Prediction of stable cutting depths in turning operation using soft computing methods

Accepted Manuscript Title: PREDICTION OF STABLE CUTTING DEPTHS IN TURNING OPERATION USING SOFT COMPUTING METHODS Author: Mehmet Alper Sofuoglu Sezan Orak PII: DOI: Reference:

S1568-4946(15)00671-7 http://dx.doi.org/doi:10.1016/j.asoc.2015.10.031 ASOC 3274

To appear in:

Applied Soft Computing

Received date: Revised date: Accepted date:

18-4-2015 23-9-2015 15-10-2015

Please cite this article as: M.A. Sofuoglu, S. Orak, PREDICTION OF STABLE CUTTING DEPTHS IN TURNING OPERATION USING SOFT COMPUTING METHODS, Applied Soft Computing Journal (2015), http://dx.doi.org/10.1016/j.asoc.2015.10.031 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

PREDICTION OF STABLE CUTTING DEPTHS IN TURNING OPERATION

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USING SOFT COMPUTING METHODS

Highlights:

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 Different soft computing methods have been used to predict stable cutting depths

depth.

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 ANN model has produced succesfull results.

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 Different experiments have been used in the models to predict stable cutting

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PREDICTION OF STABLE CUTTING DEPTHS IN TURNING OPERATION USING SOFT COMPUTING METHODS a,b

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Mehmet Alper Sofuoglua, Sezan Orakb Eskisehir Osmangazi University, Department of Mechanical Engineering, Bati Meselik, Eskisehir, Turkey [email protected], [email protected]

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Corresponding author: Mehmet Alper Sofuoglu Phone:+90 222 239 3750

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This article suggests soft computing methods to predict stable cutting depths in turning operations without chatter vibrations. Chatter vibrations cause poor surface finish. Therefore, preventing these vibrations is an important area of research. Predicting stable

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cutting depths is vital to determine the stable cutting region. In this study, a set of cutting experiments has been used and the stable cutting depths are predicted as a

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function of cutting, modal and tool-working material parameters. Regression analyses, artificial neural networks (ANN) decision trees and heuristic optimization models are

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used to develop the generalization models. The purpose of the models is to estimate stable cutting depths with minimum error. ANN produces better results compared to the

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other models. This study helps operators and engineers to perform turning operations in an appropriate cutting region without chatter vibrations. It also helps to take precautions against chatter.

Keywords: Chatter vibration, ANN, Heuristic optimization, Regression models 1. Introduction

During machining high-precision mechanical parts, the static and dynamic behaviour of the machining system is a critical factor that significantly influences the surface quality. Generally, vibrations in the machining systems can be divided into the sum of the free, forced and self-excited vibrations. Free and forced vibrations can be easily detected and suppressed and their effect is low. In contrast, chatter vibrations negatively affect surface quality of the parts. Additionally, they can lead to abnormal tool wear and tool breakage. Therefore, preventing chatter vibrations is essential. The main reason for

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chatter in turning is the regenerative effect, which is a sum of the instantaneous toolworkpiece relative vibration [1]. Regenerative chatter is effective at medium-high

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cutting speeds. In contrast, at low cutting speeds, the rubbing of the tool major flank against the machined surface, known as process damping, is likely to reduce chatter

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vibrations [2].

Metal machining is often accompanied by severe relative motion between the tool and

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the workpiece, which is referred to as chatter vibration. Turning operations are currently restricted by complicated chatter problems. These chatter problems lead to a severe deterioration of the machined surface, increase the rate of tool wear and decrease the

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spindle life. The problems are challenging because the vibrations cause a reduction in the productivity rate. Chatter vibration produces insufficient surface quality, low accuracy, excessive noise, increased tool wear, increased tool damage and high costs

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[3].

Chatter vibration in machining is prevented by selecting stable cutting parameters. To

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display the combinations of the width of cut and cutting speed, stability maps can be

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developed to determine the stable cutting parameters. As a result, determining stable cutting depths is crucial in machining operations without chatter [4-5].

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Research into chatter vibrations during turning process has a long history. Different analytical models have been developed to predict chatter stability. Studies in the literature are classified according to the number of degrees of freedom (DOF), toolworkpiece flexibilities [6-9] and tool wear and process damping [10-11]. A number of researchers have used Nyquist plots and finite element analyses and have carried out experiments measuring force and vibration in an attempt to estimate chatter stability [12-14]. In recent literature, Urbicain et al.’s [15] study focuses on the problem of identifying stability charts when cutting Inconel 718. The method finds the free-chatter regions in longitudinal chatter when the tool vibrates in the tangential direction. The study proposes a one and two degree of freedom (DOF) dynamic model to carry out the effect of the tangential mode on chip regeneration in the regenerative plane. Tyler and Schmits [16] find an analytical solution for turning and milling stability that involves process damping effects. Comparisons between the new analytical solution, time-

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domain simulation, and experiments are presented. The velocity-dependent process damping model applied in the analysis depends on a single coefficient. The process

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damping coefficient is determined experimentally via a flexure-based machining setup for a chosen tool-workpiece pair. The effects of tool wear and the cutting edge relief angle are also analysed. Otto et al. [17] study chatter vibrations in cutting processes, and

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a unified method for the computation of the stability lobes for the turning, boring, drilling and milling processes in the frequency domain is provided. The method can be

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used for fast and reliable detection of the stability lobes. The presented analysis is appropriate for getting a deep understanding of the chatter stability, which is dependent

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on the parameters of the cutting process and the structure. Chen et al. [18] proposed a new dynamic cutting force model with nominal chip thickness to estimate the stability of interrupted turning, in which the dynamical cutting force is described by a function of

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the nominal chip thickness and the dynamical chip thickness. The stability lobes of interrupted turning are acquired via the full-discretization method and Floquet theory.

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In the literature, some parameters (geometrical, material, etc.) are kept constant, and orthogonal cutting conditions are assumed. Therefore, analytical models were

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developed based on these assumptions. In some circumstances, oblique cutting

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conditions should be taken into account. Moreover, all cutting, geometrical and modal parameters have not been observed at the same time before. Furthermore, soft computing methods have not been used before to predict chatter vibrations. This study investigates all the effective cutting parameters and combines orthogonal and oblique cutting conditions at the same time. The proposed models help operators and engineers to select appropriate parameters without chatter. This study will lead to predict stable cutting depths and stability maps with different cutting parameters. This research attempts to determine the stable cutting depths without chatter. The paper has five parts. First, it reviews the extant literature relevant to chatter stability prediction. Then, soft computing methods used in the study are explained briefly. Subsequently, experimental and computational studies are presented respectively. Next, the findings are discussed and summarized. The paper concludes with a discussion of the theoretical and practical applications and directions for further research.

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2. Soft Computing Methods

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The methods used in the study are explained briefly below. 2.1. Multiple linear regression models

Multiple linear regression models predict the best-fitting linear equation for the output

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values according to the input values. The multiple linear regression equation shows a straight line, which minimises the squared differences between the estimated and real

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output values. This is a popular statistical technique that is used in estimations [19]. Multiple regression models are simple and provide an easily interpreted mathematical

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equation for predictions. This type of modelling is a long-established statistical procedure; therefore, the properties of these models should be well known. The models

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are also easily trained. The multiple linear equations are provided in Eq. (1). The error

(1) (2)

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term is shown in Eq. (2).

B0, Bi: Constant terms

yi: The dependent variable

Xi: The independent variables ei: Error term

The determination coefficient is calculated as follows (Eq.(3)):

(3)

SSerror: Sum of squares for errors SStotal: Sum of squares for total

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2.2. ANN ANN models are basic models of the operation of the nervous system. The standard

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units of neural networks are neurons. A neural network is a basic model that shows how the human brain processes information. This network simulates interconnected

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processing units. The processing units are organised in layers. A neural network is usually composed of three parts: an input layer, an output layer and hidden layers. The

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units are linked to different weights [19]

The network learns by examining specific records. The network generates an estimate

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for each record and changes the weights when an incorrect prediction occurs. This procedure is replicated, and the network improves the estimates until the stopping criteria are achieved. At first, all weights are arbitrary, and the answers are nonsensical.

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The network learns via training, and the responses are compared with the known results during the procedure. Information from this comparison is passed back through the network, and the network slowly alters the weights. After the training, the network can

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be used in future scenarios [19].

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Sum function is given as follows (Eq.(4)):

(4)

xi: Input nodes wi: Weights

b: bias

Different activation functions are used in ANN. An activation function of sigmoid is shown as an example (Eq. (5)):

(5)

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2.3. Classification®ression tree models (CART)

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Decision tree models can be represented as a collection of if-then rule sets that show the information in an understandable way. The decision-tree display is helpful to

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understand how attributes in the data can be divided, or partitioned, into subsets relevant to the problem. The rule set display is beneficial to see how particular groups of items

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relate to a specific conclusion [19].

CART node is a tree-based classification and prediction technique. The technique uses

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recursive partitioning. The purpose is to divide the training data into subgroups with similar output data. CART begins by analyzing the input data to find the best split, measured by the decrease in an impurity index that is caused by the split. The split

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defines two subgroups. These subgroups consequently split into two more subgroups, till one of the stopping criteria is triggered. All splits are binary [19].

