Performance-Based Predictive Models and Optimization Methods for Turning Operations and Applications: Part 3—Optimum Cutting Conditions and Selection of Cutting Tools

Performance-Based Predictive Models and Optimization Methods for Turning Operations and Applications: Part 3—Optimum Cutting Conditions and Selection of Cutting Tools

Journal of Journal Manufacturing of Manufacturing ProcessesProcesses Vol. 9/No. Vol. 1 9/No. 1 2007 2007 Manufacturing Engineering Research Digest Se...

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Journal of Journal Manufacturing of Manufacturing ProcessesProcesses Vol. 9/No. Vol. 1 9/No. 1 2007 2007

Manufacturing Engineering Research Digest Series

Performance-Based Predictive Models and Optimization Methods for Turning Operations and Applications: Part 3—Optimum Cutting Conditions and Selection of Cutting Tools X. Wang, TechSolve, Inc., Cincinnati, Ohio, USA Z.J. Da, EDS, Dallas, Texas, USA A.K. Balaji, University of Utah, Salt Lake City, Utah, USA I.S. Jawahir, University of Kentucky, Lexington, Kentucky, USA

Abstract

... In the USA, the correct cutting tool is selected less than 50% of the time, the tool is used at the rated cutting speed only 58% of the time, and only 38% of the tools are used up to their full tool-life capability.... This situation highlights the need for development of scientific approaches to select cutting tools and cutting conditions for optimum machining performance. Selection of cutting tools and cutting conditions is an essential element in process planning for machining. This task is traditionally carried out on the basis of the experience of process planners with the help of data from machining handbooks and tool catalogs. Process planners continue to experience great difficulties due to the lack of data on the numerous new commercial cutting tools with different materials, coatings, geometry, and chip-groove configurations for high wear resistance and effective chip breaking. Also, specific data on relevant machining performance measures such as tool life, surface roughness, chip form, and so on, are hard to find due to the lack of reliable information or predictive

This paper presents a summary of recent developments in developing performance-based machining optimization methodologies for turning operations. Four major machining performance measures (cutting force, tool wear/tool life, chip form/chip breakability, and surface roughness) are considered in the present work, which involves the development and integration of hybrid models for single and multi-pass turning operations with and without the effects of progressive tool wear. Nonlinear programming techniques were used for single-pass operations, while a genetic algorithms approach was adopted for multi-pass operations. This methodology offers the selection of optimum cutting conditions and cutting tools for turning with complex grooved tools.

Keywords: Optimization Methods, Multi-Pass Turning Operations, Performance-Based Predictive Modeling, Genetic Algorithms

Introduction Machining operations constitute a large segment of the manufacturing sector in the United States. However, a recent CIRP (The International Academy for Production Engineering) working paper (Armarego et al. 1996) reports the survey results of a major cutting tool manufacturer as,

The Manufacturing Engineering Research Digest series aims to disseminate current research in a variety of manufacturing areas. The approach is to synthesize—or digest—manufacturing research to empower the practicing engineer toward innovative problem solving. The published papers are not intended to be historically and academically exhaustive reviews, but rather to present appropriate content that has potential industrial application. The papers meet rigorous academic review standards for content, citations, and relevance to manufacturing researchers as well as pass critical evaluation by practicing manufacturing engineers. For information on how to contribute to the Manufacturing Engineering Research Digest series, send an e-mail to [email protected]

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models for these measures. Consequently, process planners are forced to choose and recommend suboptimal cutting conditions.

pabilities have inhibited the widespread use of the available optimization strategies (Armarego 1996). Traditional approaches in this area of performancebased optimization have not considered the interacting machining performance measures comprehensively, and more so, the specific functional requirement of chip breaking and the associated use of commercial complex grooved tools are not included in previous work. Figure 2 shows a schematic diagram of the new optimization methodology, which is based on genetic algorithms (GA). The process model is established by integrating metalcutting theories and an experimental database with numerical methods. And, it is applied in the optimization algorithms to predict machining performance measures. The users can control the optimization process by defining objective function, weighting factors, and constraints. The optimization process will output the optimum cutting conditions and the most suitable cutting tools as the final optimum results.

