An ANN approach for predicting subsurface residual stresses and the desired cutting conditions during hard turning

An ANN approach for predicting subsurface residual stresses and the desired cutting conditions during hard turning

Journal of Materials Processing Technology 189 (2007) 143–152 An ANN approach for predicting subsurface residual stresses and the desired cutting con...

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Journal of Materials Processing Technology 189 (2007) 143–152

An ANN approach for predicting subsurface residual stresses and the desired cutting conditions during hard turning D. Umbrello a,∗ , G. Ambrogio a , L. Filice a , R. Shivpuri b a

b

Department of Mechanical Engineering, University of Calabria, 87036 Rende (CS), Italy Industrial, Welding and Systems Engineering, The Ohio State University, 43210 Columbus (OH), USA Received 28 March 2006; received in revised form 12 December 2006; accepted 16 January 2007

Abstract Residual stresses in the hard machined surface and the subsurface are affected by materials, tool geometry and machining parameters. These residual stresses can have significant effect on the service quality and the component life. They can be determined by either empirical or numerical experiments for selected configurations, even if both are expensive procedures. The problem becomes more difficult if the objective is the inverse determination of cutting conditions for a given residual stress profile. This paper presents a predictive model based on the artificial neural network (ANN) approach that can be used both for forward and inverse predictions. The three layer neural network was trained on selected data from chosen numerical experiments on hard machining of 52100 bearing steel, and then validated by comparing with data from numerical investigations (other than those used for training), and empirical data from published literature. Prediction errors ranged between 4 and 10% for the whole data set. Hence, this ANN based regression approach provided a robust framework for forward analysis. © 2007 Elsevier B.V. All rights reserved. Keywords: Hard machining; Neural network; Residual stresses; FEM

1. Introduction Hard turning is often defined as the process of single point cutting of pieces that have hardness values over 45 HRc [1]. Recent improvements in machine tool rigidity and the development of ceramic and CBN cutting inserts allow the application of this technology to finish hard machining of hardened steels with geometrically defined cutting edges. In fact, there are numerous advantages to replace grinding with hard turning operations. Even though smaller depths of cut and feed rates are required for hard turning, the material removal rate can be much higher than in grinding for some applications [2]. A typical hard turned part which is processed on a correctly configured machine can have surface roughness below 0.3 ␮m, roundness accuracy of 0.25 ␮m and size control of 5 ␮m.



Corresponding author. Tel.: +39 0984494820; fax: +39 0984494673. E-mail addresses: [email protected] (D. Umbrello), [email protected] (G. Ambrogio), [email protected] (L. Filice), [email protected] (R. Shivpuri). URL: http://tsl.unical.it (D. Umbrello). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.01.016

For all the above reasons, it seems obvious that hard turning is an attractive replacement for many rough and finish grinding operations. However, its implementation in industry remains relatively low, particularly for critical tribological surfaces. This is because hard turning is a relatively new process and several questions remain unanswered, such as the generation of undesirable residual stress patterns and “white layers” on the machined surface [2–6]. In addition, hard machining also generates high cutting forces and temperatures that enhance tool wear when act together. Therefore, the tool geometry and machining parameters have to be carefully optimized for a given material and desired residual stress profiles. Tool wear and the characteristics of the white layer are the main constraints in selection of cutting conditions. In a hard machining process, surface integrity is often of great concern due to its impact on the product performance. It is reported that subsurface residual stresses in the machined surface can greatly influence the service quality of the component, such as fatigue life, tribological characteristics, and distortion [7]. Therefore, for desired part performance, it is important to predict and control the development of these subsurface residual stresses as a function of hard machining parameters. A typical subsurface residual stress profile is shown in Fig. 1.

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Fig. 1. Definition of penetration depth (a), beneficial depth (b), and maximum compressive residual stress (c).

