 Original Paper
 Open Access
 Published:
Taguchifuzzy multiresponse optimization in fly cutting process and applying in the actual hobbing process
International Journal of Mechanical and Materials Engineering volume 13, Article number: 6 (2018)
Abstract
Background
Applying nanofluid made by adding alumina nanoparticles to industrial oil may reduce the cutting force, friction, and cutting temperature and, from that, improve the tool life in the hobbing process. However, it is difficult to set up the experiment for the actual gear hobbing process, because measuring the cutting force and temperature in the hobbing process is very complicated and expensive. Therefore, a fly hobbing test on the horizontal milling machine was performed to simulate the actual hobbing process.
Methods
In this research, the fuzzy theory was combined with the Taguchi method in order to optimize multiresponses of the fly hobbing process as the total cutting force, the force ratio F_{z}/F_{y}, the cutting temperature, and the surface roughness.
Results
The optimal condition—A1B1C3 (the cutting speed 38 mpm\, the nanoparticle size 20 nm, and concentration 0.5%)—was determined by analyzing the performance index (FRTS) of the fuzzy model. Furthermore, this condition was applied to the actual hobbing process in the FUTU1 Company and compared with the actual conditions of this company and other conditions using the nanolubricant with 0.3% Al_{2}O_{3}, 20 nm. The results show that it can reduce a maximum 39.3% of the flank wear and 59.4% of the crater wear on the hob when using the optimal conditions.
Conclusions
The study indicates that the optimal condition determined by using TaguchiFuzzy method can be applied in the FUTU1 company with the high efficiency.
Background
The hobbing processes with complex kinematic motions cause the high friction coefficient, great cutting force, and high temperature. Those properties lead to hob wear, the main cause in reducing the quality of the hobbed gear, so using the suitable cutting fluid is very important. In recent years, nanolubricant, mixing the normal lubricant with nanoparticles, gradually became a new trend study for metal cutting enhancement. Especially, the Al_{2}O_{3} nanoparticles have many properties such as heat resistance, spherical shape, and a high specific temperature, consistent with adding to the industrial oils, so it is suitable for the machining process (Sharma et al, 2015). Malkin and Sridharan (2009) indicated that the new cutting fluids mixing the Al_{2}O_{3} powder with water were used to reduce the grinding forces and the cutting temperature and improve the surface roughness. Vasu and Reddy (2011) indicated that the using of the cutting fluids added Al_{2}O_{3} nanoparticles which can decrease the tool wear, temperature, and surface roughness in machining 600 aluminum alloys. And the influences of nanofluids on surface roughness and tool wear in the hobbing process concluded that using nanofluids with Al_{2}O_{3} nanoparticles resulted in decreasing surface roughness values (Ra, Rz) and tool wears in the manufactured spur gears, researched by Khalilpourazary and Meshkat (2014). But, the effect of Al_{2}O_{3} nanoparticle size and concentration that added to the cutting fluids in gear hobbing on the fundamental parameters of the hobbing process has not been published yet.
Further, the experiments in the hobbing process are too expensive as the cost of the hob tools or a gear hobbing machine is very high, and it is very difficult to measure the cutting force and temperature during the machining process. A fly hobbing experiment was designed to simulate the actual hobbing process by many authors as Rech (2006), Umezaki et al. (2012), and Stein et al. (2012). The present paper experimentally investigates applying new nanofluids to reduce the hob wear by reducing the cutting force, friction, and cutting temperature in the fly hobbing process. A fuzzy model based on the Taguchi experiment design has been used to optimize the multiresponses of the fly hobbing process. Using Minitab 16, the signaltonoise (S/N) ratios for different outputs of the fuzzy model (the total cutting force, the force ratio F_{z}/F_{y}, the cutting temperature, and the surface roughness) were calculated by the Taguchi method. Then, the S/N ratios are used to determine a resultant index (the FRTS index) for estimating the fly hobbing process by using fuzzy logic theory. These FRTS values were used for multiresponse optimization and gave the optimum parameter level for the fly hobbing process. Furthermore, the optimum parameters were applied for the actual hobbing process and compared with the initial parameters.
Methods
Experimental setup
A fly hobbing test was performed on milling machining with a single tool coated with the TiN film and the same profile as a hob tooth used in a gear manufacture line at the Machinery Spare Parts No.1 Joint Stock (FUTU1) Company (see Fig. 1). The cutting conditions of the fly cutting process such as cutting depth and feed rate are set as becoming the same conditions with the hob tooth carrying the biggest load on the real hobbing process used in FUTU1, shown in Table 1.
Figure 2a shows the shape of chips produced by the tips of hob teeth while Fig. 2b shows the state of cutting in slot milling. The maximum chip thickness (s) and chip length (L) are calculated from the characteristics of the hobbing process by using equations by Hoffmeister 1970. The fly cutting process is performed with the cutting depth h and feed f′ to give chips the same size as those produced by a hob tooth. The cutting depth h and feed f′ can be calculated by the formals h = r.(1 − cosθ); f′ = S/sinθ, and θ = L/r. So, the characteristics of the fly hobbing process are calculated and also showed in Table 2.
