A Review of Tool Wear Estimation Using Theoretical Analysis and Numerical Simulation Technologies

Int. Journal of Refractory Metals and Hard Materials 35 (2012) 143–151

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Int. Journal of Refractory Metals and Hard Materials

journal homepage: www.elsevier.com/locate/IJRMHM

A review of tool wear estimation using theoretical analysis and numerical simulation technologies

Bin Li ⁎

Department of Mechanical Engineering, Luoyang Institute of Science and Technology, Wangcheng Avenue 90, Luoyang 471023, Henan Province, PR China article info abstract

Article history: A thorough understanding of the material removal process in cutting is essential in selecting the tool material Received 21 February 2012 and in design, and also in assuring consistent dimensional accuracy and surface integrity of the finished prod- Accepted 7 May 2012 uct. Tool wear in cutting process is produced by the contact and relative sliding between the cutting tool and the workpiece, and between the cutting tool and the chip under the extreme conditions of cutting area. This Keywords: paper presents the information on development of study on theoretical analysis and numerical simulation of Simulation tool wear in all over the world. Hidden Markov models (HMMs) were introduced to estimate tool wear in Tool wear fl Metal cutting cutting, which are strongly in uenced by the cutting temperature, contact stresses, and relative strains at the interface. Finite element method (FEM) is a powerful tool to predict cutting process variables, which are difficult to obtain with experimental methods. The objective of this work focuses on the new development in predicting the tool wear evolution and tool life in orthogonal cutting with FEM simulations. © 2012 Elsevier Ltd. All rights reserved.

1. Introduction Although various theories have been introduced hitherto to ex- plain the wear mechanism, the complicity of the processes in the cut- Nowadays, metal cutting is a significant industry in economically ting zone hampers formulation of a sound theory of cutting tool wear. developed countries, though small in comparison to the customer in- The nature of tool wear in metal cutting, unfortunately, is not yet dustries it serves. The automobile, railway, shipbuilding, aircraft man- clear enough in spite of numerous investigations carried out over ufacture, home appliance, consumer electronics and construction the last 50 years. Friction of metal cutting is a result of complicated industries, all these have large machine shops with many thousands physical, chemical, and thermo-mechanical phenomena. Recently, of employees engaged in machining. It is estimated that 15% of the the prediction of friction of metal cutting is performed by calculating value of all mechanical components manufactured worldwide is de- tool life according to experiment and empirical tool life equations. Al- rived from machining operations [1–3]. though the equation gives the simple relationship between tool life A thorough understanding of the material removal process in and a certain cutting parameters, it gives only the information about metal cutting is essential in selecting the tool material and in design, tool life. For the researcher and tool manufacturer, tool wear progress and also in assuring consistent dimensional accuracy and surface in- and tool wear profile are also areas of concern. Tool life equation gives tegrity of the finished product. Friction of metal cutting influences no information about the wear mechanism. But capability of predicting the cutting power, machining quality, tool life and machining cost. contributions of various wear mechanism is very helpful for the design When tool wear reaches a certain value, increasing cutting force, vi- of cutting tool material and geometry. In addition, such tool life equa- bration and cutting temperature cause deteriorated surface integrity tions are valid under very limited cutting conditions. For example, and dimension error greater than tolerance. The life of the cutting when tool geometry is changed, new equation must be established by tool comes to an end. Then the cutting tool must be replaced or gro- making experiment [7,8]. und and the cutting process is interrupted. The cost and time for Metal cutting is a highly nonlinear and coupled thermo-mechanical tool replacement and adjusting machine tool increase the cost and process, where the coupling is introduced through localized heating decrease the productivity. Hence friction in metal cutting relates to and temperature rise in the workpiece, which is caused by the rapid the economics of machining and prediction of friction is of great sig- plastic flow in the workpiece and by the friction along the tool–chip in- nificance for the optimization of cutting process [4–6]. terface. With the emergency of more and more powerful computer and the development of numerical technique, numerical methods such as finite element method (FEM) [9–11], finite difference method (FDM) and artificial Intelligence (AI) are widely used in machining industry. ⁎ Tel.: +86 15937911896; fax: +86 379 65928208. Among them, FEM has become a powerful tool in the simulation of E-mail address: [email protected]. cutting process. Various variables in the cutting process such as cutting

