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3. 1

CHAPTER-3

ARTIFICIAL NEURAL NETWORK AND NEURO-FUZZY MODELLING OF

HOT EXTRUSION PROCESS, EQUAL CHANNEL ANGULAR PRESSING,

ORTHOGONAL CUTTING PROCESS AND END MILLING PROCESS

3.1 Introduction

ntelligent Manufacturing Systems (IMS) are manufacturing systems that are able to

respond to rapid changes in designs and demand, without the intervention of the

humans. To respond to the changing demand scenarios the system must be equipped

with a comprehensive manufacturing planning and control system which incorporates

vast amounts of manufacturing knowledge in a form that is accessible rapidly. The

design and implementation of these systems is one of the major challenges facing the

manufacturing engineer today.

As already discussed in chapter-1 and chapter-2, metal forming process is

characterised by a multiplicity of dynamically interacting process variables, usually

too complicated and are not amenable to analytical models. The advent of domain

specific finite element (FE) codes like FORGE 3 to handle large deformation

plasticity has made accurate analysis possible. The basic limitations of FE modelling

are code development, debugging, pre-processing and program execution which

consume a lot of time. Though FEM provides a basis for forging optimisation, but a

small change in a single process parameter requires a new forging simulation run to

predict its effects on quality of forging as well as on final forging load. Because the

potentially viable processing routes are numerous, many FEM process simulations are

necessary to identify the required process variables. Some researchers tried to apply

simplex algorithm [Kus89], genetic algorithm [Dug94, Roy97], and novel

computational methods [ChenMF95, Fou96a, Fou96b, Gel98, Lor00, Har01] for

optimisation of forging process but this required a large number of process

simulations to find a satisfactory solution. Therefore, a need is felt to develop a much

more generalised model, which can predict the final result for a wide variation in

I

Chapter-3

3. 2

process parameters quickly without resorting to extensive numerical simulations for a

given design.

To meet this demand two novel approaches i.e. Artificial Neural Network (ANN) and

Neuro Fuzzy (NF) techniques are used for modelling;

Hot extrusion process to predict the forging force required to complete the

process,

Equal Channel Angular Pressing (ECAP) to predict average equivalent strain

induced and the required forming energy,

Orthogonal cutting process to predict cutting forces for a given set of input

parameters i.e. speed, feed and depth of cut and

End milling process to predict average surface roughness and machining time.

The NF models of hot extrusion process and ECAP are developed out of training data

obtained from the Finite Element (FE) simulations detailed in chapter-2. This work

has considerable implications in selection and control of process variables in real time

and ability to achieve energy and material savings with quality improvement and is a

step towards intelligent manufacturing.

3.2 Artificial Neural Networks (ANN)

Artificial Neural networks (ANN) are systems that try to make use of some of the

known or expected organizing principles of the human brain. ANN’s most prominent

feature is to learn from examples, and then adapt themselves based on actual solution

space (training data sets) [Fau94, Hay94, Roj93]. ANN consists of a number of

independent, simple processors - the neurons. These neurons communicate with each

other via weighted connections. Learning in neural networks means to determine a

mapping from an input to an output space by using example patterns. If the same or

similar input patterns are presented to the network after learning, it should produce an

appropriate output pattern. They are particularly powerful in clustering the solution

space identifying important features [Tic00]. ANN can be used if training data is

available. It is not necessary to have a mathematical model of the problem of interest.

On the other hand ANN’s are sometimes criticized for being opaque i.e. the

knowledge they represent is stored in a non-readable form. The solution obtained

from the learning process of ANN is usually cannot be interpreted. They cannot be

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3. 3

checked whether their solution is plausible, i.e. their final state cannot be interpreted

in terms of rules. The learning process itself can take very long, and there is usually

no guarantee of success.

In this work Back-Propagation learning methodology with Levenberg -Marquardt

(LM) approximation is adopted for supervised learning of the networks and is briefly

described below:

The Back-Propagation (BP) neural network is a multiple layer network with one input

layer, one output layer and some hidden layers between input and output layers

[Fau94]. Its learning procedure is based on gradient search with least sum squared

optimality criterion. Calculation of the gradient is done by partial derivative of sum

squared error with respect to weights. This algorithm can be expressed succinctly in

the form of a pseudo-code as given below.

1. Pick a rate parameter R.2. For each sample input compute the resulting output until performance is

satisfactory 3. Compute (error)for nodes in the output layer using;

D Oz z z where D represents the desired output and O represents the actual output of the

neuron.4. Compute β for all other nodes using;

1W O Oj k j k k k k 5. Compute weight changes for all weights using;

1w rO O Oi j i j j j 6. Add up the weight changes for all sample inputs and change the weights.

The standard BP algorithm suffers from the serious drawbacks of slow convergence

and inability to avoid local minima. Therefore, BP with Levenberg -Marquardt (LM)

approximation is used in this work. LM learning rule uses an approximation of the

Newton's method to get better performance [Mor77]. This technique is relatively

faster but requires more memory. The LM update rule is:

1T TW J J I J e

Where J is the Jacobean matrix of derivatives of each error to each weight, is a

scalar and e is an error vector. If the scalar is very large, the above expression

approximates the Gradient Descent method while when it is small the above

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3. 4

expression becomes the Gauss - Newton method. The Gauss Newton method is faster

and more accurate near error minima. Hence, the aim is to shift towards the Gauss -

Newton as quickly as possible. The is decreased after each successful step and

increased only when the step increases the error.

3.3Neuro-fuzzy systems

3.3.1 Fuzzy Systems

Fuzzy logic was founded by Lofti A. Zadeh in 1965 [Zad65]. Fuzzy systems have

been developed to manage knowledge in a more natural manner. It is based on the

idea that sets are not crisp but some are fuzzy, and these can be modeled in linguistic

human terms such as large, small and medium. In fuzzy systems, rules can be

formulated that use these linguistic expressions, which allows integration of domain

expertise into model synthesis and apply them to the human behavioral problem.

Using fuzzy set theory it is easy to model the ‘fuzzy’ boundaries of linguistic terms by

introducing gradual memberships. Interpretations of membership degrees include

similarity, preference, and uncertainty [Dub96]. In general, due to their closeness to

human reasoning, solutions obtained using fuzzy approaches are easy to understand

and to apply. Due to these strengths, fuzzy systems are the methods of choice, if

linguistic, vague, or imprecise information has to be modeled [Kru99]. A fuzzy

system can be used to solve a problem if knowledge about the solution is available in

the form of linguistic if-then rules. By defining suitable fuzzy sets to represent

linguistic terms used within the rules, a fuzzy system can be created from these rules.

There is no formal model of the problem of interest and no training data required. On

the other hand fuzzy systems are mathematically opaque which makes conventional

analysis and exploitation of empirical data hard to perform.

3.3.2 Neuro-Fuzzy systems

Combinations of neural networks with fuzzy systems called as NF systems where

both models complement each other. Neuro-fuzzy systems allow to overcome some of

the individual (ANN and Fuzzy systems) weaknesses and offer some appealing

features. Neuro-Fuzzy hybrid systems combine the advantages of fuzzy systems,

which deal with explicit knowledge which can be explained and understood, and

neural networks which deal with implicit knowledge which can be acquired by

learning [Jan95, Von95, Jin00, Ang03, Abr05]. The ANN is used to define the

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3. 5

clustering in the solution space which results in creation of the fuzzy sets. The ANN

learns these clusters based on actual human behavior test data. A further advantage is

that the solution space rather than being represented point by point as some expert

systems “clumps’ the space as described by Kosko [Kos92]. This results in fewer

rules and lower computer resources and thus reduces design time and cost. On the

other hand, fuzzy logic enhances the generalization capability of a neural network

system by providing more reliable output when extrapolation is needed beyond the

limits of the training data [Lin96]. Neural networks and Fuzzy logic have some

common features such as distributed representation of knowledge, model-free

estimation, ability to handle data with uncertainty and imprecision. Fuzzy logic has

tolerance for imprecision of data, while neural networks have tolerance for noisy data

[Nau97].

A NF system is trained by a learning algorithm (usually) derived from neural network

theory. The (heuristic) learning procedure operates on local information, and causes

only local modifications in the underlying fuzzy system. The learning process is not

knowledge based, but data driven. A NF system can be viewed as a special multi-

layer feed-forward neural network. The first layer represents input variables, the

middle (hidden) layer(s) represents fuzzy rules and the last layer represents output

variables. Fuzzy sets are encoded as (fuzzy) connection weights. A NF system can

always (i.e. before, during and after learning) be interpreted as a system of fuzzy

rules. It is both possible to create the system out of training data from scratch, and it is

possible to initialize it by prior knowledge in the form of fuzzy rules. Modern NF

systems are usually represented as multilayer feed forward neural networks [Ber92,

Buc94, Buc92, Hal94, Nau96a, Nau96b]. In NF models, connection weights and

propagation and activation functions differ from common neural networks.

The NF system is capable of extracting fuzzy knowledge from numerical data and

linguistic data into the system. The goal here is to avoid difficulties encountered in

applying fuzzy logic for systems represented by numerical knowledge (data sets), or

in applying neural networks for a system presented by linguistic information (fuzzy

sets). Neither fuzzy reasoning systems nor neural networks are by themselves capable

of solving problems involving at the same time both linguistic and numerical

knowledge [Hal94]. A number of researchers have used the term hybrid systems

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3. 6

[Ful00] to depict systems that involve in some ways both fuzzy logic and neural

networks features.

A NF system approximates an n-dimensional (unknown) function that is partially

given by the training data. It is possible to view a fuzzy system as a special neural

network and to apply on a learning algorithm directly (hybrid models).

3.4 Artificial Neural Network (ANN) modelling of hot extrusion process

In this section, the ANN modelling of hot extrusion is described. The data obtained

from the FEM simulations in FORGE3 environment of hot extrusion process in

chapter-2, table 2.3 is used to train the ANN model. This model is used to predict the

extrusion load for given parameter combinations of hot extrusion in real-time without

having to perform any extensive and costly computations. For modelling hot extrusion

process a three layer network with three inputs i.e. die angle, coefficient of friction,

and initial temperature of billet and single output i.e. extrusion load is designed as

shown in figure 3.1. After training, the weights are frozen and the model is validated.

For this purpose, the input parameters to the network are sets of values that have not

been used for training the network but are in the same range as those used for training.

Fig. 3.1: Three input and one output ANN architecture of hot extrusion process

Chapter-3

3. 7

Validation enables us to test the network with regard to its capability for interpolation.

The extrusion load is thus obtained for specified set of parameters. Then an FE

simulation is performed for the same sets of parameters to determine the extrusion

load through the FE simulation. The level of agreement between the forging force

predicted by the neural network and the FE simulation indicates the efficacy of the

neural model.

For this training problem the following parameters were found to give rapid

convergence of the training network with good performance in the estimation;

First and second layers of neurons are modelled with log of sigmoid function,

and the third layer is purely linear function. Neurons taken in first and second

layers are eight (8) and five (5) respectively.

Maximum epochs considered are 1000, error goal is set to 10-8 and learning

rate for training the network is taken as 0.2.

Comparison between FE simulation results/training data and neural network results is

shown in table 3.1. The results of the validation procedure described above are given

in table 3.2. The close agreement of the values of the equivalent strain and forming

energy obtained by the neural network and the FE simulation clearly indicates that the

model can be used for predicting the extrusion force in the range of parameters under

consideration. Convergence graphs between sum squared error and number of epochs

for training process is shown in Fig. 3.2. It can be clearly seen that neural network

training got completed in just ninety four (94) epochs with the above mentioned

parameters.

The proposed ANN model is very fast and the time taken for prediction is very small.

This meta model can be used in tandem with optimizer in future for finding the

optimal hot extrusion process parameters for minimizing extrusion force.

