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Co tools during dry turning of Ti6Al4V alloy
Wear 448–449 (2020) 203229
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Temporal and spatial crater wear prediction of WC/Co tools during dry turning of Ti6Al4V alloy Sarvesh Kumar Mishra, Sudarsan Ghosh, Sivanandam Aravindan * Department of Mechanical Engineering, Indian Institute of Technology-Delhi, Hauz Khas, New Delhi, 110016, India
A B S T R A C T
A new approach is developed to predict the crater wear variation on straight grade tungsten carbide tools during titanium machining. The effect of crater wear geometry has been considered on the variation of local state variables such as normal stress (σn Þ, chip sliding velocity (vs ), and cutting temperature (T) over the contact length at varying cutting times. Experimentally determined crater profiles at progressive wear stages were geometrically replicated on the cutting tool models and used for FEM analysis. In order to account for the variation of the state variables and wear rates with respect to the tool-chip contact length, the dimensionless fractional contact length parameter is introduced in the Usui characteristic wear equation. The thermo-mechanical state variables evaluated at different fractional contact lengths and cutting time were used to obtain the wear coefficients. The crater wear profile and wear depth are predicted and the same is experimentally validated over the contact length.
1. Introduction Tool wear analysis has been considered as a tedious task for metal cutting research as it incorporates the complete spectrum of mechanical loading, thermo-chemical interactions, time, and spatial variation of material loss. None of these mentioned parameters can be considered constant when the information about the material loss is sought in terms of wear debris, adhered layer, and molecular or atomic migration of the constituent elements. Since the initial works by Taylor [1], who devel oped the empirical wear life equation (VT n ¼ C), there has been numerous attempts to modify and develop unified wear models which can accurately predict tool wear and its progression. Complex tool wear mechanisms (adhesion, abrasion, diffusion, etc.) depend on the tool-work combination, tool geometry, material properties, cutting pa rameters, and environments. The available wear models (Table 1) refer that there is a considerable amount of research which have devised wear models on the basis of different underlying wear mechanisms. The basic wear models (Burwell [2], Shaw and Dirke [3], Trigger and Chao [4], Archard [5]) have revealed that the wear volume per unit sliding distance is dependent on the applied pressure and hardness of the softer asperity in the case of tribological contact pairs. The tool wear on the rake face can be divided into the stagnation zone, active crater wear zone (due to adhesive wear and diffusive wear mechanisms), and abrasion wear zone at the chip exit. Boltzmann’s canonical distribution of diffusion [6] accurately predicts the tool wear (adhesive and dissolution wear) for a fixed
tool-work combination, limited cutting parameters, approximated con tact area (Areal ¼ Aapparent), and visco-plastic deformation at the tool-chip interface. Using FE simulations, the prediction of abrasive wear contribution over the rake face becomes difficult as the σn ; vs ; and Tint values at the chip exit zone are much lower in FE simulations than the actual exper imental conditions [13]. In order to incorporate the physical wear mechanisms in FEM simulations, abrasion-diffusion wear model [7,9, 12], diffusion wear model [6,8,10,11,14], and modified diffusion wear models [13,15] have been developed. The developed models have their own excellence in the context of studies and resulted in the close pre diction of crater/flank wear. Amongst the available wear models, the Usui wear model has been widely used for flank and crater wear simu lations due to its ability to incorporate physical wear mechanisms [10, 11,16,17]. The model is capable of closely predicting the abrasion and diffusion wear as it converts the thermomechanical load spectrum ðσ n ; _ The model is vs ; τmax ; Tint ; etc: Þ into the volumetric wear rate (w). capable of integrating the Boltzmann canonical distribution as well as mechanical effects (by considering the stresses and sliding velocity) induced during metal cutting; hence, it is overwhelmingly used for wear modelling. Constant values of local variables at the tool-chip interface ðσn ; vs ; τmax ; etc: Þ, and uniform thermal behavior ðQs ; Qint ; Tavg ; Tint ; etc:Þ offer an approximate prediction of the dynamic wear behavior during metal cutting. Exponential temperature profile, complex thermo-chemical interaction, variable interface friction and stress distribution, and nonuniform chip sliding behavior are the most critical factors for tool
* Corresponding author. E-mail address: [email protected] (S. Aravindan). https://doi.org/10.1016/j.wear.2020.203229 Received 29 May 2019; Received in revised form 5 February 2020; Accepted 5 February 2020 Available online 8 February 2020 0043-1648/© 2020 Elsevier B.V. All rights reserved.
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Nomenclature
re w w_ w_ l K
KB KM SVα x KTmax KT Tint R E
Width of crater (mm) Location of maximum crater wear (mm) Cutting edge displacement (Edge wear) Distance at the rake from the cutting edge Maximum crater wear depth (μm) Crater wear (μm) Tool-chip interface temperature (K) Universal gas constant (kJ.K-1.mol-1) Activation energy (kJ.mol-1) σn Normal contact stress (MPa) vs or vchip Chip sliding velocity (m/min) vc Cutting velocity (m/min) f Feed (mm/rev) ap Depth of cut (mm) μsticking Sticking friction coefficient μsliding Sliding friction coefficient μ Coefficient of coefficient Heat in the secondary interface Qint VBmax Maximum flank wear (μm) Tool chip contact length (μm) Lc
α
Fz ; Fx ; Fy Fxy
τmax σ mises ε_ ε σ T FEM ϕ β
τ
tc
σ flow QS rn
After initial crater formation, the wear profile results in the chip flow conditions over tool rake face which consequently change the state variables (σn ; vs ; Tint ), interface friction (μsticking ; μsliding ; μtotal Þ, and effec tive rake angle (αeffective ). The determination of these parameters with the help of experimental methods is accurate but difficult, whereas the predictive models involve numerous assumptions that impart limited accuracy to these predictions. With the help of robust computational codes to perform the high strain and high strain rate calculations, these parameters can be evaluated with considerable accuracy. It takes several weeks of duration to run a few milliseconds of the tool wear simulation at a single cutting condition (constant machining parameters, tool-work combination, and tool geometry). The data generation for the state variables up to the progressive tool wear stages (even for a few seconds) is almost difficult. Hence, the continuous tool wear simulations are not cost-effective in order to establish the database for the dynamically changing state variables. Specialized modules of tool wear have been developed in the past, which can run the tool wear simulations for longer cutting times [19] and used for running tool wear simulations satisfactorily [20,21]. In attempts to consider the influence of tool wear geometry and wear profile on state variables, very few works have been conducted. In a study conducted by Ramirez et al. [15], the wear profile is approximated according to the temperature profile variation at different levels of isotherms over the rake face. The study utilized the temperature profile to interpolate the crater wear profile based on the start of contact length (P1), the end of contact length (P2), and the locus of maximum tem perature at the interface (P3). The crater profile has been successfully predicted using this approach, assuming that KTmax always lies at the location of maximum cutting temperature. For unworn tools (or shallow crater depths), the variation of local normal stresses at contact length follows the same trend as Zorev’s hybrid friction distribution [6]; however, no specific mention of the same is available for the worn tools. The curvature of the crater wear and its profile over the contact length zone have not been utilized for volumetric wear calculation in the available research. It has been mentioned that the curvature of the crater profile (ratio of KTmax before fracture to contact length) is around 0.04 for AISI 1045 steel cutting with multilayer-coated tools [18]. The lower value of curvature for the wear profile signifies that the influence of KTmax/Lc may be neglected to wear simulations of the coated tools.
Table 1 Available wear models for volumetric wear analysis considering different wear mechanisms. References
Developed wear model
Takeyama and Murata [7]
w_ ¼ C1 vs þ C2 :exp
Usui [6,8]
w_ ¼ K:σn :vs: exp
Palmai [9]
Amir et al. [10]
�
�
E RTint
α�
T
w_ ¼ C1 vs þ C2 : � � E vs exp RTint � α� w_ ¼ K:vs: exp T
α�
Lung et al. [11]
� w_ ¼ K:τmax :vs: exp
Zanger and Schulze [12]
� α � 1 w_ ¼ K1 :vs :exp þ � α � T 2 K2 :σn :exp T � R wðx; y; tÞ ¼ aσn x; y; � � � � t Vs x; y; t exp � b dt Tðx; y; tÞ
Haddag and Nouari [13]
T
Incorporated wear mechanism/ model �
Edge radius (μm) Volumetric wear (mm3) Volumetric wear rate (mm3/min) Local wear rate at a fractional distance Pre-exponential wear coefficient Wear constant Main cutting, axial thrust and radial thrust force (N) Resultant thrust force (N) Maximum shear stress (MPa) Von-Mises’ stress (MPa) Strain rate (mm/s) Strain Flow stress (MPa) Cutting temperature (� C ) Finite element method Principle cutting edge angle Rake angle Shear Stress (MPa) Cutting time (s) Flow stress (MPa) Heat in the shear zone Nose radius (mm)
Temperature independent abrasion wear (varying with sliding distance and abrasive wear resistance), and diffusion wear Able to consider the abrasion and diffusion wear mechanism for wear of uncoated tools. Both abrasion and diffusion wear depend on the sliding distance. Flank wear prediction considering VBmax is independent of normal pressure. Wear prediction for uncoated and coated tools considering very high stresses in metal cutting. Flank wear prediction of uncoated carbide tools considering abrasion and diffusion wear mechanisms.