0263-4368/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmhm.2012.05.006 144 B. Li / Int. Journal of Refractory Metals and Hard Materials 35 (2012) 143–151 force, cutting temperature, strain, strain rate, stress, etc. can be Type of tool wear contains crater wear on rake face and flank wear predicted by performing chip formation and heat transfer analysis on flank face, which is shown in Fig. 1. Crater wear (Fig. 1) produces a in metal cutting, including those very difficult to detect by experi- wear crater of the tool rake face. The depth of the crater KT is selected mental method. Therefore friction prediction method may be devel- as the tool life criterion for carbide tools. The other two parameters, oped by integrating FEM simulation of cutting process with wear namely, the crater width KB and the crater center distance KM are im- model [12–15]. The new challenge is the implementation of effective portant if the tool undergoes re-sharpening [26]. models in a finite element environment in order to perform a reliable Flank wear (Fig. 1) results in the formation of a flank wear land. prediction of tool wear. In fact, the introduction of the finite element For the purpose of wear measurement, the major cutting edge codes and their computational improvements that make this tool is considered to be divided into the following three zones: (a) Zone able to approach machining process simulation represents a break C is the curved part of the cutting edge at the tool corner; (b) Zone point with the past and opens a new scenario [16–18]. N is the quarter of the worn cutting edge of length b farthest from This paper introduces the experimental evidence for what is the the tool corner; and (c) Zone B is the remaining straight part of the nature of the friction contact between chip and tool during chip for- cutting edge between Zones C and N. The maximum VBB max and mation and the historical development of friction models. The objec- the average VBB width of the flank wear are measured in Zone B, tive of this work focuses on some basic aspects of friction modeling in the notch wear VBN is measured in Zone N, and the tool corner cutting and in particular on the influence of friction modeling on the wear VBC is measured in Zone C. As such, the following criteria for effectiveness of the numerical simulation of the process. carbide tools are normally recommended: (a) the average width of

the ﬂank wear land VBB = 0.3 mm, if the ﬂank wear land is consid- 2. Tool wear mechanisms and models ered to be regularly worn in Zone B; (b) the maximum width of the

flank wear land VBB max=0.6 mm, if the flank wear land is not con- Tool wear has a large influence on the economics of the machining sidered to be regularly worn in Zone B. Besides, surface roughness for operations. Prediction of tool wear is complex because of the com- finish turning and the length of the wear notch VBN =1 mm can be plexity of machining system. Tool wear in cutting process is produced used. However, these geometrical characteristics of tool wear are by the contact and relative sliding between the cutting tool and the subjective and insufficient. First, they do not account for the tool workpiece and between the cutting tool and the chip under the ex- geometry (the flank angle, the rake angle, the cutting edge angle, treme conditions of cutting area; temperature at the cutting edge etc.), so they are not suitable to compare wear parameters of cutting can exceed 1000 °C. Thus, knowledge of tool wear mechanisms and tools having different geometries. Second, they do not account for capability of predicting tool life are important and necessary in the cutting regime and thus do not reflect the real amount of the metal cutting. Any element changing contact conditions in cutting work material removed by the tool during the tool operating time, area affects tool wear [19–22]. These elements come from the which is defined as the time needed to achieve the chosen tool life whole machining system comprising workpiece, tool, interface and criterion [26,27]. machine tool. In order to find out suitable way to slow down the wear process, Workpiece material and its physical properties determine the cut- many works are carried out to analyze the wear mechanism in ting force and energy for the applied cutting conditions. The optimal metal cutting [28–30]. It is found that tool wear is not formed by a performance of a cutting tool requires a right combination of the unique tool wear mechanism but a combination of several tool wear above tool parameters and cutting conditions [23]. Interface involves mechanisms. Tool wear mechanisms in metal cutting include abrasive the interface conditions. Increasingly new technologies of interface, wear, adhesive wear, solution wear, diffusion wear, oxidation wear, such as the minimum liquid lubrication, have been developed to re- etc., illustrated in Fig. 2 [31]. duce the cost of coolant. The dynamic characteristic of the machine tool, affected by the machine tool structure and all the components taking part in the cutting process, plays an important role for a suc- 2.1. Abrasive wear cessful cutting. Instable cutting processes with large vibrations result in a fluctuating overload on the cutting tool and often lead to prema- Tool material is removed away by the mechanical action of hard ture failure of the cutting edge by tool chipping and excessive tool particles in the contact interface passing over the tool face. These wear [24,25]. hard particles may be hard constituents in the work material,

