A review of cutting tool life prediction through flank wear monitoring

Abstract

Purpose

The aim of this paper is to review the literature on the prediction of cutting tool life. Tool life is typically estimated by predicting the time to reach the threshold flank wear width. The cutting tool is a crucial component in any machining process, and its failure affects the manufacturing process adversely. The prediction of cutting tool life by considering several factors that affect tool life is crucial to managing quality, cost, availability and waste in machining processes.

Design/methodology/approach

This study has undertaken the critical analysis and summarisation of various techniques used in the literature for predicting the life or remaining useful life (RUL) of the cutting tool through monitoring the tool wear, primarily flank wear. The experimental setups that comprise diversified machining processes, including turning, milling, drilling, boring and slotting, are covered in this review.

Findings

Cutting tool life is a stochastic variable. Tool failure depends on various factors, including the type and material of the cutting tool, work material, cutting conditions and machine tool. Thus, the life of the cutting tool for a particular experimental setup must be modelled by considering the cutting parameters.

Originality/value

This submission discusses tool life prediction comprehensively, from monitoring tool wear, primarily flank wear, to modelling tool life, and this type of comprehensive review on cutting tool life prediction has not been reported in the literature till now. The future suggestions provided in this review are expected to provide avenues to solve the unexplored challenges in this field.

NomenclatureRUL

remaining useful life

CBM

condition-based maintenance

N

spindle speed

V_c

cutting speed

f

feed rate

f_z

feed per tooth

a_p

depth of cut during turning

a_a

axial depth of cut during milling

a_r

radial depth of cut during milling

CNC

computer numerical controlled

ANN

artificial neural network

CNN

convolutional neural network

LSTM

long short-term memory

SBULSTM

stacked bi-directional and uni-directional long short-term memory

SDV

standard deviation value

RMS

root mean square

IMF

intrinsic mode function

EMD

empirical mode decomposition

HHT

Hilbert-Huang Transform

PCA

principal component analysis

RSM

response surface methodology

PSO

particle swarm optimization

ANOVA

analysis of variance

MCS

Monte Carlo simulation

FORM

first order reliability method

SSM

state space model

HMM

hidden Markov model

AFT

accelerated failure time

MAPE

mean absolute percentage error

AI

artificial intelligence

MIMO

multi-input-multi-output

FIS

fuzzy inference system

SVR

support vector regression

SVM

support vector machine

CGA

chaotic genetic algorithm

BPNN

back propagation neural network

SAE

sparse autoencoder

DTL

deep transfer learning

DBiLSTM

deep bidirectional long short-term memory

MAE

mean absolute error

RMSE

root mean square error

SAL

sparse augmented Lagrangian

GPR

Gaussian process regression

BRNN

bidirectional recurrent neural network

BiLSTM

bidirectional long short-term memory

BiGRU

bidirectional gated recurrent unit

DT

digital twin

BNN

Bayesian neural network

CSBLSTM

convolutional stacked bidirectional long short-term memory

TSAM

time-space attention mechanism

1. Introduction

In machining operations such as turning, milling, drilling and so on, the cutting tool serves a significant role. Tool failures in terms of tool wear and breakage affect the manufacturing process adversely (Li et al., 2020). Generally, a machining process consists of two crucial components, i.e. the machine tool and the cutting tool (Salonitis and Kolios, 2020). Despite the developments of machine tools and coating technologies, the failure of the tool in the form of wear creates major challenges in cutting processes as tool wear impacts product quality, production time and machining cost adversely (Zaretalab et al., 2020). The main purpose of the life prediction of the cutting tool is to ensure the maximum possible usage of the tool before failure (Salonitis and Kolios, 2020). Cutting tool life assessment enables prompt replacement of degraded tools. It reduces waste and tool costs. A better surface finish can be obtained if the tool is replaced on time (Chen et al., 2011). A worn tool results in the deformation of the machined surface up to a great depth, and it tears the surface. It impairs the fatigue property of the workpiece. In extreme cases, it results in the rejection of the workpiece or damage to the machine tool (An et al., 2020).

Based on research findings, tool failures constitute around 20% of the overall occurrence of machine tool failures. Moreover, the costs associated with tool maintenance account for a substantial proportion, varying from 15% to 40%, of the total production expenses (Sun et al., 2024). In the absence of accurate predictions of tool life, the general practice is to replace the tool with consideration of high safety factors by relying on the operator’s experience (Salonitis and Kolios, 2020). In industry, tools are often replaced well in advance (utilisation of expected tool life is only 50–80%) to prevent tool failure and their impact on machining (Salonitis and Kolios, 2014). Early and frequent tool replacement will lower production continuity, increase downtime and negatively impact cutting efficiency (Zhang et al., 2023).

The phenomenon of tool wear causes an elevation in cutting forces and temperatures, ultimately leading to a decrease in the surface quality of the product. Tool predictive maintenance is crucial in ensuring the machining quality. Estimating the RUL, i.e. the time from the present state to the failure state, is one of the objectives of predictive maintenance (Wu et al., 2023b). Condition-based maintenance (CBM) has been suggested as a suitable technique for mitigating unanticipated tool failure. To implement the CBM, the RUL estimation of the cutting tool is one of the key steps (Li et al., 2020). For known machining sequences, tool inventory planning can be done if the tool replacement time becomes possible to estimate (Tail et al., 2010). Therefore, accurately predicting the life or RUL of the cutting tool is essential for effectively managing quality, cost, tool life, availability and waste in machining operations.

So, accurate estimation of tool life and performance monitoring during machining are important. Many attempts have been made to develop methodologies for predicting the life or RUL of the cutting tool. Generally, these prediction methods can be categorised into physics-based, empirical, stochastic methods using probabilistic and reliability analyses, data-driven and hybrid models. In the subsequent parts of this literature, the authors have critically reviewed the available literature on cutting tool life prediction with some basic discussions on tool failure and tool wear.

1.1 Tool wear

In the process of machining, tool wear arises due to the chemical, thermal and mechanical interactions between the tool and the workpiece. Flank wear and crater wear are the two main types of tool wear that define the end of tool life. The performance of the machining process is usually associated with the extent of flank wear, as it impacts both the life of the tool and the surface quality and dimensional accuracy of the workpiece (De Barrena et al., 2023; Siddhpura and Paurobally, 2013). So, usually, the time to reach a threshold value of flank wear width during machining is considered for defining the tool life. Figure 1 shows the crater and flank wear.

The three primary mechanisms responsible for tool wear are abrasion, adhesion and diffusion. They are typically found in combination (Hanachi et al., 2019). It is important to acknowledge that other external manifestations of straining, including plastic deformation and the development of cracks, can be observed on the cutting wedge (Monkova et al., 2020). However, the present study focuses on reviewing the literature that primarily aimed to estimate the life or RUL of the cutting tool through flank wear monitoring.

1.2 Tool life

The life of the cutting tool can be expressed in different ways:

1. Metal removed volume

2. Quantity of machined workpieces

3. Time units

ISO 3685:1993 explains that when a tool fails to make parts with the required dimension and surface finish, the tool is considered to have crossed the useful tool life (Gokulachandran and Mohandas, 2015a). For a uniformly worn flank face, the machining time to reach the 0.3 mm average flank wear width value is considered the tool life. If the flank face is not regularly worn, then the maximum flank wear width value of 0.6 mm is considered the threshold value (Siddhpura and Paurobally, 2013). The failure criterion for drill tools is considered as the time at which the maximum flank wear reaches 0.6 mm (Tail et al., 2010). As per ISO 8688-2, during end milling of steel, 0.3 mm averaged flank wear over all the teeth is taken as the tool life criterion if flank wear is uniform; otherwise, 0.5 mm flank wear on any individual tooth is considered if flank wear is localised (Alauddin et al., 1997). The flank wear threshold value of 0.2 mm is used as the tool life criterion for end mill tools as per ISO 3002/1 (Tsai et al., 2005).

In general, the sequences of operations performed during cutting tool life prediction generally involve monitoring flank wear by considering the time to reach the threshold flank wear width value and then modelling the tool life by following different approaches. This paper reviews the available literature on flank wear monitoring and cutting tool life modelling approaches. The subsequent sections of this paper are structured as follows: The methodology for exploring the literature corpus and identifying the relevant studies is mentioned in Section 2. Section 3 outlines the experimental setting and procedure used in the literature to forecast the life or RUL of the cutting tool. In Section 4, tool condition monitoring methods used in the literature are mentioned. Section 5 describes the various approaches used in the literature for modelling and predicting the life or RUL of the cutting tool. In Section 6, challenges and opportunities, along with some future research suggestions, are mentioned. Finally, Section 7 provides the conclusions.

2. Literature review methodology

2.1 Search methodology

Scopus and Web of Science databases were used to get the literature corpus. Journal articles published in English from inception to March 13, 2024, were investigated for consideration in the present study. The search strategy in the Scopus database is as mentioned below.

(TITLE-ABS-KEY (“life estimation” OR “life measurement” OR “life prediction” OR “modelling of tool life” OR “prediction of cutting tool life” OR “prediction of tool life” OR “prediction of remaining useful life” OR “prediction of the remaining useful life” OR “rul prediction” OR “reliability analysis” OR “reliability assessment” OR “reliability estimation” OR “reliability evaluation” OR “reliability prediction” OR “replacement time”) AND TITLE-ABS-KEY (tool OR tools) AND TITLE-ABS-KEY (machining OR cutting OR manufacturing OR turning OR milling OR drilling OR boring OR reaming OR grinding OR slotting OR honing) AND ALL (wear OR flank)).

The search strategy in the Web of Science is as mentioned below.

“life estimation” OR “life measurement” OR “life prediction” OR “modelling of tool life” OR “prediction of cutting tool life” OR “prediction of tool life” OR “prediction of remaining useful life” OR “prediction of the remaining useful life” OR “RUL prediction” OR “reliability analysis” OR “reliability assessment” OR “reliability estimation” OR “reliability evaluation” OR “reliability prediction” OR “replacement time” (Topic) and tool OR tools (Topic) and machining OR cutting OR manufacturing OR turning OR milling OR drilling OR boring OR reaming OR grinding OR slotting OR honing (Topic) and wear OR flank (All Fields).

Besides exploring the reference list of the included studies, the literature that cited the included studies was also explored, and the relevant articles were incorporated into this review.

2.2 Criteria for eligibility

The chosen studies for this review exclusively focused on machining operations, including turning, milling, drilling, boring and slotting. The study necessitated the utilisation of tool condition monitoring and/or tool life or tool RUL prediction models such as physics-based models, empirical models, stochastic methods using probabilistic and reliability analyses, data-driven models and hybrid models. This review primarily considered literature that utilised the threshold flank wear value as the criterion for tool failure.

No restrictions were imposed on the tool wear monitoring technique, thus encompassing both direct and indirect approaches to tool condition monitoring. Likewise, various approaches employed within each modelling method were also taken into account.

Omitted from the analysis were studies that demonstrated similarity to the included studies or were not authored in the English language. The publications that were deemed more pertinent to the subject matter of this review paper were taken into account to ensure a comprehensive examination of diversified techniques of modelling the life or RUL of the cutting tool.

2.3 A summary of the included studies

A total of 88 articles are referred for this review, including four review papers (Lei et al., 2018; Mohanraj et al., 2020; Siddhpura and Paurobally, 2013; Xiao et al., 2022). The publication years and geographical sources of the referred publications are depicted in Figures 2 and 3, respectively. The data presented in Table 1 shows the distribution of referred publications classified by journals.

A total of 84 articles were considered for detailed review. Among the literature considered in the section on experimental setup and procedure, machining tests involved turning in 22 publications, milling in 18 publications, drilling in 2 publications, boring in 1 publication and slotting in 1 publication, as mentioned in Figure 4. Techniques resembling the direct method of tool condition monitoring were utilised in 10 articles among the literature analysed in the section on tool condition monitoring methods. As shown in Figure 5, publications mentioning indirect techniques of tool condition monitoring by acoustic emission, cutting force, vibration signal, power, current, torque and sensor fusion were 2, 3, 6, 1, 3, 1 and 4 in number, respectively. Under tool life or tool RUL modelling and prediction methods, the stochastic method involving probabilistic and reliability analyses was used by 26 studies, the data-driven model was applied by 20 studies, the empirical model was used by 12 studies, the physics-based model was used by 5 studies, and hybrid model was used by 5 studies as shown in Figure 6.

3. Experimental setup and procedure

This section discusses the experimental setup, i.e. machine tool, workpiece, cutting tool and tool wear monitoring methods used in the literature, along with the experimental design and input parameters taken for the estimation of the life or RUL of the cutting tool. Figure 4 shows the classification of the number of publications considered in this section based on machining types. The data presented in Figure 4 is derived from Table 2.

The discussions on the experimental setup used in the literature are clustered according to the tool life modelling methods in the below paragraphs.

Oraby and Hayhurst performed 24 experiments with the adoption of the central composite design technique by varying the V_c, f and a_p on a centre lathe during dry machining of alloy steel EN19 by using triple coated (1 µm TiN, 3 µm Al₂O₃, 5 µm TiC) carbide inserts. The tool life criterion was the average of the nose, flank and notch wear equal to 0.25 mm. The cutting forces in three directions were measured through the strain gauge dynamometer (Oraby and Hayhurst, 2004). Yin et al. performed wet machining of austenitic stainless steel (1Cr18Ni9Ti) on a CNC lathe by using the Al₂O₃/TiC micro-nano-composite ceramic tool for three levels of V_c, f and a_p, respectively. Optimal machining parameters were obtained for the maximum amount of removed metal by using range analysis. It was discovered that the fatigue behaviour of the tool controlled the cutting tool’s life at the optimum values of cutting parameters (Yin et al., 2015). In order to construct analytical tool wear models for the purpose of predicting tool life, Sagar et al. performed machining tests by turning tungsten heavy alloy (90 WHA) using uncoated carbide inserts with two different rake angles, that is, −5 and 2°. The experiments were carried out under dry conditions. The machining parameters were constant in these tests, and the tool failure criterion was tool flank wear of 600 µm. During the experiments, measurements were taken for cutting forces, temperatures and surface roughness values simultaneously at particular time intervals (Sagar et al., 2021).

