time-optimization-study-for-external-cylindrical-grinding-5ea9c306bb243

315 Time Optimization Study for External Cylindrical Grinding Nguyen Van Cuong1 Tran Thi Hong2, Nguyen Hong Linh3, Tran Ngoc Giang4, Nguyen Thanh Tu5, and Vu Ngoc Pi6,* University of

315

Time Optimization Study for External Cylindrical

Grinding

Nguyen Van Cuong1 Tran Thi Hong2, Nguyen Hong Linh3, Tran Ngoc Giang4, Nguyen Thanh Tu5, and Vu

Ngoc Pi6,*

University of Transport and Communications, Hanoi city, Vietnam1 Nguyen Tat Thanh University, Ho Chi Minh City, Vietnam2 Electric Power University, Hanoi City, Vietnam3 Thai Nguyen University of Technology, Vietnam4,5,6

*Corresponding author: 1*

Abstract— The present study deals with calculating optimal exchanged grinding wheel diameter to get the

minimum manufacturing time when external grinding tool steel To do that, four input factors covering the initial grinding wheel diameter D0, the radial grinding wheel wear per dress Wpd, the wheel life Tw, and the total dressing depth aed Also, for weighing the effect of the process parameters on the optimal exchanged wheel diameter dop, a simulation experiment was designed and performed In addition, a proposed equation

to find the optimal exchanged wheel diameter was given

Keywords— grinding; external grinding; grinding time; time optimization; replaced wheel diameter

1 Introduction

Grinding is one of the most common machining process It can give high precision and small surface roughness Therefore, the research on optimization of grinding process attracts many scientists

In practice, the grinding process consists of various types such as external grinding, internal grinding, surface grinding, centerless grinding, etc Therefore, grinding studies have been carried out surface grinding [1-3], internal grinding [4, 5], or external grinding [6-8] In addition, grinding process is affected by many factors such as lubricant mode, dressing regime and input parameters As a result, many works were conducted to find optimal factors for lubricant conditions [9, 10], for wheel dressing [11, 12], for maximal material removal rate [13, 14] or for minimum grinding cost [15-17]

2 2 Methodology

2.1 Grinding time analysis

The manufacturing time 𝑡𝑠 when external grinding can be determined by:

𝑡𝑠= 𝑡𝑐+ 𝑡𝑙𝑢+ 𝑡𝑠𝑝+ 𝑡𝑑,𝑝+ 𝑡𝑐𝑤,𝑝 (1) Where, 𝑡𝑐 , 𝑡𝑠𝑝, 𝑡𝑙𝑢, 𝑡𝑑,𝑝 and 𝑡𝑐𝑤,𝑝 are the grinding time (h), the load and unload time (h), the spark-out time (h), the time for dressing per part (h), and the time for exchanging a grinding wheel per part, respectively

𝑡𝑐, 𝑡𝑑,𝑝 and 𝑡𝑐𝑤,𝑝 is found by:

In above equations, 𝑙𝑤 (mm), 𝑎𝑒,𝑡 (mm), 𝑣𝑓𝑎 (mm/min), and 𝑓𝑟 (mm/double stroke) are the part length, the entire grinding depth of cut, the axial speed, and the radial wheel feed, respectively 𝑣𝑓𝑎 is determmined by [18]:

𝑣𝑓𝑎= 0.2557 𝑑𝑤0.0749 𝑛1.1093𝑤 𝑏𝑠0.9841, (5)

and 𝑓𝑟 is calculated as [19]:

In Equation (5), 𝑑w is the diameter of part, 𝑛w is the workpiece speed, and 𝑏s is the wheel width When grinding tool steel, 𝑛𝑤 is found as [18]:

In Equation (6), 𝑓𝑟,𝑡𝑎𝑏 is the tabled radial feed of wheel (mm/double stoke); c1 is coefficient which count for the tolerance grade 𝑡𝑔; c2 is coefficient which depends on the grinding peripheral speed 𝑣𝑠 (m/second) and the wheel diameter 𝑑𝑠; 𝑐3 is the measurement coefficient; 𝑐4 is the coefficient which refers to the effect of the ratio of the workpiece length to its diameter 𝑓𝑟,𝑡𝑎𝑏 , c1 and 𝑐2 are determined by [18]

