Cutting force analysis considering edge effects in the milling of carbon fiber reinforced polymer composite

Journal Pre-proof Cutting force analysis considering edge effects in the milling of carbon fiber reinforced polymer composite Yanli He, Jamal Sheikh-Ahmad, Shengwei Zhu, Chunlin Zhao

PII:

S0924-0136(19)30514-X

DOI:

https://doi.org/10.1016/j.jmatprotec.2019.116541

Reference:

PROTEC 116541

To appear in:

Journal of Materials Processing Tech.

Received Date:

18 April 2019

Revised Date:

2 October 2019

Accepted Date:

1 December 2019

Please cite this article as: He Y, Sheikh-Ahmad J, Zhu S, Zhao C, Cutting force analysis considering edge effects in the milling of carbon fiber reinforced polymer composite, Journal of Materials Processing Tech. (2019), doi: https://doi.org/10.1016/j.jmatprotec.2019.116541

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Cutting force analysis considering edge effects in the milling of carbon fiber reinforced polymer composite Yanli Hea* a

Jamal Sheikh-Ahmadb

Shengwei Zhua

Chunlin Zhaoa

Key Laboratory of Contemporary Design and Integrated Manufacturing Technology, Ministry of Education,

School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, P.R.China b

Department of Mechanical Engineering, Khalifa University of Science and Technology, SAN Campus,

*Corresponding author.

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E-mail address: [email protected](YL He)

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127 West Youyi Road, Xi’an, Shaanxi, 710072, P.R.China

1 Corresponding author. E-mail address: [email protected](Yanli He)

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AbuDhabi, UAE

Abstract. Machining damage incurred in milling carbon fiber reinforced polymer (CFRP) composite is closely related to the cutting force. However, the dynamic distribution of the cutting force arising from different cutting effects has not been fully investigated. In this study, a new two-region cutting model was used to analyze components of the cutting force resulting from the cutting and edge effects in the milling of CFRP. The friction coefficient was obtained as a function of the fiber cutting angle. The instantaneous magnitudes of the net cutting, pressing and

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friction forces were identified quantitatively. The variation of different force components and the corresponding specific cutting energies were studied in relation to the cutting mechanisms. The relationship between the cutting forces and machining damage was also investigated. A

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mechanistic milling force model is proposed. Comparison indicates that the model can produce

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better prediction of the milling force than the traditional model.

Keywords CFRP; Milling; Friction coefficient; Mechanistic force modeling; Delamination

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1 Introduction

In the modern aerospace industry, components made of carbon fiber reinforced polymer (CFRP)

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composites often require machining for finishing operations before assembly. However, machining has to be conducted with great care since various types of damage, e.g. fiber breakage and pullout,

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fuzzing, delamination, resin degradation, etc., are easily induced due to the multiphase and

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inhomogeneous nature of the material. The influence of the cutting conditions on machining damage and surface quality has already been discussed extensively in the literature. Sheikh-Ahmad (2009), for instance, demonstrated various studies on the machining of CFRP. It is shown that the machining quality or machinability of CFRP materials is dependent on factors such as the fiber volume fraction, fiber orientation, cutting parameters, cutting tool geometry and material. Wang et al. (1995) observed that the fiber orientation angle with respect to the cutting 2

velocity plays an important role in the chip forming mechanism, and hence the chip shape, surface roughness and cutting forces involved. Davim and Reis (2005) found that both the feed rate and cutting speed have a statistical and physical significance in the milling of CFRP. Azmi et al. (2013) showed that the feed rate has the most dominant effect on the surface roughness and machining force in the milling of glass fiber reinforced polymer composite (GFRP). Erkan et al. (2013) found that an increase in the plastic deformation rate due to an increase in the feed rate and cutting speed

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will lead to a larger delamination factor in milling woven GFRP panels. Sheikh-Ahmad et al. (2012) demonstrated that in the trimming of CFRP with burr router bits, the best machined surface quality can be achieved by the smallest feed and largest cutting speed, corresponding to smallest

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effective chip thickness. Hintze et al. (2011) observed that in milling unidirectional CFRP

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(UD-CFRP), the occurrence of delamination damage is related to a critical range of fiber cutting

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angles. Hintze and Hartmann (2013) also proposed an analytical model for delamination considering the tool geometry and its varying orientation with respect to the fibers. In a further

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study of the milling of CFRP with a weave fabric, Hintze et al. (2015) found that the delamination is influenced by the fiber undulation angle and the thickness of the top matrix layer.

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In these experiments, the machining forces are critical to the machining damage as they reflect the pressure exerted by the tool on the workpiece. The design and optimization of machining

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processes thus requires the effective modeling and prediction of cutting forces. There are many studies concerned with modeling the forces in machining FRP, including orthogonal cutting. Bhatnagar et al. (1995) probably proposed the first analytical force model based on Merchant’s model for the orthogonal cutting of UD-CFRP, with the assumption of a shear plane along the fiber direction. After the shear force and shear area were calculated, the shear strength for different

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fiber orientations was computed. The results were found to agree with the results of Iosipescu shear test from the fiber angle of 0o up to 60o. Zhang et al. (2001) also proposed an analytical mechanics-based orthogonal cutting force model that takes into consideration the forces induced in three different cutting regions. The cutting tool geometry, such as the rake angle and cutting edge radius was considered. The model can capture the major deformation mechanisms in cutting UD-FRP with fiber orientations varying from 0o to 90o. Jahromi and Bahr (2010) subsequently

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extended this model by addressing fiber orientations beyond 90o. Factors such as cutting edge

radius and resistance of the fibers to bending were considered in calculating the cutting force. This theoretical model can be applied to the machining of any unidirectional fiber composites with

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elasto-plastic matrix properties using tools with any rake angle. Using the minimum potential

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energy principle, Qi et al. (2015) proposed a force prediction model for the orthogonal machining of UD-CFRP by analyzing the deflection of a representative volume element (RVE). Subsequently,

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Chen et al. (2016) proposed a model for the fiber orientation range of 0o-180o, which captures the

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relationships between the cutting forces and key variables such as the fiber orientation, rake angle and depth of cut. There are also studies which were based on the mechanistic approach, in which

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the specific cutting energy or cutting force coefficient was considered to be dependent on the cutting parameters as well as the fiber orientation angle. Schulze et al. (2011) found that the

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cutting force coefficients increase with an increase in the cutting edge radius and a decrease in the cutting thickness when machining short glass fiber reinforced polyester. An et al. (2015) showed that the cutting force coefficients decrease as the cutting speed and depth of cut increase. This study works as a reference for achieving better machinability and less cutting energy consumption when machining CFRPs. Considering the fiber location stochasticity and individual roles that fiber

