Material removal rate and electrode wear study on the EDM of silicon carbide

Journal of Materials Processing Technology 164–165 (2005) 889–896<br /> <br /> Material removal rate and electrode wear study on<br /> the EDM of silicon carbide<br /> C.J. Luis, I. Puertas ∗ , G. Villa<br /> Mechanical, Energetics and Materials Engineering Department, Manufacturing Engineering Section, Public University of Navarre,<br /> Campus de Arrosadia, Pamplona, Navarre 31006, Spain<br /> <br /> Abstract<br /> In this work, a material removal rate (MRR) and electrode wear (EW) study on the die-sinking electrical discharge machining (EDM) of<br /> siliconised or reaction-bonded silicon carbide (SiSiC) has been carried out. The selection of the above-mentioned conductive ceramic was<br /> made taking into account its wide range of applications in the industrial field: high-temperature gas turbines, bearings, seals and lining of<br /> industrial furnaces. This study was made only for the finish stages and has been carried out on the influence of five design factors: intensity<br /> supplied by the generator of the EDM machine (I), pulse time (ti ), duty cycle (η), open-circuit voltage (U) and dielectric flushing pressure<br /> (P), over the two previously mentioned response variables. This has been done by means of the technique of design of experiments (DOE),<br /> which allows us to carry out the above-mentioned analysis performing a relatively small number of experiments. In this case, a 25−1 fractional<br /> factorial design, whose resolution is V, has been selected considering the number of factors considered in the present study. The resolution<br /> of this fractional design allows us to estimate all the main effects, two-factor interactions and pure quadratic effects of the five design factors<br /> selected to perform this study.<br /> © 2005 Elsevier B.V. All rights reserved.<br /> Keywords: EDM; Manufacturing; Wear; DOE<br /> <br /> 1. Introduction<br /> Electrical discharge machining (EDM) is a non-traditional<br /> manufacturing process based on removing material from a<br /> part by means of a series of repeated electrical discharges<br /> between a tool, called the electrode, and the part being machined in the presence of a dielectric fluid. At present, EDM<br /> is a widespread technique used in industry for high-precision<br /> machining of all types of conductive materials such as: metals, metallic alloys, graphite, or even some ceramic materials,<br /> of any hardness [1].<br /> The term, technical ceramic materials or advanced ceramic materials, is a relatively new term, which is applied to a<br /> range of various materials generally obtained from inorganic<br /> primary materials with a high grade of purity. These primary<br /> materials are subjected to typical processes in powder metallurgy technology and subsequently, to high-temperature sintering processes. With these materials, it is possible to obtain<br /> ∗<br /> <br /> Corresponding author. Tel.: +34 948 169 305; fax: +34 948 169 099.<br /> E-mail address: inaki.puerta@unavarra.es (I. Puertas).<br /> <br /> 0924-0136/$ – see front matter © 2005 Elsevier B.V. All rights reserved.<br /> doi:10.1016/j.jmatprotec.2005.02.045<br /> <br /> high-density parts which have excellent technical properties<br /> related to hardness, mechanical resistance, wear, and corrosion [2].<br /> In spite of their exceptional mechanical and chemical<br /> properties, ceramic materials have only achieved a partial<br /> acceptance in the field of industrial applications due to the<br /> difficulties in processing and the high costs associated with<br /> their manufacture. Over the past few years, the advances in<br /> the field of EDM have permitted the application of this technology to the manufacture of conductive ceramic materials.<br /> In line with current knowledge, the main inconvenience when<br /> applying the EDM technology to the field of ceramic materials is the electrical resistivity of these materials, where the<br /> limits are fixed between 100 and 300 cm [2–4].