Machining Optimization The role of optimization for machining in CAPP (computer-aided process planning) systems is extremely important due to the complex interactions that take place during the machining process. Traditional approaches in machining optimization have been limited to objective functions related to cost or productivity (Gilbert 1950; Okushima and Hitomi 1964; Armarego and Russell 1966; Zdeblick and DeVor 1981). Although such an objective is desirable, the more critical role of optimization lies in the optimization of various machining performance measures such as tool life, surface roughness, and chip form/chip breakability, as shown in Figure 1. The conflicting machining performance requirements, depending on specific applications, result in the need for the optimization of the machining process by the selection of the most suitable cutting conditions and tools, as well as information regarding changes that should be made to the various elements of the machining system to achieve optimized machining performance. Almost all relationships between the performance variables and process parameters employed by previous research are approximated by power functions with fixed empirical coefficients. This may be attributed to the nonavailability of quantitatively reliable machining performance models relating the machining performance measures to the process variables. The lack of technological performance data and equations as well as detailed machine tool specifications and ca-

Hybrid Models for Machining Performance Measures Analytical and empirical models along with selective database systems have been integrated into hybrid predictive models for turning operations. These models may be effectively used for predicting major machining performance measures, including surface roughness, cutting force, chip breakability, tool life, and material removal rate, in terms of the selected

Figure 1 Multiple Machining Performance Criteria in Machining Operations

Figure 2 Overview of Optimization Methodology

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cutting conditions: cutting speed, feed, and depth of cut. Because currently available metalcutting theories are unable to explicitly present all relationships between cutting conditions and machining performance, especially for complex grooved tools, an experimental database and bi-cubic spline data interpolation are used to supplement model predictions of machining performance.

chips and ‘1’ for well broken chips (Fang and Jawahir 1993; Balaji et al. 2006). Again, the effect of cutting speed on the chip breakability is ignored in the finish turning range due to its minimal effect found through experimental work beyond a certain critical value of cutting speed. However, the effects of feed and depth of cut are found to be much more significant on chip breakability (Jawahir, Qureshi, and Arsecularatne 1992; Da and Jawahir 1998). The predictive model for chip breakability developed from chip charts is similar to the one shown in Figure 3 and utilizes an interactive fuzzy logic based technique to predict chip breakability for a given set of cutting conditions, tool geometry, and work material for effective chip-groove profiles generated using analytically predicted chip flow direction, as shown in Figure 4 (Da and Jawahir 1998; Jawahir et al. 2000).

Surface Roughness Turning operations give much higher measured surface roughness, Ra, values than the predicted theoretical values in the finish turning range (Jawahir, Qureshi, and Arsecularatne 1992). Unfortunately, no functional relationships are available to date to describe the variation of surface roughness in terms of cutting conditions. Therefore, a database is established by measuring Ra experimentally for a set of different cutting conditions. And the predictive value of Ra is calculated by using the bi-cubic spline interpolation. Ra was represented as a function of feed and depth of cut because the effect of cutting speed was very minimal in the finish turning region.

Tool Life In machining with grooved tools, it has been observed that the traditional parameters for wear measurement (VB – flank wear, KT – crater wear) are inadequate in characterizing the multiple, concurrent, and complex wear mechanisms undergone due to the interactions of the cutting conditions and the chip-groove geometry. Jawahir et al. (1995, 1997) and Li et al. (1996, 1997) have presented a new methodology for measuring the multiple tool-wear parameters in a grooved tool. Figure 5 shows these

Cutting Force The cutting speed affects the cutting forces much less significantly than the feed and depth of cut and is, hence, ignored in the modeling of cutting force. The following relationship has been established for the cutting force, Fc (Da et al. 1995): Fc = Fz = Cz f α z d βz + Ez d γ z

(1)

where Cz and Ez are force constants, ␣z is the feed exponent, and ␤z and ␥z are depth-of-cut exponents. The last term in the equation represents the experimentally verified cutting-edge force prevalent in machining with tools having a rounded cutting edge. Chip Form/Chip Breakability Chip form/chip breakability is considered as a basic requirement in automated machining. In the present work, the previously established definition of chip form/chip breakability has been used, which assumes that the size, shape, and difficulty/ease of chip producibility determine the levels of chip breakability. According to the definition, the values of chip breakability range between 0 and 1, with ‘0’ for absolutely unbroken

Figure 3 Typical Chip Chart

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VB BW BL KT SW SD N NL1 NW1 NL2 NW2 Figure 4 Predicted Chip Chart for Effective Chip-Groove Profile (Da and Jawahir 1998)

Figure 5 Measurable Tool-Wear Parameters in a Grooved Tool (Jawahir et al. 1997)

measurable grooved tool-wear parameters for a generic grooved tool. It is apparent that accurate estimation of tool life in grooved tools is heavily dependent on accurate prediction of the tool wear rates at different locations of a grooved tool, not only because of the influence of tool geometry on surface finish and cutting forces (as in a flat-faced tool) but also because the changing tool geometry will modify the chip-flow direction and chip control in potentially detrimental ways. Even though various tool-wear mechanisms do exist, it is generally known that the gradual (progressive) tool wear is produced by temperature-dependent mechanisms. The extended Taylor equation is usually considered a good approximation to predict tool life, T (Cook1973), which is expressed in terms of cutting speed, V, feed, f, and depth of cut, d, with empirical constants C, n, m, and l as: T=

