A Study on the Derivation of Parametric Cutting Force Equations in Drilling of GFRP Composites

Glass fiber reinforced polymer matrix (GFRP) composite materials offer superior properties such as high specific strength, high specific modulus of elasticity, high damping capacity, good corrosion resistance, good tailoring ability, excellent fatigue resistance, good dimensional stability and a low coefficient of thermal expansion [1] to [8]. Hence, they are used in many fields, such as the automotive, aerospace, sporting goods, marine, chemical industry, electrical industry, etc. [5], [6], [8] and [9]. In these fields, the drilling of GRFP composite materials is generally needed for the joining of composite structures. However, drilling of GFRP implies coping with problems that are not encountered when machining other conventional materials. The drilling of GFRP composite materials may lead to widespread damage and may cause many problems, such as fiber delamination, fiber breakage, fiber pull out, stress concentration, thermal damage, microcracking, etc. due to the inhomogeneity and anisotropic nature of GFRP composite materials [4], [5] and [10]. These problems cause aesthetic problems, but may also compromise the mechanical properties of the finished part [4]. For this reason, numerous researchers have investigated the GFRP drilling process and reported the factors that affect the quality of the finished part. Hence, many researchers have investigated the influence of these factors in the drilling of GFRP composites [5] to [7] and [9] to [12]. Moreover, many researchers have investigated the effects of various parameters (cutting speed, feed rate, point angle, thrust force, cutting tool geometry, etc.) particularly on the delamination behavior of GFRP composites [13] to [17]. In addition to these studies, some researchers have investigated the modelling of the drilling of materials. Unfortunately, most of the models developed for metals have proved to be unsuitable for composites, as the cutting mechanism is different [17] to [20]. In the literature survey on machining it was observed that only the action of the cutting lips and the chisel edge are generally considered in modelling, however in the machining stage several types of damages observed in composite drilling are directly related to cutting force and torque. In particular, the structural damages mentioned above can be related to the thrust force during drilling. The presence and extension of the different kinds of damage depend on the composite material characteristics, tool geometry and material, and the process parameters [21] to [25]. The damage is particularly detrimental to the residual mechanical properties and significantly reduces the composite performance in use. Consequently, special care should be given to avoid the generation of defects during drilling. Therefore, it is particularly important when modelling the cutting action to derive analytical equations that predict the machining forces as a function of process parameters. In the present work, the aim is to derive machine force equations for the drilling of GFRP composites. Thus, GFRP composite material was drilled in a specially designed drilling system and drill torques and thrust force fluctuations were recorded using a dynamometer–amplifier–computer combination with different feed rates and drill diameters. The appropriate model for drilling GFRP was chosen and its performance tested on GFRP. The experimental data were examined using mathematical models to investigate the empirical relationships between essential parameters. The cutting forces in the drilling of GFRP materials were calculated using empirical A Study on the Derivation of Parametric Cutting Force Equations in Drilling of GFRP Composites Eda Okutan – Sedat Karabay – Tamer Sınmazçelik – Egemen Avcu Eda Okutan* – Sedat Karabay – Tamer Sınmazçelik – Egemen Avcu University of Kocaeli, Department of Mechanical Engineering, Turkey