<br /> In this work, the selected ceramic material has been siliconised or reaction-bonded silicon carbide (SiSiC), whose<br /> field of applications is in constant growth. In this way, a material removal rate (MRR) and electrode wear (EW) study<br /> has been carried out on the influence of the following design factors: intensity (I), pulse time (ti ), duty cycle (η),<br /> open-circuit voltage (U) and dielectric flushing pressure (P).<br /> <br /> 890<br /> <br /> C.J. Luis et al. / Journal of Materials Processing Technology 164–165 (2005) 889–896<br /> <br /> This has been performed using the techniques of design<br /> of experiments (DOE) and multiple linear regression analysis. In this case, a 25−1 fractional factorial design with<br /> resolution V has been employed to carry out the present<br /> study.<br /> <br /> 2. Equipment used and conductive ceramic EDMed<br /> In this section, a brief description of the EDM machine<br /> used to perform the experiments and the conductive ceramic<br /> material studied in this work will be given.<br /> 2.1. Die-sinking EDM machine<br /> The equipment used to perform the experiments was a<br /> die-sinking EDM machine of type ONA DATIC D-2030-S<br /> (Fig. 1). Also, a jet flushing system in order to assure the<br /> adequate flushing of the EDM process debris from the gap<br /> zone was employed. The dielectric fluid used for the EDM<br /> machine was a mineral oil (Oel-Held Dielektrikum IME 82)<br /> with a flash point of 82 ◦ C. The electrodes used were made of<br /> electrolytic copper (with a cross-section of 12 mm × 8 mm)<br /> and the polarity was negative.<br /> 2.2. Reaction-bonded or siliconised silicon carbide<br /> F®<br /> <br /> silicon carThe ceramic material used was REFEL<br /> bide. This reaction-bonded silicon carbide (SiSiC) is manufactured by infiltrating silicon into a porous block made of<br /> silicon carbide powder and carbon, which is then submitted<br /> to a firing process at a specific temperature. This produces<br /> <br /> Fig. 1. EDM machine used to carry out the experiments.<br /> <br /> approximately 10% of free silicon, which fills the pores. The<br /> resulting microstructure has a low level of porosity and a<br /> very fine grain, giving a density of 3.1 g/cm3 . The mechanical resistance of the material (2000–3500 MPa to compression and 310 MPa to tension, up to 1350 ◦ C), combined with<br /> a hardness (25–35 GPa, Vickers hardness) which is higher<br /> than that of tungsten carbide (WC), explains its use as an<br /> element in high-temperature gas turbines as well as bearings<br /> and seals. Furthermore, it has a high thermal conductivity<br /> (150–200 W m−1 K−1 , 20 ◦ C) and a low thermal expansion<br /> coefficient (4.3–4.6 × 10−6 K−1 , 20–1000 ◦ C), which provides it with a good resistance to thermal shock. Reactionbonded silicon carbide performs better under chemical corrosion than other ceramic materials, such as tungsten carbide or<br /> alumina (Al2 O3 ). Therefore, it is frequently used as industrial<br /> furnaces lining.<br /> The samples of silicon carbide used in the experiments were ground sheets of the following dimensions:<br /> 50 mm × 50 mm × 5 mm. Moreover, as was mentioned earlier, the electrodes used in this case were made of electrolytic<br /> copper and subjected to a negative polarity as, according to<br /> the bibliography in the EDM field and these authors’ experience [2,5], it is the most stable and recommended way to<br /> carry out the EDM process of silicon carbide.<br /> <br /> 3. Design of the experiments<br /> In the present section, the design factors and response variables selected for this work, as well as the methodology employed for the experimentation, will be described.