Int J Adv Manuf Technol (2010) 48:103–119 DOI 10.1007/s00170-009-2287-1 ORIGINAL ARTICLE Modeling the material removal rate in ultrasonic machining of titanium using dimensional analysis Jatinder Kumar & J. S. Khamba Received: 21 June 2008 / Accepted: 27 August 2009 / Published online: 13 September 2009 # Springer-Verlag London Limited 2009 Abstract Titanium is known as the metal of the future because of its excellent combination of properties such as high strength-to-weight ratio, low thermal conductivity, and high corrosion resistance. Machining of titanium, however, is considered as cumbersome with the conventional manufacturing practices, and there is a critical need of developing and establishing cost-effective methods of machining. This investigation is focused on exploring the use of ultrasonic machining, a nontraditional machining process for commercial machining of pure titanium (American Society for Testing and Materials grade-I) and evaluation of material removal rate under controlled experimental conditions. The optimal settings of parameters are determined through experiments planned, conducted, and analyzed using Taguchi method. An attempt has been made to construct a micro-model for prediction of material removal rate in ultrasonic machining of titanium using dimensional analysis. The predictions from this model have been validated by conducting experiments. The microstructure of the machined surface under different experimental conditions has been studied using scanning electron microscopy. A relation was established between the mode of material removal and the energy input rate corresponding to the different process conditions. Keywords Titanium . Ultrasonic machining . Material removal rate . Taguchi method . Micro-model . Dimensional analysis 1 Introduction Titanium and its alloys are alternative for many engineering applications due to their superior properties such as chemical inertness, high strength, stiffness at elevated temperatures, high specific strength, excellent corrosion resistance, and oxidation resistance. However, these properties also make titanium and its alloys difficult to shape and machine into a precise size and shape. As a result, their widespread applications have been hindered by the high cost of machining with current technology [13, 27]. The machining characteristics for titanium and its alloys using conventional machining processes are summarized below [10]: – – J. Kumar (*) Department of Industrial Engineering, National Institute of Technology, Kurukshetra, India e-mail: jatin.tiet@gmail.com J. S. Khamba Department of Mechanical Engineering, University College of Engineering, Punjabi University, Patiala, India – Titanium and its alloys are poor thermal conductors. As a result, the heat generated when machining titanium cannot dissipate quickly; rather, most of the heat is concentrated on the cutting edge and tool face. About 50% of the heat generated is absorbed by the tool while machining titanium alloy (Ti-6Al-4V) [1]. During machining, titanium alloys exhibit thermal plastic instability that leads to unique characteristics of chip formation. The shear strains in the chip are not uniform; rather, they are localized in a narrow band that forms serrated chips [28]. The contact length between the chip and the tool is extremely short (less than one third the contact length of steel with the same feed rate and depth of cut). This implies that the high cutting temperature and the high 104 – – Int J Adv Manuf Technol (2010) 48:103–119 stress are simultaneously concentrated near the cutting edge [6]. Serrated chips create fluctuations in the cutting force; this situation is further promoted when alpha-beta alloys are machined. The vibrational force, together with the high temperature, exerts a micro-fatigue loading on the cutting tool, which is believed to be partially responsible for severe flank wear [30]. The surface finish achieved by a single machining process is poor. Therefore, there is a crucial need for reliable and costeffective machining processes for titanium and its alloys. Over the last few decades, there have been great advancements in the development of cutting tools, including coated carbides, ceramics, cubic boron nitride, and polycrystalline diamond. These have found applications in the machining of cast iron, steels, and high temperature alloys such as nickel-based alloys and super alloys. However, none of these newer developments in cutting tool materials has had successful application in improving the machinability of titanium alloys [6]. Most cryogenic machining studies on titanium and its alloys have documented improved machinability when freezing the workpiece or cooling the tool using a cryogenic coolant. However, inherent weaknesses exist in these approaches as well [10]. Machinists have developed a few methods for commercial machining of pure titanium in manufacturing industries all over the world. Most of the machining work for titanium is related to drilling, so twist drilling and vibration-assisted drilling are two conventional machining methods being used in recent times. For other machining operations, special considerations are to be taken care of while machining titanium parts on a machine tool. Titanium and its alloys are very sensitive to changes in cutting speed. Industry generally operates at cutting speeds providing longer tool life. Moreover, because of the bouncy action generated due to low modulus of elasticity of titanium, the rigidity of a machine tool becomes an important consideration [1, 6]. The average unit power requirements for turning or milling of titanium have been found to be much lower than that for high temperature Ni/Co-based alloys or tool steel grades. As far as the cutting tools are concerned, the straight tungsten carbide (WC) cutting tools, typically C-2 grades, perform best in operations such as turning and face milling, while the high-cobalt, high-speed steels were most applicable in drilling, tapping, and end milling [30]. Economic production techniques developed for titanium and its alloys are based on a few general rules which have been summarized as: & Use low cutting speeds. Tool tip temperatures are affected more by cutting speed than by any other single variable. A change from 6 to 46 m per minute with & & & & carbide tools results in a temperature change from 427°C to 927°C. Maintain high feed rates. Temperature is not affected by feed rate so much as by speed, and the highest feed rates consistent with good machining practice should be used. A change from 0.05 to 0.51 mm per revolution results in a temperature increase of only 149°C. Use generous amounts of cutting fluid. Coolant carries away heat, washes away chips, and reduces cutting forces. Use sharp tools and