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Optimization of grinding process parameters using enumeration method
Journal of Materials Processing Technology 112 (2001) 63±67
Optimization of grinding process parameters using enumeration method R. Guptaa,*, K.S. Shishodiab, G.S. Sekhonb a
Indo Swiss Training Centre, Central Scienti®c Instruments Organisation, Chandigarh 160 020, India b Department of Applied Mechanics, IIT, New Delhi 110 016, India Received 15 June 2000; accepted 10 January 2001
Abstract The selection of grinding parameters if done on hit and miss method not only wastes time but also leads to an inef®cient process. The parameters should be so selected so as to result in an optimal solution. In this paper the ``enumeration'' method is discussed. By using this approach the user can select input parameters to achieve an optimal cutting condition. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Grinding; Optimization; Enumeration; Burn-free
1. Introduction During a grinding process, the work is forced against an abrasive wheel. As a result, material in the form of small chips is removed from the work piece. The rate of material removal depends upon the process variables, such as, wheel parameters, speeds, machine, and coolant. The selection of process variables needs experience which may not be available to the process planner. Also he/she may not have access to the knowledge of experts in the ®eld or the research ®ndings accumulated in the literature. To overcome this dif®culty ``computer based expert systems'' have been developed which provide knowledge of more than one expert and the results of research work to the user to solve his/her problems in the ®eld. This will assist in formulation of an optimal solution. The planning process for a grinding job is undertaken after the designer has ®nalized the design parameters, i.e., the shape, dimensions and surface ®nish. During the planning process the planner selects suitable machine(s) and decides process parameters. The selection of a machine depends upon the dimensions of the job, whereas other parameters are decided by the planner based on his/her experience or on some aids available to him. A typical plan for a grinding process is shown in Fig. 1 [1]. The present work is based on an expert system developed earlier by the authors [1,2]. This system has a modular
* Corresponding author. Present address: 3139, Sector-21 D, Chandigarh 160 022, India.
structure and consists of one main module and seven submodules. The sub-modules are embedded with information on G-ratio, grinding time, surface ®nish and thermal analysis. Databases on grinding machines, wheels for surface and cylindrical grinding machines, material properties have been incorporated in the program. Information on wheel speed, infeed, work speed and cutting oil has also been given in the program. Based on inputs from the user, and the interaction with the databases and other modules, the program suggests various process parameters. Information/ knowledge represented in the form of rules in the program is as follows: 1. If hardness >48 (RC) and surface is ¯at, then feed is 0.0125 mm. 2. If surface is cylindrical and material is not (cast_iron_ductile_malleable) and ®nish is high, then feed is 0.0125 mm and work velocity is 25 m/min. 3. If material is carbon steel en 8, then coolant is (dry, or water soluble oil). With the values suggested by the program, output in the form of grinding time, material removal rate etc. is evaluated and the values satisfying the process constraints are selected. In this paper a procedure called ``enumeration method'' [3] to select optimal process parameters has been described. In this procedure, the user tests different values of the process variables and evaluates the corresponding values of the desired objective while satisfying constraints imposed on the process. Since an objective function is a measure of the ef®ciency of the process, the optimum combination of the variables leads to the minimization or maximization of the objective function.
0924-0136/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 1 ) 0 0 5 4 6 - 5
64
R. Gupta et al. / Journal of Materials Processing Technology 112 (2001) 63±67
Fig. 1. A typical process planning system.