The workpiece made of chromium molybdenum steel (SCM420) was fixed on a KISTLER dynamometer. The KISTLER dynamometer mounted on the worktable of the milling machine allowed three dynamic forces to be measured. The total cutting force R is calculated from two measured forces F_{y} and F_{z}, as Fig. 3. Moreover, San Juan et al. (2010) found the formal calculation for the friction coefficient based on the thickness chip achieves its maximum value:
where: μ is the friction coefficient value and θ is the angle calculated based on the thickness chip achieving its maximum value as Fig. 2b.
According to Eq. (1), the friction coefficient can be represented by the ration force F_{z}/F_{y}; the friction coefficient value decreases when the ratio force F_{Z}/F_{y} increases. So, the ratio force F_{Z}/F_{y} was one of the output parameters of the analysis experiment.
The thermocouple type k was inserted into the workpiece in order to determine the temperature of the workpiece by using the thermometer 801E HUATO, shown in Fig. 1. The ISO VG46 industrial oil was popularly used for the gearcutting processes in the FUTU1 Company due to its economic characteristics. The Al_{2}O_{3} nanoparticles made by the US Research Nanomaterials have a high sintering temperature, heat resistance, and coefficient of heat transfer and spherical structure. According to Khalilpourazary, nanopowders were mixed with the industrial oils following the weight ratio of 0.1% ÷ 0.5% in order to produce the nanolubricant. To compare and evaluate the coolinglubrication effectiveness of the nanofluid, Al_{2}O_{3} nanoparticles with the size of 20, 80, and 135 nm, and the concentration of 0.1, 0.3, and 0.5% were selected according to the economical requirement.
Design of Taguchi experiments
The Taguchi design was chosen to research the effects of some factors on the total cutting force, the force ratio F_{z}/F_{y}, the cutting temperature, and the surface roughness in the fly hobbing process. Table 3 shows the L18 orthogonal array chosen from Taguchi’s standardorthogonalarray table. The Taguchi method popularly uses the S/N ratio to consider the influence of the survey parameters on the output parameters. The greater the value of the S/N ratio, the less the impact of the noise parameters. The S/N ratio is determined as follows (Roy, 1990):
where MSD is the mean square deviation for output parameters. The MSD values can be determined by three types of the S/N ratio characteristics: nominal the better, smaller the better, and greater the better. According to Eq. (1), the friction coefficient value decreases when the ratio force F_{Z}/F_{y} increases. Thus, to reduce the friction coefficient, the greater the better quality characteristic for the ratio force F_{Z}/F_{y} must be taken. With the total force, temperature and surface roughness, the smaller the better quality parameters were chosen to calculate the S/N ratio.
The MSD for the greater the better quality characteristic can be calculated by (Montgomery, 2004):
The MSD for the smaller the better quality characteristic can be calculated by (Montgomery, 2004):
where x_{ i } is the total cutting force and n is the number of experiments.
The fuzzy logic optimization based on the Taguchi methodology
The theory of fuzzy logic is the mathematical model, suitable to solve uncertain and vague information. So, the fuzzy model can be used to optimize multiobjects by converting the S/N ratios of the Taguchi experiment into a single index. However, the S/N ratio values are calculated for the quality properties with different units by using the Taguchi model and converted to the nonunit values. And, “the greater the better” and “the smaller the better” categories are chosen to transform the S/N ratio values into a range between 0 and 1, while 0 means the worst performance and 1 the best. The normalized value for the smaller the better category can be determined by:
The normalized value for the greater the better category can be calculated by:
where \( {x}_i^{\ast }(k) \) is the value after normalization for the kth response under ith experiment.
A fuzzy model was set up for the normalized values for the S/N ratios of the Taguchi experiment, shown in Fig. 4.
The fuzzy model consists of a fuzzifier, an inference engine, the membership functions, the fuzzy rules, and defuzzifier (Klir & Yuan, 2005). In the study, the fuzzifier uses membership functions to fuzzily the normalized values of the S/N ratios, and the inference system completes a fuzzy based on fuzzy rules to create the fuzzy index. The fuzzy rules are generated from the group IF&THEN rules of the parameter inputs.