Several researchers investigated relationships between the machining parameters and the developed subsurface residual stresses [7–18]. They found that the residual stress profiles produced in hard turning is strongly influenced by the cutting edge geometry, the properties of workpiece material (such as hardness) and the cutting conditions [7,9–18]. For example, in the research conducted by Hua et al. [18] it was shown

that a large hone edge or chamfer plus hone edge gave more compressive and deeper residual stress than single chamfer or a small hone edge. Their results indicated that a large hone radius tool produces more compressive residual stress and deeper beneficial length than small hone radius tool. Furthermore, chamfer tool increased compressive residual stress but its effect was lower than increasing the hone radius. These results are confirmed by Dahlman et al. [15]. Hua et al. [18] also found that a large feed rate as well as a high workpiece hardness increased the maximum compressive residual stress and its depth. Since the residual stress profile is affected by the design of the cutting tool, the workpiece properties and the cutting conditions, empirical and numerical modeling approaches are not very suitable for an accurate prediction of residual stresses. On the other hand, response surface methodology can be used but it is often not robust in the presence of not smooth functions. Consequently, artificial neural network (ANN) approach becomes attractive since it is fairly robust and frequently converges to the desired solution. The main drawback of ANN is the need of large data points for training and validation effort. For this reason, a FEM–ANN hybrid technique was used to generate

Table 1 Residual stress profiles (33 data points) obtained from previous researches [17–19] HRc

S (m/min)

f (mm/rev)

γ

Tool geometry

s = 0.085 × 20◦

Axial RS

Hoop RS

a (mm)

b (mm)

c (MPa)

a (mm)

b (mm)

c (MPa)

56

120 120 120 120 120 120 120 120 120 120 120 120 120 120

0.035 0.07 0.035 0.035 0.085 0.085 0.15 0.28 0.28 0.28 0.28 0.28 0.28 0.28

−6 −6 −6 −6 −6 −6 −6 −6 −6 −6 −6 −6 −6 −6

Chamfer Chamfer s = 0.085 × 20◦ Hone R = 0.15 mm Chamfer s = 0.1 × 20◦ Hone R = 0.15 mm Chamfer s = 0.1 × 20◦ Hone R = 0.1219 mm Hone R = 0.1 mm Hone R = 0.05 mm Up sharp (R = 0.02 mm) Chamfer s = 0.1 × 0◦ Chamfer s = 0.1 × 20◦ Chamfer s = 0.1 × 30◦ Chamfer s = 0.1 × 40◦

0.042 0.042 0.023 0.039 0.021 0.040 0.040 0.035 0.350 0.029 0.025 0.030 0.030 0.030

0.150 0.193 0.223 0.136 0.250 0.290 0.320 0.270 0.260 0.250 0.250 0.255 0.260 0.262

−140 −157 −204 −148 −300 −180 −348 −388 −369 −331 −332 −385 −396 −407

0.043 0.023 0.042 0.040 0.040 0.022 0.040 0.035 0.040 0.030 0.034 0.040 0.043 0.043

0.116 0.193 0.175 0.192 0.500 0.200 0.900 0.170 0.170 0.150 0.180 0.170 0.165 0.150

−180 −323 −425 −185 −621 −405 −850 −1285 −1178 −1071 −1142 −1250 −1267 −1300

62

120 120 120 120 120 120 120 120 120 180 240 106.7 120 120

0.035 0.035 0.085 0.085 0.15 0.085 0.085 0.085 0.085 0.085 0.085 0.051 0.035 0.07

−6 −6 −6 −6 −6 −6 −6 −6 −6 −6 −6 −6 −6 −6

Hone R = 0.15 mm Chamfer s = 0.1 × 20◦ Hone R = 0.15 mm Chamfer s = 0.1 × 20◦ Hone R = 0.1219 mm Up sharp (R = 0.025 mm) Hone R = 0.1 mm Chamfer s = 0.1 × 15◦ Chamfer s = 0.1 × 30◦ Hone R = 0.15 mm Hone R = 0.15 mm Up sharp (R = 0.025 mm) Chamfer s = 0.085 × 20◦ Chamfer s = 0.085 × 20◦

0.021 0.039 0.044 0.061 0.048 0.042 0.041 0.059 0.040 0.125 0.180 0.049 0.038 0.044

0.295 0.200 0.360 0.270 0.500 0.170 0.275 0.210 0.375 0.495 0.620 0.170 0.153 0.205

−236 −183 −330 −260 −370 −210 −270 −210 −380 −225 −195 −220 −165 −183

0.043 0.023 0.042 0.023 0.041 0.039 0.040 0.025 0.039 0.085 0.085 0.024 0.022 0.023

0.180 0.180 0.600 0.205 0.900 0.150 0.350 0.115 0.310 0.630 0.630 0.140 0.107 0.138

−550 −200 −835 −490 −1090 −600 −725 −450 −795 −630 −565 −585 −224 −395

66

120 120 120 120 120

0.035 0.035 0.085 0.085 0.15

−6 −6 −6 −6 −6

Hone R = 0.15 mm Chamfer s = 0.1 × 20◦ Hone R = 0.15 mm Chamfer s = 0.1 × 20◦ Hone R = 0.1219 mm