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and matrix play on the resultant cutting forces, Mei et al. (2017) proposed a stochastic model to evaluate the forces in orthogonal cutting of composites with randomly distributed unidirectional fibers. The randomizing fiber location method could overcome the limits in composite machining research caused by the unpredictable internal structure of the composites. However, as milling is not a continuous cutting process and is more complex than orthogonal cutting, most milling force models in the literature are based on the mechanistic approach. Puw

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and Hocheng (1999) presented a force model for milling UD-CFRP that takes into account the directional force responses and machining-induced damage. The specific cutting forces with

respect to cutting velocity, width of cut and depth of cut were obtained for six different

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orientations. Wang et al. (2013) proposed a model for the helical milling of UD-CFRP where the

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cutting force coefficients were obtained using the average cutting force-based method. The cutting

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force coefficients can be adjusted so as to predict the forces in different cutting parameters. Wang and Qin (2016) further obtained the relationship between the cutting force coefficients and the

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cutting parameters using the average-based method and response surface methodology (RSM). Since both the fiber cutting orientation and the undeformed chip thickness vary continuously with

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the rotation of the tool, many studies used the instantaneous milling forces for analysis of the specific cutting energy. Sheikh-Ahmad et al. (2007) modeled the instantaneous specific cutting

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energy by using a continuous function with the fiber orientation and chip thickness as the input parameters. The multiple regression and committee neural network were used to build the models separately, with both being capable of predicting the forces in the milling of unidirectional and multidirectional composites. Kalla et al. (2010) proposed a model to predict the cutting forces for helical end milling. Elemental tangential and radial cutting force coefficients were modeled using

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neural networks, and elemental oblique cutting forces were calculated using the cutting force coefficients with an orthogonal to oblique transformation method. Karpat et al. (2012) modeled the cutting force coefficients using a simple sine function form of the fiber cutting angle. This smooth function yielded good cutting force predictions in the milling of multidirectional CFRP laminates. He et al. (2017) incorporated the instantaneous chip thickness, cutting speed and the sine function of the fiber cutting angle in the polynomial regression model of the cutting force

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coefficients. Karpat and Polat (2013) proposed a cutting force model for milling multidirectional

CFRP with double helix tools. The cutting and edge coefficients are calculated based on the laminate fiber direction. The average cutting and edge coefficients for multi-directional CFRP

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laminate are calculated using the superposition principle.

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In some of the above mechanistic force models, the edge effect of the cutting tool is generally

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neglected so the measured force is assumed to be the net cutting force. In other studies, the edge force coefficients are treated as constants by using the average force. However, Maegawa et al.

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(2016) have discovered that the rubbing or the contact between the workpiece and the tool’s edge radius and flank plays a significant role during the CFRP milling process. This explains the fact

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that the radial force is usually much larger than the tangential force. Despite the many virtues of the above methods, existing cutting force models have yet to give proper consideration to the

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dynamic distribution of the cutting and edge forces, not only for the accurate force prediction, but also for the proper interpretation of the machining mechanisms. The aim of this study is to decompose and model the cutting forces at the tool edge considering the cutting effect and edge effect during the milling of CFRP, and to reveal the relationship between the cutting forces, chip formation mechanisms and machining damage. Slot milling

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experiments were conducted on UD-CFRP with different fiber orientations. The instantaneous friction coefficient between the cutting edge and workpiece was then evaluated, and the instantaneous contributions of different cutting force components were analyzed and modeled separately in a mechanistic milling force model. The prediction results delivered by the proposed model were compared against the results of a traditional model and the experimental force measurements. This work may offer a new perspective for the tool wear analysis and may serve to

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support process planning for the milling of CFRP.

2 Cutting experiments

A 4-axis vertical machining center (YHVT850Z), equipped with a Siemens-840D CNC control

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system was used to conduct slot milling experiments. The composite material was made of

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unidirectional prepregs (TC35-12K/150) subjected to an autoclave curing process. The UD-CFRP

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laminate was 6 mm in thickness and contained 43 plies with the same stacking sequence and approximately 60% fiber in volume. The tools used were customized two-tooth straight-flute 8

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mm diameter carbide end mills with a zero helix angle and a zero rake angle. The tool nose radius was about 15 m, as measured by an optical surface metrology instrument (Alicona Infinite Focus

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G4 Microscope).

The CFRP laminate was cut into rectangular pieces 230 mm×90 mm in size with the length

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parallel to the fiber direction. The workpiece penal was fixed at both ends by clamps on top of a piezoelectric dynamometer (Kistler9265B) for measuring the cutting forces. The dynamometer signal was collected and amplified by a Kistler 5019A multi-channel amplifier and transferred to a National Instruments (NI) data acquisition card. The signal was continuously sampled at a frequency of 20 kHz. The experiments were conducted under dry cutting conditions and a vacuum

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system (KARCHER) was used to collect the dust generated. The milling itself was conducted with a spindle speed of 3000 rpm and a feed rate of 0.02 mm/z. The depth of cut was set at 2 mm. After machining, the quality of the machined surface was analyzed using an Alicona Infinite Focus Microscope and a scanning electron microscope (SEM, model HITACHI SU3500). The angles for the slot milling experiments are defined in Fig. 1. The fiber orientation angle (𝜓) is the angle measured counterclockwise from the tool feed direction to the fiber direction. Four

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typical fiber orientation angles (e.g. 0o, 45o, 90o and 135o) are illustrated in the figure. The tool rotation angle (𝜃) is used here to describe the position of the cutting edge. During slot milling, an

edge starts milling at 𝜃=0o and exits milling at 𝜃=180o, with 0o <𝜃<90o corresponding to

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up-milling while 90o <𝜃<180o corresponding to down-milling. The fiber cutting angle (𝜌) is

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measured counterclockwise from the cutting velocity direction of the cutting edge towards the fiber direction. Once again, four typical fiber cutting angles (e.g. 0o, 45o, 90o and 135o) are shown

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in Fig. 1. Note that 0o and 180o are used interchangeably for 𝜓 and 𝜌.