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3. 8

Fig. 3.2: Convergence graph between sum squared error and number of epochs for hot extrusion process

Angle μ

FE simulation values and NN estimated values of Extrusion load (Tones) 1000oC 1090oC 1180oC 1260oC

FE results

NN results

FE results

NN results

FE results

NN results

FE results

NN results

15o0.4 270.11 270.59 263.07 262.51 254.24 255.13 252.22 251.220.6 273.24 272.94 265.80 265.84 258.84 258.95 257.17 256.040.8 275.04 274.15 267.90 268.37 263.32 262.97 262.98 263.06

30o0.4 247.92 246.97 238.32 237.14 230.16 229.48 226.13 225.960.6 248.50 249.04 241.09 242.19 235.71 234.83 229.78 230.090.8 249.87 248.75 247.82 245.42 240.26 240.85 233.67 233.55

45o0.4 243.18 242.72 236.34 234.71 228.19 227.97 200.90 199.990.6 244.60 244.66 240.12 238.74 232.54 231.32 205.10 204.050.8 246.80 246.78 243.09 242.89 237.92 238.18 208.33 207.30

60o0.4 234.49 234.53 216.18 215.09 208.71 208.66 181.86 180.800.6 236.56 236.50 219.27 218.94 211.82 212.37 184.03 184.020.8 238.26 238.26 220.72 219.98 218.33 217.98 185.91 185.94

75o0.4 261.93 259.33 240.77 236.76 220.74 219.94 211.77 210.940.6 263.35 262.87 242.12 240.31 222.79 220.10 206.75 207.910.8 266.07 265.14 243.85 244.43 223.83 222.50 210.82 209.95

Table 3.1: FE training data and NN estimated results for extrusion load of hot extrusion process

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3. 9

Angle μ1000oC 1260oC

FE results

NN results

FE results

NN results

15o 0.2 268.41 267.16 250.21 250.23 45o 0.3 241.72 240.47 254.24 253.95 75o 0.7 224.04 223.84 261.48 261.49

Table 3.2: Validation of FE simulation results and NN results for extrusion load of hot extrusion process

3.4 Artificial Neural Network (ANN) modelling of ECAP process

In this section, the ANN modelling of equal channel angular pressing (ECAP) process

is described. The data is obtained from the FE simulations of ECAP process described

in chapter 3, table 3.1. Table 3.3 shows the data used to train the neural network to act

as model-free estimators. This model can be used to predict the requisite forming

energy for conducting the process and equivalent strain produced in end product for

given combination of process parameters in real-time without having to perform any

extensive and costly computations.

Channel Angle (Φ) 90o



µ Avg. Eq. strain Forming Energy Avg. Eq. strain Forming Energy Avg. Eq. strain Forming Energy (KJoules) (KJoules) (KJoules)

Route ‘A’

0.00 6.551 1.192 4.579 1.030 2.934 0.7450.10 6.958 1.360 4.667 1.345 3.096 1.1950.15 7.198 1.390 4.675 1.350 3.265 1.2470.20 7.322 1.404 4.753 1.362 3.315 1.2510.25 7.325 1.406 5.126 1.367 3.374 1.2690.30 7.328 1.412 5.142 1.384 3.508 1.2950.35 7.382 1.416 5.664 1.387 3.827 1.3000.40 7.605 1.423 6.118 1.390 4.453 1.302

Route ‘BA’0.00 7.185 1.215 4.309 1.058 2.753 0.8570.10 7.232 1.397 4.623 1.208 2.795 0.8920.15 7.381 1.402 5.048 1.229 2.834 0.9130.20 7.394 1.423 5.239 1.346 2.902 1.1040.25 7.678 1.424 5.569 1.396 3.002 1.1290.30 7.721 1.429 5.682 1.457 3.095 1.1320.35 7.791 1.463 5.791 1.489 3.102 1.1400.40 7.944 1.484 5.916 1.508 3.146 1.142

Route ‘C’0.00 6.132 1.203 4.468 1.028 2.906 0.7950.10 6.235 1.367 4.702 1.296 3.272 1.2450.15 6.677 1.413 4.737 1.421 3.114 1.3270.20 6.699 1.429 4.562 1.482 3.482 1.3410.25 6.926 1.495 4.940 1.435 3.488 1.3520.30 7.057 1.463 5.393 1.510 3.870 1.3230.35 7.163 1.501 5.628 1.556 3.428 1.3500.40 7.188 1.404 5.716 1.465 3.274 1.384

Table 3.3: ANN training data: Average equivalent strain and forming energy for routes A, BA and C

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3. 10

A three layer network with two inputs i.e. coefficient of friction, and channel

intersection angle (Φ) and two outputs i.e. forming energy and equivalent strain is

designed as shown in figure 3.3. The data obtained through FE simulations for three

routes A, BA and C is used for training the ANN model. After training, the weights are

frozen and the model is validated. For this purpose, the input parameters to the

network are sets of values that have not been used for training the network but are in

the same range as those used for training.

This enables us to test the network with regard to its capability for interpolation. The

forming energy and equivalent strain are thus obtained for this set of parameters. Then

an FE simulation is performed for the same sets of parameters to determine the

forming energy and equivalent strain through the FE simulation. The level of

agreement between the forging force predicted by the neural network and the FE

simulation indicates the efficacy of the neural model.

Fig. 3.3: Two input and two output ANN architecture of ECAP process

For the training problem at hand the following parameters were found to give rapid




layers are seven (7) and four (4) respectively.

Maximum epochs considered were 1000, error goal is set at 10-6 and learning


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3. 11

The results of the validation procedure described above are given in tables 3.4, 3.5

and 3.6 for different routes. The close agreement of the values of the equivalent strain

and forming energy obtained by the neural network and the FE simulation clearly

indicates that the model can be used for predicting the forging force in the range of

parameters under consideration. Convergence graphs between sum squared error and

number of epochs for routes A, BA and C are shown in Fig. 3.4.

The model is very fast and the time taken for prediction is very small. This meta

model can also be used in tandem with optimizer in future for finding the optimal

ECAP profile and process parameters for maximizing the equivalent strain and

minimizing extrusion force.

Fig. 3.4: Convergence graph between sum squared error and number of epochs for route A, BA and C

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3. 12

Channel Intersection

Angle(Φ)

Coefficient of

Friction(µ)

FE results (Equivalent

Strain)

NN results (Equivalent

Strain)

FE results(Forming Energy)

NN results (Forming Energy)

90o

0.02 6.602 6.582 1.231 1.198

0.04 6.693 6.509 1.297 1.292

0.06 6.884 6.794 1.302 1.299

0.40 7.605 7.623 1.432 1.398

105o

0.02 4.583 4.576 1.098 1.001

0.04 4.597 4.592 1.156 1.037

0.06 4.600 4.599 1.187 1.105

0.40 6.118 6.120 1.390 1.376

120o

0.02 2.986 2.985 0.801 0.764

0.04 2.992 2.889 0.994 0.995

0.06 3.001 3.000 1.035 1.009

0.40 4.453 4.453 1.302 1.300Table 3.4: Validation of ANN model results with FE simulations for Route ‘A’


Angle(Φ)

Coefficient of

Friction(µ)


Strain)


Strain)



90o

0.02 7.188 7.043 1.223 1.222

0.04 7.192 7.149 1.297 1.301

0.06 7.201 7.200 1.302 1.300

0.40 7.944 7.900 1.484 1.464

105o

0.02 4.356 4.346 1.078 1.055

0.04 4.405 4.401 1.167 1.098

0.06 4.508 4.499 1.200 1.200

0.40 5.916 5.920 1.508 1.499

120o

0.02 2.755 2.745 0.860 0.849

0.04 2.764 2.762 0.875 0.855

0.06 2.786 2.779 0.891 0.889

0.40 3.146 3.100 1.142 1.145Table 3.5: Validation of ANN model results with FE simulations for Route ‘BA’

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3. 13


Angle(Φ)

Coefficient of

Friction(µ)


Strain)


Strain)



90o

0.02 6.145 6.112 1.234 1.210

0.04 6.203 6.200 1.296 1.295

0.06 6.225 6.198 1.301 1.300

0.40 7.188 7.010 1.404 1.401

105o

0.02 4.504 4.501 1.045 1.001

0.04 4.587 4.324 1.185 1.180

0.06 4.689 4.598 1.250 1.250

0.40 5.716 5.715 1.465 1.446

120o

0.02 2.945 2.902 0.845 0.846

0.04 3.124 3.120 0.932 0.925

0.06 3.225 3.215 1.158 1.145

0.40 3.274 3.274 1.384 1.385Table 3.6: Validation of ANN model results with FE simulations for Route ‘C’

3.5 Artificial Neural Network (ANN) modelling of End Milling Process

Intelligent manufacturing systems require intelligent models that can help the

manufacturer to meet the customer demands with existing infrastructure. The rising

demand for precision and quality in manufacturing necessitates that vast amounts of

manufacturing knowledge be incorporated in manufacturing systems. Modelling of

end milling process is attempted in this section. Surface finish in end milling depends

upon a number of variables such as cutting speed, feed rate, spindle speed, radial

depth of cut, tolerance etc. The relative effect of these variables on surface roughness

and machining time is quite considerable. A complex relationship exists between

these process parameters and hence there is a need to develop intelligent models

which can capture this complex interrelationship and enable fast computation of the

average surface roughness and machining time based on process parameters. Here a

NN model is trained with experimental results of micro end milling. Subsequently a

generic approach is developed where the applicability and effectiveness of NN model

for function approximation is used to rapidly estimate average surface roughness and

machining time

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3. 14

Present day manufacturing demands high degree of accuracy for the part to work

satisfactorily when assembled. Desired tolerances and surface finish demand great

care in selection of a manufacturing process. In recent years the miniaturization of

products has become a trend all over the world. End milling with fine grained carbide

end mills is an economical way to machine small and medium lots of small

components. In end milling operations, the tool life is very short and difficult to

predict as compared to the conventional machining. Many manufacturers change

these tools according to a very conservative schedule to avoid tool breakage until the

machining of each part is completed. The premature tool breakage can be avoided if

the cutting force in feed direction is kept below an experimentally determined limit.

The objective is the minimization of the product cost in conventional manufacturing.

However, during the manufacturing of precision parts, the achievement of very high

quality standards becomes the primary objective. Avoidance of premature tool

breakage and creation of very smooth surfaces are the primary concerns in micro

machining. Most of the time, it is very difficult to find the related analytical or

empirical expressions and proper coefficients to calculate the optimal operating

conditions for the considered material and tool. Therefore, a need is felt to develop

models which can capture this complex inter-relationship between the process

parameters and surface finish.

Experimental setup and data collection

Tansel et al. [Tan06] have experimentally measured the surface roughness and the

machining time at various test conditions. Aluminum block having 30x30x90

dimensions was machined at three stages. The first two stages, rough and semi finish

cut were the same for the entire part. A flat end mill with a 12mm diameter was used

for rough cutting. The depth of cut was 1.5mm. 3D spiral tool motions were

performed with 3mm stopovers at 2500mm/min feed rate and 5000rpm spindle speed.

The rough cutting continued until 0.6 mm thick material was left on the desired final

surface. A ball end mill with a 12mm diameter was used at the second stage to

machine the material with a 0.3mm depth of cut. The step over, feed rate and spindle

speed were 3mm, 700mm/min, and 3000rpm, respectively. After the second stage, 0.3

mm thick material was left on the desired part surface. The finishing cut (Third stage)

was performed with a ball end mill with 10mm diameter.

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3. 15

Finishing cut continued until the desired surface was obtained. The surface roughness

of the machined surface was measured by using a Mitatoyu Surftest 301 portable

surface roughness tester. The surface roughness was measured three times at 10

different regions for each cutting condition and average was calculated. The ranges of

the cutting parameters are presented in table 3.7 and the experimental values are

shown in table 3.8.