replace them at the first sign of wear, or as determined by production/cost considerations. Tool wear is not linear when cutting titanium. Complete tool failure occurs rather quickly after small initial amount of wear takes place. Never stop feeding while a tool and a workpiece are in moving contact. Permitting a tool to dwell in moving contact causes work hardening and promotes smearing, galling, seizing, and total tool breakdown. Despite the establishment of effective machining methods using conventional technology, lower tool life, and poor surface quality are two major concerns that continue to be associated with the machining of titanium components. Besides this, poor surface integrity of conventionally machined titanium parts is another area where more concentration is required. Nontraditional machining processes such as electric discharge machining and laser beam machining have been applied for drilling holes in workpieces made from titanium and its alloys, but even these processes have their own limitations; the most prominent are the surface finish and dimensional inaccuracies besides their undesirable effects on the machined surface such as heat affected zone, recast layer, and thermal stresses [16]. These adverse effects can lower the working life of the components critically. Loss of fatigue strength and hence surface integrity is another problematic area in machining of titanium. The basic fatigue properties of many titanium alloys rely on a favorable compressive surface stress induced by tool action during machining [1, 6, 28, 30]. Ultrasonic machining (USM) could be another alternative machining process that can be applied commercially to the machining of titanium, as this process is known to be free from all these adverse effects on the machined component, and the repeated impacts of abrasive grains on the work surface lead to a favorable compressive surface stress thereby improving the fatigue life of titanium components along with the surface integrity [4, 20]. However, there is critical lack of evidence for the application of USM for machining of titanium in the literature available till now. Hence, in the present investigation, USM has been explored as an alternative machining method for pure titanium (American Society for Testing and Int J Adv Manuf Technol (2010) 48:103–119 Materials (ASTM) grade-I). The material removal rate (MRR) in USM of titanium has been evaluated under established experimental conditions. Taguchi’s method for offline quality control has been used to plan and analyze the experiments. The optimal process settings have been identified, and the macro-model for MRR has been constructed. The macro-model thus obtained has been used to develop a micro-model for prediction of MRR over a wide range of input parameters. A comparison of the predictions from the micro-model with the experimental results has been made for its validation. 2 Literature review To identify the potential factors affecting MRR in USM, a cause-and-effect diagram was constructed (Fig. 1). As the diagram indicates, the MRR in USM is dependant on four primary factors: workpiece, tool, slurry, and machinerelated factors. Various investigators [3, 7, 8, 12, 18, 19, 21] have reported results indicating that the rate of material removal for a certain abrasive is a function of its concentration, grain size, and hardness besides the feed system. On increasing the abrasive grit size or slurry concentration, an optimum value of MRR is reached. Any further increase in either aspect results in difficulty in the larger grains reaching the cutting zone [3, 18] or a subsequent fall in MRR. Guzzo and Shinohara [8] reported a substantial increase in MRR obtained while using abrasive of larger grain size on account of the increase in the stress caused by the impact of abrasive particle over the workpiece surface. Neppiras [19] and Markov [18] reported that when grain size is comparable to the amplitude of vibration, the optimum level of MRR can be reached. Experimentally, Fig. 1 Cause-and-effect diagram for material removal rate 105 the ratio of the double amplitude to the mean size of the principal fraction of abrasive is 0.6 to 0.8. Goetze [7] has reported the optimum value of slurry concentration to be close to 12% (by volume) for all the abrasive grit sizes used in the investigation. The optimum concentration is thought to be one providing a single layer of abrasive over the entire work surface [16]. The amplitude of vibration (ξ) has been found to affect the machining performance of USM [4, 10]. Higher amplitude is obtained by using a tool with a larger transformation ratio, i.e., the ratio of transducer/tool diameter [27]. Smith [26] showed that MRR is proportional to ξ3/4, while other researchers [7, 21] have advocated that MRR is linearly proportional to ξ, and yet others [12, 18, 19] have suggested that MRR depends upon ξ2 for constant frequency and static load conditions. Experiments conducted by Neppiras [19] have shown that in the range of 20 to 50 kHz, the removal rate is proportional to square root of the vibration frequency. However, Kazantsev [12] reported that the abrasion rate is proportional to the frequency, while the non-linear frequency dependence of machining rate is due to the variation in abrasive concentration in the working zone. It has been reported that the machining rate is directly proportional to the tool form [13, 27] and shape factor (ratio of tool perimeter to tool area). The tool form defines the resistance to slurry circulation: a tool of narrow rectangular cross-section yielding a better machining rate than one with a square cross-section of the same area [4, 13, 27]. Use of hollow tools has been reported to result in higher rates of material removal than ones with solid geometry for the same area of the cross-section [27]. Komaraiah and Reddy [15] investigated the influence of tool material properties, i.e., hardness on the MRR in USM of glass. The different tool materials were arranged in the increasing order of V 4.1 Al 5.8 Fe 0.25 910 MPa 187 HV 4.4 g/cm3 114 GPa 68 Mpam1/2 C 0.06 N 0.05 O 0.15 MPa MPa HV g/cm3 GPa 491 650 142 4.45 108 MPa MPa HV g/cm3 GPa 220 340 115 4.51 103 Yield strength Ultimate strength Hardness Density Mod. of elasticity Fracture toughness N 0.03 C 0.08 H 0.01 Fe 0.2 Ti 99.1 Balance 0.4 N 0.014 C 0.006 H 0.0007 Fe 0.05 O 0.14 O 0.18 Ti 99.78 Chemical composition (by wt.%) of titanium (ASTM grade-V) Chemical composition (by wt.%) of titanium (ASTM grade-II) Chemical composition (by wt.