ðσn ; vs ; TÞ values computed from the FE model at the integration limits (interval dt) using 3D FE analysis only for unworn tools.
wear prediction. These variables change with tool-work material prop erties, cutting parameters, and cutting environments. The mentioned parameters and variables at the tool rake face along the tool-chip contact length should be accounted for the wear rate and consequent crater formation (Fig. 1). These variables possess dynamic nature in spatial orientation (along the contact length and wear width) and time (cutting time) during cutting. The properties and their variation at the tool-chip contact length, wear width, and cutting time are required for the determination of the wear parameters (crater profile, KTmax, KB, and KM). 2
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Fig. 1. Schematic representation of the response of the state variables with contact length and crater growth [18].
However, owing to the high wear rate of straight grade carbide tools for dry titanium machining, the geometric parameters of the crater profile must be considered to pursue its influence on local state variable and crater wear progression. Some of the wear models [12,13,15,18] have incorporated the dy namic nature of variation in σn ; vs ; and Tint over the cutting time and contact points on the tool-chip interface. The successful prediction of flank and crater wear in these studies helped to understand the dynamic nature of tool wear. These studies have used the FEM results of σn ; vs ; and Tint at different nodes of a plain (unworn) cutting tool at the initial steady stage of the cutting process. The original thermomechanical loading conditions and variables will change once the tool is worn due to the loading, frictional heat, and sliding behavior of the chips over the crater profile. In most of the cases, the characteristic wear equations have been developed considering the fluctuation in the state variables at fresh tool surface only. This approach is followed as the experimental measurement of these variables could be determined only for plain tools using a dividing tool method [6,22]. The initial steady-state values of the local state variables obtained for plain (unworn) cutting tools may not be able to approximate the state variables over the worn surface. Hence, there exists a need to analyze the dynamic nature of the state variables for the complete spectrum of cutting time and nodal points on the contact length with the progressive stages of updated wear geome try. The combined experimental and FE simulations will be helpful in devising a method that can extract the local state variables at changing cutting time and nodal points for progressive wear stages. The approach has been used to achieve the wear coefficients, which could predict the crater wear profile over the tool rake face.
details of the machine and related equipment can be found in our pre vious research [23]. The carbide distribution in the matrix of the cutting tool is shown in Fig. 2(a), which reveals the fine WC particles cemented in the binder matrix. The alloy surface was polished and etched with Kroll’s reagent according to ASTM E407-07 (10 ml HF, 5 ml HNO3 and 85 ml water) [24]. The microstructure of Ti6Al4V alloy (Fig. 2(b)) reveals the different α- and β-phase grains in the work material. The presence of two-phase microstructure (α-hcp and β-bcc phase) is one of the major causes of the machinability related problems in titanium cutting. It causes the fluctuation of the cutting forces, rapid tool wear and the formation of adiabatic shear banding even at low cutting speeds [25,26]. Initial ex periments have been conducted to delimit the steady wear zone from the degressive wear zone (initial wear). The cutting forces were measured using a 3-component piezoelectric dynamometer (Kistler 9129AA: Switzerland) mounted on the tool holder and connected with a charge amplifier (model: 5070A). Cutting forces obtained from different cutting conditions were used to find the coefficient of friction (μ). Maximum flank wear (VBmax) is measured using an optical microscope (Zeiss: SteReo Discovery) after each 30s cutting duration. After metal cutting experiments, the worn tools were cut using wire EDM and etched to remove the adhered Ti6Al4V layer from the tool surface. The SEM mi crographs (Zeiss SEM: EVO18) of the worn tools were used to realize the friction behavior, adhesion over the tool surface, crater wear measure ment, and worn area. 2.2. FE simulations for tool wear prediction Fig. 3 illustrates the steps followed in the present approach, which integrates the experimental results obtained from metal cutting and thermo-mechanical state variables from FE simulations. The method has been tried in the past for crater wear [12,15] and flank wear [11,16] prediction due to its ability to utilize the experimental results for output variables (VBmax, KT) and complex input variables ðσ n ; vs ; Tint ; Tmax ; etc: Þ for wear prediction. FE formulation is performed using AdvantEdge 7.4
2. Materials and method 2.1. Experimental method Semi-orthogonal cutting tests of Ti6Al4V alloy round bar (φ75 mm, length 300 mm) have been performed on the CNC turning center. The
Fig. 2. (a) Carbide distribution in WC/Co cutting tools, and (b) microstructure of Ti6Al4V alloy. 3
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Fig. 3. Approach for determination of wear constants for Ti6Al4V with WC/6Co tools using experimental and FE simulations.
FE simulation codes (Third Wave Systems, Minneapolis, USA). The complex metal cutting simulations generate high mesh distor tion error that results in solution inaccuracy for FE results. Using adaptive meshing and remeshing executed by Lagrangian explicit dy namic codes, the machining induced high strain and strain rate could be calculated in highly deformed areas. Owing to the nature of the present study (chip sliding over the worn tool surface generated using wear profile replication method), frequent stalling of FE simulations is ex pected due to severe mesh degradation. The element distortion errors can be minimized using the arbitrary Eularian Lagrangian (ALE) formulation that adds more nodes for solution approximation during deformation satisfying the plastic work criteria. The tetrahedral ele ments have been used with 4-node and 12� of freedom for the cutting tool and workpiece. The initial workpiece geometry is modeled with 3 mm height and 15 mm length for longitudinal cutting. Initial thermophysical properties and mechanical properties of the tool and work piece materials have been provided for UDYS (user defined yield sur face) constitutive model following modified Johnson-Cook flow stress
criteria (Eq. (1)) [27]. The material constants for Ti6Al4V alloy (Table 2) and tool-work physical properties are taken from the authors’ previous publications. Temperature-dependent material properties have been incorporated in FE simulations to respond to the thermal softening na ture of titanium alloy [28,29]. Strainratefactor
StrainHardeningTerm
σ flow ¼
Value
Parameter
Value
Yield strength (A)
782.7 MPa 498.4 MPa 0.28
Reference strain rate (_ε0 )
10
Thermal softening constant (m) Melting temperature ðTm Þ
1
0.028
Ambient temperature ðT0 Þ
25� C
Hardening modulus (B) Strain hardening coefficient (n) Strain rate sensitivity (C)
5
ThermalSensitivityfactor
fflfflfflfflffl }|fflfflfflfflfflfflfflfflffl� fflfflffl { zfflfflfflfflfflfflfflfflfflfflfflffl}|ffl� fflfflfflfflfflfflfflffl�� fflfflffl{ zfflfflfflfflfflfflffl� � m ε_ T T0 * 1 þ C:ln *1 ε_ 0 Tm T0
(1)
The prediction of the frictional behavior of the tool-chip pair under high contact stress and thermal conditions determine the accuracy of the FE simulation results. Zorev’s dual contact zone theory [30] proposed the model (Fig. 4) using a hybrid friction nature at the contact zone. Both the sticking and sliding friction vary along the contact length and govern the frictional behavior at the tool-chip interface. The contribution of normal stresses and shear stresses along the contact zone varies owing to the coexistence of the two zones. In the sliding zone, the normal stresses and frictional shear stresses are always lesser than those in the sticking zone. The normal stress follows the exponentially decreasing trend over the contact length in both the sticking and sliding zones. Whereas the frictional stress remains constant in the sticking zone and decreases exponentially in the sliding zone. The constant frictional shear stress in the sticking zone is proportional to the material shear stress at the contact zone. To realize the influence of the dual-contact zone on the coefficient of friction (Eq. (2)), cutting tests were performed by varying cutting speeds and feeds. The results were used to develop a quadratic regression equation incorporating the dual nature of the friction and obtain the value of frictional boundary conditions that are incorporated in the FE
Table 2 J-C parameters for the selected UDYS used in FE simulations [28,29]. Parameter
zfflfflfflfflfflffl}|fflfflfflfflfflffl{ ½A þ B:εn �
s-1
1660� C
4
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Fig. 4. Zorev’s hybrid friction model for dual contact zone theory [30].
simulations. The frictional behavior has been studied for Ti6Al4V-WC/ Co combination under dry cutting environment. The range of feed has been kept from 0.01 - 0.25 mm/rev and cutting speed ranging from 50130 m/min.
μ ¼ tanλ ¼
Fxy ¼
Fz :sinβ þ Fxy :cosβ Fz :cosβ Fxy :sinβ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�ffiffiffiffi 2 ðFx Þ2 þ Fy
method, the exact wear profile on the cutting tool at different cutting durations were generated and used for FE simulations. In the adopted method of worn tool geometry replication from tool wear experiments at different cutting durations, the approximation error has been minimized for wear rate calculations. The wear rate at discrete locations on the tool-chip contact length has been calculated as the scheme shown in Fig. 5. A single zone is considered as a semi-ellipsoid with a major axis and minor axis. The depth of the semi-ellipsoid is the crater depth at the selected location identified as KT11 ; KT12 ; etc: . The volumetric wear and volumetric wear rates at discrete locations have been calculated and used for the next stage of FE simulations as output variables. The local state variables have been extracted from the nodes which are contacting the chip underside for different worn ge ometries. The integration of the experimental and FE simulation results is used to finally extract the wear coefficients and validated experi mentally for the next immediate stage of tool crater wear.