SECTION A-A KB KM

KT s Plane P

Zone VBC Flank wear land

C AACrater b VB max B B VBB

VBN

Fig. 1. Types of wear on turning tools according to ANSI/ASME Tool Life Testing. B. Li / Int. Journal of Refractory Metals and Hard Materials 35 (2012) 143–151 145

Chip Oxidationwear

Diffusionwear Diffusion Tool

Wear Abrasion Adhesivewear v Adhesion Abrasivewear c Oxidation Workpiece Cutting temperature (Cutting speed, feed, etc)

Fig. 2. Wear mechanism in metal cutting.

fragments of the hard tool material removed in some way or highly Tool wear rate models are derived from one or several wear strain-hardened fragments of an unstable built-up edge. mechanisms. They provide the information about wear growth rate due to some wear mechanisms. In these modes, the wear 2.2. Adhesive wear growth rate, i.e. the rate of volume loss at the tool face (rake or flank) per unit contact area per unit time, is related to several cut- Adhesive wear is caused by the formation and fracture of welded ting process variables that have to be decided by experiment or asperity junctions between the cutting tool and the workpiece. using some methods [41,42]. Takeyama [34] derived a fundamental wear rate equation by considering abrasive wear, which is propor- tional to cutting distance, and diffusive wear. Mathew [35] analyzed 2.3. Diffusion wear the tool wear of carbide tools when machining carbon steels and results have shown that the Takeyama's diffusion equation can be Diffusion wear takes place when atoms move from the tool mate- used to effectively relate the tool wear rate to the average contact rial to the workpiece material because of the concentration differ- temperature of the tool. At cutting temperature higher than ence. The rate of diffusion increases exponentially with the increase 800 °C, the first abrasive term G(V, f)inTable 1,canbeneglected. of temperature. Molinari [43] proposed a new diffusion wear model by considering the contact temperature to be the main parameter controlling the 2.4. Oxidation wear rate of diffusion in the normal direction to the tool–chip interface. Usui [44] in the tool wear study for carbide tools derived a wear A slight oxidation of tool face is helpful to reduce the tool rate model based on the equation of adhesive wear, which involves wear. It reduces adhesion, diffusion and current by isolating the temperature, normal stress, and sliding velocity at the contact sur- tool and the workpiece. But at high temperature soft oxide layers, face.Usui'smodelisderivedfromShaw'sequationofadhesive are formed rapidly, and then taken away by the chip and the wear [45,46]. Except the constants A and B, Usui's equation includes workpiece. three variables: sliding velocity between the chip and the cutting According to the temperature distribution on the tool face, it is as- tool, tool temperature and normal pressure on tool face. These vari- sumed that crater wear is mainly caused by abrasive wear, diffusion ables can be predicted by FEM simulation of cutting process or com- wear and oxidation wear, but flank wear mainly dominated by abrasive bining analytical method and FDM. Therefore Usui's equation is wear due to hard second phase in the workpiece material [32]. very practical for the implementation of tool wear estimation As the tool wear in cutting operations involves complex wear by using FEM or by using the combination of FDM and analytical mechanisms, researchers have attempted to directly correlate the method [47]. results of tool life to the applied machining parameters (cutting speed, feed rate, and etc.). Many models are developed to describe tool wear in quantity. They can be categorized into two types: tool life models and tool wear rate models, which are shown in Table 1 [33–36]. Tool life models give the relationship between tool life and cutting pa- Table 1 rameters or variables. For example, Taylor's tool life equation reveals the Empirical tool life models and tool wear rate models. exponential relationship between tool life and cutting speed [37],see Table 1. The constants n, C, A and B are defined by doing a lot of experi- Empirical tool life models Tool wear rate models ments with cutting speed changing and fitting the experimental data Taylor's basic equation: Takeyama's wear model: n with the equation. It is very convenient to predict tool life by using this VL =C1 (n, C1 = constants) (considering abrasive wear and diffusive wear): dW ¼ ðÞþ; − E Taylor's extended equation: dt GV f D exp RT equation. In various sizes of cutting database, Taylor's tool life equation C2 L ¼ q r (G, D = constants) and its extension versions under different cutting conditions appear vp f d (p, q, r, C1 = constants) most frequently. Tool life equations are suitable to very limited range of Taylor's extended equation: Usui's wear model: C3 V ¼ p q (considering adhesive wear): cutting conditions. As the new machining technologies, e.g. high-speed- Lm f d ðÞBHN=200 r (m, p, q, r, C = constants) dW ¼ Aσ V exp − B cutting or dry cutting, are getting spread in manufacturing industry, the 3 dt n s T Taylor's basic equation: (A, B = constants) existing tool life equations need to be updated with new constants and n TL =C4 (n, C4 = constants) a lot of experimental work has to be done. In addition, except that tool L = tool life; σ = normal stress; T = cutting temperature; V = cutting speed; f = feed life can be predicted by these equations, it is difficult to get further infor- n rate; E = activation energy; Vs = sliding velocity; d = depth of cut; R = universal gas mation about the tool wear progress, tool wear profile or tool wear mech- constant; BHN = workpiece hardness; dW/dt = wear rate (volume loss per unit anisms that are sometimes important for tool designers [38–40]. contact area/unit time). 146 B. Li / Int. Journal of Refractory Metals and Hard Materials 35 (2012) 143–151