%) of titanium (ASTM grade-I) Table 1 Chemical composition and important properties of titanium and its alloy superiority as mild steel<titanium<stainless steel<silver steel<niamonic-80 A<thoriated tungsten. Also, the MRR has been found to vary in a linear proportion to the hardness of the tool being used [15, 21]. Tools with diamond tips have been shown to have good material removal characteristics [21]. It has been concluded that productivity by USM (in terms of machining rate) is primary determined by the brittleness of the work material [7, 13]. The plasticity of work material is associated with low productivity. The impact hardness has been found to have an adverse effect on machining rate. However, while machining annealed steel, the machining rates observed have been found to be significantly better than normalized or quenched ones [16]. Guzzo and Shinohara [8] outlined the ultrasonic abrasion of different hard and brittle materials using stationary USM. Results show that machining rate decreased with increase in hardness of the work material. Similar results were reported by other investigators [17, 26]. The literature review reflected that most of the research work carried out by different researchers focused on the improvement of process efficiency and efficacy while machining hard and brittle materials. The application of USM for machining of relatively tough materials (such as titanium) has been explored by a few researchers [5, 23– 25]. However, most of this work has been concentrated on the application of USM for machining of titanium alloy. Almost no effort has been put forward to investigate the machining characteristics of commercially pure titanium grades using USM. Singh and Khamba [24, 25] have investigated and modeled the machining characteristics of titanium alloy (ASTM grade-V) and pure titanium (ASTM grade-II) using static USM apparatus. In USM, the properties of work material such as hardness, toughness, and impact strength play a significant role in the variation of machining characteristics (MRR, TWR, and surface roughness). Pure titanium (ASTM grade-I) differs from titanium (ASTM grade-II) as well as titanium alloy (ASTM grade-V) to a significant extent (Table 1). From the comparison of the mechanical properties of the three grades, it is evident that pure titanium (ASTM grade-I) possesses considerably lower values of tensile strength and hardness; hence, there is a critical need to assess its machining behavior with a process like USM. Hence, pure titanium (ASTM grade-I) was selected as work material for the present investigation. Hu et al. [11] presented the modeling of MRR in rotary USM of alumina-based advanced ceramics. An approach to model the MRR during rotary USM of ceramics was proposed and applied to predict the MRR for the case of magnesia-stabilized zirconia. In this investigation, a fivefactor two-level factorial design was used to study the relationship between MRR and the controllable machining parameters. The model developed had practical application Int J Adv Manuf Technol (2010) 48:103–119 Ti 89.3 106 Int J Adv Manuf Technol (2010) 48:103–119 107 to USM of extremely hard and brittle materials such as advanced ceramics. Wiercigroch et al. [29] presented a model for prediction of MRR in ultrasonic drilling of hard materials using impact oscillator approach. Micro-cracking of work material due to impact of grains was assumed to be the material removal mechanism while constructing the model. However, the model was applicable only to hard materials. Moreover, the assumption of uniform wear over all the surface of the tool also proved to be false, as a non-uniform wear pattern was observed for the tool (over the length as well as the crosssection of the tool). In the present investigation, an attempt has been made to model the MRR in stationary USM of commercially pure titanium (ASTM grade-I), a relatively tough and ductile material. Buckingham’s pi theorem has been used for the dimensional analysis and hence construction of the model. The model developed is mechanistic in the sense that the outcome of the macro-model can be used to predict the MRR over a wide range of parameters. Also, the model is based on realistic assumptions (refer section 7), and the change in process conditions such as tool geometry and slurry concentration has been taken into account while constructing the model. Moreover, the predictions from the model have been found to agree well with the experimental results (Figs. 6, 7, and 8). 3 Materials and methods Commercially pure titanium (ASTM grade-I) has been used as the work material in the present investigation. Five different tool materials were used: high carbon steel, high speed steel, cemented carbide, titanium (ASTM grade-I), and titanium alloy (ASTM grade-V). The chemical composition and other mechanical properties of titanium and its alloy are shown in Table 1. All the tools except cemented carbide were made as one-piece unit and attached to the horn by tightening the threaded portion of the tool with the horn. Tool of cemented carbide was prepared by silver brazing the tip with replaceable threaded part at 1,200 F. Three types of abrasive materials were used: silicon carbide, aluminum oxide, and boron carbide. The abrasive slurry was prepared with a concentration equal to 25% (by mass of the abrasive to water). Three different grit sizes were selected for each abrasive material: 220, 320, and 500. The mean abrasive particle size corresponding to these mesh numbers has been detailed in Tables 2 and 3. These levels were selected by means of pilot experimentation performed to study the influence of the parameter grit size on the MRR in ultrasonic drilling of titanium. The pilot experimentation is performed to study the effect of the change in the levels of the factor of interest on the response variable. Experiments were conducted by varying the grit size of the abrasive over a wide range (from 100 to 600) while keeping all the remaining factors as unchanged. High carbon steel was used as tool material along with two types of abrasives-alumina and silicon carbide (with five different grit sizes ranging from 100 to 600), while the power rating was kept at two levels, 100 and 400 W, the ratio between the excitation power and amplitude of vibration being 1:1. The 20 experimental runs were replicated twice to obtain the results for pilot experimentation. Slurry grit sizes of 220, 320, and 500 contribute most to variation in MRR (Fig. 2); hence, these three levels were selected for final experimentation. Power rating of the ultrasonic machine was selected as another process parameter for this investigation as the effect of this parameter on MRR in USM has not been explored to a significant extent by any researcher by now. Three levels of power rating were finalized from the pilot experimentation: 100, 250, and 400 W. The process parameters and their levels selected for the final experimentation has been depicted in Tables 2 and 3. The experiments were conducted