Tool Life Distribution Research Articles

Machining condition-based stochastic modeling of cutting tool’s life

One of the major problems in the application of machining processes is the cutting tool life estimation. In this regard, different studies with various assumptions have been conducted to analyze tool wear characteristics under various cutting conditions to achieve different objectives. Traditional models for the analysis of tool life are mostly based on deterministic approaches, and the variations in cutting conditions are overlooked, and the tool life is not precisely matched with predicted values by these methods. In recent years, researchers have considered using the stochastic approach in forecasting tool life. Among them, Weibull distribution has special significance. One problem in using these approaches is the accurate estimation of tool’s life distribution functions based on the empirical information. In other words, although many researchers have considered Weibull an appropriate distribution for the cutting tool life modeling, however, the estimation of its parameters has certain inherent complexities. In this research, a hybrid methodology is presented to determine the parameters of the tool life distribution, by using the design of experiment (DOE) based on Box-Behnken design (BBD), total time on the test (TTT) transform, and golden section search (GSS). The estimation method of Weibull distribution parameters in this paper is compared with well-known techniques such as the least square method and maximum likelihood estimation. Finally, the proposed methodology was implemented in a case study, and the results were reported. The values of R2 for shape and scale parameters are 92.52% and 96.80%, respectively, which confirm the adequacy of the proposed methodology in the practical applications.

Reliability analysis of the cutting tool in plasma-assisted turning and prediction of machining characteristics

ABSTRACT Heat-assisted machining (HAM) is an alternative method for the successful machining of difficult-to-cut aerospace superalloys. However, the tool wear progression in HAM has been substantially affected by the workpiece external heating temperature along with the machining parameters. It is of great importance to precisely estimate the tool wear progression and reliability of the cutting tool operated in HAM to enhance the machining efficiency and economics. Hardened AISI4340 alloy steel was machined under plasma-arc heating conditions with WC cutting tools. The experimental results reviled that for 200°C of preheating temperature, the surface roughness noted as 2.03µm and tool life as 870s. While at 600°C, the surface roughness as 1.68µm, and tool life extended to 1885s to reach the set threshold value of 0.4mm flank wear. Notch wear as dominant tool wear mechanism at 200°C and 400°C, while it is diffusion wear at 600°C. On the establishment of stochastic tool life distribution and reliability models, tool lives measured at all heating conditions followed a Weibull distribution. Empirical models for tool wear, surface roughness, and material removal rate were postulated and validated statistically as-well-as experimentally. The derived reliability and empirical models can be used to predict the machining characteristics to enhance its performance.

Experimental study of cutting-parameter and tool life reliability optimization in inconel 625 machining based on wear map approach

As a result of its excellent properties, nickel-base superalloy has been widely used in the manufacture of shaft-disc-type components for aeroengines. However, tool wear and short tool life are prominent problems related to the machining process, because of the poor thermal conductivity, high hardness, and strong cohesiveness of nickel-base superalloy. Therefore, optimization of both the processing parameters and tool life reliability is attracting increasing research attention. In this study, coated carbide tools are used in turning tests of Inconel 625 superalloy. The wear morphologies and mechanisms of these tools under different parameters are analyzed, and a two-dimensional tool wear map is constructed. The influence of the cutting parameters on the workpiece surface roughness and flank wear is analyzed with consideration of the wear map, so as to determine the optimal cutting parameters. On this basis, a complete tool life experiment is performed, and a tool life distribution model and tool life reliability model are established to facilitate tool life reliability evaluation under the optimal parameters. These findings provide theoretical support for process optimization in Inconel 625 machining.

A mathematical model for the joint optimization of machining conditions and tool replacement policy with stochastic tool life in the milling process

One major problem in the machining process is the optimization of tool replacement policy and machining condition simultaneously. Although many studies have been developed to optimize the machining process considering the stochastic tool life, they have not optimized these two problems together. Therefore, unlike these investigations, the objective of this study is to develop an integrated mathematical model for joint-optimization of tool replacement policy and machining condition given the dependence between them and various costs in the machining process. In this paper, the dependence of cutting tool life distribution and surface roughness of workpiece to the machining conditions is modeled based on a five-step methodology initially. For this purpose, empirical data of a milling process obtained via design of experiments (DOE) based on Box-Behnken design (BBD) is used. These data, converted by total time on test (TTT), transform and using an optimization process based on golden section search (GSS), the relation between machining conditions and parameters of the tool life distribution is obtained as a full quadratic model. The R2 values for the surface roughness, shape, and scale parameters in the full quadratic models are 89.61, 92.52, and 96.80% respectively, which confirms the adequacy of the proposed methodology. Then, a mathematical optimization model is proposed for multi-pass machining with considering costs related to tool replacement policies, direct labor costs, machining costs, loading/unloading of workpiece costs, and quality costs in a machining process. The proposed model of this study can optimize both of the tool replacement policy and the machining conditions simultaneously and also it can lead to choosing the optimized policy of the continuous or the discrete tool condition monitoring approaches. This model is implemented on a case study and its result is reported. For solving the mathematical model, the electromagnetism-like mechanism algorithm is used that has the proper performance to optimize the continuous spaces.