3. Theoretical analysis procedure of tool wear and from Eq. (7), it is easy to get

Tool wear is a result of physical and chemical interactions be- 2 3 2 3 ðÞ0 ðÞ − ðÞ1 ðÞ tween the cutting tool and workpiece that remove small parts of ma- x 2 Z 2 1 6 ðÞ0 ðÞ7 6 − ðÞ1 ðÞ 7 a terial from the cutting tool [48,49]. Even though abrasive and 6 x 3 7 ¼ 6 Z 3 1 7 ð8Þ 4 ⋮ 5 4 ⋮⋮5 b adhesive wear are the most commonly encountered mechanisms, ðÞ ðÞ x 0 ðÞn −Z 1 ðÞn 1 the wear in cutting tools cannot be described completely by these mechanisms alone. Tool wear is a highly complicated process associated with many variables such as contact stress, nature and composi- where a and b are the coefﬁcients to be identiﬁed. tion of the workpiece and cutting tool, temperature on the cutting Let edge, and cutting conditions [50]. hi ¼ ðÞ0 ðÞ; ðÞ0 ðÞ; …; ðÞ0 ðÞT ð Þ 3.1. Prediction theory of gray model Yn x 2 x 3 x n 9

The gray model GM(1,1) is a time series forecasting model. It has three basic operations: accumulated generation, inverse accumulated and generation, and gray modeling. The gray forecasting model uses the 2 3 − ðÞ1 ðÞ operations of accumulated to construct differential equations. Intrin- Z 2 1 6 − ðÞ1 ðÞ 7 sically speaking, it has the characteristics of requiring less data. The B ¼ 6 Z 3 1 7 ð10Þ 4 ……5 gray model GM(1,1), i.e., a single variable ﬁrst-order gray model, is ðÞ −Z 1 ðÞn 1 summarized as follows [51]: For an initial time sequence, Also take no ðÞ0 ðÞ0 ðÞ0 ðÞ0 ðÞ0 X ¼ x ðÞ1 ; x ðÞ2 ; …; x ðÞi ; …; x ðÞn ð1Þ ðÞ 1 ðÞ ðÞ Z 1 ðÞk þ 1 ¼ x 1 ðÞk þ x 1 ðÞk þ 1 k ¼ 1; 2; …; ðÞn−1 ð11Þ 2 (0) where x (i) is the time series data at time i, and n must be equal to and or larger than 4. (0) (1) On the basis of the initial sequence X , a new sequence X is A ¼ ½a; b T ð12Þ set up through the accumulated generating operation in order to provide the middle message of building a model and to weaken the var- where Yn and B are the constant vector and the accumulated matrix iation tendency, respectively. Apply ordinary least-square method to Eq. (8) on the nobasis of Eqs. (9)–(12), coefﬁcient A becomes ðÞ ðÞ ðÞ ðÞ ðÞ X 1 ¼ x 1 ðÞ1 ; x 1 ðÞ2 ; …; x 1 ðÞi ; …; x 1 ðÞn ð2Þ − ¼ T 1 T ð Þ A B B B Yn 13 where

