**3. Experimental results and discussion**

For experiment work, experiments were performed for cutting speeds (Vc) from 50 to 200 m/min, feed (fz) at 50–800 mm/min, axial depth of cut (ap) from 0.1 to 1 mm and width of cut (ae) from 2 to 10 mm for PVD coated AlCrN coated end mill tool to achieve relationship between four input parameters (cutting speed, feed, depth of cut and width of cut) with cutting force.

A Central Composite Design (CCD) is the best design to fit for four factor and five level design. It is a very efficient design for fitting the second order model [16]. Design expert 6 was used to analyze the mathematical models for both the first order model and second order model. The overall cutting conditions with CCD are presented in **Table 3**. The normal force, feed force and axial force were recorded during each experiment and are given in **Table 3**.


#### **Table 3.**

*Design cutting condition with CCD and experimental results.* 

 By using the experimental investigation, cutting force values were obtained in set experimental conditions. The following Linear model and Quadratic model of cutting force prediction has been developed, followed by ANOVA analogy.

The F-value obtained with linear model is 14.68, which implies that the model is significant.

Final Equation in Terms of Actual Factors:

$$\begin{array}{l}\text{Fz} = \ 423.87335 \ -4.18837 \ ^\circ \text{CS} \leftarrow 0.44427 \ ^\circ \text{FEED} \\ \text{+ 319.35593} \ ^\circ \text{DOC} \leftarrow 64.54246 \ ^\circ \text{WOC} \end{array} \tag{1}$$

The F-value obtained with quadratic model is 18.87, which implies that the model is significant.

Final Equation in Terms of Actual Factors:

*Effect on Cutting Force during Hard Machining of AISI D2 Tool Steel Using AlCrN Coated Tool DOI: http://dx.doi.org/10.5772/intechopen.81083* 

 Fz = +617.35850 − 6.72213<sup>∗</sup> CS + 0.67715<sup>∗</sup> FEED − 247.57141<sup>∗</sup> DOC + 58.86704<sup>∗</sup> WOC − 7.73236E − 003<sup>∗</sup>CS<sup>∗</sup> FEED − 1.0047 0<sup>∗</sup>CS<sup>∗</sup> WOC + 1.3339 5<sup>∗</sup>FEED<sup>∗</sup>DOC + 0.047393<sup>∗</sup>CS2 + 10.93859<sup>∗</sup> WOC2 (2)

First and second order CCD models were represented by Both Eqs. (1) and (2) respectively, Results have indicated that cutting speed would give significant effect on cutting force values followed by feed and depth of cut.

From the above results, it is indicated that the error of linear model is much more compared to the error of quadratic model. The average error of the linear model was 0.06 derived by the equation and average error of linear model was 0.02 derived by the equation. From that comparison, it is clear that the quadratic model is more reliable to predict the cutting force model with CCD design. Also it is revealed that the Central Composite Design (CCD design) is a very efficient design for fitting the second order model [13].

By using Eqs. (1) and (2), theoretical values are calculated and compared with practical value from **Table 3**. From that comparison, the average errors for linear and quadratic models are calculated using following equation;

Average Error (ε) for Linear model.

Avg ε (linear) = Σ sum of linear errors/Σ Total number of trial (T) = 0.06. Average Error (ε) for Quadratic model.

Avg ε (quad) = Σ sum of quadratic errors/Σ Total number of trial (T) = 0.02.

From the above result, the percentage average error between measured and predicted cutting force of both models is less than 10% as well as the average percentage error for quadratic model being less than 5%.

#### **4. Conclusion**

 This research work has been carried out to develop a mathematical model to predict cutting forces in end milling of AISI D2 tool steel by using the experimental results obtained through the concept of RSM. From the result, the first order (linear) model as well as the second order (quadratic) mathematic model have been developed. Validity or adequacy of the models has been evaluated by ANOVA, which indicates that the models are reliable. These models are valid within the ranges of the cutting parameters in end milling which for cutting speeds (Vc) was from 50 to 200 m/min, feed (fz) was from 50 to 800 mm/min, axial depth of cut (ap) from 0.1 to 1 mm and width of cut (ae) from 2 to 10 mm. Both models (linear and CCD quadratic) have shown similar trends. The percentage average of error between the measured and predicted cutting force of both models is less than 10% but we found that the average percentage error is less than 5% for the quadratic model.

*Proceedings of the 4th International Conference on Innovations in Automation...* 

## **Author details**

Ravikumar Dasharathlal Patel1 and Sanket N. Bhavsar2

1 GTU, Gujarat, India

2 G H Patel College of Engineering and Technology, Gujarat, India

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Effect on Cutting Force during Hard Machining of AISI D2 Tool Steel Using AlCrN Coated Tool DOI: http://dx.doi.org/10.5772/intechopen.81083* 

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