V

1n

C f 1 m d1 l

flank wear width of groove backwall wear length of groove backwall wear depth of groove backwall wear width of secondary face wear depth of secondary face wear nose wear notch wear length on main cutting edge notch wear width on main cutting edge notch wear length on secondary cutting edge notch wear width on secondary cutting edge

⎛V ⎞ T = TRWg ⎜ R ⎟ ⎝V⎠

Wc n

(3)

where T = tool life, V = cutting speed, n = Taylor’s tool-life exponent, Wc = tool coating effect factor, Wg = chip-groove effect factor, TR = reference tool life, and VR = reference cutting speed. The coating effect factor, Wc, and the chip-groove effect factor, Wg, is determined as Wc =

n km and Wg = n1 n2 nc f d

(4)

where nc is the actual tool-life slope modified by the coating effect, which can be determined from the actual tool-life, m is machining operation effect factor (with m = 1 considered for turning), and n1, n2, and k are empirical constants. Effect of Progressive Tool Wear The general prediction of machining performance is based on the assumption that cutting tools are fresh in every pass. However, in the actual machining process, cutting tools are subjected to progressive tool wear on different tool faces. The machining perfor-

(2)

More recent work on tool life includes the effects of tool coatings and chip-groove geometry, and the corresponding tool-life equation is expressed as (Jawahir et al. 1997)

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Kilic (1985) uses geometric programming techniques for the selection of cutting conditions. Armarego, Kee, and Smith (1986) developed computer-based strategies using force and power constraints for optimizing single-pass turning operations. Arsecularatne, Hinduja, and Barrow (1992) used the maximum allowable force and chip control as constraints in their optimization work. More recently, Meng, Arsecularatne, and Mathew (2000) developed a new method for predicting optimum cutting conditions using a variable flow stress theory providing cutting forces, stresses, etc., along with a verification of constraints such as the built-up edge formation, plastic deformation of the cutting tool, and so on. El-Gizawy and El-Sayed (2002) used a nonlinear goal programming method with varying priority level multi-objective strategies for single-pass turning operations. Wang et al. (2002) developed a deterministic approach for the selection of economic cutting conditions using a host of practical constraints. Armarego and Ostafiev (2003), in a recent follow-up work, presented a multi-constraint optimization method for using coated chip-breaker tools in single-pass turning. Da, Sadler, and Jawahir (1997) developed a hybrid process model that defines the relationships between the dependent performance variables (surface roughness, cutting force, chip breakability, material removal rate, and tool life) and the independent parameters (cutting speed, feed, and depth of cut) based on the classical theories of metalcutting and a representative database of experimental results (Da et al. 1995). Nonlinear optimization techniques, based on the hybrid process model, were applied to obtain the optimum cutting conditions. Subsequently, Da, Sadler, and Jawahir (1998) and Sadler et al. (1998, 1999) used a multiple-criteria optimization method and presented a methodology for predicting the optimum cutting conditions and selection of tool inserts by considering the effects of progressive tool wear on the machining performance. The goal of multiple-criterion optimization of machining processes is to establish trade-offs among the various conflicting machining performance measures to achieve optimum economic performance of the operation. In addition to tool life and material removal rate, all other machining performance measures such as surface roughness, cutting force, and chip breakability will significantly affect the economic performance of machining, such as profit rate, production cost, and so on. The com-

mance will vary significantly with the progression of the overall tool wear, which leads to different optimum cutting conditions for a given cutting tool at different wear states. In multi-pass turning operations, if the same tool insert is used for all passes, the effect of tool wear must be considered in all subsequent passes. The reciprocal of tool life will be defined as the wear rate, R. R=

1 1 = V n3 f n1 d n2 T kmC

(5)

where n3 and C are n3 =

1 1 and C = TR (VR ) nc nc

(6)

If a tool insert has been used in N known previous operations, the tool-wear index can be defined as N

