Modeling of machining processes is more than a century old with the pioneering work of Taylor [1907]. Taylor’s empirical model relates cutting speed and tool life in an empirical manner requiring a huge amount of data for each tool-job combination. The predictions by this model are in an average sense. In general, there is a large amount of statistical variation in the tool life in machining. Ernst and Merchant [1941] were perhaps the first to present a physics based mathematical model of an orthogonal machining process. However, as discussed by Astakhov [2005], the model of Ernst and Merchant is inadequate for a realistic modeling of the machining processes. A number of other physics based models have been proposed, but all of them invariably contain several simplifying assumptions. Moreover, to use these models for the machining performance prediction, often a large amount of data from experiments is needed. Bhattacharyya [1984] has presented different mathematical models for obtaining the optimum machining parameters in turning process. However, these models do not have provision to incorporate the quality of
machined parts. Nassirpour and Wu [1977] defined the statistical parameters and geometric properties of the surface profile. Experiments were conducted to study the influence of feed rate, nose radius and cutting speed on the surface geometry. They observed that surface finish improves as the cutting speed increases. They have constructed response surface contours for centerline average (Ra) values of surface roughness, which can be used to choose a cutting condition for a given surface finish.
Sundaram and Lambert [1981] studied the effect of speed, feed, nose radius, depth of cut, time of cut and tool coating. They used multiple regression technique to develop mathematical model. Rao [1986] developed a microcomputer-based technique for monitoring flank wear on a single point cutting tool in turning operation. He used a wear index in real time as the ratio of the dynamic force amplitude of the tool holder to the amplitude of the vibration at the same frequency.
This wear index was found to be independent of all cutting force variables within the range of variables investigated, but is affected by work-piece hardness. Koren et al.
[1991] proposed three methods for flank wear estimation under varying cutting conditions in turning. These methods use recursive least-squares algorithms and can be applied when there are stepwise variations in one of the cutting conditions.
Method 1 was based on a standard error-estimation algorithm. In this method, change in cutting force was analysed. Methods 2 and 3 contain real time test of the estimation of reliability and therefore start the wear estimation after some initial observation period. Oraby and Hayhurst [1991] and Ravindra et al. [1993] proposed mathematical models to describe the wear-time and wear-force relationships for turning operation. Cutting force components have been found to correlate well with progressive wear and tool failure. The results show that the ratio between force components is a better indicator of the wear process, compared with the estimate obtained using absolute values of the forces.
Subhash et al. [2000] established the empirical relations for predicting surface residual stresses, surface roughness, dimensional instability and tool life by response surface methodology as a prerequisite for their proposed optimization technique.
They used regression analysis and found that feed and depth of cut are most influencing parameters on residual stresses, dimensional stability as well as surface
finish. Choudhury and Kishore [2000] developed a mathematical model for the estimation of flank wear and concluded that force increases linearly with tool wear land width. Flank wear has been calculated indirectly by measuring an easily measurable quantity such as ratio of the feed force to vertical force.
Smithy et al. [2000] developed a model to predict the worn tool forces. Their theoretical analysis shows that for a given tool and work-piece material combinations, the incremental increase in the cutting force due to tool flank wear is solely a function of the amount and nature of the wear and is independent of cutting condition in which tool wear was produced. However, in practical shop floor experiments, there is a lot of statistical variation and uncertainty in data and results may not conform to their theory.
Kumar et al. [2001] developed some empirical relations to relate the surface roughness with feed and vibration. These empirical relations are developed based on theoretical reasoning and experimental observation. It was observed that to a reasonable degree of accuracy, vibration feedback could play a role in predicting the surface roughness. Suresh et al. [2002] developed a surface roughness prediction model in turning using a response surface methodology to produce the factor effects of the individual process parameters. The surface roughness prediction model was optimized using genetic algorithm (GA). Noordin et al. [2004] studied the application of response surface methodology to describe the performance of coated carbide tools in turning of AISI 1045 steels. The response variables were surface finish and tangential force. ANOVA revealed that feed was the most significant factor influencing the response variables that were investigated. Ozel and Karpat [2005] studied the predictive modeling of surface roughness and tool wear in hard turning using regression model and neural network model. In their study, effects of cutting edge geometry, workpiece hardness, feed rate and cutting speed on surface roughness and tool wear were experimentally investigated. They used a four factor two level factorial design.
Several physics based models have been proposed for the prediction of cutting forces in turning [Reddy et al., 2001; Rao and Shin, 1999, Clancy and Shin, 2002;
Parakkal et al. 2002]. The more detailed information about the machining can be obtained by finite element method (FEM), which is a numerical method for solving
differential equations by discretizing the domain into a number of small elements. A number of researchers have employed the FEM for the prediction of temperature in machining as described in the survey paper by Abukhshim et al. [2006]. Joshi et al.
[1994] analyzed the orthogonal machining process by using an Eulerian FEM formulation. They considered the viscoplasticity in modeling of the material. Özel [2006] simulated the orthogonal machining process using an updated Lagrangian FEM formulation and investigated the effect of friction models on the results.
Besides the simulation of machining process, the finite element model has been used for the predictions of tool wear and fracture of the cutting tool [Ahmad et al., 1989;
Xie et al., 2005; Cakir and Sik, 2005; Filice et al. 2007]. It has also been used for predicting the integrity (residual stresses, micro-hardness and microstructure) of machined surfaces [Monaghan and Brazil, 1997; Wen et al., 2006].
Difficulty in the determination of input parameters required in a physics-based model has prevented its applicability at the shop floor. For example, determination of appropriate value of flow stress and friction during machining is a challenging task [Özel, 2006]. The empirical models do not require the determination of any basic parameter like flow stress; however, they require a huge amount of experimental data for proper fitting of the model. Often it is difficult to find a suitable function that can fit the experimental data. This prompted the researchers to explore the application of soft computing based methods to machining, which is discussed in the following section.