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CART permits the tree to grow to a large size before pruning based on more

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complicated criteria. This may cause smaller trees which have better cross-validation properties. An increase in the number of terminal nodes usually decreases the risks in

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the training data [19].

The Gini impurity, information gain, and variance reduction are the metrics used in the model. The metrics are calculated as follows (Eq.(7)-(8)):

(7) (8)

fi: the fraction of items labelled with value i in the set. The variance reduction of node N is defined as the total reduction of the variance of the target variable x resulting from the split at this node (Eq. (9)):

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(9)

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S, St, Sf: the set of presplit sample indices.

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2.4. Heuristic Optimization Models

Genetic, cuckoo search and particle swarm algorithms are explained below.

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2.4.1. Genetic algorithm

A genetic algorithm (GA) is a heuristic algorithm using natural selection and the

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population genetics mechanism [20-21]. The fundamental idea of a GA is about the biological process of survival and adaptation. In the genetic algorithm method, different

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algorithm are given below.

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decision variables are shown using string of finite length code [22-23]. The steps of the

1. Identify the preliminary population.

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2. Identify the fitness of the population. 3. Reproduce the population.

4. Identify the crossover point. 5. Identify if mutation happens. 6. Step 2 is repeated with the new population until the condition is achieved. Mechanisms used in the genetic algorithm are given below. 1. Encoding: The decision variables of a problem are encoded into a finite length string. 2. Selection: Selection mechanism is used to increase the chances of the survival of the fittest individuals. There are many conventional and user specified selection systems particular to the problem configuration [24].

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3. Crossover: The crossover operator plays a crucial role in generating a new generation. The crossover operator brings together two chromosomes to generate a new

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chromosome. 4. Mutation: Mutation consists of the modification of the value of each ‘gene’ of a

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solution. Mutation operation restores lost or unexplored genetic material into the population [25].

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2.4.2. Cuckoo search algorithm

Cuckoo search (CS) is a heuristic optimization algorithm that is developed by Yang and

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Deb [26]. The theory of this algorithm is about cuckoo birds. Three rules are used in this algorithm.

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1. Each cuckoo lays one egg and puts its egg in an arbitrarily selected nest. 2. The best nest with high-quality eggs will continue for the future generation.

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3. The number of available hosts’ nests is fixed, and the egg is laid by a cuckoo by the

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host bird with a probability pa ϵ [0, 1].

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2.4.3. Particle swarm optimization Particle swarm optimization was developed by J. Kennedy and R.C. Eberhart in 1995. This method is used where the gradient is too hard or impossible to derive. It includes many desirable properties like low computation and easy to use. In particle swarm optimization, particles set their movements in a search plane using their flying experience and their neighbours. Each particle has its own pieces of information. These are position (xi), velocity (vi) and its best position (pbesti). At first, particles are

randomly distributed throughout the solution space. Each particle has its random velocities which are assigned initially [27]. Following rules are valid for each particle (Eq. (10)-(11)). (10)

(11)

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should be provided to avoid particle to get out of feasible solution space. : acceleration coefficients

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,

,

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: best location of particle’s neighbour

: two random numbers that show sthocastic behaviour of the algorithm

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d: dimension of solution space

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k: the number of iteration 2.4.3.1. PSO with fmincon

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After PSO terminated, it calculates the minimum value of the objective function with given constraints and bounds below (Eq.12-16).

c x   0

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ceq x   0

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Constraints:

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Objective function: min f(x)

A.x  b

Aeq.x  beq

(12) (13) (14) (15)

Bounds:

lowerbound  x  upperbound

(16)

b, beq: vectors A, Aeq: matrices c(x), ceq(x): functions that return vectors, might be nonlinear f(x): function that returns a scalar, might be nonlinear

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x, lb, ub: vectors or matrices that show boundary limits The method uses interior-point, trust reflective, sequential quadratic programming and

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active set algorithms [28]. 2.4.3.2. PSO with Pattern Search

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After PSO terminated, Pattern search searches a local minimum of a function with starting point X0 and using the constraints which are given below (Eq. 17-18) [28].

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Pattern search is used for non-continuous or non-differentiable functions.

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A.x  b Aeq.x  beq

(18)

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3. Experimental Study

(17)

Hammer and cutting tests were carried out during experiments to obtain vibration

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3.1.1. Hammer test

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characteristics. Details are given below.

An accelerometer was connected in the feeding direction, and the hammer hit in the X

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direction. After the hammer test, all data were processed using the Cut-Pro 8.0 software, and the structural coefficients were calculated. The mass (m), stiffness coefficient (k), damping ratio (ζ), and natural frequency (wn) of the tool were evaluated during the

hammer test. The tests were performed using a hammer by connecting different overhang length of tools. The hammer test was performed separately for each overhang length of tools because the rigidity of the system changes for every setup. The hammer test was performed after the tool was set. Hammer test is shown in Figure 1.

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3.1.2. Cutting test

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Figure 1. Hammer test

AISI 4140, AISI 1040, Al-2024, Al-7075, and Inconel 718 materials were used in the

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experiments. The cutting speeds were 355, 500, and 710 rpm. The chatter sound was recorded using a microphone and processed using a program in the LabView 7.1 software package. The LabView 7.1 software was used during the cutting tests to investigate the stable cutting depths without chatter. The stable cutting depths were obtained by trying different cutting depths at different cutting speeds. Cutting test is shown in Figure 2.

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Figure 2. Cutting test

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Detailed explanation about experiments is given in Turkes’s [29] and Sofuoglu’s [30-

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31] studies. The results of the experiments are given in the Appendix. 4. Computational Study

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In the computational study, experimental results are taken from Turkes [29], Sofuoglu [30, 31] and Gok [32] and are given in the Appendix (Table A.1.). The stable cutting depth is a dependent variable, whereas the different workpieces and insert materials, geometries, cutting and modal parameters are independent variables. The data (192 points) were taken into consideration and randomly divided into 122 training experiments (Table A.2.) and 70 test experiments. 4.1. Multiple regression analysis Multiple regression models were developed to predict the stable cutting depths. The enter method was used in the models. The independent variables are given in Table 1. The dependent variable is the stable cutting depth. Three different models were developed, and the determination coefficients were calculated.

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Table 1. The independent variables of the developed models Model 2

Model 3

Workpiece diameter

Workpiece diameter

Workpiece length

Workpiece length

Workpiece length

Tool overhang length

Tool overhang length

Tool overhang length

Tool length

Stiffness coefficient

Damping ratio

Damping ratio

Tool length

Tool cross section

Approach angle

Tool length

End cutting angle

Approach angle

Side rake angle

End cutting angle

Workpiece hardness

Side relief angle

The number of revolutions

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Approach angle

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Workpiece hardness

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The number of revolutions

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Side rake angle

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Workpiece hardness The number of revolutions

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Model 1

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The determination coefficients of the regression models are shown in Table 2. Taking into account determination coefficients in training and testing stage, the first model produces better results compared to the other models. The performance of the three models is nearly identical. Although the third model includes fewer independent variables, the training and testing performance of this model is close to the other developed models.

Table 2. The determination coefficients (R2) of the three developed models Models

Training (R2)

Testing (R2)

1st model

0.904

0.859

2nd model

0.901

0.846

3rd model

0.863

0.839

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4.2. ANN ANN models have been developed to predict stable cutting depths. The input layer of the models are given in Table 4.

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Table 3. The input layer nodes in the models

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nodes are given in Table 3. The output node is the stable cutting depth. The parameters

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Input nodes Workpiece diameter

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Workpiece length

Tool overhang length Stiffness coefficient

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Damping ratio

Tool cross section

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Tool length

Approach angle

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End clearance angle Back rake angle End cutting angle Side relief angle Side rake angle Insert hardness

Workpiece hardness The number of revolutions

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Table 4. The parameters used in the learning stage of the ANN

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Parameters Properties that are selected: Set random seed, Prevent overtraining Stop on accuracy: %95-%97 Optimize: memory Mode: Simple The number of output layers: 1 The number of input layers: 16

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In Table 5, the results of five different training methods are shown. One hidden layer was used in the Quick, Prune and Multiple models, whereas two hidden layers were

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used in the other models. Three, four, and nine neurons have been used in the hidden layer of the Quick, Multiple, and Prune models, respectively. In total, 230 and 11 neurons have been used in the Dynamic model; and 30 and 20 neurons have been used

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in the Exhaustive Prune model. The Dynamic and Exhaustive Prune models contain more hidden layers and number of neurons.

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Table 5. The results of trained neural network models

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Topologystatistical results

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Quick

Dynamic

Training methods

Multiple

Prune

Exhaustive Prune

The topology

16:3:1

16:230:11:1

16:4:1

16:9:1

16:30:20:1

of the models The lowest

-1.93

-1.45

-1.681

-1.47

-1.79

error The highest

1.99

2.058

2.168

1.97

1.83

error Mean Squared

0.2552

0.200

0.1955

0.2709

0.2619

Error Mean absolute

0.1180

0.082

0.09

0.137

0.13

error Determination

0.92

0.94

0.94

0.918

0.918

1.7381

1.6369

1.7433

1.6762

1.7617

2

coefficient (R ) Standard Error

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The models that best fit the data are the Dynamic and Multiple models in the training stage. The results of the Quick, Prune and Exhaustive Prune models are similar. To

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examine the results of the model, the models were further tested. The determination coefficients of the training and testing stages are shown in Table 6. The models that have fit the data most are Dynamic, Multiple and Prune in the testing stage. The

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predicted values according to different models are given in the Appendix (Table A.3.). Stability diagrams with real and predicted values are given for Al-2024 and AISI-1040

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in Figure 3-4. Predicted results are very close to the experimental data.