2. Objective function The objective function is an expression whose maximum or minimum value is to be derived as a function of process parameters. In grinding problems the objective function could be (i) to achieve minimum grinding time, i.e., to get maximum material removal rate or (ii) to get maximum material removal per unit volume of the abrasive used, i.e., maximization of the G-ratio subject to the process constraints. The above schemes have been employed in formulating the objective functions and are described below. 2.1. Objective function based on minimizing grinding time In this method, the objective can be stated to be either to minimize the grinding time or to maximize the material removal rate. The material removal rate for surface grinding and cylindrical grinding is given by the following equations [4]. For surface grinding, Qmat Vtrav ap X
(1)
For cylindrical and internal grinding, Qmat P Vtrav ap dw
(2)
where Qmat is the material removal rate, Vtrav the traverse speed, ap the infeed, X the cross-feed and dw the workpiece diameter. The grinding time tg depends upon material removal rate and can be expressed as: tg
A Qmat
(3)
In Eq. (3), A is a constant. For the grinding time to be minimum, @tg =@Qmat 0, the material removal rate should be the highest possible. From Eqs. (1) and (2), it is evident that the material removal rate depends upon traverse speed and the infeed. Both conditions are machine dependent. In practice, it is convenient to control the infeed to close limits. Therefore, in this paper infeed has been considered as a parameter to be
optimized satisfying objective function subject to the process constraints. 2.2. Objective function based on maximum G-ratio The G-ratio is de®ned as the volume of material removed per unit volume of wheel wear. The material removal parameter lw [5] is given by the following relation: l w A1
Vw =Vs 3=19 1 2C=3LL11=119 Vs de 43=304 Vol0:47 R27=19 dg 5=38
(4)
where A1 is a constant, Vw the workpiece speed, Vs the wheel speed, de the equivalent wheel diameter, C the depth of dress, L the dress lead, R the workpiece material's hardness and Vol is given by the relationship: Vol 1:33H 2:2ST 8 where H is the wheel hardness and ST the wheel structure number). The wheel material removal parameter ls is expressed by the following relation [6]: ls A2
L2 1 C=LFn Vs de 1:2Vol Vol0:85
(5)
where A2 is a constant and Fn the normal force intensity. The G-ratio is given by dividing Eq. (4) by Eq. (5): G-ratio A3
Vw =Vs 3=19 1 2C=3Lde 1:2=Vol 0:141 Vol0:38 L27=19 1 C=L Fn dg 5=38 R27=19 (6)
where A3 is a constant. Perusal of Eqs. (1), (2) and (6) shows that the variables of interest during optimization of grinding operations are those listed below:
Material properties. Grinding wheel parameters. Infeed. Workpiece speed. Grinding wheel speed. Dress condition.
For ®nish grinding, surface ®nish is an important consideration. If the process generates a ®nish value better than desired, it only adds to the cost of grinding. As such, surface
R. Gupta et al. / Journal of Materials Processing Technology 112 (2001) 63±67
65
Fig. 2. Proposed optimizing scheme. WRT* with respect to
®nish has been taken to be a process constraint for selection of the process parameters.
most promising variable. The parameters which affect the process are discussed in the following paragraphs.
2.3. Proposed optimization technique
3.1. Infeed
The optimization scheme as incorporated in the program is shown in Fig. 2. Corresponding to a set of values of input variables, a set of output parameters and a corresponding value of objective function, is obtained. The user can feed his/her own data for different variables effecting the process. This leads to a number of solution sets. From all the solution sets so obtained, the user can select conditions which would result in best performance with respect to the desired objective.
In this approach optimal infeed value is computed according to a trial infeed value. Output parameters namely wheel parameters, grinding time, G-ratio are computed by employing the trial infeed value. The infeed value is modi®ed by the program in the immediate vicinity of the ®rst trial infeed value both by increasing and decreasing in small steps of 0.0025 mm. Theses values are 0.0025, .0050, .0075 mm. The G-ratio, grinding time and surface ®nish are computed for each modi®ed infeed value. For the user's trial value of 0.014 mm as infeed, the G-ratio, surface ®nish and grinding time are computed and are given in Table 1. The results can be further re®ned by inputing an infeed value from the ®rst iteration and the process can be repeated with
3. Parameters for optimal solution A number of variables can be considered for optimization of the process as shown in Fig. 2. However, infeed is the
66
R. Gupta et al. / Journal of Materials Processing Technology 112 (2001) 63±67
Table 1 Output parameters for a cylindrical grinding workpiece Input Workpiece diameter (initial/final) Length Material Material hardness Surface finish Grain size Infeed Dress lead Wheel diameter Wheel thickness Workspeed Burn risk factor
52/51.85 mm 200 mm En 14 55 RC 0.3 mm 80 0.014 mm 0.05 mm 250 mm 25 mm 28 m/min 80%
