Journal of Environmental Science and Engineering A 5 (2016) 606-611 doi:10.17265/2162-5298/2016.12.002 D DAVID PUBLISHING Cost Optimization of Surface Grinding Process Vu Ngoc Pi1, Luu Anh Tung1, Le Xuan Hung1 and Banh Tien Long2 1. Thai Nguyen University of Technology, Thai Nguyen 23000, Vietnam 2. Ha Noi University of Technology, Ha Noi 100000, Vietnam Abstract: This paper introduces a new study on cost optimization of surface grinding. In the study, the effects of grinding parameters including the dressing regime parameters, the wheel life and the initial grinding wheel diameter on the exchanged grinding wheel diameter which were investigated. In addition, the influence of cost parameters including the machine tool hourly rate and the grinding wheel cost were taken into account. In order to find the optimum exchanged grinding wheel diameter, a cost optimization problem was built. From the results of the optimization problem, a model for determination of the optimum exchanged grinding wheel diameter was found. By using the optimum diameter, both the grinding cost and grinding time can be reduced significantly. Key words: Grinding, grinding process, surface grinding, cost optimization. 1. Introduction Grinding is a machining process which uses a grinding wheel as a cutting tool. It is a major machining process which accounts for about 20-25% of the total expenditures on machining operations in industries [1]. As a result, there have been many studies that have been subjected to optimization of grinding process such as for external cylindrical grinding [2-4], for surface grinding [5-7] and for internal grinding process [8-10]. In practice, grinding machines with fixed revolutions of grinding wheel are used widely, especially in developing countries because of their low cost. Also, in grinding process, during the wheel lifetime, the diameter of grinding wheel will reduce gradually because of the wheel wear and dressing. Therefore, with this kind of machines the grinding wheel peripheral speed will decrease and the grinding time as well as the grinding cost per part will increase. From that point of view, the effect of the exchanged grinding wheel diameter on the total grinding cost should be taken into account in the optimization problem of grinding process for optimum using of this kind of machines. From previous studies, it was learned that, until now, there is still lack of study on the optimization of surface grinding process which take into account the effect of the exchanged grinding wheel diameter. This paper introduces a cost optimization study for surface grinding. In the study, the influences of many grinding process parameters as well as cost components were taken into account. Also, a new and effective way of using the surface grinding wheel was proposed. Using this way, both the grinding cost and grinding time can be reduced significantly. 2. Cost Analysis for Surface Grinding Process In surface grinding process, the manufacturing single cost per piece Csin can be determined as Eq. (1): Csin  ts  Cmt , h  C gw, p (1) in which, Cmt , h -Machine tool hourly rate (USD/h) including wages, overhead, and cost of maintenance etc.; Cgw, p -Grinding wheel cost per workpiece (USD/workpiece); Cgw, p can be calculated by: C gw, p  C gw / n p , w (2)  Corresponding author: Vu Ngoc Pi, Ph.D., main research fields: abrasive machining, optimum design. where, Cgw is the cost of a surface grinding wheel Cost Optimization of Surface Grinding Process 607 (USD/piece); n p , w is total number of workpieces ground by a grinding wheel and it can be written [11]: n p , w   d s ,0  d s ,e   n p , d /  2  rs  aed , ges   (3) where, d s ,0 is the initial grinding wheel diameter (mm); d s , e is exchanged grinding wheel diameter (mm);  rs is the radial grinding wheel wear per dress (mm/dress); aed , ges is total depth of dressing cut (mm); n p , d is number of workpieces per dress and is given by: Fig. 1 n p , d  t w / tc (4) in which, tw is wheel life (h); The optimum values of the wheel life are from 10 to 30 minutes [12]; tc is grinding time (h). In surface grinding, the grinding time can be expressed