Diffusion Theory Applied to Tool-Life Stochastic Modeling Under a Progressive Wear Process

In this paper, a novel approach to the derivation of the tool-life distribution, when the tool useful life ends after a progressive wear process, is presented. It is based on the diffusion theory and exploits the Fokker–Planck equation. The Fokker–Planck coefficients are derived on the basis of the injury theory assumptions. That is, tool-wear occurs by detachment of small particles from the tool working surfaces, which are assumed to be identical and time-independent. In addition, they are supposed to be small enough to consider the detachment process as continuous. The tool useful life ends when a specified total volume of material is thus removed. Tool-life distributions are derived in two situations: (i) both Fokker–Planck coefficients are time-dependent only and (ii) the diffusion coefficient is neglected and the drift is wear-dependent. Theoretical results are finally compared to experimental data concerning flank wear land in continuous turning of a C40 carbon steel bar adopting a P10 type sintered carbide insert. The adherence to the experimental data of the tool-life distributions derived exploiting the Fokker–Planck equation is satisfactory. Moreover, the tool-life distribution obtained, when the diffusion coefficient is neglected and the drift is wear-dependent, is able to well-represent the wear behavior at intermediate and later times.

Stochastic theory of tool life - theoretical developments on the injury theory

This paper aims at presenting a revisited and extended version of the injury theory, originally developed by Ramalingam and Watson (1977) and Ramalingam (1977). This theory allows deriving tool-life distributions when either a single catastrophic event or a gradual and cumulative wear process terminates the tool useful life. Since these models cover great importance in tool-life modelling, this paper would contribute in this direction with further observations and results, giving special attention to the mathematical formulation. In particular, besides deriving known results following a different approach, we extend the theory to the case of multiple machines with both single- and multi-tool configurations. Moreover, as examples we derive different expressions of the tool-life distribution in the cases studied related to particular formulations of the injury rate.

A Reliability Based Approach for Predicting Optimal Tool Replacement Time

Turning can be classified as both rough and finishing process. Any failure during this process will cause a huge loss in terms of raw materials cost. In machining operation, to avoid failures and related consequences, tools are often replaced well before the end of their useful life time. Only 50-80% of the expected tool life is typically used. This is especially the case of production systems where process robustness is critical. Unfortunately, such a strategy leads to increased tool costs. Even though the cost of the tools is often assumed to be only 2-4% of the manufacturing costs, there are studies suggesting that tool costs can be much higher. The main objective of this paper is to outline a procedure for estimating the optimal tool replacement time based on the tool performance calculated using reliability function. This paper includes the selection of a suitable tool life distribution, modeling of reliability functions of cutting tool based on the flank wear as the major failure criteria, Experimental study to validate the reliability function developed for cutting tool, Development of total time on test (TTT) transformation to give brief idea regarding the failure rate of cutting tool.

Tool planning for a lights-out machining system

The goal of most advanced manufacturing systems is to continuously improve uptime while reducing the amount of direct supervision required for operations. However, when there is randomness in system components, this improvement can be difficult to attain. For instance, when automating metal cutting operations, the randomness of tool life requires ensuring that there are sufficient cutting tools available on the machines to meet unsupervised production requirements, and variations in tool life can make planning challenging. This paper focuses on the problem of selecting the cutting speeds for processing a set of part types by an unsupervised metal cutting flexible machine in such a situation. The machine is set up to operate unsupervised for a specific known duration. The tool magazine of this machine is preloaded with tools commensurate with the processing requirements. The lifetime of each tool is random, with the coefficient of variation assumed to be constant, and a system for online monitoring of the tool condition is available. The objective in this situation is to ensure that disruption is minimized—in other words, that the machine operates while ensuring some minimum probability of completion. This is referred to as the required service level. This paper presents models for determining the optimal magazine loading and cutting speeds that will meet a required service level. Solutions obtained using commonly available nonlinear programming solvers are included for illustration, and differences when the tool life distributions are either normal or Erlang are contrasted.

