- Email: [email protected]
Cutting force predictive modelling of hard turning operation using fuzzy logic
Materials Today: Proceedings xxx (xxxx) xxx
Contents lists available at ScienceDirect
Materials Today: Proceedings journal homepage: www.elsevier.com/locate/matpr
Cutting force predictive modelling of hard turning operation using fuzzy logic Vikas Sharma a,b, Pawan Kumar b,⇑, Joy Prakash Misra b a b
Department of Mechanical, GLA University Mathura, 281406, India Department of Mechanical Engineering, NIT Kurukshetra, 136119, India
a r t i c l e
i n f o
Article history: Received 15 November 2019 Received in revised form 30 December 2019 Accepted 1 January 2020 Available online xxxx Keywords: Cutting force Fuzzy logic Turning Modelling Regression ANOVA
a b s t r a c t In this experimental study hard turning was performed under wet cutting environment. Purpose of this study was to predict and analyze the cutting force so induced during hard turning operation. Cutting speed, feed and depth of cut were taken as the controllable variables and their effect on cutting force was analyzed. The experimentation was carried out using L9 orthogonal array. The ANOVA analysis used in this study revealed the contribution of each machining parameter on cutting force. Furthermore, the cutting force models were developed for the prediction purpose using regression and fuzzy logic method. The fuzzy model so developed was found adequate and better than regression model for prediction purpose. The prediction efficiency for both models was determined using RMSE. Ó 2020 Elsevier Ltd. All rights reserved. Selection and of the scientific committee of the 10th International Conference of Materials Processing and Characterization.
1. Introduction Machining performed on workpiece material having hardness more than 45 HRC is known as hard machining. Turning is the most common and widely used machining process used in manufacturing industries to get a machined part from hard materials [1–5]. But as their name suggests they are difficult to machine, but due to their large application area these material are in demand. AISI D3 is one of them, and is widely used in die making industries due to its good hardness, strength and toughness at higher temperature. Other application areas of AISI D3 steel includes: blanking, stamping, cold forming dies and punches for long runs, lamination dies, bending, forming, and seaming rolls, cold trimmer dies or rolls, burnishing dies or rolls, plug gages, drawing dies for bars or wire, slitting cutters, lathe centers subject to severe wear [6]. Therefore there comes a need to investigate and improve the machinability of this material. Cutting forces (CF) so induced during machining is such a machinability parameter, and we considered it for our investigation also. The various factors which affect cutting force during turning operation are well depicted by Fig. 1. Researcher tried to evaluate the machinability of AISI D3 steel but few study found in literature so far related to modelling of cut-
⇑ Corresponding author.
ting force parameter modeling. As machining processes are complex in nature. The predictive models helps to machinist and researches for parameters selection and optimization without performing large number of experiments [7]. Al-Ahmari used cutting parameters namely cutting speed, feed, depth of cut and nose radius as input parameter and cutting forces and surface roughness as response parameters to study the machinability during turning operation. Further, empirical models were developed and compared using RSM and NN model [8]. Aouici et al. used ceramic cutting tool to turn AISI D3 hardened steel by taking feed rate, cutting speed and depth of cut input parameter effect on SR, tangential force, specific cutting force and power. They suggested an optimal setting to machine AISI D3 hardened steel [9]. Zerti et al. used Taguchi method to minimize cutting forces and other machinability parameters. The turning tests were performed on AISI D3 steel using CC650 grade ceramic inserts without coolant [10]. Bouchelaghem et al. used CBN insert to study the machinability of hardened steel and developed a relationship between machining parameters and responses namely SR, CF and TW using RSM [11]. Bensouilah et al. conducted hard turning of AISI D3 cold work tool steel using ceramic tools CC6050 and CC650. The performances were further modeled using regression technique. This comparative study was further well analyzed using ANOVA analysis of S/N ratio of the responses [12]. Esmaeil Soltani and Hesam Shahali investigated machinability of AISI D3 tool steel
E-mail address: [email protected] (P. Kumar). https://doi.org/10.1016/j.matpr.2020.01.018 2214-7853/Ó 2020 Elsevier Ltd. All rights reserved. Selection and of the scientific committee of the 10th International Conference of Materials Processing and Characterization.