1 Vi n3 fi n1 din2 ti i =1 kmC N

w = ∑ Ri ti = ∑ i =1

(7)

where Vi, fi, di, and ti are cutting speed, feed, depth of cut, and the time interval of the i-th operation, respectively. If the cutting parameters vary continuously with time in the operation, the tool-wear index can be rewritten as N ⎛ ti ⎞ N ⎛ ti 1 ⎞ w = ∑ ⎜ ∫ Ri dt ⎟ = ∑ ⎜ ∫ Vi n3 fi n1 din2 dt ⎟ i =1 ⎝ 0 ⎠ i =1 ⎝ 0 kmC ⎠

(8)

According to the definition, the tool-wear index for a new tool insert is 0. And, the tool is considered failed if the tool-wear index reaches 1. The machining performance for the tool after some known usage, w, can be predicted by p = Wp ( w) ⋅ pu (V , f , d )

(9)

where Wp is a function of tool-wear index, w, independent of cutting conditions V, f, and d, which represent the tool-wear effect on the machining performance, p, for example, Ra, Fc, or CB, and is the machining performance predicted by assuming unworn tools, for example, Ra(u), Fc(u), or CBu.

Optimization of Single-Pass Finish Turning Operations A large domain of knowledge exists on singlepass turning. An early work by Eskicioglu, Nisli, and 65

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As an example, the optimum cutting conditions will be determined for cutting tool TNMG332-CG1 to show the effect of weighting factors. The work material is AISI 1045 steel. Because there was no cutting fluid applied, a higher cutting force, a rougher surface, and a shorter tool life would be expected. The test data are shown in Table 1. And, for this tool insert, the Taylor constant and exponents are C = 214233, n = 0.642, m = 1.815, and l = 1.337. The optimization results are shown in Table 1, and the optimization results for CR = CF = CT = CM = CCB = 0.2 are graphically illustrated in Figure 6 with the cutting speed V = 230 m/min. In this case study, the optimum is located inside the feasible region instead of on its boundary. In Figure 6, the contours of the objective function are drawn as thin solid curves and the constraints are drawn as thick solid curves. The shaded region indicates the feasible region enclosed by those constraints. Another case study is to make the optimum selection of a cutting tool insert for specified requirements and to determine the corresponding machining conditions. The cutting tool will be selected from a group of tool inserts, including TNMG332-CG1, TNMG331-CG1, and TNMG331-CG2, which have very different chip grooves or nose radii. The results are listed in Table 2 and illustrated in Figure 7, which shows the contours of the objective function (material removal rate) and the feasible regions for all three tool inserts in the feed and depth-of-cut space where the cutting speed is 400 m/min. In Figure 7, there are no constraints on T and MR, and CM = 1.0, CR = CF = CT = CCB = 0. The value of the objective function at the optimum for TNMG332CG1 is 238.5% larger than that for TNMG331-CG1 and 143.6% than that for TNMG331-CG2. There-

prehensive optimization criterion proposed by Sadler et al. (1998, 1999) includes the effects of all major technological machining performance measures and the effect of progressive tool wear. For single-pass problems, the parameters Ra, Fc, T, MR, and CB denote the surface roughness, cutting force, tool life, material removal rate, and chip breakability, respectively. Corresponding constraints on these machining performance measures are assumed as Ra´, Fc´, T´, MR´, and CB´. CR, CF, CT, CM, and CCB are weighing factors for these performance measures. The objective function can be constructed as ⎛F′ −F ⎞ ⎛R ′ −R ⎞ a c c U (V , f , d ) = C R ⎜ a ⎟+ ⎟ + CF ⎜ ⎜⎝ F ′ ⎟⎠ ⎜⎝ R ′ ⎟⎠ a c ⎛M −M ′⎞ ⎛ T − T ′⎞ ⎛ CB − CB′ ⎞ (10) R CT ⎜ + CM ⎜ R ⎟ + CCB ⎜ ⎟ ⎝ CB′ ⎟⎠ ⎝ T′ ⎠ ⎝ M ′ ⎠ R

Constraints are represented as: Ra ≤ Ra ′ , Fc ≤ Fc ′ , T ≥ T ′,

(11)

M R ≥ M R ′ , CB ≥ CB′

Hence, the optimization problem becomes Maximize

U (V , f , d )

With respect to V , f , d Subject to

Ra ≤ Ra ′ , Fc ≤ Fc ′ , T ≥ T ′, M R ≥ M R ′ , CB ≥ CB′

(12)

Vmin ≤ V ≤ Vmax , fmin ≤ f ≤ fmax , dmin ≤ d ≤ dmax

Table 1 Constraints and Optimization Results for Single-Pass Finish Turning Operations

Cutting Parameters and Performance Measures Cutting speed, V (m/min.) Feed, f (mm/rev) Depth of cut, d (mm) Surface roughness, Ra (µm) Cutting force, Fc (N) Chip breakability, CB Material removal rate, MR (mm3/min.) Tool life, T (min.) Value of utility function