Cutting speed (m/min)

Feed Rate (mm/tooth)

Radial depth of cut (mm)

Tolerance(mm)

74-123 0.07-0.12 0.1-0.3 0.01-0.001

Table 3.7: Range of cutting parameters

No Cutting Speed

(m/min)

Feed rate(mm/tooth)

Radial depth

ofcut

(mm)

Tolerance(mm)

Expérimental values by Tansel et al. [Tan06]

Estimated values using ANN Model

Average surface

roughness (µm)

Machining Time (min)

Average surface

roughness (µm)

MachiningTime (min)

1 74 0.07 0.1 0.001 0.26 64 0.2600 64.00722 98.5 0.07 0.1 0.001 0.31 47 0.3100 46.99963 123 0.07 0.1 0.001 0.27 45 0.2701 45.00144 74 0.095 0.1 0.001 0.32 48 0.3200 48.00335 98.5 0.095 0.1 0.001 0.36 36 0.3599 35.99826 123 0.095 0.1 0.001 0.85 29 0.8500 29.00387 74 0.12 0.1 0.001 0.48 39 0.4800 39.00128 98.5 0.12 0.1 0.001 0.37 28 0.3700 27.99719 123 0.12 0.1 0.001 1.58 24 1.5800 23.9982

10 74 0.07 0.2 0.001 0.36 32 0.3599 31.997711 98.5 0.07 0.2 0.001 0.59 24 0.5900 23.997312 123 0.07 0.2 0.001 0.52 19 0.5200 18.993913 74 0.095 0.2 0.001 0.51 23 0.5099 23.001814 98.5 0.095 0.2 0.001 0.53 17 0.5300 17.008215 123 0.095 0.2 0.001 0.81 15 0.8100 15.007216 74 0.12 0.2 0.001 0.53 21 0.5300 21.000217 98.5 0.12 0.2 0.001 0.47 14 0.4700 14.000118 123 0.12 0.2 0.001 0.93 12 0.9300 12.001619 74 0.07 0.3 0.001 0.49 22 0.4901 22.003020 98.5 0.07 0.3 0.001 0.50 17 0.5000 16.999321 123 0.07 0.3 0.001 1.22 13.3 1.2200 13.299022 74 0.095 0.3 0.001 0.42 15.3 0.4201 15.298223 98.5 0.095 0.3 0.001 0.58 12 0.5800 11.993924 123 0.095 0.3 0.001 1.31 09 1.3100 9.003225 74 0.12 0.3 0.001 0.67 13 0.6700 12.998326 98.5 0.12 0.3 0.001 0.47 10 0.4701 10.009927 123 0.12 0.3 0.001 0.98 7.3 0.9800 7.293328 74 0.07 0.1 0.0055 0.37 64 0.3700 63.996929 98.5 0.07 0.1 0.0055 0.30 49 0.3000 49.000430 123 0.07 0.1 0.0055 0.37 48 0.3700 47.997631 74 0.095 0.1 0.0055 0.53 45 0.5300 44.986532 98.5 0.095 0.1 0.0055 0.47 37 0.4699 37.000933 123 0.095 0.1 0.0055 0.64 29 0.6400 28.992334 74 0.12 0.1 0.0055 0.65 39 0.6500 38.999735 98.5 0.12 0.1 0.0055 0.52 30.3 0.5201 30.305836 123 0.12 0.1 0.0055 1.15 23.3 1.1500 23.301237 74 0.07 0.2 0.0055 0.49 33 0.4901 33.003238 98.5 0.07 0.2 0.0055 0.89 24 0.8900 24.0006

Chapter-3

3. 16

39 123 0.07 0.2 0.0055 0.71 20.3 0.7100 20.304740 74 0.095 0.2 0.0055 0.80 24 0.8000 23.989741 98.5 0.095 0.2 0.0055 0.66 29 0.6600 28.995742 123 0.095 0.2 0.0055 0.76 15 0.7599 14.994843 74 0.12 0.2 0.0055 0.58 20.3 0.5800 20.305744 98.5 0.12 0.2 0.0055 0.32 15 0.3200 14.989545 123 0.12 0.2 0.0055 0.77 12 0.7699 11.998046 74 0.07 0.3 0.0055 0.57 22 0.5700 21.993247 98.5 0.07 0.3 0.0055 1.22 16.3 1.2200 16.303048 123 0.07 0.3 0.0055 0.83 13.3 0.8300 13.296549 74 0.095 0.3 0.0055 0.69 16.3 0.6900 16.313650 98.5 0.095 0.3 0.0055 0.91 12.3 0.9100 12.311851 123 0.095 0.3 0.0055 0.90 9.3 0.9000 9.293052 74 0.12 0.3 0.0055 0.66 13 0.6597 12.987753 98.5 0.12 0.3 0.0055 0.73 10 0.7300 10.003754 123 0.12 0.3 0.0055 0.82 08 0.8200 7.991455 74 0.07 0.1 0.01 0.42 65 0.4200 64.999556 98.5 0.07 0.1 0.01 0.20 49 0.2000 48.999957 123 0.07 0.1 0.01 0.57 39 0.5700 38.999958 74 0.095 0.1 0.01 0.47 48 0.4700 48.003159 98.5 0.095 0.1 0.01 0.40 36 0.4000 35.998960 123 0.095 0.1 0.01 0.51 30 0.5100 30.002361 74 0.12 0.1 0.01 0.48 38 0.4800 38.004062 98.5 0.12 0.1 0.01 0.59 35 0.5900 34.997063 123 0.12 0.1 0.01 0.47 24 0.4698 24.000064 74 0.07 0.2 0.01 0.66 34 0.6600 33.998965 98.5 0.07 0.2 0.01 0.78 24.3 0.7800 24.299166 123 0.07 0.2 0.01 1.27 20 1.2700 19.997967 74 0.095 0.2 0.01 0.50 25 0.5000 25.004968 98.5 0.095 0.2 0.01 0.58 18 0.5800 18.002669 123 0.095 0.2 0.01 0.66 14 0.6601 14.000070 74 0.12 0.2 0.01 0.62 19 0.6200 18.995171 98.5 0.12 0.2 0.01 0.60 15.3 0.6000 15.300472 123 0.12 0.2 0.01 0.62 12 0.6199 12.001873 74 0.07 0.3 0.01 0.58 23 0.5800 23.001774 98.5 0.07 0.3 0.01 0.70 17 0.6999 16.997475 123 0.07 0.3 0.01 0.71 13.3 0.7101 13.307876 74 0.095 0.3 0.01 0.68 18.3 0.6801 18.292677 98.5 0.095 0.3 0.01 0.72 12.3 0.7199 12.290278 123 0.095 0.3 0.01 1.05 10.3 1.0500 10.298379 74 0.12 0.3 0.01 0.85 09.3 0.8502 9.311580 98.5 0.12 0.3 0.01 0.61 10 0.6101 9.990481 123 0.12 0.3 0.01 0.62 08 0.6200 8.0151

Table 3.8: Experimental and ANN estimated values for average surface roughness and machining time

For the above training problem the following parameters were used to give rapid




layers are fifteen (15) and six (6) respectively.

Maximum epochs considered are 1000, error goal was set at 10-6 and learning


Chapter-3

3. 17

The results of the validation procedure described in the modelling of ECAP are given

in table 3.9. The close agreement of the values of the average surface roughness and

machining time obtained by the neural network and reported in Tansel et al. [Tan06]

clearly indicates that the model can be used for predicting the output in the range of

parameters under consideration. Figure 3.5 shows four inputs and two outputs ANN

architecture of end milling process. Convergence graph between sum squared error

and number of epochs is shown in Figure 3.6.

Fig. 3.5: Four input and two output ANN architecture of end milling process

No Cutting Speed

(m/min)

Feed rate(mm/tooth)

Radial depth

ofcut

(mm)

Tolerance(mm)

Experimental values by Tansel et al. [Tan06]

Estimated values using ANN Model

Average surface

roughness (µm)

MachiningTime (min)

Average surface

roughness (µm)

Machining Time min)

1 98.5 0.095 0.1 0.001 0.36 36 0.35 35.992 98.5 0.095 0.1 0.0055 0.47 37 0.47 373 123 0.07 0.3 0.0055 0.83 13.3 0.83 13.294 98.5 0.12 0.1 0.01 0.59 35 0.59 34.995 74 0.07 0.3 0.01 0.58 23 0.58 23

Table 3.9: Validation of estimated values of average surface roughness and machining time using ANN model with experimental values

Chapter-3

3. 18

Fig. 3.6: Convergence graph between sum squared error and number of epochs for end milling process

3.6 Artificial Neural Network (ANN) modelling of Orthogonal Cutting Process

Cutting force estimation is an important criterion that determines the economics of

machining and is of engineering interest in intelligent manufacturing. A complex

relationship exists between process parameters like speed, feed, depth of cut, tool

geometry and cutting forces. There is a need to develop models that can capture this

interrelationship and enable fast computation of the cutting forces based on these

parameters. Here NN modelling of cutting forces for a given set of input parameters

i.e. speed, feed and depth of cut is done and the results obtained from NN model

compare favorably with the experimental data sets of cutting forces.

Nagaraju et al. [Nag97] have experimentally measured the actual cutting forces at

various cutting conditions to see the influence of speed, feed, and depth of cut on the

two dimensional cutting force system in metal cutting operation. Mild steel specimen

and high speed steel tool material are used in these experiments. They have also

attempted to develop artificial neural network (NN) model for the cutting forces by

using the simple back propagation algorithm. However, the predicted values from

their model show quite a large variation from the actual experimentally observed

cutting forces. The predicted values by NN model used in this work are much closer

as can be observed from the results listed in Table 3.10.

Chapter-3

3. 19

Speed(m/min)

Feed(mm)

Depthof

Cut(mm)

Exp. Valuesof Cutting

Forces

Values byNagaraju et al.

[Nag97]

Values byNN Network

Fc(N) Ft(N) Fc(N) Ft(N) Fc(N) Ft(N)29 0.440 1.0 571.4 380.9 750 537.1 571.7 379.429 0.212 1.0 457.1 361.9 505 392 457.1 361.129 0.107 1.0 304.7 228.6 418 338 304.1 231.122 0.440 1.0 523.8 285.7 690 499 523.8 287.222 0.107 1.0 276.2 209.5 382 315 275.3 205.017 0.440 1.0 476.2 285.7 629 463 474.8 285.217 0.212 1.0 385.7 238.0 411 332.8 387.3 237.317 0.107 1.0 238.1 142.8 358 300 237.1 147.813 0.440 1.0 428.5 333.3 588 439 430.1 333.513 0.212 1.0 333.3 285.7 390 319 332.3 286.413 0.107 1.0 238.1 190.5 346 291 239 188.729 0.212 1.2 571.4 428.5 526 402 571.2 429.729 0.107 1.2 400.0 342.8 432 346 400.1 339.422 0.440 1.2 523.8 380.9 712 5111 524.3 426.622 0.212 1.2 457.4 342.9 468 368 459.6 346.522 0.107 1.2 361.9 304.7 393 321 361.7 308.417 0.440 1.2 666.7 428.5 653 476 666.1 429.917 0.212 1.2 476.2 380.9 425 341 474.4 377.617 0.107 1.2 342.8 285.7 367 305 343.6 282.413 0.440 1.2 761.9 428.5 612 452 761.7 427.813 0.107 1.2 323.8 280.9 352 296 322.9 288.929 0.440 1.5 904.7 666.7 793 561 904.5 666.329 0.212 1.5 523.8 428.6 559 421 524.7 427.029 0.107 1.5 447.6 400 456 361 447.2 400.222 0.440 1.5 1000 714.2 742 529 1000 714.322 0.212 1.5 619.1 523.8 497 384 617.4 525.422 0.107 1.5 333.3 285.7 412 334 333.7 286.317 0.440 1.5 714.2 523.8 687 496 714.4 524.217 0.212 1.5 523.8 428.5 449 356 523.4 429.213 0.440 1.5 574.2 476.1 674 473 574.9 475.313 0.212 1.5 428.5 333.3 422 339 429.1 332.713 0.107 1.5 285.7 204.7 364 304 284.9 207.1

Table 3.10: Experimental and estimated values of NN network for cutting force (Fc) and tangential cutting force (Ft)

The following parameters in ANN were used to give rapid convergence of the training

network;

Two ANN models are developed for cutting force (Fc) and tangential cutting

force (Ft).

