless Wire Saw Cutting of Al2O3/TiC Ceramics,” Key Engineering Materials, Vol. 315-316, pp. 571-574, 2006. 13. 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