Constraints

Optimization Results for CR = CF = CT = CM = CCB = 0.2

Optimization Results for CT = 0.6, CF = CR = CM = CCB = 0.1

230 0.109 0.978 0.763 313 0.814 24559 5.688 0.3928

230 0.127 0.513 1.044 224 0.700 15000 8.486 0.7517

230 – 400 0.056 – 0.254 0.254 – 1.905 1.6 400 0.7 15000 4.0

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Figure 6 Graphical Illustration of Optimization Results

Figure 7 Comparative Analysis to Select the Most Suitable Cutting Tool

fore, the advantage in selecting TNMG332-CG1 over the other two inserts is obvious.

search highlights the use of advanced computeraided methods (Kee 1994; Mesquita, Krastera, and Doytchinov 1995), fuzzy logic applications (Alberti and Perrone 1999), nonlinear mathematical models (Al-Ahmari 2001), genetic algorithms (Onwubolu and Kumalo 2001; Chen and Chen 2003), ant colony systems (Vijayakumar et al. 2003), and scatter search methods (Chen 2004) for multi-pass machining optimization. The optimization objective of multi-pass turning operations differs from that of single-pass operations. In rough turning operations, the highest possible material removal rate is desired, within the constraints of other appropriate machining performance measures. However, the surface roughness, which is largely irrelevant in rough turning, is the most important measure in comparison with all other measures in finish turning operations. To implement the importance of one or more of the machining perfor-

Optimization of Multi-Pass Turning Operations Optimization of multi-pass turning operations plays an important role in process planning for machining because multi-pass machining operations are more widely used than single-pass operations in the manufacturing industry. To achieve overall optimal results in multi-pass turning operations, trade-offs are usually established not only among the various conflicting machining performance measures, but also among all passes in a given turning operation. Early work on optimization of multi-pass machining operations shows the economic benefits of machining (Ermer and Kromodihardjo 1981). Agapiou (1992) used a dynamic programming method to determine optimum cutting conditions. Subsequent re-

Table 2 Constraints and Optimization Results for Cutting Tool Selection

Cutting Parameters and Performance Measures Cutting speed (m/min.) Feed (mm/rev) Depth of cut (mm) Surface roughness (µm) Cutting force (N) Chip breakability Objective function (MMR mm3/min.)

Constraints 230 – 400 0.056 – 0.254 0.254 – 1.905 0.8 400 0.45

TNMG332-CG1 400 0.110 1.281 0.731 400 0.72 56300

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TNMG331-CG1 400 0.063 0.935 0.8 235 0.45 23603

TNMG331-CG2 400 0.075 1.311 0.8 400 0.68 39196

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mance measures in optimization, various weighting factors are applied to these measures in the objective function. The optimization of single-pass finish turning operations has been extended to cover multi-pass turning using genetic algorithms (Wang et al. 2002).

where d is the total depth of cut. Because the goals of optimization for different passes in multi-pass turning operations are different, different constraints and weighting factors of the objective function are applied to each pass.

Objective Functions for Multi-Pass Turning Operations For multi-pass problems, the objective function in optimization processes is the sum of objectives of all passes. The total objective function is

Genetic Algorithms (GAs) Genetic algorithms (GAs) are algorithms based on the mechanics of natural selection and natural genetics, which are more robust and more likely to locate a global optimum (Goldberg 1989). It is because of this feature that a GA moves through the solution space starting from a group of points and not from a single point. To apply a GA to the optimization of machining, the cutting conditions are encoded as genes by binary encoding. A set of genes is combined together to form a chromosome, which is used to perform those basic mechanisms in a GA such as crossover and mutation. Crossover is the operation by which parts of two chromosomes are exchanged to generate new offspring. This is an important feature of such algorithms because it enables a rapid exploration of the entire search space. Mutation is the occasional random alteration of some bits in the chromosome that is applied after crossover to provide a small randomness to the new chromosome to prevent premature loss of some potentially important information in the chromosome. To evaluate each individual or chromosome, the encoded cutting conditions are decoded from the chromosome and are used to predict machining performance measures. The fitness or objective function is a function needed in the optimization process and in the selection of the next generation in the GA. After a number of iterations of the GA, the optimal cutting conditions are obtained by comparing the values of the objective functions among all individual trials. Besides weighting factors and constraints, suitable parameters of a GA are required for this methodology to operate efficiently. GA techniques have recently been used for the selection of optimum machining conditions (Da and Jawahir 1998).

