# Cutting Force Prediction for Armour Steel Drilling using Fuzzy Set Theory

DOI : 10.17577/IJERTV2IS100950

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#### Cutting Force Prediction for Armour Steel Drilling using Fuzzy Set Theory

C.Chenna Raidu1, A.Velayudham2

1-2Scientist, Combat Vehicles Res & Dev Estt. / DRDO, Avadi, Chennai, India, 600 054.

Abstract

Machining of Armour steel at high hardness is a highly interest of defence researchers, where most applications find in armour vehicles used such kind RHA. Usually tools are underutilized in the fully atomized CAD/CAM environment, this has the effect of increased frequency of the tool changes and therefore increased cost. Effective parameter prediction and there by increase the tool life is vital. This paper describes the prediction of cutting forces for given independent parameters such as cutting speed and feedrates on high hardness armour steel to and fuzzy based model developed to establish the cutting database for optimum utilisation of tool life without carrying out costly experiments. The model has been developed with cemented carbide cutting tool and fuzzy logic principles for predicting cutting forces of given cutting conditions in the hard drilling operation. The strategy and action of the skilled machine tool operator for selecting cutting speed and feedrate has been described by the fuzzy set theory. The results showed a good correlation between the experimental results with fuzzy logic model.

keywords : Rolled Homogeneous Armour(RHA), Fuzzy Logic, Hard Drilling

1. Introduction

Computer Numerically Controlled (CNC) machine tools have been widely used in industry for producing high precision machined parts. Automatic machining operation of CNC machine tools requires appropriate cutting parameters prescribed by the programmers, based upon their experience and knowledge. Usually, conservative parameters are employed to avoid tool breakage and system instability problems [5] that will result in the increase of machining time and reduce productivity of CNC machines. Hard machining is performed under unique technological and thermo mechanical conditions and as expected, the process mechanisms (chip formation, heat generation, tool wear) differ substantially from those observed in machining soft materials [4].

Nowadays machining data selection is an important component of the CAD/CAM system and plays a very important role in the efficient utilization of machine tools and influences the product quality. For this reason rule based fuzzy system have been incorporated into many CAD/CAM system in order to get optimum machining parameters[1].

The premise of these model-based control strategies implemented on complex dynamic systems is to establish a reasonable mathematical model for controller design. This paper deals with the application of fuzzy in order to use the experimental data for carbide tool optimization of drilling parameters so as to achieve targets of enhancing tool life and improving workpiece surface finish [7]. The fuzzy logic prediction modules were operating upon different set of rules [8]. The min-max based rule applied here for estimating the Thrust force (Ft) and Torque (Tq) of hard drilling process [9].

2. Artificial Intelligent Control System

The evolution in the control area has been fuelled by two major concerns, the need to deal with increasingly complex systems, and the need to accomplish increasingly demanding design requirements with less prior knowledge of the system and its environment, that is, the need to control under increased uncertainty. The use of the artificial intelligent control techniques in control system can be seen as a natural step in the development of control methodology to meet the complex challenges, such as machining process control.

1. Data fuzzification

Fuzzy logic is a discipline that has been successful in automated reasoning of expert systems. Uncertainty, vagueness, ambiguity, and impreciseness are some of problems found in relationships between inputs and outputs of real world systems, and these can be tackled effectively by utilizing treatment of fuzzy logic. Fuzzification is a kind of process in which the input data, precise or imprecise, is converted into a kind of linguistic form, which is easily perceptible by the human minds, for example very short and highly hard etc. Expert system then uses these fuzzified data to give

answers to imprecise and vague questions and also describe the reality level of those answers.

as triangle shapes which are shown in Figure 1 and Figure 2.