0.023 0.040 0.040 0.060 0.003

0.189 0.210 0.460 0.405 0.565

−340 −212 −400 −298 −427

0.043 0.025 0.040 0.023 0.040

0.192 0.185 0.570 0.270 0.900

−610 −237 −921 −535 −1223

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a reasonable data points which permitted to avoid the expensive and time consuming experimental tests. In particular, this paper introduces briefly the numerical model used in the generation of residual stress data, the framework of the ANN approach and its training and validation for hard turning of AISI 52100 bearing steel, that is through hardened in the range of 50–64 HRc.

data set. In particular, the influence of rake angle, the chamfered angle, the cutting speed as well as the tool shape were included in order to create a more extensive design space, able to investigate the following relationship: Residual stress profile (aAXIAL , bAXIAL , cAXIAL , aHOOP , bHOOP , cHOOP ) = f (material parameters (hardness, flow stress),

2. Generation of residual stress data: numerical investigations

tool shape (cutting edge geometry),

Unfortunately, few residual stress profiles can be acquired from previously published empirical and numerical investigations [17,18]. And these data are not enough to identify the following relationship: σr = σr (p, g, M)

145

(1)

where σ r is the residual stress profile both for axial and hoop directions, p represents the process conditions, g denotes the cutting edge geometry, and M indicates the material characteristics such as hardness and flow stress. For this reason and taking into account previous residual stress profiles [17–19] shown in Table 1, an extensive numerical plan was developed (Fig. 2) to populate the residual stress

machining conditions (rake angle, cutting velocity, feed)) (2) A finite element (FE) model was developed previously by some of the authors for hard machining of 52100 bearing steels [20]. This model used the elastic–plastic constitutive law, Brozzo’s fracture criterion and a hardness based flow stress behaviour to represent the physics and thermodynamics of hard machining in a numerical FE analysis. More details of this model and its use in predicting subsurface residual stress can be found in references [17–19]. It is important to underline that the assumed rheological model and the predicted residual stress profiles obtained

Fig. 2. The plan for numerical investigations (53 new data points).

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Fig. 3. Effect of cutting speed on both maximum axial and circumferential compressive residual stresses. Investigated case: hone edge preparation, R = 0.15 mm; rake angle γ = −6◦ ; initial hardness, 62 HRc; feed rate, and f = 0.085 mm/rev.

by numerical simulations were already validated [17] by a numerical–experimental comparison. Selected results from these references and from new FE simulations, relevant to the development of the ANN model, are discussed in the following. 2.1. Influence of process conditions and initial hardness The numerical results showed that more compressive residual stress in both axial and circumferential direction of the machined surface can be obtained if higher values of the feed rate were chosen. Also the beneficial depth increased with the tool feed even if its effect was more relevant along the hoop direction. Similarly, the penetration depth was higher when higher values of both feed and hardness were selected. Furthermore, using the same cutting parameters, larger compressive residual stresses were generated if the workpiece material was heat treated to a higher hardness. The beneficial depth increased at increasing hardness, as well as the penetration depth. On the contrary, smaller compressive residual stresses were generated by choosing higher cutting speed (Fig. 3), even if larger beneficial depth (Fig. 4a) and penetration depth (Fig. 4b) can be observed in all the investigated cases (more relevant along the axial direction).

Fig. 5. Influence of tool rake angle on both maximum axial and circumferential compressive residual stresses. Investigated case: hone edge preparation, R = 0.15 mm; cutting speed, S = 120 m/min; feed rate, and f = 0.035 mm/rev.

2.2. Influence of cutting edge geometry The increase of either the rake angle or the chamfer angle as well as the hone cutting edge radius allowed an increase in the compressive residual stress in the subsurface; at the same time, it caused a tool temperature arising. As expected, both the beneficial depth and the penetration depth increased with larger tool edge geometry and rake angle. In particular, it can be observed, in Fig. 5, that a higher rake angle (commonly important when a round tool is used) generated a higher hoop compressive residual stress, while it did not affect the maximum axial residual stress. Moreover, in the most of the investigated cases, both the beneficial depth and the penetration depth increased at increasing the tool rake angle, when a cutting hone edge preparation was used (Fig. 6a and b). Fig. 7 reports the influence of chamfer tool angle showing an higher maximum compressive axial and hoop residual stresses for higher chamfer angles. The beneficial depth increased with increasing of the chamfer angle, even if it showed (Fig. 8a) a threshold effect at 20◦ . The penetration depth of residual stress increased with the increasing chamfer angle along the hoop direction, while the effect was opposite along the axial direction (Fig. 8b). In addition, the effect of tool shape was also investigated. Fig. 9 shows how both maximum com-

Fig. 4. Effect of cutting speed on beneficial depth (a) and penetration depth (b). Investigated case: hone edge preparation, R = 0.15 mm; rake angle γ = −6◦ ; initial hardness, 62 HRc; feed rate, and f = 0.085 mm/rev.