Xk Substituting A in Eq. (7) with Eq. (13), the approximate equation ðÞ ðÞ x 1 ðÞ¼k x 0 ðÞi k ¼ 1; 2; …; n ð3Þ becomes the following ¼ i 1 ðÞ ðÞ − x^ 1 ðÞ¼k þ 1 x 0 ðÞ1 −b=a e ak þ b=a ð14Þ Mean sequence is ðÞ ðÞ where x^ 1 ðÞk þ 1 is the predicted value of x^ 1 ðÞk þ 1 at time (k +1). ðÞ1 ðÞ¼ : ðÞ1 ðÞþ : ðÞ1 ðÞ− ðÞ¼ ; ; …; ð Þ z k 0 5x k 0 5x k 1 k 2 3 n 4 After the completion of an inverse accumulated generating opera- ðÞ ðÞ tion on Eq. (14), x^ 0 ðÞk þ 1 , the predicted value of x^ 0 ðÞk þ 1 at and it also means time (k + 1) becomes available and therefore, ðÞ ðÞ ðÞ ðÞ 1 ¼ 1 ðÞ; 1 ðÞ; …; 1 ðÞ ð Þ ðÞ ðÞ ðÞ z z 2 z 3 z n 5 x^ 0 ðÞk þ 1 ¼ x^ 1 ðÞk þ 1 −x^ 1 ðÞk ðÞk ¼ 0; 1; 2; 3; …; n ð15Þ

So the differential equations of this gray model can be expressed as 3.2. Prediction theory of Markov chain

ðÞ ðÞ Hidden Markov models (HMMs) were introduced by Baum and col- x 0 ðÞþk az 1 ðÞ¼k bkðÞ¼ 2; 3; ⋯; n ð6Þ leagues at the end of the 1960s. Then, Baker and Jelinek implemented this theory for speech processing applications in the 1970s. Currently, (0) In the differential equation, x (k) is named as gray derivative, a is HMM is a state-of-the-art technique for speech recognition because of (1) named as evolution system, z (k) is named as evolution system its elegant mathematical structure and the availability of computer im- background values, b is named as gray action, if the numbers k=2, plementation of these models. Recently, HMM applications have been … 3, , n are introduced in the equation, the equation can be expressed spreading steadily to other engineering ﬁelds that include communica- as tion systems, target tracking, machine tool monitoring, fault detection 8 and diagnosis, robotics and character recognition [52–58]. > ðÞ0 ðÞþ ðÞ1 ðÞ¼ <> x 2 az 2 b If the observations are continuous signals (or vectors), a continu- ðÞ0 ðÞ1 x ðÞþ3 az ðÞ¼3 b ð Þ ous probability distribution function in the form of a ﬁnite mixture > 7 :> …… is assigned to each state instead of a set of discrete probabilities ðÞ0 ðÞ1 x ðÞþn az ðÞ¼n b [59]. In this case, the parameters of the continuous probability B. Li / Int. Journal of Refractory Metals and Hard Materials 35 (2012) 143–151 147 distribution function are often approximated by a weighted sum of M Suppose the component of state transition probability matrix P(k) (k) Gaussian distributions η, is the Pij , and