(2) (3)
For crater wear analysis, the experimental crater wear area is measured using SEM micrographs, and the profile is shown in Fig. 5. The crater cross-section profiles after the careful sectioning of cutting tools are obtained using SEM micrographs. The cross-section profile of the worn tools has been replicated on the CAD model. The pointwise co ordinates at different loci on worn tool profiles are traced, integrated, and smoothened to generate a CAD (.dxf) file that replicates the exact profile of worn tool on the rake surface. Using the geometry replication
Fig. 5. Schematic representation for volumetric wear calculation of crater wear. 5
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3. Results and discussion
wear constants. The wear profile generated on the tool rake face at in tervals 180 s–300 s has been modeled on the cutting tools for FE simu lations. The resulting wear profiles were used for the determination of thermo-mechanical state variables and extracting the wear constants. The use of KTmax value (hence highest volumetric wear rate) for eval uation of the wear constant will be misleading as the crater depth changes both spatially and temporally. The KT values at distinct points are incorporated over the worn tool profile, which is capable of approximating the wear rates collectively for a single cutting condition.
3.1. Experimental determination of crater wear profile on plain cutting tools The determination of wear constants is an essential factor for tool wear simulations. Evaluation of wear constants should be done experi mentally once the steady-state wear has been achieved during metal cutting operations. To differentiate the end of initial degressive wear zone and the start of constant wear rate zone (steady-state wear), VBmax has been measured at selected cutting conditions (vc ¼ 80 m= min ;f ¼ 0:12 mm=rev; ap ¼ 1mm; replicates ¼ 3) (Fig. 6). After progressive cutting time up to 200 s, the steady-state wear zone can be identified when the slope of the flank wear curve becomes nearly constant. Considering the selected machining conditions and flank wear criteria (VBmax ¼ 200 μm), the steady-state is achieved for cutting time greater than 200 s. The crater wear profiles obtained for the cutting time from 180 s, 240 s, and 300 s have been considered for a combination of experimental and FEM-based approaches to achieve wear constant calculations. An experimental approach has been used to calculate the volumetric wear rate, and FEM analysis is used to obtain the state variables. The wear profile generated over the tool rake face was approximated as a semi-ellipsoid with the semi-major axis (a) ¼ width of the crater, the semi-minor axis (b) ¼ contact length (Lc ), and depth (c) ¼ maximum crater depth (KTmax). In idealized condition, the width of the crater can be approximated to the depth of cut value (a ¼ ap ). The crater wear generated over the rake face and corresponding cross-section were used to measure KTmax, and crater area with the help of a microscope and approximated crater area (Lc . ap ) had been plotted in Fig. 7(a). The variation in the measured and approximated crater wear is nominal, but the approximation may further lead to error in the volumetric wear rate. The same has been plotted for volumetric wear separately in Fig. 7(b). The error in measurement is within acceptable limits, and the volumetric wear rate with the help of approximate analysis can be used. However, the measured values were used for further investigation of the volumetric wear rate and calculation of wear constants. The measured volumetric wear rates fall in the range of 1:386 � 10 3 mm3 = min at 60 s 2:219 � 10 3 mm3 =min at 360 s. The volumetric rates at initial and end cutting durations have been avoided and intermediate wear rates (steady wear) have been considered for the calculation of
3.2. Determination of the coefficient of friction for semi-orthogonal cutting The frictional behavior during metal cutting is heavily influenced by tool-work combination, cutting parameters, and cooling environments. The interface friction values control the thermomechanical spectrum; hence, the exact demarcation of the physical phenomena over the con tact length must be understood. The experimental μ values are plotted in Fig. 8 with distinct regions of sliding and sticking friction zone separated by a dotted line over the range of cutting speeds and feeds. The begin ning of sticking zone was calculated using von-Mises’ criteria which corresponds to μsliding ¼ p1ffi3ffi ¼ 0:577 (maximum value of sliding friction).
At lower feed values, friction is mainly contributing to the sticking zone at all cutting speeds. The feed values f ¼ 0.01–0.02 mm/rev have resulted in high frictional values in sticking zones, which suggest higher adhesion at lower feeds. The limited contact length at lower feeds re stricts the chip sliding; hence, sliding friction does not contribute to the friction values at lower feeds. With increasing feed values the transition from sticking to sliding friction appears at lower cutting speeds, and a clear distinction can be observed for vc ¼ 50 m=min and 70 m=min. Thermal softening of work-material at higher cutting speeds dominates the sticking behavior, and friction is mainly contributed by sticking friction with the highest values at low feeds. The decrease in friction has been observed with increasing feed up to 0.1 mm/rev – 0.15 mm/rev which reflects minimum friction at high cutting speeds. The increased contact length and high thermal softening behavior dominate the sticking friction at high feed and speed conditions. A regression equation (Eq. (4)) has been developed for the prediction of the coefficient of friction from the experimental results with adj. R2-value ¼ 0.728 using Matlab codes (MatlabR2017a).
Fig. 6. Progressive flank wear and corresponding variation of the coefficient of friction. 6
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Fig. 7. (a) Variation of crater wear, crater depth and (b) volumetric wear at different cutting time.
Fig. 8. Sliding and sticking friction contribution for different cutting parameters under dry cutting at (a) 50 m/min, (b) 70 m/min, (c) 90 m/min, (d) 110 m/min, and (e) 130 m/min.
μ ¼ 0:8521 þ 0:007vc
9:09f
0:00035v2c þ 0:0115vc :f þ 25:9f 2
zones were observed with sparse microscopic patches adhered to the rake face. The area of the sticking zone increases with the feed and ac celerates the formation of built-up edge formation at higher feeds. At low feeds, μ values fall in the range of sticking friction (μ > 0:577Þ, whereas the tool-chip interface micrographs reveal only the abrasion
(4)
The interface sliding and sticking behavior are explained with the help of micrographs corresponding to different feeds at vc ¼ 90 m= min (Fig. 9). At lower feeds (f < 0.1 mm/rev), the stagnation and abrasion 7
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Fig. 9. Contact interface behavior on tool surface at vc ¼ 90 m/min and (a) f ¼ 0.01 mm/rev, (b) f ¼ 0.02 mm/rev, (c) f ¼ 0.15 mm/rev and (d) f ¼ 0.2 mm/rev.
marks over the tool rake face except for some localized microscopic adhesion patches. The higher friction values corresponding to low feeds (f < 0.1 mm/rev) are not attributed to these abrasion marks. In these cases, it can be proposed that due to the lower feed values, the contact remains confined to the cutting edge only and most of the material sliding occurs at the sticking zone. Due to the increased contribution of the sticking zone, high tangential force is required to slide the chips over the dead metal zone overcoming the sticking conditions, which leads to higher friction coefficients. The coefficient of friction with chip reduction coefficient � � chip thickness ξ ¼ uncut over different cutting speeds and feeds has been chip thickness
used to evaluate the volumetric wear rates according to the method mentioned in Fig. 5. Fig. 10 shows different tool wear profiles and corresponding cross-section at varying cutting times. The technique helps to obtain the experimental volumetric wear rate and the wear constants following Eq. (5). Based on the experimental results, the localized tool wear incorporating the spatial variation at discrete points on the tool-chip contact length (0 < x � lc ) has been predicted by Eq. (6) [6]. � � � α� dw Volumetric wear rate ¼ w_ ¼ K:σn :vs: exp (5) dt T
correlated from experimental results (Appendix 1). At lower feeds, higher ξ values have been achieved that corresponds to high chip thickening and high frictional stresses at tool rake face. At cutting speed vc ¼ 50 m=min and 70 m=min, lower values of chip reduction coefficient (ξ < 2:0Þ reflects the reduced frictional values in the sliding zone. The trend has not been observed at vc ¼ 90 m=min 130 m=min where sticking friction zone has been achieved at higher feeds, although ξ values remain below the limiting value ðξ < 2:0). This shows that below a critical velocity, the frictional coefficient is dominated by the sliding nature of tool-chip interaction. Once the critical velocity exceeds, the contribution of the sliding friction to total friction diminishes even when the chip reduction coefficient remains below the limiting value. The friction coefficients at different cutting speeds and feeds are best fitted according to power-law distribution (Appendix 2).
Local wear rateðw_ l Þ ¼ K: � ln
� w_ l :Lc ¼ ln K σn :vs : x
α T
� � � α� x :σ n :vs: exp lc T
(6) (7)
The simulation results for tc ¼ 180 s 300s respectively with fully grown chip sliding at the conforming worn tool profiles were used to extract the state variables. The conformity of the chip flow over the worn profiles asserts that the nodal points on the tool surface extract the value of state variables with truncated chances of the data probing errors. Pointwise locus on the tool rake surface over the worn profile has been probed for von-Mises’ stresses, normal stress, chip load, chip sliding velocity, and the interface temperature. The variation of inverse temperature is highly influential for the prediction of the volumetric wear (crater wear) [6,31]. The wear rates with inverse temperature were used to obtain wear coefficients following Eq. (7). FEM simulation results help to extract the localized state variables and calculate the volumetric wear loss and subsequent wear constants. The values of state variables were further used to plot a semi-logarithmic diagram (Fig. 11). Regression analysis of the semi-logarithmic plot represents the average local specific wear rates at
3.3. FE analysis for the evaluation of wear constants and prediction of the wear profile The modeled equation (Eq. (4)) has been used to determine the co efficient of friction for simulations under the selected cutting parame ters. The experimental results obtained for tool wear profiles have been 8
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Fig. 10. Experimental crater wear profiles at varying tc used for evaluating volumetric wear.
Fig. 11. Average local specific wear rate variation with inverse temperature from FEM analysis.
