Taguchifuzzy multiresponse optimization in fly cutting process and applying in the actual hobbing process
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.
Keywords
Gear hobbing Optimization Fuzzy Fly cutting Cutting fluid NanofluidBackground
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
The parameters of the hobbing process (from FUTU1)
Tool  Module (mm)  Outside diameter (mm)  Rake angle (°)  Depth of cut (mm)  Feed rate (mm)  Spindle speed (mpm) 

DTRDINAATIN  1.75  60  0  4375  1.27  200–300 
The dimensions of maximum chips produced during hobbing and the cutting condition required to produce the same chips in fly hobbing on the milling machine
Hobbing process  Fly hobbing process on milling machine  

Number of threads of hob  Feed of hob (mm/rev)  Length of chips (mm)  Max thickness of chip (mm)  Depth of cut (mm)  Feed of table (mm/rev) 
1  1.27  12.92  0.108  2.75  0.259 
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
Experimental design based on L18 orthogonal array
Exp. no.  Cutting speed A (mpm)  Nano. size B (nm)  Nano. con. C (%) 

1  38  20  0.1 
2  38  20  0.3 
3  38  20  0.5 
4  38  80  0.1 
5  38  80  0.3 
6  38  80  0.5 
7  38  135  0.1 
8  38  135  0.3 
9  38  135  0.5 
10  50  20  0.1 
11  50  20  0.3 
12  50  20  0.5 
13  50  80  0.1 
14  50  80  0.3 
15  50  80  0.5 
16  50  135  0.1 
17  50  135  0.3 
18  50  135  0.5 
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.
where x_{ i } is the total cutting force and n is the number of experiments.
The fuzzy logic optimization based on the Taguchi methodology
where \( {x}_i^{\ast }(k) \) is the value after normalization for the kth response under ith experiment.
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.

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;
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 and normalized values for input parameters
Exp. no.  The cutting force  Temperature  Surface roughness  

F_{y} (N)  F_{z} (N)  R  S/N (R)  F_{z}/F_{y}  S/N (F_{z}/F_{y})  t  S/N (t)  Ra  S/N(Ra)  
1  277.8  78.3  288.62  − 49.2066  0.282  − 10.9994  32.6  − 30.2644  0.1817  14.8129 
2  232.6  73.6  243.97  − 47.7466  0.316  − 9.99464  29.3  − 29.3374  0.1175  18.59924 
3  190.8  61.7  200.53  − 46.0435  0.323  − 9.80586  24.7  − 27.8539  0.2022  13.88438 
4  282.9  77.3  293.27  − 49.3454  0.273  − 11.2691  32.1  − 30.1301  0.3705  8.624236 
5  255.2  72.1  265.19  − 48.4711  0.283  − 10.9789  27.6  − 28.8182  0.312  10.11691 
6  235.6  70.1  245.81  − 47.8119  0.298  − 10.5291  24.1  − 27.6403  0.5125  5.806123 
7  293.3  82.2  304.60  − 49.6746  0.280  − 11.0488  34.7  − 30.8066  0.5888  4.600644 
8  282.8  80.8  294.12  − 49.3704  0.286  − 10.8814  30.9  − 29.7992  0.4327  7.276262 
9  260.1  74  270.42  − 48.6408  0.285  − 10.9182  27.0  − 28.6273  1.0337  − 0.28789 
10  282.4  75.2  292.24  − 49.3148  0.266  − 11.4929  34.8  − 30.8316  0.1423  16.9359 
11  246.3  72.3  256.69  − 48.1883  0.294  − 10.6465  30.1  − 29.5713  0.0894  20.97325 
12  222  69.1  232.51  − 47.3287  0.311  − 10.1375  25.1  − 27.9935  0.161  15.86348 
13  296.2  78.3  306.37  − 49.7251  0.264  − 11.5565  34.0  − 30.6296  0.3059  10.28841 
14  262.8  74.1  273.05  − 48.7247  0.282  − 10.9961  29.1  − 29.2779  0.25  12.0412 
15  242.9  70.9  253.04  − 48.0636  0.292  − 10.6956  27.7  − 28.8496  0.57  4.882503 
16  295  84.6  306.89  − 49.7397  0.287  − 10.849  36.2  − 31.1742  0.3565  8.958809 
17  283  80.8  294.31  − 49.3761  0.286  − 10.8875  32.3  − 30.1841  0.4319  7.292336 
18  263.5  76.2  274.30  − 48.7644  0.289  − 10.7765  28.2  − 29.0050  0.9397  0.540215 
Fuzzy rule table
TT  X (R)  X (F_{z}/F_{y})  X (T)  X (Ra)  FRTS 