The efficiency range of economical cutting conditions and tool replacement under the age replacement strategy

This paper presents models for calculating the optimal cutting feed rate, spindle speed, and age of preventive tool replacement for a standalone cutting machine. The optimal cutting conditions are determined and analysed for three different objective functions: minimum expected cycle time, minimum expected cost per unit, and maximum expected profit-rate, under the Age Replacement Strategy (ARS) and assuming that the tool-life distribution function is Normal. We show that the first two objective functions are separable, and present an efficient, one-dimensional search procedure for the optimization. A definition of the efficiency ranges of feed rate and standard age of tool replacement is suggested for the ARS, which improves the efficiency range defined in the literature for the Failure Replacement Strategy (FRS).

Optimization of the machining economics problem under the periodic control strategy

This paper presents a model for calculating the optimal cutting feed rate, spindle speed, and periodic control interval for a standalone cutting machine. The optimal cutting conditions are determined for the maximum expected 'profit rate' criterion, under the assumption that the Normal distribution function represents the tool-life distribution. When the cutting operation and the load/unload process are preformed automatically without any supervisor, it is not necessary to employ a full-time operator for the machine. Thus, we used the Periodic Control Strategy, under which the operator attends to the cutting machine only at predefined calendar times. We have developed an approximate model that was studied using simulations. The model appears to be very efficient.

A dynamic tool requirement planning model for flexible manufacturing systems

Despite their strategic potential, tool management issues in flexible manufacturing systems (FMSs) have received little attention in the literature. Nonavailability of tools in FMSs cuts at the very root of the strategic goals for which such systems are designed. Specifically, the capability of FMSs to economically produce customized products (flexibility of scope) in varying batch sizes (flexibility of volume) and delivering them on an accelerated schedule (market response time) is seriously hampered when required tools are not available at the time needed. On the other hand, excess inventory of tools in such systems represents a significant cost due to the expensive nature of FMS tool inventory. This article constructs a dynamic tool requirement planning (DTRP) model for an FMS tool planning operation that allows dynamic determination of the optimal tool replenishments at the beginning of each arbitrary, managerially convenient, discrete time period. The analysis presented in the article consists of two distinct phases: In the first phase, tool demand distributions are obtained using information from manufacturing production plans (such as master production schedule (MPS) and material requirement plans (MRP)) and general tool life distributions fitted on actual time-to-failure data. Significant computational reductions are obtained if the tool failure data follow a Weibull or Gamma distribution. In the second phase, results from classical dynamic inventory models are modified to obtain optimal tool replenishment policies that permit compliance with such FMS-specific constraints as limited tool storage capacity and part/tool service levels. An implementation plan is included.

Prediction of tool failure rate in turning hardened steels

This paper presents a stochastic model for predicting the tool failure rate in turning hardened steel with ceramic tools. This model is based on the assumption that gradual wear, chemical wear, and premature failure (i.e. chipping and breakage) are the main causes of ending the tool life. A statistical distribution is assumed for each cause of tool failure. General equations for representing tool-life distribution, reliability function, and failure rate are then derived. The assumed distributions are then verified experimentally. From the experimental results, the coefficients of these equations are determined. Further, the rate of failure is used as a characteristic signature for qualitative performance evaluation. The results obtained show that the predicted rate of ceramic tool failure is 20% (in the first few seconds of machining) and it increases with an increase in cutting speeds. These results indicate that there will always be a risk that the tool will fail at a very early stage of cutting. Such a possibility should not be overlooked when developing proper tool replacement strategies. Finally, the results also give the tool manufacturers information which can be used to modify the quality control procedures in order to broaden the use of ceramic tools.

Optimal solutions for the machining economics problem with stochastically distributed tool lives

This paper proposes analytical models and numerical procedures for simultaneously determining the optimal cutting speed and tool replacement policy in machining economics problems with stochastic tool lives when the objective is the minimization of the machining cost per part. It is shown that the objective function is separable for certain phase type tool life distributions, including Gamma, which leads to an efficient solution procedure.

A Statistical Tool Replacement Procedure for the Design of a High-Reliability Machining System.

This study presents a statistical model for analyzing the reliability of a machining system considering a tool life distribution, as well as a statistical procedure for the design of a high-reliability machining system. Interruption of machining due to sudden tool failure or excessive tool wear is detrimental in automated machining systems. Not only does it disrupt production, but it also creates an obstacle in the construction of completely automated unmanned machining systems. High-reliability is a prerequisite for the design of an efficient and economical machining system. This study : ( 1 ) presents a new criterion (i. e., reliability criterion) for the design of a machining system, ( 2 ) defines the reliability of a machining system, ( 3 ) develops a statistical model to analyze the reliability of a machining system, and ( 4 ) presents a statistical procedure for the design of high-reliability machining systems.