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Table 6. The training and testing results of the neural networks Training (R2)

Testing (R2)

Quick

0.92

0.854

Dynamic

0.94

0.885

0.94

0.887

0.918

0.887

0.918

0.854

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Models

Multiple

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Exhaustive Prune

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Prune

Figure 3. Stability map for Al-2024 material with real and predicted values

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Figure 4. Stability map for AISI-1040 material with real and predicted values Taking into account determination coefficients in training and testing stage, Multiple

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4.3. CART

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model produces better results compared to the other models.

In this stage, five different models were developed. The first model has two tree depths,

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whereas the fifth model has six tree depths. The inputs of the models are given in Table 7. The output is the stable cutting depth. The determination coefficients of the five models are given in Table 8 for both the training and testing stage. Increasing the tree depth enhances the performance of the models. Although undesired results for the first and second models in the training stage were noted, the testing results agree with the experimental data.

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Table 7. Inputs of the models Inputs

1st model

Workpiece hardness,

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Models

The number of revolutions Workpiece hardness

2nd model

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Insert hardness

Approach angle

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The number of revolutions Workpiece hardness

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3rd model

Approach angle Insert hardness

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Tool overhang length

The number of revolutions Workpiece hardness

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4th model

5th model

Stiffness coefficient

The number of revolutions Approach angle Insert hardness Tool overhang length Stiffness coefficient Damping ratio Workpiece hardness The number of revolutions Approach angle Insert hardness Tool overhang length Stiffness coefficient Damping ratio Workpiece diameter

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Table 8. The determination coefficients of five developed models

1st model

2

0.521

2nd model

3

0.773

3rd model

4

0.936

4th model

5

0.876

5th model

6

0.893

Testing (R2)

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Training (R2)

0.859 0.846

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Tree depth

0.839 0.817 0.828

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Models

Taking into account determination coefficients in training and testing stage, the third

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model produces better results compared to the other models.

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4.4. Heuristic optimization models

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Heuristic linear models were developed in the training process, and the testing procedure was applied for validation. The objective function of the linear model is

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defined in Eq. (19)-(20). Objective function:

(19) (20)

experimental stable cutting depths (mm). : predicted stable cutting depths (mm).

: error between experimental and predicted values.

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The bounds of the linear model are given in Table 9. The magnitudes and signs of the bounds are determined based on a previous study [31]. Simulations have been run on a

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Pentium PC with 2.13 GHz Intel Processor and 2 GB of RAM.

Upper bounds 20 0 0 20 20 20 20 0 0 0 20 20 20 0 20 0

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Lower bounds 0 -20 -20 0 0 0 0 -20 -20 -20 0 0 -20 -20 -20 -20

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Variables Workpiece diameter (X1) Workpiece length (X2) Tool overhang length (X3) Stiffness coefficient (X4) Damping ratio (X5) Tool cross section (X6) Tool length (X7) Approach angle (X8) End clearance angle (X9) Back rake angle (X10) End cutting angle (X11) Side relief angle (X12) Side rake angle (X13) Workpiece hardness (X14) Insert hardness (X15) The number of revolutions (X16)

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Table 9. Variables, lower and upper bounds

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4.4.1. Genetic algorithm

According to Table 9 (bounds) and Eq. (19-20) (objective function), genetic algorithm has been used to predict stable cutting depths. Different population sizes (50, 100, 200, 300), reproduction crossover fractions (0.5, 0.7, 0.8, 0.9, 1) and crossover functions (scatter, single point, two point, intermediate, heuristic) have been tried to tune parameters accurately. The parameters and results of the model are given in Table 10. Table 10. The parameters and results of the genetic algorithm Parameters-statistical variables Population size Crossover fraction Crossover function Function evaluations Computational time (minutes) Objective function value R2 (training)

Values 300 0.8 Heuristic (Crossover ratio:1.5) 137700 2.14 97.1 0.796

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R2 (testing)

0.795

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Convergence behavior of the algorithm is given in Figure 5. Figure 5 reveals that there

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d

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has been sharp drop in 100 iterations. After 100 iterations, it decreases slowly.

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Figure 5. Convergence behavior of the genetic algorithm 4.4.2. Cuckoo search algorithm According to Table 9 (bounds) and Eq. (19-20) (objective function), cuckoo search algorithm has been used to predict stable cutting depths. Different discovery rates (between 0-1) and levy exponents (between 1-5) have been tried to tune parameters accurately. The parameters and results of the model are shown in Table 11. Table 11. The parameters and results of the cuckoo search algorithm Parameters-statistical variables The number of nests The number of iterations Discovery rate Levy exponent Computational time (minutes) Objective function value R2 (training) R2 (testing)

Values 25 200000 0.05 1 2.46 37.34 0.904 0.858

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4.4.3. Particle swarm algorithm

According to Table 9 (bounds) and Eq. (19-20) (objective function), particle swarm

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algorithm has been used to predict stable cutting depths. Different self adjustment coefficients (0.5, 1, 1.5, 2, 2.5 ), social adjustment coefficients (0.5, 1, 1.5, 2, 2.5), swarm size (25, 50, 75, 100, 125, 150, 160) and inertia rates (between 0-1) have been

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tried to tune parameters accurately. The parameters and results of the model are presented in Table 12.

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Parameters-statistical variables The number of nests The number of iterations Function evaluations Self adjustment coefficient Social adjustment coefficient Swarm size Inertia rate Computational time (minutes) Objective function value R2 (training) R2 (testing)

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Table 12. The parameters and results of the particle swarm algorithm Values 25 1808 180900 0.5 1 100 [0.3-0.7] 2.41 37.34 0.904 0.857

Convergence behaviour of the algorithm is shown in Figure 6. Figure 6 shows that there has been steep decline in 400 iterations. After 400 iterations, it decreases slowly.

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Figure 6. Convergence behaviour of the particle swarm algorithm Particle swarm algorithm has also hybrid function options. Using same parameter

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values in Table 12, pattern search and fmincon options have been selected. These hybrid

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function options have been used after the particle swarm algorithm terminated. The results of hybrid function options are given in Table 13. The results are improved

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slightly compared to the non-hybrid particle swarm algorithm. The coefficients of the particle swarm algorithm-fmincon are presented in Table 14. Table 13. The results of hybrid function options in the particle swarm algorithm Hybrid algorithms

Training (R2)

Testing (R2)

Particle swarm algorithm-Pattern search Particle swarm algorithmfmincon

0.904

0.904

Function evaluations

Computational time (minutes)

0.8575

Objective function value 37.34

263300

3.5

0.8582

37.34

207600

2.77

Table 14. The coefficients of the particle swarm algorithm-fmincon Coefficients Coefficients

X1 0.043 X10 -0.56

X2 - 0.003 X11 0.0226

X3 -0.04 X12 0.211

X4 0 X13 0.365

X5 9.60 X14 -0.026

X6 0.0006 X15 0.002

X7 0.076 X16 -0.005

X8 0

X9 -0. 69

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5. Discussion Different models used in this study are compared in Table 15 according to

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determination coefficients. ANN and all heuristic optimization models include 16 criteria which are given in Table 3 and Table 9, whereas Regression and CART model

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contain 13 and 6 criteria and they are given in Table 1 and Table 7 respectively. ANN model produces better results according to determination coefficients in training and

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testing stage compared with the other models. CART algorithm, regression model and the other heuristic optimization models have also produced successful results. Except

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genetic algorithm, there is a slight difference between models.

Table 15. Comparison of different soft computing models according to determination

Training (R2) 0.904 0.94 0.936 0.796 0.904 0.904

Testing (R2) 0.859 0.887 0.86 0.795 0.858 0.857

0.904

0.8575

0.904

0.8582

Ac ce p

te

d

Models Regression (1st model) ANN (Multiple) CART algorithm (3rd model) Genetic algorithm Cuckoo search algorithm Non hybrid particle swarm algorithm Particle swarm algorithm-Pattern search Particle swarm algorithm-fmincon

M

coefficients

In Table 16, computational time and objective function values are compared for heuristic optimization models. During analyses, it has been observed that appropriate parameter tuning of heuristic models decreases computational time. It has been obtained that computational time of the models is nearly same, whereas cuckoo search and particle swarm algorithms have lower objective function values than genetic algorithm. Non hybrid particle swarm algorithm is superior to the other models taking into consideration computational time and objective function values.