Chao and Hwang considered V_c, f, a_p, rake angle of the tool, hardness and composition (% of C, Si, Mn, P, S, Cu, Ni and Cr) of the workpiece as input variables. A total of 60 runs of dry orthogonal turning were performed on a traditional lathe, and times to reach 0.7 mm maximum flank wear on steel tool T-15 inserts were observed during machining of AISI S1017C and S1045C workpieces (Chao and Hwang, 1997). Alauddin et al. planned 24 experiments of slot milling under central composite design by taking five levels of V_c, f_z and a_a, respectively. The slot milling operations were performed on cold-rolled steel by using slot drills made of high-speed steel in a vertical milling machine, and the time to reach 0.5 mm maximum flank wear (tool life criterion as per ISO 8688-2) on the end tooth was measured (Alauddin et al., 1997). Dos Santos et al. selected four sets of V_c, f_z and depth of cut to get the Extended Taylor’s tool life equation’s coefficients and performed dry face milling on AISI 1045 rolled steel in CNC milling by using triple-coated cemented carbide inserts. The criterion for tool life was regarded as a maximum flank wear value of 0.7 mm. Five tests were performed, in addition, to improve the reliability of Taylor’s equation (Dos Santos et al., 1999). Axinte et al. considered 2³⁻¹ fractional factorial design by taking each of V_c, f and a_p at two levels to ascertain the extended Taylor’s equation’s coefficients. The turning experiments were performed using six different cutting fluids on a CNC lathe, where the workpiece material was 316L stainless steel, and the insert specification was TNMG160408QM. The tool life standard was considered to be 0.3 mm flank wear as per ISO 3685: 1993 (Axinte et al., 2001). To get the effects of cutting parameters, Ojha and Dixit initially adopted the 2³ full factorial design, and then the levels were modified according to the effects of V_c, f and a_p. The rolled steel bar was turned under the dry condition in the HMT-made NH-26 lathe using TiN-coated tungsten carbide inserts for various machining conditions. The wear on the tool was noted with the completion of each machining pass, and the time for threshold flank wear (0.8 mm) was obtained by extrapolating the wear-time curve (Ojha and Dixit, 2005). Tsai et al. conducted high-speed milling on SKD61 tool steel blocks by utilising the cemented tungsten carbide tool with the TiAlN coating under varying V_c, f_z and a_a. As per ISO 3002/1, the flank wear width of 0.2 mm was taken as the threshold (Tsai et al., 2005). To mitigate the limitations of the traditional design of experiments techniques, the group method of data handling was adopted for eleven input parameters (nine parameters related to the geometry and two regime parameters) with five levels of each. The deep-hole gun drilling was performed on malleable cast iron using carbide K30 tips. The tool life criterion was the average flank wear width of 1.0 mm. In extreme cases, exorbitant tool vibration and/or squeal were also considered the criteria of tool life (Astakhov and Galitsky, 2005). To train the artificial neural network (ANN), Natarajan et al. performed machining on a precision high-speed VDF lathe by varying the V_c, f and a_p. The workpiece material and the cutting tool were high carbon steel and tungsten carbide, respectively. The flank wear value of 0.3 mm was considered the tool life benchmark, and machining was stopped depending on the length of cut to observe the flank wear through a tool maker’s microscope (Natarajan et al., 2007). Sahin selected the L₉ orthogonal array to study the influences of V_c, f and the hardness of the tool material on the tool life. A CNC lathe was used to conduct the tool life testing using three types of cutting tools: mixed alumina ceramic, coated ceramic, and CBN. The workpiece material was hardened AISI 52100 bearing steel, on which the finishing operation was performed. With the consideration of 0.3 mm flank wear as the tool life standard, the flank wear was measured at 5, 10, 15 and 30 min of machining (Sahin, 2009). For the machining of iron-nickel-based superalloy N-155 on a CNC lathe for 5 levels of V_c and f, carbide tools with TiAlN coatings through the PVD method were used. For experimental design, the central composite design was adopted. With the tool life criteria as per ISO 3685 (1993), tool wear was observed at particular time gaps through a toolmakers’ microscope to check the attainment of the threshold flank wear width (Davoodi and Eskandari, 2015). To develop the tool life prediction model during the turning of high-strength vermicular graphite cast iron, Lin et al. performed a single-factor turning test, and the test was continued until the average wear bandwidth value of the tool’s flank exceeded 0.3 mm (Lin et al., 2020).

Hitomi et al. considered the tool wear value as a criterion for reliability analysis of the cutting tools and performed tool life tests on carbon steel billet by using carbide cutting tools in a high-speed lathe under dry conditions. They performed experiments at two levels of V_c, f and a_p to determine the tool wear distribution (Hitomi et al., 1979). Klim et al. performed climb face milling on stainless steel 17-4PH by using SEM 43A (ANSI) triple-coated inserts. Flank and crater wear were measured at particular time intervals for constant feed as well as variable feed operations to construct the reliability model of the cutting tool (Klim et al., 1996). Lin performed face milling operations on stainless steel by using carbide UTi20T, and chipping on the rake face of the cutting tool was considered the tool life criterion. It was monitored through an optical microscope. In cases of no chipping, the flank wear width of 0.3 mm was taken as the tool life benchmark (Lin, 1998). To establish the accuracy of the reliability-dependent failure rate model (AE model), Wang et al. conducted tool wear experiments in a heavy-duty lathe under dry conditions. The workpiece material was high carbon steel S55C, and the insert was sintered carbide. With the consideration of 0.3 mm as the limiting value of flank wear, the experiments were performed for five levels of V_c, though f and a_p remained constant (Wang et al., 2001). Tail et al. performed machining on a metallic-matrix composite of GRA-Ni by using titanium nitride coated steel drills under dry conditions and examined how cutting speed affects tool life. Three levels of spindle speed were considered, and other parameters were kept constant. The maximum flank wear value of 0.6 mm was taken as the benchmark for tool life (Tail et al., 2010). In a vertical lathe, Vagnorius et al. conducted machining tests on Inconel 718 using CBN inserts at a specific value of V_c, f and a_p. The maximum width of flank wear on the minor flank face of 0.6 mm was considered the tool life criterion. The insert was removed after, on average, 32 s of machining to check the wear through a toolmaker’s microscope, and the procedure was continued until the tool life criterion was reached. In this manner, a total of 12 cutting edges were tested (Vagnorius et al., 2010). Salonitis and Kolios considered V_c and f at three levels each and performed dry turning of high carbon steel C55E on a high-speed CNC machine tool. The cutting tool was the tungsten carbide insert. With the consideration of 0.3 mm flank wear as the threshold, periodic measurements of the flank wear were carried out using an optical microscope (Salonitis and Kolios, 2014). Aramesh et al. performed semi-finishing turning operations on the titanium metal matrix composite superalloy using coated carbide inserts. By selecting both the V_c and f at three levels, experiments were performed on a 5-axis Boehringer NG 200 CNC turning centre with the adaptation of the 2² experimental design, in which one additional centre point was considered. By taking into account the initial, steady and rapid tool wear phases, the reaching of the maximum flank wear length of 0.2 mm in the third phase served as the tool life criterion (Aramesh et al., 2016). The experimental design followed the Box-Behnken design to investigate the impact of cutting parameters on the distribution parameters of tool life. A total of 65 experiments, i.e. 13 experiments with 5 replicates, were performed on CNC milling, where three levels of N, f and depth of cut were considered. The workpiece material was steel AISI 304, and the cutting tool was the cemented carbide insert. The machining kept going until the maximum flank wear width reached 0.3 mm (Zaretalab et al., 2018). Liu et al. performed the experiments in two stages. In the first stage, to get optimum cutting parameters, a two-dimensional tool wear map was constructed by changing V_c and f during Inconel 625 machining by using PVD-TiAlN-coated carbide tools with traditional cooling on a CNC lathe. By considering the flank wear width value of the tool and the surface quality of the worked surface, optimum cutting speed and feed rate were obtained. After that, 12 inserts were machined in the second stage under optimum cutting conditions by considering the tool life benchmark as either the 0.6 mm flank wear value or tipping of the tool edge (Liu et al., 2020). To depict the variation pattern of cutting forces with the flank wear, Salonitis and Kolios performed up milling operations on Ti-6Al-4V alloy by using PVD and CVD-coated inserts using oil-based commercial coolant fluid. Six sets of experiments were performed for several values of V_c and f_z. Cutting forces were measured using a piezoelectric multi-component dynamometer during the experiments. The measurement of tool wear was conducted using an optical microscope at regular intervals. The ISO 3685:1993 standard was referred to for this flank wear measurement (Salonitis and Kolios, 2020). To establish the reliability of ceramic tools in terms of the mechanical characteristics of the tool material, Xu et al. tested the Vickers hardness and indentation fracture toughness of Si₃N₄-based ceramic tools. The tool life for 25 tool tips was measured during the machining of quenched carbon steel T10A in a CNC lathe under dry conditions at a particular V_c, f and a_p (Xu et al., 2021). Das et al. performed dry turning experiments on the Inconel 800 workpiece using PVD-coated carbide inserts at three levels of V_c, f, a_p and tool nose radius following the Taguchi L₉ experimental design. Tool condition after each machining pass was measured through an optical microscope (Das et al., 2024).

At a particular V_c, f and a_p, Chen et al. machined the steel bar by using diamond carbide tools on a CNC lathe. The threshold flank wear width was considered to be 0.6 mm, as per ISO 3685. The wear was assessed through a micro-optical system featuring a built-micrometer, a CCD camera and an LED light. The tool vibration was observed through the accelerometer (Chen et al., 2011). On AISI 1060 steel, the face milling operation was carried out in order to forecast the cutting temperature and tool life. The input parameters were V_c, f_z, depth of cut and flank wear. Five levels of each input parameter were considered. Tool wear and temperature change on the flank face were measured by a digital microscope and a Cr-Ni thermocouple, respectively. For experimental design, the four factorial 2k central compositional experimental plan was applied (Kovac et al., 2014). Li et al. considered 0.6 mm flank wear as the threshold value and performed milling experiments on the FV520B workpiece at a particular cutting condition with four different milling cutters in a CMV 850A machining centre (Li et al., 2015). With the adoption of the Taguchi L₁₈ orthogonal array for three levels of N, f and depth of cut, IS2062 steel was machined in a vertical milling machine by using uncoated tungsten carbide inserts. The time to reach 0.6 mm flank wear width was considered the tool life standard, and the measurement of flank wear was done by the ARCS video measuring machine (Gokulachandran and Mohandas, 2015b). To get the features that were sensitive to tool wear, Sun et al. did end milling experiments on a steel workpiece by using the carbide tool for four levels of N, f and depth of cut by adopting the orthogonal experimental plan. Three force sensors, three accelerometers and one acoustic emission sensor were used to collect the signals. The portable data acquisition system acquired signals from the sensors, and flank wear was quantified by a small tool microscope (Sun et al., 2016). The RUL prediction of the cutting tool using health index similarity was verified by using the data obtained from the slotting operation of a special turbine rotor in a manufacturing facility. The workpiece material was 30Cr2Ni4MoV, a structural steel with low alloy and high strength. Seven J1-formed slotting cutters, made of high-speed steel, were used for a particular N and f. The acoustic emission signals were obtained from an acoustic emission senor that was mounted on the rotor, and the flank wear value was monitored after each cutter's lifespan through an optical microscope. The failure time was reached when the cutter was unable to guarantee the quality of the workpiece, and all seven cutters were used until failure (Liu et al., 2019). Four sets of studies with boring tool blades were completed with the consideration of rotating speed, f and cutting depth as input parameters. By adopting the indirect method of tool condition monitoring, the torque signal was used to monitor the process. For the tool life criterion, reaching flank wear at the blunt standard was considered (Zhou et al., 2019). Yang et al. performed the down-milling operation without cutting fluid on the TC4 workpiece by using solid carbide and coated cemented carbide tools at two levels of V_c, f_z and a_r, respectively. The average values of the flank wear on the 4 teeth were observed, and when these values reached 0.4 mm, the tools were considered failure as per the ISO 3685 standard (Yang et al., 2019). To verify the effectiveness of the suggested RUL model of the cutting tool, Li et al. performed experiments on the stainless steel workpiece for two levels of feed and depth of cut in a milling machine. The V_c was kept constant. All experiments were continued until the end of the useful life of the tool inserts. Two vibration sensors, two acoustic emission sensors and two motor current sensors were installed on the machine tools for condition monitoring. The collection of sensor data was achieved by a data acquisition board (Li et al., 2020). To experimentally verify the convolutional neural network-stacked bi-directional and uni-directional long short-term memory (CNN-SBULSTM) network in RUL prediction, different spindle speeds, feed rates and tool coatings were considered during milling of the TC4 workpiece. The cyber-physical system was adopted to monitor spindle power and tool position from the PLC controller. The vibration and current signals were collected from the accelerometer and current sensors, respectively (An et al., 2020). To verify the accuracy of the cutting tool RUL prediction approach using the Hurst exponent and CNN-LSTM, Zhang et al. utilised the 2010 PHM Society Conference Data Challenge dataset. The dataset comprised milling of stainless steel under dry conditions at a particular N, f, a_a and a_r on a high-speed CNC machine by using six ball nose tungsten carbide cutters, each comprising 3-flutes. The force, vibration and acoustic emission sensors were utilised to get the sensor signals, and the flank wear of each flute was measured by microscope after each cut (Zhang et al., 2021). De Barrena et al. performed 12 experimental trials on the 19NiMoCr6 steel workpiece using the P25 grade uncoated inserts at fixed cutting conditions (De Barrena et al., 2023). Bagga et al. performed turning experiments on the AISI 4140 steel workpiece using the PVD-coated carbide inserts. Three levels of V_c, f and a_p were considered, and the flank wear value of 0.4 mm was taken as the tool life criterion (Bagga et al., 2023). To validate a tool RUL model developed through a hybrid network based on the feature enhancement module (FEMNet), Wu et al. performed turning experiments on the 40Gr metal rod using a CNC machine tool. Vibration signals of the same kind of cutting tools under three different cutting conditions were collected, and the flank wear of the tools was measured in regular intervals through a stereo microscope (Wu et al., 2023a).

Zhang et al. carried out the plane milling operation on a specific kind of car brake disc made of cast iron HT200 to evaluate their hybrid model for tool RUL prediction by combining the CNN and multistage Wiener process. The milling cutter, made of a hard alloy, was used for cutting. Various working conditions were created by adjusting the N, cutting depth and f. Vibration data was collected using a three-axis sensor, while wear on the ball end milling cutter's four cutting edges was measured using an electron microscope. The milling cutter's actual wear was determined by the average wear of these edges. Initial, normal and severe wear states were used to categorise the tool wear states (Zhang et al., 2023). To validate the proposed nonlinear ensemble RUL prediction, Feng et al. conducted the experiment of milling cutters on a CNC machine where carbide milling cutters were used to mill the 45# steel workpiece under two different working conditions. During the experiment, the signals were collected through the accelerometer, current sensor, force sensor and free-field microphone. The tool wear width was measured with a vision microscope (Feng et al., 2024). To verify the proposed data-model linkage tool RUL prediction method, Li et al. performed milling experiments on the 508-III steel workpiece using the carbide-coated inserts without using the coolant. Tool wear conditions were monitored through vibration, acoustic emission, cutting sensors and an industrial camera (Li et al., 2024).