U (Vi , fi , di (i = 1, 2,…, N )) ⎧ ⎛R ′ −R ⎞ ⎛F ′ −F ⎞ ⎫ ci ai c ⎪C ⎜ ai ⎟+⎪ ⎟ + CFi ⎜ i Ri ⎪ ⎜ R ′ ⎟ ′ ⎜ ⎟⎠ ⎪ ⎝ Fci ⎠ ai ⎪ ⎝ ⎪ ⎪ ⎛ ⎛M −M ′⎞ ⎪ N Ti − Ti ′ ⎞ ⎪ ⎪ Ri Ri ⎟ +⎬ = ∑ ⎨CTi ⎜ ⎟ + C Mi ⎜ i =1 ⎜ ⎟ ⎜⎝ M R ′ ⎟⎠ ⎪ ⎪ ⎝ Ti ′ ⎠ i ⎪ ⎪ ⎛ CB − CB ′ ⎞ ⎪ ⎪ i ⎪CCBi ⎜ i ⎪ ⎟ ⎜⎝ CB ′ ⎟⎠ ⎪ ⎪ i ⎩ ⎭

(13)

where N is the number of passes in a turning operation, Vi is the cutting speed, fi is the feed, and di is the depth of cut for each pass. Constraints are represented as: Rai ≤ Rai ′ , Fci ≤ Fci ′ , Ti ≥ Ti ′ , M Ri ≥ M Ri ′ , CBi ≥ CBi ′

(i = 1, 2,…, N )

(14)

Hence, the optimization problem becomes Maximize

U (Vi , fi , di (i = 1, 2,…, N ))

With respect to Vi , fi , di (i = 1, 2,…, N ) Subject to

Rai ≤ Rai ′ , Fci ≤ Fci ′ , Ti ≥ Ti ′ , M Ri ≥ M Ri ′ , CBi ≥ CBi ′ Vmin(i) ≤ Vi ≤ Vmax(i) , fmin(i) ≤ fi ≤ fmax(i) ,

Optimization for Two-Pass and Three-Pass Turning Operations In this case, the optimum cutting conditions for each pass in a turning operation will be determined for a specific cutting tool, TNMG332-CG1, to show

(15)

dmin(i) ≤ di ≤ dmax(i) N

∑ di = d (i = 1, 2,…, N )

i =1

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how a GA works in this problem. The work material is AISI 1045 steel. The test data are shown in Table 3. No cutting fluids were applied. For this tool insert, the Taylor constant and exponents are C = 214233, n = 0.462, m = 1.815, and l = 1.337. First, a two-pass turning operation is considered. Because there are two different passes, medium turning and finish turning, different weighting factors need to be defined for each pass. Material removal rate is the prime objective in medium turning. Thus, the weighting factor CM is set equal to 0.6 and all other weighting factors, Ci (i = R, F, T, CB), are made equal to 0.1. Similarly, because low surface roughness is a priority in finish turning, the weighting factor CR is set equal to 0.6 and all other weighting factors, Ci (i = F, M, T, CB), are made equal to 0.1. Different constraints for medium and finish turning were applied. A comparatively broad range of constraints were given in medium turning because there are fewer requirements for machining quality in medium turning than in finish turning. The weighting factors and constraints are shown in Table 4. The total depth of cut and several parameters are given to run the GA program. The results are shown in Table 5. Then the methodology is applied to a three-pass turning operation. The three passes include medium turning, semi-finish turning, and finish turning. The optimum cutting conditions of each pass in a threepass turning operation are determined for the same cutting tool (TNMG332-CG1), work material (AISI 1045 steel), and the same test data shown in Table 1 is used in this case. Different weighting factors are defined for each turning pass. In medium turning and finish turning, the weighting factors are the same as those in the

two-pass turning operation. However, all machining performance measures are considered having the same importance in semi-finish turning. Thus, all weighting factors are given as 0.2 in semi-finish turning. Different constraints for medium, semi-finish, and finish turning were applied. The weighting factors and constraints are shown in Table 3. The optimization results are shown in Table 6. Feasible regions of those three passes are illustrated in Figures 8, 9, and 10. These figures shows that the feasible regions in those passes differ significantly because the weighting factors and constraints are different. Because there is a constraint on the total depth of cut, the optimum results of the multi-pass turning operation are an optimum combination of cutting conditions in those feasible regions. In Tables 4 and 5, the optimization results of twopass and three-pass turning operation with the same total depth of cut, 3.1 mm, are presented. Comparing these two results, the difference between twopass and three-pass turning operations is observed. Because the feeds and depths of cut in medium and semi-finish turning of the three-pass turning operation are much smaller than the feed and depth of cut in medium turning of the two-pass turning operation, the cutting forces are smaller and the tool life is longer. However, there is one more pass, semi-finish turning, in the three-pass turning operation, which results in an increase in machining time, and hence, production cost. Optimum Selection of Cutting Tool Inserts for Two-Pass Turning Operations The new methodology developed optimum selection of cutting tool inserts for given requirements