as: tc  lc  w c  ae,tot / 1000  vw  v f  f d  N t  (5) where, lc is the calculated grinding length (mm); lc  lw  (20 30) with lw is the length of the workpieces (mm); w c is the calculated grinding width (mm); w c  w w  w gw  5 with w w is the width of the workpieces (mm) and w gw is the grinding wheel width (mm) (Fig. 1); ae,tot is total depth of cut (mm); vw is the work speed (m/s); v f is work feed rate (mm/min); f d is downfeed (mm/pass) and N t is number of workpieces per grinding time. The work speed vw can be determined as [13]: When grinding cast iron v w  5 (m/s); when Schema of surface grinding. determining the work feed rate [13], the Eq. (7) for determination of N Ra was found (with R 2  0.984 ): 0.983 2.44 / N Ra v f  46.1  wgw (7) The downfeed f d is determined by the Eq. (8) [13]: f d  f d ,t  c1  c2  c3 (8) With f d ,t is the tabulated downfeed (mm/pass); f d ,t depends on workpiece materials, the total depth of cut ae ,tot and the work feed rate v f . It can be determined as follows [14]: When grinding cast iron f d ,t is calculated by the following regression equation (with R 2  0.9995 ): 0.993 f d ,t  3.05  ae,0.584 tot  v f (9) When grinding carbon steel and alloy steel f d ,t can be determined as (with R 2  0.9995 ): grinding heat resistant steel, stainless steel and tool steel vw  25 (m/s); 1.01 f d ,t  226  HRC 1.34  ae0.604 ,tot  v f When grinding carbon steel, alloy steel and brass vw depends on the Rockwell hardness of workpiece HRC. From the tabulated data for finding vw [13], vw can be calculated by the Eq. (6) (with When grinding heat resistant steel, stainless steel R  0.9668 ): 2 vw  0.0598  HRC 1.4 (6) The work feed rate v f depends on the required roughness grade number N Ra and the grinding wheel width w gw . From the tabulated data for (10) and tool steel, f d ,t is calculated by the following equation (with R 2  0.998 ): 0.985 f d ,t  0.649  ae0.651 ,tot  v f (11) c1 -coefficient which depends on the workpiece material and the required tolerance grade tg ; it can be determined as follows [14]: When grinding structural carbon steel, chromium steel and tool steels (with R 2  0.9996 ): Cost Optimization of Surface Grinding Process 608 c1  4.13  tg 0.474 (12) (20) we have: When grinding molybdenum and tungsten steels td , p  td  t g / t w (with R 2  0.999 ): c1  3.33  tg 0.458 When grinding high-temperature steels (13) tcw, p is time for changing a grinding wheel per workpiece (h); tcw, p can be calculated as: and tcw, p  tcw / n p , w (14) With tcw is time for changing a grinding wheel (h). The following equation is given by substituting Eqs. (3) into (22): stainless steels (with R  0.9997 ): 2 c1  1.87  tg 0.477 When grinding high-speed steels and tungsten alloy R 2  0.9962 ): 3. Optimization Problem For surface grinding process, the cost optimum problem can be expressed as the Eq. (24): (16) min Csin  f (d s ,e ) c2 -coefficient which depends on grinding wheel diameter d s and on the density of the workpieces loaded on the machine table Dw ; c2 can be Cmt ,h min  Cmt , h  Cmt ,h max ; C gw min  Cgw  Cgw max ; (17) c3 -Coefficient which depends on the grinding machine age; c3  1 if the age is less than 10 years; c3  0.85 if the age is from 10 to 20 years and d s ,0 min  d s ,0  d s ,0 max aed , ges min  aed , ges  aed , ges max c3  0.7 if the age is more than 20 years [13]; t s -Manufacturing time includes auxiliary time (h); (h); tsp -spark-out time (h); tsp is calculated by: tc  lc  w c / 1000  vw  v f  N t  (19) td , p -dressing time per piece (h): td , p  t d / n p , d tw min  tw  tw max ; ae,tot min  ae,tot  ae,tot max ; (18) where, tlu -time for loading and unloading workpiece (20) With td is dressing time (h); Substituting (4) into Eq. (25)  rs min   rs   rs max ; in surface grinding process, the manufacturing time can be express as: ts  tc  tlu  tsp  td , p  tcw, p (24) with the following constraints: calculated by the Eq. (17) (with R 2  0.9985 ) [14]: c2  0.0292  d s0.5151 / Dw0.4949 23) (15) When grinding cast iron and copper alloys (with c1  5.92  tg 0.434 (22) tcw, p  2tcw  rs  aed , ges  /  n p , d  d s ,0  d s ,e   steels (with R 2  0.9969 ): c1  0.61  tg 0.466 (21) From Eqs. (1), (24) and (25), a computer program was built for determining the optimum of the exchanged grinding wheel diameter in order to get the minimum grinding cost. The data of the constraints used in the program were chosen: Cmt ,h  10  50 (USD/h); C gw  5  25 (USD/piece); d s ,0  250  500 aed , ges  0.08  0.2  rs  0.1  0.3 (mm); ; (mm/dress); Tw  10  30 (min); (mm). ae,tot  0.05  0.15 Cost Optimization of Surface Grinding Process 4. Results and Discussions The relation between the exchanged grinding wheel diameter and the manufacturing single cost per part were shown in Fig. 2. The data used in this example were: Cmt , h = 32 (USD/h); Cwp = 14 (USD/piece); d s ,0 = 400 (mm); N t = 35; lc = 200 (mm); w c = 150 (mm); Dw = 0.7; aed , ges = 0.12 (mm);  rs = 0.1 (mm/dress); ae ,tot = 0.1 (mm); HRC = 57; t w = 20 (min); tcw = 20 (min). It was found that the grinding cost strongly depends on the exchanged grinding wheel diameter. In addition, it gets the minimum value when the exchanged diameter equals a value d s ,eop (Fig. 2). This value is called “optimum diameter”. It was noted that the optimum diameter was much larger than the traditional exchanged diameter. In this case, the optimum diameter was 335 mm (Fig. 2) while the traditional exchanged diameter was about 220 mm. Also, with the optimum diameter the grinding cost per piece was 0.072 (USD/p.) when it was 0.08 (USD/p.) with traditional exchanged diameter (220 mm). Calculating for the grinding time, with optimum diameter it was 1.03 (min/p.) and with the traditional exchanged diameter it was 1.20 (min/p.). Consequently, in this case, grinding with 609 optimum diameter can reduce the grinding cost for 10% and the grinding time for 14.17%. The influences of grinding process parameters as well as cost parameters on the optimum diameter were investigated. It was found that the optimum diameter depends on the machine tool hourly rate (Fig. 3a), the grinding wheel cost C gw (Fig. 3b), the radial grinding wheel wear per dress (Fig. 3c), the wheel life (Fig. 3d), the total depth of dressing cut (Fig. 3e) and the initial grinding wheel diameter (Fig. 3f). In addition, the optimum diameter depends strongly on the initial grinding wheel diameter. It was also found that the optimum diameter does not depend on the required tolerance grade. This is because the downfeed f d , which is affected by the required tolerance grade, does not depend on the grinding wheel diameter (Eqs. (8-16)). Based on the results of the optimization program, the following regression model (with R 2 = 0.9999) was proposed for determination of the optimum diameter: 0.0299 0.0239 d s , eop  0.5096  C mt  C gw  ,h S Fig. 2 Manufacturing single cost versus exchanged grinding wheel diameter. 0.028 Tw0.0469  aed0.0204  d s1.0519 , ges   rs ,0 (26) Cost Optimization of Surface Grinding Process 610 Fig. 3 (a) (b) (c) (d) (e) (f) Cost and process factors versus optimum diameter. Cost Optimization of Surface Grinding Process 5. Conclusion A study on cost optimization of surface grinding was carried out. The cost structures for surface grinding process were analyzed. Also, the influences of cost components as well as grinding process parameters on the optimum exchanged grinding wheel diameter were investigated. In order to determine of the optimum exchanged diameter for getting the minimum grinding cost, a computer program was built. From the results of the optimization program, a regression model for calculation of the optimum exchanged diameter was proposed. Grinding with optimum diameter can save a lot of both the grinding cost and the grinding time. Besides, by using an explicit model, the optimum diameter for surface grinding process can be determined very simply. [4] [5] [6] [7] [8] [9] Acknowledgements The work described in this paper was supported by Thai Nguyen University of Technology for a scientific project. References [1] [2] [3] Malkin, S., and Guo, C. S. 2008. “Grinding Technology: Theory and Applications of Machining with Abrasives.” Industrial Press. Li, G. S., Wang, L. S., and Yang, L. 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