<br /> 3.1. Design factors selected<br /> There are a large number of factors to consider within<br /> the EDM process, but in this work the level of the generator intensity (I), pulse time (ti ), duty cycle (η), open-circuit<br /> voltage (U) and dielectric flushing pressure (P) have only<br /> been taken into account as design factors. The reason why<br /> these five factors have been selected as design factors is that<br /> they are the most widespread and used amongst EDM researchers.<br /> The intensity (I) depends on the different power levels that<br /> can be supplied by the EDM machine generator. It represents<br /> the maximum value of the discharge current intensity. The<br /> intensity values used in the EDM machine programming are<br /> power levels of the generator, these corresponding with values of the peak intensity (Ip ), which is applied between the<br /> electrode and the part to be EDMed.<br /> Pulse time or on-time (ti ) is the duration of time (in ␮s) the<br /> current is allowed to flow per cycle. On the other hand, duty<br /> cycle (η) is the percentage of pulse time relative to the total<br /> cycle time. This third factor is calculated by dividing pulse<br /> time by the total cycle time (i.e., pulse time plus pause time),<br /> where pause time or off-time (to ) is the duration of time (in<br /> ␮s) between two consecutive sparks.<br /> <br /> C.J. Luis et al. / Journal of Materials Processing Technology 164–165 (2005) 889–896<br /> <br /> Open-circuit voltage (U) is the value of the electric tension<br /> applied between the part to be machined and the electrode just<br /> before the discharge is produced. Finally, the dielectric flushing pressure (P) is the pressure of the dielectric jet removing<br /> the EDM splinter or debris from the gap zone. This pressure<br /> value is measured by a pressure gauge in the EDM machine.<br /> 3.2. Response variables selected<br /> The response variables selected for this study refer to the<br /> speed of the EDM process, i.e., material removal rate (MRR),<br /> and the efficiency of the copper electrode used, i.e., volumetric electrode wear (EW). These response variables are defined<br /> in Eqs. (1) and (2), respectively:<br /> MRR =<br /> EW =<br /> <br /> volume of material removed from part<br /> time of machining<br /> <br /> volume of material removed from electrode<br /> volume of material removed from part<br /> <br /> (1)<br /> (2)<br /> <br /> Although there are some other ways of measuring MRR and<br /> EW [6], in this work we have calculated them by the weight<br /> difference of the sample and the electrode just before and<br /> after being subjected to the EDM process. Moreover, density<br /> values of 3.10 and 8.96 g/cm3 were chosen for silicon carbide<br /> and electrolytic copper, respectively, in order to assess MRR<br /> and EW.<br /> 3.3. Fractional factorial design employed<br /> The design of experiments (DOE) technique is a powerful work tool which allows us to model and analyse the<br /> influence of determined process variables over other specified variables, which are usually known as response variables.<br /> These response variables are unknown functions of the former design variables, which are also known as design factors<br /> [7–9].<br /> Within the design of experiments, there are various types<br /> that can be considered. One of the most widely known ones<br /> is the factorial design; this consists in experimenting with all<br /> the possible combinations of variables and levels. Nevertheless, if the number of design factors is reasonably high, as<br /> in this case, and it is possible to assume that certain highorder interactions are negligible, the information on the main<br /> effects and the low-order interactions may be obtained by<br /> running only a fraction of the complete factorial experiment.<br /> These fractional factorial designs are among the most widely<br /> used types of designs for product and process design and for<br /> process improvement [7].