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As shown in Fig. 1, 𝜌 changes continuously as the tool rotates during the milling process. The relationship between 𝜌 and 𝜓 and 𝜃 is expressed in Eq. (1). Generally, 𝜌 increases from the

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value of 𝜓 at cutting edge entry. When it reaches 180o, it returns to zero and increases again, and finally reaches 𝜓 at cutting edge exit. 𝜌 = 𝜓 + 𝜃 if 𝜌 ≥ 180 then 𝜌 = mod(𝜌, 180)

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(1)

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Feed

Feed ρ=90° θ=90 °ρ=135° θ=135°

Ω ρ=45 ° ° θ=45°

ρ=135° θ=90° ρ= 0/180°

Ω ρ=90 ° θ=45 °

Rake angle

α

Cutting tool

θ=135° γ Vc

ρ=0° θ=0 °

O (a) ψ=0°

ρ= 0/180° ρ=45° θ=0 ° θ=180°

O (b) ψ=45°

ρ=135°

Feed

ρ=135° θ=45 °

Feed

ρ=0/180° θ=90° ρ=45 ° θ=135°

Ω

ρ=45 ° θ=90° ρ=90° θ=135°

Ω ρ= 0/180° θ=45°

Vc

ρ=0°(180°) ρ=90 ° θ=0°

O (c)ψ=90°

Clearance angle

ρ

ρ=45 ° θ=180 °

ρ=90° ρ=135° θ=180° θ=0°

O (d)ψ=135°

Vc

Vc

ρ=90°

ρ=45°

ρ=135 ° θ=180 °

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Fig. 1. Definition of various angles in slot milling.

In the experiment, the four typical fiber orientation angles were achieved by adjusting the feed direction with respect to the workpiece, as shown in Fig. 2. The measured forces in the

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dynamometer coordinates were transformed to cutting forces in the feed coordinates. The cutting

force signal showed a periodicity pattern in the time domain after the cutting reached a steady

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state, while the forces for one tooth engagement cycle (i.e. half a revolution) were sampled from

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the force signals in this study. For the spindle speed and sampling frequency used, each cutting cycle consisted of 200 force data samples (i.e. 0.9° per sample). To reduce the effect of dynamic

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oscillation in the signals, five different cutting cycles were selected in the steady cutting period and averaged. Due to the difficulty in determining the exact time of the beginning of cutting for

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each tooth, the first force data point in the cycle was assumed to occur at the tool rotation angle of

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0.7°, which is arbitrarily chosen between 0° and 0.9°. Fig. 3 shows the variation of the resulted feed and normal forces (Ff and Fn) with respect to the tool rotation angle from 0° to 180°. These are characteristic force signals for each tooth engagement and they repeat themselves every half a revolution. Due to the anisotropic nature of CFRP, the forces in the four fiber orientations showed different patterns. In the stable force records in the experiments, the axial cutting forces were near to zero 9

due to the absence of inclination angle of the cutting edge and they were therefore not considered.

Ψ= 0

o

Ψ= 135o

Ψ= 45o

Fn

Fn

Ff

Ψ= 90o

Fn Ff Ff

X

Ff

Fn

Y Dynamometer axis

Fiber direction

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Fig. 2. Cutting in relation to the different fiber orientation angles.

(b)

(d)

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(c)

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(a)

Fig. 3. Feed and normal forces for different fiber orientations: (a) 0o; (b) 45o; (c) 90o; and (d) 135o.

3 Cutting force and damage analysis

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3.1 Cutting force model incorporating friction effect

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The total milling force is made up of elements induced by different mechanisms associated with the cutting process, including fiber cutting, ploughing and pressing. Maegawa et al. (2016) proposed a two-region cutting model that takes into consideration the friction and pressing effects. This model was therefore used for analysis of the milling force in this study, as shown in Fig. 4. Around the tool edge, Region 1 represents the fiber cutting region where the chip is made and Region 2 represents the pressing region where the ploughing and friction effects are dominant. 10

The cutting forces in Region 1 are defined by Merchant’s cutting force circle, in which the net cutting force, R, is divided into components along and perpendicular to the velocity direction, i.e.: 𝐹𝑡1 = 𝑅 cos(𝛽 − 𝛼) 𝐹𝑟1 = 𝑅 sin(𝛽 − 𝛼)

(2)

where, 𝛽 is the friction angle on the rake face and 𝛼 is the rake angle of the cutting edge. In the pressing region (Region 2), Fr2 works to press the CFRP composite below the flank surface of the tool perpendicular to the velocity direction and is represented by P. The friction force, Ft2, in the

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velocity direction is assumed to follow the Coulomb friction law with a friction coefficient 𝜇. For anisotropic CFRP, the friction coefficient was assumed to vary with fiber cutting angle due to the difference in the interactions between the tool surfaces and fibers at different fiber angles. 𝐹𝑡2 = 𝜇𝐹𝑟2 = 𝜇𝑃

Ft1 β-α R

Region 2

ϕ

Cutting tool

γ

Ft2

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Fr1

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Cutting direction

α

Region 1

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(3)

Fr2(=P)

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Fiber orientation

Fig. 4. Components of the total cutting force as per the model proposed by Maegawa et al. (2016).

The total tool acting forces along and perpendicular to cutting velocity direction, Ft and Fr, are:

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𝐹𝑡 = 𝐹𝑡1 + 𝐹𝑡2 = 𝑅 cos(𝛽 − 𝛼) + 𝜇𝑃 𝐹𝑟 = 𝐹𝑟1 + 𝑃 = 𝑅 sin(𝛽 − 𝛼) + 𝑃 (4)

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Ft and Fr can be calculated from the feed and normal forces (Ff and Fn) as indicated in Fig. 5

and by using Eq. (5), where 𝜃 is the tool rotation angle as defined earlier. 𝐹 cos 𝜃 { 𝑡} = [ 𝐹𝑟 sin 𝜃

− sin 𝜃 𝐹𝑓 ]{ } cos 𝜃 𝐹𝑛

(5)

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Fn

Fr Ff



Ft

Tool feed

Fig. 5. The feed and normal forces and their tangential and radial components.

𝑅=

𝑃=

𝐹𝑡 − 𝜇𝐹𝑟 cos(𝛽 − 𝛼) − 𝜇 sin(𝛽 − 𝛼)

𝐹𝑡 sin(𝛽−𝛼)−𝐹𝑟 cos(𝛽−𝛼) μsin(𝛽−𝛼)−𝑐𝑜𝑠(𝛽−𝛼)

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The forces P and R can thus be obtained by solving Eq. (4) as follows:

(6)

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It is noted here that the rake angle, 𝛼, was zero for the tool used in this experiment. The friction angle, 𝛽, can be determined from Eq. (7) when 𝜇 is known: 𝛽 = tan−1 𝜇

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(7)

In Merchant’s metal cutting model, 𝛽 is associated with the sliding friction between the chip

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and the rake face. However when milling CFRP, powdered chips are generated so the friction between the uncut chip and the tool edge is used. It is assumed that the friction coefficient in

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Region 2 will reasonably define the friction behavior around the tool edge in the slot milling of

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CFRP.