XM ðÞ¼ ημ ; ; ; ≤ ≤ ð Þ ðÞk bj Ot cjm jm Ujm Ot 1 j N 16 ¼ ðÞ= ; ¼ ; ; …; ð Þ Pij Mij k Mi i j 1 2 n 23 m¼1 where c is a weighting (mixture) coefficient, m is the mean vector, jm jm expresses the system probability for state j, and the known condition U is the covariance matrix and M is the number of mixture compo- jm is m moment for state i, order the P(k), which we can get in Eq. (20), nents, a typical observation sequence is denoted as O={O , O ,…, O }. ij 1 2 T M is the sample number of primary data falling into the state i η(μ, U, O) is a multivariate Gaussian probability density function with i according to certain probability; M (k) is the sample number of pri- mean vector m and covariance matrix U, that is ij mary data from system moment Qi to moment Qj by k step. When we confirm the transfer moment Qd, also the change inter- 1 1 −1 ημðÞ¼; U; O pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp − ðÞO−μ ′U ðÞO−μ ð17Þ val [Q , Q ] could be ascertained, let the prediction data Y(k) to the ðÞ2π njjU 2 1d 2d halfway point as follows: where n is the dimensionality of O. ∈ ðÞ Consider the random process {xn, n T} and set of discrete condi- ðÞ¼ðÞþ = ¼ ^ 0 ðÞþðÞþ = ð Þ Yk Q 1d Q 2d 2 x k Ai Bi 2 24 tions I={i0, i1, i2,…}. If for any integer n∈T, the conditional probability as p ¼ x ¼ i x ¼ i ; x ¼ i ; …; jx ¼ i Þ¼p ¼ x ¼ i jx ¼ i Þ nþ1 nþ1 0 0 1 1 n n nþ1 nþ1 n n 4. Simulation procedure of tool wear ð18Þ It is postulated in this study that the growth of tool wear can be ∈ where the random process {xn, n T} can be called Markov chain, and evaluated at discrete points in time, although in reality it is a contin- the probability uous process. The proposed procedure for predicting tool wear is shown in Fig. 3 [32]. In every calculation cycle, chip formation and ðÞk ¼ ¼ ¼ Þ; ðÞ; ∈ ðÞ Pij pxmþk j xm i i j I 19 heat transfer analysis jobs are submitted to analyze the steady-state cutting process and obtain the cutting process variable values neces- expresses the system probability at m+k moment for state j, and the sary for the calculation of wear rate at steady state. Nodal wear rate is (k) known condition is m moment for state i, order the Pij , and we can calculated by using the tool wear mathematical model. Based on the get the following matrix: calculated nodal wear rate, a suitable cutting time increment is searched by program according to a user-specified VB increment 2 3 ðÞk ⋅⋅⋅ ðÞk value. Then the nodal displacement due to wear in the cutting time ðÞ P11 P1n P k ¼ 4 ⋅⋅⋅ ⋅⋅⋅ ⋅⋅⋅ 5 ð20Þ increment is calculated at every tool face node, and the tool geometry ðÞk ⋅⋅⋅ ðÞk is updated according to the calculated nodal displacement. If the pro- Pn1 Pm duced flank wear VBB is smaller than the user-defined tool reshape This matrix is called k step transition probability matrix of Markov criterion VBB max, a second tool wear calculation cycle starts with chain, and the updated tool geometry [61,62].

Xn ðÞ Start k ¼ ð Þ Pij 1 21 j¼1 Chip formation analysis Hidden Markov models are an extension of Markov chains. A Markov chain is a random process of discrete-valued variables involving a number of states linked by a number of possible transitions. At different Heat transfer analysis times, the system is in one of these states; each transition between the states has an associated probability, and each state has an associated Cutting time increment observation output for tool wear estimation. Nodal wear rate calculation calculation 3.3. Prediction of tool wears with state division Nodal displacement The classiﬁcation methods of state division are relative value calculation method, relative error method, standardization of residual deviation method and parallel curve method [60]. Based on the prediction Next calculation cycle ðÞ data of x^ 0 ðÞk curves in the gray model GM(1,1), and bar areas para- Tool geometry updating lleled with prediction data curves are divided, every bar areas consti- tute the corresponding state interval Qi, which can be expressed as:

¼ ½; ; ¼ ; ; …; No Q i Q 1i Q 2i i 1 2 n VB>=VB max? ¼ ðÞ0 ðÞþ ð Þ Q 1i x k Ci 22 ¼ ðÞ0 ðÞþ Yes Q 2i x k Di End where Ci and Di are the constant vector based on data of tool wears, and n is the number of state interval. Fig. 3. Procedure for predicting tool wear. 148 B. Li / Int. Journal of Refractory Metals and Hard Materials 35 (2012) 143–151