<br /> The design finally chosen was a 25−1 fractional factorial<br /> one with four central points. This design has a resolution of V,<br /> which means that no main effect or two-factor interaction in<br /> this model is aliased with any other main effect or two-factor<br /> interaction. The addition of four central points allows us to<br /> carry out lack-of-fit tests for the first-order models proposed,<br /> where a total of 20 experiments for these first-order designs<br /> <br /> 891<br /> <br /> Table 1<br /> Levels selected for the five design factors of the 25−1 design<br /> Factors<br /> <br /> Levels<br /> −1<br /> <br /> I<br /> ti (␮s)<br /> η<br /> U (V)<br /> P (kPa)<br /> <br /> 0<br /> <br /> +1<br /> <br /> 3<br /> 30<br /> 0.4<br /> −120<br /> 20<br /> <br /> 4<br /> 50<br /> 0.5<br /> −160<br /> 40<br /> <br /> 5<br /> 70<br /> 0.6<br /> −200<br /> 60<br /> <br /> were made. In case the first-order model turned out not to be<br /> adequate for modelling the behaviour of the response variable<br /> to be studied, this was widened by adding 10 star points, thus<br /> giving a central composite design with the star points located<br /> in the centres of the faces. Thus, the case of the secondorder model consisted of a total of 30 experiments, i.e., the<br /> previous 20 of the first-order model plus the new 10 of the star<br /> points.<br /> The low and high levels selected for intensity, pulse time,<br /> duty cycle, open-circuit voltage and dielectric flushing pressure were: 3 and 5, 30 and 70 ␮s, 0.4 and 0.6, −120 and<br /> −200 V and finally, 20 and 60 kPa, respectively. The levels of the intensity factor (3 and 5) are equivalent to 2 and<br /> 6 A, respectively. A summary of the levels selected for the<br /> factors to be studied is shown in Table 1. The previous selection of variation levels was made taking into account that<br /> the authors wanted this study to be focused on the area of<br /> the finish machining stages, owing to the influence that a<br /> good surface quality has on such important properties, in the<br /> case of ceramic materials, such as fatigue and wear resistance<br /> [8,9].<br /> Table 2 shows the design matrix for the second-order models as well as the values obtained in the experiments for the<br /> response variables studied in this work, i.e., MRR and EW.<br /> As can be observed in this table, rows 1–16 correspond to the<br /> fractional factorial design, rows 17–26 correspond to the star<br /> points and finally, the central points are placed in the four<br /> last rows of the design matrix. On the other hand, the design<br /> matrix for the first-order model of MRR and EW would be<br /> obtained simply by eliminating the 10 rows corresponding to<br /> the star points.<br /> The graphs, models and tables that are to be presented<br /> in the following two sections were produced using the DOE<br /> module of the software STATGRAPHICS® plus v. 5.0.<br /> <br /> 4. Results and analysis of MRR<br /> A first-order model was proposed for the response variable MRR, where this was rejected as a result of the values<br /> obtained for the curvature test that can be seen in Table 3.<br /> As in this case the P-value, which is equal to 0.0002, is<br /> lower than 0.05, the null hypothesis that there are no pure<br /> quadratic effects in the model is therefore rejected, accepting<br /> <br /> 892<br /> <br /> C.J. Luis et al. / Journal of Materials Processing Technology 164–165 (2005) 889–896<br /> <br /> Table 2<br /> Design matrix for the second-order models of MRR and EW<br /> I<br /> 1<br /> 2<br /> 3<br /> 4<br /> 5<br /> 6<br /> 7<br /> 8<br /> 9<br /> 10<br /> 11<br /> 12<br /> 13<br /> 14<br /> 15<br /> 16<br /> 17<br /> 18<br /> 19<br /> 20<br /> 21<br /> 22<br /> 23<br /> 24<br /> 25<br /> 26<br /> 27<br /> 28<br /> 29<br /> 30<br /> <br /> ti (␮s)<br /> <br /> η<br /> <br /> U (V)<br /> <br /> P (kPa)<br /> <br /> EW (%)<br /> <br /> MRR (mm3 /min)<br /> <br /> 3<br /> 5<br /> 3<br /> 5<br /> 3<br /> 5<br /> 3<br /> 5<br /> 3<br /> 5<br /> 3<br /> 5<br /> 3<br /> 5<br /> 3<br /> 5<br /> 3<br /> 5<br /> 4<br /> 4<br /> 4<br /> 