INTRODUCTION
Glass fiber reinforced polymer matrix (GFRP) composite materials offer superior properties such as high specific strength, high specific modulus of elasticity, high damping capacity, good corrosion resistance, good tailoring ability, excellent fatigue resistance, good dimensional stability and a low coefficient of thermal expansion [1] to [8].Hence, they are used in many fields, such as the automotive, aerospace, sporting goods, marine, chemical industry, electrical industry, etc. [5], [6], [8] and [9].In these fields, the drilling of GRFP composite materials is generally needed for the joining of composite structures.However, drilling of GFRP implies coping with problems that are not encountered when machining other conventional materials.The drilling of GFRP composite materials may lead to widespread damage and may cause many problems, such as fiber delamination, fiber breakage, fiber pull out, stress concentration, thermal damage, microcracking, etc. due to the inhomogeneity and anisotropic nature of GFRP composite materials [4], [5] and [10].These problems cause aesthetic problems, but may also compromise the mechanical properties of the finished part [4].For this reason, numerous researchers have investigated the GFRP drilling process and reported the factors that affect the quality of the finished part.Hence, many researchers have investigated the influence of these factors in the drilling of GFRP composites [5] to [7] and [9] to [12].Moreover, many researchers have investigated the effects of various parameters (cutting speed, feed rate, point angle, thrust force, cutting tool geometry, etc.) particularly on the delamination behavior of GFRP composites [13] to [17].In addition to these studies, some researchers have investigated the modelling of the drilling of materials.Unfortunately, most of the models developed for metals have proved to be unsuitable for composites, as the cutting mechanism is different [17] to [20].In the literature survey on machining it was observed that only the action of the cutting lips and the chisel edge are generally considered in modelling, however in the machining stage several types of damages observed in composite drilling are directly related to cutting force and torque.In particular, the structural damages mentioned above can be related to the thrust force during drilling.The presence and extension of the different kinds of damage depend on the composite material characteristics, tool geometry and material, and the process parameters [21] to [25].The damage is particularly detrimental to the residual mechanical properties and significantly reduces the composite performance in use.Consequently, special care should be given to avoid the generation of defects during drilling.Therefore, it is particularly important when modelling the cutting action to derive analytical equations that predict the machining forces as a function of process parameters.
In the present work, the aim is to derive machine force equations for the drilling of GFRP composites.Thus, GFRP composite material was drilled in a specially designed drilling system and drill torques and thrust force fluctuations were recorded using a dynamometer-amplifier-computer combination with different feed rates and drill diameters.The appropriate model for drilling GFRP was chosen and its performance tested on GFRP.The experimental data were examined using mathematical models to investigate the empirical relationships between essential parameters.The cutting forces in the drilling of GFRP materials were calculated using empirical equations and the results were compared with the measured data to verify the accuracy of the derived equations for the drilling of glass fiber reinforced polymer matrix materials.Moreover, following investigation of the test data for the derivation of empirical equations, hole surface morphology of GFRP samples were investigated using an optical microscope and scanning electron microscope (SEM).

Specimen Preparation and Mechanical Properties
In this study, [0°/+45°/90°/-45°] oriented glass fiber reinforced polymer matrix composite samples were used.Samples were cut to 200×37×10 mm rectangles from 200×200×10 mm plates.Properties of the laminate are presented in Table 1.The polymeric matrix material is an orthophtalic polyester and composite laminates were produced using the vacuum assisted resin transfer molding technique.

Equipments and Machine Tools Used in the Test Set-up
In the experiment, an Arsenal PK-40 drilling machine was used.Properties of the drill machine are shown in Table 2. Other equipment used in addition to the drilling machine are four axes piezoelectric type Kistler drill dynamometers and their auxiliary devices for measuring machining forces.Thus, the measurement set up combination consists of a Kistler-9272 drill dynamometer, Kistler-5070A amplifier and computer.When machining, the signal produced by the dynamometer related to the thrust force and torque is transferred by RS-232 connection to the computer.The data acquisition process is performed using a program called as DynoWare written by Kistler Co.In the drilling of GFRP samples, DIN 338 HSS drills with a right hand helical form and 118° point angle with four different diameters were used.

Drilling Process of GFRP Samples
Tests were performed without using any coolant in the drilling operation.The revolution of the drill machine spindle was set at a constant speed of 265 rpm.Machining of the GFRP samples was performed with different diameters of drills and different feed rates.The drilling force measurement plan for GFRP material is shown in Table 3.To minimize vibration during machining, ythe drill dynamometer was fixed to the table of the machine table rigidly without distorting the sensitive parts of the device.Then, all connections between the stations for measuring and data acquisition were made.Drill studies were performed by using the drill force measurement plan.Each drill was worked with samples at four different feed rates.These combinations were repeated five times on the GFRP samples.The collected results were then analyzed using the DynoWare-Kistler data acquisition program.Mean values of the fluctuation curve due to thrust force and torque were determined and the tabulated data were used to investigate the empirical equations.

Derivation of Drill Torque Equation on GFRP
A cutting model for drilling was chosen to study the empirical equations related to the forces in a drilling process performed on GFRP.We chose to use Shaw and Oxford's drill model.Since this model was originally used on metal cutting parameters, it was not clear from the outset whether the model would be suitable for detection of the cutting forces on GFRP.Thus, the study also tests the validity of the proposed model.Using Eq. ( 1) and the collected test data, the empirical torque equation with respect to drill diameter and drill feed rate was determined [26] and [27].In Eq. ( 1), a is evaluated by the relationship between the specific cutting energy, u and f•d [26].For a given GFRP material, s is considered a constant in order to simplify the complex calculations.