4.1. Chip formation analysis area moves upwards into the chip and the material below the separation area moves downwards to join in the machined surface. The chip formation model was created using the implicit FEM soft- According to the sliding velocities of the workpiece material ware, which uses an updated Lagrangian formulation. This means points along tool–chip interface, a more exact position of the max that the material is attached to the mesh, with periodic remeshing principal stress can be displayed with point tracking technology in to avoid severe element distortion [63]. A very fine mesh was used Fig. 6. It can be assumed that material failure is taking place in this near the tool tip in the deformation zone of the workpiece and the area. By varying cutting parameters or tool geometry, the dependency edge of the tool as shown illustratively in Fig. 4. Automatic end adap- of strain at failure on temperature, strain rate, pressure, etc. also can tive remeshing was used to take into account the severe distortion of be studied. mesh elements near the tool tip. It is well accepted that the influence of strain, strain rate and tem- 4.2. Heat transfer analysis perature on work flow stress must be included in successful simulations of machining: many empirical equations have been developed To reach a thermally steady state for the cutting tool, the simula- to describe this. Johnson–Cook constitutive equation was used to de- tion needs to be run for a much longer cutting period on the order scribe the material's performance in the cutting process. The full ex- of a half second. This will considerably increase the computational pression for flow stress σ, including strain path effects, could be time and data storage capacity, making cutting simulations expen- calculated as follow [64]: sive. Therefore, an approximate method was used to obtain the stead- y state tool temperatures, which involves the pure heat transfer ε_ θ −θ analysis for the tool only. In the cutting phase the cutting tool is heat- σ ¼ εn þ m þ − : ðÞθ− 2 B 1 C ln θ −θ a exp 0 00005 700 ed by the heat flux acted on the tool–chip and tool–workpiece inter- 1000 m r fl fl f ð25Þ face. The total heat ux is composed of frictional heat ux q and conductive heat flux qc. Frictional heat flux is created due to the sliding friction between the workpiece material and the tool face [67]. ε_ ε fl θ where the , re ect the strain rate and strain. is the temperature; The amount of frictional heat flux into the cutting tool is calculated θ θ m is the temperature of melting point; r is the room temperature, by Eq. (27) [68]. and the value is 20 °C. The coefficients B, C, n and a are material constants. The shear failure model is based on the value of the equivalent r q ¼ ðÞ1−f ⋅η⋅τ⋅v ð27Þ plastic strain at element integration points [65]. When the equivalent s plastic strain reaches the strain at failure εpl, then the damage param- f where τ is the frictional stress; ν is the sliding velocity; η specifies eter w exceeds 1, and material failure takes place. If at all the integra- s the fraction of mechanical energy converted into thermal energy; tion point material failure takes place, the element is removed from and f gives the fraction of the generated heat flowing into the the mesh. The damage parameter, w,isdefined as workpiece. 0 1 Therefore frictional heat flux is influenced by chip form, sliding pl Δε condition and contact with the tool face. w ¼ ∑@ f A ð26Þ εpl Conductive heat flux is caused by the temperature difference of f tool–chip and tool–workpiece at the interface. It is governed by Eq. (28). Δεpl where f is an increment of the equivalent plastic strain. The sum- mation is performed over all increments in the analysis. pl Normally, equivalent plastic strain at failure, ε , is obtained by c ¼ ðÞθ −θ ðÞ f q k B A 28 using experimental methods [66]. By employing the continuous chip formation analyzing methods, it is possible to determine stain at fail- where qc is the conductive heat flux crossing the interface from point ure without making any experiment. Observing the movement of ma- A on the workpiece to point B on the cutting tool; k is the gap conduc- terial points on the chip underside and the machined workpiece tance; and θ is the nodal temperature on the surface. surface in steady-state chip formation process, a separation area of Therefore conductive heat flux is temperature dependent. Both the workpiece material could be found. heat flux components are varying from node to node and the basic The velocity of material points at workpiece nodes on the chip un- nodal heat flux data can be obtained from the chip formation analysis. derside and the machined surface is shown in Fig. 5, the separation The calculated heat flux on the tool surface that represents the in- area is between Node 1 and Node 3. The material above the separation terface heating from the chip/workpiece objects was applied as cus- tomized thermal boundary conditions on the contact elements. For (a) the initial process (b) the cutting process Stress-Max σ Principal max/MPa 1540 917 292 Rake face -333 Node 4 Node 3 -958 Node 1 Node 2 -1580 -2210

Dividing node Flank face -2830 -3460

Fig. 4. Finite element meshing of the deformation zone in the initial and cutting Fig. 5. Velocity of material points at workpiece nodes on the chip underside and the process. machined surface. B. Li / Int. Journal of Refractory Metals and Hard Materials 35 (2012) 143–151 149

Stress-Max σ Principal max/MPa 1540

917

292

-333 Node4 -958 Node3 Node1 -1580 Node2 -2210

-2830

-3460

Fig. 6. Max principal stress displayed with point tracking technology.