Infeed (mm)
G-ratio
Surface finish (mm)
Grinding time (s)
Critical specific energy (J/mm3)
Output 0.014 0.0115 0.0165 0.019
43 52.3 36.4 31.7
0.32 0.30 0.35 0.37
16 20 14 12
32 ± ± ±
Output (literature example) 0.010
62.4
0.25
62.5
this value. Thus, from the solution set, infeed that meets the objective best can be selected. 3.2. Grinding machine Depending upon the workpiece dimensions, more than one machine may be suitable for the operation. The user can select each of the suggested machines for analysis one after the other. The material removal rate for each machine is likely to be different due to the different characteristics of each machine. This will result in a different grinding time for each machine. Thus with iteration on machines, conditions which meet the desired criterion can be selected. 3.3. Wheel parameters Another approach to obtain optimal grinding conditions can be employed wherein the wheel parameters, i.e., grain size, wheel speed, are varied and corresponding output parameters are determined. The output parameters that satisfy the objective function and meet the constraints can help in deciding optimal input conditions. 4. Infeed for burn-free workpiece condition An important consideration during grinding is the ``burning'' of a workpiece. During this condition the workpiece sustains high surface temperature which may result in residual stresses in the workpiece and could be harmful to its life cycle. As given in Table 1 for an infeed of 0.014 the speci®c energy is 32 J/mm3, i.e., beyond this value there is a likelyhood of the workpiece having burn marks [1,7]. So, for
critical components the user can assume some safety factor to ensure a ``burn-free'' workpiece. The infeed for the ``burn-free'' condition can be determined on the basis of the critical speci®c energy [7]. If the burn risk factor is ``f'' and threshold speci®c grinding energy is s, then the infeed ap for ``burn-free'' condition is given by following equation: 1:33 1=2 1=4 1=2 1:13a ap S1 6:2de Vw (7) Kycrit where S1 f s, a is thermal diffusivity, K the thermal conductivity and ycrit the critical temperature for ``workpiece burn'' condition. A value for the burn risk factor ``f'' can be assigned depending upon the nature of the component being ground. The infeed ap as computed from Eq. (7) will result in a ``burn-free'' workpiece. For the input data (Table 1) and a ``burn-free'' factor of 80%, the predicated output parameters are given in Table 2. 5. Validation The optimization procedure as described above has been validated by comparing the predicted output with a test Table 2 Burn-free workpiece condition Infeed (mm)
G-ratio
Surface finish (mm)
Grinding time (s)
0.02
29
0.38
11
R. Gupta et al. / Journal of Materials Processing Technology 112 (2001) 63±67
example taken from literature [8]. The program was run with an arbitrary infeed value of 0.014 mm. Thus a solution set was generated (Table 1). The output of the system is comparable to the literature example. 6. Conclusion Selection of grinding process parameters is made easy by employing ``expert system''. Thereupon optimal grinding conditions can be formulated by operating ``enumeration'' technique on the process parameters which have been suggested by the expert system. The proposed technique generates a number of solution sets for each of the input parameter. The user can then select a set with values comparable to the desired output and satisfying the process constraints and the objective. Input variables which can be considered for obtaining optimal conditions include wheel and machine parameters with infeed being the most promising candidate. For critical components, condition for ``burn-free'' workpiece can also be determined.
67
References [1] R. Gupta, Computer aided planning of grinding operations for ferrous components, Ph.D. Thesis, IIT, Delhi, 1995. [2] R. Gupta, G.S. Sekhon, K.S. Shishodia, CAP-GO computer-aided planning of grinding operations for ferrous components, J. Mater. Process. Technol. 65 (1997) 34±40. [3] R.S. Gar®nkel, G.L. Nenhauser, in: Auriel, et al. (Eds.), An Introduction to Integer Programming and its Application in Engineering in Optimization and Design, Prentice-Hall, Englewood Cliffs, NJ, 1973. [4] G. Boothroyd, W.A. Knight, Fundamentals of Machining and Machine Tools, 2nd Edition, Marcel Dekker, New York, 1989. [5] R.P. Hahn, R.P. Lindsay, Principles of grinding. Part II. The metal removal parameter, in: C. Bhateja, R. Lindsay (Eds.), Grinding Theory Techniques and Troubleshooting, 1982, pp. 11±17 (originally printed in machinery, September 1971b). [6] R.P. Hahn, R.P. Lindsay, Principles of grinding. Part III. The wheel removal parameter, in: C. Bhateja, R. Lindsay, (Eds.), Grinding Theory Techniques and Trouble Shooting, 1982, pp. 18±24 (originally printed in machinery, September 1971C). [7] S. Malkin, Grinding Technology, Theory and Applications of Machining with Abrasives, Ellis Horwood/Wiley, Chichester, UK/ New York, 1989. [8] P.S. Midha, C.B. Zhu, G.J. Trmal, et al., Optimum selection of grinding parameters using process modelling and knowledge based system approach, J. Mater. Process. Technol. 28 (1991) 189±198.