Please cite this article as: V. Sharma, P. Kumar and J.P. Misra, Cutting force predictive modelling of hard turning operation using fuzzy logic, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2020.01.018
2
V. Sharma et al. / Materials Today: Proceedings xxx (xxxx) xxx
Fig. 1. Fishbone diagram for cutting force.
with Al2O3/TiC mixed ceramic tool in turning operation. Central composite design (CCD) of RSM was used to model and optimize hard turning of AISI D3 hardened steel. The sequential approximation optimization (SAO) was used to minimize the CF and SR. Effect of cutting speed, feed rate, hardness and tool corner radius was evaluated in this experimental study [13]. The present work consist of modeling cutting force and its evaluation study when machining hardened AISI D3 steel using WC cutting tool. Cutting forces evolution was investigated taking cutting parameters (v, f, d), and using regression technique machining parameters were correlated with cutting force to develop a statistical model. Later on a better model was proposed by utilizing better technique i.e. fuzzy logic. Hence performance of regression and fuzzy logic models, based on machining parameters for cutting force prediction were compared.
2. Material and method Taguchi’s L9 OA was used for experimentation. This method was initially used for offline quality control, but it is also successfully used for various process controls. The traditional approaches i.e. full factorial approach involves large number of experiments. While using OA, few experiments are required to describe a system. These OA are orthogonal means factor levels are weighted equally [14,15]. Due to this, effect of one parameter does not affect the influence of another parameter. Therefore it becomes possible to know the effect of each parameter independently on response. 2.1. Experimental design using Taguchi method Input parameters and their levels used for experimentation are shown in Table 1. These parameters and levels were selected by doing pilot experiments and literature survey. A water base coolant
Table 1 Cutting parameters and levels. Parameters
Notation
Unit
Parameter levels
Cutting speed Feed Depth of cut
s f d
rpm mm/rev mm
192 0.05 0.2
325 0.1 0.6
420 0.2 1
(grade: SAE 40) is used throughout experiments for ease of machining and cooling purpose. 2.2. Tables machine setup and instrument used In this study AISI D3 steel rod having diameter 25 mm was used as workpiece material. The chemical composition of workpiece material is shown in Table 2. Experiments were carried out on a rigid, high power precision NH22 (HMT, India) lathe equipped with dynamometer for experimentation. The used machine tool and dynamometer are shown in Fig. 2. The carbide inserts CCMT 060,208 (Sandvik-Coromant make) were used for machining. 3. Results and analysis Results obtained from L9 OA experimentation are shown in Table 3. The experimental observations were analyzed through ANOVA using MINITAB software. The analysis revealed that as
Table 2 Chemical composition of AISI D3 steel. Alloying elements % Composition
C 2.2
Cr 12
Ni 0.3
W 1
P 0.03
Si 0.6
Cu 0.25
Mn 0.4
Please cite this article as: V. Sharma, P. Kumar and J.P. Misra, Cutting force predictive modelling of hard turning operation using fuzzy logic, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2020.01.018
3
V. Sharma et al. / Materials Today: Proceedings xxx (xxxx) xxx
Fig. 2. (a) Experimental set up used; (b) Lathe tool dynamometer.
Table 3 Test results. Exp. Runs
1 2 3 4 5 6 7 8 9
Response parameter
Error
Cutting speed
Cutting parameter Feed
Depth of cut
Cutting Force (kgf)
Fuzzy
Regression
s (rpm)
f (mm/rev)
d (mm)
Experimental values
Fuzzy predicted
Regression predicted
420 420 420 325 325 325 192 192 192
0.20 0.10 0.05 0.20 0.10 0.05 0.20 0.10 0.05
1.0 0.6 0.2 0.6 0.2 1.0 0.2 1.0 0.6
133 22 10 25 24 38 31 82 26
114.71 29.96 28.28 28.62 29.96 28.62 28.28 71.48 28.28
98.24 42.12 1.6 64.355 8.235 58.475 29.444 67.284 23.564 RMSE
18.28 7.96 18.28 3.62 5.96 9.37 2.71 10.51 2.28 10.49
34.76 20.12 11.6 39.35 15.76 20.47 1.55 14.71 2.43 21.57
cutting speed varies, there is slight fall in cutting force and after that it increases. This is due to increase in resistance force with increase in tool wear at higher cutting speed. While in case of depth of cut and feed, cutting force rapidly increases with increasing parameter levels. The cutting parameters used can be ranked as depth of cut, feed and cutting speed, having effect on cutting force. Fig. 3 is showing influence of cutting parameter on cutting force. This plot reveals that cutting force is directly proportional
s
90
to feed (f) and depth of cut (d). The highest value of cutting force is obtained at the third level of each cutting parameter. The increase in CF value with the increase in feed (f) and depth of cut (d) is due to increase in load on cutting tool tip. This increase in load at cutting tool tip induces additional cutting force as extra material has to be removed. To know the contribution of machining parameter on this induced cutting force, ANOVA analysis was performed. The results of ANOVA analysis are shown in Table 4.