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Fig. 6. Influence of tool rake angle on beneficial depth (a) and penetration depth (b). Investigated case: hone edge preparation, R = 0.15 mm; cutting speed, S = 120 m/min; feed rate, and f = 0.035 mm/rev.

Fig. 7. Influence of chamfer angle on both maximum axial and circumferential compressive residual stresses. Investigated case: chamfer edge preparation, s = 0.1 mm × α; initial hardness, 62 HRc; cutting speed, S = 180 m/min; feed rate, and f = 0.035 mm/rev.

pressive axial and hop residual stresses can be reached by using a large hone edge with a high rake angle. Furthermore, higher chamfer angles permitted to reach good compressive residual stresses. Also the beneficial depth (Fig. 10a) was more sensitive to large hone edges even if in this case lower rake angles were required. Finally, the penetration depth (Fig. 10b) reached the

Fig. 9. Influence of tool shape on both maximum axial and circumferential compressive residual stresses. Investigated cases: initial hardness, 62 HRc; cutting speed, S = 120 m/min; feed rate, and f = 0.085 mm/rev.

higher values at increasing of the rake angle for hone edge preparation and choosing medium chamfer angle when a chamfer tool was used. 3. Development of ANN framework ANNs are one of the most powerful computer analysis techniques, based on the statistical regression approach. Currently,

Fig. 8. Influence of chamfer angle on the beneficial depth (a) and penetration depth (b). Investigated case: chamfer edge preparation, s = 0.1 mm × α; initial hardness, 62 HRc; cutting speed, S = 180 m/min; feed rate, and f = 0.035 mm/rev.

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Fig. 10. Influence of tool shape on the beneficial depth (a) and penetration depth (b). Investigated cases: initial hardness, 62 HRc; cutting speed, S = 120 m/min; feed rate, and f = 0.085 mm/rev.

ANNs are used in many fields of engineering for modeling complex relationships which are difficult to describe with physical models. They are very useful in applications where conventional analytical or numerical models are either not available or too complex and difficult to solve. In the last years, the ANNs have been extensively applied in the modeling of many metal-cutting operations such as turning, milling and drilling [21–23]. For example, a large number of applications of ANN models to predict tool wear and tool life were reported in literature. An exhaustive review of current literature on this topic is presented by Sick [24]. Other applications include the use of ANN approaches to determine the optimal cutting conditions for efficient and economic production [25–27] and the investigation of surface roughness [28]. As far as the authors know, no studies are available on the use of ANN for predicting subsurface residual stresses in hard machining. Neural networks are non-linear mapping systems that consist of simple processors, which are called neurons, linked by weighted connections. Each neuron has inputs and generates an output that can be seen as the reflection of local information that is stored in connections. The output signal of a neuron is sent to other neurons as input signals via interconnections. Since the capability of a single neuron is limited, complex function can be realized by connecting many neurons. It is widely reported that structure of neural network, representation of data, normalization of inputs–outputs and appropriate selection of activation functions have strong influence on the effectiveness and performance of the trained neural network [29]. A neural network often consists of at least three layers, i.e. input, hidden and output layers and the backpropagation training methodology, that is commonly used in the training neural networks, can be summarized as follows. Consider the multilayer feed-forward neural network given in Fig. 11 and one of its hidden neuron. The net input to unit k in the hidden layer is: nk =

J  j=1

Cj,k ij + ϑk

and its output of unit k will be hk = fnk . In the same manner, the net input in the output layer is: nz =

K 

Dk,z hk + φz

(4)

k=1

and its output of unit z will be oz = fnz , where f is the activation function (linear, sigmoid or tanh are the commonly used), Cj,k and Dk,z the weights between the neurons input–hidden neurons and hidden–output neurons and, finally, θ k and φz are the biases on the hidden and output neurons, respectively. The performance index, PI, during the iterations is selected as the total error between the desired output and one given in the training data set: PI =

Z 

(odesidered − ocalculated ) z z

(5)

z=1

The backpropagation algorithm proceeds as follows: firstly, inputs are presented to the network and error are calculated; secondly, sensitivities are propagated from the output layer to the first layer; then, weights and biases are updated using the follow equations: hidden layer : Cj,k = −α

∂PI , ∂Cj,k

ϑk = −α

(3) Fig. 11. Structure of a neural network.