Table 2 summarizes the experimental setup found in the considered literature in chronological order.

4. Tool condition monitoring methods

The direct and indirect approaches can be used to check the condition of cutting tools (Zhou et al., 2019). In the direct method, the actual wear value is observed. Certain parameters correlating to flank wear are measured in an indirect method of tool condition monitoring (Chen et al., 2011; Siddhpura and Paurobally, 2013). Figure 5 displays the number of articles taken into consideration for this part according to different approaches to tool condition monitoring.

Below, both the direct and indirect approaches to tool condition monitoring are briefly covered.

4.1 Direct method

As the worn part of the tool has higher reflecting qualities, any type of wear can be directly quantified using the direct method. This approach makes it impossible to observe tool conditions online (Drouillet et al., 2016). Tool wear is evaluated using optical or image detection when utilising the direct technique (Zhou et al., 2019).

The wear on the tool was monitored through a toolmaker’s microscope at appropriate intervals (Alauddin et al., 1997; Amaitik et al., 2006; Natarajan et al., 2007). The experiment was stopped at a particular interval, and wear was measured through a microscope (Sahin, 2009; Vagnorius et al., 2010). The Olympus Camedia digital camera C-770 ultra zoom was used to get photographs of drills for every 10 mm of drilling operation. Through “Irfan View” software, the wear was measured from the captured photos (Tail et al., 2010). Without removing the insert or tool, flank and rake faces were photographed digitally under a handheld microscope (60x magnification) to track tool wear at particular time gaps. The width of flank wear was then measured against the threshold value using the calibrated digital pictures (Karandikar et al., 2014a). In each experiment, after machining the workpiece, the insert was withdrawn from the holder. As the machine vision system was able to analyse the tool wear, the threshold value of the flank wear, which was used as the criterion of tool life, was noticed by taking the picture of the cutting tool. This procedure was continued until the threshold value of tool wear was reached (Zaretalab et al., 2018). The turning operation of the RR1000 alloy was done using CVD-coated carbide inserts. The criterion for tool life was 0.2 mm. A wild microscope with a toolmakers table with digital micrometre heads was applied for tool wear measurement (Hood et al., 2018). The direct monitoring of tool wear using machine vision was proposed by Bagga et al. The monitoring system for tool condition was comprised of the image sensor, lens and lighting system (Bagga et al., 2023).

4.2 Indirect method

During the interaction of the cutting tool with the workpiece, physical phenomena such as plastic deformation and friction occur; thus, energy, in the form of vibration, heat, cutting forces, acoustic emission, etc., is discharged, and their consistent changes with the growing tool wear are observed (Zhang, 2011). So, through the indirect method, the process parameters, which are in correlation with flank wear, are monitored. Though this method provides a less accurate result than the direct method, online measurement can be done through this method with greater ease (Siddhpura and Paurobally, 2013). Through these methods, acoustic emission sensors, vibration sensors, cutting force sensors, or other types of sensors are used to examine tool working conditions, and by using signal processing technology, the extracted signals from the sensor data are utilised to obtain the actual physical condition of the cutting tool (Li et al., 2020). Sensor signals and signal processing techniques are crucial to the accuracy of an automatic tool condition detection system (Xiao et al., 2022).

4.2.1 Acoustic emission

Acoustic emission is an event in which the radiation of acoustic waves happens when the material undergoes deformation, metal cutting, or fracture (Mohanraj et al., 2020). As the acoustic emission signals have a relationship with the cutting tool’s wear, this signal can be used as an index to estimate the cutting tool’s reliability (Li et al., 2015). Acoustic emission sensors are less intrusive since their frequency range is significantly greater than environmental frequencies. Though cost and installation are favourable, in order to combat overload and non-voluntary noises, acoustic emission calibration is absolutely essential. Besides, the values of the sensor can be affected if the sensor is not mounted and located properly (Drouillet et al., 2016).

During the milling process, acoustic emission data and force signals were gathered to evaluate the cutting tool's flank wear. The signals were then processed using feature extraction. To create the cutting tool life model, acoustic emission signals in frequency domains with wavelet packet decomposition were used as input parameters (Li et al., 2015). The PCI-2-based acoustic emission configuration was utilised, and to measure the acoustic emission signals, the acoustic emission sensor was mounted on the turbine rotor, where slotting operations were performed. The signal data was obtained and saved on the computer's hard disc using the AEwin software. The captured acoustic emission signals were time series data sampled at 1 MHz. Data mining was done to obtain pertinent information for creating health indexes (HIs) because of the voluminous and noisy nature of the raw data (Liu et al., 2019).

4.2.2 Cutting force

In the monitoring of tool condition, cutting force is often thought to be the most sensitive indication of tool wear. The cutting forces often rise with tool wear (Jain and Raj, 2017; Li et al., 2020). Cutting force-based tool condition monitoring has significant limitations, however, including sensor cost and mounting issues (Ghosh et al., 2007).

The force signals were collected by the dynamometer during the milling of TC4. The frequency with which the sampling was carried out was 1,000 Hz. The cutting force's root mean square value (RMSV), average value (AV) and standard deviation value (SDV) all exhibited an increased trend during the time domain analysis stage, along with a rise in flank wear. Eight frequency band energy values and the SDV of four frequency band energy values were examined during the wavelet analysis. The correlation coefficients of these characteristic quantities were studied. Then, the characteristic quantities were utilised to estimate the RUL of the cutting tool (Yang et al., 2019). Forces were sampled at a rate of 5 kHz during machining to illustrate the relationship between cutting force and flank wear. Noise from the structural modes on the force measurements was removed through the Kalman filter. After measurement, the signals were detrended, i.e. normalised. On the cutting force data, FFT (Radix-2 technique) and CWT (Morlet wavelet) analyses were carried out to acquire the pertinent features indicative of flank wear (Salonitis and Kolios, 2020). To generate the tool RUL prediction model, cutting force data in the X direction was used. The raw signals were processed to obtain the time, frequency and time-frequency domain features. The salient features in correlation with the tool degradation were selected by computing the monotonicity score (Wang et al., 2021).

4.2.3 Vibration signals

A vibration sensor is used as it is cost-effective and easy to implement for online monitoring (Chen et al., 2011).

During machining, vibration signals, as well as cutting tool wear, were quantified. Cutting tool wear-related characteristics were extracted from the vibration data by wavelet packet decomposition and correlation analysis. The salient features were combined in a logistic regression model to estimate the cutting tool reliability (Chen et al., 2011). By analysing vibration signals, it was found that the trends of the root mean square (RMS) and peak of the time domain index were changing more obviously with the tool degradation during the finish turning of the carbon steel by ceramic inserts (Ding and He, 2011). During the cutting process, the cutting forces, tool vibrations and acoustic signals were recorded under specific circumstances and at a channel frequency of 50 KHz. Through the rise in vibration magnitude, RMS was able to identify the variance in cutting energy caused by tool wear. In order to track tool wear and forecast the RUL of the tool, the RMS of the vibration signals was used as a health index (Yu et al., 2017). During operation, vibration signals and cutting tool wear were measured. To extract the significant features, wavelet packet decomposition, time-domain statistics and correlation analysis were applied. The high-dimensional feature data’s dimension was reduced using the singular value decomposition method (Chen et al., 2019). In order to monitor vibration signals during turning, Wu et al. installed three integrated circuits piezoelectric sensors. The flank wear was measured through a stereo microscope (Wu et al., 2023a). A three-axis vibration sensor was employed to collect vibration signals at each phase of tool wear. The vibration data was first turned into a wavelet scalogram using a wavelet transform. The wavelet scalogram was then used to create a fixed-size RGB image. Because it exhibits a sharp contrast and accurately depicts the wear condition information for the milling cutting tools, the complex Morlet wavelet was chosen. The conditional variational autoencoder with CNN (CCVAE) network was employed to generate similar images to the initial ones, thereby achieving data augmentation. The expanded dataset from CCVAE was fed into the CNN model (Zhang et al., 2023).

4.2.4 Power

Due to the fact that an AC motor's power consumption is proportional to torque, power and cutting forces correlate with each other. Thus, there is a link between power sensor data and tool wear (Drouillet et al., 2016).

During the down milling operation of stainless steel by carbide tool inserts, the spindle power was recorded through a universal power cell that was integrated with the data acquisition system. The time domain root mean square power was obtained for each layer cutting. To estimate the RUL of the cutting tool, power sensor data was applied to train the neural network (Drouillet et al., 2016).

4.2.5 Motor current

Due to its relationship with cutting force, the spindle motor current is sensitive to cutting tool wear. Due to the adverse cost and installation of force-based devices, the spindle motor current offers a cost-effective alternative to cutting force in online tool condition monitoring (Hanachi et al., 2019; Li et al., 2020).

For the estimate of tool wear in face milling, the relevance vector machine was used to understand the relationship between tool flank wear and sensor fusion of spindle motor current AC and DC sections (Zhang, 2011). Both the time domain and frequency domain features were extracted from the spindle motor current sensors installed in the milling machine. To select the salient feature, the least absolute shrinkage and selection operator (LASSO) algorithm was performed. Kurtosis in the time domain was found to be the most sensitive feature to indicate tool wear (Li et al., 2020). Eleven time-domain features of the current signal were extracted by Feng et al. to train the BNN, and the Wiener process is modelled using the RMS (Feng et al., 2024).

4.2.6 Torque signal

One of the process monitoring signals that is associated with tool wear during machining is the torque signal. Though it is less sensitive to tool wear than the cutting force signal, the benefit of the torque signal is that it is less expensive and that installation and measurement are simple (Zhou et al., 2019).

Tool wear characteristics were gathered from the torque signal, which was used as a process monitoring signal to keep tabs on the condition of the tool. The amplitude average of the intrinsic mode function (IMF) decomposed by the empirical mode decomposition (EMD) and the large amplitude point in the Hilbert-Huang Transform (HHT) edge spectrum were used to build the feature vector of the tool wear (Zhou et al., 2019).

4.2.7 Sensor fusion technique

In this technique, features to estimate tool wear were taken from a number of machining zone signals by using several sensors (Ghosh et al., 2007; Mohanraj et al., 2020).

The wear condition of the tool was observed at a particular interval to check whether the flank wear threshold value was reached or not. At the same time, signals like cutting force, vibration and acoustic emission were acquired for 1 s with 20 KHz sampling frequency. By using the EMD method, each original signal was processed and divided into a number of IMFs. Some IMFs’ marginal spectra’s average and maximum amplitudes were retrieved and used as sensitive features. The sensitive features derived from the signals were used to form the characteristic matrix that described the in-process tool condition (Sun et al., 2016). During experimental runs, cutting forces, vibration and acoustic emission signals were collected for 1 s with 200 kHz sampling frequency. Each signal sample was divided into ten pieces of 0.1 s each. The raw signals were decomposed into some IMFs by using the EMD method. The sensitive features were obtained by calculating some singular value entropies (SVEs) (Sun et al., 2018). The vibration, force and acoustic emission signals were collected from sensors like accelerometers, dynamometers and acoustic emission sensors during the dry milling of stainless steel using tungsten carbide cutters with a 3-fluted ball nose. Then, the Hurst exponent-based signal partition method was used, and it resulted in higher accuracy for tool wear prediction than domain-feature extraction and principal component analysis (PCA) dimensionality reduction (Zhang et al., 2021). To monitor tool wear conditions during machining, three-directional vibration and acoustic emission sensors were positioned near the cutting area. Additionally, two sets of Hall current sensors were utilized to capture the currents of the machine spindle and feed motor, respectively, which can indirectly characterize the cutting force while avoiding interference with the machining operation. Tool wear measurements were conducted using an industrial camera after the completion of machining each layer of the workpiece material (Li et al., 2024).

Table 3 summarizes the tool condition monitoring methods.

5. Approaches used for modelling and predicting the life or RUL of the cutting tool

Diverse methods for modelling and forecasting the life or RUL of the cutting tool can be found in the literature. These approaches include:

1. Physics-based models

2. Empirical models

3. Stochastic methods using probabilistic and reliability analyses

4. Data-driven models

5. Hybrid models

Figure 6 shows the number of publications considered in this section based on tool life modelling methods.

5.1 Physics-based models

The physics-based models elucidate the processes of degradation by formulating mathematical models that are developed based on the failure mechanisms or the first principle of damage (Liu and Zhu, 2020). This method necessitates tool wear experiments to estimate the tool life model coefficients (Karandikar et al., 2021).

The connection between cutting tool lifespan and average flank contact temperature was verified through experiments involving the cutting of mild steel using H.S.S. tools. The assumption made was that the contact between the flank face of the tool and the workpiece occurs discretely, and the main mechanism for tool wear was adhesion. It was found that for a certain cutting tool-workpiece pair, the indices and constant of the expression are independent of cutting conditions. Then, the tool life analysis for orthogonal cutting was extended to oblique cutting (Venuvinod et al., 1990). It was discovered that tool wear mostly affected forces in the feed and radial directions. To develop a mathematical model of tool life with the input data and achieve the highest level of statistical significance through non-linear regression analysis, a ratio between the thrust component of force (which is the resultant of the feed and radial components of force) and the power component of force (which is the vertical component of force acting at the tool tip) was used (Oraby and Hayhurst, 2004). The failure types of the Al₂O₃/TiC micro-nano-composite ceramic tool were cutting edge breakage and tool material peeling off brought on by slow crack propagation in the ceramic tool while machining austenitic stainless steel (1Cr18Ni9Ti) under wet conditions. The tensile stress, induced by the cutting forces during machining, generated microcracks from the existing defects and also caused the propagation of cracks. The ceramic tool life was estimated by evaluating the fatigue tool life since the resistance to slow crack propagation and the fatigue nature of the tool material are closely related. The fatigue life of the ceramic tool under the applied stress $\sigma$ was stated as:(1)$t_f=B{\left(\frac{{\sigma }_i}{\sigma }\right)}^N\times {{\sigma }_i}^{-2}$where ${\sigma }_i$ was the inherent flexural strength. For a particular material and environment, $B$ and $N$ were the parameters that described slow crack growth. The thermal effects on the strength degradation of the cutting tool in wet cutting were ignored (Yin et al., 2015). A physical model was constructed to examine the impact of vibration on tool wear. The tool life was estimated by considering the fatigue resistance of the cutting tool material and the parameters of tool vibration. The static and dynamic characteristics of the cutting tool were studied in diverse machining settings using different cutting tools with various clamping types. Compared to cutting tools with wedge lock and lever lock types, the double clamp type of cutting tool produced better results (Ghorbani et al., 2018). Based on the observed wear mechanism, that is, adhesion, Sagar et al. considered four tool wear rate models for the prediction of flank wear growth and tool life. These models include Usui model, Matsumura model, Zhao model and modified Zhao model. The model constants were determined from experimental tests (Sagar et al., 2021).