3.2 Determining the friction coefficients

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After the numerical control program completes the cutting, the tool still runs for a few rotations before it reaches a complete stop. During this short period of time, the cutting effect is eliminated if the force drops to a small enough magnitude. At that time the measured forces will be induced purely by the pressing and friction between the tool edge and the workpiece in Region 2. The friction coefficient can thus be determined from the ratio between the tangential and radial

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components of the measured forces at this stage, with the friction behavior being assumed to be the same as it was during the preceding cutting stage. To reduce the possibility of measurement errors, the delta (decreasing value) of the cutting forces in the last two subsequent tool rotations was sampled. Using this method, the friction coefficients were obtained from Eq. (3). An example is shown in Fig. 6 for the 45° orientation layout. At cutting edge entry, the friction coefficient is very large

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(above 1.0) followed by a rapid drop. This is because this stage corresponds to a transient dynamic

response of the measuring system as the cutting edge first impacts the workpiece. The friction coefficient at this period is unstable and unreliable. Thus, the first 20 data samples from the

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cutting edge entry (corresponding to 18o of tool rotation) are excluded from the analysis.

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3

2

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Friction coefficient

2.5

1.5 1

0 0

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0.5

31

60

91

121

152

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Tool rotation angle (deg)

Fig. 6. Variation of the friction coefficient with the tool rotation angle (45° orientation).

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Fig. 7 shows the friction coefficients obtained for the four orientation layouts grouped together with respect to the tool rotation angle (Fig. 7a) and fiber cutting angle (Fig. 7b). It can be seen that the friction coefficients vary between approximately zero and 0.65. The variation of the friction coefficient with the fiber cutting angle is similar across the four layouts, with the friction coefficient increasing to a maximum and then decreasing as the fiber cutting angle further

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increases (Fig. 7b). The maximum friction coefficients appear at fiber cutting angles between 57° and 75°. This is because, in this region, the fibers are oriented against the tool cutting velocity and tend to bounce back after the cutting edge has passed over and also because the machined surface roughness is usually high for this range of fiber orientations, as has been previously demonstrated (Wang et al., 2017). Note that there is a general decrease in the value of the friction coefficients as

down-milling. 0.7

Orientation 0 Deg. Orientation 45 Deg.

0.6

Orientation 90 Deg. Orientation 135 Deg.

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0.4 0.3 0.2

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Friction coefficient

0.5

0 0

31

60

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0.1

91

121

152

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Tool rotation angle (deg)

(a)

Orientation 0 Deg. Orientation 45 Deg.

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0.7 0.6

Orientation 90 Deg. Orientation 135 Deg.

0.5

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Friction coefficient

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the tool rotates from entry to exit (Fig. 7a), which indicates a higher friction in up-milling than in

0.4 0.3 0.2 0.1

0 0

31

60

91

121

152

Fiber cutting angle (deg)

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(b) Fig. 7. Variation of the friction coefficients with (a) tool rotation angle and (b) fiber cutting angle.

Fig. 8 shows the variation of the friction coefficient and friction angle with respect to the fiber cutting angle averaged across all four fiber orientation layouts. Note that the friction angle can reach as high as 24° at the fiber cutting angle of approximately 65°. The friction coefficient can also be interpolated as a function of the fiber cutting angle, as shown in the figure. 30

0.5 0.45

20

0.3

15

0.25 0.2 Average friction

0.1

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10

0.15

Average friction interpolated

0.05

Friction angle

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Friction coefficient

0.35

0 31

60 91 121 Fiber cutting angle (deg)

5 0

152

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0

Friction angle (deg)

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25

0.4

Fig. 8. The average friction coefficient and friction angle with respect to the fiber cutting angle.

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A few studies in the literature have considered the friction behavior of fiber reinforced

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composites in closed (pin-on-disk) and open tribosystems. Berg at al. (1972) studied the friction and wear of steel pins on a rotating UD-GFRP disk and found that the friction coefficient under

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dry sliding fell within the range of 0.15-0.32. The friction coefficient varied slightly depending upon the sliding speed and normal pressure. Nayak et al. (2005) studied the friction behavior of UD-GFRP on a rotating HSS disk and reported that the friction coefficient increased from 0.3 to 0.9 with the increase of fiber orientation, with the highest value corresponding to fiber orientations perpendicular to the sliding velocity. On the other hand, Voss et al. (2017) showed that the friction

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coefficient varied only slightly with fiber orientation when a diamond coated carbide pin was sliding against UD-CFRP. The range of variation was just 0.12 to 0.14, with the highest value occurring at 0/180 o and 90o and the lowest occurring at 30 o and 150o. Klinkova et al. (2011) studied the friction coefficient between TiN-coated carbide and randomly structured CFRP and found that the friction coefficient decreased from 0.25 to 0.1 when the sliding velocity increased from 10 to 120 m/min. The results presented here have the added virtue of being more

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comprehensive as they cover the friction behavior for all fiber cutting angles from 0o to 180o.

3.3 Analysis of the net cutting force

Once the friction coefficient has been obtained, the net cutting force and pressing force can be

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calculated using Eq. (6). The net cutting forces in the tangential and radial directions and the

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friction force can be calculated using Eqs. (2) and (3) respectively. In view of the significant difference between the friction coefficients across the four orientation layouts (as shown in Fig.

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7(b)), the friction coefficients for each specific orientation rather than their average value are used in the force calculation so as to ensure the accuracy of the results. Fig. 9 presents the three force

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components for 45° fiber orientation. Generally, the pressing force (P) is significantly larger than

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the net cutting force (R) or the friction force (𝐹𝑡2). And, the peak or maximum value of the friction force usually coincides with that of the pressing force. 200

Net cutting force

160

Pressing force

140

Friction force

Force (N)

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180

120 100

80 60 40 20 0 0

31

60

91

121

152

Tool rotation angle (deg)

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Fig. 9. The cutting force, pressing force and friction force for 45° orientation.

The variation of the net cutting force with the tool rotation angle, i.e. the combined effects of the chip thickness and fiber cutting angle, is shown in Fig. 10. It can be seen that the 0° orientation layout produces the largest peak net cutting force (45 N), occurring at a tool rotation angle of around 70°. The 135° orientation produces the second largest peak net cutting force (30 N) at a tool rotation angle of around 100°. The 90° orientation has the smallest peak net cutting force (20

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N) at a tool rotation angle of about 150°. None of these peaks correspond to the maximum chip

thickness, but all occur at similar fiber cutting angles (55°-70°). This suggests that this range of fiber cutting angles is associated with a relatively high specific net cutting energy. The peak net

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cutting force in the 45° orientation layout occurs at a tool rotation angle of 100°. Here this may be

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attributed to the large instantaneous chip thickness. The minimum net cutting forces for the 45°,

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90° and 135° fiber orientation layouts occur at tool rotation angles of around 150°, 95° and 60°, respectively. It is noteworthy that, for the 90° orientation layout, the minimum force occurs at a

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large instantaneous chip thickness with a fiber cutting angle of 5°, while the minimum forces for both the 45° and 135° orientations occur at 15° fiber cutting angle, indicating that the fiber cutting

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angle range of 5°-15° requires a very small specific net cutting energy. Generally, these observations show that the fiber cutting angle has a stronger influence on the net cutting force than

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the instantaneous chip thickness.