Table 3 Test Data for Tool Insert TNMG332-CG1 (Work material: AISI1045 steel)

Performance Depth of cut (mm) Feed (mm/rev) 0.056 0.074 0.107 0.130 0.191 0.254

Surface Roughness, Ra (µm)

Cutting Force, Fc (N)

Chip Breakability (0–1)

0.254

0.635

1.016

1.905

0.254

0.635

1.016

1.905

0.254

0.635

1.016

1.905

0.584 0.635 0.762 1.041 1.676 2.642

0.660 0.762 0.838 1.067 1.651 2.692

0.508 0.559 0.737 0.914 1.448 2.540

0.508 0.737 0.838 1.041 1.473 2.692

107 120 152 169 223 285

152 183 227 259 375 482

223 254 317 384 562 807

338 459 584 700 990 1271

0.10 0.10 0.50 0.50 0.50 0.50

0.10 0.12 0.70 0.70 0.80 0.91

0.20 0.20 0.80 0.80 0.75 0.80

0.12 0.12 0.16 0.16 0.60 0.60

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Figure 9 Graphical Illustration of Feasible Region in Semi-Finish Turning

Figure 8 Graphical Illustration of Feasible Region in Medium Turning

obtained, as shown in Table 7. The table shows that the value of the objective function at the optimum for TNMG331-CG2 is larger than that for TNMG332CG1. TNMG331-CG2 is a better choice for both depths of cut mainly due to the significantly larger material removal rate in medium pass and smaller forces in finish pass, although very similar surface roughness is produced by both tool inserts in the finish pass. Figure 11 illustrates the contour plots with feasible regions for both inserts under the two different conditions (i.e., medium and finish). Practical Application of Proposed New Methodology Because current process planning software packages lack optimization functions based on machining performance, the new methodology of performance-based optimization for multi-pass turning operations can be integrated as an independent module into the process planning software. The integrated predictive model for machining performance is easily expandable to include other machining performance measures such as production cost, machining time, and sustainability rating. The users can also use experimental data to establish their own performance-based models and employ the optimization methodology. The new methodology can be implemented as single-user PC-based software or multiuser Web-based technical service.

Figure 10 Graphical Illustration of Feasible Region in Finish Turning

and determination of corresponding machining conditions is demonstrated in this case. The cutting tool inserts will be selected between TNMG332-CG1 and TNMG331-CG2, which have different nose radii and chip-grooves (CG1 & CG2). The weighting factors and constraints for each tool insert are the same, as shown in Table 7. Because the experimental data of the two tool inserts are different, different optimization results are

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Table 4 Weighting Factors and Constraints in Two-Pass and Three-Pass Turning

Turning Pass

Weighting Factors

CR CF CM CT CCB

V (m/min.) f (mm/rev) d (mm) Ra´ (µm) Fc´ (N) MR´ (mm3/min.) CB´ T´ (min.)

Two-Pass Turning Medium Finish 0.1 0.6 0.1 0.1 0.6 0.1 0.1 0.1 0.1 0.1 150 – 250 0.15 – 0.254 1.20 – 1.905 3.2 1200 30000 0.6 6.00

250 – 400 0.056 – 0.15 0.254 – 1.20 0.8 500 15000 0.7 2.00

Medium 0.1 0.1 0.6 0.1 0.1

Three-Pass Turning Semi-Finish 0.2 0.2 0.2 0.2 0.2

Finish 0.6 0.1 0.1 0.1 0.1

150 – 250 0.15 – 0.254 1.00 – 1.905 3.2 1200 30000 0.6 6.00

200 – 350 0.08 – 0.18 0.50 – 1.50 1.6 800 20000 0.7 4.00

300 – 400 0.056 – 0.15 0.254 – 1.00 0.8 500 10000 0.7 2.00

Table 5 Optimization Results for Two-Pass Turning

Total Depth of Cut (mm) Turning Pass Optimum V (m/min.) Cutting f (mm/rev) Conditions d (mm) Ra (µm) Predicted Fc (N) Machining MR (mm3/min) Performance CB T (min.)