∂PI ∂ϑk

(6)

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Table 2 ANN performance (E on 18 testing cases): (a) penetration depth; (b) beneficial depth; (c) max compressive residual stress ANN Conf.

Axial

IN HIDD OUT

a (%)

b (%)

c (%)

a (%)

b (%)

c (%)

AVE E (%)

8 8 8 8 8 8 8 8 8 8 8 8 8 8

11.12 6.68 9.16 15.50 9.32 20.27 12.81 9.50 6.48 8.32 9.97 7.34 8.16 5.70

13.48 11.14 16.54 12.74 14.67 18.96 22.24 17.27 20.36 19.41 20.28 18.81 16.43 20.19

17.90 15.37 7.22 10.10 8.90 8.64 6.88 10.19 9.55 12.37 9.31 13.77 9.76 13.00

28.13 26.54 29.58 42.66 13.40 34.48 26.53 12.79 30.11 20.97 70.08 36.89 24.98 42.00

7.99 11.33 4.14 12.31 2.92 7.23 7.24 11.65 4.05 4.92 5.86 4.47 5.03 12.24

9.36 9.81 2.99 3.07 3.59 5.01 2.99 4.78 3.45 5.13 4.26 3.99 3.32 2.78

14.66 13.48 11.61 16.06 8.80 15.76 13.12 11.03 12.33 11.85 19.96 14.21 11.28 15.98

56 66 76 86 96 10 6 11 6 12 6 13 6 14 6 15 6 16 6 18 6 20 6

output layer : Dk,z = −α

∂PI , ∂Dk,z

Hoop

φz = −α

∂PI ∂φz

(7)

where α is the learning rate, which should be selected small enough for true approximation and, at the same time, large enough to speed up convergence. Minimizing the performance index on the training sets, may not result in a network with superior generalization capability. Methods such as Bayesian regularization, early stopping, etc., are commonly used to improve the generalization in neural networks where there is a limited amount of data [30]. In this study, the steepest descent optimization method (simple backpropagation) is used together with Bayesian regularization in training neural networks with good generalization capability. Moreover, both the steepest descent optimization method and Bayesian regularization permit to decrease the possibility of overfitting. The non-linear sigmoid activation functions are used in the input–hidden–output layers and the input data are normalized in the range of [−1,1]. The weights and the biases of the network are initialized to small random values to avoid sharp saturation in the activation functions. Throughout this study, the data set is divided into two sets. Neural networks were trained by using training data set and their generalization capacity was evaluated by using test set. Slug’s neural network toolkit was used to train neural networks [31]. 4. Training and testing the ANN model framework The numerical results obtained through the extensive numerical simulation campaign (Fig. 2), together with those collected from previous publications [17–19], were utilized to train the developed ANN at varying process parameters, namely feed rate, cutting speed, workpiece hardness, tool edge radius, rake angle (for hone edge preparation) and chamfer angle (for chamfer edge tool). As far as the cutting edge geometry is concerned, both hone and chamfer tools were taken into account. For each combination of these parameters, both the axial and hoop residual stress profiles were obtained.

This neural network was trained with 68 data points (cutting conditions) and tested on 18 data points (cutting conditions) that were randomly chosen from different cutting conditions from the complete data set (86 cutting conditions). A single data point in the input data set consisted of tool shape, tool, workpiece hardness, HRc, tool radius or chamfer thick, R, feed, f, speed, S, rake angle (hone edge) or chamfer angle, γ, and the output data set consisted of six neurons representing the compressive residual stress, beneficial and penetration depth (namely c, b, a) both for axial and hoop directions. Moreover, several network configurations were implemented for optimising the predictive performance, and the best one was achieved by including in the data points the logarithmic function of HRc/100 and the speed/100. Finally, an optimization procedure was implemented to determine the best number of neurons in the hidden layer that was fixed equal to 9 as illustrated in Table 2. In particular, an error function (E) between the validation numerical data (YNi ) and the predicted residual stress profiles (YPi ) was used to identify the best configuration: E=

N 

(YPi − YNi )2

(8)

i=1

where N indicates the total number of points utilized for the network testing (N = 18). Fig. 12 shows the final NN architecture where the feedforward three layers were connected by the follow sigmoid expressions: 1 

Input–hidden : hk = 1+e

8 C i +θk j=1 j,k j





hidden–output : oz = 1+e



,

1

9 D h +φz k=1 k,z k



(9)

Finally, Figs. 13–15 show the predictions obtained for the maximum compressive residual stress, beneficial and penetra-

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Fig. 12. The neural network architecture.