Page 25 of 46

Table 16. Comparison of heuristic optimization models according to computational time and objective function value Objective function values 97.1 37.34 37.34

3.5

37.34

cr

ip t

Computational time (minutes) 2.14 2.46 2.41

2.77

37.34

us

Heuristic optimization models Genetic algorithm Cuckoo search algorithm Non hybrid particle swarm algorithm Particle swarm algorithm-Pattern search Particle swarm algorithm-fmincon

Comparison of experimental and ANN results are presented in Figure 7. Experimental

an

data and predicted results are close and the data fit well. If the cutting depth exceeds stable cutting depth limits, chatter vibrations will occur and the cutting operation is

Ac ce p

te

d

M

unstable.

Figure 7. Comparison of experimental and computational results in testing stage for

ANN (Multiple model) In Table 17, criteria are given according to their relative contribution to stable cutting depths. Workpiece hardness and the number of revolutions are more effective variables than the others for five models.

Page 26 of 46

Table 17. Criteria and their relative contributions in ANN models.

Quick Dynamic Multiple Prune Exhaustive Prune

0.41 0.35 0.46 0.40 0.40

The number of revolutions (rpm) 0.33 0.33 0.33 0.34 0.35

The other parameters (14 parameters) 0.26 0.32 0.21 0.26 0.25

ip t

Workpiece hardness (HV)

us

cr

Models

The summary of the regression model is given in Table 18. The results show that increase in workpiece hardness and the number of revolutions leads to decrease in stable

an

cutting depth.

Unstandardized Coefficients B 26.538 4.25E-002 -2.53E-002 -3.48E-002 1.74E-008 10.062 5.33E-004 7.31E-002 -0.216 4.49E-002 -0.121 0.359 -2.65E-002 -5.23E-003

te

Ac ce p

(Constant) Workpiece diameter Workpiece length Tool overhang length Stiffness coefficient Damping ratio Tool cross section Tool length Approach angle End cutting angle Side relief angle Side rake angle Workpiece hardness The number of revolutions

Std. Error 2.535 .015 .004 .007 .000 2.592 .001 .018 .025 .014 .060 .094 .002 .000

d

Variables

M

Table 18. The summary of the regression model (Model-1)

Standardized Coefficients Beta .254 -.562 -.284 .067 .135 .034 .447 -.989 .332 -.193 .431 -1.007 -.596

t

Sig.

10.467 2.892 -5.966 -4.899 .942 3.881 .522 4.097 -8.548 3.238 -2.004 3.820 -12.835 -17.859

.000 .005 .000 .000 .348 .000 .602 .000 .000 .002 .048 .000 .000 .000

The proposed models are new methods to avoid chatter vibration compared to different analytical models in the literature. This method can be used and it is easily applicable to different manufacturing environments. It helps operators, engineers and the other decision

makers

to

predict

proper

cutting-tool

conditions

without

chatter.

Approximately 200 data have been used in the models so it also produces reliable results. Furthermore, the models calculate stable cutting depths in a faster way compared to the other analytical methods. These results help operators to choose cutting-tool conditions without chatter vibrations in rough and finish machining.

Page 27 of 46

5. Conclusions In this study, different soft computing models have been developed to predict the stable

ip t

cutting depths. The factors that affect the stable cutting depth have been observed with an experimental study [29-32]. Data have been combined from these studies for

cr

computational study. Taking into account all the models, ANN produced successful results compared with the other models. Moreover, except genetic algorithm, there are

us

slight differences between heuristic, regression and decision tree models according to the determination coefficient performance values. It has been observed that workpiece

an

hardness and the number of revoulutions are effective criteria to avoid chatter problem. In the next studies, different prediction methods (support vector machine etc.) might be developed with addition of different experiments. Also, further research might explore

M

the prediction of stable cutting depths for different process (milling, drilling, etc.) without chatter. Additionally, different optimization models (artificial bee colony

te

References

d

algorithms etc.) might be developed.

Ac ce p

[1] Y. Altintas, E. Weck, Chatter stability of metal cutting and grinding, CIRP Annals – Manufacturing Technology, 53, (2004), p.619–642. [2] Y. Altintas, M. Eynian, H. Onozuka, Identification of dynamic cutting force coefficients and chatter stability with process damping, CIRPAnnals - Manufacturing Technology, 57, (2008), p.371–374. [3] G. Quintana, F.J. Campa, J. Ciurana, L.N. Lopez de Lacalle, Productivity improvement through chatter-free milling in workshops, Proc. IMechE Part B: J. Eng. Manuf., 225, (2011), p. 1163-1174. [4] J. Tlusty, Manufacturing Processes and Equipment Prentice Hall, New Jersey, USA, (2000). [5] C.M. Taylor, N.D. Sims, S.Turner, Process damping and cutting tool geometry in machining, Materials Science and Engineering, vol. 26, (2011), p. 1-17 [6] E.Budak, E.Ozlu, Analytical modelling of chatter stability in turning and boring operations: a multi-dimensional approach, CIRPAnnals—Manufacturing Technology 56 (2007) 401–404.

Page 28 of 46

[7] E.Ozlu, E.Budak, Comparison of one-dimensional and multi-dimensional models instability analysis of turning operations, International Journal of Machine Tools and Manufacture 47 (2007) 1875–1883.

ip t

[8] Z.Dombovari, D.A.W.Barton, R.Eddie Wilson, G.Stepan, On the global dynamics of chatter in the orthogonal cutting model, International Journal of Non-Linear Mechanics 46 (2011) 330–338.

us

cr

[9] G.Urbikain, L.N. Lopez deLacalle, F.J.Campa, A.Fernandez, A.Elias, Stability prediction in straight turning of a flexible workpiece by collocation method, International Journal of Machine Tools and Manufacture 54–55 (2012) 73–81.

an

[10] Y.Kurata, S.D.Merdol, Y.Altintas, N.Suzuki, E.Shamoto, Chatter stability in turning and milling within process identified process damping, Journal of Advanced Mechanical Design Systems and Manufacturing 4 (2010). 1107–1118.

M

[11] L.T. Tunc, E.Budak, Effect of cutting conditions and tool geometry on process damping in machining, International Journal of Machine Tools and Manufacture 57 (2012) 10–19

d

[12] N.Suzuki, K.N.E.Shamoto, K.Yoshino, Effect of cross transfer function on chatter stability in plunge cutting, Journal of Advanced Mechanical Design, Systems, and Manufacturing 4 (2010) 883–891

Ac ce p

te

[13] C.M.Taylor, S.Turner, N.D.Sims, Chatter, process damping, and chip segmentation in turning: a signal processing approach, Journal of Sound and Vibration 329 (2010) 4922-4935. [14] E.Turkes, S.Orak, S.Neseli, S.Yaldiz, Linear analysis of chatter vibration and stability for orthogonal cutting in turning, International Journal of Refractory Metals and Hard Materials 29 (2011) 163-169. [15] G. Urbicain, A. Palacios, A. Fernandez, A.Rodrigues, L.N. Lacalle, A.E. Zuniga, Stability Prediction Maps in Turning of Difficult-to-cut Materials. Procedia Engineering 63, (2013), 514–522 [16] C.T. Tyler, T.L. Schmitz, Analytical process damping stability prediction. Journal of Manufacturing Processes, 15, (2013), 69–76 [17] A. Otto, S. Rauh, M. Kolouch, Extension of Tlusty’s law for the identification of chatter stability lobes in multi-dimensional cutting processes, International Journal of Machine Tools and Manufacture, 82-83, (2014), p.50-58 [18] L. Chen, L. Zhang, J. Man, Effect of Nominal Chip Thickness on Stability of Interrupted Turning. Advances in Mechanical Engineering, (2014), 1–7 [19] SPSS Clementine 11.1 Help Topics, Integral Solutions, USA, (2007).

Page 29 of 46

[20] J. H. Holland, Hierarchical descriptions of universal spaces and adaptive systems, (1968)

ip t

[21] J. Holland, Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor. (Technical Report ORA Projects 01252 and 08226).Ann Arbor: University of Michigan, Department of Computer and Communication Sciences, (1975)

cr

[22] D. E Goldberg, and C. H. Kuo, Genetic algorithms in pipeline optimization, J. Computing in Cïv. Engrg., ASCE, 1(2), (1987), 128-141,

us

[23] D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison- Wesley Publishing Co., Inc., Reading, Mass, (1989).

an

[24] R. Sivaraj and T. Ravichandran, Review of selection methods in genetic algorithm, International Journal of Engineering Science and Technology (IJEST), 3(5), (2011), 3792-3797.

M

[25] M. Srinivas and L. M. Patnaik, Adaptive Probabilities of Crossover and Mutation in Genetic Algorithms, IEEE Transactions on systems, man and cybernetic, 24(4), (1994), 656-667

te

d

[26] X.S. Yang, and Deb. S. Cuckoo search via Lévy flights. In World Congress on Nature and Biologically Inspired Computing (NaBIC 2009), USA: IEEE, (2009), 210– 214.