on an “AP-500 model Sonic-Mill” ultrasonic machine (Sonic-Mill, Albuquerque, NM, USA). The complete setup consisted of four subsystems: power supply, module unit, slurry re-circulating system, and workpiece holder. The USM equipment used for this research has been depicted in Fig. 3, with all its components clearly marked. The ultrasonic drilling action takes place by means of excitation of the tool. The vibrating tool hammers the abrasive particles flowing in the cutting zone, and machining takes place by microchipping of the work surface. The horn of the USM machine was made of titanium alloy (ASTM grade-V), and the same horn was used for conducting all the experiments for uniformity in Table 2 Process parameters and their values at different levels Symbol Parameter Level 1 Level 2 Level 3 Level 4 Level 5 A B C D E Tool material Abrasive type Grit size Power rating Slurry concentration HCS Alumina 220 (64µm) 100 20% HSS SiC 320 (36µm) 250 25% Titanium Boron carbide 500 (19µm) 400 30% Ti alloy Cemented carbide 108 Int J Adv Manuf Technol (2010) 48:103–119 Table 3 Constant parameters Frequency of vibration Static load Amplitude of vibration Depth of cut Thickness of workpiece Tool geometry 21 kHz 1.63 kg 25.3–25.8µm 2 mm 10 mm Straight cylindrical (with diameter 8 mm) Slurry temperature Slurry flow rate Slurry media 28°C (ambient room temperature) 36.4× 103 mm3/min Water results. In USM, the amplitude of vibration at the tool tip depends on the mass of the tool to a large extent. As the tool materials involved in this investigation possessed a wide spectrum of the value of density, the tool design was given a lot of practical consideration. The dimensions of the each tool were determined to keep the mass of the tool fixed at 50 gm. Using a tool of mass greater than this value (50 gm) results in overloading of the machine, and the machining is automatically stopped by the unit. To measure the MRR, the time taken for drilling each hole was recorded using a stopwatch. Each hole was drilled with a diameter of 8 mm and straight cylindrical geometry. The workpiece was weighed before and after drilling each hole using electronic balance. The weight loss for drilling each hole was thus recorded. The volumetric MRR (mm3/min) was calculated by taking the ratio of weight loss of the workpiece per hole to the product of drilling time per hole and density of the tool material. 4 Experimentation and data collection Before finalizing a particular orthogonal array for the purpose of designing the experiments, the following two things must be established [22]: 1. The number of parameters and interactions of interest 2. The number of levels for the parameters of interest. Fig. 2 Effect of grit size on material removal rate Fig. 3 Ultrasonic machining apparatus used for experimentation In the present investigation, four different process parameters have been selected as already discussed. The tool material factor has five levels, whereas all other parameters such as abrasive type, grit size, and power rating of the machine have three levels each. Hence, L18 array (in modified form) was selected for the present investigation. L18 array has a special property that the twoway interactions between the parameters are partially confounded with various columns. Hence, their impact on the main effects of the parameters under consideration is minimized [2]. It is not possible to assess the possible two factor interactions in L18 array but the main effects of different process parameters can be assessed with reasonEffect of grit size on MRR MRR (cubic mm/min) 1.8 P=100 W, Alumina slurry, HCS tool 1.5 1.2 P= 100 W, Silicon carbide slurry, HCS tool 0.9 0.6 P= 400 W, Alumina slurry, HCS tool 0.3 P= 400 W, Silicon carbide, HCS tool 0 100 220 320 Grit Size 500 600 Int J Adv Manuf Technol (2010) 48:103–119 109 able accuracy. According to the scheme of the experimentation outlined in the L18 orthogonal array (Table 4), holes were drilled in the work pieces which were prepared in the form of rectangular discs with thickness of 10 mm. Each trial was replicated twice; hence, three holes were drilled for each of the 18 trial runs and, moreover, all the 54 trial runs were executed in completely randomized fashion to reduce the effect of experimental noise to the maximum possible extent. Figure 4 shows the workpiece containing some holes drilled with USM. The flow rate of the abrasive slurry was maintained constant at a value of 36.4 × 103 mm3/min. To avoid any possibility of dullness of the edges of the abrasive grains, a large volume of slurry was prepared. The experimental results for MRR are summarized in Table 5. A wide variation in the MRR values was observed, with a mean of 0.57 mm3/min, the lowest value at 0.11 mm3/min, and the highest value at 1.44 mm3/min. Fig. 4 Holes drilled by ultrasonic machining in the titanium workpieces larger values of MRR. Hence, the higher-the-better type S/ N ratio was used for transforming the raw data [9]. h¼ 10 log 10 ( n 1 X 1 : n 1 y2i ) 5 Analysis of data where yi is the value of the characteristic in an observation i, and n is the number of observations or number of repetitions in a trial. 5.1 Evaluation of S/N ratios 5.2 Assessment of the main effects The S/N ratio is obtained using Taguchi’s method. Here, the term “signal” represents the desirable value (mean), and the “noise” represents the undesirable value (standard deviation). Thus, the S/N ratio represents the amount of variation present in the performance characteristic. Depending upon the objective of the performance characteristic, there can be various types of S/N ratios. Here, the desirable objective is The main effects can be studied by the level average response analysis of raw data or of S/N data. The analysis is done by averaging the raw and/or S/N data at each level of each parameter and plotting the values in graphical form. The level average responses from the raw data help in analyzing the trend of the performance characteristic with respect to the variation of the factor under study. The level Table 4 Experimental control log based on L18 OA Experiment number Tool material Abrasive Grit size Power rating 1 2 3 4 5 HCS HCS HCS HSS HSS Alumina SiC B4C Alumina SiC 220 320 500 220 320 100 250 400 250 400 6 7 8 9 10 11 12 13 14 15 16 17 18 HSS Titanium Titanium Titanium Titanium alloy Titanium alloy Titanium alloy Cemented carbide Cemented carbide Cemented carbide HCS HCS HCS B4C Alumina SiC B4C Alumina SiC B4C Alumina SiC B4C Alumina SiC B4C 500 320 500 220 500 220 320 320 500 220 500 220 320 100 100 250 400 400 100 250 400 100 250 250 400 100 110 Experiment number MRR (mm3/min) Average MRR (mm3/min) S/N ratio (dB) R1 R2 R3 1 2 3 4 5 6 7 8 9 10 11 12 0.31 0.64 1.09 0.40 0.74 0.21 0.13 0.24 1.33 0.27 0.18 0.47 