this purpose, a user subroutine was developed [69,70]. Fig. 7 plots wherew_ is nodal average wear rate; wt_ ðÞis the nodal wear rate; Ζ is the distribution of temperature on the chip and tool face at steady the time span of one milling cycle; i is the nodal label; and j is the state in different cutting speeds by the finite element analysis. The milling cycle number. cutting tool is aluminum based ceramic tool, and the workpiece is It is very difficult to get the function of nodal wear rate. But nodal AISI 1045 steel, and the simulation is with the following parameters: wear rate values at some discrete time points can be obtained by sam- cutting speed v=160–320 m/min, cutting depth ap =0.2 mm, and pling cutting process variables during chip formation and heat trans- feed rates f=0.1 mm/r. fer analysis and then calculating the individual nodal wear rate As the chip flow and tool temperature solutions were obtained in values. Based on these nodal wear rate values, an approximate two separate phases, the process variables for the chip/workpiece and nodal average wear rate can be calculated by following Eq. (30). the tool had to be combined by an external program to display the results in their entirety in the post-processor [71]. Pn _ þ _ ⋅ − ⋅ 1 wðÞi;j;k wðÞi;j;kþ1 tkþ1 tk 2 4.3. Nodal wear rate calculation 1 w_ ¼ ð30Þ ðÞi;j Z Nodal wear rate varies with the cutting time. In the cutting phase, tool wear takes place under the contact of the tool with the work- where n means that the entire milling cycle is divided into n−1 small piece. In cooling phase, nodal wear rate is equal to zero and no portions by n evenly spaced time points; k is the time point number; wear produced. Nodal average wear rate is calculated by Eq. (29) [32]. and nodal wear rate is calculated at every time point. In the real calculation, sampling of cutting process variables and the calculation of nodal wear rate are not performed in the entire milling cycle because no wear takes place in the cooling phase. þ t0 Z _ ∫ wðÞ; ðÞt dt _ t0 i j wðÞ; ¼ ð29Þ i j Z 4.4. Tool wear prediction on rake and flank face

The tool wear on the rake face and tool tip normally follows a crater shape in the cross section. Therefore, tool rake adjustments by (a) 160 m/min (Tmax =699°C) (b) 320 m/min (Tmax =1040°C) moving individual surface nodes in the normal direction can be used to account for varying wear depths along the tool rake face. The wear depth for each node is described by its nodal wear rate alone, as the wear rate (volume loss per unit area per unit time) is equivalent to the wear depth under the two-dimensional condition.

Therefore, for the given cutting time increment Δtk =tk + 1 −tk, the nodal displacement caused by tool wear between two simulation cy- cles can be approximated by Eq. (31) [24].

Fig. 7. Distribution of temperature on the chip and tool face at steady state in different Δ ¼ _ ⋅Δ ; ¼ ; …; ð Þ cutting speeds. di;k wi;k tk i 1 N 31 150 B. Li / Int. Journal of Refractory Metals and Hard Materials 35 (2012) 143–151

Node displacement s /µm 2

1.78 Rake face 1.56

1.33 KT 1.11 Node k 0.89 Node k Node i(xi,yi) 0.67

Node i+1(xi ,yi ) KM +1 +1 0.44

Flank face 0.22 VBB 0

Fig. 8. Tool wear prediction on rake and ﬂank faces.

_ where wi;k isthewearrateforthenodei at time tk and is as- 2. The simulations using a cutting tool with constantly updated rake sumed to be constant throughout the time period Δtk. N is the face and flank face geometries have shown that it is possible to total number of the contact nodes. Δdi,k the nodal displacement predict the evolution of tool wear at any given cutting time from for the node i corresponding to Δtk. The total wear depth for the FEM simulations by using the methodology proposed in this study. node i is thus equal to the vector sum of all incremental nodal 3. As the chip flow and tool temperature solutions were obtained in displacements associated with the node i throughout the total two separate phases, the process variables for the chip/workpiece cutting time. and the tool had to be combined by an external program to display Individual nodal movement method can also be applied to the tool the results in their entirety in the post-processor. flank face, if the obtained nodal wear rates on the flank wear land are uniform so that a realistic flat flank wear land can be generated. A re- Acknowledgments lationship between the flank wear rate w_ and the flank wear width fi fi VBB was derived from their geometrical de nition. For an in nitesi- The work described in this paper is supported by the National mal time increment dt, the increase in VBB can be expressed by Natural Science Foundation of China (No. 51105188), the Natural Eq. (32) [25]. 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