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50 Orientation 0 Deg.

45

Orientation 45 Deg.

40

Orientation 90 Deg.

Net cutting force (N)

Orientation 135 Deg.

35 30 25 20 15 10 5 0

31

60 91 121 Tool rotation angle (deg)

152

Fig. 10. Variation of the net cutting force with the tool rotation angle.

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0

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At a particular tool rotation angle, the instantaneous uncut chip thickness in all four layouts is assumed to be identical, while the fiber cutting angles will differ. The influence of the fiber cutting

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angle on the net cutting force was therefore studied at four different tool locations: tool rotation

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angles of 30°, 75°, 120°, and 165°, as shown in Fig. 11. Intervals of 45° can ensure the comparison is made among the same set of fiber cutting angles (e.g. 30°, 75°, 120°, and 165°).

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The 75° fiber cutting angle consistently generates the largest net cutting force, followed by 120° and 165°, with 30° generating the smallest net cutting force. This indicates a significant change in

Force (N)

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45 40 35 30 25 20 15 10 5 0

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the chip formation mechanism with the change in fiber cutting angle.

30.4

Fiber cutting angle 30.4 Deg. Fiber cutting angle 75.4 Deg. Fiber cutting angle 120.4 Deg. Fiber cutting angle 165.4 Deg.

75.4 120.4 Tool rotation angle (deg)

165.4

Fig. 11. The net cutting force for different fiber cutting angles. 18

For a particular fiber cutting angle in Fig. 11, the forces at the four tool locations were obtained from different fiber orientation layouts, so they were averaged and shown in the line chart in Fig. 12 (a). Similarly, Figs. 12 (b) and 12(c) show the variation of the average net cutting force with respect to different fiber cutting angles. The forces shown in Fig. 12 (b) were obtained from the four fiber layouts at tool rotation angles of 15°, 60°, 105°, and 150°, while the forces in Fig. 12 (c) were obtained from the four fiber layouts at tool rotation angles of 45°, 90° and 135°. For the 15°,

ro of

60°, 105° and 150° fiber cutting angles, 60° produces the highest and 15° the smallest net cutting

force. For the 0°, 45°, 90° and 135° fiber cutting angles, 90° produces the highest and 0° the smallest net cutting force.

-p

20 15 10 5 0 30.4

75.4

120.4

165.4

lP

Fiber cutting angle (deg)

(a) 30 25 20

na

Average force (N)

re

Average force (N)

25

15 10 5 0 15.1

60.1

105.1

150.1

(b)

Average force (N)

Jo

20

ur

Fiber cutting angle (deg)

15 10

5 0

0.7

45.7

90.7

135.7

Fiber cutting angle (deg)

(c) Fig. 12. The average net cutting force for different fiber cutting angles.

19

The net cutting force was further decomposed into tangential and radial components (𝐹𝑡1 and 𝐹𝑟1 ) using Eq. (2). The results are shown in Fig. 13 for the four fiber orientations. Generally, the magnitude of tangential force and its variation pattern are very close to the net cutting force, indicating a very small friction angle. The tangential cutting forces for the 0°, 90°, and 135° layouts reach their peaks at fiber cutting angles between 55°-70° because of a high specific cutting energy. For the 45° layout it reaches its peak at 100° of tool rotation angle more due to a large chip

ro of

thickness. The smallest tangential net cutting force for the different orientations corresponds to

fiber cutting angles in the range of 5°-15°. This is consistent with the trend of the average net cutting force shown in Fig. 12. The radial components of the net cutting force are usually smaller

-p

than the tangential force, with patterns similar to those of the net cutting force, except for the 45°

re

orientation. The peaks of the radial cutting force for fiber orientations of 0°, 90°, and 135° occur at

lP

fiber cutting angles of 55°-70°, while for the 45° orientation it occurs at around 75°(corresponding to 30° tool rotation angle). Again, the smallest radial net cutting forces in all orientations

na

correspond to a fiber cutting angle range of 5°-15°. The force patterns for the 45° fiber orientation indicate that the fiber cutting angle has a stronger influence on the radial net cutting force than on

ur

the tangential net cutting force. 45 40 35

25

Tangential net cutting force Ft1 Radial net cutting force Fr1

20

Force (N)

Jo

30

Net cutting force

Force(N)

50

25 20

Net cutting force Tangential net cutting force Ft1 Radial net cutting force Fr1

15 10

15

5

10

5

0

0 0

31

60

91

121

0

152

(a)

31

60

91

121

Tool rotation angle (deg)

Tool rotation angle (deg)

(b)

20

152

25

35

Tangential net cutting force Ft1

30

Radial net cutting force Fr1

25

Force (N)

Force (N)

20

Net cutting force

15 10

Net cutting force Tangential net cutting force Ft1 Radial net cutting force Fr1

20 15 10

5 5 0

0 0

31

60

91

121

152

0

Tool rotation angle (deg)

31

60

91

121

152

Tool rotation angle (deg)

(c)

(d)

Fig. 13. The tangential and radial forces with tool rotation angle for (a) 0o, (b) 45o, (c) 90o, (d) 135o fiber

ro of

orientations.

Table 1 summarizes the variations of the fiber cutting angles corresponding to the maximum and minimum values of the net cutting force as well as the components in tangential and radial

-p

directions. The high net cutting force (and the tangential and radial components) at similar ranges of fiber cutting angles (55°-70°) is most likely attributed to the macro-fracture chip formation

re

mode (Type V). Severe elastic bending of the fibers occurs ahead of the cutting edge before

lP

fracture, which requires additional energy. The compression stress at the cutting edge then causes the fibers and matrix to crack at or below the machined surface. The cutting forces associated with

na

this mode are often high and fluctuating. The reason for the small net cutting force in the fiber cutting angle range of 5°-15° is that the cutting is acting along the fiber/matrix interface in Type I

Table 1

ur

chip formation mode, which makes the cutting easy.

Jo

Fiber cutting angles for the maximum and minimum values of the net cutting force and its tangential and radial

Max R

Min R

Max Ft1

Min Ft1

Max Fr1

Min Fr1

ψ = 0/180°

68°-70°

---

68°-70°

---

68°-70°

---

ψ = 45°

145°-148°

15°-17°

145°-148°

15°-17°

75°-78°

15°-17°

ψ = 90°

60°-62°

5°-7°

60°-62°

5°-7°

56°-58°

5°-7°

ψ = 135°

55°-58°

13°-15°

53°-55°

13°-15°

59°-61°

13°-15°

components.