� � varying fractional contact length loci
x lc
with respect to inverse tem
perature. The intercept at the Y-axis and the slope of the linear equation correspond to K and α values, respectively. The wear constants K ¼ 8:13 � 10 8 and α ¼ 244.63 have been obtained for WC-Ti6Al4V pair under dry cutting conditions. The error bar shows the standard deviation of local specific wear rate over different fractional contact length. The values of K and α determined from the logarithmic plot were used to tj Þ. The calculate the wear rate in the next time interval ðΔt ¼ tjþ1 time interval for next cutting duration is kept to 30 s and the volumetric � � wear rates with discretized lxc locations are determined. KTjþ1 ¼ KTj þ
� � dw : tjþ1 dt j
tj
�
Fig. 12. (a) Experimental measurement of crater wear over the tool-chip contact zone at different loci of Lc and (b) comparison of results for crater wear (at tc ¼ 330 s).
curate prediction of KTmax locus. The values of KT at the start (x � 0:1Lc ) and end of the wear profile (0:85Lc � x � 1:0Lc ) show a high deviation from the experimental results. The maximum difference in the experimental and predicted crater wear at x � 0:1Lc and 0:85Lc � x � 1:0Lc are 37.3% and 108% respectively (Fig. 12(b)). For the initial loci of wear profile, KT values are overpredicted due to the inability of the used wear model to consider the edge wear. In the pre sent study, the wear model and the wear constants derived from the simulation results couldn’t account for the edge dulling ðSVα value) nature during cutting. The generation of SVα is due to high dynamic stresses generated over an infinitesimally small area (cutting edge) that undergoes rapid loss of tool material from the cutting edge (Fig. 12(a)). This might be the resulting source of error for the KT values (x � 0:1Lc ) as the edge wear corresponds to 20μm � SVα � 25μm (for x < 0:05Lc ). The inherently high stresses at the cutting edge and
(8)
In the case of 2D FEM simulations, the extrapolated KT values can be predicted using Eq. (8). The wear profile has been predicted for cutting time ¼ 330 s considering the initial point of wear variables at tc ¼ 300 s (nearest values). The wear constant (K, α) obtained from the analysis of data (180 s–300 s) is able to minimize the error in the extrapolated calculation for the predicted wear stage (tc ¼ 330 s). The values are plotted for varying contact length locations from 0:1Lc � x � Lc and compared with the experimental values (Fig. 12(a)). The results can generate the approximate wear profile with an ac 9
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nearly stagnant chip sliding (vs e0) result in the severe edge dulling with increasing cutting time. The wear behavior at the zone very near to cutting edge couldn’t be modeled according to the available wear models in the literature, which are capable of considering only the adhesion, abrasion, dissolution wear mechanisms (single or combina tion of these mechanisms). The experimental crater wear profile in Fig. 12(b) doesn’t have an error bar as the profile is extracted from the mid-zone of the crater area. A nearly similar trend to the crater profile will be observed from the mid-zone crater section; hence, a single wear profile was extracted and plotted. There is a fair agreement between experimental and simulated crater profile at the mid-section of worn tool profile and the error range (ΔKT ¼ 3:12%at x ¼ 0:2Lc and ΔKT ¼ 20:5%at x ¼ 0:4Lc ) lies within the acceptable limits. The developed model fairly predicts the crater wear profile over the selected fractional contact length along the rake face.
sectioning of the cutting tool using wire EDM. The metal cutting is a dynamic process, and so is the tool wear and worn surface geometry. The worn profile geometry and the method of cross-sectioning will change depending on the cutting parameters used (mainly ap ; Lc ; and f). As the depth of cut changes (increased or decreased from the presently used value), the wear profile changes (spans over the cutting edge or con centrates at the tool nose). The different sectioning methods will obtain different crater profiles. In that case, the geometrical errors will be present in the replicated wear geometry at the tool surface. Proper care must be taken in this regard to avoid any chance of error generated due to improper cross-sectioning of the tool wear profile. (b) The non-conformance of the tool-chip interface at the rake face generated by the geometry replication method Wear profiles obtained from the metal cutting experiments have been finely replicated using the coordinate measurement over the rake face, and appropriate CAD models have been replicated. The error in non-singularities of worn profiles has been reduced by smoothening the replicated CAD geometries before the meshing of the tools to avoid meshing errors. Also, the tool has been finely meshed at the surface, and the mesh size is selected after mesh convergence tests for different profiles. During FE simulations, the sliding of the chip at the rake surface is conformal to the generated profile at the total contact length zone except at some discrete locations. As shown in Fig. 13, the nonconformance of the tool-chip interaction is present at the rake face as the chip tends to move in the exit half of the contact zone (x > 0:65Lc ). The non-conformance of the sliding chips may cause the error in the values of state variables as it will reduce the local state variables (σn ; Tint ; etc:) or increase the value of vs at neighboring nodes. Although appropriate care has been taken to minimize the influence of such errors using statistical tools and its occurrence is limited at the interface (at a single discrete location in the considered case), this inevitably may cause the error in FEM results if ignored. A similar
3.4. Challenges in the present research and suggested direction for improvement The research presents an approach to obtain the spatial and temporal wear prediction during the metal cutting process using the geometry replication method on the modeled tools. The unworn tool geometry selected for wear studies may not be able to exactly predict the local state variables at varying tool-chip contact zone. The exact determina tion of worn tool geometry from metal cutting experiments and its replication on the cutting tools’ model are considered as another method to closely predict the tool wear using FE simulations. However, certain sources of error have been identified in the present study that causes deviation in the obtained wear profile and crater wear depth at different loci on the contact length zone. (a) Errors in geometry replication on the tool surface The crater wear profile is generated at the tool surface after careful
Fig. 13. Non-conformance error present at the tool-chip interface on the worn tool profiles. 10
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observation in some of the previous studies has been reported as a result of wear geometry update using a user-defined subroutine to update the tool surface geometry due to wear (nodal displacement). In the present study, any user-defined subroutine has not been incorporated into the wear model; hence, the presence of the nodal displacement can be ignored. The same is considered as an error in the geometry replication, which, if occurs at multiple nodes, may influence the accuracy of the proposed method. These errors should be taken adequate care beforehand to achieve the accurate FE formulations, generation of local state variable data, and wear results. Despite these challenges, the selected approach for crater wear prediction has resulted in a good agreement with the experimen tally observed wear profile. The increased overestimation of crater wear in the maximum temperature zone can be further smoothened using a number of tool wear tests for different cutting speeds, feeds, and depth of cut values. Also, the edge dulling of the cutting tools is not incorporated in the used wear model which has resulted in disagreement at the initial wear profile (for x � 0:1Lc ) in the simulation results. The stagnation zone at the tool chip contact zone and the impact of the cutting tool engagement at highly worn tools can be considered as shortcomings, which may be looked into future studies.
the wear constants. The following conclusions are withdrawn: 1. A friction model has been developed to incorporate the stick-slip behavior of Zorev’s hybrid friction theory in FE simulations. 2. Local wear rates, state variables and crater profiles extracted at tc ¼ 3; 4; 5 minand contact zones ð0:1Lc � x � 1:0Lc Þresulted in wear constants K ¼ 8:13 � 10 8 and α ¼ 244.63. 3. A characteristic wear model with the dimensionless parameter � � x lc has been proposed. The developed model offers fair prediction in the mid-section of the crater wear within the error range ðΔKT ¼ 3:12% 20:5%Þ. 4. The maximum error in the wear prediction appears at the start ðx � 0:1Lc ) of the contact length zones (ΔKT ¼ 37:33%Þdue to inability of the developed model to predict the edge wear (SVα ). Declaration of the conflict of interests Authors hereby declare that the present research work does not have any conflict of interest. Acknowledgment
4. Conclusions
The authors thank Central Research Facility (CRF-IIT Delhi) to pro vide help for SEM micrographs and Third Wave Systems (Minneapolis, USA) for providing the academic lease of the AdvantEdge 7.4 FEM codes. Additionally, the first author thanks MHRD, India, to provide financial support for pursuing Ph.D. at IIT Delhi.
The present study proposed a hybrid approach comprising the experimental and FE simulation methods for crater wear prediction during dry turning of Ti6Al4V alloy. Experimental crater wear profiles were modeled on the cutting tool to carry out FEM simulations and generate state variables’ database. A modified wear model incorporating the contact length factor in Usui wear model has been used to determine
Appendix: 1 Experimentally obtained coefficient of friction (μ) values at varying machining parameters vc (m/min)
f (mm/rev)
0.01 0.02 0.05 0.1 0.15 0.2 0.25
50
70
90
110
130
1.172 1.074 0.706 0.521 0.505 0.520 0.515
1.067 0.744 0.653 0.508 0.585 0.515 0.680
1.121 1.330 0.880 0.684 0.623 0.716 0.965
1.402 0.897 0.748 0.572 0.643 0.742 0.830
1.051 1.074 0.873 0.662 0.742 0.705 0.793
Experimental values of chip reduction coefficient (ξ) at varying machining parameters vc (m/min)
f (mm/rev)
0.01 0.02 0.05 0.1 0.15 0.2 0.25
50
70
90
110
130
7.02 4.1 2.14 1.75 2.0 1.29 1.65
8.53 6.27 2.07 1.73 1.44 1.6 1.47
6.52 5.01 2.34 1.9 1.75 1.57 1.8
8.11 6.63 2.98 1.99 1.64 1.52 1.55
7.69 5.0 1.94 1.85 1.69 1.56 1.65
11
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Appendix: 2 Power law distribution of coefficient of friction modeled from experimental results μ ¼ C1 :f
C2
vc (m/min)
C1
C2
50 70 90 110 130
0.3003 0.3924 0.568 0.4497 0.576
0.3023 0.1950 0.1664 0.2178 0.1377
Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.wear.2020.203229.