𝑓𝑟,𝑡𝑎𝑏= 150.3605 𝑑𝑤−0.9331 𝑣𝑓𝑎−0.4922 (2 𝑎𝑒,𝑡)0.2194 (8)

In Equations (3) and (4), 𝑡𝑑 and 𝑡𝑐𝑤 are the time of dressing and the time for replacing grinding wheel (h);

𝑛𝑝,𝑑 is the total parts per dress and 𝑛𝑝,𝑤is the total parts ground by a grinding wheel which can be found by:

𝑛𝑝,𝑤=(𝑑𝑠,0−𝑑𝑠,𝑒) 𝑛𝑝,𝑑

Where, 𝑑𝑠,𝑜 is the initial wheel diameter (mm), 𝑑𝑠,𝑒 is the exchanged wheel diameter (mm)

2.2 Optimization problem

It can be found from the manufacturing time analysis (Section 2.1), if wheel diameter 𝑑𝑠,𝑒 is in large values, the grinding time is reduced as 𝑓𝑟 will be increased (see Equations (2), (6) and (10)) Also, in this case, the total parts ground by a grinding wheel (Equation (12)) is reduced That will lead to the reduction of the time for wheel exchanging per part (Equation (4)) and therefore the grinding time will be increased Therefore, there will be an optimal value of the exchanged wheel diameter with which the grinding time is the smallest Hence, the optimization problem for finding the optimal exchanged wheel diameter to get the minimal grinding time is stated as

subject to

2.3 Experimental work

To understand the effect of input factors on the optimal exchanged wheel diameter, a simulation experiment has been considered In this experiment, the input elements are shown in Table 1 In addition, the experiment was carried out with 2 ^ 4 = 16 test runs because it was planed with full factorial design and with 4 input parameters Moreover, a program was constructed for conducting the experiment The plan of the experiment and the output response (the optimal exchanged wheel diameter 𝑑𝑜𝑝) are described in Table 2

Table 1 Input factors

317

Table 2 Screening experimental works and the result values of dop StdOrder RunOrder CenterPt Blocks Do Wpd aed Tw dop

3 Results and discussion

Figure 1 illustrates the main effects of each input factors for dop It can be understood that D0 is the most influential factor to dop, while Wgw is not affected Also, aed and Tw has very small effect on dop

The Pareto diagram of standardized effects on dop is shown in Figure 2 It is found from the diagram that the

original grinding wheel diameter (factor A), the total depth of dressing cut (factor C) and the wheel life (factor D) are significantly impacted factors because the reference line crosses them Also, the interactions CD

(aed*Tw), AC (D0*aed ) and AD (D0*Tw ) have less impact on optimal diameter

Figure 1 Main effects plot for dop

Figure 2 Pareto chart of the standardized effects on dop

Figure 3 Normal plot for dop

The normal chart of standardized effects is shown in Figure 3 As seen in the chart, most factors including the wheel life (factor D), the total depth of dressing cut (factor C), the radial wheel wear per dress (factor B) and the interactions CD (aed*Tw), AD (D0* Tw) and AC (D0* aed) are close to the reference line That mean these

factors have a small effect on the optimal diameter dop In contrast, the initial wheel diameter D0 (factor A) is farthest from the reference line It shows that D0 is the most influential factor on dop Moreover, D0, Tw, and

the interactions CD and AD have positive effects on dop If they increase, dop grows Besides, aed and the interaction AC have negative affects on dop dop will reduce if these factors increase

Figure 4: Estimated effects and coefficients for dop

The estimated effects and the coefficients for dop after ignoring the insignificant effects on it is described in Figure 4 It can be seen from the figure that all factors including the initial grinding wheel D0, the radial grinding wheel wear per dress Wpd, the total depth of dressing cut aed, the wheel life Tw, and the interactions D0*aed, D0*Tw, aed*Tw have significant effects on the response dop (as their P-values are less than 0.05) Therefore, the optimal exchanged wheel diameter dop can be determined by:

0

319

The Equation (15) is the best fit with the experimental data because all the R-sq and R-sq(adj) are in 100% (Table 3) Therefore, this Equation can be used to determine the optimal exchanged wheel diameter when external cylindrical grinding tool steel