These results are consistent with the results of orthogonal cutting experiments of UD-CFRP reported in the literature. Wang and Zhang (2003) found that the horizontal cutting force reaches 21

its peak at 60° fiber cutting angle when cutting the UD-CFRP panel with the depths of cut of 50 and 100 micrometers. Wang et al. (1995) observed the minimum horizontal cutting force at 10° fiber cutting angle. The radial net cutting force is not comparable to the vertical or thrust force in orthogonal cutting experiments in the literature because in those studies, the vertical or thrust forces also contained the pressing force due to the bouncing back effect in Region 2 as demonstrated (Wang and Zhang, 2003).

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3.4 Analysis of the pressing and friction forces

As shown earlier, the pressing force makes up the majority of the total radial force. The variations of the pressing force and friction force with the tool rotation angle are shown in Fig. 14.

-p

The fiber cutting angles corresponding to the maximum and minimum values of the pressing and

re

friction forces are summarized in Table 2. Among the four fiber orientations, the tool rotation angle corresponding to the peak pressing force decreases as the fiber orientation angle increases.

lP

However, all peaks appear at similar fiber cutting angles (around 160o-175o), indicating that there

na

is a relatively high specific pressing energy for this range of fiber cutting angles. The minimum pressing force for the 0°, 90° and 135° orientation layouts appears at tool rotation angles of 65°,

ur

145° and 100°, respectively, corresponding to fiber cutting angles of 55o-65o. This indicates a very small specific pressing energy for this range of angles. Interestingly, the range of fiber cutting

Jo

angles for the minimum pressing force corresponds to the range of angles for the maximum net cutting force. A possible reason for the low pressing force in this range of angles is that the fibers severely bend forward ahead of the cutting edge before fracture at or below the cutting line. As the fibers bounce back away from the clearance face under elastic recovery, their projected height becomes shorter and their pressure on the clearance face is reduced. The fibers in this range of

22

angles are usually neatly cut without any overhanging fibers or delamination, which also helps to reduce the pressing force. At the opposite extreme, the fibers in the fiber cutting angle range of 160o-175o are almost parallel to the cutting velocity direction and their deformation is less severe. The fibers are pushed under the tool nose without much scope for deformation, making them push harder against the clearance face. There is also extensive elastic recovery of the overhanging fibers in this range of fiber cutting angles as a result of delamination and their contact with the tool edge.

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The issue of delamination is discussed further in Section 3.5.

As the friction coefficients remain less than 1 in Fig. 7, the friction force always has a smaller

magnitude than the pressing force in each fiber orientation layout. They also generally follow a

-p

similar variation pattern, as shown in Fig. 14 (b). However, as the friction coefficient varies with

re

tool rotation, the fiber cutting angles for the maximum and minimum values of the friction force

Table 2. Orientation 0 Deg. Orientation 45 Deg.

200

Orientation 90 Deg.

na

120 100 80 60

Jo

40

Friction force (N)

140

35

Orientation 90 Deg.

30 25 20 15

5 0

0

31

Orientation 45 Deg.

10

20

0

Orientation 0 Deg.

40

Orientation 135 Deg.

Orientation 135 Deg.

160

ur

Pressing force (N)

180

lP

are somewhat different from those for the maximum and minimum pressing force, as shown in

60 91 121 Tool rotation angle (deg)

0

152

31

60

91

121

152

Tool rotation angle (deg)

(a)

(b)

Fig. 14. Variation of (a) pressing force and (b) friction force with tool rotation angle. Table 2 Fiber cutting angles corresponding to the maximum and minimum pressing and friction force values for different fiber orientations. Max P(Fr2)

Min P(Fr2) 23

Max Ft2

Min Ft2

ψ = 0/180°

160°-162°

64°-66°

142°-144°

64°-66°

ψ = 45°

173°-175°

---

165°-167°

---

ψ = 90°

170°-172°

55°-57°

169°-171°

44°-46°

ψ = 135°

173°-175°

56°-58°

160°-162°

47°-49°

The influence of the fiber cutting angle on the average pressing and friction forces is shown in Fig. 15. The forces for each fiber cutting angle are averaged across the four fiber orientations at tool rotation angles of 45o, 90o and 135o. Among the four fiber cutting angles, 0o produces the largest pressing and friction forces, followed by 135o and 90o, while 45o produces the smallest

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ones. This mechanism was explained earlier. 160 Pressing force

120

Friction force

100 80 60

-p

Average force (N)

140

40

0 0.7

45.7

90.7

135.7

Fiber cutting angle (deg)

re

20

lP

Fig. 15. Influence of the fiber cutting angle on the average pressing and friction forces.

3.5 Effect of the cutting forces on delamination

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Delamination might be induced during the milling process as a result of the cutting forces pushing against unsupported fibers. Determining the mechanism of delamination damage is

ur

crucial for the optimal design of the processes and parameters for milling CFRP products. In this

Jo

study, delamination appears in the form of uncut or overhanging fibers, visible as fluffing or fuzzing of the machined edge as illustrated in Fig. 16. It is recognized that delamination occurs in a critical fiber cutting angle range of 90° ≤ ρ < 180°, as demonstrated (Hintze et al., 2011). For the 0o orientation layout, delamination mainly appeared in the semi-circular tip of the slot in the down-milled side (bottom half) while the up-milled side exhibited no delamination. Delamination appeared in front of the tool feed for the 45o orientation and in the up-milled region (upper half of 24

the semi-circle) for the 90o orientation. For the 135o fiber orientation, delamination appeared on both up-milled and down-milled edges (entry and exit sides).

Feed

Feed

Fiber

Fiber

Fiber

(0o)

Feed

Fiber

(45o)

(90o)

(135o)

Fig. 16. The appearance of delamination for different fiber orientations.

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Feed

The possible association between the occurrence of delamination and the cutting forces was studied. Among all the force components discussed earlier, it was observed that the delamination

-p

regions (e.g. fiber cutting angles of 90o-180o) coincide most with the regions of high friction force.

re

This suggests that the friction force may be closely associated with delamination in milling, as

lP

either the result or the cause of delamination. The high friction force could be the result of delamination because the presence of overhanging fibers on the machined edge impedes the

na

passage of the tool edge, thus increasing the friction force. On the other hand, the high friction force could also itself be the cause of the delamination. An example of delamination on the

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down-milled edge of the 135o layout is shown in Fig. 17. It can be seen that the fluffing of the fibers only appears on the top ply of the laminate, with the machined surface below retaining a

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fairly good surface finish. This delamination was most likely induced by the mode III fracture. The friction force results in an out-of-plane shear effect on the uncut chip in the cutting velocity direction, which is the main cause of mode III fracture. In such a hypothesis, there might be a critical friction force beyond which delamination could be induced. According to the results shown in Fig. 14(b), the critical friction force for delamination in this experiment was estimated to

25

be between 10 N and 15 N. Cutting velocity

Cutting velocity

(a)

(b) o

ply. (b) SEM image of the machined surface.