First and second layers of neurons in both models are modelled with log of

sigmoid function, and the third layer is purely linear function. Neurons taken

in first and second layers are five (5) and four (4) respectively.

Chapter-3

3. 20

Maximum epochs considered are 1000, error goal was set at 10-6 and learning


The results of the validation procedure are given in table 3.11. The close agreement of

the values obtained by the neural network and those reported by Nagaraju et al. along

with experimental values clearly indicates that the model can be used for predicting

the output in the range of parameters under consideration. Figure 3.7 shows three

inputs and two outputs ANN architecture of orthogonal cutting process. Convergence

graph between sum squared error and number of epochs is shown in Figure 3.8.

Speed(m/min)

Feed(mm)

Depthof

Cut(mm)


Forces

Values byNagaraju et al.

[Nag97]

Values byNN Network

Fc (N) Ft (N) Fc (N) Ft (N) Fc (N) Ft (N)22 0.212 1.0 419.0 257.1 451 356 419 256.729 0.440 1.2 714.3 476.2 769 546 714 478.113 0.212 1.2 571.4 380.9 402 327 572.8 380.717 0.107 1.5 380.9 238.1 381 314 381.9 234.8

Table 3.11: Validation of estimated values of cutting forces using ANN model with experimental values and NN values reported by Nagaraju et al.

Fig. 3.7: Two ANN architectures of orthogonal cutting process with three inputsand single output

Chapter-3

3. 21

Fig. 3.8: Convergence graph between sum squared error and number of epochs for orthogonal cutting process (Fc) and (Ft)

3.7 Neuro-Fuzzy modelling of hot extrusion process

In this section, the NF modelling of hot extrusion is described. The data obtained from

the FEM simulations of hot extrusion process; chapter-2, table 2.3 is used to train the

NF model. This model can be used to predict the extrusion forces for given parameter

combinations of hot extrusion in real-time without having to perform any extensive

and costly computations. A three input NF network is shown in figure 3.9.

Fig. 3.9: Three input and one output neuro-fuzzy network for hot extrusion process

Chapter-3

3. 22

Neuro-fuzzy inference system under consideration has three inputs viz. die angle (θ),

coefficient of friction (α) and initial temperature of billet (ν), and one output extrusion

load (f). The first order, four input fuzzy model, the fuzzy ‘if- then rules’ of Takagi

and Sugeno type [Tak85, Sug98] has the following form.

Rule 1: If θ is A1, α is B1 and ν is C1 then

1 1 1 1 1f p q r t

Rule 2: If θ is A2, α is B2 and ν is C2 then

2 2 2 2 2f p q r t

Rule 3: If θ is A3, α is B3and ν is C3 then

3 3 3 3 3f p q r t

where, , , ,p q r ti i i i are consequent parameters.

Thus we have constructed an adaptive network which is functionally equivalent to a

Takagi and Sugeno’s fuzzy inference system.

Layer1:

Every node in this layer is a square node, with a node function, 1 ( )O Ai i ,

where θ is the input to node i, and Ai, is the linguistic label associated with this node

function. In this architecture ( )iA is bell shaped with maximum equal to 1 and

minimum equal to 0.

1( )

21

Ai bici

ai

where , ,a b ci i i are the premise parameters.

Layer 2:

The function of node in this layer is to multiply the incoming signals and produce the

product of all inputs. For instance;

Chapter-3

3. 23

( ) x ( ) x ( )

1, 2......27

1, 2,3.

1, 2,3.

1, 2,3.

1, 2,3.

j k lwi A B C

i

j

k

l

m

Each node output represents the firing strength of a rule.

Layer 3:

The input firing strength is normalized in this layer and output is called normalized

firing strengths.

1 2 27

1, 2, 3......27, ..........

wiw iiw w w

Layer 4:

Every node i in this layer is a parameterized function. The node function is

4O w f w p q r ti ii i i i i i

where i =1, 2……27 and wi is the output of previous layer, and , , ,p q r ti i i i is a

parameter set. Parameters in this layer are referred as consequent parameters.

Layer 5:

The single node in this layer computes the overall output as the summation of all

incoming signals, i.e.

5O overall output w fi iii

The system is initialized with a number of membership functions and a rule base.

Learning consists of two separate passes. In the forward pass, the consequent

parameters are determined by least square method and antecedent parameters are

updated by a gradient descent algorithm in the backward pass.

From the equations obtained in layer four (4) and five (5) it is observed that, given

the values of premise parameters, the overall output is expressed as linear

combinations of the consequence parameters.

Chapter-3

3. 24

The output f can be rewritten as

27

127

( ) ( ) ( ) ( )1

f w fi ii

f w p w q w r w ti i i ii i i ii

This is linear in the consequent parameters. The FE simulation results and NF

estimated results for extrusion load are shown in table 3.12. The close agreement of

simulated and trained values given by the developed neuro fuzzy model clearly shows

the efficacy of the model. The training information and the parameters of NF

architecture is shown in Table 3.13. The initial and final membership functions for the

NF model developed are shown in Fig. 3.10.

θ μ

FE simulation values and NF estimated values of Extrusion load (Tones) 1000oC 1090oC 1180oC 1260oC

FE results

NF results

FE results

NF results

FE results

NF results

FE results

NF results

15o0.4 270.11 270.16 263.07 263.10 254.24 254.26 252.22 252.23 0.6 273.24 273.25 265.80 265.79 258.84 258.83 257.17 257.17 0.8 275.04 275.04 267.90 267.90 263.32 263.32 262.98 262.97

30o0.4 247.92 247.93 238.32 238.32 230.16 230.16 226.13 226.13 0.6 248.50 248.48 241.09 241.06 235.71 235.71 229.78 229.79 0.8 249.87 249.87 247.82 247.79 240.26 240.26 233.67 233.69

45o0.4 243.18 243.17 236.34 236.34 228.19 228.19 200.90 200.89 0.6 244.60 244.57 240.12 240.13 232.54 232.53 205.10 205.09 0.8 246.80 246.77 243.09 243.06 237.92 237.91 208.33 208.31

60o0.4 234.49 234.48 216.18 216.15 208.71 208.78 181.86 181.82 0.6 236.56 236.56 219.27 219.24 211.82 211.82 184.03 184.04 0.8 238.26 238.24 220.72 220.71 218.33 218.33 185.91 185.92

75o0.4 261.93 261.33 240.77 239.96 220.74 220.34 211.77 211.640.6 263.35 263.27 242.12 241.91 222.79 222.10 206.75 205.990.8 266.07 265.94 243.85 243.33 223.83 223.40 210.82 210.55

Table 3.12: FE simulation results and NF estimated results for extrusion load of hot extrusion process

Chapter-3

3. 25

Fig. 3.10: Initial and final membership functions for the NF model of hot extrusion process

Number of nodes: 78Number of linear parameters: 108Number of nonlinear parameters: 27Total number of parameters: 135Number of training data pairs: 60Number of checking data pairs: 30Number of fuzzy rules: 27

Table 3.13: Training information of NF model for hot extrusion process

Validation of neuro-fuzzy model for hot extrusion process: After developing the

NF model from training it by FE simulation data the model is validated. For this, the

input parameters to the NF model are sets of values that have not been used for

training the model but are in the same range as those used for training. This enables us

to test the network with regard to its capability for interpolation. The final extrusion

force is thus obtained for this set of parameters. Then an FE simulation is performed

for the same sets of parameters to determine the extrusion force. The level of

agreement between the extrusion force predicted by NF model and the FE simulation

indicates the conformity of the NF model. The results of the validation procedure

described above are given in table 3.14. The close agreement of the values of the final

extrusion force obtained by the NF model and the FE simulation clearly indicates that

Chapter-3

3. 26

the model can be used for predicting the extrusion force in the range of parameters

under consideration. The model is very fast and prediction can be done in real time.

Angle μ1000oC 1260oC

FE results

NF results

FE results

NFresults

15o 0.2 268.41 267.98 250.21 248.61 45o 0.3 241.72 240.47 254.24 253.99 75o 0.7 224.04 223.99 261.48 259.92

Table 3.14: Validation of results of hot extrusion load obtained by FEM and Neuro-fuzzy model

3.8 Neuro-Fuzzy modelling of ECAP process

In this section, the neuro-fuzzy modelling of ECAP process is described. The data

obtained from the FEM simulations, Chapter 3, table 3.1 are used to train the NF

model. The neuro-fuzzy inference system under consideration has two inputs: channel

intersection angle (Φ) and coefficient of friction (µ) and two outputs: average

equivalent strain and forming energy. To achieve better accuracy in the results, the

prediction of average equivalent strain and forming energy are carried out separately

by two independent NF models in parallel as shown in figure 3.11. The inputs are

simultaneously fed to the two NF models and NF model-I fulfil the prediction of the

average equivalent strain, and NF model-II evaluates the forming energy. As the two

NF models are also trained separately, most suitable NF model parameters could be

found and thus better accuracy of prediction is attained. These models can be used to

predict the average equivalent strain and forming energy for given parameter

combinations of ECAP process in real-time without having to perform any extensive

and costly computations.

Chapter-3

3. 27

Fig. 3.11: Neuro-fuzzy model with a parallel prediction scheme

Two inputs and one output neuro-fuzzy networks of NF model for ECAP process are

shown below:

Fig. 3.12: Two input and one output (average equivalent strain) neuro-fuzzy network-I for ECAP process

Chapter-3

3. 28

Fig. 3.13: Two input and one output (forming energy) neuro-fuzzy network-II for ECAP process

For a first-order, two-input fuzzy model, the fuzzy if- then rules of Takagi and

Sugeno type have the following form:

Rule 1: If Φ is B1and µ is C1, then

f1 = (q1Φ + r1µ +t1)

Rule 2: If Φ is B2 and µ is C2, then

f2 = (q2Φ + r2µ +t2)

where {qi ,ri ,ti}are consequent parameters.

Thus, we have constructed an adaptive network that is functionally equivalent to

Takagi and Sugeno’s fuzzy inference system.

Layer1:

Every node in this layer is a square node, with a node function, 1 ( )Aii wherein θ

is the input to node i, and Ai is the linguistic label associated with this node function.

In this architecture, ( )Ai is bell shaped with maximum equal to 1 and minimum

equal to 0.

2

1( )

1

iA

i

i

bic

a

where , ,i i ia b c are the premise parameters.

Chapter-3

3. 29

Layer 2:

The function of the node in this layer is to multiply the incoming signals and produce

the product of all inputs. For instance,

( )x ( ) 1, 2......9

1,2,3,4,51,2,3,4,5

k li B Cwi

kl

Each node output represents the firing strength of a rule.

Layer 3:

The input firing strength is normalized in this layer, and output is called normalized

firing strengths.

1 2 9

, 1,2,3...9..........i

iw

w iw w w

Layer 4:

Every node i in this layer is a parameterized function. The node function is

4i ii i i i iw f w q r t

wherein i =1, 2……9 and iw is the output of the previous layer, and , ,i i iq r t is a

parameter set. Parameters in this layer are referred to as consequent parameters.

Layer 5:

The single node in this layer computes the overall output as the summation of all

incoming signals, i.e.

51 i i

i

overall output w f

The system is initialized with a number of membership functions and a rule base.