f
d
Mean of Cutting Force (kgf)
80
70
60
50
40
30
20 192
325
420
0.05
0.10
0.20
0.2
0.6
1.0
Fig. 3. Influence of cutting parameter on CF.
Please cite this article as: V. Sharma, P. Kumar and J.P. Misra, Cutting force predictive modelling of hard turning operation using fuzzy logic, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2020.01.018
4
V. Sharma et al. / Materials Today: Proceedings xxx (xxxx) xxx
Table 4 ANOVA results for cutting force. Source
DoF
SS Adj
Adj MS
F
P
% contribution
Cutting speed Feed Depth of cut Error Total
1 1 1 5 8
58.2 2154.3 5890.7 4189 12292.2
58.23 2154.29 5890.67 837.81
0.07 2.57 7.03
0.803 0.17 0.045
0.47 17.53 47.92 34.08
ANOVA results revealed the relative importance and contribution of each cutting parameters on cutting force. Depth of cut (d) and feed (f) were found main factors, and having 47.08% and 17.53% contribution on cutting force respectively. Cutting speed (s) is having negligible contribution on cutting force. Hence its effect can be neglected. 4. Fuzzy modeling of cutting force Fuzzy logic is an artificial intelligence based technique which employs fuzzy set. Using fuzzy logic we can define the intermediate values between traditional values like hot/cold, black/white etc. It is based on multi valued logic and its degree of truth ranges in between 0 and 1. Lotfi Aliasker Zadeh in 1964 for the first introduced this concept for the reasoning [16]. It mimics the human behaviour for reasoning, and uses the concept of grade of membership. Fuzzy logic core technique is based on following basic concepts. Fuzzy sets: A fuzzy set is a generalization to classical set and having smooth boundary. The degree to which an object can belong to fuzzy ranges from 0 to 1 and is known as membership value. Membership functions (MF): It is curve which maps the input space values to a membership value. These curves are backbone of fuzzy theory. Trapezoidal shape membership functions were used for the present case to characterize the fuzziness of elements in the set. Linguistic variables: These variables are used to define the input and output of a system. These variables are used for sharing knowledge and concepts with human beings and could be of qualitatively and quantitatively nature. Possibility distributions: It is constraints on the value of a linguistic variable imposed by assigning it a fuzzy set. Fuzzy rules: Fuzzy rules are used for capturing vagueness in knowledge. The conclusions about any conditions are made using these rules which are generally ‘‘if-then” statements. Fuzzy inference system: This is the unit which does calculations based on fuzzy rules and gives output. This output is further defuzzified and a crisp value is obtained. In this study centre of area method was used for the defuzzification. Fig. 4 is showing the prediction plot for regression and fuzzy model. For better visualization experimental values are also plotted along with predicted values. It is easily despicable form Fig. 4 that regression values get overshot. While small difference is observed between fuzzy predicted and experimental values. Fig. 5 is showing the residual plots for both models. The residual are plotted against experimental runs. As there is no pattern or there is randomization, means model are free from inherent error. From Fig. 5 it is easily observable that for regression model residual variation is very lager. This means regression model is not adequate for prediction purposes. On the other hand there is small residual variation for the fuzzy model and also having less RSME. This means fuzzy model is better for prediction of cutting force in compression with regression model develop within considered parametric range.
Fig. 4. Experimental Vs predicted cutting forces.
Fig. 5. Residual plot of cutting forces.