4 Conclusions

A time optimization work for calculating the optimal exchanged wheel diameter in external grinding tool steel was presented In this work, the manufacturing time when external grinding was considered because it was chosen as the target of the optimization problem Also, four input parameter including the initial wheel diameter, the radial grinding wheel wear per dress, the total depth of dressing cut, and the wheel life were selected for the examination In addition, to assess the influences of the input parameters on the optimal exchanged wheel diameter, a simulation experiment was planned and conducted Lastly, based on the results

of the optimization problem, a regression equation for finding the optimal exchanged wheel diameter was recommended The optimal exchanged wheel diameter can be determined simply and effectively as the proposed model is explicit

5 Acknowledgments

The authors gratefully acknowledge Thai Nguyen University of Technology for supporting this work

6 References

[1] Saravanan, R., P Asokan, and M Sachidanandam, A multi-objective genetic algorithm (GA) approach for

optimization of surface grinding operations International journal of machine tools and manufacture, 2002

42(12): p 1327-1334

[2] Asokan, P., et al., Optimization of surface grinding operations using particle swarm optimization technique 2005

[3] Rao, R.V., D.P Rai, and J Balic, Surface grinding process optimization using Jaya algorithm, in Computational

Intelligence in Data Mining—Volume 2 2016, Springer p 487-495

[4] Pi, V.N., et al., Cost optimization of internal grinding J Mater Sci Eng B, 2016 6: p 291-296

[5] Akintseva, A and P Pereverzev Complex optimization of parameters for controlling the cycle of internal

grinding by the method of dynamic programming in MATEC Web of Conferences 2017 EDP Sciences

[6] Pi, V.N., V.H Khiem, and N.N Huong Cost optimization of external cylindrical grinding in Applied Mechanics

and Materials 2013 Trans Tech Publ

[7] Tu, H.X., et al., Calculation of optimum exchanged grinding wheel diameter when external grinding tool steel

9CrSi Int J Mech Eng Robot Res, 2019 8(1): p 59-64

[8] Tu, H.X., et al., Determining optimum parameters of cutting fluid in external grinding of 9CrSi steel using

Taguchi technique SSRG Int J Mech Eng, 2018 5(6): p 1-5

[9] García, G.E., et al., Optimization of surface roughness on slitting knives by titanium dioxide nano particles as an

additive in grinding lubricant The International Journal of Advanced Manufacturing Technology, 2018

96(9-12): p 4111-4121

[10] Zhang, Y., et al., Experimental evaluation of the lubrication performance of MoS2/CNT nanofluid for minimal

quantity lubrication in Ni-based alloy grinding International Journal of Machine Tools and Manufacture, 2015

99: p 19-33

[11] Liu, Y., et al., Investigation of different grain shapes and dressing to predict surface roughness in grinding using

kinematic simulations Precision Engineering, 2013 37(3): p 758-764

[12] Hung, L.X., et al., OPTIMUM DRESSING PARAMETERS FOR MAXIMUM MATERIAL REMOVAL RATE

WHEN INTERNAL CYLINDRICAL GRINDING USING TAGUCHI METHOD

[13] Dai, C., et al., Influence of grain wear on material removal behavior during grinding nickel-based superalloy

with a single diamond grain International Journal of Machine Tools and Manufacture, 2017 113: p 49-58

[14] Gao, G.F., et al Modeling of Material Removal Rate in Two-Dimensional Ultrasonic Grinding Complex

Ceramics in Key Engineering Materials 2008 Trans Tech Publ

[15] Tran, T.-H., et al., Optimization of replaced grinding wheel diameter for minimum grinding cost in internal

grinding Applied Sciences, 2019 9(7): p 1363

[16] Tran, T.-H., et al., Optimization of Replaced Grinding Wheel Diameter for Surface Grinding Based on a Cost

Analysis Metals, 2019 9(4): p 448

[17] Thi-Hong, T., et al., Optimization of Replaced Grinding Wheel Diameter for Minimum Grinding Cost in Internal

Grinding Applied Sciences, 2019 9(7)

[18] Long, B.T., et al., Building cutting regime formulas for internal grinding J Sci Technol, 2016 9: p 15-18

[19] L.M Kozuro, A.A.P., E.I Remizovski, P.S Tristosepdov, Handbook of Grinding (in Russian) 1981: Publish

Housing of High-education, Minsk

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