Ac ce p

[27] G. S. Tewolde, D. M. Hanna, and R. E. Haskell, “Enhancing performance of PSO with automatic parameter tuning technique,” in Proc. IEEE Swarm Intell. Symp., (2009), pp. 67-73. [28] Matlab Help Topics, Mathworks, USA, (2015). [29] E. Turkes, Theoretical and experimental analysis of process damping in machine tool chatter vibration, PhD. Thesis, University of Osmangazi, Eskisehir, Turkey, (2007) [30] M. A. Sofuoglu, Investigation of Chatter Stability Limits and Chatter Vibration in Turning Operations Using Artificial Neural Networks, Master thesis, University of Osmangazi, Eskisehir, Turkey, (2015). [31] M.A. Sofuoglu, Sezan Orak, Hybrid Decision Making Approach to Prevent Chatter Vibrations, Applied Soft Computing Journal (2015) (Article in Press) [32] F. Gok, Investigation the effect of insert material on chatter vibration in turning operations, Master thesis, University of Osmangazi, Eskisehir, Turkey, (2015) [Unpublished].

Page 30 of 46

ip t

Vitae

cr

Mehmet Alper Sofuoglu

He is a research assistant in the department of Mechanical Engineering Department at

us

the Eskisehir Osmangazi University. He is studying his Master of Science at Eskisehir Osmangazi University. He has focussed on manufacturing and mechanical vibrations.

an

He has collaborated actively with researchers in several other disciplines of Industrial

Sezan Orak

te

d

M

Engineering and Management.

Ac ce p

She is an Assistant Professor Doctor in the department of Mechanical Engineering Department at the Eskisehir Osmangazi University. She completed her Ph.D. at Anadolu University. She has focused on mechanical, chatter vibrations and manufacturing issues in recent years.

Page 31 of 46

ip t cr us an M d te Ac ce p

APPENDIX

Page 32 of 46

ip t cr

Table A.1. The results of the experiments Workpiece length (mm)

Overhang length (mm)

Workpiece material

Natural frequency (Hz)

Stiffness coefficient(N/m)

1

1010

60

300

70

1696

2.15E+07

2

1010

60

300

70

1696

2.15E+07

3

1010

60

300

70

1696

4

1010

60

300

70

1696

5

1010

60

300

70

1696

6

1010

60

300

70

1696

7

1010

60

300

70

1696

8

1010

60

300

80

1101

9

1010

60

300

80

1101

10

1010

60

300

80

11

1010

60

300

12

1010

60

300

13

1010

60

14

1010

60

15

1010

60

16

1010

60

17

1010

60

18

1010

60

19

1010

60

20

1010

21

1010

22

1010

23

1010

24

Damping ratio

Tool cross section (mm2)

Tool length (mm)

Approach angle (0)

End relief angle (0)

Back rake angle (0)

1.92E-02

400

130

90

7

0

1.92E-02

us

Experiment no

Workpiece diameter (mm)