Optimization of grinding process parameters using enumeration method R. Guptaa,*, K.S. Shishodiab, G.S. Sekhonb a
Indo Swiss Training Centre, Central Scienti®c Instruments Organisation, Chandigarh 160 020, India b Department of Applied Mechanics, IIT, New Delhi 110 016, India Received 15 June 2000; accepted 10 January 2001
Abstract The selection of grinding parameters if done on hit and miss method not only wastes time but also leads to an inef®cient process. The parameters should be so selected so as to result in an optimal solution. In this paper the ``enumeration'' method is discussed. By using this approach the user can select input parameters to achieve an optimal cutting condition. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Grinding; Optimization; Enumeration; Burn-free
1. Introduction During a grinding process, the work is forced against an abrasive wheel. As a result, material in the form of small chips is removed from the work piece. The rate of material removal depends upon the process variables, such as, wheel parameters, speeds, machine, and coolant. The selection of process variables needs experience which may not be available to the process planner. Also he/she may not have access to the knowledge of experts in the ®eld or the research ®ndings accumulated in the literature. To overcome this dif®culty ``computer based expert systems'' have been developed which provide knowledge of more than one expert and the results of research work to the user to solve his/her problems in the ®eld. This will assist in formulation of an optimal solution. The planning process for a grinding job is undertaken after the designer has ®nalized the design parameters, i.e., the shape, dimensions and surface ®nish. During the planning process the planner selects suitable machine(s) and decides process parameters. The selection of a machine depends upon the dimensions of the job, whereas other parameters are decided by the planner based on his/her experience or on some aids available to him. A typical plan for a grinding process is shown in Fig. 1 [1]. The present work is based on an expert system developed earlier by the authors [1,2]. This system has a modular
* Corresponding author. Present address: 3139, Sector-21 D, Chandigarh 160 022, India.
structure and consists of one main module and seven submodules. The sub-modules are embedded with information on G-ratio, grinding time, surface ®nish and thermal analysis. Databases on grinding machines, wheels for surface and cylindrical grinding machines, material properties have been incorporated in the program. Information on wheel speed, infeed, work speed and cutting oil has also been given in the program. Based on inputs from the user, and the interaction with the databases and other modules, the program suggests various process parameters. Information/ knowledge represented in the form of rules in the program is as follows: 1. If hardness >48 (RC) and surface is ¯at, then feed is 0.0125 mm. 2. If surface is cylindrical and material is not (cast_iron_ductile_malleable) and ®nish is high, then feed is 0.0125 mm and work velocity is 25 m/min. 3. If material is carbon steel en 8, then coolant is (dry, or water soluble oil). With the values suggested by the program, output in the form of grinding time, material removal rate etc. is evaluated and the values satisfying the process constraints are selected. In this paper a procedure called ``enumeration method'' [3] to select optimal process parameters has been described. In this procedure, the user tests different values of the process variables and evaluates the corresponding values of the desired objective while satisfying constraints imposed on the process. Since an objective function is a measure of the ef®ciency of the process, the optimum combination of the variables leads to the minimization or maximization of the objective function.
0924-0136/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 1 ) 0 0 5 4 6 - 5
64
R. Gupta et al. / Journal of Materials Processing Technology 112 (2001) 63±67
Fig. 1. A typical process planning system.