5. Conclusions In this study wet turning of AISI D3 steel was performed. The cutting forces were measured and influence of machining parameters was also determined. Taguchi’s L9 orthogonal array used for experimentation was found suitable for this purpose. The ANOVA study revealed that feed and depth of cut having 17.53% and 47.08% contribution on induced cutting force during hard turning of AISI D3 steel. Also the developed fuzzy model found better than regression model for the cutting force prediction. As the resulted fuzzy model having only 10.49% RMSE which is permission under statistical limit.
Please cite this article as: V. Sharma, P. Kumar and J.P. Misra, Cutting force predictive modelling of hard turning operation using fuzzy logic, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2020.01.018
V. Sharma et al. / Materials Today: Proceedings xxx (xxxx) xxx
CRediT authorship contribution statement Vikas Sharma: Conceptualization, Methodology, Investigation. Pawan Kumar: Formal analysis, Visualization, Software, Data curation, Writing - original draft, Formal analysis, Visualization. Joy Prakash Misra: Supervision, Writing - review & editing. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] T. Özel, Y. Karpat, Int. J. Mach. Tools Manuf. 45 (2005) 467–479. [2] E. Zeren, T. Özel, Rep. No MARL-01 Rutgers State Univ. N. J. (2002).
5
[3] W. König, A. Berktold, K.-F. Koch, CIRP Ann. 42 (1993) 39–43. [4] A. Mohammadi, H. Zarepour, Trans. Tech. Publ. (2010) 303–314. [5] R.K. Kountanya, Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 222 (2008) 969– 980. [6] M.A. Yallese, J.F. Rigal, K. Chaoui, L. Boulanouar, Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 219 (2005) 35–55. [7] P. Kumar, J.P. Misra, Mater. Sci. Forum. 969 (2019) 750–755. [8] A.M.A. Al-Ahmari, J. Mater. Process. Technol. 190 (2007) 305–311. [9] H. Aouici, H. Bouchelaghem, M.A. Yallese, M. Elbah, B. Fnides, Int. J. Adv. Manuf. Technol. 73 (2014) 1775–1788. [10] O. Zerti, M.A. Yallese, R. Khettabi, K. Chaoui, T. Mabrouki, Int. J. Adv. Manuf. Technol. 89 (2017) 1915–1934. [11] H. Bouchelaghem, M.A. Yallese, T. Mabrouki, A. Amirat, J.F. Rigal, Mach. Sci. Technol. 14 (2010) 471–501. [12] H. Bensouilah, H. Aouici, I. Meddour, M.A. Yallese, T. Mabrouki, F. Girardin, Measurement. 82 (2016) 1–18. [13] E. Soltani, H. Shahali, International AMPT Conference (2011). [14] K. Pawan, J.P. Misra, DAAAM Int. Sci. Book. (2018) 285–296. [15] P. Kumar, J.P. Misra, Emerg. Trends Mech. Eng. (2020) 229–243. [16] L.A. Zadeh, Inf. Control. 8 (1965) 338–353.
Please cite this article as: V. Sharma, P. Kumar and J.P. Misra, Cutting force predictive modelling of hard turning operation using fuzzy logic, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2020.01.018
Contents lists available at ScienceDirect
Materials Today: Proceedings journal homepage: www.elsevier.com/locate/matpr
Cutting force predictive modelling of hard turning operation using fuzzy logic Vikas Sharma a,b, Pawan Kumar b,⇑, Joy Prakash Misra b a b
Department of Mechanical, GLA University Mathura, 281406, India Department of Mechanical Engineering, NIT Kurukshetra, 136119, India
a r t i c l e
i n f o
Article history: Received 15 November 2019 Received in revised form 30 December 2019 Accepted 1 January 2020 Available online xxxx Keywords: Cutting force Fuzzy logic Turning Modelling Regression ANOVA
a b s t r a c t In this experimental study hard turning was performed under wet cutting environment. Purpose of this study was to predict and analyze the cutting force so induced during hard turning operation. Cutting speed, feed and depth of cut were taken as the controllable variables and their effect on cutting force was analyzed. The experimentation was carried out using L9 orthogonal array. The ANOVA analysis used in this study revealed the contribution of each machining parameter on cutting force. Furthermore, the cutting force models were developed for the prediction purpose using regression and fuzzy logic method. The fuzzy model so developed was found adequate and better than regression model for prediction purpose. The prediction efficiency for both models was determined using RMSE. Ó 2020 Elsevier Ltd. All rights reserved. Selection and of the scientific committee of the 10th International Conference of Materials Processing and Characterization.