2.70 Medium 150 0.249 1.589 2.516 1106 60372 0.65 6.138

2.90 Finish 262 0.103 1.111 0.693 332 30037 0.74 4.026

Medium 150 0.241 1.753 2.126 1082 60459 0.64 6.091

3.10 Finish 257 0.103 1.147 0.690 342 30353 0.73 4.118

Medium 150 0.209 1.901 1.761 1068 60000 0.63 6.032

Finish 254 0.103 1.199 0.689 357 31415 0.70 4.069

Table 6 Optimization Results for Three-Pass Turning

Total Depth of Cut (mm) Turning Pass Optimum V (m/min.) Cutting f (mm/rev) Conditions d (mm) Ra (µm) Predicted Fc (N) Machining MR (mm3/min) Performance CB T (min.)

Medium 150 0.183 1.329 1.302 686 36705 0.65 8.521

3.10 Semi-Finish 200 0.131 0.776 1.026 303 20266 0.76 8.315

Finish 345 0.104 0.995 0.723 305 35827 0.77 2.396

Medium 150 0.240 1.695 2.356 1108 61140 0.64 6.145

3.70 Semi-Finish 237 0.167 1.010 1.196 487 40072 0.67 4.120

Finish 334 0.104 0.995 0.718 303 34450 0.76 2.579

Concluding Remarks The major findings of this work are:

• Single and multi-pass turning operations are considered with several case studies involving the use of weighing factors for various machining performance measures. • A new methodology has been developed for cutting tool selection for a given operation.

• A performance-based machining optimization system has been developed for predicting optimum cutting conditions in turning operations. • Hybrid models are developed, integrated, and utilized in the current work.

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Table 7 Results of Optimal Tool Selection

Total Depth of Cut (mm) Tool Insert Turning Pass Optimum V (m/min.) Cutting f (mm/rev) Conditions d (mm) Ra (µm) Predicted Fc (N) Machining MR (mm3/min) Performance CB T (min.) Value of Utility Function

2.3 (C) TNMG332-CG1 TNMG331-CG2 Medium Finish Medium Finish 157 263 162 344 0.173 0.106 0.155 0.080 1.219 1.081 1.749 0.551 1.202 0.716 2.063 0.707 600 331 835 192 33135 30006 44009 15197 0.62 0.78 0.60 0.73 8.604 4.043 6.491 4.351 0.5323 0.6088

2.5 (D) TNMG332-CG1 TNMG331-CG2 Medium Finish Medium Finish 158 257 151 332 0.177 0.104 0.165 0.080 1.368 1.132 1.891 0.609 1.241 0.697 2.257 0.711 681 340 948 205 38399 30179 47148 16238 0.61 0.74 0.60 0.70 7.616 4.138 6.889 4.347 0.6241 0.6596

Figure 11 Optimal Selection of Cutting Tool Inserts

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This work involves the use of analytical, empirical, and hybrid predictive models for predicting machining performance measures for use in the optimization system for machining a given work material under a given range of cutting conditions using certain cutting tools defined by a given tool geometry, tool material and coating. Also, the effects of inherent machine tool dynamics affecting the machining performance and the variability of work material properties or the cutting tool parameters are not considered in this paper. However, the methodologies presented in this paper, being very generic in nature, can be applied for other sets of operating conditions, work materials, and cutting tools. Future work would, however, be necessary to validate these methodologies.

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Authors’ Biographies

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Xiqun Wang is currently a machining research engineer at TechSolve, Inc. Dr. Wang has years of experience in the area of manufacturing, specifically machinability, machining predictive modeling, and machining optimization. He earned his MS and PhD degrees in mechanical engineering from the University of Kentucky and his BS in mechanical design and manufacturing from Tsinghua University, Beijing, China. Z.J. Da earned his PhD in mechanical engineering in 1997 the University of Kentucky. He received his MS and BS degrees in aerospace engineering from the Nanjing Aeronautical Institute, Nanjing, Jiangsu, China. A.K. Balaji is an assistant professor of mechanical engineering and director of the sustainability and manufacturing research laboratory at the University of Utah. Professor Balaji obtained his MS and PhD degrees in mechanical engineering at the University of Kentucky in 1996 and 2000, respectively. His research interests lie in the areas of predictive modeling of manufacturing processes, tribology of manufacturing processes, bio-mimetic applications in manufacturing, and sustainable manufacturing. I.S. Jawahir received his PhD from the University of New South Wales, Sydney, Australia, in 1986. He is currently with the University of Kentucky serving as a professor of mechanical engineering and the James F. Hardymon Chair in Manufacturing Systems. His current research interests include modeling and optimization of machining operations and sustainable product design and manufacture.

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