INTRODUCTION
High speed hard turning is a new approach that attracts manufacturing firms
due to its several advantages, especially for its economical aspects. High speed
hard turning reduces the machining cost for three reasons: reducing the machining
steps, eliminating the coolant system and reducing the machining time together
with all costs associated with the machining time (Adesta
et al., 2008).
Energy has been considered as an integral part of the machining process but
it has not given the proper attention when estimating the machining cost (Gupta,
2005). All the machining processes require material inputs and then transform
them into products and wastes by input energy into these processes (Gutowski
et al., 2006).
Cost of energy depends on the power (in watt or joule per second) consumed
during the machining. Motors that run idle have noload losses but when it is
cutting it consumes higher power. Furthermore, the efficiency of the machine
tool also has an effect of the power consumed (Gupta, 2005).
Thus estimating the cost of energy should be classified according to the machine
load.
Energy consumed in machining may be estimated by various techniques. It can be estimated both by direct or indirect measurement. Direct method is the method that needs to measure directly the current, voltage and the power factor during all the machining stages. Direct measurement method is a costly method and needs direct monitoring but it gives the exact power consumed during the process so it can be used for modeling as well as to validate the results when using other methods.
Indirect methods can be divided into two main methods according to the basics
thermodynamics (Dahmus and Gutowski, 2004; Gutowski
et al., 2006; Abukhshim et al., 2006;
Gutowski et al., 2007; Gutowski
et al., 2009) or estimating the power based on the forces and velocities
relationship (Acosta et al., 1997; Campatelli,
2009).
One of the fundamental requirements is the ability to accurately predict the
output performance of machining processes (Suhail et
al., 2011). Many researchers used and compared between different methods
in modeling and predicting the machining responses and machining costs such
as the regression analysis techniques and the neural network techniques (Doniavi
et al., 2007; Reddy et al., 2008;
Farahany et al, 2010; Habeeb
et al, 2010). The models developed by those researchers are mostly
empirical relations between cutting speeds, feed rate and depth of cuts.
This research focuses on the variable costs of power consumption in high speed hard turning through direct experimental method. The approach used two different techniques then their results were compared to find the best solution. This method reduces the margin of error when predicting the different output parameters by combining artificial intelligent and statistical techniques.
EXPERIMENTAL WORK
Experimental works were carried out on dry cutting conditions on CNC turning
machine type Power Path 15 High Speed Version. The insert chosen for this research
was a mixed ceramic (Al_{2}O_{3} TiC) type CC650 (http://www.coromant.sandvik.com/).
CC650 is a mixed ceramic grade based on alumina with an addition of titanium
carbide and the insert type used is TNGA 160408. It is highly recommended in
finishing operations of hardened steel because of its high wear resistant and
good thermal properties (http://www.coromant.sandvik.com).
BoxBehnken Designs (BBD) is used to calibrate full quadratic models. They are designed for response surface methodology (RSM). BBD with four parameters (cutting speed, rake angle, feed rate and depth of cut) for three levels and five center points was performed as shown in Table 1.
The power measured by using three Digital Current Meters for each phase to measure the current, digital voltmeter for measuring the voltage and Cos load factor for measuring the power factor. Equation 1 was used for calculating the power during the different stages of the process:
where, I is the current, V is the voltage and Cosø is the power factor which is the direct method for estimating the energy consumed by the machine tool during all the stages of the machining.
By using a double force component analogue turning dynamometer the cutting force and the feeding force were measured. This dynamometer consists of a typical commercial tool holder (approaching angle 90°) type (PTGNR2020k16 Sandvik), two strain gauges type (fla1011) were mounted at the maximum strain determined area which were also electrical connected in a halfbridge Wheatstone circuit (Fig. 1).
Then by using MATLAB 2009b software, the energy was predicted by using the
neural network method. Artificial Neural Networks (ANNs) are one of the most
powerful computer modeling techniques, currently being used in many fields of
engineering for modeling complex relationships which are difficult to describe
with physical models (Gutowski et al., 2007; Lin
et al., 2001).
Table 1: 
Cutting parameters in BBD 


Fig. 1: 
Tool holder load cell 
MATHEMATICAL MODEL
Machining time and power consumption are two connected factors. Estimating
and predicting the power cost cannot be done without estimating the machining
time. Estimating the machining time based on Fig. 2 and the
previous work of Gara et al. (2008) which illustrate
the cutting tool route in CNC machine. The time elements for the cutting tool
movement were broken down into seven elements as in Eq. 2:

Fig. 2: 
Cutting tool route in CNC machine 
Equation 3, 4, 5, 6,
7, 8 and 9 were used to
estimate the time for each movement element, Eq. 10 used
for estimating the tool change time:
The power usually estimated by measuring the cutting forces and by using cutting velocity and cutting force as in Eq. 11:
The products processed on the machine have different power requirements and the energy consumed is changed by different stages of the machine work and this equation estimates the power only in the time that the work piece and the cutting tool are in touch.
In this research, the cost of machining energy was divided into three main parts:
• 
Start up machine. This cost will be calculated with the cost
rate of the machine tool because CNC turning machine usually start up daily 
• 
Running the machine without cutting (E_{1}) 
• 
Running the machine with cutting (E_{2}). It was found that the
results deviated approximately by 16% from the actual measurement when using
Eq. 12: 
Following equation applied:
The quantitative form of relationship between the desired response and independent input variables is represented as in Eq. 19:
where, Y is the desired response and F is the response function. By using the design of expert software it was found that in the procedure of analysis, the approximation of Y was proposed using the fitted secondorder polynomial regression model which is called the quadratic model for power consumption. The quadratic model of Y for four parameters can be written as follows:
where, c_{o }constant, c_{i}, c_{ii} and c_{ij} represent the coefficients of linear, quadratic and cross product terms, respectively. X_{i} reveals the coded variables that correspond to the studied machining parameters.
RESULTS AND DISCUSSION
The final models that comes out from the software in terms of actual factors after eliminating the insignificant model factors becomes as the following:
As shown in Table 2, R^{2} is close to one in the two models and very close and almost unity with the adjusted R^{2} which means that the models are reliable for prediction the energy and the cost of the energy. The predicted R^{2} for the modified models increased and becomes higher which indicate how well the model predicts the responses for new observation.
Finally, the adequate precision which measures the signal to noise ratio are high enough and more than 4, therefore the modified models can be used to navigate the design space.
Table 2: 
Statistical summary of the energy models 