1. Introduction Machining performed on workpiece material having hardness more than 45 HRC is known as hard machining. Turning is the most common and widely used machining process used in manufacturing industries to get a machined part from hard materials [1–5]. But as their name suggests they are difficult to machine, but due to their large application area these material are in demand. AISI D3 is one of them, and is widely used in die making industries due to its good hardness, strength and toughness at higher temperature. Other application areas of AISI D3 steel includes: blanking, stamping, cold forming dies and punches for long runs, lamination dies, bending, forming, and seaming rolls, cold trimmer dies or rolls, burnishing dies or rolls, plug gages, drawing dies for bars or wire, slitting cutters, lathe centers subject to severe wear [6]. Therefore there comes a need to investigate and improve the machinability of this material. Cutting forces (CF) so induced during machining is such a machinability parameter, and we considered it for our investigation also. The various factors which affect cutting force during turning operation are well depicted by Fig. 1. Researcher tried to evaluate the machinability of AISI D3 steel but few study found in literature so far related to modelling of cut-
⇑ Corresponding author.
ting force parameter modeling. As machining processes are complex in nature. The predictive models helps to machinist and researches for parameters selection and optimization without performing large number of experiments [7]. Al-Ahmari used cutting parameters namely cutting speed, feed, depth of cut and nose radius as input parameter and cutting forces and surface roughness as response parameters to study the machinability during turning operation. Further, empirical models were developed and compared using RSM and NN model [8]. Aouici et al. used ceramic cutting tool to turn AISI D3 hardened steel by taking feed rate, cutting speed and depth of cut input parameter effect on SR, tangential force, specific cutting force and power. They suggested an optimal setting to machine AISI D3 hardened steel [9]. Zerti et al. used Taguchi method to minimize cutting forces and other machinability parameters. The turning tests were performed on AISI D3 steel using CC650 grade ceramic inserts without coolant [10]. Bouchelaghem et al. used CBN insert to study the machinability of hardened steel and developed a relationship between machining parameters and responses namely SR, CF and TW using RSM [11]. Bensouilah et al. conducted hard turning of AISI D3 cold work tool steel using ceramic tools CC6050 and CC650. The performances were further modeled using regression technique. This comparative study was further well analyzed using ANOVA analysis of S/N ratio of the responses [12]. Esmaeil Soltani and Hesam Shahali investigated machinability of AISI D3 tool steel
E-mail address: [email protected] (P. Kumar). https://doi.org/10.1016/j.matpr.2020.01.018 2214-7853/Ó 2020 Elsevier Ltd. All rights reserved. Selection and of the scientific committee of the 10th International Conference of Materials Processing and Characterization.
Please cite this article as: V. Sharma, P. Kumar and J.P. Misra, Cutting force predictive modelling of hard turning operation using fuzzy logic, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2020.01.018
2
V. Sharma et al. / Materials Today: Proceedings xxx (xxxx) xxx
Fig. 1. Fishbone diagram for cutting force.
with Al2O3/TiC mixed ceramic tool in turning operation. Central composite design (CCD) of RSM was used to model and optimize hard turning of AISI D3 hardened steel. The sequential approximation optimization (SAO) was used to minimize the CF and SR. Effect of cutting speed, feed rate, hardness and tool corner radius was evaluated in this experimental study [13]. The present work consist of modeling cutting force and its evaluation study when machining hardened AISI D3 steel using WC cutting tool. Cutting forces evolution was investigated taking cutting parameters (v, f, d), and using regression technique machining parameters were correlated with cutting force to develop a statistical model. Later on a better model was proposed by utilizing better technique i.e. fuzzy logic. Hence performance of regression and fuzzy logic models, based on machining parameters for cutting force prediction were compared.