References
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Wear journal homepage: http://www.elsevier.com/locate/wear
Temporal and spatial crater wear prediction of WC/Co tools during dry turning of Ti6Al4V alloy Sarvesh Kumar Mishra, Sudarsan Ghosh, Sivanandam Aravindan * Department of Mechanical Engineering, Indian Institute of Technology-Delhi, Hauz Khas, New Delhi, 110016, India
A B S T R A C T
A new approach is developed to predict the crater wear variation on straight grade tungsten carbide tools during titanium machining. The effect of crater wear geometry has been considered on the variation of local state variables such as normal stress (σn Þ, chip sliding velocity (vs ), and cutting temperature (T) over the contact length at varying cutting times. Experimentally determined crater profiles at progressive wear stages were geometrically replicated on the cutting tool models and used for FEM analysis. In order to account for the variation of the state variables and wear rates with respect to the tool-chip contact length, the dimensionless fractional contact length parameter is introduced in the Usui characteristic wear equation. The thermo-mechanical state variables evaluated at different fractional contact lengths and cutting time were used to obtain the wear coefficients. The crater wear profile and wear depth are predicted and the same is experimentally validated over the contact length.
1. Introduction Tool wear analysis has been considered as a tedious task for metal cutting research as it incorporates the complete spectrum of mechanical loading, thermo-chemical interactions, time, and spatial variation of material loss. None of these mentioned parameters can be considered constant when the information about the material loss is sought in terms of wear debris, adhered layer, and molecular or atomic migration of the constituent elements. Since the initial works by Taylor [1], who devel oped the empirical wear life equation (VT n ¼ C), there has been numerous attempts to modify and develop unified wear models which can accurately predict tool wear and its progression. Complex tool wear mechanisms (adhesion, abrasion, diffusion, etc.) depend on the tool-work combination, tool geometry, material properties, cutting pa rameters, and environments. The available wear models (Table 1) refer that there is a considerable amount of research which have devised wear models on the basis of different underlying wear mechanisms. The basic wear models (Burwell [2], Shaw and Dirke [3], Trigger and Chao [4], Archard [5]) have revealed that the wear volume per unit sliding distance is dependent on the applied pressure and hardness of the softer asperity in the case of tribological contact pairs. The tool wear on the rake face can be divided into the stagnation zone, active crater wear zone (due to adhesive wear and diffusive wear mechanisms), and abrasion wear zone at the chip exit. Boltzmann’s canonical distribution of diffusion [6] accurately predicts the tool wear (adhesive and dissolution wear) for a fixed
tool-work combination, limited cutting parameters, approximated con tact area (Areal ¼ Aapparent), and visco-plastic deformation at the tool-chip interface. Using FE simulations, the prediction of abrasive wear contribution over the rake face becomes difficult as the σn ; vs ; and Tint values at the chip exit zone are much lower in FE simulations than the actual exper imental conditions [13]. In order to incorporate the physical wear mechanisms in FEM simulations, abrasion-diffusion wear model [7,9, 12], diffusion wear model [6,8,10,11,14], and modified diffusion wear models [13,15] have been developed. The developed models have their own excellence in the context of studies and resulted in the close pre diction of crater/flank wear. Amongst the available wear models, the Usui wear model has been widely used for flank and crater wear simu lations due to its ability to incorporate physical wear mechanisms [10, 11,16,17]. The model is capable of closely predicting the abrasion and diffusion wear as it converts the thermomechanical load spectrum ðσ n ; _ The model is vs ; τmax ; Tint ; etc: Þ into the volumetric wear rate (w). capable of integrating the Boltzmann canonical distribution as well as mechanical effects (by considering the stresses and sliding velocity) induced during metal cutting; hence, it is overwhelmingly used for wear modelling. Constant values of local variables at the tool-chip interface ðσn ; vs ; τmax ; etc: Þ, and uniform thermal behavior ðQs ; Qint ; Tavg ; Tint ; etc:Þ offer an approximate prediction of the dynamic wear behavior during metal cutting. Exponential temperature profile, complex thermo-chemical interaction, variable interface friction and stress distribution, and nonuniform chip sliding behavior are the most critical factors for tool
* Corresponding author. E-mail address: [email protected] (S. Aravindan). https://doi.org/10.1016/j.wear.2020.203229 Received 29 May 2019; Received in revised form 5 February 2020; Accepted 5 February 2020 Available online 8 February 2020 0043-1648/© 2020 Elsevier B.V. All rights reserved.
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Nomenclature
re w w_ w_ l K
KB KM SVα x KTmax KT Tint R E
Width of crater (mm) Location of maximum crater wear (mm) Cutting edge displacement (Edge wear) Distance at the rake from the cutting edge Maximum crater wear depth (μm) Crater wear (μm) Tool-chip interface temperature (K) Universal gas constant (kJ.K-1.mol-1) Activation energy (kJ.mol-1) σn Normal contact stress (MPa) vs or vchip Chip sliding velocity (m/min) vc Cutting velocity (m/min) f Feed (mm/rev) ap Depth of cut (mm) μsticking Sticking friction coefficient μsliding Sliding friction coefficient μ Coefficient of coefficient Heat in the secondary interface Qint VBmax Maximum flank wear (μm) Tool chip contact length (μm) Lc
α
Fz ; Fx ; Fy Fxy
τmax σ mises ε_ ε σ T FEM ϕ β
τ
tc
σ flow QS rn
After initial crater formation, the wear profile results in the chip flow conditions over tool rake face which consequently change the state variables (σn ; vs ; Tint ), interface friction (μsticking ; μsliding ; μtotal Þ, and effec tive rake angle (αeffective ). The determination of these parameters with the help of experimental methods is accurate but difficult, whereas the predictive models involve numerous assumptions that impart limited accuracy to these predictions. With the help of robust computational codes to perform the high strain and high strain rate calculations, these parameters can be evaluated with considerable accuracy. It takes several weeks of duration to run a few milliseconds of the tool wear simulation at a single cutting condition (constant machining parameters, tool-work combination, and tool geometry). The data generation for the state variables up to the progressive tool wear stages (even for a few seconds) is almost difficult. Hence, the continuous tool wear simulations are not cost-effective in order to establish the database for the dynamically changing state variables. Specialized modules of tool wear have been developed in the past, which can run the tool wear simulations for longer cutting times [19] and used for running tool wear simulations satisfactorily [20,21]. In attempts to consider the influence of tool wear geometry and wear profile on state variables, very few works have been conducted. In a study conducted by Ramirez et al. [15], the wear profile is approximated according to the temperature profile variation at different levels of isotherms over the rake face. The study utilized the temperature profile to interpolate the crater wear profile based on the start of contact length (P1), the end of contact length (P2), and the locus of maximum tem perature at the interface (P3). The crater profile has been successfully predicted using this approach, assuming that KTmax always lies at the location of maximum cutting temperature. For unworn tools (or shallow crater depths), the variation of local normal stresses at contact length follows the same trend as Zorev’s hybrid friction distribution [6]; however, no specific mention of the same is available for the worn tools. The curvature of the crater wear and its profile over the contact length zone have not been utilized for volumetric wear calculation in the available research. It has been mentioned that the curvature of the crater profile (ratio of KTmax before fracture to contact length) is around 0.04 for AISI 1045 steel cutting with multilayer-coated tools [18]. The lower value of curvature for the wear profile signifies that the influence of KTmax/Lc may be neglected to wear simulations of the coated tools.
Table 1 Available wear models for volumetric wear analysis considering different wear mechanisms. References
Developed wear model
Takeyama and Murata [7]
w_ ¼ C1 vs þ C2 :exp
Usui [6,8]
w_ ¼ K:σn :vs: exp
Palmai [9]
Amir et al. [10]
�
�
E RTint
α�
T
w_ ¼ C1 vs þ C2 : � � E vs exp RTint � α� w_ ¼ K:vs: exp T
α�
Lung et al. [11]
� w_ ¼ K:τmax :vs: exp
Zanger and Schulze [12]
� α � 1 w_ ¼ K1 :vs :exp þ � α � T 2 K2 :σn :exp T � R wðx; y; tÞ ¼ aσn x; y; � � � � t Vs x; y; t exp � b dt Tðx; y; tÞ
Haddag and Nouari [13]
T
Incorporated wear mechanism/ model �
Edge radius (μm) Volumetric wear (mm3) Volumetric wear rate (mm3/min) Local wear rate at a fractional distance Pre-exponential wear coefficient Wear constant Main cutting, axial thrust and radial thrust force (N) Resultant thrust force (N) Maximum shear stress (MPa) Von-Mises’ stress (MPa) Strain rate (mm/s) Strain Flow stress (MPa) Cutting temperature (� C ) Finite element method Principle cutting edge angle Rake angle Shear Stress (MPa) Cutting time (s) Flow stress (MPa) Heat in the shear zone Nose radius (mm)
Temperature independent abrasion wear (varying with sliding distance and abrasive wear resistance), and diffusion wear Able to consider the abrasion and diffusion wear mechanism for wear of uncoated tools. Both abrasion and diffusion wear depend on the sliding distance. Flank wear prediction considering VBmax is independent of normal pressure. Wear prediction for uncoated and coated tools considering very high stresses in metal cutting. Flank wear prediction of uncoated carbide tools considering abrasion and diffusion wear mechanisms.