Learning consists of two separate passes. In the forward pass, the consequent

parameters are determined by least square method and antecedent parameters are

updated by a gradient descent algorithm in the backward pass. From the equations

obtained in layers 4 and 5, it is observed that, given the values of premise

Chapter-3

3. 30

parameters, the overall output is expressed as linear combinations of the consequence

parameters. The output f can be rewritten as

9

19

1 1 11( ) ( ) ( )

f w fi iif w q w r w ti i ii

This is linear in the consequent parameters. Learning consists of forward and

backward passes. The forward pass of the learning algorithm continues up to nodes

at layer 4, and consequent parameters are determined by the method of least squares.

In the backward pass, the error signal propagates backward to update the premise

parameters by gradient descent.

The FE simulation results/training data and NF estimated results for average

equivalent strain and forming energy are shown in table 3.15 and table 3.16

respectively. The close agreement of simulated and trained values given by the

developed neuro fuzzy model clearly shows the efficacy of the model. The training

information and the parameters of NF architecture are shown in Table 3.17. The

initial and final membership functions for the NF model developed are shown in Fig.

3.14.

Chapter-3

3. 31

Table 3.15: Training data and NF estimated results for average equivalent strain of ECAP process

Route‘A’

Φ = 90o Φ = 105o Φ = 120o

Coefficient of Friction

(µ)

Average Equivalent

Strain(FE result)

Average Equivalent

Strain(NF result)

Average Equivalent

Strain(FE result)

Average Equivalent

Strain(NF result)

Average Equivalent

Strain( FE result)

Average Equivalent

Strain(NF result)

0.00 6.551 6.551 4.579 4.580 2.934 2.9350.10 6.958 6.950 4.667 4.665 3.096 3.0960.15 7.198 7.197 4.675 4.675 3.265 3.2600.20 7.322 7.322 4.753 4.753 3.315 3.3150.25 7.325 7.324 5.126 5.125 3.374 3.3750.30 7.328 7.329 5.142 5.142 3.508 3.5080.35 7.382 7.380 5.664 5.660 3.827 3.8260.40 7.605 7.605 6.118 6.120 4.453 4.453

Route ‘BA’

Φ = 90o Φ = 105o Φ = 120o


(µ)

Average Equivalent

Strain(FE result)

Average Equivalent

Strain(NF result)

Average Equivalent

Strain(FE result)

Average Equivalent

Strain(NF result)

Average Equivalent

Strain(FE result)

Average Equivalent

Strain(NF result)

0.00 7.185 7.185 4.309 4.309 2.753 2.7490.10 7.232 7.230 4.623 4.623 2.795 2.8010.15 7.381 7.401 5.048 5.042 2.834 2.8250.20 7.394 7.404 5.239 5.232 2.902 2.8950.25 7.678 7.675 5.569 5.570 3.002 3.0000.30 7.721 7.720 5.682 5.685 3.095 3.0650.35 7.791 7.795 5.791 5.790 3.102 3.1000.40 7.944 7.943 5.916 5.914 3.146 3.152

Route ‘C’

Φ = 90o Φ = 105o Φ = 120o


(µ)

Average Equivalent

Strain(FE result)

Average Equivalent

Strain(NF result)

Average Equivalent

Strain(FE result)

Average Equivalent

Strain(NF result)

Average Equivalent

Strain(FE result)

Average Equivalent

Strain(NF result)

0.00 6.132 6.131 4.468 4.474 2.906 2.9050.10 6.235 6.242 4.702 4.700 3.272 3.2700.15 6.677 6.685 4.737 4.745 3.114 3.1140.20 6.699 6.702 4.562 4.569 3.482 3.4860.25 6.926 6.918 4.940 4.940 3.488 3.4880.30 7.057 7.054 5.393 5.393 3.870 3.8700.35 7.163 7.163 5.628 5.624 3.428 3.4250.40 7.188 7.190 5.716 5.720 3.274 3.281

Chapter-3

3. 32

Route ‘A’

Φ = 90o Φ = 105o Φ = 120o


(µ)

FormingEnergy

(FE result)

FormingEnergy

(NF result)

FormingEnergy

(FE result)

FormingEnergy

(NF result)

FormingEnergy

(FE result)

FormingEnergy

(NF result)

0.00 1.192 1.190 1.030 1.030 0.745 0.7450.10 1.360 1.356 1.345 1.345 1.195 1.1950.15 1.390 1.390 1.350 1.348 1.247 1.2380.20 1.404 1.400 1.362 1.357 1.251 1.2470.25 1.406 1.402 1.367 1.359 1.269 1.2610.30 1.412 1.412 1.384 1.380 1.295 1.2950.35 1.416 1.414 1.387 1.387 1.300 1.3000.40 1.423 1.424 1.390 1.392 1.302 1.302

Route ‘BA’

Φ = 90o Φ = 105o Φ = 120o


(µ)

FormingEnergy

(FE result)

FormingEnergy

(NF result)

FormingEnergy

(FE result)

FormingEnergy

(NF result)

FormingEnergy

(FE result)

FormingEnergy

(NF result)

0.00 1.215 1.210 1.058 1.058 0.857 0.8420.10 1.397 1.397 1.208 1.202 0.892 0.8920.15 1.402 1.400 1.229 1.215 0.913 0.9010.20 1.423 1.414 1.346 1.346 1.104 1.1110.25 1.424 1.418 1.396 1.388 1.129 1.1250.30 1.429 1.453 1.457 1.451 1.132 1.1300.35 1.463 1.447 1.489 1.490 1.140 1.1400.40 1.484 1.460 1.508 1.512 1.142 1.137

Route ‘C’

Φ = 90o Φ = 105o Φ = 120o


(µ)

FormingEnergy

(FE result)

FormingEnergy

(NF result)

FormingEnergy

(FE result)

FormingEnergy

(NF result)

FormingEnergy

(FE result)

FormingEnergy

(NF result)

0.00 1.203 1.200 1.028 1.021 0.795 0.7910.10 1.367 1.367 1.296 1.296 1.245 1.2230.15 1.413 1.424 1.421 1.420 1.327 1.3140.20 1.429 1.437 1.482 1.467 1.341 1.3400.25 1.495 1.495 1.435 1.419 1.352 1.3320.30 1.463 1.445 1.510 1.523 1.323 1.3090.35 1.501 1.500 1.556 1.536 1.350 1.3160.40 1.404 1.401 1.465 1.465 1.384 1.375

Table 3.16: Training data and NF estimated results for forming energy(kJ) of ECAP process

Chapter-3

3. 33


Table 3.17: Training parameters of NF architecture for ECAP process

Fig. 3.14: Initial and final membership functions for the NF model of ECAP process

Validation of neuro-fuzzy model for ECAP process: After developing the NF

model from training it by FE simulation data the model is validated. For this, the input

parameters to the NF model are sets of values that have not been used for training the

model but are in the same range as those used for training. This enables us to test the

network with regard to its capability for interpolation. The final extrusion force is thus

obtained for this set of parameters. Then an FE simulation is performed for the same

sets of parameters to determine the extrusion force. The level of agreement between

the extrusion force predicted by NF model and the FE simulation indicates the

conformity of the NF model. The results of the validation procedure described above

are given in table 3.18. The close agreement of the values of the average equivalent

strain and forming energy obtained by the NF model and the FE simulation clearly

indicates that the model can be used for predicting these output parameters in the

range of parameters under consideration. The model is very fast and prediction can be

done in real time.

Chapter-3

3. 34

S. No. Φ µAverage Equivalent

StrainForming Energy

(KJoules)FEM result

NF result FEM result

NF result

1. 90o 0.02 7.237 7.018 1.289 1.0902. 90o 0.06 7.493 6.990 1.423 1.1143. 90o 0.08 7.556 7.174 1.444 1.3254. 105o 0.02 5.572 5.201 1.123 1.1245. 105o 0.06 5.584 5.235 1.302 1.4526. 105o 0.08 5.649 5.186 1.387 1.2887. 120o 0.02 4.368 3.869 0.927 0.8928. 120o 0.06 4.571 4.621 1.109 1.0119. 120o 0.08 4.738 4.739 1.154 1.155

Table 3.18: Validation of average equivalent strain and forming energy results of NF model with FE results

3.9 Neuro-Fuzzy modelling of orthogonal cutting process

Cutting force estimation is an important criterion that determines the economics of

machining and is of engineering interest in intelligent manufacturing. A complex

relationship exists between process parameters like speed, feed, depth of cut, tool

geometry and cutting forces. There is a need to develop models that can capture this

interrelationship and enable fast computation of the cutting forces based on these

parameters. Here NF modelling of cutting forces for a given set of input parameters

i.e. speed, feed and depth of cut is attempted and the results obtained from NF model

compare favorably with the experimental data sets of cutting forces.

NF inference system under consideration has three inputs viz. Speed (α), feed (ν) and

depth of cut (γ), and one output cutting force (f). The neuro fuzzy network model is

shown in figure 3.15. The adaptive NF network model is developed on similar pattern

as described in section 3.7 and 3.8. This system is also initialized with a number of

membership functions and a rule base. Learning consists of two separate passes. In

the forward pass, the consequent parameters are determined by least square method

and antecedent parameters are updated by a gradient descent algorithm in the

backward pass.

Chapter-3

3. 35

Fig. 3.15: A three input and one output NF network model for orthogonal cutting process

From the equations obtained in layer 4 and 5 it is observed that given the values of

premise parameters, the overall output is expressed as linear combinations of the

consequence parameters. The output f can be rewritten as:

27

127

( ) ( ) ( ) ( )1 1 1 11

f w fi ii

f w q w r w s w ti i i ii

The forward pass of the learning algorithm continues up to nodes at layer 4 and

consequent parameters are determined by the method of least squares. In the

backward pass, the error signal propagates backward to update the premise parameters

by gradient descent.

Nagaraju [Nag97] have experimentally measured the actual cutting forces at various

cutting conditions to see the influence of speed, feed, and depth of cut on the two

dimensional cutting force system in metal cutting operation. Mild steel specimen and

high speed steel tool material are used in these experiments. They have also attempted

to develop an artificial neural network (ANN) model for the cutting forces by using

the simple back propagation algorithm. However, the predicted values from their

Chapter-3

3. 36

model show quite a large variation from the actual experimentally observed cutting

forces. Hans Raj [Hans98] used NN trained with LM learning rule and obtained

results closer than the Nagaraju [Nag97]. The predicted values by NF model used in

this work are much closer as can be observed from the results. The experimental

results and the estimated values reported by Nagaraju [Nag97], Hans Raj [Hans98]

and NF model are listed in table 3.19.