2. Material and method Taguchi’s L9 OA was used for experimentation. This method was initially used for offline quality control, but it is also successfully used for various process controls. The traditional approaches i.e. full factorial approach involves large number of experiments. While using OA, few experiments are required to describe a system. These OA are orthogonal means factor levels are weighted equally [14,15]. Due to this, effect of one parameter does not affect the influence of another parameter. Therefore it becomes possible to know the effect of each parameter independently on response. 2.1. Experimental design using Taguchi method Input parameters and their levels used for experimentation are shown in Table 1. These parameters and levels were selected by doing pilot experiments and literature survey. A water base coolant
Table 1 Cutting parameters and levels. Parameters
Notation
Unit
Parameter levels
Cutting speed Feed Depth of cut
s f d
rpm mm/rev mm
192 0.05 0.2
325 0.1 0.6
420 0.2 1
(grade: SAE 40) is used throughout experiments for ease of machining and cooling purpose. 2.2. Tables machine setup and instrument used In this study AISI D3 steel rod having diameter 25 mm was used as workpiece material. The chemical composition of workpiece material is shown in Table 2. Experiments were carried out on a rigid, high power precision NH22 (HMT, India) lathe equipped with dynamometer for experimentation. The used machine tool and dynamometer are shown in Fig. 2. The carbide inserts CCMT 060,208 (Sandvik-Coromant make) were used for machining. 3. Results and analysis Results obtained from L9 OA experimentation are shown in Table 3. The experimental observations were analyzed through ANOVA using MINITAB software. The analysis revealed that as
Table 2 Chemical composition of AISI D3 steel. Alloying elements % Composition
C 2.2
Cr 12
Ni 0.3
W 1
P 0.03
Si 0.6
Cu 0.25
Mn 0.4
Please cite this article as: V. Sharma, P. Kumar and J.P. Misra, Cutting force predictive modelling of hard turning operation using fuzzy logic, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2020.01.018
3
V. Sharma et al. / Materials Today: Proceedings xxx (xxxx) xxx
Fig. 2. (a) Experimental set up used; (b) Lathe tool dynamometer.
Table 3 Test results. Exp. Runs
1 2 3 4 5 6 7 8 9
Response parameter
Error
Cutting speed
Cutting parameter Feed
Depth of cut
Cutting Force (kgf)
Fuzzy
Regression
s (rpm)
f (mm/rev)
d (mm)
Experimental values
Fuzzy predicted
Regression predicted
420 420 420 325 325 325 192 192 192
0.20 0.10 0.05 0.20 0.10 0.05 0.20 0.10 0.05
1.0 0.6 0.2 0.6 0.2 1.0 0.2 1.0 0.6
133 22 10 25 24 38 31 82 26
114.71 29.96 28.28 28.62 29.96 28.62 28.28 71.48 28.28
98.24 42.12 1.6 64.355 8.235 58.475 29.444 67.284 23.564 RMSE
18.28 7.96 18.28 3.62 5.96 9.37 2.71 10.51 2.28 10.49
34.76 20.12 11.6 39.35 15.76 20.47 1.55 14.71 2.43 21.57
cutting speed varies, there is slight fall in cutting force and after that it increases. This is due to increase in resistance force with increase in tool wear at higher cutting speed. While in case of depth of cut and feed, cutting force rapidly increases with increasing parameter levels. The cutting parameters used can be ranked as depth of cut, feed and cutting speed, having effect on cutting force. Fig. 3 is showing influence of cutting parameter on cutting force. This plot reveals that cutting force is directly proportional
s
90
to feed (f) and depth of cut (d). The highest value of cutting force is obtained at the third level of each cutting parameter. The increase in CF value with the increase in feed (f) and depth of cut (d) is due to increase in load on cutting tool tip. This increase in load at cutting tool tip induces additional cutting force as extra material has to be removed. To know the contribution of machining parameter on this induced cutting force, ANOVA analysis was performed. The results of ANOVA analysis are shown in Table 4.
f
d
Mean of Cutting Force (kgf)
80
70
60
50
40
30
20 192
325
420
0.05
0.10
0.20
0.2
0.6
1.0
Fig. 3. Influence of cutting parameter on CF.