Table 4 summarizes the physics-based models in tool life modelling.

5.2 Empirical models

In this method, the model coefficients are measured from the tool life experimental data (Karandikar et al., 2021).

From the tool life data for reaching 0.7 mm flank wear, a simple linear regression model was developed by considering all input variables. From the F-test and backward stepwise regression method, the significant and uncorrelated variables were obtained, and the normality test was performed to verify that. After that, the backpropagation neural network method was utilised to build the cutting tool life model from the screened variables. The suggested model was compared with the backward stepwise regression and the neural network methods by examining outliers, average error, standard deviation and the t-test. Though the proposed backpropagation neural network method was able to predict better results, it required more steps, as transformation or reconstruction of data would be required if the normality of the screened variables was not assured (Chao and Hwang, 1997). Tool life in terms of V_c, f_z and a_a was modelled by using the response surface methodology (RSM) in end milling of cold-rolled steel using slot drills made of high-speed steel, and the parameters were estimated through the least squares method (Alauddin et al., 1997). To obtain the coefficients of the Extended Taylor’s equation, an optimum experimental design was considered. The minimum value of the ratio of maximum and minimum singular values in the matrix of the tool life’s sensitivity to changes in the machining parameters served as the foundation for the experimental design. The confidence intervals for the coefficients were obtained using the maximum a posteriori sequential estimator. After nine tests, the mean percent error of the tool life was calculated, and the error was roughly 46%. However, the proposed experimental design made it possible to minimise the number of tests needed in comparison with the fractional factorial design (Dos Santos et al., 1999). From regression analysis using the least squares method, coefficients of the extended Taylor’s tool life equation were estimated for different cutting fluids, and tool life measurement uncertainty was quantified (Axinte et al., 2001). To reduce the consumption of resources, tool failure time was estimated through extrapolation by fitting a best-fit line to the steady wear zone data. With the use of neural networks, lower, upper and most likely estimates of tool life were obtained. Though some predicted values differed considerably from experimental values, tool life estimation was better than multiple regression (Ojha and Dixit, 2005). From the experimental data of high-speed milling under different cutting conditions, an optimal abductive network was developed by using a predicted squared error criterion to predict the tool life. The error in prediction was less than 10% (Tsai et al., 2005). A mathematical model was developed using the simplified algorithm of the group method of data handling. The model correlated the tool life with various regime and design parameters of the gun-drilling of cast iron. The range of regime parameters should be chosen properly so that resonance phenomena do not affect the drill’s performance. The model coefficients were obtained from the training data set. The complex nature of tool life was observed, which also depends on the interactions of the design and process variables (Astakhov and Galitsky, 2005). Using least squares regression analysis, factory data on milling cast iron was used to create a mathematical model of tool life. Though the first order tool life model considered V_c and f as input variables, the cutting depth was kept constant. The tool life contours were formed for five different cutting tool materials (Amaitik et al., 2006). To train the ANN from the experimental data, particle swarm optimisation (PSO) was applied. The input vectors comprised V_c, f, a_p and flank wear, whereas tool life was the output vector. The result was compared with the back-propagation method (Natarajan et al., 2007). To get the influences of cutting parameters on tool life, the 2³ full factorial design, taking each of V_c, f and a_p at two levels, was adopted. From the experimental data, the tool life model was obtained by adopting multiple regression analysis. V_c and the interaction of V_c and a_p had greater effects on tool life, respectively (Mehrban et al., 2008). To study the influences of cutting parameters, i.e. V_c and f, on tool life and volume of material removed during machining of superalloy, the RSM was adopted to construct the quadratic tool life model. The model’s adequacy was checked through the analysis of variance (ANOVA) (Davoodi and Eskandari, 2015). Lin et al. developed a tool life prediction model based on the grey theory for coated ceramic tools using a single-factor turning test (Lin et al., 2020).

Table 5 summarizes the empirical models in tool life modelling.

5.3 Stochastic methods using probabilistic and reliability analyses

This method generally assumes that the tool life or tool degradation process follows a certain distribution.

According to a chi-squared test of goodness of fit, tool wear followed a logarithmic normal distribution. Using the multiple regression technique, the distribution of practical tool wear was obtained. The estimation of cutting tool life values was then done by using point estimation and interval estimation. The distribution of tool wear was utilised to obtain the distribution of tool life as well as the reliability function (Hitomi et al., 1979). From the experimental data, a reliability model was developed by considering both flank and crater wear with the adoption of the Weibull distribution with two parameters. With the assumption that the events of flank and crater wear reaching the critical values are independent and exclusive, tool life was studied by considering the feed variation during machining of 17-4PH stainless steel in milling. The reliability formula was expressed as:(2)$R\left(t\right)=\exp \left[-{\left(\frac{t}{{\theta }_{VB}}\right)}^{b_{VB}}\right]P\left(VB\right)+\exp \left[-{\left(\frac{t}{{\theta }_{KT}}\right)}^{b_{KT}}\right]P\left(KT\right)$when the flank wear value (VB) exceeds the critical flank wear value (VB_max), the probability of this happening was given by $P\left(VB\right)$. Similarly, the chance of a situation where the crater wear value (KT) exceeds the critical crater wear value (KT_max) was denoted by $P\left(KT\right)$. $b_{VB}$ and $b_{KT}$ were the shape parameters of flank wear and crater wear life distributions, respectively. ${\theta }_{VB}$ and ${\theta }_{KT}$ were the scale parameters of flank wear and crater wear life distributions, respectively. It was found that there was an improvement in the reliability of the cutting tool during variable feed milling compared to constant feed operations (Klim et al., 1996). The reliability of the face milling tool was assessed using a three-parameter Weibull distribution, and the effects of cutting conditions were observed by considering chipping as a tool life criterion. When face-milling stainless steel, it was found that wear, not chipping, was the cause of failure (Lin, 1998). From the available experimental results of tool life, it was found that the reliability-dependent failure rate model (AE model) was better than the lognormal and Weibull distribution models in explaining the reliability of the cutting tool subjected to flank wear. The reliability formula under the reliability-dependent failure rate model (AE model) was expressed as follows:(3)$R\left(t\right)=\frac{(A_0+A_1)}{A_1+A_0\exp \left[\left(A_0+A_1\right)t\right]}$where, the embedded decay factor ($A_0$) varied with the type of tool, its shape and the material of the workpiece. The loss of a cutting tool’s reliability due to flank wear can be characterised by the process-dependent decay factor ($A_1$). The reliability-dependent failure rate model’s accuracy in describing the algebraic relation between failure rate and reliability was then verified using tool life experiments (Wang et al., 2001). The proportional hazards model with the two-parameter Weibull reliability function was applied to estimate the tool replacement time. The reliability function $R\left(t\right)$ under the Weibull proportional hazards model was expressed as:(4)$R\left(t\right)=e^{-{(\frac{t}{\theta })}^{\beta }{e}^{\left(z\alpha \right)}}$where $\beta$ was the shape parameter and $\theta$ was the scale parameter. The cutting speed, represented by the time-independent covariate $z$, affected both the reliability and hazard functions, as measured by the coefficient $\alpha$. Three criteria for tool replacement were considered: a defined fixed reliability value, a defined fixed hazard rate and the least possible value of cutting cost. Though the proportional hazards model can consider both the ageing process and cutting conditions, in the present study, only cutting speed was considered in the cutting conditions category (Tail et al., 2010). Modelling tool failure due to the combined effects of gradual wear and hidden defects was done using the Weibull distribution, while modelling tool failure due to an external source of stress was done using a homogeneous Poisson process. With the assertion that progressive wear or internal defects were the major reasons for tool failure, a mixed Weibull model was used for tool life distribution in this study. For a randomly selected tool in a sample, the following reliability function was obtained with regard to wear failures:(5)$R_w\left(t\right)=\left(1-p\right).e^{-{\left(\lambda t\right)}^{\alpha }}+p.e^{-{\left({\lambda }_{b}t\right)}^{{\alpha }_b}}$where $p$ was the probability of picking a bad tool. $\lambda$ and $\alpha$ were the scale and shape parameters of normal tools of good quality. ${\lambda }_b$ and ${\alpha }_b$ were the scale and shape parameters of the bad tools. An age replacement policy was applied based on the minimum average cost per replacement cycle. The optimal tool replacement age and goodness-of-fit of the model were examined by a graphical method based on the empirical total time on test (TTT) plot. Though the method was verified on Inconel 718 machining by CBN tools, the process parameters were fixed, and there weren't enough data points to determine the defective tools' distribution parameters (Vagnorius et al., 2010). RMS and peak in time domain index of the vibration signals were found in relation to the tool degradation process and thus taken as covariates of the proportional hazards model. With consideration of the lognormal distribution of the baseline hazard rate, a reliability function was obtained. The proportional reliability function $R\left(t,Z\right)$ was expressed as:(6)$R\left(t,Z\right)=\exp (-{{\displaystyle \int }}_0^t\frac{\frac{1}{\sigma t\sqrt{2\pi }}\exp \left[-\frac{{(\ln t-\mu )}^2}{2{\sigma }^2}\right]}{1-\frac{1}{\sigma \sqrt{2\pi }}{\displaystyle \underset{0}{\overset{t}{\int }}}\frac{1}{t}\exp \left[-\frac{{(\ln t-\mu )}^2}{2{\sigma }^2}\right]dt}\exp ({\gamma }_1{Z}_{1RMS}+{\gamma }_2{Z}_{2P})dt)$where $\mu$ was the mean and $\sigma$ was the standard deviations of the lognormal distribution. $Z_{1RMS}$ and $Z_{2P}$ stood for the RMS and peak (P) indices in the time domain, respectively. The regression coefficients were represented by ${\gamma }_1$ and ${\gamma }_2$, respectively. With the application of the maximum likelihood estimation, the parameters of the model were estimated (Ding and He, 2011). Under the constant cutting condition, the degradation of cutting tools was described by the Gamma process, which took into consideration the monotonic continuous-time and continuous-state stochastic behaviour of tool wear. Then, the probability density function of the cutting tool’s quantity reduction due to wear was obtained from the Gamma process, and accordingly, the reliability function was developed (Li and Zhang, 2012). A methodology based on the combinations of stochastic response surface and surrogate modelling techniques, together with Monte Carlo simulations (MCS) and first-order reliability methods (FORM) for the estimation of reliability indices, was presented by Salonitis and Kolios for the reliability assessment of cutting tool wear (Salonitis and Kolios, 2014). With the assumption of progressive wear as the tool life end criteria, tool life distribution was obtained from diffusion theory by utilising the Fokker-Planck equation. Under the premise of injury theory, the coefficients of the equation were calculated (Braglia and Castellano, 2014). From the literature review, the prior joint distribution of constants in the Taylor tool life equation was obtained. As Bayesian inference allows a model to consider uncertainty through probability distribution, it was used to update Taylor’s tool life constants from experimental data on 1,018 steel workpiece milling by using the uncoated carbide tool. Despite the potential drawbacks of Taylor’s tool life equation, it was applied due to its better understanding among the manufacturing community. After comparing with the least squares method, it was observed that Bayesian inference provided good results with a small sample size. Another section of this work considered an expanded version of Taylor’s tool life equation that took into account the turning's cutting speed and feed rate. The Metropolis–Hastings algorithm of the Markov Chain Monte Carlo (MCMC) method was used to estimate the equation’s constants via Bayesian inference. In order to estimate the tool life probability density function, initial assumptions concerning Taylor’s tool life constants were revised in light of the outcomes of turning tests (Karandikar et al., 2014a, b). With the consideration of tool wear as the product quality deterioration indicator, a quantitative model was developed to study the worsening of product quality. By applying the Weibull distribution as a stochastic tool life distribution, a tool replacement model was developed by balancing the costs of tool failure, tool replacement, lost production potential and deteriorating product quality (Xu and Cao, 2015). Liu et al. developed a tool wear mechanism-based non-linear and non-Gaussian state space model (SSM). The particle filter method projected the degradation trend, and then, using the degradation state and a threshold value, the conditional reliability of the milling cutters was obtained (Liu et al., 2016). The progressive tool wear states under various cutting situations were determined using the proportional hazards model with a baseline Weibull distribution. Cutting speed and feed rate were taken as the covariates during the machining of titanium metal matrix composites by using coated carbide inserts. Three zones – initial, steady and rapid wear zones – were used to categorise the tool wear states. The event of interest was determined to be the achievement of each wear state's end. The tool life spent in the $i$ ^th state was presented as:(7)$Totaltoollife=\frac{{\int }_0^{\infty }t{f}_i\left(t,Z\right)dt}{R_i\left(0,Z\right)}$where $Z$ represents the covariates. The Weibull distribution’s probability density function after considering for covariates was written as $f_i\left(t,Z\right)$. Given that the observation time was zero and the effects of the covariates were taken into account, $R_i\left(0,Z\right)$ was the reliability function. The model parameters were estimated using the maximum likelihood algorithm (Aramesh et al., 2016). In the literature, the proportional hazards model was also used to determine the cutting tool’s reliability function (Shaban et al., 2017; Shaban and Yacout, 2018). While turning hardened steel, the ceramic cutting tool’s reliability was investigated. The study considered continuous and interrupted cutting. By ignoring the effects of the crack growth velocity, statistical aspects of damage to the original tool material were investigated on the basis of damage mechanics and micromechanics. To evaluate the tool’s performance, a tool performance indicator was developed by combining the effects of the original flaws in the tool’s microstructure, the macro-mechanical characteristics of the tool material, and the tool’s external loads. From tool life data, the Weibull distribution was obtained as a tool life distribution in accordance with that of the tool performance metric. The tool reliability function $R\left(L\right)$ was defined as:(8)$R\left(L\right)=e^{-{(\frac{L}{{\eta }_j})}^{{\beta }_j}}$where ${\beta }_j$ was the Weibull distribution’s shape parameter, and ${\eta }_j$ was its scale parameter (Cui et al., 2017). Multiple hidden Markov models (HMMs) were used in a weighted manner to represent the dynamic behaviour of the progression of wear while taking wear rate into consideration as the hidden state in the HMM. The weighted HMM was used to develop a probabilistic method for estimating tool wear and RUL, which allows for the continuous management of tool wear by accounting for all possible wear rates between two preset cuts (Yu et al., 2017). From the experimental tool life data under optimum cutting conditions, a normal distribution model of the tool life distribution was created by studying the probability-probability plots and performing the residual test. The tool life distribution’s probability density function, denoted by $f\left(t\right)$, and the reliability function, denoted by $R\left(T\right)$, were respectively represented as:(9)$f\left(t\right)=\frac{1}{\sqrt{2\pi }\sigma }\exp \left[-\frac{{\left(t-\mu \right)}^2}{2{\sigma }^2}\right]$(10)$R\left(T\right)=1-F\left(t\right)=1-{\displaystyle \underset{0}{\overset{T}{\int }}}f\left(t\right)dt$where $\mu$ and ${\sigma }^2$ stood for the mean and variance of the tool life, respectively (Liu et al., 2020). By observing the linearity of the relationship between the average cutting force and the flank wear during the machining of Ti-6Al-4V alloy, it was decided to consider the critical value of the normalised force as a tool life criterion. This failure criterion was considered a limit-state function. The MCS was then used to estimate the failure probability, defined as the probability with which the limit state was exceeded. However, the stochastic nature of this limit state criterion had a great impact on tool reliability, so a large number of experiments must be performed to know the particular relation between flank wear and cutting force (Salonitis and Kolios, 2020). The hardness and fracture toughness of Si₃N₄-based ceramic tools were found to follow normal and lognormal distributions, respectively, in mechanical testing. With abrasive wear considered as a tool wear mechanism, the joint distribution of hardness and fracture toughness was used to define the probability density function of the wear life. The tool reliability function was denoted as follows when the necessary tool life was greater than $t_e$:(11)$R\left(T\right)={\displaystyle \underset{K_{IC},HV}{\overset{\frac{3}{4}\ln K_{IC}+\frac{1}{2}\ln HV>\ln t_e-\ln \frac{V_m}{C}}{\iint }}}f\left(K_i\right)f\left({HV}_i\right)d{K}_{i}d{HV}_i$where $K_{IC}$ was the ceramic tool’s fracture toughness and $HV$ was its hardness, respectively. $V_m$ was the maximum volume of wear when the tool achieved the blunt grinding standard and $C$ was a coefficient that was determined by the workpiece’s material, the machining parameters, and other friction conditions. $f\left(K_i\right)$ and $f\left({HV}_i\right)$ were the probability density function of the fracture toughness distribution and the hardness distribution, respectively. From experimental tool life data, a lognormal distribution was found suitable for tool wear life distribution. Although the error was less than 5% when the reliability was above 0.5, the error in tool life reliability prediction was observed due to the limited sample size and consideration of process idealisation (Xu et al., 2021). Han et al. introduced a hierarchical Dirichlet process-HMM (HDP-HMM) approach for estimating tool wear and predicting tool life. Based on the Pearson correlation coefficient, RMS of vibration in X dimension was selected as observation. The k-means algorithm was used to provide the initial number of wear states and probability distributions. Metropolis–Hastings algorithm was used to update the number of wear states, transition probability and omission probability. With the prediction of wear state sequence, tool life was predicted under a given threshold of wear. The proposed method was compared with weighted HMM and conventional HMM (Han et al., 2021). To realise tool condition monitoring through on-time cutting data, an event-based approach was proposed. From the monitored sensor data of the tool, a health indicator was obtained by using PCA. Further, the health indicator was optimised by using the exponential smoothing strategy. Then, an exponential degradation model was applied to predict the tool life. The parameters of the model were modified with the arrival of new observation data by using the Bayesian method (Wang et al., 2021). Sun et al. also applied an exponential degradation model to forecast the RUL of the tool. The parameters of the degradation model were updated iteratively through the combination of Bayesian inference and the expectation-maximization algorithm. Subsequently, estimating the tool wear condition entailed extrapolating the deterioration curve using particle filtering techniques, with the aim of reaching a predefined failure threshold and calculating the RUL (Sun et al., 2024). Das et al. utilized accelerated failure time (AFT) models, with distributions such as Weibull, lognormal and log-logistic distributions, to analyse the reliability of the cutting tool based on predictor variables (Das et al., 2024).