ðσn ; vs ; TÞ values computed from the FE model at the integration limits (interval dt) using 3D FE analysis only for unworn tools.
wear prediction. These variables change with tool-work material prop erties, cutting parameters, and cutting environments. The mentioned parameters and variables at the tool rake face along the tool-chip contact length should be accounted for the wear rate and consequent crater formation (Fig. 1). These variables possess dynamic nature in spatial orientation (along the contact length and wear width) and time (cutting time) during cutting. The properties and their variation at the tool-chip contact length, wear width, and cutting time are required for the determination of the wear parameters (crater profile, KTmax, KB, and KM). 2
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Fig. 1. Schematic representation of the response of the state variables with contact length and crater growth [18].
However, owing to the high wear rate of straight grade carbide tools for dry titanium machining, the geometric parameters of the crater profile must be considered to pursue its influence on local state variable and crater wear progression. Some of the wear models [12,13,15,18] have incorporated the dy namic nature of variation in σn ; vs ; and Tint over the cutting time and contact points on the tool-chip interface. The successful prediction of flank and crater wear in these studies helped to understand the dynamic nature of tool wear. These studies have used the FEM results of σn ; vs ; and Tint at different nodes of a plain (unworn) cutting tool at the initial steady stage of the cutting process. The original thermomechanical loading conditions and variables will change once the tool is worn due to the loading, frictional heat, and sliding behavior of the chips over the crater profile. In most of the cases, the characteristic wear equations have been developed considering the fluctuation in the state variables at fresh tool surface only. This approach is followed as the experimental measurement of these variables could be determined only for plain tools using a dividing tool method [6,22]. The initial steady-state values of the local state variables obtained for plain (unworn) cutting tools may not be able to approximate the state variables over the worn surface. Hence, there exists a need to analyze the dynamic nature of the state variables for the complete spectrum of cutting time and nodal points on the contact length with the progressive stages of updated wear geome try. The combined experimental and FE simulations will be helpful in devising a method that can extract the local state variables at changing cutting time and nodal points for progressive wear stages. The approach has been used to achieve the wear coefficients, which could predict the crater wear profile over the tool rake face.
details of the machine and related equipment can be found in our pre vious research [23]. The carbide distribution in the matrix of the cutting tool is shown in Fig. 2(a), which reveals the fine WC particles cemented in the binder matrix. The alloy surface was polished and etched with Kroll’s reagent according to ASTM E407-07 (10 ml HF, 5 ml HNO3 and 85 ml water) [24]. The microstructure of Ti6Al4V alloy (Fig. 2(b)) reveals the different α- and β-phase grains in the work material. The presence of two-phase microstructure (α-hcp and β-bcc phase) is one of the major causes of the machinability related problems in titanium cutting. It causes the fluctuation of the cutting forces, rapid tool wear and the formation of adiabatic shear banding even at low cutting speeds [25,26]. Initial ex periments have been conducted to delimit the steady wear zone from the degressive wear zone (initial wear). The cutting forces were measured using a 3-component piezoelectric dynamometer (Kistler 9129AA: Switzerland) mounted on the tool holder and connected with a charge amplifier (model: 5070A). Cutting forces obtained from different cutting conditions were used to find the coefficient of friction (μ). Maximum flank wear (VBmax) is measured using an optical microscope (Zeiss: SteReo Discovery) after each 30s cutting duration. After metal cutting experiments, the worn tools were cut using wire EDM and etched to remove the adhered Ti6Al4V layer from the tool surface. The SEM mi crographs (Zeiss SEM: EVO18) of the worn tools were used to realize the friction behavior, adhesion over the tool surface, crater wear measure ment, and worn area. 2.2. FE simulations for tool wear prediction Fig. 3 illustrates the steps followed in the present approach, which integrates the experimental results obtained from metal cutting and thermo-mechanical state variables from FE simulations. The method has been tried in the past for crater wear [12,15] and flank wear [11,16] prediction due to its ability to utilize the experimental results for output variables (VBmax, KT) and complex input variables ðσ n ; vs ; Tint ; Tmax ; etc: Þ for wear prediction. FE formulation is performed using AdvantEdge 7.4
2. Materials and method 2.1. Experimental method Semi-orthogonal cutting tests of Ti6Al4V alloy round bar (φ75 mm, length 300 mm) have been performed on the CNC turning center. The
Fig. 2. (a) Carbide distribution in WC/Co cutting tools, and (b) microstructure of Ti6Al4V alloy. 3
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Fig. 3. Approach for determination of wear constants for Ti6Al4V with WC/6Co tools using experimental and FE simulations.
FE simulation codes (Third Wave Systems, Minneapolis, USA). The complex metal cutting simulations generate high mesh distor tion error that results in solution inaccuracy for FE results. Using adaptive meshing and remeshing executed by Lagrangian explicit dy namic codes, the machining induced high strain and strain rate could be calculated in highly deformed areas. Owing to the nature of the present study (chip sliding over the worn tool surface generated using wear profile replication method), frequent stalling of FE simulations is ex pected due to severe mesh degradation. The element distortion errors can be minimized using the arbitrary Eularian Lagrangian (ALE) formulation that adds more nodes for solution approximation during deformation satisfying the plastic work criteria. The tetrahedral ele ments have been used with 4-node and 12� of freedom for the cutting tool and workpiece. The initial workpiece geometry is modeled with 3 mm height and 15 mm length for longitudinal cutting. Initial thermophysical properties and mechanical properties of the tool and work piece materials have been provided for UDYS (user defined yield sur face) constitutive model following modified Johnson-Cook flow stress
criteria (Eq. (1)) [27]. The material constants for Ti6Al4V alloy (Table 2) and tool-work physical properties are taken from the authors’ previous publications. Temperature-dependent material properties have been incorporated in FE simulations to respond to the thermal softening na ture of titanium alloy [28,29]. Strainratefactor
StrainHardeningTerm
σ flow ¼
Value
Parameter
Value
Yield strength (A)
782.7 MPa 498.4 MPa 0.28
Reference strain rate (_ε0 )
10
Thermal softening constant (m) Melting temperature ðTm Þ
1
0.028
Ambient temperature ðT0 Þ
25� C
Hardening modulus (B) Strain hardening coefficient (n) Strain rate sensitivity (C)
5
ThermalSensitivityfactor
fflfflfflfflffl }|fflfflfflfflfflfflfflfflffl� fflfflffl { zfflfflfflfflfflfflfflfflfflfflfflffl}|ffl� fflfflfflfflfflfflfflffl�� fflfflffl{ zfflfflfflfflfflfflffl� � m ε_ T T0 * 1 þ C:ln *1 ε_ 0 Tm T0
(1)
The prediction of the frictional behavior of the tool-chip pair under high contact stress and thermal conditions determine the accuracy of the FE simulation results. Zorev’s dual contact zone theory [30] proposed the model (Fig. 4) using a hybrid friction nature at the contact zone. Both the sticking and sliding friction vary along the contact length and govern the frictional behavior at the tool-chip interface. The contribution of normal stresses and shear stresses along the contact zone varies owing to the coexistence of the two zones. In the sliding zone, the normal stresses and frictional shear stresses are always lesser than those in the sticking zone. The normal stress follows the exponentially decreasing trend over the contact length in both the sticking and sliding zones. Whereas the frictional stress remains constant in the sticking zone and decreases exponentially in the sliding zone. The constant frictional shear stress in the sticking zone is proportional to the material shear stress at the contact zone. To realize the influence of the dual-contact zone on the coefficient of friction (Eq. (2)), cutting tests were performed by varying cutting speeds and feeds. The results were used to develop a quadratic regression equation incorporating the dual nature of the friction and obtain the value of frictional boundary conditions that are incorporated in the FE
Table 2 J-C parameters for the selected UDYS used in FE simulations [28,29]. Parameter
zfflfflfflfflfflffl}|fflfflfflfflfflffl{ ½A þ B:εn �
s-1
1660� C
4
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Fig. 4. Zorev’s hybrid friction model for dual contact zone theory [30].
simulations. The frictional behavior has been studied for Ti6Al4V-WC/ Co combination under dry cutting environment. The range of feed has been kept from 0.01 - 0.25 mm/rev and cutting speed ranging from 50130 m/min.
μ ¼ tanλ ¼
Fxy ¼
Fz :sinβ þ Fxy :cosβ Fz :cosβ Fxy :sinβ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�ffiffiffiffi 2 ðFx Þ2 þ Fy
method, the exact wear profile on the cutting tool at different cutting durations were generated and used for FE simulations. In the adopted method of worn tool geometry replication from tool wear experiments at different cutting durations, the approximation error has been minimized for wear rate calculations. The wear rate at discrete locations on the tool-chip contact length has been calculated as the scheme shown in Fig. 5. A single zone is considered as a semi-ellipsoid with a major axis and minor axis. The depth of the semi-ellipsoid is the crater depth at the selected location identified as KT11 ; KT12 ; etc: . The volumetric wear and volumetric wear rates at discrete locations have been calculated and used for the next stage of FE simulations as output variables. The local state variables have been extracted from the nodes which are contacting the chip underside for different worn ge ometries. The integration of the experimental and FE simulation results is used to finally extract the wear coefficients and validated experi mentally for the next immediate stage of tool crater wear.