Please cite this article as: V. Sharma, P. Kumar and J.P. Misra, Cutting force predictive modelling of hard turning operation using fuzzy logic, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2020.01.018
4
V. Sharma et al. / Materials Today: Proceedings xxx (xxxx) xxx
Table 4 ANOVA results for cutting force. Source
DoF
SS Adj
Adj MS
F
P
% contribution
Cutting speed Feed Depth of cut Error Total
1 1 1 5 8
58.2 2154.3 5890.7 4189 12292.2
58.23 2154.29 5890.67 837.81
0.07 2.57 7.03
0.803 0.17 0.045
0.47 17.53 47.92 34.08
ANOVA results revealed the relative importance and contribution of each cutting parameters on cutting force. Depth of cut (d) and feed (f) were found main factors, and having 47.08% and 17.53% contribution on cutting force respectively. Cutting speed (s) is having negligible contribution on cutting force. Hence its effect can be neglected. 4. Fuzzy modeling of cutting force Fuzzy logic is an artificial intelligence based technique which employs fuzzy set. Using fuzzy logic we can define the intermediate values between traditional values like hot/cold, black/white etc. It is based on multi valued logic and its degree of truth ranges in between 0 and 1. Lotfi Aliasker Zadeh in 1964 for the first introduced this concept for the reasoning [16]. It mimics the human behaviour for reasoning, and uses the concept of grade of membership. Fuzzy logic core technique is based on following basic concepts. Fuzzy sets: A fuzzy set is a generalization to classical set and having smooth boundary. The degree to which an object can belong to fuzzy ranges from 0 to 1 and is known as membership value. Membership functions (MF): It is curve which maps the input space values to a membership value. These curves are backbone of fuzzy theory. Trapezoidal shape membership functions were used for the present case to characterize the fuzziness of elements in the set. Linguistic variables: These variables are used to define the input and output of a system. These variables are used for sharing knowledge and concepts with human beings and could be of qualitatively and quantitatively nature. Possibility distributions: It is constraints on the value of a linguistic variable imposed by assigning it a fuzzy set. Fuzzy rules: Fuzzy rules are used for capturing vagueness in knowledge. The conclusions about any conditions are made using these rules which are generally ‘‘if-then” statements. Fuzzy inference system: This is the unit which does calculations based on fuzzy rules and gives output. This output is further defuzzified and a crisp value is obtained. In this study centre of area method was used for the defuzzification. Fig. 4 is showing the prediction plot for regression and fuzzy model. For better visualization experimental values are also plotted along with predicted values. It is easily despicable form Fig. 4 that regression values get overshot. While small difference is observed between fuzzy predicted and experimental values. Fig. 5 is showing the residual plots for both models. The residual are plotted against experimental runs. As there is no pattern or there is randomization, means model are free from inherent error. From Fig. 5 it is easily observable that for regression model residual variation is very lager. This means regression model is not adequate for prediction purposes. On the other hand there is small residual variation for the fuzzy model and also having less RSME. This means fuzzy model is better for prediction of cutting force in compression with regression model develop within considered parametric range.
Fig. 4. Experimental Vs predicted cutting forces.
Fig. 5. Residual plot of cutting forces.
5. Conclusions In this study wet turning of AISI D3 steel was performed. The cutting forces were measured and influence of machining parameters was also determined. Taguchi’s L9 orthogonal array used for experimentation was found suitable for this purpose. The ANOVA study revealed that feed and depth of cut having 17.53% and 47.08% contribution on induced cutting force during hard turning of AISI D3 steel. Also the developed fuzzy model found better than regression model for the cutting force prediction. As the resulted fuzzy model having only 10.49% RMSE which is permission under statistical limit.
Please cite this article as: V. Sharma, P. Kumar and J.P. Misra, Cutting force predictive modelling of hard turning operation using fuzzy logic, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2020.01.018
V. Sharma et al. / Materials Today: Proceedings xxx (xxxx) xxx
CRediT authorship contribution statement Vikas Sharma: Conceptualization, Methodology, Investigation. Pawan Kumar: Formal analysis, Visualization, Software, Data curation, Writing - original draft, Formal analysis, Visualization. Joy Prakash Misra: Supervision, Writing - review & editing. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] T. Özel, Y. Karpat, Int. J. Mach. Tools Manuf. 45 (2005) 467–479. [2] E. Zeren, T. Özel, Rep. No MARL-01 Rutgers State Univ. N. J. (2002).
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Please cite this article as: V. Sharma, P. Kumar and J.P. Misra, Cutting force predictive modelling of hard turning operation using fuzzy logic, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2020.01.018