Speedm/min

Feedmm

Depth ofCutmm


Forces,(N)

Valuesby [Nag97]

Values byLM Network,

[Hans98](N)

Valuesby NFmodel

(N)Fc Ft Fc Ft Fc Ft Fc Ft

29 0.440 1.0 571.4 380.9 750 537.1 571.7 379.4 571.4001 380.900129 0.212 1.0 457.1 361.9 505 392 457.1 361.1 457.1001 361.899929 0.107 1.0 304.7 228.6 418 338 304.1 231.1 304.7000 228.600022 0.440 1.0 523.8 285.7 690 499 523.8 287.2 523.8000 285.699822 0.107 1.0 276.2 209.5 382 315 275.3 205.0 276.1998 209.499617 0.440 1.0 476.2 285.7 629 463 474.8 285.2 476.2000 285.700517 0.212 1.0 385.7 238.0 411 332.8 387.3 237.3 385.6998 238.000717 0.107 1.0 238.1 142.8 358 300 237.1 147.8 238.1003 142.800813 0.440 1.0 428.5 333.3 588 439 430.1 333.5 428.5000 333.299713 0.212 1.0 333.3 285.7 390 319 332.3 286.4 333.3001 285.699613 0.107 1.0 238.1 190.5 346 291 239 188.7 238.0998 190.499529 0.212 1.2 571.4 428.5 526 402 571.2 429.7 571.3999 428.500129 0.107 1.2 400.0 342.8 432 346 400.1 339.4 400.0000 342.800122 0.440 1.2 523.8 380.9 712 5111 524.3 426.6 523.8001 380.900022 0.212 1.2 457.4 342.9 468 368 459.6 346.5 457.3998 342.900222 0.107 1.2 361.9 304.7 393 321 361.7 308.4 361.9000 304.699917 0.440 1.2 666.7 428.5 653 476 666.1 429.9 666.6999 428.499817 0.212 1.2 476.2 380.9 425 341 474.4 377.6 476.2006 380.899617 0.107 1.2 342.8 285.7 367 305 343.6 282.4 342.8000 285.700213 0.440 1.2 761.9 428.5 612 452 761.7 427.8 761.9001 428.500113 0.107 1.2 323.8 280.9 352 296 322.9 288.9 323.8000 280.899929 0.440 1.5 904.7 666.7 793 561 904.5 666.3 904.7001 666.700029 0.212 1.5 523.8 428.6 559 421 524.7 427.0 523.7999 428.600029 0.107 1.5 447.6 400 456 361 447.2 400.2 447.6001 399.999922 0.440 1.5 1000 714.2 742 529 1000 714.3 999.9998 714.199822 0.212 1.5 619.1 523.8 497 384 617.4 525.4 619.1000 523.800122 0.107 1.5 333.3 285.7 412 334 333.7 286.3 333.3003 285.700017 0.440 1.5 714.2 523.8 687 496 714.4 524.2 714.2005 523.800717 0.212 1.5 523.8 428.5 449 356 523.4 429.2 523.7999 428.499913 0.440 1.5 574.2 476.1 674 473 574.9 475.3 574.1997 476.099613 0.212 1.5 428.5 333.3 422 339 429.1 332.7 428.5000 333.300113 0.107 1.5 285.7 204.7 364 304 284.9 207.1 285.7004 204.7000

Table 3.19: Experimental and estimated values of cutting forces for speed, feed and depth of cut

Chapter-3

3. 37

The results of the validation procedure are given in table 3.20. The close agreement of

the values obtained by the experimental values reported by Nagaraju et al. and

predicted values by NF model clearly indicates that the model can be used for

predicting the output in the range of parameters under consideration. Training

parameters and initial and final membership functions of NF model for cutting forces

(Fc & Ft) are shown in table 3.21 and figure 3.16.

Speed(m/min)

Feed(mm)

Depthof

Cut(mm)


Forces [Nag97]Values byNF Model

Fc (N) Ft (N) Fc (N) Ft (N)22 0.212 1.0 419.0 257.1 419 257.029 0.440 1.2 714.3 476.2 714 476.213 0.212 1.2 571.4 380.9 571.2 380.817 0.107 1.5 380.9 238.1 380.9 238.0

Table 3.20: Validation of estimated values of cutting forces using NF model with experimental values reported by Nagaraju et al.


Table 3.21: Training parameters of NF architecture for orthogonal cutting

process (Fc & Ft)

Fig. 3.16: Initial and final membership functions of orthogonal cutting forces(Fc & Ft)

Chapter-3

3. 38

3.10 Neuro-Fuzzy modelling of end milling process

The data obtained from the mentioned experimental setup in table 3.8, section 3.5 is

used to train the NF model for end milling process. The NF model is developed on

similar pattern as developed for forming processes in section 3.7 and 3.8. Neuro-fuzzy

inference system under consideration has four inputs as shown in figures 3.17 and

3.18 viz. cutting speed, feed rate, radial depth of cut, tolerance and one output

machining time and average surface roughness. The overall output is expressed as

linear combinations of the consequent parameters. The output f can be rewritten as

81

181

( ) ( ) ( ) ( ) ( )1

f w fi ii

f w p w q w r w s w ti i i i ii i i i ii

This is linear in the consequent parameters. The forward pass of the learning

algorithm continues up to nodes at layer 4 and consequent parameters are determined

by the method of least squares. In the backward pass, the error signal propagates

backward to update the premise parameters by gradient descent.

Fig. 3.17: A four input and one output (machining time) neuro-fuzzy network model for end milling

Chapter-3

3. 39

Fig. 3.18: A four input and one output (average surface roughness) neuro-fuzzy network model for end milling

The experimental values reported by Tansel et al. [Tan06] and the computed values

after training NF model are listed in table 3.22. The close agreement of the values

obtained by the model and those reported by Tansel et al., [Tan06] clearly indicates

that the model can be used for predicting the values in the range of parameters under

consideration. The model is very fast and the time taken for prediction is negligible.

NoCutting Speed

(m/min)

Feed rate(mm/tooth)

Radial depth

ofcut

(mm)

Tolerance(mm)


Estimated values using Neuro Fuzzy Model

Average surface

roughness (µm)

MachiningTime (min)

Average surface

roughness (µm)

MachiningTime (min)

1 74 0.07 0.1 0.001 0.26 64 0.26 64.002 98.5 0.07 0.1 0.001 0.31 47 0.31 47.003 123 0.07 0.1 0.001 0.27 45 0.27 45.004 74 0.095 0.1 0.001 0.32 48 0.32 48.005 98.5 0.095 0.1 0.001 0.36 36 0.35 35.996 123 0.095 0.1 0.001 0.85 29 0.85 29.007 74 0.12 0.1 0.001 0.48 39 0.48 39.008 98.5 0.12 0.1 0.001 0.37 28 0.37 27.999 123 0.12 0.1 0.001 1.58 24 1.58 23.99

10 74 0.07 0.2 0.001 0.36 32 0.35 31.9911 98.5 0.07 0.2 0.001 0.59 24 0.59 23.9912 123 0.07 0.2 0.001 0.52 19 0.52 18.9913 74 0.095 0.2 0.001 0.51 23 0.51 23.0014 98.5 0.095 0.2 0.001 0.53 17 0.53 17.0015 123 0.095 0.2 0.001 0.81 15 0.81 15.0016 74 0.12 0.2 0.001 0.53 21 0.53 21.0017 98.5 0.12 0.2 0.001 0.47 14 0.47 14.0018 123 0.12 0.2 0.001 0.93 12 0.93 12.0019 74 0.07 0.3 0.001 0.49 22 0.49 22.0020 98.5 0.07 0.3 0.001 0.50 17 0.50 16.9921 123 0.07 0.3 0.001 1.22 13.3 1.22 13.29

Chapter-3

3. 40

22 74 0.095 0.3 0.001 0.42 15.3 0.42 15.2923 98.5 0.095 0.3 0.001 0.58 12 0.58 11.9924 123 0.095 0.3 0.001 1.31 09 1.31 9.0025 74 0.12 0.3 0.001 0.67 13 0.67 12.9926 98.5 0.12 0.3 0.001 0.47 10 0.47 10.0027 123 0.12 0.3 0.001 0.98 7.3 0.98 7.2928 74 0.07 0.1 0.0055 0.37 64 0.37 63.9929 98.5 0.07 0.1 0.0055 0.30 49 0.30 49.0030 123 0.07 0.1 0.0055 0.37 48 0.37 47.9931 74 0.095 0.1 0.0055 0.53 45 0.53 44.9832 98.5 0.095 0.1 0.0055 0.47 37 0.47 37.0033 123 0.095 0.1 0.0055 0.64 29 0.64 28.9934 74 0.12 0.1 0.0055 0.65 39 0.65 38.9935 98.5 0.12 0.1 0.0055 0.52 30.3 0.52 30.3036 123 0.12 0.1 0.0055 1.15 23.3 1.15 23.3037 74 0.07 0.2 0.0055 0.49 33 0.49 33.0038 98.5 0.07 0.2 0.0055 0.89 24 0.89 24.0039 123 0.07 0.2 0.0055 0.71 20.3 0.71 20.3040 74 0.095 0.2 0.0055 0.80 24 0.80 23.9841 98.5 0.095 0.2 0.0055 0.66 29 0.66 28.9942 123 0.095 0.2 0.0055 0.76 15 0.76 14.9943 74 0.12 0.2 0.0055 0.58 20.3 0.58 20.3044 98.5 0.12 0.2 0.0055 0.32 15 0.32 14.9845 123 0.12 0.2 0.0055 0.77 12 0.77 11.9946 74 0.07 0.3 0.0055 0.57 22 0.57 21.9947 98.5 0.07 0.3 0.0055 1.22 16.3 1.22 16.3048 123 0.07 0.3 0.0055 0.83 13.3 0.83 13.2949 74 0.095 0.3 0.0055 0.69 16.3 0.69 16.3150 98.5 0.095 0.3 0.0055 0.91 12.3 0.91 12.3151 123 0.095 0.3 0.0055 0.90 9.3 0.90 9.2952 74 0.12 0.3 0.0055 0.66 13 0.66 12.9853 98.5 0.12 0.3 0.0055 0.73 10 0.73 10.0054 123 0.12 0.3 0.0055 0.82 08 0.82 7.9955 74 0.07 0.1 0.01 0.42 65 0.42 64.9956 98.5 0.07 0.1 0.01 0.20 49 0.20 48.9957 123 0.07 0.1 0.01 0.57 39 0.57 38.9958 74 0.095 0.1 0.01 0.47 48 0.47 48.0059 98.5 0.095 0.1 0.01 0.40 36 0.40 35.9960 123 0.095 0.1 0.01 0.51 30 0.51 30.0061 74 0.12 0.1 0.01 0.48 38 0.48 38.0062 98.5 0.12 0.1 0.01 0.59 35 0.59 34.9963 123 0.12 0.1 0.01 0.47 24 0.47 24.0064 74 0.07 0.2 0.01 0.66 34 0.66 33.9965 98.5 0.07 0.2 0.01 0.78 24.3 0.78 24.2966 123 0.07 0.2 0.01 1.27 20 1.27 19.9967 74 0.095 0.2 0.01 0.50 25 0.50 25.0068 98.5 0.095 0.2 0.01 0.58 18 0.58 18.0069 123 0.095 0.2 0.01 0.66 14 0.66 14.0070 74 0.12 0.2 0.01 0.62 19 0.62 18.9971 98.5 0.12 0.2 0.01 0.60 15.3 0.60 15.3072 123 0.12 0.2 0.01 0.62 12 0.62 12.0073 74 0.07 0.3 0.01 0.58 23 0.58 23.0074 98.5 0.07 0.3 0.01 0.70 17 0.70 16.9975 123 0.07 0.3 0.01 0.71 13.3 0.71 13.3076 74 0.095 0.3 0.01 0.68 18.3 0.68 18.2977 98.5 0.095 0.3 0.01 0.72 12.3 0.72 12.2978 123 0.095 0.3 0.01 1.05 10.3 1.05 10.2979 74 0.12 0.3 0.01 0.85 09.3 0.85 9.3180 98.5 0.12 0.3 0.01 0.61 10 0.61 1081 123 0.12 0.3 0.01 0.62 08 0.62 8.01

Table 3.22: Experimental and estimated values for given average surface roughness and machining time

Chapter-3

3. 41

The results of the validation of developed NF model are given in table 3.23. The close

agreement of the values of the average surface roughness and machining time in

comparison with the results obtained by the neural network in section 3.5 clearly

indicates that this NF model is more suitable to act as function approximator in

optimizers described in subsequent chapters. The training information of NF model is

shown in table 3.24 and membership functions are shown in figure 3.19.