130

90

7

0

1.92E-02

400

130

90

7

0

2.15E+07

1.92E-02

400

130

90

7

0

2.15E+07

1.92E-02

400

130

90

7

0

2.15E+07

1.92E-02

400

130

90

7

0

2.15E+07

1.92E-02

400

130

90

7

0

1.02E+07

3.97E-02

400

130

90

7

0

1.02E+07

3.97E-02

400

130

90

7

0

1101

1.02E+07

3.97E-02

400

130

90

7

0

80

1101

1.02E+07

3.97E-02

400

130

90

7

0

80

1101

1.02E+07

3.97E-02

400

130

90

7

0

300

80

1101

1.02E+07

3.97E-02

400

130

90

7

0

300

80

1101

1.02E+07

3.97E-02

400

130

90

7

0

300

90

944.6

5.71E+06

4.15E-02

400

130

90

7

0

300

90

944.6

5.71E+06

4.15E-02

400

130

90

7

0

300

90

944.6

5.71E+06

4.15E-02

400

130

90

7

0

300

90

944.6

5.71E+06

4.15E-02

400

130

90

7

0

ce pt

ed

M an

400

2.15E+07

90

944.6

5.71E+06

4.15E-02

400

130

90

7

0

300

90

944.6

5.71E+06

4.15E-02

400

130

90

7

0

60

300

90

944.6

5.71E+06

4.15E-02

400

130

90

7

0

60

300

100

839.3

5.24E+06

1.75E-02

400

130

90

7

0

60

300

100

839.3

5.24E+06

1.75E-02

400

130

90

7

0

1010

60

300

100

839.3

5.24E+06

1.75E-02

400

130

90

7

0

25

1010

60

300

100

839.3

5.24E+06

1.75E-02

400

130

90

7

0

26

1010

60

300

100

839.3

5.24E+06

1.75E-02

400

130

90

7

0

Ac

300

60

Page 33 of 46

ip t cr

Table A.1. The results of the experiments (continued) 60

300

100

839.3

5.24E+06

28

1010

60

300

100

839.3

5.24E+06

29

1010

60

300

110

768.5

4.50E+06

30

1010

60

300

110

768.5

4.50E+06

31

1010

60

300

110

768.5

32

1010

60

300

110

768.5

33

1010

60

300

110

768.5

34

1010

60

300

110

768.5

35

1010

60

300

110

768.5

36

1050

60

300

70

1644

37

1050

60

300

70

1644

38

1050

60

300

70

1644

39

1050

60

300

70

40

1050

60

300

41

1050

60

300

42

1050

60

43

1050

60

44

1050

60

45

1050

60

46

1050

60

47

1050

48

1050

49

1050

50

1050

51 52

1.75E-02

400

130

90

7

0

1.75E-02

400

130

90

7

0

3.90E-02

400

130

90

7

0

3.90E-02

400

130

90

7

0

us

1010

M an

27

3.90E-02

400

130

90

7

0

4.50E+06

3.90E-02

400

130

90

7

0

4.50E+06

3.90E-02

400

130

90

7

0

4.50E+06

3.90E-02

400

130

90

7

0

4.50E+06

3.90E-02

400

130

90

7

0

2.24E+07

2.56E-02

400

130

90

7

0

2.24E+07

2.56E-02

400

130

90

7

0

2.24E+07

2.56E-02

400

130

90

7

0

1644

2.24E+07

2.56E-02

400

130

90

7

0

70

1644

2.24E+07

2.56E-02

400

130

90

7

0

70

1644

2.24E+07

2.56E-02

400

130

90

7

0

300

70

1644

2.24E+07

2.56E-02

400

130

90

7

0

300

80

1097

7.32E+06

2.00E-02

400

130

90

7

0

300

80

1097

7.32E+06

2.00E-02

400

130

90

7

0

300

80

1097

7.32E+06

2.00E-02

400

130

90

7

0

300

ce pt

ed

4.50E+06

1097

7.32E+06

2.00E-02

400

130

90

7

0

300

80

1097

7.32E+06

2.00E-02

400

130

90

7

0

60

300

80

1097

7.32E+06

2.00E-02

400

130

90

7

0

60

300

80

1097

7.32E+06

2.00E-02

400

130

90

7

0

60

300

90

1055

8.39E+06

2.67E-02

400

130

90

7

0

1050

60

300

90

1055

8.39E+06

2.67E-02

400

130

90

7

0

1050

60

300

90

1055

8.39E+06

2.67E-02

400

130

90

7

0

53

1050

60

300

90

1055

8.39E+06

2.67E-02

400

130

90

7

0

54

1050

60

300

90

1055

8.39E+06

2.67E-02

400

130

90

7

0

Ac

80

60

Page 34 of 46

ip t cr

Table A.1. The results of the experiments (continued) 60

300

90

1055

8.39E+06

56

1050

60

300

90

1055

8.39E+06

57

1050

60

300

100

801.9

4.53E+06

58

1050

60

300

100

801.9

4.53E+06

59

1050

60

300

100

801.9

60

1050

60

300

100

801.9

61

1050

60

300

100

801.9

62

1050

60

300

100

801.9

63

1050

60

300

100

801.9

64

1050

60

300

110

801.3

65

1050

60

300

110

801.3

66

1050

60

300

110

801.3

67

1050

60

300

110

68

1050

60

300

69

1050

60

300

70

1050

60

71

7075

60

72

7075

60

73

7075

60

74

7075

60

75

7075

76

7075

77

7075

78

7075

79 80

2.67E-02

400

130

90

7

0

2.67E-02

400

130

90

7

0

1.52E-02

400

130

90

7

0

1.52E-02

400

130

90

7

0

us

1050

M an

55

1.52E-02

400

130

90

7

0

4.53E+06

1.52E-02

400

130

90

7

0

4.53E+06

1.52E-02

400

130

90

7

0

4.53E+06

1.52E-02

400

130

90

7

0

4.53E+06

1.52E-02

400

130

90

7

0

4.76E+06

1.36E-02

400

130

90

7

0

4.76E+06

1.36E-02

400

130

90

7

0

4.76E+06

1.36E-02

400

130

90

7

0

801.3

4.76E+06

1.36E-02

400

130

90

7

0

110

801.3

4.76E+06

1.36E-02

400

130

90

7

0

110

801.3

4.76E+06

1.36E-02

400

130

90

7

0

300

110

801.3

4.76E+06

1.36E-02

400

130

90

7

0

300

70

1520

2.28E+07

2.39E-02

400

130

90

7

0

300

70

1520

2.28E+07

2.39E-02

400

130

90

7

0

300

70

1520

2.28E+07

2.39E-02

400

130

90

7

0

300

ce pt

ed

4.53E+06

1520

2.28E+07

2.39E-02

400

130

90

7

0

300

70

1520

2.28E+07

2.39E-02

400

130

90

7

0

60

300

70

1520

2.28E+07

2.39E-02

400

130

90

7

0

60

300

70

1520

2.28E+07

2.39E-02

400

130

90

7

0

60

300

90

973.6

6.60E+06

3.33E-02

400

130

90

7

0

7075

60

300

90

973.6

6.60E+06

3.33E-02

400

130

90

7

0

7075

60

300

90

973.6

6.60E+06

3.33E-02

400

130

90

7

0

81

7075

60

300

90

973.6

6.60E+06

3.33E-02

400

130

90

7

0

82

7075

60

300

90

973.6

6.60E+06

3.33E-02

400

130

90

7

0

Ac

70

60

Page 35 of 46

ip t cr

Table A.1. The results of the experiments (continued) 60

300

90

973.6

6.60E+06

84

7075

60

300

90

973.6

6.60E+06

85

7075

60

300

110

732.5

4.53E+06

86

7075

60

300

110

732.5

4.53E+06

87

7075

60

300

110

732.5

88

7075

60

300

110

732.5

89

7075

60

300

110

732.5

90

7075

60

300

110

732.5

91

7075

60

300

110

732.5

92

1050

60

300

70

1178

93

1050

60

300

70

1178

94

1050

60

300

70

1178

95

1050

60

300

70

96

1050

60

300

97

1050

60

300

98

1050

60

300

1050

60

1050

60

101

1050

60

102

1050

60

103

1050

104

1050

105

1050

106

1050

107 108

400

130

90

7

0

3.33E-02

400

130

90

7

0

9.54E-02

400

130

90

7

0

9.54E-02

400

130

90

7

0

9.54E-02

400

130

90

7

0

4.53E+06

9.54E-02

400

130

90

7

0

4.53E+06

9.54E-02

400

130

90

7

0

4.53E+06

9.54E-02

400

130

90

7

0

4.53E+06

9.54E-02

400

130

90

7

0

2.12E+07

2.39E-02

625

130

90

7

0

2.12E+07

2.39E-02

625

130

90

7

0

2.12E+07

2.39E-02

625

130

90

7

0

1178

2.12E+07

2.39E-02

625

130

90

7

0

70

1178

2.12E+07

2.39E-02

625

130

90

7

0

70

1178

2.12E+07

2.39E-02

625

130

90

7

0

70

1178

2.12E+07

2.39E-02

625

130

90

7

0

ed

4.53E+06

ce pt

99 100

3.33E-02

us

7075

M an

83

300

90

982.8

1.41E+07

3.33E-02

625

130

90

7

0

300

90

982.8

1.41E+07

3.33E-02

625

130

90

7

0

300

90

982.8

1.41E+07

3.33E-02

625

130

90

7

0

300

982.8

1.41E+07