Fig. 1. Specific energy u versus f•d in drilling
The test data is checked using Eq. ( 1) to see whether there is a correlation between the measured and calculated values using the [26] to [30].Specific cutting energy is defined as given in Eq. ( 2) [24] to [25]: ( Fig. 1 shows the use of the test results on the evaluation of specific cutting energy versus (f•d) drawn in logarithmic scale.From the slope of the regression curve, the a value was determined to be a = 0.31.
After determination of drill torque data, "feed rate versus drill torque" and "drill diameter versus drill torque" graphics were drawn on a logarithmic scale to find out the relationship between of them.The graphics are shown in Figs. 2 and 3, respectively.  . .
In Fig. 1, the value of the specific energy on the vertical line cut by the regression curve shown to be around 390 N/mm 2 .Using this value, Eqs. ( 5) to (7) can be derived for the drill torque in GFRP.
Eq. ( 9) is then inserted in Eq. ( 4).Thus, the required drilling torque on glass fiber reinforced polyester composite material can be derived as given in Eq. (10).

Derivation of the Drill Thrust Force Equation on GFRP
With the help of dimensional analysis, Shaw and Oxford's parametric relation for drill thrust force is presented in Eq. ( 11) [26].
where T v is axial force [daN], K 12 , K 13 , K 14 are constants and a = 0.31.In the Eq. ( 11), the value of a has been calculated to be a = 0.3.Moreover s, which is the distance between imperfections in the material, is taken to be a constant value (s = 1) for simplification.The thrust force equation can then be defined by Eq. ( 12).
After performing machining, the collected data related to thrust force are plotted in logarithmic scale and the corresponding graphs are drawn with combinations of "Thrust force versus to feed rate" and "Thrust force versus to drill diameter" in Figs. 4 and  5, respectively.  .
The measured data are input into the thrust force Eq. (12).Then the relationship between the can be determined as shown in Fig. 6.The equation of the line in Fig. 6 has been derived as given in Eq. ( 13).The equation for this line defines teh "thrust force" in drilling of GFRP samples.

Comparison of the Theoretical Results and Experimental Results
In this section, the theoretical results of the drill torque and thrust values were calculated by using derived empirical equations as a function of feed rate and drill diameter.The results were then compared with the experimental records.In Figs. 7 and 8 comparisons of the theoretical and data on drill torques and thrust force are given as a function of feed rate and drill diameter.

Fig. 7. Comparison of experimental and theoretical drill torque values as a function of feed rate and drill diameter
Machining of composite materials differs significantly in many respects from machining of conventional metals and their alloys.In the machining of composites, the material behavior is not only nonhomogeneous and anisotropic, but it also depends on diverse reinforcement and matrix properties, as well as on the volume fraction of matrix and reinforcement.The tool encounters, alternatively, matrix and reinforcement materials, whose response to machining can be entirely different.Graphics shows good correlations between the measured and calculated values.Nominal fluctuation of the measured and theoretical values is around 5% and this is an acceptable level for this kind of handmade artificial materials.In Fig. 8, the variation between the experimental and theoretical drill trust values of the samples drilled with 10 mm drills seems greater compared to the samples drilled with 4mm, 6mm, and 8mm drills.The reason for this result can be explained by the higher probability of encountering imperfections, due to the inhomogeneous nature of the GFRP composites, with the increase in the tool diameter.The important topic in the machining of a composite material is to detect real hole entry defects, the circular defect and damage from a heat source in the wall of the hole, the lamination at the exit hole.Therefore, following analysis of test data for the derivation of empirical equations, hole surface morphology of GFRP samples was investigated by using an optical microscope and scanning electron microscope (SEM).From the various machining operations, a brief summary of drilling performance and defects has been presented below, with views of the samples.
As expected, all forms of defects occurred as shown in Figs. 9 and 10.In Fig. 9, the exit side of the tools from the samples with delaminated fibers are shown.
As seen in Figs.9a, b, c and d, limited delaminations were observed on the drilling surfaces.Such limited delaminations may not cause remarkable defects in GFRP composites.However, for further understanding of delaminations and cutting effects in GFRP holes, Good adhesion between the matrix and fibers is observed in these figures.In Fig. 12c and d, fiber tips broken during the drilling process are shown.
As seen in Figs.10c and d, fibers were broken in a brittle manner during the drilling process.However, they remained embedded in the polyester matrix and limited delaminations were observed.From Figs. 9 and 10, we can conclude that glass fibers have a strong adhesion to the polyester matrix.Thus, it has been determined that surface quality and dimensional ovality are at an acceptable level for mechanical connecting using bolts.