Cutting Speed

(m/min)

Feed rate(mm/tooth)

Radial depthof

cut(mm)

Tolerance(mm)


Estimated values using NF Model

Average surface

roughness (µm)

MachiningTime (min)

Average surface

roughness(µm)


98.5 0.095 0.1 0.001 0.36 36 0.36 3698.5 0.095 0.1 0.0055 0.47 37 0.47 37123 0.07 0.3 0.0055 0.83 13.3 0.83 13.2998.5 0.12 0.1 0.01 0.59 35 0.59 3574 0.07 0.3 0.01 0.58 23 0.58 23Table 3.23: Validation of estimated values of average surface roughness and

machining time using NF model with experimental values


Table 3.24: Training Parameters of NF architecture for end milling process

Fig. 3.19: Initial and final membership functions for the NF model of end millingprocess

Chapter-3

3. 42

3.11 Statistical Regression Modelling

Regression modelling is a statistical tool for the investigation of relationships between

two or more variables. It establishes the relationship between a dependent variable or

response that depends upon one or more independent variables. In this section

statistical regression models for hot extrusion process, ECAP, orthogonal cutting

process and end milling process are developed and are compared with NF models,

discussed in the previous sections. A brief introduction of regression model is as

follows:

Regression modelling is used when two or more variables are thought to be

systematically connected by a linear relationship. Suppose we wish to develop an

empirical model relating a single dependent variable or response ‘y’ to the two

independent or regressor variables x1 and x2. A model that might describe this

relationship is:

0 1 1 2 2y x x

Above equation is a linear regression model with two independent variables, where

0 , 1 and 2 are unknown parameters. The model describes a plane in the two

dimensional x1, x2 space. The parameter 0 defines the intercept of the plane and

parameters 1 and 2 are called regression coefficients. The is the error term.

The regression model fitting in this work is done using a statistical software package

known as MINITAB 15. It can be used for learning about statistics as well as

statistical research. Statistical analysis computer applications have the advantage of

being accurate, reliable, and generally faster than computing statistics and drawing

graphs by hand. Minitab is user friendly and is relatively easy to use.

In order to judge the accuracy of the regression prediction model, relative percentage

error ϕ and average relative percentage error ϕa are used which are defined as:

100%FE V

FE

P E

P

Chapter-3

3. 43

1

n

ia

n

where PFE is predicted finite element simulation value , EV is estimated value of the

model and n is the number of observations.

3.11.1 Regression modelling of hot extrusion process

Statistical regression model is developed using Minitab 15 for hot extrusion process

and is compared with NF model and FE model. Through the regression analysis of

the results, the values of the model coefficients have been obtained and the regression

equation for extrusion load as response is given as under:

Load = 405 – 0.562 Angle + 14.7 Friction – 0.135 Temp

The Minitab output for hot extrusion is shown below:

The regression equation isLoad = 405 - 0.562 Angle + 14.7 Friction - 0.135 Temp

Predictor Coef SE Coef T PConstant 405.43 21.98 18.44 0.000Angle -0.56187 0.08338 -6.74 0.000Friction 14.69 10.83 1.36 0.180Temp -0.13490 0.01818 -7.42 0.000

S = 13.7006 R-Sq = 64.6% R-Sq(adj) = 62.7%

Analysis of Variance

Source DF SS MS F PRegression 3 19208.5 6402.8 34.11 0.000Residual Error 56 10511.5 187.7Total 59 29720.1

Source DF Seq SSAngle 1 8523.9Friction 1 345.5Temp 1 10339.1

Unusual Observations

Obs Angle Load Fit SE Fit Residual St Resid13 75.0 261.93 234.27 4.46 27.66 2.14R15 75.0 266.07 240.14 4.46 25.93 2.00R57 60.0 185.91 213.50 3.84 -27.59 -2.10R

R denotes an observation with a large standardized residual.

Chapter-3

3. 44

The comparison of both the models i.e. NF model and Regression Analysis (RA)

model with FE modeled values in terms of relative percentage error for hot extrusion

process are shown in table 3.25. Error comparison of both the models is also shown

in table 3.26. Graph in fig. 3.20 shows comparison of FE modeled extrusion load

values and predicted values of NF and RA models.

Die Angle

(o)

Coefficientof

Friction

Temp.of

billet(oC)

FE Modeledextrusion

load(Tons)

NFmodeledextrusion

load(Tons)

RA modeledextrusion

load(Tons)

Relative Error (ϕ)obtained by RA

(%)

RelativeError (ϕ)obtainedby NF

(%) 15 0.2 1000 268.41 267.98 264.51 1.45 0.1645 0.3 1000 241.72 240.47 249.12 3.06 0.5175 0.7 1000 224.04 223.99 238.14 6.29 0.0215 0.2 1260 250.21 248.61 229.41 8.31 0.6445 0.3 1260 254.24 253.99 214.02 15.81 0.0975 0.7 1260 261.48 259.92 203.04 22.35 0.60Table 3.25: Comparison of NF and RA models for predicting extrusion load

using relative percentage error

ModelMinimum relative error

(%)

Maximum relative error

(%)

Averagerelative error (ϕa)

(%)Neuro-Fuzzy (NF) 0.02 0.64 0.33

Regression Analysis (RA) 1.45 22.35 9.54Table 3.26: Error comparison of NF and RA models

Fig. 3.20: Comparison of FE modeled extrusion load values and predicted values of NF and RA models

Chapter-3

3. 45

The result of average percentage error (ϕa) is 0.33% for NF model as shown in table

3.26 for validation data set (n=6) and 9.54% for RA model. This means that the NF

model could predict the average equivalent strain with 99.67% accuracy as compared

to RA model with 90.46% accuracy. Further, R-squared (R2) and R-squared adjusted

(R2adj) values are also calculated which show the goodness of fit of the neuro-fuzzy

and regression models. For NF model the R2 value is 98.9% and R2adj is 99.1%. For

RA model the R2 value is 64.6% and R2adj is 62.7%. The NF model clearly

outperforms the statistical regression model.

3.11.2 Regression modelling of ECAP process

The regression models for average equivalent strain and forming energy of ECAP

process are also developed using Minitab 15 and are compared with NF model and FE

model. Through the regression analysis of the results, the values of the model

coefficients have been obtained and the regression equation for average equivalent

strain and forming energy are given as under:

Average Equivalent Strain = 17.7 - 0.125 angle + 3.07 friction

Forming Energy = 1.75 - 0.00583 angle + 0.763 friction

The Minitab output is shown below:

Regression Analysis ECAP Route A: Strain versus Angle, Friction

The regression equation isStrain = 17.7 - 0.125 Angle + 3.07 Friction

Predictor Coef SE Coef T PConstant 17.6656 0.4381 40.32 0.000Angle -0.124571 0.004061 -30.67 0.000Friction 3.0685 0.3984 7.70 0.000

S = 0.243688 R-Sq = 97.9% R-Sq(adj) = 97.7%



Source DF Seq SSAngle 1 55.864Friction 1 3.522


Chapter-3

3. 46

Obs Angle Strain Fit SE Fit Residual St Resid24 120 4.4530 3.9445 0.1068 0.5085 2.32R


The comparison of both the models i.e. NF model and Regression Analysis (RA)

model with FE modeled values in terms of relative percentage error for average

equivalent strain are shown in table 3.27. Error comparison of both the models is also

shown in table 3.28. Graph in fig. 3.21 shows comparison of FE modeled average

equivalent strain values and predicted values of NF and RA models.

Channel Angle

(o)

Coefficientof

Friction

FE modeledAverage

EquivalentStrain

NFmodeledAverage

EquivalentStrain

RA modeledAverage

EquivalentStrain


(%)


(%) 90 0.02 7.237 7.018 6.653 8.07 3.0390 0.06 7.493 6.990 6.761 9.77 6.7190 0.08 7.556 7.174 6.815 9.80 5.05105 0.02 5.572 5.201 4.703 15.59 6.66105 0.06 5.584 5.235 4.811 13.84 6.25105 0.08 5.649 5.186 4.865 13.87 8.19120 0.02 4.368 3.869 2.753 36.97 11.42120 0.06 4.571 4.621 2.861 37.41 1.09120 0.08 4.738 4.739 2.915 38.47 0.02

Table 3.27: Comparison of NF and RA models for predicting average equivalent strain using relative percentage error

ModelMinimum relative error

(%)

Maximum relative error

(%)

Averagerelative

error (ϕa)(%)

Neuro-Fuzzy (NF) 0.02 11.42 5.38Regression Analysis (RA) 8.07 38.47 20.42

Table 3.28: Error comparison of NF and RA models for average equivalent strain

Chapter-3

3. 47

Fig. 3.21: Comparison of FE modeled average equivalent strain values and predicted values of NF and RA models

The result of average percentage error (ϕa) is 5.38% of average equivalent strain for

NF model as shown in table 3.28 for validation data set (n=9) and 20.42% for RA

model. This means that the NF model could predict the average equivalent strain with

94.62% accuracy as compared to RA model with just 79.58% accuracy. Further, R-

squared (R2) and R-squared adjusted (R2adj) values are also calculated which show

the goodness of fit of the neuro-fuzzy and regression models. For NF model the R2

value is 99.2% and R2adj is 99.6%. For RA model the R2 value is 97.9% and R2adj is

97.7%.The results clearly shows that values of NF model are quite consistent in

comparison with RA modeled values.

The Minitab output for forming energy is shown below:

Regression Analysis ECAP Route A: Energy versus Angle, Friction

The regression equation isEnergy = 1.75 - 0.00583 Angle + 0.753 Friction

Predictor Coef SE Coef T PConstant 1.7484 0.1692 10.33 0.000Angle -0.005829 0.001569 -3.72 0.001Friction 0.7525 0.1539 4.89 0.000

Chapter-3

3. 48

S = 0.0941400 R-Sq = 64.2% R-Sq(adj) = 60.8%



Source DF Seq SSAngle 1 0.12233Friction 1 0.21182


Obs Angle Energy Fit SE Fit Residual St Resid17 120 0.7450 1.0489 0.0454 -0.3039 -3.68R


The comparison of. NF model and Regression Analysis (RA) model with FE modeled

values in terms of relative percentage error for forming energy are shown in table

3.29. Error comparison of both the models is shown in table 3.30. Graph in fig. 3.22

shows comparison of FE modeled forming energy and predicted values of NF and RA

models.

Channel Angle

(o)

Coefficientof

Friction

FE modeledForming Energy

(KJ)

NFmodeledForming Energy

(KJ)

RA modeledForming Energy

(KJ)


(%)


(%) 90 0.02 1.289 1.269 1.251 2.95 1.5590 0.06 1.423 1.349 1.284 9.77 5.2090 0.08 1.444 1.325 1.301 9.90 8.24105 0.02 1.123 1.120 1.136 1.15 0.27105 0.06 1.302 1.288 1.170 10.14 1.07105 0.08 1.387 1.299 1.187 14.42 6.34120 0.02 0.927 0.892 1.022 10.25 3.78120 0.06 1.109 1.099 1.055 4.87 0.90120 0.08 1.154 1.100 1.072 7.10 4.68Table 3.29: Comparison of NF and RA models for predicting forming energy

using relative percentage error

Model

Minimum relative

error (%)

Maximum relative

error(%)

Averagerelative

error (ϕa)(%)

Neuro-Fuzzy (NF) 0.27 8.24 3.56Regression Analysis (RA) 1.15 14.42 7.84

Table 3.30: Error comparison of NF and RA models for forming energy

Chapter-3

3. 49

Fig. 3.22: Comparison of FE modeled forming energy values and predicted values of NF and RA models

The results shown in Table 3.29, 3.30 and Fig. 3.22 again clearly shows that values of

NF model are quite consistent in comparison with RA modeled values with those of

FE modeled values of forming energy for ECAP process. The result of average

percentage error (ϕa) is 3.56% of forming energy for NF model as shown in table 3.30

for validation data set (n=9) and 7.84% for RA model. This means that the NF model

could predict the forming energy with 96.44% accuracy as compared to RA model

with 92.16% accuracy. Further, R-squared (R2) and R-squared adjusted (R2adj) values

are also calculated which show the goodness of fit of the neuro-fuzzy and regression

models. For NF model the R2 value is 97.9% and R2adj is 98.2%. For RA model the

R2 value is 64.2% and R2adj is 60.8%. The NF model performance is again found to

be better than the statistical regression model.