2. Fuzzy output defuzzification

Defuzzification process is defined as the conversion of a fuzzy quantity, represented by a membership function, to precise or crisp quantity. There are two commonly used techniques for defuzzification of fuzzy quantities [1]. They are max method and union centroid method. In cases where the membership function, characterizing the

VSL SLO MED UMS HIS

Âµ=1

0

0 3.2 6.4 9.6 12.8

VHS

16

fuzzy quantity, has a unique peak point the crisp value corresponding to the peak of the function is

Figure 1 Membership function of cutting speed (V)

taken to be the best representative value of the fuzzy quantity. This is called max method. For the second method of defuzzification, the weighted average of the membership functions or the centre of the gravity of the area bounded by the membership function curve is computed to be most

VSF SLF MEF UMF HIF

Âµ=1

0

0 1.2 2.4 3.6 4.8

VHF

6

typical crisp value of the fuzzy quantity. All the output fuzzy sets after rules application will undergo union operation and its centroid will be calculated in the union centroid method. Weighted centroid methods suggested in this paper. The method is similar to union centroid except undergoing fuzzy union operation.

3. Fuzzy models

The main objective of fuzzy logic based system identification is to model the system behavior, i.e., to explain the interactions among inputs and the relationships between the inputs and the output of a system, in the form of a fuzzy rule based system. A

two-input-two-output fuzzy control system for

Figure 2 Membership function of feedrate (f)

3.2 Fuzzy output membership function

In this process, input can be combination of two features cutting speed and feedrate. The membership function for output fuzzy variables (thrust force and torque) are shown in Figs 3 & 4 respectively.

LT LR LO PM ME UM HI HR HT

Âµ=1

drilling operations is used in this study. The fuzzy logic controller (FLC) consists of a membership

0

0 3 6 9

12 15

18 21 24

function, a knowledge base, an inference engine, and a defuzzifier. The function of each block is described as follows.

Figure 3 Membership function of thrust force (Ft)

3.1 Fuzzy input membership function

Cutting speed is the most concerned parameter of the machining, It is combined with the other attributes as linguistic data for the cutting force process. There are six membership functions used for cutting speed that show the degree of potential

as Very Slow speed, Slow speed, Medium speed,

LT

Âµ=1

0

0

LR LO

2 4

PM ME

6 8

UM HI HR HT

10 12 14 16

Upper medium speed, High speed and Very High speed denoted as VSL,SLO,MED,UME,HIS and VHS respectively. Similarly the another input feed rate had the six membership Viz., Very Slow feed, Slow feed, Medium feed, Upper medium feed, High feed and Very high feed denoted as VSF,SLF,MEF,UMF,HIF and VHF respectively. The input membership function is well-distributed

Figure 4 Membership function of torque (Tq)

There are nine membership functions for thrust force and torque that shows the degree of potential as Lowest, Lower, Low, Pre medium, Medium, Upper medium, High, Higher and Highest denoted as LT,LR,LO,PM,ME,UM,HI,HR and HT

respectively.

1. Fuzzy set rules

The model applies the straightforward fuzzy

[1 1] the input combinations are shown in Figure 5 and Figure 6.

rules, which are, If the cutting speed is Very slow THEN the thrust force is Lowest. A set of fuzzy rules has been constructed for the drilling operation, based on the knowledge extracted from the skilled machine tool operator, Tool manufacturers catalog or machining data handbook [2] they are as follows:

VSL SLO MED UMS HIS

Âµ=1

a

b

0

0 3.2 6.4 9.6 12.8

VHS

16

Table 1 Fuzzy rules in matrix form Figure 5 Fuzzy rule interaction with cutting speed

 Cuttin g speed (V) Feed rate (f) VSF SLF MEF UM F HIF VH F VSL LT LR LR LR LR LO LO LO LO PM PM PM SLO LR LR LR LO LO LO PM PM PM ME ME ME MED LT LR LR LR LR LO LO PM LO PM PM ME UMS LR LO LO PM PM PM ME ME UM UM HR HI HIS PM PM ME PM ME UM UM ME UM ME HI UM VHS ME PM ME ME UM ME HI UM HR HI HT HT
 Cuttin g speed (V) Feed rate (f) VSF SLF MEF UM F HIF VH F VSL LT LR LR LR LR LO LO LO LO PM PM PM SLO LR LR LR LO LO LO PM PM PM ME ME ME MED LT LR LR LR LR LO LO PM LO PM PM ME UMS LR LO LO PM PM PM ME ME UM UM HR HI HIS PM PM ME PM ME UM UM ME UM ME HI UM VHS ME PM ME ME UM ME HI UM HR HI HT HT