Table 6 summarizes the stochastic methods using probabilistic and reliability analyses for tool life modelling.

5.4 Data-driven models

This tool life monitoring technique uses in-process sensor data, such as vibration sensors, acoustic emission sensors, cutting force sensors, current sensors and so on, to anticipate tool wear or tool RUL in real time (Karandikar et al., 2021; Li et al., 2020). In recent years, artificial intelligence (AI) technology has grown rapidly. AI models offer the advantage of effectively handling extensive and intricate datasets (Xiao et al., 2022). Machine learning techniques empower the discovery of patterns within underlying data, and the tool wear data gathered during the actual production of components can be harnessed within a machine learning framework to forecast tool life (Karandikar et al., 2021). Nevertheless, the performance of AI models is significantly influenced by data preprocessing and feature extraction (Xiao et al., 2022). In data-driven models, typically, machine learning or deep learning techniques are employed for tool life or tool RUL modelling.

From the in-process vibration signals, which were salient in correlation with tool wear, the reliability of the lathe cutting tool was studied using the logistic regression model. If at time $t_i$, the cutting tool condition feature was a $k+1$ dimensional vector $X_i={\left(1,x_{1i},x_{2i},\dots ,x_{ki}\right)}^{\prime }$, the tool state was $y_i$ (under normal state, $y_i=1$, otherwise $y_i=0$), and the reliability function of the cutting tool was given as:(12)$R\left(t_i|X_i\right)=P\left(y_i=1|X_i\right)=\frac{e^{\left(B{X}_i\right)}}{1+e^{\left(B{X}_i\right)}}$where $B=\left({\beta }_0,{\beta }_1,\dots ,{\beta }_k\right)$ was the model parameter vector and ${\beta }_0>0$. The parameters of the model were estimated by maximising the log-likelihood function. The study assumed similar vibration characteristics for all tools with increasing tool wear (Chen et al., 2011). The logistic regression model was also used by Li et al. for the operational reliability evaluation of cutting tools by using cutting force and acoustic emission signals. The reliability prediction model was written as:(13)$R\left(t\right)=P\left(y_t=1|X\left(t\right)\right)=\frac{\exp ({\beta }_0+{\beta }_1{x}_1+\dots +{\beta }_n{x}_n)}{1+\exp ({\beta }_0+{\beta }_1{x}_1+\dots +{\beta }_n{x}_n)}$where $R\left(t\right)$ was the reliability function in relation to the time variable $t$. $X\left(t\right)=\left[x_1\left(t\right),x_2\left(t\right),\dots x_n\left(t\right)\right]$ was the feature vector of tool degradation and $y_1,y_2,\dots ,y_n$ were the tool conditions, each of which had a value of either 0 or 1. The subscript indicated testing time. The parameter vector for the model was ${\beta =(\beta }_0,{\beta }_1,\dots {\beta }_n)$ (Li et al., 2015). Face milling's cutting temperature and tool life were investigated in relation to cutting speed, feed rate, depth of cut and flank wear. The multi-input-multi-output (MIMO) Mamdani fuzzy inference system (FIS) was applied to calculate tool life as well as cutting temperature due to Mamdani FIS’s ability to provide feasible results with a comparatively simpler structure than Sugeno FIS. Tool life in AISI 1060 steel machining was found to decrease with increasing cutting speed (Kovac et al., 2014). The Sugeno FIS and support vector regression (SVR) were utilised to predict the RUL of cutting tools. The Gaussian radial kernel function was selected as the best kernel function of the support vector machine (SVM) as the RMS values of the Gaussian radial function were lower. A comparison between the two prediction methods was studied (Gokulachandran and Mohandas, 2015b). The RUL of the tools used in milling processes was calculated using data from the spindle power sensor and the curve fitting technique of an ANN. It was found that tool wear affected the value of the RMS power (P_rms) in the time domain (Drouillet et al., 2016). The sensitive features were acquired from force, vibration and acoustic emission signals. The characteristic matrix was developed from the features, and it was refined to decrease redundant information by applying the kernel PCA method. A measurement was made of the principal angle between the normal state and running state matrices. The cosine value of the minimum principal angle was used to evaluate the tool’s operational reliability. With the operational reliability value and machining parameters as inputs to the chaotic genetic algorithm (CGA)-back propagation neural network (BPNN) model, the cutting tool’s RUL was evaluated (Sun et al., 2016). For the prediction of tool life automatically in turning operations, an ANN model was trained by taking the automatically estimated flank wear and utilising an ANN model-integrated image processing programme. The method was compared with the method in which the flank wear was measured conventionally. Though within the permissible range, the fully automatic method produces a higher error (Mikołajczyk et al., 2018). The high dimensional features were extracted from the actual monitored data, and the dimension was decreased by PCA to build the health index (HI). The developed HIs were then used to check the similarity between the test and reference cutting tools. Both the distance and spatial direction similarity were considered, and they were quantified using the Euclidean distance and cosine distance, respectively. Finally, a weighted average of the RULs of the most comparable HI segments across all reference cutting tools was used to forecast the RUL of the cutting tool now under examination. In this work, historical samples were similar to the test sample, but methods must be developed that can be used for dissimilar datasets (Liu et al., 2019). A sparse autoencoder (SAE) was first trained using past failure data and the RUL details of a cutting tool in an offline approach using the deep transfer learning (DTL) technique. To model the mapping function between the learned features and the corresponding RUL, a nonlinear regression layer was combined with the trained SAE. Once SAE and the nonlinear regression model were trained, they were used to predict RUL online with a new tool (Sun et al., 2019). Support vector space was suggested for use with a single sample CNC turning tool to assess the cutting tool’s operating reliability. After the feature data's dimensions were reduced, a hypersphere space was created using related data, and the relative distance between the sample points and the hypersphere space was computed. The semi-normal function was used to explain the mapping relationship between the relative distance and the operation reliability of the tool (Chen et al., 2019). The long short-term memory (LSTM) network was adopted to estimate the RUL of cutting tools due to its unique effectiveness in providing solutions in cases of complex correlations and memory accumulation effects. Under different working conditions and after extracting wear characteristics from the torque signal, an LSTM model was developed (Zhou et al., 2019). During the machining process, the force signal was recorded and analysed to determine the characteristic quantity most indicative of tool wear. The characteristic vector was fed into the RUL prediction model for the cutting tool. The model was developed based on the trajectory similarity-based prediction (TSBP) algorithm. The optimal solution was realised by the differential evolution-support vector regression (DE-SVR) algorithm. The PHM Society's (2010) public data set was used for the integrated predictive model's training and performance evaluation (Yang et al., 2019). To predict the RUL of the cutting tool from the limited data, time windows were proposed to track the tool conditions using sensor data. The adjacent time windows were adaptively consolidated by considering outliers. The deep bidirectional long short-term memory (DBiLSTM) network was trained by using adjacent time windows. The multi-step ahead rolling prediction was performed to predict system degradation. The RUL was obtained on the basis of reaching the rolling prediction value at the predetermined benchmark of tool failure. To compare the studied method with other approaches, the mean absolute error (MAE) and root mean square error (RMSE) were analysed (Li et al., 2020). For monitoring sensor signals, the CNN was considered to extract the local feature as well as reduce the dimension. The SBULSTM network was designed for the purpose of denoising and encoding temporal information. Then, many fully connected layers were constructed on top of the CNN-SBULSTM network to introduce non-linearity into the output, and a single regression layer was used to get the desired RUL. Several metrics, including Score, RMSE and Accuracy, were used to evaluate the proposed method's efficacy in comparison to that of existing machine learning models and deep learning models. It resulted in satisfactory outcomes (An et al., 2020). For the partition of complex and multi-sourced signals, a Hurst exponent-based method was explored by establishing the correlations between signals and tool wear progression. Then, the RUL of the cutting tools was predicted using a hybrid CNN-LSTM algorithm. Each CNN in the CNN-LSTM algorithm dealt with a single kind of signal. The fusion of the features extracted from the signals occurred in a concatenated layer. The synchronised signals were then used to estimate the cutting tool’s RUL by feeding them into an LSTM regression layer. While the predicted tool life value came closer to the actual value as machining progressed, the relative error was still significant at the outset of the process (Zhang et al., 2021). Li et al. presented a hybrid approach to forecasting the RUL of cutting tools. The connection between sensor signals and tool wear was initially determined using SVR. Initial wear, normal wear and severe wear were identified as the three stages of tool wear, each having its own unique stress variations and wear patterns. The SVM was employed to identify the current wear stage, providing prior information for a Bayesian framework. On the basis of the developed Bayesian framework, the parameters of the tool wear model were updated iteratively using the sliding time window and particle filter technique. The improved tool wear model was then able to provide predictions about the state space of tool wear and the RUL. The effectiveness of this method was confirmed through an experiment using a high-speed CNC milling machine under a single working condition, but its performance in other working conditions may vary (Li et al., 2022). Qin et al. addressed the problem of installing numerous sensors on the machine to gather a wider range of data by proposing a novel feature network dictionary in the offline training phase. This dictionary expanded the pool of potential features while operating within limited sensor constraints, aiming to encompass as much valuable information as possible. Following feature selection via the sparse augmented Lagrangian (SAL) technique, RUL for cutting tools was calculated using the Gaussian process regression (GPR) methodology. Using the PHM Society's down milling operation experiment from 2010, the effectiveness of the suggested SAL and GPR frameworks was verified (Qin et al., 2023). De Barrena et al. identified optimum features using the random forest recursive feature elimination (RF-RFE) technique, and with the application of two types of bidirectional recurrent neural networks (BRNN), i.e. bidirectional long short-term memory (BiLSTM) and bidirectional gated recurrent units (BiGRU), tool RUL was predicted in a turning process. The cutting conditions were constant in their study (De Barrena et al., 2023). Bagga et al. introduced a tool life prediction system based on computer vision, wherein images of the tool wear zone were captured during turning operations. Image processing techniques, coupled with machine learning systems – specifically, gradient-boosted decision model and SVM – were utilized in their approach (Bagga et al., 2023). Wu et al. presented a hybrid network based on the feature enhancement module (FEMNet), combining the feature enhancement module and BiLSTM for tool RUL prediction (Wu et al., 2023a).

Table 7 summarizes the data-driven models for tool life modelling.

5.5 Hybrid models

Hybrid models to predict the life or RUL of the tool are obtained by combining multiple models.