4<br /> 4<br /> 4<br /> 4<br /> 4<br /> 4<br /> 4<br /> 4<br /> 4<br /> <br /> 30<br /> 30<br /> 70<br /> 70<br /> 30<br /> 30<br /> 70<br /> 70<br /> 30<br /> 30<br /> 70<br /> 70<br /> 30<br /> 30<br /> 70<br /> 70<br /> 50<br /> 50<br /> 30<br /> 70<br /> 50<br /> 50<br /> 50<br /> 50<br /> 50<br /> 50<br /> 50<br /> 50<br /> 50<br /> 50<br /> <br /> 0.4<br /> 0.4<br /> 0.4<br /> 0.4<br /> 0.6<br /> 0.6<br /> 0.6<br /> 0.6<br /> 0.4<br /> 0.4<br /> 0.4<br /> 0.4<br /> 0.6<br /> 0.6<br /> 0.6<br /> 0.6<br /> 0.5<br /> 0.5<br /> 0.5<br /> 0.5<br /> 0.4<br /> 0.6<br /> 0.5<br /> 0.5<br /> 0.5<br /> 0.5<br /> 0.5<br /> 0.5<br /> 0.5<br /> 0.5<br /> <br /> −120<br /> −120<br /> −120<br /> −120<br /> −120<br /> −120<br /> −120<br /> −120<br /> −200<br /> −200<br /> −200<br /> −200<br /> −200<br /> −200<br /> −200<br /> −200<br /> −160<br /> −160<br /> −160<br /> −160<br /> −160<br /> −160<br /> −120<br /> −200<br /> −160<br /> −160<br /> −160<br /> −160<br /> −160<br /> −160<br /> <br /> 60<br /> 20<br /> 20<br /> 60<br /> 20<br /> 60<br /> 60<br /> 20<br /> 20<br /> 60<br /> 60<br /> 20<br /> 60<br /> 20<br /> 20<br /> 60<br /> 40<br /> 40<br /> 40<br /> 40<br /> 40<br /> 40<br /> 40<br /> 40<br /> 20<br /> 60<br /> 40<br /> 40<br /> 40<br /> 40<br /> <br /> 10.29<br /> 7.34<br /> 19.82<br /> 10.01<br /> 11.87<br /> 9.83<br /> 13.55<br /> 12.16<br /> 12.66<br /> 7.48<br /> 16.06<br /> 7.91<br /> 12.84<br /> 11.63<br /> 16.33<br /> 9.29<br /> 13.29<br /> 7.47<br /> 6.61<br /> 6.74<br /> 6.92<br /> 10.50<br /> 10.92<br /> 8.00<br /> 7.24<br /> 6.65<br /> 6.61<br /> 7.06<br /> 7.25<br /> 7.51<br /> <br /> 0.033<br /> 0.104<br /> 0.020<br /> 0.116<br /> 0.049<br /> 0.091<br /> 0.030<br /> 0.136<br /> 0.051<br /> 0.312<br /> 0.030<br /> 0.267<br /> 0.092<br /> 0.344<br /> 0.055<br /> 0.354<br /> 0.032<br /> 0.283<br /> 0.244<br /> 0.177<br /> 0.147<br /> 0.168<br /> 0.087<br /> 0.258<br /> 0.195<br /> 0.201<br /> 0.189<br /> 0.199<br /> 0.199<br /> 0.201<br /> <br /> that there is statistical evidence of curvature in the first-order<br /> model, for a confidence level of 95%. Thus, that the proposed first-order model is suitable for a significance level<br /> α of 0.05 is rejected and so, the second-order model is<br /> selected.<br /> Table 4 shows the ANOVA table for the case of the<br /> second-order model proposed, where now, the total number of degrees of freedom is equal to 29. As can be observed in this table, there are three effects with a P-value<br /> less than 0.05, which means that they are significant for<br /> a confidence level of 95%. These significant effects, arranged in order of importance, are: the main effects of intensity and voltage and finally, the interaction effect between<br /> them.<br /> On the other hand, a value of 0.9794 was obtained for the<br /> R2 -statistic, which signifies that the model explains 97.94%<br /> of the variability of MRR, whereas the adjusted R2 -statistic<br /> (R2 ) is 0.9335.<br /> adj<br /> <br /> The equation of the second-order proposed model is that<br /> shown in Eq. (3):<br /> MRR = −0.985466 + 0.151912 · I − 0.00642768 · ti<br /> +3.08858 · η − 0.000251344 · U−0.00216784 · P<br /> −0.0344143 · I 2 + 0.00035 · I · ti +0.02125 · I · η<br /> +0.00114688 · I · U + 0.0000375 · I · P<br /> +0.0000464643 · ti2 + 0.0020625 · ti · η<br /> −0.00000921875 · ti · U + 0.00001125 · ti · P<br /> −3.44143 · η2 + 0.002375 · η · U<br /> −0.0020625 · η · P − 0.0000121339 · U 2<br /> +0.00000859375 · U · P + 0.0000152143 · P 2<br /> (3)<br /> <br /> Table 3<br /> Analysis of variance table for the curvature test of the first-order model of MRR<br /> Source of variation<br /> <br /> Sum of squares<br /> <br /> Degrees of freedom<br /> <br /> Mean square<br /> <br /> F-ratio<br /> <br /> P-value<br /> <br /> Curvature<br /> Pure error<br /> Total error<br /> <br /> 0.014258<br /> 0.000088<br /> 0.014346<br /> <br /> 1<br /> 3<br /> 4<br /> <br /> 0.014258<br /> 0.000029<br /> <br /> 486.06<br /> <br /> 