2. Objective function The objective function is an expression whose maximum or minimum value is to be derived as a function of process parameters. In grinding problems the objective function could be (i) to achieve minimum grinding time, i.e., to get maximum material removal rate or (ii) to get maximum material removal per unit volume of the abrasive used, i.e., maximization of the G-ratio subject to the process constraints. The above schemes have been employed in formulating the objective functions and are described below. 2.1. Objective function based on minimizing grinding time In this method, the objective can be stated to be either to minimize the grinding time or to maximize the material removal rate. The material removal rate for surface grinding and cylindrical grinding is given by the following equations [4]. For surface grinding, Qmat Vtrav ap X
(1)
For cylindrical and internal grinding, Qmat P Vtrav ap dw
(2)
where Qmat is the material removal rate, Vtrav the traverse speed, ap the infeed, X the cross-feed and dw the workpiece diameter. The grinding time tg depends upon material removal rate and can be expressed as: tg
A Qmat
(3)
In Eq. (3), A is a constant. For the grinding time to be minimum, @tg =@Qmat 0, the material removal rate should be the highest possible. From Eqs. (1) and (2), it is evident that the material removal rate depends upon traverse speed and the infeed. Both conditions are machine dependent. In practice, it is convenient to control the infeed to close limits. Therefore, in this paper infeed has been considered as a parameter to be
optimized satisfying objective function subject to the process constraints. 2.2. Objective function based on maximum G-ratio The G-ratio is de®ned as the volume of material removed per unit volume of wheel wear. The material removal parameter lw [5] is given by the following relation: l w A1
Vw =Vs 3=19 1 2C=3LL11=119 Vs de 43=304 Vol0:47 R27=19 dg 5=38
(4)
where A1 is a constant, Vw the workpiece speed, Vs the wheel speed, de the equivalent wheel diameter, C the depth of dress, L the dress lead, R the workpiece material's hardness and Vol is given by the relationship: Vol 1:33H 2:2ST 8 where H is the wheel hardness and ST the wheel structure number). The wheel material removal parameter ls is expressed by the following relation [6]: ls A2
L2 1 C=LFn Vs de 1:2Vol Vol0:85
(5)
where A2 is a constant and Fn the normal force intensity. The G-ratio is given by dividing Eq. (4) by Eq. (5): G-ratio A3
Vw =Vs 3=19 1 2C=3Lde 1:2=Vol 0:141 Vol0:38 L27=19 1 C=L Fn dg 5=38 R27=19 (6)
where A3 is a constant. Perusal of Eqs. (1), (2) and (6) shows that the variables of interest during optimization of grinding operations are those listed below:
Material properties. Grinding wheel parameters. Infeed. Workpiece speed. Grinding wheel speed. Dress condition.
For ®nish grinding, surface ®nish is an important consideration. If the process generates a ®nish value better than desired, it only adds to the cost of grinding. As such, surface
R. Gupta et al. / Journal of Materials Processing Technology 112 (2001) 63±67
65
Fig. 2. Proposed optimizing scheme. WRT* with respect to
®nish has been taken to be a process constraint for selection of the process parameters.
most promising variable. The parameters which affect the process are discussed in the following paragraphs.
2.3. Proposed optimization technique
3.1. Infeed
The optimization scheme as incorporated in the program is shown in Fig. 2. Corresponding to a set of values of input variables, a set of output parameters and a corresponding value of objective function, is obtained. The user can feed his/her own data for different variables effecting the process. This leads to a number of solution sets. From all the solution sets so obtained, the user can select conditions which would result in best performance with respect to the desired objective.
In this approach optimal infeed value is computed according to a trial infeed value. Output parameters namely wheel parameters, grinding time, G-ratio are computed by employing the trial infeed value. The infeed value is modi®ed by the program in the immediate vicinity of the ®rst trial infeed value both by increasing and decreasing in small steps of 0.0025 mm. Theses values are 0.0025, .0050, .0075 mm. The G-ratio, grinding time and surface ®nish are computed for each modi®ed infeed value. For the user's trial value of 0.014 mm as infeed, the G-ratio, surface ®nish and grinding time are computed and are given in Table 1. The results can be further re®ned by inputing an infeed value from the ®rst iteration and the process can be repeated with
3. Parameters for optimal solution A number of variables can be considered for optimization of the process as shown in Fig. 2. However, infeed is the
66
R. Gupta et al. / Journal of Materials Processing Technology 112 (2001) 63±67
Table 1 Output parameters for a cylindrical grinding workpiece Input Workpiece diameter (initial/final) Length Material Material hardness Surface finish Grain size Infeed Dress lead Wheel diameter Wheel thickness Workspeed Burn risk factor
52/51.85 mm 200 mm En 14 55 RC 0.3 mm 80 0.014 mm 0.05 mm 250 mm 25 mm 28 m/min 80%