An EMD and BPNN based model to monitor cutting tool wear was created from the force, vibration and acoustic emission signals collected during the machining process. With the assumption that flank wear is normally distributed, the Wiener process was applied to model the cutting tool wear process. With the implementation of the L₁₆ orthogonal experimental plans, prior estimations of the parameters of the RUL model were done by the expectation-maximization algorithm. Through the Bayesian method, the parameters of the RUL model were updated (Sun et al., 2018). Luo et al. proposed a hybrid method of cutting tool life prediction based on Digital Twin (DT) (Luo et al., 2020). The collected vibration data was subjected to a time-frequency analysis by Zhang et al. using the wavelet transform. To address the issue of unbalanced data at various cutting tool wear phases, they employed a CCVAE network. This network expanded the results of the time-frequency analysis, enabling monitoring of the cutting tool's wear status and wear amount through the CNN. Subsequently, the cutting tool’s RUL was predicted using the multistage Wiener process method. The RUL $T_t$ was provided as:(14)$T_t=\inf \left\{t^{\prime }:X\left(t+t^{\prime }\right)\ge W_n|X\left(t\right)\le W_n\right\}=\inf \{t^{\prime }:X\left(t+t^{\prime }\right)-X\left(t\right)\ge W_n-X\left(t\right)\}$where the wear degradation values $X\left(t\right)$ and $X\left(t+t^{\prime }\right)$ were measured at time $t$ and $t+t^{\prime }$, respectively, and $W_n$ was the failure threshold (Zhang et al., 2023). Feng et al. proposed a new nonlinear ensemble RUL prediction framework based on dynamic-matched weights. The framework aggregated a Bayesian neural network (BNN) model and a nonlinear Wiener process degradation model through a nonlinear weighting formulation. Then, a novel ensemble weight dynamic matching algorithm was designed to attain time-varying weight matching and enhance prediction accuracy. Subsequently, the ensemble RUL prediction result was described by the probability density function of the remaining life. Through two milling cutter experiments, the proposed RUL prediction framework was verified (Feng et al., 2024). Li et al. proposed a data-model linkage tool RUL prediction under the Bayesian framework. A convolutional stacked bidirectional long short-term memory network with time-space attention mechanism (CSBLSTM-TSAM) was developed in the data-driven module, and a three-stage tool RUL prediction model based on the nonlinear Wiener process was established in the physical modelling module. The real-time estimated tool wear of the data-driven module was used as the observed value of the physical model, and the model parameters were dynamically updated by the weight-optimized particle filter algorithm under a Bayesian framework (Li et al., 2024).

Table 8 summarizes the hybrid models for life or RUL prediction of the tool.

All the methods collected in this study are summarised in Figure 7.

6. Challenges and opportunities

Even after significant advancements in the study of cutting tool life prediction, several issues in this area must be researched further. In this section, the challenges and opportunities are discussed, along with some suggestions.

The cutting tool life prediction becomes difficult with few or no event data. This happens generally in the case of new tools or where tool failure is not permitted for high-value jobs. Though some publications addressed the issue of the tool’s RUL prediction by using limited data (Li et al., 2020; Zhang et al., 2023), small sample sizes can limit the accuracy and generalisability of the results. Physics-based approaches may be used to solve this issue, but a proper understanding of the physics of failure is needed. Also, most of these models depend on preset cutting conditions and tool geometry (An et al., 2020). It appears that the concept of accelerated testing of the cutting tool can be performed to save time and reduce expenses associated with tool life tests for valuable workpieces. During accelerated testing, the component is exposed to higher levels of parameters that cause it to fail faster than it would under normal operating conditions. It may be investigated into using the accelerated testing method in cutting conditions that are more severe than those advised for normal use to obtain degradation data. Subsequently, this data can be used to extrapolate and estimate the reliability of the cutting tool under normal operating conditions. The fundamental assumption of accelerated testing is that the failure mode and mechanism observed at elevated levels of parameters are similar to those under recommended usage conditions. Thus, the ideal range of parameters must be finalized prior to use in accelerated testing.

To avoid unplanned tool failure, especially for superalloys, in which short tool life is a major problem, optimization of cutting parameters must be done to develop a reasonable tool replacement strategy. Improper selection of cutting parameters results in unplanned tool failure and damage to the costly workpiece. Among the publications reviewed, limited articles were found where the authors studied the optimization of cutting parameters during the machining of superalloy, but none considered the depth of cut and tool geometry (nose radius) as input parameters. The impact of cutting conditions can be investigated not only on tool life but also on a number of machinability metrics. As a result, cutting parameters must be optimized using a multi-response approach that takes into account output factors, including tool life, surface roughness and cutting forces.

Among the reviewed publications, only one (Vagnorius et al., 2010) considered the mixed Weibull model. This model can be used to estimate how long a cutting tool will last before failure due to wear or because the load on the tool is too great for its intended purpose.

In online monitoring of tool wear, the sensor signal is time-series data. In this case, feature extraction and feature selection are major challenges. Expressing the intrinsic properties of the sequence data and obtaining long-term dependencies from the sequence data are major problems. The LSTM network may not be sufficiently robust to process raw time series data directly despite its ability to learn long-term dependencies. The introduction of the CNN-SBULSTM network to handle sequence data by An et al. (2020) spurred further research into the field, leading to the emergence of new studies.

Machine learning and AI are pivotal in the realm of tool life prediction via flank wear monitoring, a subject predominantly explored in subsections 5.4 and 5.5. Looking ahead, there are several opportunities for the application of machine learning and AI in this field. For instance, Bagga et al. presented an approach to predicting tool life by integrating AI and machine vision (Bagga et al., 2022). Hung et al. aimed to develop a tool wear monitoring system based on system-on-chip (SoC) technology, incorporating signal processing, deep learning and decision-making (Hung et al., 2022). In order to anticipate the remaining tool life, Chang and Hsu created online smart machine box (SMB) monitoring with an HMI (human-machine interface) dashboard based on the BPNN and force modelling (Chang and Hsu, 2023). Nowadays, the proliferation of sensors in machine tools has led to a significant surge in input data volume. Deep learning, a relatively recent addition to the AI modelling landscape, demonstrates enhanced performance compared to conventional AI models when dealing with complex datasets (Xiao et al., 2022). AI-driven advancements in cutting tool life prediction are continuously evolving, and new research and applications are emerging.

7. Conclusion

Cutting tool life prediction techniques applied in various publications have been discussed. This review covers the experimental settings that include turning, milling, drilling, boring and slotting operations. Besides the life or RUL prediction methods, the procedures used in these publications to monitor flank wear have also been discussed. The following observations can be drawn from this discussion:

1. Cutting tool life is a stochastic variable; it depends upon the tool, work materials, cutting conditions, machine tool and so on. Traditional models of tool life, which are deterministic, fail to consider the variations in cutting conditions (Zaretalab et al., 2020). From Taylor’s model, the deterministic nature of tool life is obtained (Salonitis and Kolios, 2014). Therefore, it is necessary to estimate the cutting tool’s reliability function, taking into account the machining parameters for a given experimental setup.

2. The direct methods of tool condition monitoring provide high measurement accuracy. However, these methods are affected by the machining environment and require downtime for the detection of wear.

3. The indirect methods of tool condition monitoring are appropriate for online flank wear prediction, even though they provide a less precise measurement. However, it is crucial to place the sensors properly and identify the signals that really matter for the degradation of the tool.

4. If the model is constructed with an adequate understanding of failure mechanisms and the correct calculation of model parameters, physics-based approaches may provide an accurate estimate of tool life. Thus, the application of this method is not feasible if the physics of the damage is difficult to understand (Lei et al., 2018).

5. In an empirical model of tool life, the model parameters are obtained from failure experiments. However, empirical methods may not provide better information beyond the range of the sample data, so it is very hard to predict tool life accurately.

6. In the probabilistic method of tool life modelling, it is difficult to predict the life of the cutting tool using the reliability function if failure data is not available. In the case of an improper assumption of distribution, a high error in prediction will result (Li et al., 2020).

7. The amount and quality of degradation data heavily influence the accuracy of the prediction of the data-driven strategy. Due to limited data, the various patterns and random fluctuations within the degradation data may provide unacceptable inaccuracies in tool life prediction (Liu et al., 2019).

8. Most of the publications reviewed are application-specific. Tool life depends not only on machining time but also on cutting conditions, cutting tool material, workpiece material, machine tool type, etc. Therefore, it is still necessary to create a standard way to generalize the tool life forecast technique.

9. In literature, superalloys are rarely considered workpiece materials for cutting tool life prediction. As superalloys are hugely used in diversified industries, studying the tool life during the machining of these superalloys under various cutting conditions is in high demand.

This review paper does have some limitations. Given the large number of studies on the topic of this review paper, it is likely that we might have missed some pertinent studies in the process of searching and selecting the articles. Moreover, this review did not consider the grey literature, including conference papers and books.

Figure 1

Tool wear (a) crater wear (b) flank wear

[Figure omitted. See PDF]

Figure 2

Distribution of referred publications based on publication years

[Figure omitted. See PDF]

Figure 3

Distribution of referred publications according to countries/regions

[Figure omitted. See PDF]

Figure 4

Number of publications considered under experimental setup based on machining types (Data source: Table 2)

[Figure omitted. See PDF]

Figure 5

Number of publications featuring tool condition monitoring methods (Data source: Table 3)

[Figure omitted. See PDF]

Figure 6

Number of publications considered based on the tool life or tool RUL modelling methods (Data source: Table 4, Table 5, Table 6, Table 7, Table 8)

[Figure omitted. See PDF]

Figure 7

Approaches used for modelling and predicting the life or RUL of the cutting tool

[Figure omitted. See PDF]

Table 1

The number of publications categorized by journals

Journals	Number of publications
International Journal of Advanced Manufacturing Technology	21
Measurement	6
Proceedings of the Institution of Mechanical Engineers Part B-Journal of Engineering Manufacture	6
Mechanical Systems and Signal Processing	5
International Journal of Machine Tools and Manufacture	4
Journal of Manufacturing Systems	4
Ceramics International	3
Journal of Intelligent Manufacturing	3
Journal of Materials Processing Technology	3
Journal of Engineering for Industry-Transactions of the ASME	2
Journal of Manufacturing Processes	2
Precision Engineering-Journal of the International Societies for Precision Engineering and Nanotechnology	2
Proceedings of the Institution of Mechanical Engineers Part O-Journal of Risk and Reliability	2
Wear	2
AI Edam-Artificial Intelligence for Engineering Design Analysis and Manufacturing	1
Archives of Civil and Mechanical Engineering	1
Engineering Failure Analysis	1
European Journal of Operational Research	1
IEEE Access	1
IEEE Transactions on Industrial Informatics	1
IEEE Transactions on Reliability	1
International Journal of Material Forming	1
International Journal of Production Research	1
Journal of Manufacturing Science and Engineering-Transactions of the ASME	1
Journal of Materials Research and Technology-JMR&T	1
Journal of Mechanical Science and Technology	1
Machining Science and Technology	1
Mathematical Problems in Engineering	1
Proceedings of the Institution of Mechanical Engineers Part J-Journal of Engineering Tribology	1
Quality and Reliability Engineering International	1
Quality Engineering	1
Reliability Engineering and System Safety	1
Robotics and Computer-Integrated Manufacturing	1
Sensors	1
Engineering Applications of Artificial Intelligence	1
International Journal of System Assurance Engineering and Management	1
International Journal of Quality and Reliability Management	1