0.27 0.58 1.21 0.28 0.63 0.15 0.12 0.27 1.09 0.26 0.20 0.55 0.36 0.75 0.99 0.30 0.80 0.15 0.07 0.35 1.24 0.38 0.15 0.36 0.31 0.66 1.10 0.33 0.72 0.17 0.11 0.29 1.22 0.30 0.18 0.46 −10.26 −3.80 0.71 −10.02 −2.94 −15.70 −20.45 −11.17 1.64 −10.72 −15.24 −7.15 13 14 15 16 17 18 0.59 0.32 1.25 0.14 1.30 0.30 0.50 0.27 1.40 0.17 1.45 0.45 0.72 0.36 1.16 0.18 1.56 0.36 0.60 0.32 1.27 0.16 1.44 0.37 −4.67 −10.17 2.00 −15.89 3.07 −8.99 5.3 Analysis of variance (ANOVA) The percentage contribution of various process parameters on the selected performance characteristic can be estimated by performing analysis of variance (ANOVA). Thus, information about how significant the effect of each controlled parameter is on the quality characteristic of interest can be obtained. The total variation in the result is the sum of variation due to various controlled factors and their interactions and variation due to experimental error. The ANOVA for raw data and S/N data have been performed to identify the significant parameters and to quantify their effect on the performance characteristic. The ANOVA based on the raw data signifies the factors, which affect the average response, but it misses the insight into the effect of the parameters on the variability of the process [20]. However, ANOVA based on S/N ratio takes into account both these aspects and, hence, it is used here. The pooled ANOVA results for S/N data and raw data are given in Tables 6 and 7, respectively. The most favorable conditions or optimal levels of process parameters have been established by analyzing response curves of S/N ratio associated with the raw data. Average Response Graph 1.00 MRR (cubic mm/min) average response plots based on the S/N data help in optimizing the objective function under consideration. The peak points of these plots correspond to the optimum condition. The main effects of raw data and those of the S/N ratio are shown in Fig. 5. 0.80 0.60 0.40 0.20 0.00 A1 A2 A3 A4 A5 B1 B2 B3 C1 C2 C3 D1 D2 D3 Factor level S/N Ratio Response Graph -2.00 -4.00 S/N value Table 5 Experimental results of material removal rate Int J Adv Manuf Technol (2010) 48:103–119 -6.00 -8.00 -10.00 -12.00 -14.00 A1 A2 A3 A4 A5 B1 B2 B3 C1 C2 C3 D1 D2 D3 Factor level A1-HCS A2-HSS A3-Ti A4-Ti alloy A5-Carbide; B1-Alumina B2-Silicon carbide B3-Boron carbide; C1-220 C2-320 C3-500; D1-100W D2-250 W D3-400 W Fig. 5 Effects of process parameters on material removal rate raw data and S/N ratio. Main effects (A=tool, B=abrasive, C=grit size, D= power rating, E=slurry concentration) Int J Adv Manuf Technol (2010) 48:103–119 111 Table 6 Analysis of variance results for material removal rate (S/N data) Source DF Seq. SS Adj. SS Adj. MS F Tool Abrasive Grit size Power rating Error Total 4 2 2 2 7 17 114.812 175.197 97.573 384.277 34.817 806.677 114.812 175.197 97.573 384.277 34.817 28.703 87.598 48.787 192.139 4.974 5.77 17.61 9.81 38.63 (% P) 14.2 21.7 12.1 47.6 4.4 Ftab value is obtained from statistical tables and represents probability of the event that the observed F value resulted just by chance. If F>Ftab, the factor is significant at 95% confidence level Ftab =F(4,43) = 2.60; F(2,43) = 3.21 DF degrees of freedom, Seq. SS sequential sum of squares, Adj. MS adjusted mean square error, % P percent contribution 5.4 Prediction of the mean After determination of the optimum condition, the mean of the response at the optimum condition is computed. This value is calculated by considering only the significant factors that are concluded by ANOVA. It may also happen that the predicted combination of the parameters be identical to one of the trial combinations executed already during the final experimentation stage. Under such situations, the most direct way to estimate the mean of that treatment combination is to average out all the results for the trials that are set at that particular levels [22]. 6 Results and discussions It can be observed from Fig. 5 that tool material used affects the MRR very significantly. Moreover, the different tool materials used in the experimentation can be ranked in the order of increasing MRR as titanium alloy, high speed steel, titanium, high carbon steel, and cemented carbide. The highest MRR has been recorded with cemented carbide as the tool material. This can be attributed to its very higher hardness (92 RC) as compared to the other tool materials used in this investigation. In USM, the indentation of abrasive grains in work and tool is inversely proportional to the hardness ratio of tool and work materials. Hence, use of a harder tool results in more indentation in the work piece as compared to tool, increasing the MRR [12, 14, 21]. Use of a tougher and ductile tool such as titanium or titanium alloy tends to lower the MRR as it encourages the plastic deformation of the tool as well as work material, which was conformed from the microstructure analysis of the machined samples. High carbon steel, being harder than high speed steel and titanium, has also been found to perform better than these tools in terms of MRR. In fact, the difference in the performance of high carbon steel and cemented carbide tools has been marginal, the later being on the higher side. It can also be concluded that the MRR increases with the increase in relative hardness of the tool-work combination, which has also been suggested by many other researchers [13, 17, 26]. The type of abrasive used has been found to produce a significant effect on MRR. It has been observed that use of boron carbide as abrasive results in more MRR as compared to that achieved with the use of alumina or silicon carbide. Boron carbide has 50–80% more cutting power as compared to other abrasive materials used in this investigation. Hence, the use of boron carbide as abrasive results is faster erosion of work surface thereby improving the MRR [3, 17]. The MRR obtained has been found to increase with the increase in coarseness of the abrasive grains. This is again in accordance with the findings of most investigators [7, 8, 18, 19, 27]. As reported in the literature [27], two main wear mechanisms act on the USM process: hammering and free impact of the abrasive particles. The primary mechanism is the hammering action of abrasive particles into the workpiece Table 7 Analysis of variance results for material removal rate (raw data) Source DF Seq. SS Adj. SS Adj. MS Ftab =F(4,43) = 2.60; F (2,43) = 3.21 Tool Abrasive Grit size Power rating Error Total 4 2 2 2 43 53 1.25 1.97 1.57 3.88 0.72 9.39 1.25 1.97 1.57 3.88 0.72 0.31 0.98 0.79 1.94 0.017 Order of significance: (1) power rating, (2) abrasive type, (3) grit size, and (4) tool F 18.5 58.1 46.5 114.5 (% P) 13.7 21.3 17.2 42.0 5.8 112 material. Decreasing the surface density of abrasive particles by increasing the grit size