4. Specific cutting energy and cutting force modeling

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Fig. 17. Delamination on the down-milled edge of 135 fiber orientation layout. (a) Microscope image of the top

In mechanistic cutting force models, the cutting forces are defined as the product of the chip

-p

load and the cutting force coefficients. The instantaneous undeformed chip thickness in slot

tooth and 𝜃 is the tool rotation angle.

lP

𝑡𝑐 = 𝑓𝑡 sin 𝜃

re

milling is calculated using Eq. (8), where 𝑡𝑐 is the undeformed chip thickness, 𝑓𝑡 is the feed per

(8)

Once the net cutting force, pressing force and friction force have been identified, they can be

na

expressed in terms of the instantaneous specific cutting energies for the cutting and edge effects, as shown in Eq. (9). Here, Ktc and Krc are the cutting force coefficients for the tangential and radial

ur

net cutting forces, respectively. Kte and Kre are the edge force coefficients responsible for the

Jo

friction and pressing forces, respectively. 𝑎𝑝 is the axial depth of cut. The instantaneous force coefficients Ktc, Kte, Krc, and Kre can then be obtained using Eq. (10). 𝐹𝑡 = 𝑅 cos(𝛽 − 𝛼) + 𝜇𝑃 = 𝑎𝑝 (𝑓𝑡 𝑠𝑖𝑛𝜃 ∙ 𝐾𝑡𝑐 + 𝐾𝑡𝑒 ) { 𝐹𝑟 = 𝑅 sin(𝛽 − 𝛼) + 𝑃 = 𝑎𝑝 (𝑓𝑡 𝑠𝑖𝑛𝜃 ∙ 𝐾𝑟𝑐 + 𝐾𝑟𝑒 ) 𝐾𝑡𝑐 =

𝑅 cos(𝛽−𝛼)

𝐾𝑟𝑐 =

𝑅 sin(𝛽−𝛼)

𝑎𝑝 ∙𝑓𝑡 𝑠𝑖𝑛𝜃 𝑎𝑝 ∙𝑓𝑡 𝑠𝑖𝑛𝜃

𝐾𝑡𝑒 = {

𝐾𝑟𝑒 =

= =

（9）

𝐹𝑡1 𝑎𝑝 ∙𝑓𝑡 𝑠𝑖𝑛𝜃

𝐹𝑟1 𝑎𝑝 ∙𝑓𝑡 𝑠𝑖𝑛𝜃

(10)

𝜇𝑃 𝑎𝑝 𝑃 𝑎𝑝

26

The variation of the cutting force coefficients with the tool rotation is shown in Fig. 18 for the four fiber orientation layouts. At cutting exit point, the Ktc and Krc are usually very large due to the size effect. Excluding the cutting entry and exit regions, the maximum Ktc and Krc for all orientations appear in the fiber cutting angle range of 55o-70o and the minimum Ktc and Krc appear in the fiber cutting angle range of 5o-15o. The reason for the consistency across all four orientations, without any exception such as the 45o orientation in Table 1, is the inclusion of

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rotation-dependent chip thickness in the calculation of the cutting force coefficients. The maximum Kre and Kte occur in the fiber cutting angle ranges of 160o-175o and 142o-170o,

respectively. The minimum Kre and Kte occur in the fiber cutting angle ranges of 55o-65o and

-p

44o-65o, respectively.

600

Orientation 90 Deg.

2500 2000 1500

500 0 0

31

na

1000

60

91

121

300 200

0

152

0

(b)

Jo

ur

400

100

Tool rotation angle (deg)

(a)

Orientation 0 Deg. Orientation 45 Deg. Orientation 90 Deg. Orientation 135 Deg.

500

lP

Orientation 135 Deg.

Krc (N/mm2)

Orientation 45 Deg.

3000

Ktc (N/mm2)

700

Orientation 0 Deg.

3500

re

4000

27

31

60 91 121 152 Tool rotation angle (deg)

Orientation 0 Deg.

20

Orientation 45 Deg.

18

Orientation 90 Deg.

16

Orientation 135 Deg.

90 80

14

70 12

Kre (N/mm)

Kte (N/mm)

Orientation 0 Deg. Orientation 45 Deg. Orientation 90 Deg. Orientation 135 Deg.

100

10 8

60 50 40

6

30

4

20

2

10

0

0 0

31

60 91 121 Tool rotation angle (deg)

152

0

60 91 121 Tool rotation angle (deg)

(d)

152

ro of

(c)

31

Fig. 18. The cutting force coefficients (a) Ktc, (b) Krc, (c) Kte, (d) Kre.

The average cutting force coefficients for specific fiber cutting angles are shown in Fig. 19. Out

-p

of the four fiber cutting angles (45o, 90o, 135o and 0/180o), 45o has the largest tangential net

re

cutting force coefficient and the smallest pressing and friction force coefficients. The 90o fiber cutting angle has the largest radial net cutting force coefficient. The fiber cutting angle of 0/180o

friction force coefficients.

na

600

Ktc

400

Krc

300

ur

Average cutting force coefficients(N/mm2)

500

200 100

Average edge force coefficients (N/mm)

lP

has the smallest tangential and radial net cutting force coefficients, but the largest pressing and

0

45.7

Jo

0.7

90.7

135.7

80 70 60 50 40 30 20 10 0

Kre Kte

0.7

Fiber cutting angle (deg)

45.7

90.7

135.7

Fiber cutting angle (deg)

(a)

(b)

Fig. 19. Effect of the fiber cutting angle on average cutting force coefficients (a) Ktc Krc and (b) Kte Kre.