Source(s): Authors’ own work

Table 2

Summary of the experimental setups reported in the considered literature

Authors	Machine tool	Parameters	Workpiece material	Cutting tool	Tool condition monitoring method	Tool life criteria	Remarks
Hitomi et al. (1979)	High speed lathe	Vc: 175 and 100 m/min, f: 0.2 and 0.15 mm/rev, ap: 1.50 and 2 mm	Carbon steel	Carbide tool	Direct method	Flank wear value	Dry cutting
Klim et al. (1996)	NC machining centre	Vc: 92 m/min, f: 0.8 mm/rev or for variable sequence in line with the designated cycle, Depth of cut: 1 mm	Stainless steel 17-4PH (630 AISI)	SEM 43A (ANSI), triple coated inserts	Direct method – toolmaker microscope and scanning electron microscope	Critical values of crater and flank wear	Climb face milling operation
Chao and Hwang (1997)	Traditional lathe	Vc, f, ap, rake angle of the tool, hardness and composition of the workpiece	AISI S1017C and S1045C	High speed steel tool T-15	Direct method	Maximum flank wear = 0.7 mm	Dry orthogonal turning operation
Alauddin et al. (1997)	Vertical milling machine	Vc: 24–38 m/min, fz: 0.045–0.27 mm/tooth, aa: 0.4–1 mm	Cold rolled steel	High speed steel slot drills	Direct method – toolmakers’ microscope	Maximum flank wear = 0.5 mm	Slot milling operation
Lin (1998)	Vertical milling machine	Vc: 60 m/min, f: 1.0 mm/rev, Depth of cut: 0.6 mm	Stainless steel	Carbide UTi20 T	Direct method - optical microscope	Chipping of the rake face or 0.3 mm flank wear	Dry face milling operation
Dos Santos et al. (1999)	CNC milling machine	Vc: 100–300 m/min, fz: 0.05–0.20 mm/rev/tooth, Depth of cut: 1–2.50 mm	AISI 1045 rolled steel	Triple coated cemented carbide inserts	Direct method	Maximum flank wear = 0.7 mm	Dry face milling operation
Axinte et al. (2001)	CNC lathe	Vc: 220 and 245 m/min, f: 0.2 and 0.35 mm/rev, ap: 1.5 and 2 mm	AISI 316L stainless steel	Coated carbide tools	Direct method - optical microscope	Flank wear = 0.3 mm	Turning using 6 different cutting fluids
Wang et al. (2001)	Heavy-duty lathe	Vc: 62.67–313.37 m/min, f: 0.08 mm/rev, ap: 1.0 mm	High carbon steel S55C	Sintered carbide inserts	Direct method	Limiting flank wear value of 0.3 mm	Dry machining
Oraby and Hayhurst (2004)	Centre lathe	Vc: 50–200 m/min, f: 0.06–0.6 mm/rev, ap: 1.3–3 mm	Alloy steel 709M40 (EN 19)	Triple coated carbide inserts	Direct method	Average of nose, flank and notch wear = 0.25 mm	Dry cutting
Ojha and Dixit (2005)	Lathe	Vc: 135–270 m/min, f: 0.04–0.32 mm/rev, ap: 0.3–1.2 mm	Rolled steel	TiN coated tungsten carbide	Direct method - Axiotech microscope	Maximum flank wear = 0.8 mm	Dry turning
Tsai et al. (2005)	High-speed milling machining centre	Vc: 314–628 m/min, fz: 0.0075–0.15 mm/tooth, aa: 0.5–1.5 mm	SKD61 tool steel	TiAlN coated cemented tungsten carbide tool	Direct method- tool microscope	Threshold flank wear ≤0.2 mm	End milling operation
Astakhov and Galitsky (2005)	Deep hole gun drilling	Vc: 19.8–53.8 m/s, f: 0.11–0.21 mm/rev, Tool geometry: 9 parameters with each of 5 levels	Malleable cast iron	Carbide K30 tips	Direct method	Average flank wear width of 1.0 mm or excessive tool vibration	A 7% concentration water-soluble coolant was used
Natarajan et al. (2007)	High speed VDF lathe	Vc: 30–190 m/min, f: 0.01–2.5 mm/rev, ap: 0.5–4 mm	High carbon steel	Tungsten carbide	Direct method – tool maker’s microscope	Flank wear width of 0.3 mm
Sahin (2009)	CNC lathe	Vc: 100–196 m/min, f: 0.06–0.117 mm/rev, ap: 0.2 mm, Tool hardness: 2,145, 2,250, 3660 HV	Hardened AISI 52100 bearing steels	Mixed alumina ceramic, coated ceramic and CBN	Direct method - Optical tool microscope	Flank wear width of 0.3 mm	Dry cutting
Tail et al. (2010)	High speed drilling	N: 6,000–10000 rpm, f: 1.67 mm/rev.	Metallic–matrix composite of GRA-Ni	Titanium nitride coated steel drills	Direct method - Digital camera	Maximum flank wear width of 0.6 mm	Dry condition machining
Vagnorius et al. (2010)	Vertical lathe	Vc: 150 m/min, f: 0.2 mm/rev, ap: 0.25 mm	Inconel 718	CBN inserts	Direct method- toolmaker’s microscope	Maximum flank wear width of 0.6 mm on minor flank face	Emulsion, 4% as coolant
Chen et al. (2011)	CNC lathe	Vc: 200 m/min, f: 0.15 mm/rev, ap: 2 mm	45# steel bar	Diamond carbide tool	Vibration signals and micro-optical system	Maximum flank wear width = 0.6 mm
Salonitis and Kolios (2014)	High speed CNC turning	Vc: 300, 400 and 500 m/min, f: 0.05, 0.15 and 0.25 mm/rev, ap: 0.8 mm	High carbon steel C55 (EN10083-2)	Tungsten carbide	Direct method - Optical microscope	Flank wear width = 0.3 mm	Dry cutting
Kovac et al. (2014)	Milling machine	Vc: 1.83–4.65 m/s, fz: 0.142–0.351 mm/tooth, Depth of cut: 0.67–3.37 mm, Flank wear width: 0.08–0.4 mm	AISI 1060 steel	P25 face milling cutter	Direct method - Microscope		Dry face milling operation
Li et al. (2015)	Milling machine	N: 1,000 rpm, f: 400 mm/min, Depth of cut: 0.4 mm	FV520B	Tool CMV-850A machining centre	Acoustic emission and cutting force signals	Width of flank wear> 0.6 mm
Gokulachandran and Mohandas (2015b)	Vertical milling machine	N: 250–1,000 rpm, f: 50–125 mm/min, Depth of cut: 0.1–0.2 mm	IS2062 steel	Uncoated tungsten carbide inserts	Direct method -ARCS Video measuring machine	Flank wear width = 0.6 mm	Dry cutting
Yin et al. (2015)	CNC lathe	Vc: 60, 80 and 100 m/min, f: 0.1, 0.125 and 0.15 mm/rev, ap: 0.1, 0.2 and 0.3 mm	Austenitic stainless steel (1Cr18Ni9Ti)	Al2O3/TiC micro-nano-composi-te ceramic tool	Direct method - Microscope	Maximum width of flank wear = 0.6 mm	Extreme pressure emulsified cutting fluid
Davoodi and Eskandari (2015)	CNC lathe	Vc: 50–90 m/min, f: 0.1–0.2 mm/rev, ap: 1 mm	Iron–nickel-base superalloy N-155	PVD TiAlN-coated carbide tools	Direct method - toolmakers microscope	Average flank wear = 0.3 mm or maximum flank wear = 0.6 mm	Water based emulsion containing 10% oil was used as coolant
Sun et al. (2016)	Carver PMS_A8 milling machine	N: 3,000–6,000 rpm, f: 50–200 mm/min, Depth of cut: 0.4–1 mm	45# steel	Carbide tool	Tool microscope, cutting force, vibration and acoustic emission signals	Flank wear width of 0.4 mm	Flat end milling operation
Aramesh et al. (2016)	5-axis Boehringer NG 200 CNC turning center	Vc: 40–80 m/min, f: 0.15–0.35 mm/rev, ap: 0.2 mm	Ti-6Al-4V alloy	TH1000 coated carbide inserts	Direct method - Optical microscope	Maximum flank wear of 0.2 mm at rapid wear state	Dry cutting
Zaretalab et al. (2018)	CNC milling	N: 3,000–4,500 rpm, f: 0.1–0.3 mm/rev, Depth of cut: 0.1–0.2 mm	Steel AISI304	Three edge cemented carbide inserts	Direct method – Tool image through a machine vision	Maximum flank wear width of 0.3 mm
Liu et al. (2019)	Slotting cutter	N: 200 rpm, f: 15 mm/min	Structural steel 30Cr2Ni4MoV	High speed steel M42-4	Acoustic emission signals and optical microscope	When the cutter was unable to guarantee the quality of the workpiece
Zhou et al. (2019)	DMG125H Machine left	Rotating speed: 600–1,300 rpm, f: 40–260 mm/min, Cutting depth: 0.1–0.9 mm	QT500-7GB/T1348-1988	Titanium-nitride coated blade	Torque signal	Reaching of tool flank wear to blunt standard	Boring tool blade experiments
Yang et al. (2019)	CNC milling	Vc: 25, 31 m/min, fz: 0.015, 0.02 mm/tooth, aa: 5 mm, ar: 2, 3 mm	TC4	Solid carbide, and coated cemented carbide	Cutting force signals and microscope	Tool flank wear value of 0.4 mm	Down-milling without cutting fluid
Lin et al. (2020)	CNC lathe	Vc: 300 m/min, f: 0.1 mm/rev, ap: 1 mm	Vermicular graphite cast iron	Multicomponent nitride-coated Al2O3–TiC composite ceramic tools	Optical microscope	Average wear bandwidth value of the tool’s flank = 0.3 mm	Turning tests under dry conditions
Liu et al. (2020)	CNC lathe	Vc: 25–175 m/min, f: 0.02–0.3 mm/rev, ap: 0.5 mm	Inconel 625	PVD- TiAlN- coated carbide tools	Direct method - Microscope	Tool tipping or a width of flank wear greater than 0.6 mm	Turning operation using TRIM E206 emulsion, at 5–7% concentration in water
Li et al. (2020)	Milling machine	Vc: 200 m/min, f: 0.25 and 0.5 mm/rev, Depth of cut: 0.75 and 1.5 mm	Stainless steel	Tungsten carbide tool	Spindle motor current sensors and microscope
Salonitis and Kolios (2020)	CNC milling	Vc: 75–125 m/min, fz: 0.08–0.12 mm/tooth, Depth of cut: 3 mm	Ti-6Al-4V alloy	Inserts with PVD and CVD coating	Cutting force signals and optical microscope	According to ISO 3685:1993	Oil-based coolant fluid
An et al. (2020)	CNC vertical machining centre	Vc: 50 and 75 m/min, fz: 0.03 and 0.04 mm/tooth, aa: 1.2 mm, ar: 2 mm	Titanium alloy TC4	TiAlN-coated cemented carbide, Solid carbide, TiN-coated cemented carbide	Spindle vibration, spindle motor current, tool position, spindle power		Dry milling operation
Sagar et al. (2021)	CNC turning centre	Vc: 50 m/min, f: 0.1 mm/rev, ap: 0.15 mm	90 WHA	Uncoated carbide inserts with two different rake angles	Stereomicroscope	Tool flank wear of 600 µm	Dry conditions
Zhang et al. (2021)	High speed CNC machine – dry milling	N: 10,400 rpm, f: 1,555 mm/min, aa: 0.2 mm, ar: 0.125 mm	Stainless steel	3-flute tungsten carbide cutters	Cutting force, vibration and acoustic emission signals and microscope	All flutes' average flank wear value	The data came from the PHM Data Challenge in 2010
Xu et al. (2021)	CNC lathe	Vc: 90 m/min, f: 0.15 mm/rev, ap: 0.2 mm	Quenched carbon steel T10A	Si3N4/(W,Ti)C/Y2O3/MgO/Al2O3 composite ceramic tool	Direct method – handheld microscope and scanning electron microscope	Maximum flank wear width = 0.6 mm	Dry cutting
De Barrena et al. (2023)	Lathe	Vc: 200 m/min, f: 0.1 mm/rev, ap: 2 mm	19NiMoCr6 steel	P25 grade uncoated inserts	Cutting force, vibration, sound, acoustic emission, current, voltage signals and profilometer	Maximum flank wear value of 250 µm
Bagga et al. (2023)	CNC lathe	Vc: 70, 100 and 130 m/min, f: 0.1, 0.15 and 0.2 mm/rev, ap: 0.3, 0.4 and 0.5 mm	AISI 4,140 steel	PVD-coated carbide inserts	Direct tool wear monitoring using machine vision	Tool flank wear value of 0.4 mm
Wu et al. (2023a)	CNC machine tool (turning)	Vc: 60, 70 and 80 m/min, f: 0.10, 0.12 and 0.08 mm/rev, ap: 0.7, 0.5 and 1 mm	40Gr metal	CCMT- 09T304LF KC5025	Vibration signals and stereo microscope
Zhang et al. (2023)	CNC milling	N: 600, 800 and 1,000 rpm, Cutting depth: 0.50, 0.75 and 1 mm, f: 220, 240 and 260 mm/min	Cast iron HT200	Hard alloy milling cutter	Vibration sensor and electron microscope	Initial wear (0–0.1 mm). Normal wear (0.1–0.35 mm)Severe wear (>0.35 mm)
Feng et al. (2024)	CNC machine (milling)	N: 3,500 and 4,500 rpm, f: 300 and 400 mm/min, Depth of cut: 1.75 and 1.50 mm	45# steel	APMT1135 carbide milling cutters	Current signal and vision microscope	Wear width (average wear width) of flank face ≥300 µm
Li et al. (2024)	Five-axis CNC machining centre (milling)	N: 1,000 rpm, fz: 1 mm/tooth, Cutting depth: 0.3 mm	508-III steel	High-feed milling cutter with five indexable carbide-coated inserts	Vibration, acoustic emission, current signals and an industrial camera	Maximum flank wear width ≥0.45 mm	No coolant
Das et al. (2024)	Lathe	Vc: 139.60–225.73 m/min, f: 0.18034–0.254 mm/rev, ap: 0.75–1.25 mm, Tool nose radius: 0.4, 0.8 and 1.2 mm	Inconel 800	PVD-coated carbide inserts	Optical microscope	Maximum flank wear width of 0.3 mm or when notch wear or chipping appears	Dry turning

Source(s): Authors’ own work

Table 3

Summary of the tool condition monitoring methods

Authors	Machining type	Tool condition monitoring method for life or RUL prediction
Alauddin et al. (1997)	Milling	Toolmaker’s microscope
Natarajan et al. (2007)	Turning	Toolmaker’s microscope
Amaitik et al. (2006)	Milling	Toolmaker’s microscope
Sahin (2009)	Turning	Optical tool microscope
Vagnorius et al. (2010)	Turning	Toolmaker’s microscope
Tail et al. (2010)	Drilling	Olympus Camedia digital camera and “Irfan View” software
Karandikar et al. (2014a)	Milling	Handheld microscope
Zaretalab et al. (2018)	Milling	Captured image of cutting tool using a machine vision
Hood et al. (2018)	Turning	Wild microscope with a toolmakers table with digital micrometre heads
Bagga et al. (2023)	Turning	Captured image of the cutting tool using a machine vision
Li et al. (2015)	Milling	Acoustic emission and cutting force signals
Liu et al. (2019)	Slotting	Acoustic emission signals and optical microscope
Yang et al. (2019)	Milling	Cutting force signals and microscope
Salonitis and Kolios (2020)	Milling	Cutting force signals and optical microscope
Wang et al. (2021)	Milling	Cutting force and a microscopy system
Chen et al. (2011)	Turning	Vibration signals and micro-optical system
Ding and He (2011)	Turning	Vibration signals and video microscopy system
Yu et al. (2017)	Milling	Vibration signals
Chen et al. (2019)	Turning	Vibration signals and micro-optical system
Wu et al. (2023a)	Turning	Vibration signals and a stereo microscope
Zhang et al. (2023)	Milling	Vibration signals and electron microscope
Drouillet et al. (2016)	Milling	Power sensor data
Zhang (2011)	Milling	Spindle motor current
Li et al. (2020)	Milling	Spindle motor current sensors and microscope
Feng et al. (2024)	Milling	Current signal and vision microscope
Zhou et al. (2019)	Boring	Torque signal
Sun et al. (2016)	Milling	Cutting force, vibration and acoustic emission signals and tool microscope
Sun et al. (2018)	Milling	Cutting force, vibration and acoustic emission signals and tool microscope
Zhang et al. (2021)	Milling	Cutting force, vibration and acoustic emission signals and microscope
Li et al. (2024)	Milling	Vibration, acoustic emission and current signals and an industrial camera

Source(s): Authors’ own work

Table 4

Summary of tool life modelling methods under physics-based models

Authors	Machining type	Tool life modelling method	Remarks
Venuvinod et al. (1990)	Turning	Using the power law that existed between cutting tool life and mean flank contact temperature. Then, the tool life analysis for orthogonal cutting was extended to oblique cutting	A strong correlation was found between the calculated and observed tool lifetimes. By increasing tool obliquity, flank wear land contact temperatures were decreased. This basically clarified how obliquity affects tool life
Oraby and Hayhurst (2004)	Turning	Non-linear regression analysis techniques considering the variation of a ratio of force components	The ratio of the thrust components of force and the power component of force was used instead of the absolute values of forceBy comparing the model’s predictions to those of an extended Taylor model and to the findings of experiments, the model’s strong predictive power was demonstrated
Yin et al. (2015)	Turning	By estimating fatigue tool life	The modelling of tool life took into account tool breakage brought on by slow crack propagationAt tensile stress of 500–600 MPa, the estimated life of the tool was between 1 and 41 min. The model was validated using forty repeated tests, and the tool lifetimes fell within the predicted range of 5–21.4 min
Ghorbani et al. (2018)	Turning	Based on the tool material's fatigue strength and parameters of tool vibrations	The estimated loading cycles to failure of tools with various forms of clamping were evaluated, and the lever lock type had a lower estimateThe experimental tool life study found that the computation of the suggested method could forecast the life of carbide inserts with 20% accuracy
Sagar et al. (2021)	Turning	Analytical tool wear rate models	The modified Zhao model showed the best results in flank wear predictions among the four considered models. Tool life values were predicted at different cutting speeds using this model, and the error percentage for the predicted tool life was between 4 and 7%