(2) (3)
For crater wear analysis, the experimental crater wear area is measured using SEM micrographs, and the profile is shown in Fig. 5. The crater cross-section profiles after the careful sectioning of cutting tools are obtained using SEM micrographs. The cross-section profile of the worn tools has been replicated on the CAD model. The pointwise co ordinates at different loci on worn tool profiles are traced, integrated, and smoothened to generate a CAD (.dxf) file that replicates the exact profile of worn tool on the rake surface. Using the geometry replication
Fig. 5. Schematic representation for volumetric wear calculation of crater wear. 5
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3. Results and discussion
wear constants. The wear profile generated on the tool rake face at in tervals 180 s–300 s has been modeled on the cutting tools for FE simu lations. The resulting wear profiles were used for the determination of thermo-mechanical state variables and extracting the wear constants. The use of KTmax value (hence highest volumetric wear rate) for eval uation of the wear constant will be misleading as the crater depth changes both spatially and temporally. The KT values at distinct points are incorporated over the worn tool profile, which is capable of approximating the wear rates collectively for a single cutting condition.
3.1. Experimental determination of crater wear profile on plain cutting tools The determination of wear constants is an essential factor for tool wear simulations. Evaluation of wear constants should be done experi mentally once the steady-state wear has been achieved during metal cutting operations. To differentiate the end of initial degressive wear zone and the start of constant wear rate zone (steady-state wear), VBmax has been measured at selected cutting conditions (vc ¼ 80 m= min ;f ¼ 0:12 mm=rev; ap ¼ 1mm; replicates ¼ 3) (Fig. 6). After progressive cutting time up to 200 s, the steady-state wear zone can be identified when the slope of the flank wear curve becomes nearly constant. Considering the selected machining conditions and flank wear criteria (VBmax ¼ 200 μm), the steady-state is achieved for cutting time greater than 200 s. The crater wear profiles obtained for the cutting time from 180 s, 240 s, and 300 s have been considered for a combination of experimental and FEM-based approaches to achieve wear constant calculations. An experimental approach has been used to calculate the volumetric wear rate, and FEM analysis is used to obtain the state variables. The wear profile generated over the tool rake face was approximated as a semi-ellipsoid with the semi-major axis (a) ¼ width of the crater, the semi-minor axis (b) ¼ contact length (Lc ), and depth (c) ¼ maximum crater depth (KTmax). In idealized condition, the width of the crater can be approximated to the depth of cut value (a ¼ ap ). The crater wear generated over the rake face and corresponding cross-section were used to measure KTmax, and crater area with the help of a microscope and approximated crater area (Lc . ap ) had been plotted in Fig. 7(a). The variation in the measured and approximated crater wear is nominal, but the approximation may further lead to error in the volumetric wear rate. The same has been plotted for volumetric wear separately in Fig. 7(b). The error in measurement is within acceptable limits, and the volumetric wear rate with the help of approximate analysis can be used. However, the measured values were used for further investigation of the volumetric wear rate and calculation of wear constants. The measured volumetric wear rates fall in the range of 1:386 � 10 3 mm3 = min at 60 s 2:219 � 10 3 mm3 =min at 360 s. The volumetric rates at initial and end cutting durations have been avoided and intermediate wear rates (steady wear) have been considered for the calculation of
3.2. Determination of the coefficient of friction for semi-orthogonal cutting The frictional behavior during metal cutting is heavily influenced by tool-work combination, cutting parameters, and cooling environments. The interface friction values control the thermomechanical spectrum; hence, the exact demarcation of the physical phenomena over the con tact length must be understood. The experimental μ values are plotted in Fig. 8 with distinct regions of sliding and sticking friction zone separated by a dotted line over the range of cutting speeds and feeds. The begin ning of sticking zone was calculated using von-Mises’ criteria which corresponds to μsliding ¼ p1ffi3ffi ¼ 0:577 (maximum value of sliding friction).
At lower feed values, friction is mainly contributing to the sticking zone at all cutting speeds. The feed values f ¼ 0.01–0.02 mm/rev have resulted in high frictional values in sticking zones, which suggest higher adhesion at lower feeds. The limited contact length at lower feeds re stricts the chip sliding; hence, sliding friction does not contribute to the friction values at lower feeds. With increasing feed values the transition from sticking to sliding friction appears at lower cutting speeds, and a clear distinction can be observed for vc ¼ 50 m=min and 70 m=min. Thermal softening of work-material at higher cutting speeds dominates the sticking behavior, and friction is mainly contributed by sticking friction with the highest values at low feeds. The decrease in friction has been observed with increasing feed up to 0.1 mm/rev – 0.15 mm/rev which reflects minimum friction at high cutting speeds. The increased contact length and high thermal softening behavior dominate the sticking friction at high feed and speed conditions. A regression equation (Eq. (4)) has been developed for the prediction of the coefficient of friction from the experimental results with adj. R2-value ¼ 0.728 using Matlab codes (MatlabR2017a).
Fig. 6. Progressive flank wear and corresponding variation of the coefficient of friction. 6
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Fig. 7. (a) Variation of crater wear, crater depth and (b) volumetric wear at different cutting time.
Fig. 8. Sliding and sticking friction contribution for different cutting parameters under dry cutting at (a) 50 m/min, (b) 70 m/min, (c) 90 m/min, (d) 110 m/min, and (e) 130 m/min.
μ ¼ 0:8521 þ 0:007vc
9:09f
0:00035v2c þ 0:0115vc :f þ 25:9f 2
zones were observed with sparse microscopic patches adhered to the rake face. The area of the sticking zone increases with the feed and ac celerates the formation of built-up edge formation at higher feeds. At low feeds, μ values fall in the range of sticking friction (μ > 0:577Þ, whereas the tool-chip interface micrographs reveal only the abrasion
(4)
The interface sliding and sticking behavior are explained with the help of micrographs corresponding to different feeds at vc ¼ 90 m= min (Fig. 9). At lower feeds (f < 0.1 mm/rev), the stagnation and abrasion 7
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Fig. 9. Contact interface behavior on tool surface at vc ¼ 90 m/min and (a) f ¼ 0.01 mm/rev, (b) f ¼ 0.02 mm/rev, (c) f ¼ 0.15 mm/rev and (d) f ¼ 0.2 mm/rev.
marks over the tool rake face except for some localized microscopic adhesion patches. The higher friction values corresponding to low feeds (f < 0.1 mm/rev) are not attributed to these abrasion marks. In these cases, it can be proposed that due to the lower feed values, the contact remains confined to the cutting edge only and most of the material sliding occurs at the sticking zone. Due to the increased contribution of the sticking zone, high tangential force is required to slide the chips over the dead metal zone overcoming the sticking conditions, which leads to higher friction coefficients. The coefficient of friction with chip reduction coefficient � � chip thickness ξ ¼ uncut over different cutting speeds and feeds has been chip thickness
used to evaluate the volumetric wear rates according to the method mentioned in Fig. 5. Fig. 10 shows different tool wear profiles and corresponding cross-section at varying cutting times. The technique helps to obtain the experimental volumetric wear rate and the wear constants following Eq. (5). Based on the experimental results, the localized tool wear incorporating the spatial variation at discrete points on the tool-chip contact length (0 < x � lc ) has been predicted by Eq. (6) [6]. � � � α� dw Volumetric wear rate ¼ w_ ¼ K:σn :vs: exp (5) dt T
correlated from experimental results (Appendix 1). At lower feeds, higher ξ values have been achieved that corresponds to high chip thickening and high frictional stresses at tool rake face. At cutting speed vc ¼ 50 m=min and 70 m=min, lower values of chip reduction coefficient (ξ < 2:0Þ reflects the reduced frictional values in the sliding zone. The trend has not been observed at vc ¼ 90 m=min 130 m=min where sticking friction zone has been achieved at higher feeds, although ξ values remain below the limiting value ðξ < 2:0). This shows that below a critical velocity, the frictional coefficient is dominated by the sliding nature of tool-chip interaction. Once the critical velocity exceeds, the contribution of the sliding friction to total friction diminishes even when the chip reduction coefficient remains below the limiting value. The friction coefficients at different cutting speeds and feeds are best fitted according to power-law distribution (Appendix 2).
Local wear rateðw_ l Þ ¼ K: � ln
� w_ l :Lc ¼ ln K σn :vs : x
α T
� � � α� x :σ n :vs: exp lc T
(6) (7)
The simulation results for tc ¼ 180 s 300s respectively with fully grown chip sliding at the conforming worn tool profiles were used to extract the state variables. The conformity of the chip flow over the worn profiles asserts that the nodal points on the tool surface extract the value of state variables with truncated chances of the data probing errors. Pointwise locus on the tool rake surface over the worn profile has been probed for von-Mises’ stresses, normal stress, chip load, chip sliding velocity, and the interface temperature. The variation of inverse temperature is highly influential for the prediction of the volumetric wear (crater wear) [6,31]. The wear rates with inverse temperature were used to obtain wear coefficients following Eq. (7). FEM simulation results help to extract the localized state variables and calculate the volumetric wear loss and subsequent wear constants. The values of state variables were further used to plot a semi-logarithmic diagram (Fig. 11). Regression analysis of the semi-logarithmic plot represents the average local specific wear rates at
3.3. FE analysis for the evaluation of wear constants and prediction of the wear profile The modeled equation (Eq. (4)) has been used to determine the co efficient of friction for simulations under the selected cutting parame ters. The experimental results obtained for tool wear profiles have been 8
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Fig. 10. Experimental crater wear profiles at varying tc used for evaluating volumetric wear.
Fig. 11. Average local specific wear rate variation with inverse temperature from FEM analysis.