3.33E-02

625

130

90

7

0

300

90

982.8

1.41E+07

3.33E-02

625

130

90

7

0

60

300

90

982.8

1.41E+07

3.33E-02

625

130

90

7

0

60

300

90

982.8

1.41E+07

3.33E-02

625

130

90

7

0

60

300

110

717.9

4.56E+06

9.54E-02

625

130

90

7

0

1050

60

300

110

717.9

4.56E+06

9.54E-02

625

130

90

7

0

1050

60

300

110

717.9

4.56E+06

9.54E-02

625

130

90

7

0

109

1050

60

300

110

717.9

4.56E+06

9.54E-02

625

130

90

7

0

110

1050

60

300

110

717.9

4.56E+06

9.54E-02

625

130

90

7

0

Ac

90

60

Page 36 of 46

ip t cr

Table A.1. The results of the experiments (continued) 60

300

110

717.9

4.56E+06

112

1050

60

300

110

717.9

4.56E+06

113

1010

60

300

70

1624

2.90E+06

114

1010

60

300

70

1624

2.90E+06

115

1010

60

300

70

1624

116

1010

60

300

80

1403

117

1010

60

300

80

1403

118

1010

60

300

80

1403

119

1010

60

300

90

1216

120

1010

60

300

90

1216

121

1010

60

300

90

1216

122

1050

60

300

70

1348

123

1050

60

300

70

124

1050

60

300

125

1050

60

300

126

1050

60

127

1050

60

128

1050

60

129

1050

60

130

1050

60

131

1050

132

1050

133

1050

134

1050

135 136

9.54E-02

625

130

90

7

0

9.54E-02

625

130

90

7

0

9.81E-02

400

110

72

3

-3

9.81E-02

400

110

72

3

-3

us

1050

M an

111

9.81E-02

400

110

72

3

-3

2.17E+06

6.28E-02

400

110

72

3

-3

2.17E+06

6.28E-02

400

110

72

3

-3

2.17E+06

6.28E-02

400

110

72

3

-3

1.44E+06

2.21E-02

400

110

72

3

-3

1.44E+06

2.21E-02

400

110

72

3

-3

1.44E+06

2.21E-02

400

110

72

3

-3

9.91E+06

3.37E-02

625

130

72

3

-3

1348

9.91E+06

3.37E-02

625

130

72

3

-3

70

1348

9.91E+06

3.37E-02

625

130

72

3

-3

70

1379

6.07E+06

6.83E-02

625

130

72

3

-3

300

70

1379

6.07E+06

6.83E-02

625

130

72

3

-3

300

90

1217

2.65E+06

5.54E-02

625

130

72

3

-3

300

90

1217

2.65E+06

5.54E-02

625

130

72

3

-3

300

90

1217

2.65E+06

5.54E-02

625

130

72

3

-3

300

ce pt

ed

2.90E+06

1217

2.65E+06

5.54E-02

625

130

72

3

-3

300

90

1217

2.65E+06

5.54E-02

625

130

72

3

-3

60

300

110

915

1.42E+06

2.40E-02

625

130

72

3

-3

60

300

110

915

1.42E+06

2.40E-02

625

130

72

3

-3

60

300

110

915

1.42E+06

2.40E-02

625

130

72

3

-3

1050

60

300

110

915

1.42E+06

2.40E-02

625

130

72

3

-3

7075

60

300

90

1302

1.44E+06

1.97E-02

625

130

72

3

-3

137

7075

60

300

90

1302

1.44E+06

1.97E-02

625

130

72

3

-3

138

7075

60

300

90

1302

1.44E+06

1.97E-02

625

130

72

3

-3

Ac

90

60

Page 37 of 46

ip t cr

Table A.1. The results of the experiments (continued) 60

300

90

1302

1.44E+06

7075

60

300

90

1302

1.44E+06

141

7075

60

300

90

1302

1.44E+06

142

4140

40

300

80

1187

2.86E+06

143

4140

40

300

80

1187

144

4140

40

300

80

1187

145

4140

40

300

90

1039

146

4140

40

300

90

1039

147

4140

40

300

90

1039

148

4140

40

300

100

825

149

4140

40

300

100

825

150

4140

40

300

100

151

4140

40

300

110

152

4140

40

300

110

153

4140

40

154

I718

100

155

I718

100

156

I718

100

157

I718

100

158

I718

100

159

I718

160

1040

161

1040

162

1040

163

1.97E-02

625

130

72

3

-3

1.97E-02

625

130

72

3

-3

1.97E-02

625

130

72

3

-3

6.27E-02

625

150

93

5

-5

2.86E+06

6.27E-02

625

150

93

5

-5

2.86E+06

6.27E-02

625

150

93

5

-5

1.73E+06

4.92E-02

625

150

93

5

-5

1.73E+06

4.92E-02

625

150

93

5

-5

1.73E+06

4.92E-02

625

150

93

5

-5

1.19E+06

2.07E-02

625

150

93

5

-5

1.19E+06

2.07E-02

625

150

93

5

-5

825

1.19E+06

2.07E-02

625

150

93

5

-5

724

8.29E+05

3.28E-02

625

150

93

5

-5

724

us

7075

140

ed

M an

139

3.28E-02

625

150

93

5

-5

110

724

8.29E+05

3.28E-02

625

150

93

5

-5

100

100

835

1.11E+06

3.10E-02

625

150

93

5

-5

100

100

832

1.11E+06

3.10E-02

625

150

93

5

-5

100

100

832

1.11E+06

3.10E-02

625

150

93

5

-5

100

110

781

9.17E+05

4.78E-02

625

150

93

5

-5

100

ce pt

8.29E+05

300

781

9.17E+05

4.78E-02

625

150

93

5

-5

100

110

781

9.17E+05

4.78E-02

625

150

93

5

-5

60

300

80

1096

2.95E+06

3.40E-02

625

150

93

5

-5

60

300

80

1096

2.95E+06

3.40E-02

625

150

93

5

-5

60

300

80

1096

2.95E+06

3.40E-02

625

150

93

5

-5

1040

60

300

90

1028

1.94E+06

3.58E-02

625

150

93

5

-5

164

1040

60

300

90

1028

1.94E+06

3.58E-02

625

150

93

5

-5

165

1040

60

300

90

1028

1.94E+06

3.58E-02

625

150

93

5

-5

166

1040

60

300

100

825

1.11E+06

3.03E-02

625

150

93

5

-5

Ac

110

100

Page 38 of 46

ip t cr

Table A.1. The results of the experiments (continued) 60

300

100

825

1.11E+06

168

1040

60

300

100

825

1.11E+06

169

1040

60

300

110

725

6.65E+05

170

1040

60

300

110

725

6.65E+05

171

1040

60

300

110

725

172

7075

60

300

90

1147

173

7075

60

300

90

1147

174

7075

60

300

90

1147

175

7075

60

300

100

929

176

7075

60

300

100

929

177

7075

60

300

100

929

178

7075

60

300

110

562

179

7075

60

300

110

180

7075

60

300

181

2024

40

300

182

2024

40

183

2024

40

184

2024

40

185

2024

40

186

2024

40

187

2024

188

2024

189

2024

190

2024

191 192

3.03E-02

625

150

93

5

-5

3.03E-02

625

150

93

5

-5

3.32E-02

625

150

93

5

-5

3.32E-02

625

150

93

5

-5

us

1040

M an

167

3.32E-02

625

150

93

5

-5

1.82E+06

6.30E-02

625

150

100

5

0

1.82E+06

6.30E-02

625

150

100

5

0

1.82E+06

6.30E-02

625

150

100

5

0

1.16E+06

3.69E-02

625

150

100

5

0

1.16E+06

3.69E-02

625

150

100

5

0

1.16E+06

3.69E-02

625

150

100

5

0

4.46E+05

2.20E-02

625

150

100

5

0

562

4.46E+05

2.20E-02

625

150

100

5

0

110

562

4.46E+05

2.20E-02

625

150

100

5

0

80

1343

3.74E+06

6.54E-02

625

150

100

5

0

300

80

1343

3.74E+06

6.54E-02

625

150

100

5

0

300

80

1343

3.74E+06

6.54E-02

625

150

100

5

0

300

90

1190

2.04E+06

7.80E-02

625

150

100

5

0

300

90

1190

2.04E+06

7.80E-02

625

150

100

5

0

ce pt

ed

6.65E+05

300

1190

2.04E+06

7.80E-02

625

150

100

5

0

300

100

972

1.43E+06

2.18E-02

625

150

100

5

0

40

300

100

972

1.43E+06

2.18E-02

625

150

100

5

0

40

300

100

972

1.43E+06

2.18E-02

625

150

100

5

0

40

300

110

850

1.11E+06

4.39E-02

625

150

100

5

0

2024

40

300

110

850

1.11E+06

4.39E-02

625

150

100

5

0

2024

40

300

110

850

1.11E+06

4.39E-02

625

150

100

5

0

Ac

90

40

Page 39 of 46

Table A.1. The results of the experiments (continued) Experiment End cutting no angle (0)

Side relief angle (0)

Side rake angle (0)

Workpiece hardness (HV)

Insert hardness (HV)

The number of revolutions (rev/min.)

Stable cutting depth (mm)