CONCLUSIONS
From the above study on the derivation of empirical equations related to GFRP using a conventional drill, the following results can be summarized.
1) It was determined that when the drill diameter and feed rate are increased while machining GFRP, the thrust force and drill torque increase.This result also verifies that if the drill diameter is increased then the un-deformed chip material volume increases.This means that for processing of continuous chip formation at high feed rates, a higher power requirement is demanded by the tool to get rid of cutting, friction and extrusion forces.This creates high torque and thrust forces in the machining operations.2) In this study, the model we used, which was developed for metals by Shaw and Oxford, showed very good accordance with the derivation of the empirical relationship for the drilling of glass fiber reinforced oriented "0°/+45°/90°/-45°" in the polymer matrix composite.As a conclusion, the equations presented below can be used to estimate the machining forces on drilling operations for the defined composites.
3) Comparing the measured and empirical results for drilling forces, some differences have been determined.These differences are unavoidable due to the microstructure of the GFRP.Not surprisingly, the machining characteristics of the composite materials with a non-isotropic nature results in fluctuations compared to homogenous and isotropic or quasi-isotropic materials.Therefore, cutting force fluctuation should be expected from the machining of these kinds of materials.However, these differences are not that important for estimating the level of machining forces by empirical equations as empirical equations give approximate values to engineers not exact ones.Finally by tolerating some of the deviations, the derived empirical relations for similar types materials can be used effectively to give some design and constructive ideas.4) In this study, the main aim was to determine the relationship between cutting forces and the essential parameters of the machining tool.
Additionally, machined hole quality and damage development due to drill feeding of the material were also very important.Delamination of the fibers occurred at the exit side of the holes, although it was determined that surface quality and dimensional ovality are at an accepted level for mechanical connecting with bolts.Surface quality and roughness of the machined holes are due to structural discontinuities in the GFRP.Discontinuities of the artificial materials were also determined to be essential reasons for the force fluctuations.5) Chisel edge length relative to drill diameter is indicative of delamination of GFRP due to increasing thrust force [31].This effect also can be seen somewhat in the Fig. 8 by increases in the mesured thrust force rather than by the calculated data for the same cutting parameters.6) Structural parts made of composite frequently have to be drilled in the structural, aircraft and automobile industries.However, little is known about the conditions between the drilling tool and material.This study aimed to show whether the model verified for ferro-alloys can be used for pre-estimation of drilling forces in the machining of GFRP composites.It has been proven that drilling forces applied to construction parts designed for the structural and machine industry can be easily determined.This will help to prevent excessive force application during these processes in order to prevent damage to composite structures.
where M d is drill torque, [N•cm], H B Brinell hardness of GFRP samples, [kg/mm 2 ], f feed rate, [mm/rev], d drill diameter, [mm], S the average distance between imperfections in the material, [mm] and a, K 6 , K 7 constants.

Fig. 2 .
Fig. 2. Drill torque versus to drill feed rate on GFRPThe slope of the curves in Figs.4 and 5are as 0.42 and 0.51, respectively.The ratio [c/d], which is the ratio of length of the chisel edge to drill diameter, taken as a constant (0.213) for the drills used in the experiments[26].

Fig. 3 .
Fig. 3. Drill torque versus to drill diameter on GFRP Consequently Eq. (1) can be transformed into a simplified form as given in Eq. (3) by substituting these numerical values.M K f d d = 8 0 42 051 . ., (3) or M K H f d d B = 9

Fig. 8 .
Fig. 8.Comparison of experimental (a) and theoretical (b) drill thrust values as a function of feed rate and drill diameter 3.4 Investigation of Hole Surface Morphology of Drilled GFRP Samples

Fig. 10 .
Fig. 10.SEM photos of; (a) vertical cut of the drill holes and (c) view surfaces of drilled GFRP samples under different magnifications

Table 1 .
Properties of composite samples

Table 2 .
Feed rates and angular speed of main shaft of drilling machine

Table 3 .
Drill force measurement plan