Fig. 3: 
Deviation between the measured and predicted values of energy 

Fig. 4: 
Perturbation plot 
The deviation between the measured and the predicted values was approximately equal to 1% as shown in Fig. 3.
The perturbation plot for the energy shows that the cutting speed is the most significant factor of increasing the energy as shown in Fig. 4.
ANN ALGORITHM
In order to train a neural network to perform some task, we must adjust the weights of each unit in such a way that the error between the desired output and the actual output is reduced. This process must calculate how the error changes as each weight is increased or decreased slightly.
The back propagation algorithm is the most widely used method for determining
the error weight. The NFTOOL box in the MATLAB 2009 has been used. The algorithm
computes each error weight by first computing the rate at which the error changes
as the activity level of a unit is changed. For output units, the error changes
simply the difference between the actual and the desired output.

Fig. 5: 
Flow chart of ANN predicting 

Fig. 6: 
Deviation of energy in ANN 
After calculating all the changes in the hidden layer just before the output
layer, the error changes for other layers, moving from layer to layer in opposite
direction to the way activities propagate through the network. This is what
gives back propagation its name. This procedure is done by the NFTOOL in the
MATLAB 2009.

Fig. 8: 
Validation and error test 
Figure 5 shows the flow chart of predicting the energy cost
by using the NFTOOL box.
Then the MATLAB M file is generated from the software as the following:
Then the best prediction when using 20 hidden layers gives deviation approximately
2.6 % from the actual values as shown in Fig. 6.
Figure 7 shows the structure of the system that shows the 20 hidden layers with two output layers.
The error and validation test are illustrated in Fig. 8 for the ANN method and shows that the after 8 runs the system give the best values.
CONCLUSION
Based on the previous results, it can now be concluded that:
• 
The power consumed in the process is increasing with the increasing
of the cutting speed, feed rate, depth of cut and the negative direction
of the rake angle. The perturbation plot for the power consumption shows
that the cutting speed is the most significant factor of increasing the
power consumption. Increasing the cutting speed usually reduces the cutting
forces but at the same time the load on the electrical motors increases
and as a result the energy increases. However increasing the cutting speed
increase the material removal rate thus the cost of removing the material
per volume will decrease 
• 
The feed rate and depth of have also a negative effect on the power due
to the increasing of the cutting forces 
• 
The negative rake angle usually reduce the load on the cutting tool tip
but at the same time increases the cutting and the feeding force and a result
the power will increase 
• 
The developed models can be used in the design boundary to estimate the
cost of energy 
• 
The use of BBD method gave better results when compared to the ANN method
because the ANN method depends on training the system by input data, so
the accuracy of the output depends on the data quantity since Neural Networks
require larger data in order to be more effective 
• 
BBD design does not contain any points at the extremes of the cubic region
of the space design and all of the design points are either on a sphere
or at the center of a sphere 
• 
The statistical analysis for the input data by fitting the normal distribution
curve with the histogram shows that BBD is smoother and more compatible
with the normal distribution curve and that gives more stable and accurate
modeling as shown in Fig. 9 

Fig. 9: 
Normal distribution curve with histogram input data (BBD) 
SYMBOLS
D 
: 
Work piece diameter 
F 
: 
Feed rate 
e_{x} 
: 
Engagement distance on Zaxis 
e_{x} 
: 
Degagement distance on Xaxis 
k 
: 
Number of passes 
L 
: 
Tool life 
l 
: 
Work piece length 
N 
: 
Spindle speed 
n_{tool} 
: 
No of tool posts in the turret. 
p_{1} 
: 
Initial position of the turret. 
p_{2} 
: 
Position of the used tool 
MRV 
: 
Volume removed in one pass 
d 
: 
Depth of cut 
Z_{o} 
: 
Abciss of the O_{t }point 
V_{o} 
: 
Rapid speed 
t_{c} 
: 
Cutting time 
t_{h} 
: 
Handling time 
t_{tc} 
: 
Tool changing time 
t_{o} 
: 
Tool movement at the rapid speed 
T_{oA} 
: 
From zero point to cutting point 
t_{pch} 
: 
Total tool changing time 
V_{c} 
: 
Cutting speed 
V_{f} 
: 
Feeding speed 
X_{o} 
: 
Tidy of the O_{t }point 
r_{speed} 
: 
Rotation speed of the turret 
w 
: 
Work piece weigh 
C_{E} 
: 
Total cost of energy 
E_{c} 
: 
Energy charge cost 
E_{1} 
: 
Energy during start up 
E_{2} 
: 
Energy during running 
E_{3} 
: 
Energy during machining 
C_{E1} 
: 
Energy cost during start up 
C_{E2} 
: 
Energy cost during running 
C_{E3} 
: 
Energy cost during machining 