10

0

0

108

2.85E+03

90

7.8

2

10

0

0

108

2.85E+03

125

7.4

3

10

0

0

108

2.85E+03

180

6.7

4

10

0

0

108

2.85E+03

250

5

10

0

0

108

2.85E+03

355

6

10

0

0

108

2.85E+03

500

7

10

0

0

108

2.85E+03

710

8

10

0

0

108

2.85E+03

90

9

10

0

0

108

2.85E+03

125

10

10

0

0

108

2.85E+03

11

10

0

0

108

2.85E+03

12

10

0

0

108

2.85E+03

13

10

0

0

108

14

10

0

0

108

15

10

0

0

108

16

10

0

0

108

17

10

0

0

18

10

0

0

19

10

0

0

20

10

0

0

21

10

0

22

10

0

23

10

0

ip t

1

6

5.3

us

cr

4.5 3.8

7.4

6.8

6.2

250

5.5

355

4.9

an

180

500

4.3

2.85E+03

710

3.7

2.85E+03

90

6.5

125

6

2.85E+03

180

5.4

108

2.85E+03

250

5

108

2.85E+03

355

4.5

108

2.85E+03

500

3.7

0

108

2.85E+03

710

3.2

0

108

2.85E+03

90

5.8

0

108

2.85E+03

125

5.3

Ac ce p

te

M

2.85E+03

108

d

2.85E+03

24

10

0

0

108

2.85E+03

180

4.8

25

10

0

0

108

2.85E+03

250

4.2

26

10

0

0

108

2.85E+03

355

3.8

27

10

0

0

108

2.85E+03

500

3.3

28

10

0

0

108

2.85E+03

710

2.8

29

10

0

0

108

2.85E+03

90

5.1

30

10

0

0

108

2.85E+03

125

4.7

31

10

0

0

108

2.85E+03

180

4.2

32

10

0

0

108

2.85E+03

250

3.8

33

10

0

0

108

2.85E+03

355

3.5

34

10

0

0

108

2.85E+03

500

3

35

10

0

0

108

2.85E+03

710

2.5

36

10

0

0

193

2.85E+03

90

4.7

37

10

0

0

193

2.85E+03

125

4.2

38

10

0

0

193

2.85E+03

180

3.6

39

10

0

0

193

2.85E+03

250

3

40

10

0

0

193

2.85E+03

355

2.5

41

10

0

0

193

2.85E+03

500

2

Page 40 of 46

Table A.1. The results of the experiments (continued) 193

2.85E+03

710

1.5

43

10

0

0

193

44

10

0

0

193

2.85E+03

90

4.5

2.85E+03

125

4

45

10

0

0

46

10

0

0

193

2.85E+03

180

3.5

193

2.85E+03

250

2.8

47

10

0

0

193

2.85E+03

355

2.3

48

10

49

10

0

0

193

2.85E+03

500

0

0

193

2.85E+03

710

50

10

0

0

193

2.85E+03

90

51

10

0

0

193

2.85E+03

125

52

10

0

0

193

2.85E+03

180

53

10

0

0

193

2.85E+03

250

54

10

0

0

193

2.85E+03

55

10

0

0

193

2.85E+03

56

10

0

0

193

2.85E+03

57

10

0

0

193

58

10

0

0

193

59

10

0

0

193

60

10

0

0

193

61

10

0

0

62

10

0

0

63

10

0

0

64

10

0

0

65

10

0

66

10

0

67

10

0

ip t

0

1.8 1.3 4

cr

0

us

10

3.5 3

2.4

355

2

500

1.5

710

1.1

90

3.8

2.85E+03

125

3.3

2.85E+03

180

2.8

2.85E+03

250

2.3

193

2.85E+03

355

1.8

193

2.85E+03

500

1.3

193

2.85E+03

710

1

193

2.85E+03

90

3

0

193

2.85E+03

125

2.5

0

193

2.85E+03

180

2.3

0

193

2.85E+03

250

1.9

Ac ce p

te

M

2.85E+03

d

an

42

68

10

0

0

193

2.85E+03

355

1.5

69

10

0

0

193

2.85E+03

500

1.1

70

10

0

0

193

2.85E+03

710

0.8

71

10

0

0

150

2.85E+03

90

7.8

72

10

0

0

150

2.85E+03

125

7

73

10

0

0

150

2.85E+03

180

6.3

74

10

0

0

150

2.85E+03

250

5.5

75

10

0

0

150

2.85E+03

355

4.8

76

10

0

0

150

2.85E+03

500

4

77

10

0

0

150

2.85E+03

710

3.5

78

10

0

0

150

2.85E+03

90

7

79

10

0

0

150

2.85E+03

125

6.2

80

10

0

0

150

2.85E+03

180

5.5

81

10

0

0

150

2.85E+03

250

4.7

82

10

0

0

150

2.85E+03

355

4

83

10

0

0

150

2.85E+03

500

3.5

84

10

0

0

150

2.85E+03

710

3

85

10

0

0

150

2.85E+03

90

6.3

Page 41 of 46

Table A.1. The results of the experiments (continued) 10

0

0

150

2.85E+03

125

5.5

87

10

0

0

150

2.85E+03

180

4.7

88

10

0

0

150

2.85E+03

250

4

89

10

0

0

150

2.85E+03

355

3.3

90

10

0

0

150

2.85E+03

500

2.7

91

10

0

0

150

2.85E+03

710

2.3

92

10

0

0

197

2.85E+03

90

93

10

0

0

197

2.85E+03

125

94

10

0

0

197

2.85E+03

180

95

10

0

0

197

2.85E+03

250

96

10

0

0

197

2.85E+03

355

97

10

0

0

197

2.85E+03

500

98

10

0

0

197

2.85E+03

710

1.6

99

10

0

0

197

2.85E+03

90

4.5

100

10

0

0

197

2.85E+03

125

4.2

101

10

0

0

197

102

10

0

0

197

103

10

0

0

197

104

10

0

0

197

105

10

0

0

106

10

0

0

107

10

0

0

108

10

0

0

109

10

0

110

10

0

111

10

0

ip t

86

5

4.3

3.2 2.7 2.1

180

3.6

2.85E+03

250

3

2.85E+03

355

2.5

2.85E+03

500

2

197

2.85E+03

710

1.5

197

2.85E+03

90

4.1

197

2.85E+03

125

3.9

197

2.85E+03

180

3.3

0

197

2.85E+03

250

2.7

0

197

2.85E+03

355

2.3

0

197

2.85E+03

500

1.8

Ac ce p

te

M

2.85E+03

d

an

us

cr

3.7

112

10

0

0

197

2.85E+03

710

1.3

113

18

3

-3

105

2.11E+03

355

9.8

114

18

3

-3

105

2.11E+03

500

6

115

18

3

-3

105

2.11E+03

710

4.5

116

18

3

-3

105

2.11E+03

355

7.5

117

18

3

-3

105

2.11E+03

500

5.8

118

18

3

-3

105

2.11E+03

710

4.2

119

18

3

-3

105

2.11E+03

355

7.3

120

18

3

-3

105

2.11E+03

500

5.5

121

18

3

-3

105

2.11E+03

710

4

122

18

3

-3

197

2.11E+03

180

7

123

18

3

-3

197

2.11E+03

250

5.8

124

18

3

-3

197

2.11E+03

355

5.1

125

18

3

-3

197

2.11E+03

500

4.4

126

18

3

-3

197

2.11E+03

710

4

127

18

3

-3

197

2.11E+03

180

6.5

128

18

3

-3

197

2.11E+03

250

5.6

129

18

3

-3

197

2.11E+03

355

4.4

Page 42 of 46

Table A.1. The results of the experiments (continued) 18

3

-3

197

2.11E+03

500

3.9

131

18

3

-3

197

2.11E+03

710

3.4

132

18

3

-3

197

2.11E+03

250

5.5

133

18

3

-3

197

2.11E+03

355

4.7

134

18

3

-3

197

2.11E+03

500

3.6

135

18

3

-3

197

2.11E+03

710

3.2

136

18

3

-3

150

2.11E+03

125

137

18

3

-3

150

2.11E+03

180

138

18

3

-3

150

2.11E+03

250

139

18

3

-3

150

2.11E+03

355

140

18

3

-3

150

2.11E+03

500

141

18

3

-3

150

2.11E+03

710

142

35

-7

-2

203

1800

355

4.3

143

35

-7

-2

203

1800

500

3.7

144

35

-7

-2

203

1800

710

3.1

145

35

-7

-2

203

146

35

-7

-2

203

147

35

-7

-2

203

148

35

-7

-2

203

149

35

-7

-2

150

35

-7

-2

151

35

-7

-2

152

35

-7

-2

153

35

-7

154

35

-7

155

35

-7

ip t

130

9

8.2

an

us

cr

7.5 6.8 6 5

355

3.7

1800

500

3.2

1800

710

2.4

1800

355

3

203

1800

500

2.4

203

1800

710

2

203

1800

355

2.6

203

1800

500

2.3

-2

203

1800

710

1.6

-7

450

4000

355

1.8

-7

450

4000

500

1.5

Ac ce p

te

d

M

1800

156

35

-7

-7

450

4000

710

1.2

157

35

-7

-7

450

4000

355

1.6

158

35

-7

-7

450

4000

500

1.2

159

35

-7

-7

450

4000

710

1

160

35

-7

-7

158

1800

355

4.5

161

35

-7

-7

158

1800

500

3.7

162

35

-7

-7

158

1800

710

3.2

163

35

-7

-7

158

1800

355

3.7

164

35

-7

-7

158

1800

500

3.1

165

35

-7

-7

158

1800

710

2.5

166

35

-7

-7

158

1800

355

3

167

35

-7

-7

158

1800

500

2.5

168

35

-7

-7

158

1800

710

2

169

35

-7

-7

158

1800

355

2.8

170

35

-7

-7

158

1800

500

2.3

171

35

-7

-7

158

1800

710

1.5

172

45

0

0

160

1388

355

4.1

173

45

0

0

160

1388

500

3.5

Page 43 of 46

Table A.1. The results of the experiments (continued) 45

0

0

160

1388

710

2.9

175

45

0

0

160

1388

355

3.7

176

45

0

0

160

1388

500

2.9

177

45

0

0

160

1388

710

2.7

178

45

0

0

160

1388

355

3.4

179

45

0

0

160

1388

500

2.7

180

45

0

0

160

1388

710

181

45

0

0

134.5

1388

355

182

45

0

0

134.5

1388

500

183

45

0

0

134.5

1388

710

184

45

0

0

134.5

1388

355

185

45

0

0

134.5

1388

500

186

45

0

0

134.5

1388

187

45

0

0

134.5

1388

188

45

0

0

134.5

1388

189

45

0

0

134.5

190

45

0

0

134.5

191

45

0

0

134.5

192

45

0

0

134.5

ip t

174

2.4 4.7

us

cr

4.1 3.5 4.3 3.6 3.1

355

3.6

500

3.1

an

710

710

2.6

1388

355

3.4

1388

500

2.9

1388

710

2.4

M

1388

d

Table A.2. Experiment numbers (Training)

te

3 4 5 7 8 9 11 13 17 18 20 22 23 24 26 27 29 30 32 33 34 35 37 39 41 42 44 45 46 49 51 55 56 59 62 63 64 65 66 67 68 69 70 71 72 73 74 76 79 82 83 86 87 89 90 91 92 95 96 98 99

Ac ce p

100 102 103 106 107 111 112 113 114 115 116 117 118 120 121 122 124 126 128 130 131 134 135 136 137 139 140 142 145 148 149 151 152 155 156 157 158 159 160 161 163 164 167 169 173 174 175 176 177 178 179 180 182 183 184 185 186 187 188 190 191

Page 44 of 46

Table A.3. Experimental and predicted stable cutting depths for ANN models Experiment no

Experimental Value (mm)

Predicted value (mm) (Quick)

Predicted value (mm) (Dynamic)

Predicted value (mm) (Multiple)

Predicted value (mm) (Prune)

Predicted value (mm) ( Exhaustive Prune)

1

7,80

8,17

7,87

8,33

7,83

8,19

2

7,40

7,86

7,65

7,96

7,56

7,93

4,50

4,24

4,88

4,59

4,54

4,41

6,20

6,19

5,67

6,31

6,40

6,51

12

4,90

4,79

4,90

5,05

5,00

4,88

14

3,70

3,10

3,45

3,50

3,04

2,78

15

6,50

6,33

6,03

6,40

6,56

6,61

16

6,00

6,01

5,59

6,06

6,25

19

4,50

4,36

4,49

4,56

4,44

21

3,20

2,90

3,10

3,18

2,73

25

4,20

4,42

4,62

4,28

4,51

28

2,80

2,43

2,70

2,65

2,35

31

4,20

4,59

4,44

4,54

4,70

36

4,70

5,39

4,77

5,54

38

3,60

4,38

3,63

4,33

40

2,50

3,04

2,35

2,93

43

4,50

4,26

4,37

4,27

47

2,30

2,67

2,44

48

1,80

2,20

1,67

50

4,00

3,81

4,08

52

3,00

3,22

53

2,40

2,87

54

2,00

2,45

57

3,80

3,23

58

3,30

3,03

60

2,30

61

1,80

75

4,80

77

3,50

78

ip t

6 10

6,28 4,30 2,56

us

cr

4,44 2,27 4,68

5,65

5,62

4,80

4,70

3,51

3,31 4,43

2,87

2,74

2,05

2,35

2,24

3,77

an

4,58

2,54

3,99

3,12

3,51

3,37

2,85

2,75

3,11

2,99

2,07

2,33

2,64

2,54

3,48

3,17

3,52

3,39

3,19

d

M

4,15

3,41

3,30

3,19

2,18

2,39

2,66

2,60

2,15

1,66

2,06

2,29

2,26

4,20

4,61

4,32

4,54

4,46

2,39

2,30

2,51

2,69

2,43

7,00

5,12

5,30

5,17

5,34

5,27

80

5,50

4,39

4,85

4,39

4,58

4,47

81

4,70

3,92

4,57

3,94

4,06

3,94

84

3,00

2,17

1,93

2,16

2,17

2,08

85

6,30

4,57

4,37

4,88

4,70

4,77

88

4,00

3,81

3,57

4,04

3,69

3,72

93

4,30

4,73

4,15

4,59

4,79

4,68

94

3,70

4,18

3,66

4,09

4,31

4,18

97

2,10

2,34

1,84

2,41

2,53

2,37

101

3,60

3,22

3,51

3,27

3,37

3,21

Ac ce p

te

2,95

2,47

Table A.3. Experimental and predicted stable cutting depths for ANN models (continued) 104

2,00

2,03

1,64

2,07

2,14

2,04

105

1,50

1,65

1,35

1,59

1,76

1,68

108

3,30

3,22

3,52

3,30

3,05

3,06

109

2,70

2,96

3,04

3,00

2,78

2,78

110

2,30

2,62

2,37

2,59

2,45

2,44

119

7,30

6,86

6,74

7,15

6,63

6,75

123

5,80

8,15

7,92

7,94

7,58

7,86

Page 45 of 46

PREDICTION OF STABLE CUTTING DEPTHS IN TURNING OPERATION USING SOFT COMPUTING METHODS

Different experiments from different studies have been chosen

ip t

to predict stable cutting depths

us

cr

Experimental data have been divided into training and testing

Different soft computing methods have been used for

an

computational study

M

ANN have produced succesfull results compared with the other

Ac ce p

te

d

models

Page 46 of 46