VSF SLF MEF UMF HIF

Âµ=1

VHF

a

b

0

0 1.2 2.4 3.6 4.8 6

Figure 6 Fuzzy rule interaction with feedrate

1. VSL (0.6875) AND VSF (0.1667) will yield LT (0.1667) AND LR (0.1667) – Rule 1.

2. VSL (0.6875) AND SLF (0.8333) will yield LR (0.6875) AND LR (0.6875) – Rule 2.

#### 3.3.1 Fuzzy rules in Linguistic Form

1. If cutting speed is VSL (very slow speed) AND Feedrate is VSF (very slow feed) THEN Thrust force will be LT (Lowest) AND Torque will be LR (Lower)

2. If cutting speed is VSL (very slow speed) AND Feedrate is SLF (slow feed) THEN Thrust force will be LR (Lower) AND Torque will be LR (Lower)

..

36. If cutting speed is VHS (very high speed) AND Feedrate is VHF (very high feed) THEN Thrust force will be HT (Highest) AND Torque will be HT (Highest)

The above rule has an AND operation and using min-max algorithm this rule will yield a result, that is minimum between the degree of cutting speed AND feedrate and can be defined as follows

(LT, LR)= min{ (VSL) , (VSF)}

Taking all the combinations of the two inputs and applying the AND operation and it yields the following four membership values, for example the

1. SLO (0.3125) AND VSF (0.1667) will yield LR (0.1667) AND LO (0.1667) – Rule 7.

2. SLO (0.3125) AND SLF (0.8333) will yield LR (0.3215) AND LR (0.3215) – Rule 8.

Table 2 Thrust Force value

 Thrust force 0 1 2 3 4 5 – 24 LT 0.17 0.17 0.17 0 0 0 0 0 LR 0 0.33 0.67 0.69 0.67 0.33 0 0 LR 0 0.17 0.17 0.17 0.17 0.17 0 0 LR 0 0.31 0.31 0.31 0.31 0.31 0 0

Table 3 The max value for thrust force

 0 1 2 3 4 5 – 24 0.17 0.33 0.67 0.69 0.67 0.33 0 0

A

A

Average thrust value Ave arg e value A

EQ. (1)

The centriod Equation (1) used to calculate the thrust force index (TFI) as follows, and the defuzzied thrust force shown in Figure 7

TFI 0 0.17 1 0.33 2 0.67 3 0.69 4 0.69 5 0.33

0.17 0.33 0.67 0.69 0.67 0.33

TQI 1 0.5 2 0.69 3 0.5 4 0.17 5 0.17

0.5 0.69 0.5 0.17 0.17

TFI = 2.82 TQI = 2.42

LT LR LO

PM ME

UM HI HR HT

LT LR LO

PM ME

UM HI HR HT

Âµ=1

2.82

Âµ=1

2.42

0

0 3 6 9

12 15

18 21 24

0

0 2 4

6 8 10

12 14 16

Figure 7 Truncated defuzzified thrust force

THRUST FORCE CRISP VALUE =

Figure 8 Truncated defuzzified torque

TORQUE CRISP VALUE =

TFI Ft

Ft

EQ.(2)

TQI

24

diff min

Fqdiff Fqmin

EQ.(2)

16

2.82 1800 700

2.42

24

1.95 0.8

= 911.5 N

The outcome of Equation 2 gives the interpretation of crisp value for the given cutting condition, say for the value of V = 22.5 m/min and f =0.066 mm/rev (75mm/min) for the Ã˜6.4mm twist drill the thrust force is Ft = 912 N. Similarly the torque index generated using min-max rule as shown in Table 4 and 5 respectively.