0.0002<br /> <br /> C.J. Luis et al. / Journal of Materials Processing Technology 164–165 (2005) 889–896<br /> <br /> 893<br /> <br /> Table 4<br /> Analysis of variance table for the second-order model of MRR<br /> Source of variation<br /> <br /> Sum of squares<br /> <br /> Degrees of freedom<br /> <br /> Mean square<br /> <br /> F-ratio<br /> <br /> P-value<br /> <br /> A:I<br /> B:ti<br /> C:η<br /> D:U<br /> E:P<br /> AA<br /> AB<br /> AC<br /> AD<br /> AE<br /> BB<br /> BC<br /> BD<br /> BE<br /> CC<br /> CD<br /> CE<br /> DD<br /> DE<br /> EE<br /> Total error<br /> Total<br /> <br /> 0.144901<br /> 0.001013<br /> 0.003173<br /> 0.066856<br /> 0.000080<br /> 0.002909<br /> 0.000784<br /> 0.000072<br /> 0.033672<br /> 0.000009<br /> 0.000848<br /> 0.000272<br /> 0.000870<br /> 0.000324<br /> 0.002909<br /> 0.001444<br /> 0.000272<br /> 0.000926<br /> 0.000756<br /> 0.000091<br /> 0.005940<br /> 0.287711<br /> <br /> 1<br /> 1<br /> 1<br /> 1<br /> 1<br /> 1<br /> 1<br /> 1<br /> 1<br /> 1<br /> 1<br /> 1<br /> 1<br /> 1<br /> 1<br /> 1<br /> 1<br /> 1<br /> 1<br /> 1<br /> 9<br /> 29<br /> <br /> 0.144901<br /> 0.001013<br /> 0.003173<br /> 0.066856<br /> 0.000080<br /> 0.002909<br /> 0.000784<br /> 0.000072<br /> 0.033672<br /> 0.000009<br /> 0.000848<br /> 0.000272<br /> 0.000870<br /> 0.000324<br /> 0.002909<br /> 0.001444<br /> 0.000272<br /> 0.000926<br /> 0.000756<br /> 0.000091<br /> 0.000660<br /> <br /> 219.53<br /> 1.53<br /> 4.81<br /> 101.29<br /> 0.12<br /> 4.41<br /> 1.19<br /> 0.11<br /> 51.02<br /> 0.01<br /> 1.29<br /> 0.41<br /> 1.32<br /> 0.49<br /> 4.41<br /> 2.19<br /> 0.41<br /> 1.40<br /> 1.15<br /> 0.14<br /> <br /> 0.0000<br /> 0.2468<br /> 0.0560<br /> 0.0000<br /> 0.7354<br /> 0.0652<br /> 0.3041<br /> 0.7483<br /> 0.0001<br /> 0.9096<br /> 0.2862<br /> 0.5367<br /> 0.2805<br /> 0.5012<br /> 0.0652<br /> 0.1732<br /> 0.5367<br /> 0.2666<br /> 0.3123<br /> 0.7190<br /> <br /> where the variable values have been specified according to<br /> their original units. The ANOVA table shown in Table 4 can<br /> be used in order to simplify the models, especially for the<br /> case of polynomial ones. In this way, the simplified model<br /> which presents the highest value for the adjusted R2 -statistic<br /> is that shown in Eq. (4):<br /> MRR = −0.99879 + 0.152933 · I − 0.00529342 · ti<br /> +3.05541 · η − 0.000528938 · U − 0.001375 · P<br /> −0.0330263 · I 2 + 0.00035 · I · ti<br /> +0.00114687 · I · U + 0.0000499342 · ti2<br /> −0.00000921875 · ti · U − 3.30263 · η2<br /> <br /> Fig. 2. Main effects plot for MRR.<br /> <br /> +0.002375 · η · U − 0.0000112664 · U 2<br /> <br /> giving the latter a better flushing of the EDM debris. With<br /> respect to duty cycle, although its influence is not significant,<br /> MRR tends to increase until a maximum peak (near its central<br /> value of 0.5) after which MRR decreases. If pause time (to )<br /> <br /> +0.00000859375 · U · P<br /> <br /> (4)<br /> <br /> where now, the adequacy statistics are 0.9755 (R2 ) and 0.9555<br /> (R2 ). Nevertheless, the first model (with no simplifications)<br /> adj<br /> is to be considered in this study on MRR in order to take into<br /> account the contribution of all the possible effects.<br /> Figs. 2 and 3 show the main effects plot and interaction<br /> plot for material removal rate, respectively. As can be observed in Fig. 2, the most influential factors are intensity and<br /> open-circuit voltage, where the three remaining factors for<br /> a 95% confidence level have no influence on MRR. Moreover, material removal rate greatly increases when these two<br /> factors are increased, where these tendencies are the ones<br /> that one could expect a priori, as more energetic pulses usually lead to a higher material removal and on the other hand,<br /> an increase in the ionisation or breakdown voltage results in<br /> an increase in both the discharge energy and the work gap,<br /> <br /> Fig. 3. Interaction plot for MRR.<br /> <br />