The fuzzy rules can be shown as:

Rule i: If x_{1} is A_{i1}; x_{2} is A_{i2}; x_{3} is A_{i3}...; and x_{ j } is A_{ ij } then y_{ i } is C_{ i };

i = 1; 2; ... ; N;
where N is the total number of fuzzy rules, x_{ j } (j = 1,2,….s) are the normalized values, y_{i} are the fuzzy values, and A_{ij} and C_{i} are fuzzy sets defined by membership functions μ_{ Aij }(x_{ j }) and μ_{ Ci }(y_{ j }), respectively. The Mamdani implication method is chosen to perform for the inference of a set of different rules; the collected output for the N rules is
And then, the defuzzifier converts the fuzzy outputs into the absolute values. The defuzzification method is used to find nonfuzzy value y_{0} (in this paper, the nonfuzzy value is FRTS): \( {y}_{\mathrm{o}}=\frac{\sum {y}_i.{\mu}_{C_i}\left({y}_i\right)}{\sum {\mu}_{C_i}\left({y}_{i.}\right)} \)
Results and discussion
Multiobjective optimization
The S/N ratio is used to determine the optimal parameter settings. The values S/N for the total cutting forces, the ratio forces F_{z}/F_{y}, the cutting temperatures, and the surface roughness were calculated by Minitab 16, shown in Table 4. The normalized input parameters were calculated by the formulas (5) and (6), shown in Table 4. In this study, the fuzzy model has been designed by MATLAB 9, in order to optimize multiresponses for the fly hobbing process, illustrated in Fig. 5. There are three fuzzy sets for variables of input parameters: small (S), medium (M) and high (H). The membership functions of the output variable are illustrated in Fig. 6. With four inputs and their three fuzzy sets, there are 34 (81) fuzzy rules used for this model. And there are seven fuzzy sets for variables of FRTS: very very small (VVS), very small (VS), small (S), medium (M), high (H), very high (VH), and very very high (VVH). The fuzzy rules are determined and shown in Table 4. The final FRTS output values were calculated by the defuzzification method applying the fuzzy rules in Table 5 with the Mamdani inference of MATLAB 9 software and shown in Fig. 7. The maximum value of FRTS has the highest ranking and the minimum value of FRTS has the lowest ranking as also shown in Table 6. The maximum average FRTS for minimum total cutting force, maximum ratio force F_{z}/F_{y}, minimum cutting temperature, and minimum surface roughness are obtained at a level 1 (38 mpm) of cutting speed, level 1 (20 nm) of nanoparticle size, and level 3 (0.5%) of nanoparticle concentration is A1B1C3.
The analysis of variance (ANOVA)
The ANOVA analysis results with 96.8% confidence intervals were used to determine the impact of the coefficient on the multiple responses (FRTS) and shown in Table 7. The values of critical F ratio were determined and shown in Table 7. The result indicates that control parameters B (nanoparticle size) and C (nanoparticle concentration) are the greatest effect parameters to the FRTS values (Table 8).
Applying the optimal conditions on the actual hobbing process
The flank wear of hob with optimal conditions and normal conditions were measured by the Zeiss optical microscope after the 500th gears were machined, shown in Fig. 8. Figure 8a shows the flank wear of the hob under the normal conditions using the normal oils (177.84 μm), and the result shows that the TiN coating was cracked and stripped; the great mechanism wears of the HSS material were detected. Figure 8b shows the flank wear of the hob under the optimal conditions using the nanolubricants (107.98 μm). This result indicated that the width of flank wear using the optimal conditions using nanofluids is smaller than that using the normal condition of the FUTU 1 Company. It clearly reveals that the width of flank wear reduces about 39.3% under the optimal condition with the nanolubricant compared to the normal conditions.
After 500 gears were machined, the crater wear of the rake surface of hob was taken by the Zeiss optical microscope at three positions on the rake face (right, center, and left), shown in Figs. 9 and 10. The result revealed that a portion of the TiN coating is removed from the rake face. Figure 9 shows the crater wear of hob (right 154.72 μm, center 163.22 μm, and left 158.98 μm position on rake face) after machining 500 gears with the normal conditions using a normal lubricant (Fig. 10) and the crater wear on hob (right 66.28 μm, center 63.38 μm, and left53.88 μm position on rake face) after machining 500 gears with the optimal conditions using the nanolubricant. The result indicated that the width of the crater wear area under the nanolubricant is clearly smaller than that under the normal lubricant. Hence, some dents can be found on the rake surface under normal oils, while nothing on the rake face under nano oils.
Conclusions
A single fuzzy multiresponse performance index (FRTS) was determined by using a fuzzy logic model based on the Taguchi methods to optimize multiple responses in the fly hobbing process. The research results show that the fly hobbing test can be used to study the gear hobbing process before applying in the actual hobbing process. The results also indicate that the nanoparticle concentrations and the nanoparticle size are the greatest effect factors to fuzzy multiresponse performance index (FRTS) by using the fuzzy logic model based on the Taguchi method with the fly hobbing process. The optimum parameter values for different control parameters have been suggested as nanoparticle concentration 0.5%, nanoparticle size 20 nm, and cutting speed 38 nm. Applying the optimal conditions in the actual hobbing process was investigated in the FUTU 1 Company and reduced 39.3% the flank wear and 59.4% the width of crater wear. This result initially indicated the efficiency of using nanoparticles in the gear hobbing process with the actual conditions of the FUTU1 Company in Vietnam.
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Acknowledgements
The authors acknowledge the device support under Thai Nguyen University of Technology, Hanoi University of Science and Technology, and Machinery Spare Parts No.1 Joint Stock Company (FUTU1), Vietnam.
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Contributions
NT and HV set up the experiment model and performed the design of the Taguchi experiment. HS used MATLAB software to set up the fuzzy logic optimization model. NT, HV, and HS participated in the analysis and discussion of results. All authors read and approved the final manuscript.
Corresponding author
Correspondence to Minh Tuan Ngo.
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Keywords
 Gear hobbing
 Optimization
 Fuzzy
 Fly cutting
 Cutting fluid
 Nanofluid