Table 4 Torque value

 To 0 rque fo 1 rce 2 3 4 5 6 – 16 LR 0 0.17 0.17 0.17 0 0 0 0 0 LR 0 0.5 0.69 0.5 0 0 0 0 0 LO 0 0 0 0.17 0.17 0.17 0 0 0 LR 0 0.32 0.32 0.32 0 0 0 0 0

Table 5 The Max value for torque

 0 1 2 3 4 5 6 – 16 0 0.5 0.69 0.5 0.17 0.17 0 0 0

A

A

Average torque value Ave arg e value A

EQ. (1)

The centriod Equation (1) used to calculate the torque index (TQI) as follows, and the defuzzied torque shown in Figure 8.

16

=1.09 N-m

The outcome of Equation 2 gives the interpretation of crisp value for the given cutting condition, say the value of V = 22.5 m/min and f

=0.066 mm/rev (75mm/min) for the Ã˜6.4mm twist drill the torque is Tq = 1.09 N-m.

1. Results and Discussions

1. Cutting force

The drilling thrust force depends on the geometry of the drill (diameter, point angle, lip length, evolution of the cutting angles along the edges, etc.) as well as on the cutting conditions (cutting speed, feed rate, lubrication, etc.) and on the materials properties. The cutting force has been measured by using dynamometer (Kistler 9271A). Though different types of dynamometers are available for different cutting applications, the compliance of machine tools, leading to chatter and dimensional error, and lack of overload protection limit their application owing to high cost. The control of the cutting force of a drill is of particular interest when a high surface finish and part dimensional accuracy are desired.

2. Work material properties

The material used is the ARMOX 500T steel. The material finds wide application for vehicle armor and respective mechanical properties of material has been denoted in Table 6 as follows.

Table 6 Mechanical properties of material

 Hardn ess (HRc) Charpy- V40 10×10 (J) Yield strength (MPa) Tensile strength (MPa) % Elong ation 50-52 min 25 min 1275 1480- 1750 11-13
3. Tool geometry specification

The solid carbide with parallel shank twist drill was used in this experiment. The geometric parameters of conventional two flute twist drills are determined by their manufacturing parameters. The key features of the drill are the diameter, the lip relief angle, the point angle, web thickness and the helix angle are shown in Table 7.

Table 7 Drill nomenclature

 Drill Dia (D) Lip relief Angle Point Angle () Web Thickness (w) Helix Angle (h) 6.4mm 12Â° 118Â° 1.2mm 30Â°

Table 8 Comparison of Experimental and Fuzzy crisp cutting force values

 Cutting condition Index value Experimental Fuzzy based value CS FR TFI T QI Thru st Force Torq ue Thrust Force Tor que 20 0.06 0.92 2 770 0.992 826.9 1.04 0.08 4.51 4 850 1.248 1048.1 1.29 0.1 9.01 6 1075 1.632 1325.6 1.53 30 0.06 2.58 2 785 1.056 929.10 1.04 0.08 7.5 6 950 1.440 1232.5 1.53 0.1 13.5 10 1950 2.176 1602.5 2.02 40 0.06 12 6 1750 1.216 1510.0 1.78 0.08 16.5 9 1900 1.792 2089.6 2.38 0.1 23.1 15. 4 2125 2.624 2194.5 2.68

Figure 9 Comparison of experimental and fuzzy crisp values of thrust force (Ft)

Figure 10 Comparison of experimental and fuzzy crisp values of torque (Tq)

2. Conclusions

The conclusions resulting summery as follows

• The fuzzy model gives good prediction to the experimental results.

• The relationship of given cutting condition to the cutting forces were evaluated using fuzzy set theory.

• The fuzzy model can be used to adapt CIM(Computer Integrated Manufacturing) for upcoming technologies.

• This paper describes the development stages of a fuzzy logic model for metal cutting. The model is based on the assumption that the relationship between the cutting condition of a given material and the cutting forces is an imprecise relationship, and can be described and evaluated by the theory of fuzzy sets.

• The objective of the model is to facilitate the computerization process of the vast machining information.

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