Simultaneous determination of optimal machining conditions and tool replacement policies in constrained machining economics problems by geometric programming

This paper presents an analytical model for the simultaneous determination of the optimal machining conditions (cutting speed and feed) and the optimal tool replacement policy in constrained machining economics problems by geometric programming. The optimal preventive tool replacement policy is initially determined as a tool life fractile (independent of the underlying tool life distribution) and then it is expressed as actual tool life by utilizing the underlying tool life distribution applicable to the combination of tool material, workpiece properties, and machining conditions. Constraints on the optimal values of cutting speeds, feeds, and/or optimal tool replacement policy based on maximum allowable values and/or surface finish requirements are handled through the optimization of the dual objective function. It is shown that the optimal cost distribution does not depend on the cost coefficients in the objective function. Finally, the model is applied to two-stage systems where the necessary condition...

Optimum tool replacement policies with penalty cost for unforeseen tool failure

Models for tool replacement strategies in manufacturing systems introducing a penalty cost if the tool fails during the cut are proposed. These models are developed for general stochastic tool life distribution and applied to the case of a log-normal distribution.

Data Dependent Systems Approach to Stochastic Tool Life and Reliability

A Data Dependent Systems approach is outlined for obtaining tool life distribution and reliability models directly from shop floor and/or laboratory failure data. The approach does not require any a-priori knowledge of the distribution and can be used with a limited amount of data. Estimation of the first order model is illustrated by application to HSS tools in turning. The tool life signatures at three different speeds are exhibited in the form of plots of hazard rate, reliability and failure time probability density functions. Formulation of simple tool replacement strategies from these plots by the shop personnel is illustrated; the mathematical expressions given for these functions can be used to develop more elaborate optimal strategies in computerized adaptive control. It is shown that most of the commonly used tool life distributions are well approximated by special cases of the first order model and hence are included in the approach.

Tool Life Distributions—Part 3: Mechanism of Single Injury Tool Failure and Tool Life Distribution in Interrupted Cutting

Tool life distribution under production machining conditions must be suitably accounted for in any rational design of large volume or automated machining lines. Reliable data on the type of distributions likely to be encountered are, however, unavailable. To remedy this, using relevent physical arguments, probabilistic models of tool failure which produce distribution functions germane to tool life scatter have been proposed and developed in earlier parts of this paper. An arbitrarily introduced hazard function was used to predict the life distributions likely to be obtained. The details of the mechanisms giving rise to tool failure were, however, not examined. Mechanistic questions connected with the single-injury tool failure (tool fracture) are examined in this part. The arbitrarily introduced hazard function is shown to have a physical basis. It is shown that the hazard function is determined by the interaction between the characteristics of the environment in which the tool operates and the mechanical properties of the tool material. The concepts outlined and the mechanistic model of tool failure proposed have been tested experimentally in interrupted cutting. It is shown that the predicted Weibull-distributed tool life is obtained when tool failure is due to a single injury and that the parameters of the Weibull distribution are governed by the properties of the tool material as well as those of the machining system.

Tool-Life Distributions—Part 2: Multiple-Injury Tool-Life Model

The single-injury tool-life model developed in Part 1 of this paper is extended to the case of tool failure due to a multitude of injuries. The expected tool-life distribution in the case of tool failure from multiple injuries due to constant, time-independent stochastic hazards is shown to be a gamma distribution. The result obtained is based on a linear wear-rate assumption. The model is further extended to ensure applicability in the nonlinear wear region. It is shown that the expectation of a log-normal tool-life distribution when tool failure is due to crater wear is not unrealistic. No specific mechanism of tool wear is used to develop the model. The nature of the hazards and the wear mechanisms that are consistent with the multiple-injury tool-life model will be discussed in a subsequent work.

Tool-Life Distributions—Part 1: Single-Injury Tool-Life Model

The statistical variability of tool life in production machining must be accounted for in any rational design of large-volume or automated manufacturing systems. The probabilistic approach needed for such a design is presently limited by lack of data on tool-life distributions and by lack of knowledge of the underlying causes giving rise to tool-life scatter. Given these circumstances, on the basis of relevant physical arguments one may construct probabilistic models that produce distribution functions germane to the problem of tool-life scatter. This paper is concerned with such a study. This first part presents the results obtained on the assumption that the useful life of a tool is terminated by a single, catastrophic injury. Cases where resistance to tool failure is time-independent and time-dependent are examined. The case of tool failure caused by multiple injuries will be presented in Part 2.