In this study, Ktc, Krc, Kte, and Kre are modeled as a function of the chip thickness 𝑡𝑐 and the fiber cutting angle 𝜌. A reasonable polynomial was chosen to represent the effects of the chip thickness and fiber cutting angle on the cutting force coefficients (shown in Eq. (11)). Nonlinear 28

regression was used to fit the mathematical function to the experimental cutting force coefficients shown in Fig. 18. The constants for the polynomial function obtained by regression are listed in Table 3. With these constants, Ktc, Krc, Kte, and Kre under different cutting parameters can be predicted using Eq. (11) for the same tool-workpiece pair. Ft and Fr can then be calculated using Eq. (9) and the feed and normal forces, Ff and Fn, can be further calculated using Eq. (5). 𝐾 = (𝑎1 + 𝑎2 𝑡𝑐 + 𝑎3 𝑡𝑐2 + 𝑎4 𝑡𝑐3 )(𝑎5 + 𝑎6 𝜌 + 𝑎7 𝜌2 + 𝑎8 𝜌3 +𝑎9 𝜌4 + 𝑎10 𝜌5 )

(11)

Table 3

Krc

Kte

66.1413

-1.04476

6.02796

-4937.97

10169.5

2446.49

1986.18

𝑎4

𝑎5

𝑎6

5.22094e+

3.3496

-34.640

06

6

9

-1.24612

4.1262e+0

1.2173

-14.333

e+06

7

1

-180398

4.4632e+0

1.3288

-4.2717

6.1463

6

3

1

42553.5

-50497.9

-170023

3.6651

𝑎7

𝑎8

𝑎9

𝑎10

-106.09

38.004

-4.7861

2

1

6

39.373

-33.135

11.264

-1.3561

5

9

3

5

-3.9634

1.2267

-0.1431

5

3

8

42

-9.9174

11.495

-6.4758

1.8395

-0.1987

4

6

6

4

85

117.3

lP

Kre

93.8524

𝑎3

-p

Ktc

𝑎2

re

𝑎1

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Coefficients for the regression function (proposed model).

As a verification of the proposed model, the cutting forces were predicted for the milling of the

na

unidirectional laminate with 30o fiber orientation. For comparison, the cutting forces were also predicted using the traditional method which assumes that the tangential and radial forces are

ur

induced purely by the cutting effect, leaving only the cutting force coefficients (Kt and Kr) to be considered. Table 4 shows the constants for the regression function in this case. Fig. 20 shows the

Jo

feed and normal forces predicted by the two models against the experimental results. It can be seen that the proposed new model performs better than the traditional one in terms of magnitude and trend of cutting force. Table 5 lists the difference between the predicted and experimental forces for the two models. The improved model that considers the pressing and friction forces predicts the cutting forces with half the error of the traditional model.

29

Table 4 Coefficients for the regression function (traditional model).

Kt

𝑎1

𝑎2

𝑎3

𝑎4

𝑎5

93.25

-7259

264100

-2.80276e+06

31.2173

𝑎6 -149.62

86

327.69

𝑎8 -263.186

6

53.57

-7056

86

.16

446076

-1.00688e+07

441.497

-1273.74

1681.8

-1029.2

3

𝑎9

𝑎10

90.571

-11.218

9

4

298.70

-32.138

5

8

Jo

ur

na

lP

re

-p

ro of

Kr

𝑎7

30

150 100

Force (N)

50 0 0

31

60

91

121

152

-50

-100 -150 -200

Ff by traditional model Fn by traditional model Ff by proposed model Fn by proposed model Experimental Ff Experimental Fn

Tool rotation angle (deg)

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Fig. 20. Comparison of the experimental and predicted cutting forces using the proposed and the traditional models (30o orientation layout). Table 5 Comparison of the forces predicted by the two models.

Traditional model

89

96.5

73.7

-158.5

(8.4% Error)

(17.1%Error)

-164.8

-143.4

re

Max Fn

Proposed model

-p

Max. Ff

Experiment

(4% Error)

lP

5 Conclusions

(9.5% Error)

By using a cutting model incorporating both the cutting region and the pressing region, the

na

friction behavior in the pressing region was investigated and analyzed. The different cutting force

ur

components acting in the two regions were identified, analyzed and modeled separately, including the net cutting force, pressing force and friction force. The findings of this study can be

Jo

summarized as follows:

(1) The friction coefficient during the milling process is dependent on the fiber cutting angle,

with an initial increase, then a decrease as the fiber cutting angle increases. The maximum friction coefficient appears at a fiber cutting angle of around 65°. (2) The maximum net cutting forces (including the tangential and radial components) are

31

observed in the fiber cutting angle range of 55°-70° and the minimum ones are observed in the range of 5°-15°. These two angle ranges also correspond to the maximum and minimum values of the specific net cutting energies, excluding the cutting entry and exit regions. (3) The maximum pressing force and specific pressing force energy are observed in the fiber cutting angle range of 160o-175o, while the minimum ones are observed in the range of 55o-65o. The friction force shows a similar pattern, with the maximum and minimum values being

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observed at fiber cutting angles of 142o-170o and 44o-65o, respectively.

(4) The four specific cutting force energies were modeled as a function of the instantaneous

chip thickness and instantaneous fiber cutting angle. The parameters for each function were

-p

identified through nonlinear regression. This model provides a more accurate prediction of the

re

cutting forces than the model that neglects the edge effects. Declaration of interests

na

Acknowledgments

lP

☐ √The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

ur

This work is partially supported by Chinese Foreign Talents Introduction and Academic Exchange Program [Grant No. B13044].

Jo

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high-strength UD-CFRP laminates based on orthogonal cutting method. Compos. Struct. 131, 374-383. Azmi, A.I., Lin, R.J.T., Bhattacharyya, D., 2013. Machinability study of glass fibre-reinforced polymer composites during end milling. Int. J. Adv. Manuf. Technol. 64, 247-261.

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Berg, C.A., Batra, S., Tirosh, J., 1972. Friction and wear of graphite fiber composites. J Res Nat Bur Stand Sect C Eng Instrum. 76, 41-52. Bhatnagar, N., Ramakrishnan, N., Naik, N.K., Komanduri, R., 1995. On the machining of fiber reinforced plastic (FRP) composite laminates. Int. J. Mach. Tools. Manuf. 35, 701-716. Chen, L.X., Zhang, K.F., Cheng, H., Qi, Z., Meng, Q., 2016. A cutting force predicting model in orthogonal machining of unidirectional CFRP for entire range of fiber orientation. Int. J. Adv. Manuf.

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Technol. 89, 1-14.

Davim, J.P., Reis, P., 2005. Damage and dimensional precision on milling carbon fiber-reinforced plastics using design experiments. J. Mater. Process Technol. 160, 160-167.

-p

Erkan, Ö., Işık, B., Çiçek, A., Kara, F., 2013. Prediction of damage factor in end milling of glass

re

fibre reinforced plastic composites using artificial neural network. Appl. Compos. Mater. 20, 517-536.

lP

He, Y.L., Qing, H.N., Zhang, S.G., Wang, D.Z., Zhu, S.W., 2017. The cutting force and defect analysis in milling of carbon fiber-reinforced polymer (CFRP) composite. Int. J. Adv. Manuf. Technol.

na

93,1829-1842.

Hintze, W., Hartmann, D., Christoph S. Schütte, C., 2011. Occurrence and propagation of

ur

delamination during the machining of carbon fibre reinforced plastics (CFRPs) – an experimental study. Compos. Sci. Technol. 71, 1719-1726.

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Hintze, W., Hartmann, D., 2013. Modeling of delamination during milling of unidirectional CFRP.

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