Infeed (mm)
G-ratio
Surface finish (mm)
Grinding time (s)
Critical specific energy (J/mm3)
Output 0.014 0.0115 0.0165 0.019
43 52.3 36.4 31.7
0.32 0.30 0.35 0.37
16 20 14 12
32 ± ± ±
Output (literature example) 0.010
62.4
0.25
62.5
this value. Thus, from the solution set, infeed that meets the objective best can be selected. 3.2. Grinding machine Depending upon the workpiece dimensions, more than one machine may be suitable for the operation. The user can select each of the suggested machines for analysis one after the other. The material removal rate for each machine is likely to be different due to the different characteristics of each machine. This will result in a different grinding time for each machine. Thus with iteration on machines, conditions which meet the desired criterion can be selected. 3.3. Wheel parameters Another approach to obtain optimal grinding conditions can be employed wherein the wheel parameters, i.e., grain size, wheel speed, are varied and corresponding output parameters are determined. The output parameters that satisfy the objective function and meet the constraints can help in deciding optimal input conditions. 4. Infeed for burn-free workpiece condition An important consideration during grinding is the ``burning'' of a workpiece. During this condition the workpiece sustains high surface temperature which may result in residual stresses in the workpiece and could be harmful to its life cycle. As given in Table 1 for an infeed of 0.014 the speci®c energy is 32 J/mm3, i.e., beyond this value there is a likelyhood of the workpiece having burn marks [1,7]. So, for
critical components the user can assume some safety factor to ensure a ``burn-free'' workpiece. The infeed for the ``burn-free'' condition can be determined on the basis of the critical speci®c energy [7]. If the burn risk factor is ``f'' and threshold speci®c grinding energy is s, then the infeed ap for ``burn-free'' condition is given by following equation: 1:33 1=2 1=4 1=2 1:13a ap S1 6:2de Vw (7) Kycrit where S1 f s, a is thermal diffusivity, K the thermal conductivity and ycrit the critical temperature for ``workpiece burn'' condition. A value for the burn risk factor ``f'' can be assigned depending upon the nature of the component being ground. The infeed ap as computed from Eq. (7) will result in a ``burn-free'' workpiece. For the input data (Table 1) and a ``burn-free'' factor of 80%, the predicated output parameters are given in Table 2. 5. Validation The optimization procedure as described above has been validated by comparing the predicted output with a test Table 2 Burn-free workpiece condition Infeed (mm)
G-ratio
Surface finish (mm)
Grinding time (s)
0.02
29
0.38
11
R. Gupta et al. / Journal of Materials Processing Technology 112 (2001) 63±67
example taken from literature [8]. The program was run with an arbitrary infeed value of 0.014 mm. Thus a solution set was generated (Table 1). The output of the system is comparable to the literature example. 6. Conclusion Selection of grinding process parameters is made easy by employing ``expert system''. Thereupon optimal grinding conditions can be formulated by operating ``enumeration'' technique on the process parameters which have been suggested by the expert system. The proposed technique generates a number of solution sets for each of the input parameter. The user can then select a set with values comparable to the desired output and satisfying the process constraints and the objective. Input variables which can be considered for obtaining optimal conditions include wheel and machine parameters with infeed being the most promising candidate. For critical components, condition for ``burn-free'' workpiece can also be determined.
67
References [1] R. Gupta, Computer aided planning of grinding operations for ferrous components, Ph.D. Thesis, IIT, Delhi, 1995. [2] R. Gupta, G.S. Sekhon, K.S. Shishodia, CAP-GO computer-aided planning of grinding operations for ferrous components, J. Mater. Process. Technol. 65 (1997) 34±40. [3] R.S. Gar®nkel, G.L. Nenhauser, in: Auriel, et al. (Eds.), An Introduction to Integer Programming and its Application in Engineering in Optimization and Design, Prentice-Hall, Englewood Cliffs, NJ, 1973. [4] G. Boothroyd, W.A. Knight, Fundamentals of Machining and Machine Tools, 2nd Edition, Marcel Dekker, New York, 1989. [5] R.P. Hahn, R.P. Lindsay, Principles of grinding. Part II. The metal removal parameter, in: C. Bhateja, R. Lindsay (Eds.), Grinding Theory Techniques and Troubleshooting, 1982, pp. 11±17 (originally printed in machinery, September 1971b). [6] R.P. Hahn, R.P. Lindsay, Principles of grinding. Part III. The wheel removal parameter, in: C. Bhateja, R. Lindsay, (Eds.), Grinding Theory Techniques and Trouble Shooting, 1982, pp. 18±24 (originally printed in machinery, September 1971C). [7] S. Malkin, Grinding Technology, Theory and Applications of Machining with Abrasives, Ellis Horwood/Wiley, Chichester, UK/ New York, 1989. [8] P.S. Midha, C.B. Zhu, G.J. Trmal, et al., Optimum selection of grinding parameters using process modelling and knowledge based system approach, J. Mater. Process. Technol. 28 (1991) 189±198.