Fig. 13. FEM max compressive RS vs. ANN results for 18 testing cases (MSEHoop = 3.59%, MSEAxial = 8.90%).

Fig. 14. FEM beneficial depth vs. ANN results for 18 testing cases (MSEHoop = 2.92%, MSEAxial = 14.67%).

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151

Fig. 15. FEM penetration depth vs. ANN results for 18 testing cases (MSEHoop = 13.40%, MSEAxial = 9.32%).

tion depth along both the hoop and the axial directions. It can be observed from these figures that the network predictions were in good agreement with FEM results. 5. Discussion of the results It is clear that the trained ANN supplied good results if the data from numerical simulation are used for training and testing. Since a more rigorous validation task should be based on experimental investigation results, an experimental campaign was performed on AISI 52100 specimens with different initial hardness, cut by a PCBN chamfer tool (20◦ × 0.085 mm), for a cutting speed of 120 m/min and two different feed rates (0.28 and 0.56 mm/rev). The residual stress profiles were measured using the X-ray diffraction technique and by removing thin material

slices by chemical machining. Furthermore, to validate the ANN predictions for wider range of experimental conditions, experimental data from published works [9,12] were also included in the validation data set. Comparisons of predicted residual stress profiles with those experimentally found are shown in Table 3. In order to evaluate the network fitness, a new error function was defined as follow:      aANN − aEXP   bANN − bEXP  1     eANN = ×  +  3 aEXP bEXP    cANN − cEXP   × 100 +  (10)  cEXP The trained ANN model gave satisfactory results with the error ranging between 4 and 10% (Table 3).

Table 3 ANN performance on experimental residual stress profiles Cutting conditions

S = 120 m/min; f = 0.28 mm/rev; 56 HRc; chamfer: 20◦ × 0.085 mm γ = −6◦ S = 120m/min; f = 0.56mm/rev; 56 HRc; chamfer: 20◦ × 0.085 mm γ = −6◦ S = 120 m/min; f = 0.28 mm/rev; 62 HRc; chamfer: 20◦ × 0.085 mm γ = −6◦ S = 120 m/min; f = 0.56 mm/rev; 62 HRc; chamfer: 20◦ × 0.085 mm γ = −6◦ S = 121.9 m/min; f = 0.15 mm/rev; 57 HRc; hone: R = 0.122 mm; γ = −5◦ (Thiele and Melkote, 1999 [9]) S = 121.9 m/min; f = 0.15 mm/rev; 41 HRc; hone: R = 0.122 mm; γ = −5◦ (Thiele and Melkote, 1999 [9]) S = 106.7 m/min; f = 0.051 mm/rev, 62 HRc; up-sharp: R = 0.025 mm γ = −6◦ (Agha and Liu, 2000 [12])

Stress component

EXP

ANN

eANN (%)

a (mm)

b (mm)

c (MPa)

a (mm)

b (mm)

c (MPa)

Axial

0.0235

0.2460

−388

0.0248

0.2640

−392

4.6

Hoop Axial

0.0350 0.0262

0.175 0.2560

−1175 −530

0.0396 0.0284

0.1646 0.2798

−1201 −495

7.1 8.1

Hoop Axial

0.0400 0.0250

0.178 0.2510

−1448 −396

0.0426 0.0270

0.1555 0.2788

−1391 −394

7.7 6.6

Hoop Axial

0.0378 0.0270

0.184 0.2720

−1379 −599

0.0422 0.0287

0.1773 0.2811

−1328 −528

6.3 7.2

Hoop Hoop

0.0410 0.0250

0.191 0.21

−1490 −1150

0.0428 0.0227

0.1559 0.1950

−1431 −994

8.9 9.9

Hoop

0.0300

0.18

−700

0.0289

0.1891

−717

3.7

Axial

0.0500

0.1450

−248

0.0428

0.1530

−223

Hoop

0.0310

0.132

−583

0.033

0.1148

−554

10 8.2

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