3.11.3 Regression modelling of orthogonal cutting process

Through the regression analysis of the results, the values of the model coefficients

have been obtained and the regression equations of cutting forces (Ft and Fc) are given

as under:

Ft = - 330 + 6.34 Speed + 521 Feed + 348 Depth of cut

Fc = - 343 + 7.56 Speed + 956 Feed + 349 Depth of cut

Chapter-3

3. 50

The Minitab output for cutting force (Ft) is shown below:

Regression Analysis Orthogonal cutting: Ft versus Speed, Feed and Depth of cut

The regression equation isFt = - 330 + 6.34 Speed + 521 Feed + 348 Depth of cut

Predictor Coef SE Coef T PConstant -330.07 80.50 -4.10 0.000Speed 6.338 1.919 3.30 0.003Feed 521.35 81.33 6.41 0.000Depth of cut 347.98 54.79 6.35 0.000

S = 64.5591 R-Sq = 77.0% R-Sq(adj) = 74.5%


Source DF SS MS F PRegression 3 390102 130034 31.20 0.000Residual Error 28 116700 4168Total 31 506803

Source DF Seq SSSpeed 1 36781Feed 1 185188Depth of cut 1 168133


Obs Speed Ft Fit SE Fit Residual St Resid25 22.0 714.2 560.7 23.9 153.5 2.56R32 13.0 204.7 330.1 27.1 -125.4 -2.14R


The Minitab output for cutting force (Fc) is shown below:

Regression Analysis: Fc versus Speed, Feed, Depth of cut

The regression equation isFc = - 343 + 7.56 Speed + 956 Feed + 349 Depth of cut

Predictor Coef SE Coef T PConstant -342.7 108.3 -3.17 0.004Speed 7.557 2.581 2.93 0.007Feed 955.6 109.4 8.74 0.000Depth of cut 348.55 73.68 4.73 0.000

S = 86.8243 R-Sq = 79.3% R-Sq(adj) = 77.1%

Chapter-3

3. 51


Source DF SS MS F PRegression 3 811037 270346 35.86 0.000Residual Error 28 211077 7538Total 31 1022114

Source DF Seq SSSpeed 1 41205Feed 1 601147Depth of cut 1 168685


Obs Speed Fc Fit SE Fit Residual St Resid20 13.0 761.9 594.3 30.6 167.6 2.06R25 22.0 1000.0 766.8 32.1 233.2 2.89R


The NF model and Regression Analysis (RA) model with FE modeled values in terms

of relative percentage error for cutting forces (Ft and Fc) is shown in table 3.31. Error

comparison of both the models is shown in table 3.32. Graphs in fig. 3.23 and 3.24

shows comparison of FE modeled cutting forces (Ft and Fc) and predicted values of

NF and RA models.

Speed(m/min

Feed(mm)

Depthof

Cut(mm)


Forces[Nag et al.]

(N)

NF Modeled Values

(N)

RA ModeledValues

(N)

Relative Error (ϕ)

(NF Model)(%)

Relative Error (ϕ)

(RA Model)(%)

Fc Ft Fc Ft Fc Ft Fc Ft Fc Ft

22 0.212 1.0 419.0 257.1 417.9 256.9 374.99 267.93 0.26 0.07 10.5 4.2129 0.440 1.2 714.3 476.2 712.2 475.2 715.68 500.70 0.29 0.21 0.19 5.1413 0.212 1.2 571.4 380.9 569.2 382.9 476.75 280.47 0.38 0.52 16.56 26.3617 0.107 1.5 380.9 238.1 382.9 236.9 411.31 355.52 0.52 0.50 7.98 49.31Table 3.31: Comparison of NF and RA models for predicting cutting forces (Ft

and Fc) using relative percentage error

Model

CuttingForces(N)

Minimum relative

error (%)

Maximum relative

error(%)

Averagerelative

error (ϕa)(%)

Neuro-Fuzzy (NF)Fc 0.26 0.52 0.36Ft 0.07 0.52 0.32

Regression Analysis (RA)Fc 0.19 16.56 8.80Ft 4.21 49.31 21.25

Table 3.32: Error comparison of NF and RA models for cutting forces (Ft and Fc)

Chapter-3

3. 52

Fig. 3.23: Comparison of experimental values of cutting force (Fc) and predicted values of NF and RA models

Fig. 3.24: Comparison of experimental values of cutting force (Ft) and predicted values of NF and RA models

Further, R-squared (R2) and R-squared adjusted (R2adj) values are also calculated

which show the goodness of fit of the neuro-fuzzy and regression models. For NF

model the R2 value is 92.3% and R2adj is 93.7% for Ft and 93.2% and 95.3% for Fc.

For RA model the R2 value is 77.0% and R2adj is 79.3% for Ft and 79.3% and 77.1%

for Fc.

Chapter-3

3. 53

3.11.4 Regression modelling of end milling process

The regression equations and the values of the model coefficients of surface roughness and machining timing are given as under.

Surface Roughness = - 0.288 + 0.00549 Cutting Speed + 1.47 Feed rate + 1.22 Depth of cut + 0.95 Tolerance

Machining Time = 99.0 - 0.235 Cutting Speed - 258 Feed rate - 135 Depth of cut + 46 Tolerance

The Minitab output for surface roughness is shown below:

Regression Analysis: Roughness versus Cutting Speed, Feed rate, Depth of cut and Tolerance

The regression equation isRoughness = - 0.288 + 0.00549 Cutting Speed + 1.47 Feed rate + 1.22 Depth of cut + 0.95 Tolerance

Predictor Coef SE Coef T PConstant -0.2878 0.1777 -1.62 0.109Cutting Speed 0.005488 0.001196 4.59 0.000Feed rate 1.467 1.172 1.25 0.215Depth of cut 1.2185 0.2930 4.16 0.000Tolerance 0.947 6.512 0.15 0.885

S = 0.215336 R-Sq = 84.4% R-Sq(adj) = 81.0%



Source DF Seq SSCutting Speed 1 0.97607Feed rate 1 0.07260Depth of cut 1 0.80179Tolerance 1 0.00098


CuttingObs Speed Roughness Fit SE Fit Residual St Resid 9 123 1.5800 0.6860 0.0633 0.8940 4.34R24 123 1.3100 0.8930 0.0561 0.4170 2.01R36 123 1.1500 0.6902 0.0561 0.4598 2.21R47 99 1.2200 0.7262 0.0479 0.4938 2.35R66 123 1.2700 0.7430 0.0561 0.5270 2.53R


Chapter-3

3. 54

The Minitab output for machining time is shown below:

Regression Analysis: Machining Time versus Cutting Speed, Feed rate, Depth of cut and Tolerance

The regression equation isMachining Time = 99.0 - 0.235 Cutting Speed - 258 Feed rate - 135 Depth of cut + 46 Tolerance

Predictor Coef SE Coef T PConstant 99.049 4.178 23.71 0.000Cutting Speed -0.23515 0.02813 -8.36 0.000Feed rate -257.78 27.56 -9.35 0.000Depth of cut -134.759 6.891 -19.56 0.000Tolerance 46.1 153.1 0.30 0.764

S = 5.06370 R-Sq = 87.7% R-Sq(adj) = 87.0%



Source DF Seq SSCutting Speed 1 1792.3Feed rate 1 2242.7Depth of cut 1 9806.4Tolerance 1 2.3


Cutting MachiningObs Speed Time Fit SE Fit Residual St Resid 1 74 64.000 50.174 1.489 13.826 2.86R28 74 64.000 50.381 1.319 13.619 2.79R55 74 65.000 50.589 1.489 14.411 2.98R


The NF model and Regression Analysis (RA) model with FE modeled values for

surface roughness and machining time is shown in table 3.33. Comparison of NF and

RA models in terms of relative percentage error is shown in table 3.34. Error

comparison of both the models is shown in table 3.35. Graphs in fig. 3.25 and 3.26

show comparison of FE modeled surface roughness and machining time and predicted

values of NF and RA models.

Chapter-3

3. 55

Cutting Speed

(m/min)

Feed rate

(mm/tooth)

Radial depth

ofcut

(mm)

Tolerance(mm)

Experimental values by Tansel et al.

Estimated values usingNF Model

Estimated values using

RA ModelAverage surface

roughness (µm)

MachiningTime (min)

Average surface

roughness (µm)

MachiningTime (min)

Average surface

roughness(µm)

MachiningTime (min)

98.5 0.095 0.1 0.001 0.36 36 0.35 34.99 0.51 37.8898.5 0.095 0.1 0.0055 0.47 37 0.45 36.99 0.52 38.09123 0.07 0.3 0.0055 0.83 13.3 0.81 12.89 0.86 11.7898.5 0.12 0.1 0.01 0.59 35 0.57 33.99 0.56 31.8574 0.07 0.3 0.01 0.58 23 0.56 21.99 0.60 23.51Table 3.33: Comparison of NF and RA models for predicting average surface

roughness and machining time

Relative error (ϕ)(NF Model) (%)

Relative error (ϕ)(RA Model) (%)

Average surface roughness

(µm)


Average surface roughness

(µm)

MachiningTime (min)

2.77 2.80 41.66 5.224.25 0.02 10.63 2.92.40 3.08 3.61 11.423.38 2.88 5.08 9.003.44 4.39 3.44 2.21

Table 3.34: Comparison of NF and RA models using relative percentage errorfor average surface roughness and machining time

Model Parameter

Minimum relative

error (%)

Maximum relative

error(%)

AverageRelative

Error (ϕa)(%)

Neuro-Fuzzy (NF)Average surface roughness (µm) 2.40 4.25 4.06

Machining Time (min) 0.02 4.39 3.29

Regression Analysis (RA)Average surface roughness (µm) 3.44 41.66 16.10

Machining Time (min) 2.21 11.42 7.68Table 3.35: Error comparison of NF and RA models for average surface

roughness and machining time

Chapter-3

3. 56

Fig. 3.25: Comparison of experimental values of surface roughness and predicted values of NF and RA models

Fig. 3.26: Comparison of experimental values of machining time and predicted values of NF and RA models

The result of average percentage error (ϕa) is 4.06% and 3.29% of surface roughness

and machining time respectively for NF model as shown in table 3.35 for validation

data set (n=5) and 16.10% and 7.68% of surface roughness and machining time

Chapter-3

3. 57

respectively for RA model. This means that the NF model could predict the surface

roughness with 95.94% and machining time with 96.71% accuracy as compared to

RA model with 83.90% and 92.32% accuracy. Further, R-squared (R2) and R-squared

adjusted (R2adj) values are also calculated which show the goodness of fit of the

neuro-fuzzy and regression models. For NF model the R2 value is 94.9% and R2adj is

96.6% for surface roughness and 93.2% and 95.3% for machining time. For RA

model the R2 value is 84.4% and R2adj is 81.0% for surface roughness and 87.7% and

87% for machining time. The NF model clearly appears to outperform the statistical

regression model.

The utility of NN and NF models in intelligent modelling of manufacturing processes

such as hot extrusion process and equal channel angular pressing (ECAP) process

along with manufacturing processes such as orthogonal cutting process and end

milling process is demonstrated in this chapter. Modelling of the process parameters

depicts the advantage of using FE simulation data for NN and NF models. Once the

models are trained appropriately, they act as an advisor and facilitate the designer in

selection of process parameters for predicting output in real-time. NN and NF models

have emerged as new alternative methods for estimating the outputs in an intelligent

manufacturing environment. These techniques easily capture the intricate

relationships between various process parameters and can be easily integrated into

existing manufacturing environment. They also open new avenues of parameter

estimation, optimization and on-line control of complex manufacturing systems.

Moreover, the statistical regression analysis (RA) model approach is also used to

construct models to evaluate the final results. The results obtained with both NF and

RA models are validated and error statistics are tabulated. The NF model performance

is found to be better and it clearly outperformed the statistical regression analysis

(RA) model.

***********End of chapter 3************

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