induces a greater augmentation of the effective stress due to each particle acting on the work surface, thus increasing the MRR. The secondary mechanism is the impact of free abrasive particles (accelerated by the vibrating tool) over the work surface. In this case, an increase in grit size increases the weight. The impact force against the workpiece surface also increases. Thus, under both mechanisms, the effective load acting on the work surface increases with grit size, which in turn increases the effectiveness of micro-cracking thereby increasing the MRR. As shown in Fig. 5, MRR drops rapidly, while grit size is changed from 220 to 320 and drops further from 320 to 500, but at a diminishing rate. After crossing the grit size of 320 (36 µm), the mean particle size of the abrasive continues to come closer to the mean gap between the tool and work as well as the vibration amplitude (25.3–25.8µm), which promotes more efficient machining of work material. It has also been observed that for a given tool material, MRR obtained is highest at that particular grit size–power level combination which corresponds to the highest value for tool wear rate. In other words, MRR is maximum at the points of maximum TWR. This is an inherent characteristic of the process and has also been found to be applicable in USM of titanium from this research. As far as the effect of power rating of the ultrasonic machine on MRR is concerned, any increase in power rating produced a substantial increment in the rate of machining (Fig. 5) as the momentum with which the abrasive particles strike with the work surface increased manifold with a corresponding increment in power rating [16]. The particles with higher momentum remove larger chunks of material from the work surface, promoting the increase in MRR. As titanium is a tough material with good strain hardening capability, the relative tool-work hardening plays a large role in the indifferent behavior of MRR with change in power rating [16]. With regards to the S/N response, the values of S/N ratio have been found to be highest for those factor levels that correspond to highest average response. Hence, these factor levels can be termed as optimum from the point of view of average response as well as S/N response. Hence, it can be concluded from this discussion that input parameters settings of ultrasonic power rating at 400 W, with cemented carbide tool and boron carbide slurry with a coarse grit size of 220, have given the optimum results for MRR when titanium (ASTM grade-I) was machined. 6.1 Macro-model for MRR MRR is “larger-the-better” type characteristic. Therefore, higher values of MRR are considered to be optimal. It is clear from Fig. 5 that MRR is highest at the fifth level of Int J Adv Manuf Technol (2010) 48:103–119 tool material parameter (A5), third level of abrasive material parameter (B3), first level of the grit size (C1), and third level of power rating (D3). The main effects of the S/N ratio are also highest at these levels of the parameters. To establish the relative significance of the individual factors, ANOVA has been performed, both on raw data and S/N data (Tables 6 and 7). The F values for various factors as estimated from the general linear model have been compared with the tabulated F values (Ftab) against the particular combination of factor degrees of freedom (DOF) and error DOF. If the estimated F value turns out to be significantly greater than the tabulated F value, the corresponding factor is termed as significant [2, 8]. The factors with larger F values (estimated) are deemed to be having more significance from a statistical point of view. The percent contribution of each factor has also been tabulated. With regarding to the average response, power rating factor has emerged as most significant with a percent contribution of 42% (Tables 5 and 7), followed by abrasive type (21.3%) and slurry grit size (17.2%). Tool material factor can be termed as the least significant for MRR with a percent contribution of 13.7%. However, for S/N response, power rating has been found to be having highest percent contribution (47.6%) followed by abrasive type (21.7%). Remaining factors have been found to be almost equally significant. The percent contributions of various factors have been depicted in Fig. 6 for both raw data as well as S/N response data. 6.2 Conformation experiments The Taguchi approach for predicting the mean performance characteristics and determination of confidence intervals for the predicted mean has been applied. Three confirmation experiments for each performance characteristics have been performed at optimal settings of the process parameters, and the average value has been calculated. The average values of the performance characteristics obtained through the confirmation experiments must be within the 95% confidence interval (α = 0.05), CICE (fixed number of confirmation experiments). For MRR, the overall mean of the population is µ = 0.56. The predicted optimum value of MRR is calculated as: mMRR ¼ ðmA5 þ mB3 þ mC1 þ mD3Þ ð3mÞ ¼ 1:52 For calculation of CICE, the following equation [20] has been used: CICE sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   ffi 1 1 ¼ Fa ð1; fe Þ þ Ve neff R ð1Þ Int J Adv Manuf Technol (2010) 48:103–119 Fig. 6 Contributions of significant parameters to material removal rate (S/N data and raw data) 113 Percent contribution in variation of MRR (Raw data) Error 5% Percent contribution in the variation of MRR (S/N data) Error 4% A 14% A 14% B 21% D 43% C 12% C 17% Fa ð1; fe Þ Ve Ve neff N neff R B 22% D 48% the F-ratio at a confidence level of (1-α) against DOF1 and error DOF fe (for MRR, fe = 43, so Fa is 4.05) error variance for MRR 0.017 (Table 7) N ¼ ð2Þ 1 þ Total DF involved in estimation of mean total number of experiments 54=ð1 þ 10Þ ¼ 4:90 sample size for confirmatory experiments=3 Hence, putting all the values in Eq. 1, CICEðMRRÞ ¼ 0:18 The 95% confidence interval for µMRR is CICEðMRRÞ ¼ 1:34 < mMRR < 1:70 From the confirmation experiments, the average value of MRR obtained is 1.69, which is well contained by the confidence interval. Hence, the validity of experimental design is conformed, and the optimized process setting can be used as a macro-model (Table 8) for further development of the micro-model for prediction of MRR under varying conditions. values of MRR over a wide range of input parameters. As per Taguchi design, MRR in USM is dependent on type of tool/abrasive, ultrasonic power, and slurry grit size. The following assumptions have been made while developing the mathematical model for the above situation: 1. The frequency of ultrasonic vibration is fixed throughout the experimentation and it is of the order of 21 kHz± 200 Hz. 2. The amplitude of vibration is constant throughout the experimentation and is of the order of 25.3–25.8µm. The USM set up contains a provision for maintaining the amplitude of vibration constant under variable excitation power conditions. 