Source(s): Authors’ own work

Table 5

Summary of tool life modelling methods under empirical models

Authors	Machining type	Tool life modelling method	Remarks
Chao and Hwang (1997)	Turning	Backpropagation neural network method	The backward stepwise regression method was used to screen out significant and uncorrelated variables prior to constructing the backpropagation neural network modelsIt was observed from the t-test, that the predictions for the training and the predicted data were close to the experimental tool life at the 5% level of significance
Alauddin et al. (1997)	Milling	RSM	The tool life was found to decrease with increasing speed, feed and axial depth of cutFrom the ANOVA, it was concluded that the models were adequate with 95% confidence intervals
Dos Santos et al. (1999)	Milling	Extended Taylor’s equation	The proposed experimental design made it possible to minimise the number of tests needed in comparison with the fractional factorial designThe mean percent error of the tool life was calculated after nine tests, and the error was approximately 46%
Axinte et al. (2001)	Turning	Extended Taylor’s equation	The performance of six different cutting fluids was evaluated by comparing their effects on tool lifeThe pooled estimate of tool life uncertainty, taking into account all tests, was 30%
Ojha and Dixit (2005)	Turning	Neural networks	The coefficient of determination (R2) was good (0.92) for neural networks in comparison with multiple regression (R2 = 0.34)
Tsai et al. (2005)	Milling	Abductive network	The constructed network took into account the connections between tool life and process parameters like Vc, fz and aaThe end mill life's forecast error was found to be less than 10%
Astakhov and Galitsky (2005)	Drilling	Group method of data handling to tool life testing	Nine geometry-related parameters as well as two regime parameters (feed rate and cutting speed) were taken as input variables
Amaitik et al. (2006)	Milling	Multi-linear regression analysis	Tool life was most significantly influenced by cutting speed, with feed rate coming in secondThe relevance of the model and its applicability in predicting tool life were justified by the high F-ratio values
Natarajan et al. (2007)	Turning	Neural network with PSO technique	Inputs included Vc, f, ap and flank wear, and the output was tool lifeThe proposed method yielded nearly identical outcomes to, and even improved upon, the back propagation technique
Mehrban et al. (2008)	Turning	Multiple regression analysis	Tool life was most affected by Vc and the interaction between Vc and apThe ANOVA was used to assess the accuracy of the model. With an F-value of 26.48, the model was statistically significant
Davoodi and Eskandari (2015)	Turning	RSM	Vc was shown to be the most significant factor in tool life, accounting for 55.84% of the totalANOVA was used to confirm that the model was adequate
Lin et al. (2020)	Turning	Grey model	The prediction model was developed based on a single-factor turning testThe examination of the model’s predictive outcomes revealed that the short-term prediction error of the grey model was below 5%

Source(s): Authors’ own work

Table 6

Summary of tool life modelling methods under stochastic methods using probabilistic and reliability analyses

Authors	Machining type	Tool life or tool RUL modelling method	Remarks
Hitomi et al. (1979)	Turning	Using the logarithmic normal distribution as the tool wear distribution, reliability function of the tools was obtained	As cutting speed increased, the cutting tool's reliability decreasedThe cutting tool failure rate was aligned with theoretical predictions at a flank wear limit of 0.4 mm. Yet, at a limit of 0.3 mm, the experimental failure rate deviated from the theoretical predictions for high failure rates
Klim et al. (1996)	Milling	Two-parameter Weibull distribution	When comparing constant feed to variable feed operations, the average tool life increased by 20%–43%The Kolmogorov–Smirnov test at the 0.95 confidence level was utilized to make the fit decision
Lin (1998)	Milling	Three-parameter Weibull distribution	The feed rate range was separated into three areas in terms of tool life by chipping
Wang et al. (2001)	Turning	Reliability-dependent failure rate model (AE model)	The variation of the process-dependent decay factor but not the variation of the embedded decay factor had a greater impact on the mean time of failure-free timeFor the lognormal distribution model and the Weibull distribution, the computed RMS error between the predicted value and the experimented value was 2.5741 and 2.7885%, respectively; however, for the reliability-dependent failure rate model (AE model), the RMS error was just 1.6626%
Tail et al. (2010)	Drilling	Weibull proportional hazards model	The model’s covariate was the cutting speedThe model was validated by constructing the confidence interval
Vagnorius et al. (2010)	Turning	Mixed Weibull model	The process parameters were fixedThe goodness-of-fit of the model was examined by a graphical method based on the empirical total time on test (TTT) plot
Ding and He (2011)	Turning	Proportional hazards model	As covariates, RMS and the peak of the time domain index derived from vibration signals were chosen
Li and Zhang (2012)		Gamma process	Under the invariant machining conditions, the examination of the cutting tool reliability was carried out
Salonitis and Kolios (2014)	Turning	Combinations of stochastic response surface and surrogate modelling methods, coupled with MCS and FORM	When compared to cutting speed, the influence of feed rate on the tool’s reliability was found to be less significant
Braglia and Castellano (2014)	Turning	Diffusion theory by utilizing Fokker–Planck equation
Karandikar et al. (2014a)	Milling	Bayesian inference approach	Tool life values were predicted at different spindle speeds
Karandikar et al. (2014b)	Turning	Bayesian inference approach	At various feed rates and cutting speeds, tool life values were predicted
Xu and Cao (2015)		Weibull distribution	Product quality loss, penalty cost for potential tool failure, production capacity loss and tool replacement cost were all taken into account to determine the best time to replace the tools
Liu et al. (2016)	Milling	Non-linear and non-Gaussian SSM	The reliability evaluation was more accurate when the prediction was made from a point close to failure
Aramesh et al. (2016)	Turning	Proportional hazards model with a baseline Weibull distribution	Cutting time and cutting parameters (cutting speed and feed rate) were taken into account to calculate an expected tool lifeFor all experimental runs, a 95% confidence interval revealed that the discrepancy between the predicted and mean measured tool lifetimes was <8%
Shaban and Yacout (2018)	Turning	Proportional hazards model	Cutting time and cutting parameters (cutting speed and feed rate) were taken into account to calculate the expected tool lifeThe model was verified by using the Kolmogorov–Smirnov goodness-of-fit test, which yielded a p-value of 0.248773
Shaban et al. (2017)	Turning	Proportional hazards model	Cutting time and cutting parameters (cutting speed and feed rate) were taken into account to calculate the expected tool lifeThe model was verified by using the Kolmogorov–Smirnov goodness-of-fit test, which yielded a p-value of 0.0965714
Cui et al. (2017)	Turning	Weibull distribution	By ignoring the effects of the crack growth velocity, statistical aspects of the original tool material damage were investigated on the basis of damage mechanics and micromechanics
Yu et al. (2017)	Milling	Weighted HMM	Tools' wear was tracked using the RMS of vibration dataWeighted HMM performed better than regular HMM, with prediction accuracy close to 1 for each testing cutter
Liu et al. (2020)	Turning	The tool life distribution model was obtained as normal distribution model	The optimal cutting parameters were obtained through the wear map approachAt optimal cutting conditions, when $R\left(T\right)$ was 0.9, the tool replacement time should be 70 min. When $R\left(T\right)$ was 0.5, the tool replacement time should be 80 min
Salonitis and Kolios (2020)	Milling	MCS	By increasing the cutting speed and feed rate, reliability decreasedValidation results showed that at experimentally obtained failure times, the probabilities of failure obtained from the proposed method were in the interval between 80 and 90%
Xu et al. (2021)	Turning	Lognormal distribution as the tool wear distribution	The joint distribution of the tool's hardness and fracture toughness expressed the wear life probability density functionIf the ceramic tool's reliability was above 0.5, the results indicated that the difference between its theoretically reliable life and its real life was less than 5% under the same reliability
Han et al. (2021)	Milling	HDP-HMM	The proposed method was compared with weighted HMM and conventional HMM
Wang et al. (2021)	Milling	Exponential degradation model	The monotonicity score was used to narrow down the cutting force signal in the X direction to six featuresWhen looking 200 and 100 steps ahead, the prediction inaccuracies of the approach provided in this research were 8.65 and 2.34%, respectively
Sun et al. (2024)	Milling	Exponential degradation model	The methodology proposed in this research was recommended for predicting RUL in cases where the degradation signal of the system exhibits an exponential trend
Das et al. (2024)	Turning	AFT models	The effects of covariates (Vc, f, ap and tool nose radius) on the reliability of the cutting tool were studiedThe MAPE between the experimental tool life and predicted mean time to failure (MTTF) of cutting tools was 13.74% for the lognormal AFT model

Source(s): Authors’ own work

Table 7

Summary of tool life modelling methods under data-driven models

Authors	Machining type	Tool life or tool RUL modelling method	Remarks
Chen et al. (2011)	Turning	Logistic regression model	By correlation analysis, four time-domain, three wavelet packet energy and one entropy feature from vibration signals were used as inputsWith a 0.6 mm flank wear width as the failure criterion, tool no. 12 had an estimated error of 1.42%
Li et al. (2015)	Milling	Logistic regression model	The input variables for the regression model were chosen to be the wavelet packet energy of the cutting force and the acoustic emission signals across a variety of frequency bandsThe error of model 1 (considering acoustic emission and milling force) was 0.0296. The error of model 2 (considering the acoustic emission vector) was 0.037
Kovac et al. (2014)	Milling	The MIMO Mamdani FIS	As cutting speed increased, tool life droppedThere was an average 11.6% discrepancy between the expected and actual tool lifespans in the tests
Gokulachandran and Mohandas (2015b)	Milling	Sugeno FIS and SVR	The predictive neuro fuzzy model was found to be superior to the SVR model at estimating the RUL of tool
Drouillet et al. (2016)	Milling	ANN	The root mean square power (Prms) value in the time domain was observed to be sensitive to tool wearWith a mean error of approximately 1 min, it was discovered that the anticipated RUL values and curves were in good agreement with the actual RUL values and curves
Sun et al. (2016)	Milling	CGA-BPNN	Each original cutting force, vibration and acoustic emission signal was split into a number of IMFs using the EMD technique. The average and maximum amplitudes of the marginal spectra of some IMFs were employed as sensitive featuresWhen comparing evaluated RUL to monitored RUL, the largest absolute difference was less than 3.3 min
Mikołajczyk et al. (2018)	Turning	ANN	The predicted tool life was stated with a maximum error of 2.1 min and an average error of 1.10 min
Liu et al. (2019)	Slotting	Health index (HI) similarity	It was determined that six features of acoustic emission signals were significantly linked to tool wearThe MAE and RMSE of the proposed method were 0.6581 and 0.9333 in comparison with 2.0149 and 2.4234 for LS-SVR
Sun et al. (2019)	Turning	DTL network based on SAE	The prediction error was greater in the absence of feature transfer learning than it was in the presence of DTL learning
Chen et al. (2019)	Turning	Support vector space	The seven-dimensional salient features of vibration signals were reduced to a two-dimensional feature matrix by singular value decomposition
Zhou et al. (2019)	Boring	LSTM network	The feature vector was constructed using the mean amplitude of the EMD-derived IMF and the peak amplitude of the HHT edge spectrumIn this paper, the test points were evaluated using the R-squared statistic, and the resulting value was R2 = 0.7806
Yang et al. (2019)	Milling	Trajectory similarity and SVR	The time-domain AV, RMSV and SDV of the cutting force were incorporated into the prediction model, as were the energy values of 8 frequency bands and the SDV of energy values from 4 frequency bands in the wavelet analysis stepWhen applied to the stable stages of Tools 1, 2 and 3, this integrated prediction model achieved an accuracy of 88.5%, 87.5% and 90.5% for RUL predictions, respectively
Li et al. (2020)	Milling	Adaptive time window and DBiLSTM neural network	It was determined that the time domain kurtosis of the spindle motor current signals was the most significant of tool wearFor milling Case 1 (long tool life), the MAE and RMSE of the suggested technique were 0.1130 and 0.1592, while for milling Case 4 (short tool life), they were 0.0748 and 0.0950, respectively
An et al. (2020)	Milling	CNN-SBULSTM network	In experiment 1, the CNN-SBULSTM network improved accuracy by 25%, score by 38% and RMSE by 77% when compared to the random forest model. Additionally, the CNN-SBULSTM network outperformed the 2-layer CNN by a small margin, improving results in terms of score (+0.27%), RMSE (−3%) and accuracy (+3%)
Zhang et al. (2021)	Milling	CNN-LSTM algorithm	Vibration, cutting force and acoustic emission signals were separated using the Hurst exponent-based signal division approachThe results of the case study used in this study demonstrated that the proposed methodology achieved an accuracy of 87.3% in its predictions
Li et al. (2022)	Milling	SVR, SVM, sliding time window, and particle filter algorithm	Through an experiment with a single working situation, the effectiveness of this strategy was studiedThe proposed method's RMSE was 0.0202, the lowest of the other methods utilized for comparison
Qin et al. (2023)	Milling	SAL and GPR	Results from multiple case studies were compared to show that the proposed method was effective
De Barrena et al. (2023)	Turning	BRNN (BiLSTM and BiGRU)	RMS value of feed force was obtained as the best predictor of tool RUL.The RUL prediction RMSE of the proposed BiLSTM and BiGRU models, compared with the next model that obtained better results, improved by 4.03 and 3.61%, respectively
Bagga et al. (2023)	Turning	Gradient-boosted trees and SVM	The validation of the proposed models indicated that the SVM and boosted tree methods yielded maximum absolute errors of 5.89 and 7.56%, respectively
Wu et al. (2023a)	Turning and milling	Feature enhancement module and BiLSTM	The generalization ability of the proposed method was evaluated by using turning and milling tool wear data sets

Source(s): Authors’ own work

Table 8

Summary of tool life modelling methods under hybrid models

Authors	Machining type	Tool life or tool RUL modelling method	Remarks
Sun et al. (2018)	Milling	BPNN and Wiener process	Some SVEs were extracted as sensitive features from the top five IMFs after decomposing each cutting force, vibration and acoustic emission signal into several IMFsThe discrepancies between the predicted and measured RULs of cutting tools were between −5 min and 2.75 min
Luo et al. (2020)	Milling	A hybrid approach of physical model and data-driven based on Digital Twin (DT)	The RUL prediction error ratio of the hybrid approach was 3.17% at initial stage, 3.56% at medial stage and 6.27% at end stage and all are smaller than the single-strategy approaches
Zhang et al. (2023)	Milling	CNN and multistage Wiener process	The input data was created by expanding the complex Morlet wavelet scalogram of vibration signals and combining the original and generated image dataThe multistage nonlinear Wiener process model achieved the best RMSE and cumulative relative accuracy (CRA) values out of the four approaches evaluated
Feng et al. (2024)	Milling	BNN and Wiener process-based RUL ensemble model	The comparisons of MAE and RMSE using two milling experiments datasets ensure the supremacy of the proposed nonlinear ensemble model over the individual models. Comparisons with the existing classical methods were performed and the proposed method outperforms with a CRA greater than 0.6
Li et al. (2024)	Milling	CSBLSTM-TSAM and nonlinear Wiener process	The effectiveness of the proposed method was validated through single and multi-condition milling experiments.

Source(s): Authors’ own work