1  S  S  S  S  VVS 
2  S  S  S  M  VS 
3  S  S  S  H  VS 
4  S  S  M  S  VS 
5  S  S  M  M  VS 
6  S  S  M  H  S 
7  S  S  H  S  S 
8  S  S  H  M  S 
9  S  S  H  H  S 
10  S  M  S  S  S 
11  S  M  S  M  S 
12  S  M  S  H  S 
13  S  M  M  S  S 
14  S  M  M  M  S 
15  S  M  M  H  S 
16  S  M  H  S  M 
17  S  M  H  M  M 
18  S  M  H  H  M 
19  S  H  S  S  S 
20  S  H  S  M  S 
21  S  H  S  H  S 
22  S  H  M  S  M 
23  S  H  M  M  M 
24  S  H  M  H  M 
25  S  H  H  S  M 
26  S  H  H  M  M 
27  S  H  H  H  M 
28  M  S  S  S  S 
29  M  S  S  M  S 
30  M  S  S  H  S 
31  M  S  M  S  S 
32  M  S  M  M  M 
33  M  S  M  H  M 
34  M  S  H  S  M 
35  M  S  H  M  M 
36  M  S  H  H  M 
37  M  M  S  S  M 
38  M  M  S  M  M 
39  M  M  S  H  M 
40  M  M  M  S  M 
41  M  M  M  M  M 
42  M  M  M  H  M 
43  M  M  H  S  M 
44  M  M  H  M  M 
45  M  M  H  H  M 
46  M  H  S  S  H 
47  M  H  S  M  H 
48  M  H  S  H  H 
49  M  H  M  S  H 
50  M  H  M  M  H 
51  M  H  M  H  H 
52  M  H  H  S  VH 
53  M  H  H  M  VH 
54  M  H  H  H  VH 
55  H  S  S  S  M 
56  H  S  S  M  M 
57  H  S  S  H  M 
58  H  S  M  S  M 
59  H  S  M  M  M 
60  H  S  M  H  H 
61  H  S  H  S  H 
62  H  S  H  M  H 
63  H  S  H  H  H 
64  H  M  S  S  H 
65  H  M  S  M  H 
66  H  M  S  H  H 
67  H  M  M  S  H 
68  H  M  M  M  H 
69  H  M  M  H  H 
70  H  M  H  S  VH 
71  H  M  H  M  VH 
72  H  M  H  H  VH 
73  H  H  S  S  VH 
74  H  H  S  M  VH 
75  H  H  S  H  VH 
76  H  H  M  S  VH 
77  H  H  M  M  VH 
78  H  H  M  H  VH 
79  H  H  H  S  VH 
80  H  H  H  M  VH 
81  H  H  H  H  VVH 
The fuzzy value FRTS
Exp. no.  V (mpm)  Size (nm)  Nano con. (%)  x(R)  x(F_{z}/F_{ y })  x(T)  x(Ra)  FRTS  Ranks 

1  38  20  0.1  0.144  0.318  0.257  0.710  0.348  11 
2  38  20  0.3  0.539  0.892  0.520  0.888  0.657  3 
3  38  20  0.5  1.000  1.000  0.940  0.667  0.837  1 
4  38  80  0.1  0.107  0.164  0.295  0.419  0.285  13 
5  38  80  0.3  0.343  0.330  0.667  0.489  0.418  6 
6  38  80  0.5  0.522  0.587  1.000  0.287  0.5  4 
7  38  135  0.1  0.018  0.290  0.104  0.230  0.269  14 
8  38  135  0.3  0.100  0.386  0.389  0.356  0.365  10 
9  38  135  0.5  0.297  0.365  0.721  0.000  0.406  7 
10  50  20  0.1  0.115  0.036  0.097  0.810  0.224  15 
11  50  20  0.3  0.420  0.520  0.454  1.000  0.5  4 
12  50  20  0.5  0.652  0.811  0.900  0.760  0.714  2 
13  50  80  0.1  0.004  0.000  0.154  0.497  0.177  16 
14  50  80  0.3  0.275  0.320  0.537  0.580  0.384  8 
15  50  80  0.5  0.453  0.492  0.658  0.243  0.5  4 
16  50  135  0.1  0.000  0.404  0.000  0.435  0.336  12 
17  50  135  0.3  0.098  0.382  0.280  0.357  0.366  9 
18  50  135  0.5  0.264  0.446  0.614  0.039  0.435  5 
The analysis of variance (ANOVA)
Analysis of variance (ANOVA) for the FRTS
Source  DF  Seq SS  Adj SS  Adj MS  F  P 

Cutting speed (A)  1  0.0112  0.0112  0.0112  12.13  0.025 
Nanoparticle size (B)  2  0.125357  0.125357  0.062679  67.87  0.001 
Nanoparticle concentration (C)  2  0.259467  0.259467  0.129734  140.47  0.000 
A × B  2  0.020931  0.020931  0.010466  11.33  0.023 
A × C  2  0.000827  0.000827  0.000413  0.45  0.668 
B × C  4  0.071170  0.071170  0.017792  19.27  0.007 
Error  4  0.003694  0.003694  0.000924  –  – 
Total  17  0.492647  –  –  –  – 
Response table for FRTS
Level  Cutting speed (A)  Nanoparticle size (B)  Nanoparticle con. (C) 

1  0.4539  0.5467  0.2732 
2  0.4040  0.3773  0.4483 
3  –  0.3628  0.5653 
Delta  0.0499  0.1838  0.2922 
Rank  3  2  1 
Applying the optimal conditions on the actual hobbing process
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.
Notes
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.
Authors’ 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.
Competing interests
The authors declare that they have no competing interests.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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