3. The static feed force is maintained constant at a value of 1.63 kg. 4. The factors that turned out to be insignificant from Taguchi design have been omitted from the micro-modeling. The Buckingham’s pi theorem proves that, in a physical problem including “n” quantities in which there are “m” dimensions, the quantities can be arranged into “n–m” independent dimensionless parameters. In this approach, dimensional analysis is used for developing the relations. Now, MRR “Z” depends upon four input parameters: ultrasonic power, tool hardness factor, slurry hardness factor, and grit size of slurry. The slurry hardness factor indicates the Knoop hardness of the slurry used. Again, by selecting: 7 Micro-model for prediction of MRR M (mass) L (length) T (time) The macro-model developed through Taguchi design has further been used to form a micro-model to predict the as basic dimensions, the dimensions of the foregoing quantities would then be: Table 8 Macro-model for material removal rate Optimization of MRR Tool material Abrasive material Grit size Power rating Cemented carbide Boron carbide 220 (coarse) 400 W (80%) 1. 2. 3. 4. 5. The MRR “Z” (mm3/min); L3 T−1 Power rating “P” (watt); M L2 T−3 Tool hardness factor “H” (GPa); M L−1 T−2 Slurry hardness factor “μs” (GPa); M L−1 T−2 Slurry grit size “ρ” (mm); L 114 Int J Adv Manuf Technol (2010) 48:103–119 Now, Thus, Z ¼ f ðP; H; ms ; rÞ ð3Þ In this case, n = 5 and m = 3; hence, we can have (n–m = 2) π1 and π2 two dimensionless groups. Taking Z and H as the quantities (randomly) which will go in π1 and π2 respectively, we obtain: p 2 ¼ H ðms Þ 1 ðPÞ0 ðrÞ0 ð9Þ p 2 ¼ H=ms The functional relationship is of the form, p 1 ¼ f ðp 2 Þ ð10Þ Hence, a1 b1 g1 p 1 ¼ Z ðms Þ ðPÞ ðrÞ ð4Þ p 2 ¼ H ðms Þa2 ðPÞb2 ðrÞg2 ð5Þ Zms =P ¼ f ðH=ms Þ Substituting the dimensions of each quantity and equating to zero, the ultimate exponent of each basic dimension is achieved, since the “πis” are dimensionless groups. Solving for π1, we get, p 1 ¼ L3 T 1 Here,  M L 1T   2 a1 ML2 T  3 b1 ðLÞg1 ð6Þ 1 2a1 3b1 ¼ 0 Z:ms =P ¼ Hf ð1=ms Þ   Z ¼ C P:H=m2s ð12Þ where C is a constant of proportionality. To calculate “C”, experiments were performed by keeping P=m2s unchanged, varying H (different tool materials) to find out Z. To know the impact of H on MRR, experiments were performed by “changing one factor at a time” approach thus with changing only the tool material and keeping all other factors constant. The actual experimental data has been presented in Table 9. The data collected has been further used for finding the best fitting curve as depicted in Fig. 7. Thus, the regression equation for MRR in this case is a 1 þ b1 ¼ 0 On solving, a1 ¼ 1; b1 ¼ It has been found experimentally that Z directly goes with H [15, 21]. Hence, 7.1 Case I (400 W power rating, alumina slurry, and 220 grit size) a1 þ 2b1 þ g 1 ¼ 0 3 ð11Þ 1; g 1 ¼ 0 Hence, p 1 ¼ Z ðms ÞðPÞ 1 ðrÞ0 ð7Þ  Z ¼ 2:807 3:681 H þ 1:496 H 2  0:07040 H 3 :P=m2s ð13Þ p 1 ¼ Zms =P Similarly, we get p2 ¼ M L 1 T 2  M L 1T   2 a2 1 þ a2 þ b2 ¼ 0 a2 þ 2b2 þ g 2 ¼ 0 1 2 2a2  3 b2 ðLÞg2 7.2 Case II (400 W power rating, silicon carbide slurry, and 220 grit size) 3b2 ¼ 0 Solving, we get, a2 ¼ ML2 T Similarly, the experimentation was performed with silicon carbide slurry and boron carbide slurry using all the tool materials used in this investigation, keeping the power rating (400 W) and grit size (220) unchanged. The best fitted curves for these two cases are given below (Figs. 8 and 9): 1; b2 ¼ 0; g 2 ¼ 0 The regression equation for MRR is   Z ¼ 8:215 10:91 H þ 4:503 H 2 0:2125 H 3 :P=m2s ð14Þ Int J Adv Manuf Technol (2010) 48:103–119 Table 9 Effect of tool hardness factor on material removal rate 115 Abrasive type Tool material Alumina High carbon steel High speed steel Titanium Titanium alloy Cemented carbide High carbon steel High speed steel Titanium Titanium alloy Cemented carbide High carbon steel High speed steel Titanium Titanium alloy Cemented carbide Boron carbide Silicon carbide Power rating=400 W, grit size=220 Mean MRR (mm3/min) 1.9 1.68 1.15 1.36 18.5 1.9 1.68 1.15 1.36 18.5 1.9 1.68 1.15 1.36 18.5 0.85 0.70 0.57 0.38 1.02 1.55 1.33 1.20 0.86 1.67 1.42 1.20 0.92 0.60 1.54 Best fitting curve vs. experimental results 1.6 Mean MRR (cubic mm/min) Fig. 7 Material removal rate vs tool hardness factor (P=400 W, alumina slurry, 220 grit size) Tool hardness (GPa) S = 0.11 R2 = 0.95 1.4 1.2 1- H.C.S 2- H.S.S 3- Ti 4- Ti alloy 5- WC 1 0.8 0.6 0.4 0.2 0 0 1 2 3 4 5 6 Tool Mean MRR (experimental data) Predicted value from model Experimental conditions: Abrasive used: Alumina, Grit Size: 220, Power Input: 80% (400 W), Work material: Titanium Best fitting curve vs. experimental results 2.5 Mean MRR (cubic mm/min) Fig. 8 Material removal rate vs tool hardness factor (P=400 W, silica slurry, 220 grit size) S = 0.38 R2 = 0.92 2 1- H.C.S 2- H.S.S 3- Ti 4- Ti alloy 5- WC 1.5 1 0.5 0 0 1 2 3 4 5 6 Tool Mean MRR (experimental data) Predicted value from model Experimental conditions: Abrasive used: Silicon Carbide, Grit Size: 220, Power Input: 80% (400 W), Work material: Titanium 116 Int J Adv Manuf Technol (2010) 48:103–119 Best fitting curve vs. experimental results 2.5 Mean MRR (cubic mm/min) Fig. 9 Material removal rate vs tool hardness factor (P=400 W, boron carbide slurry, 220 grit size) S = 0.38 R2 = 0.94 2 1- H.C.S 2- H.S.S 3- Ti 4- Ti alloy 5- WC µs= 27 GPa 1.5 1 0.5 0 0 1 2 3 4 5 6 Tool Mean MRR (experimental data) Predicted value from model Experimental conditions: Abrasive used: Boron Carbide, Grit Size: 220, Power Input: 80% (400 W), Work material: Titanium 7.3 Case III (400 W power rating, boron carbide slurry, and 220 grit size) The regression equation for MRR is  Z ¼ 11:30 14:10 H þ 5:614 H 2  0:2636 H 3 :P=m2s ð15Þ be further enhanced for developing mathematical model in terms of other input parameters such as static load, amplitude of vibration, and frequency of vibration using optimum input parametric settings based upon macro-model. 