� � varying fractional contact length loci
x lc
with respect to inverse tem
perature. The intercept at the Y-axis and the slope of the linear equation correspond to K and α values, respectively. The wear constants K ¼ 8:13 � 10 8 and α ¼ 244.63 have been obtained for WC-Ti6Al4V pair under dry cutting conditions. The error bar shows the standard deviation of local specific wear rate over different fractional contact length. The values of K and α determined from the logarithmic plot were used to tj Þ. The calculate the wear rate in the next time interval ðΔt ¼ tjþ1 time interval for next cutting duration is kept to 30 s and the volumetric � � wear rates with discretized lxc locations are determined. KTjþ1 ¼ KTj þ
� � dw : tjþ1 dt j
tj
�
Fig. 12. (a) Experimental measurement of crater wear over the tool-chip contact zone at different loci of Lc and (b) comparison of results for crater wear (at tc ¼ 330 s).
curate prediction of KTmax locus. The values of KT at the start (x � 0:1Lc ) and end of the wear profile (0:85Lc � x � 1:0Lc ) show a high deviation from the experimental results. The maximum difference in the experimental and predicted crater wear at x � 0:1Lc and 0:85Lc � x � 1:0Lc are 37.3% and 108% respectively (Fig. 12(b)). For the initial loci of wear profile, KT values are overpredicted due to the inability of the used wear model to consider the edge wear. In the pre sent study, the wear model and the wear constants derived from the simulation results couldn’t account for the edge dulling ðSVα value) nature during cutting. The generation of SVα is due to high dynamic stresses generated over an infinitesimally small area (cutting edge) that undergoes rapid loss of tool material from the cutting edge (Fig. 12(a)). This might be the resulting source of error for the KT values (x � 0:1Lc ) as the edge wear corresponds to 20μm � SVα � 25μm (for x < 0:05Lc ). The inherently high stresses at the cutting edge and
(8)
In the case of 2D FEM simulations, the extrapolated KT values can be predicted using Eq. (8). The wear profile has been predicted for cutting time ¼ 330 s considering the initial point of wear variables at tc ¼ 300 s (nearest values). The wear constant (K, α) obtained from the analysis of data (180 s–300 s) is able to minimize the error in the extrapolated calculation for the predicted wear stage (tc ¼ 330 s). The values are plotted for varying contact length locations from 0:1Lc � x � Lc and compared with the experimental values (Fig. 12(a)). The results can generate the approximate wear profile with an ac 9
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nearly stagnant chip sliding (vs e0) result in the severe edge dulling with increasing cutting time. The wear behavior at the zone very near to cutting edge couldn’t be modeled according to the available wear models in the literature, which are capable of considering only the adhesion, abrasion, dissolution wear mechanisms (single or combina tion of these mechanisms). The experimental crater wear profile in Fig. 12(b) doesn’t have an error bar as the profile is extracted from the mid-zone of the crater area. A nearly similar trend to the crater profile will be observed from the mid-zone crater section; hence, a single wear profile was extracted and plotted. There is a fair agreement between experimental and simulated crater profile at the mid-section of worn tool profile and the error range (ΔKT ¼ 3:12%at x ¼ 0:2Lc and ΔKT ¼ 20:5%at x ¼ 0:4Lc ) lies within the acceptable limits. The developed model fairly predicts the crater wear profile over the selected fractional contact length along the rake face.
sectioning of the cutting tool using wire EDM. The metal cutting is a dynamic process, and so is the tool wear and worn surface geometry. The worn profile geometry and the method of cross-sectioning will change depending on the cutting parameters used (mainly ap ; Lc ; and f). As the depth of cut changes (increased or decreased from the presently used value), the wear profile changes (spans over the cutting edge or con centrates at the tool nose). The different sectioning methods will obtain different crater profiles. In that case, the geometrical errors will be present in the replicated wear geometry at the tool surface. Proper care must be taken in this regard to avoid any chance of error generated due to improper cross-sectioning of the tool wear profile. (b) The non-conformance of the tool-chip interface at the rake face generated by the geometry replication method Wear profiles obtained from the metal cutting experiments have been finely replicated using the coordinate measurement over the rake face, and appropriate CAD models have been replicated. The error in non-singularities of worn profiles has been reduced by smoothening the replicated CAD geometries before the meshing of the tools to avoid meshing errors. Also, the tool has been finely meshed at the surface, and the mesh size is selected after mesh convergence tests for different profiles. During FE simulations, the sliding of the chip at the rake surface is conformal to the generated profile at the total contact length zone except at some discrete locations. As shown in Fig. 13, the nonconformance of the tool-chip interaction is present at the rake face as the chip tends to move in the exit half of the contact zone (x > 0:65Lc ). The non-conformance of the sliding chips may cause the error in the values of state variables as it will reduce the local state variables (σn ; Tint ; etc:) or increase the value of vs at neighboring nodes. Although appropriate care has been taken to minimize the influence of such errors using statistical tools and its occurrence is limited at the interface (at a single discrete location in the considered case), this inevitably may cause the error in FEM results if ignored. A similar
3.4. Challenges in the present research and suggested direction for improvement The research presents an approach to obtain the spatial and temporal wear prediction during the metal cutting process using the geometry replication method on the modeled tools. The unworn tool geometry selected for wear studies may not be able to exactly predict the local state variables at varying tool-chip contact zone. The exact determina tion of worn tool geometry from metal cutting experiments and its replication on the cutting tools’ model are considered as another method to closely predict the tool wear using FE simulations. However, certain sources of error have been identified in the present study that causes deviation in the obtained wear profile and crater wear depth at different loci on the contact length zone. (a) Errors in geometry replication on the tool surface The crater wear profile is generated at the tool surface after careful
Fig. 13. Non-conformance error present at the tool-chip interface on the worn tool profiles. 10
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observation in some of the previous studies has been reported as a result of wear geometry update using a user-defined subroutine to update the tool surface geometry due to wear (nodal displacement). In the present study, any user-defined subroutine has not been incorporated into the wear model; hence, the presence of the nodal displacement can be ignored. The same is considered as an error in the geometry replication, which, if occurs at multiple nodes, may influence the accuracy of the proposed method. These errors should be taken adequate care beforehand to achieve the accurate FE formulations, generation of local state variable data, and wear results. Despite these challenges, the selected approach for crater wear prediction has resulted in a good agreement with the experimen tally observed wear profile. The increased overestimation of crater wear in the maximum temperature zone can be further smoothened using a number of tool wear tests for different cutting speeds, feeds, and depth of cut values. Also, the edge dulling of the cutting tools is not incorporated in the used wear model which has resulted in disagreement at the initial wear profile (for x � 0:1Lc ) in the simulation results. The stagnation zone at the tool chip contact zone and the impact of the cutting tool engagement at highly worn tools can be considered as shortcomings, which may be looked into future studies.
the wear constants. The following conclusions are withdrawn: 1. A friction model has been developed to incorporate the stick-slip behavior of Zorev’s hybrid friction theory in FE simulations. 2. Local wear rates, state variables and crater profiles extracted at tc ¼ 3; 4; 5 minand contact zones ð0:1Lc � x � 1:0Lc Þresulted in wear constants K ¼ 8:13 � 10 8 and α ¼ 244.63. 3. A characteristic wear model with the dimensionless parameter � � x lc has been proposed. The developed model offers fair prediction in the mid-section of the crater wear within the error range ðΔKT ¼ 3:12% 20:5%Þ. 4. The maximum error in the wear prediction appears at the start ðx � 0:1Lc ) of the contact length zones (ΔKT ¼ 37:33%Þdue to inability of the developed model to predict the edge wear (SVα ). Declaration of the conflict of interests Authors hereby declare that the present research work does not have any conflict of interest. Acknowledgment
4. Conclusions
The authors thank Central Research Facility (CRF-IIT Delhi) to pro vide help for SEM micrographs and Third Wave Systems (Minneapolis, USA) for providing the academic lease of the AdvantEdge 7.4 FEM codes. Additionally, the first author thanks MHRD, India, to provide financial support for pursuing Ph.D. at IIT Delhi.
The present study proposed a hybrid approach comprising the experimental and FE simulation methods for crater wear prediction during dry turning of Ti6Al4V alloy. Experimental crater wear profiles were modeled on the cutting tool to carry out FEM simulations and generate state variables’ database. A modified wear model incorporating the contact length factor in Usui wear model has been used to determine
Appendix: 1 Experimentally obtained coefficient of friction (μ) values at varying machining parameters vc (m/min)
f (mm/rev)
0.01 0.02 0.05 0.1 0.15 0.2 0.25
50
70
90
110
130
1.172 1.074 0.706 0.521 0.505 0.520 0.515
1.067 0.744 0.653 0.508 0.585 0.515 0.680
1.121 1.330 0.880 0.684 0.623 0.716 0.965
1.402 0.897 0.748 0.572 0.643 0.742 0.830
1.051 1.074 0.873 0.662 0.742 0.705 0.793
Experimental values of chip reduction coefficient (ξ) at varying machining parameters vc (m/min)
f (mm/rev)
0.01 0.02 0.05 0.1 0.15 0.2 0.25
50
70
90
110
130
7.02 4.1 2.14 1.75 2.0 1.29 1.65
8.53 6.27 2.07 1.73 1.44 1.6 1.47
6.52 5.01 2.34 1.9 1.75 1.57 1.8
8.11 6.63 2.98 1.99 1.64 1.52 1.55
7.69 5.0 1.94 1.85 1.69 1.56 1.65
11
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Appendix: 2 Power law distribution of coefficient of friction modeled from experimental results μ ¼ C1 :f
C2
vc (m/min)
C1
C2
50 70 90 110 130
0.3003 0.3924 0.568 0.4497 0.576
0.3023 0.1950 0.1664 0.2178 0.1377
Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.wear.2020.203229.
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