8 Microstructure analysis The results of macro-model are based upon the concept of robust design; Taguchi analysis highlights that MRR is affected by ultrasonic power rating; tool hardness factor, slurry grit size, and optimized results for the said case comes up with the use of cemented carbide tool at 400 W of ultrasonic power and boron carbide slurry with 220 grit size. The three cases described here express MRR in machining of pure titanium at a specific power rating for particular slurry type by varying hardness of the tool, i.e., by selecting different tool materials. The same methodology can The machined samples were etched with Kroll’s reagent (2% HF, 10% HNO3, and 88% distilled water), and the microstructure was then studied using scanning electron microscope at a magnification of ×1,500. The microstructures obtained have been shown in Figs. 10, 11, 12, 13, 14, 15, 16, and 17. In mechanical shaping processes for brittle materials such as USM, material has been found to be removed by the propagation and intersection of cracks [4, 16, 18]. Fig. 10 Microstructure of titanium (experiment number 1) Fig. 11 Microstructure of titanium (experiment number 2) Int J Adv Manuf Technol (2010) 48:103–119 117 Fig. 12 Microstructure of titanium (experiment number 3) Fig. 15 Microstructure of titanium (experiment number 6) Fig. 13 Microstructure of titanium (experiment number 4) Fig. 14 Microstructure of titanium (experiment number 5) Fig. 16 Microstructure of titanium (experiment number 8) Fig. 17 Microstructure of titanium (experiment number 13) 118 While the cutting of brittle materials is performed, in general, by brittle fracture, the chip can be removed plastically at an extremely small depth of cut [11, 19, 21]. In other words, the mechanism of material removal may change from brittle fracture to plastic deformation at extremely small MRRs while machining with USM. From the microstructures of the machined samples of titanium (Figs. 10, 11, 12, 13, 14, 15, 16, and 17), the mode of material removal could be easily established. Further, the way the fracture propagates through the material could be related to the rate of energy input (work surface) during machining which, in turn, depends upon the process conditions, i.e., the input parameter settings in that situation. Consequently, an attempt was made to describe the mechanism of material removal in USM of titanium in terms of the process conditions. It was observed that the process settings that involve higher rate of energy input to the work surface (experiment number 5 and 13) eventually lead to purely cleavage type of fracture, where the material is removed by propagation and intersection of the median and lateral cracks. This could be very well recognized from the sharp edges and the elongated projected regions in the microstructures (Figs. 14 and 17). The process conditions that involve a moderate level of energy input to the work surface during machining lead to realization of a mixed mode of material removal where the brittle fracture of the work surface is preceded by considerable plastic deformation and work hardening. Depending on the level of energy input (as the term “moderate” is used for a considerable range of energy), the dominance of one or the other of the two possible modes could be established. For experimental trials 2 and 8 (Figs. 11 and 16), the dominance of brittle fracture or cleavage type of fracture can be easily recognized. For experimental trials 3 and 4, the dominance of ductile failure has been evidenced, where a large number of equiaxed round dimples could be observed (Figs. 12 and 13). Figures 10 and 15 (experiments 1 and 6) indicate the presence of a network of large number of spherical dimples or micro-cavities with uniform shape and even distribution, which could be related to the sheer ductile failure of the machined surface. Moreover, the fractured surface shows white and dark contrast in which the brighter contrast is the projected portion of the fractured surface which is comparatively larger than that observed in case of high energy input conditions. This indicates ductile type of failure, and slightly longer duration was required to fracture the surface. From the microstructure analysis, no evidence of microcracking or surface disintegrity could be observed. Hence, it can be presumed that USM does not produce any surface damage to the machined titanium component, which can be very critical for enhancement of the service life of the components. Int J Adv Manuf Technol (2010) 48:103–119 9 Conclusions This research is aimed at exploring the use of USM for cost-effective machining of titanium and establishing optimized process settings for MRR through Taguchi’s technique for designing the experiments. The following conclusions have been drawn from this research: 1. Optimum MRR in USM of titanium can be achieved by using a tool material of higher hardness (cemented carbide) along with a higher power rating (400 W), coarse grit size (220), and a hard abrasive (boron carbide) material. 2. With regards to the average response, power rating factor has emerged as most significant factor with a percent contribution of 42%, followed by abrasive type (21.3%) and slurry grit size (17.2%). Tool material factor can be termed as the least significant for MRR with a percent contribution of 13.7%. 3. USM is a very random process. Minor fluctuations in the process variables such as slurry concentration can cause significant alteration in the results; hence, it is very important to maintain the fixed parameters as constant with the highest possible accuracy. 4. The outcome of the macro-model has been used for further development of a micro-model for prediction of MRR over a wide range of input parameters. Buckingham’s π-theorem has been used for constructing the micro-model for prediction of MRR in terms of tool hardness, power rating of the ultrasonic machine, and slurry hardness factor. The same methodology can be extended for development of mathematical model under different conditions of input parameters. 5. The material removal in USM of titanium could be directly related to the energy input rate for the particular process settings used for the machining. A higher level of input energy rate promotes the brittle fracture or cleavage of the work surface (Figs. 14 and 17). For extremely small values of energy input, purely ductile failure mode was observed (Figs. 10 and 15). It is possible to obtain a mixed mode of removal by manipulating the process settings. Acknowledgements The authors will like to thank Dr. V.K. Jain (Professor, Mechanical Engineering Department, Indian Institute of Technology, Kanpur) and Dr. Simon Barnard (Consultant, BSI International, UK) for providing technical guidance for the experimental work. The authors are also thankful to Mr. Trilok Singh and Mr. Sukhdev Chand (Lab Superintendents, MED, Thapar University, Patiala, India) for providing laboratory facilities. The authors are thankful to Mr. Charlie White (Sonic-Mill, Albuquerque, USA) for providing the necessary materials needed for this research work. Int J Adv Manuf Technol (2010) 48:103–119 References 1. ASM Int (1988) Titanium: a technical guide. ASM Int, Materials Park, pp 75–85 2. Bagchi TP (1993) Taguchi methods explained: practical steps to robust design. 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