comparative study of force analysis and heat generation in grinding

8/11/2019 COMPARATIVE STUDY OF FORCE ANALYSIS AND HEAT GENERATION IN GRINDING

1/4

COMPARATIVE STUDY OF FORCE ANALYSIS

AND HEAT GENERATION IN GRINDING

Biswajit Das1, Purnendu Das2, Soumyajit Roy3 and Priyankar Datta4

Mechanical Engineering Department

Indian Institute of Technology Kharagpur

Kharagpur, West Bengal, India

[email protected], [email protected], soumyajit [email protected] and [email protected]

AbstractHeat generation in grinding process is a compli-cated phenomenon compared to other metal cutting processes.High specific energy is required in grinding in contrast toother machining processes. Before analyzing heat generationprocess, detailed force analysis is needed as forces play animportant role for calculating specific energy in grinding.Several authors have worked on the force models in different

ways. Due to plastic deformation and rubbing action, bothtemperature of the job and grinding wheel becomes veryhigh. This high temperature causes burn, crack formation andtensile residual stress in the job. Two comparative force modelsand temperature analysis of the job have been presented inthis paper. The temperature equation may be solved eitherby numerical process or some other methods to depict thetemperature distribution inside the job.

Keywords Grinding, Modelling, Work fraction, Specificenergy, Force, Temperature.

I. INTRODUCTION

Grinding is a commonly used method for finish ma-

chining. Grinding wheel wear, dynamic performance of themachine tool, geometric accuracy and surface quality of theworkpiece are greatly influenced by grinding forces. For this,some considerable research works were done by a numberof researchers in this area.

Based on the experimental results, tangential grindingforce was modelled in terms of shear deformation forceand frictional force by Malkin and Cook [1][2]. Anothergrinding force model was established on the basis of grind-ing experiments, and the formula to evaluate normal chipformation force was proposed by Li and Fu [3]. Badger andTorrance [4] proposed two kinds of grinding force models;the first is based on Challen and Oxleys two dimensional (2-D) plane strain slip line field theory, and the second one isbased on the three dimensional (3-D) pyramid shape asperitymodel suggested by Williams and Xie. There are severalother mathematical models of force analysis available.

Designing a technological process, such as grindingentails to deal with heating problem of the workpiece to beground. During grinding, large amount of mechanical energyis transformed into heat, which is accumulated in the contactzone between grinding device and the workpiece. Therefore,it is of considerable industrial interest to understand the

generation of heat and its conduction in order to minimizeenergy losses and to increase efficiency.

Classical modeling of grinding problem was done usingcoupled system of partial differential equations (PDEs).Andrews et al. [5] and Gu et al. [6] have shown how tocalculate the evolution of interconnected temperature field

in the wheel, the workpiece and the applied fluid. Most ofthe works reported in the literature on thermal aspects ofgrinding deal with experimental and numerical analysis, asdetailed in ref. [7-9] among others. In this paper, only thePDE involving heat conduction and heat generation due toplastic deformation and rubbing action is considered.

II. MATHEMATICALM ODEL OFG RINDING FORCES

In this paper, authors shall discuss two force models asgiven by Tang et al. [11] and Patnaik et al. [10]. Both modelsare based on the model proposed by Malkin [12]. The modelproposed by Tang [11] does not include any ploughing force,but model made by Patnaik [10] involved ploughing force.

According to Tang (2009) model,

Fn = Fn,ch+ Fn,slFt = Ft,ch+ Ft,sl (1)

However, according to Patnaik (2010) model force has threecomponents,

F =Fch+ Fsl+ Fpl (2)

Suffix n indicates normal force component, and suffix tindicates tangential force component. Suffix ch indicateschip formation force, sl stands for sliding or friction forceand suffix pl denotes ploughing force.

Accordingly, specific grinding energy is divided into

specific chip formation energy, uch, and specific slidingenergy,usl. The specific chip formation energy uch as givenby Malkin and Cook [2] can be determined by equation 3.

uch=Ft,chVs

Vwapb (3)

where, Vs is the grinding wheel velocity, Vw is work piecefeed velocity, as shown in Fig. 1, ap is the grinding depthand b is the grinding width.

Review Paper ETW 2013


2/4

Fig. 1. Shows cutting action of abrasive in grinding

A. Chip formation force

Specific chip formation energy, uch can be separated intotwo parts: static chip formation energy, us and dynamic chipformation energy, ud.

uch= us+ ud (4)

Here, static chip formation energy, us is a constant which isdetermined by experiment according to work material and

grinding wheel material. Dynamic specific chip formationenergyudis determined by element material, grinding wheelmaterial and process parameters.

Experimental results obtained by Shinji et al. [13] indi-cate that shear strain rate is given by,

=10v sin cos 0accos( 0)

vk

ac(5)

where, is the shear angle , v is the cutting velocity, ac iscutting depth, k is a constant. From equation (5), it is clearthat cutting depth and cutting velocity v have remarkableinfluence on shear strain rate in shear zone.

It is generally agreed that grinding process of metal issimilar to turning and milling, and material is removed by

shear process [12]. Hence, conclusion deduced from cuttinganalysis can be applied to the research on chip deformationforce in grinding. Depth of cut in metal cutting correspondsto average uncut chip thickness, ag in grinding. Averageuncut chip thickness as proposed by Shinji [13] is given by

ag = agmax

2 =

a0.25p v0.5w

(Cr)0.5d0.25e v0.5s

(6)

where, Cis the number of effective abrasive blades in unitarea of grinding wheel, r is the ratio of chip width tochip thickness and de is the equivalent diameter of wheel.Substituting equation (6) in equation (5),

=

k(Cr)0.5d0.25v1.5

a0.25v0.5 (7)Experimental data indicated [14] that shear flow stress isin direct proportion to logarithmic shear strain rate approx-imately. So, dynamic chip formation energy,

Ud= K2ln

0(8)

where, K2 and 0 are constants and determined from exper-iments.

1) Calculation of chip force formation: Chip formationenergy is expressed by the following equation,

uch= us+ K2lnk(Cr)0.5d0.25v1.5

a0.25v0.50(9)

ConsideringK1 = us +K2ln k(Cr)0.5d0.25

e v1.5

s

0, equation (9)

yields,

uch= K1+ K2ln v1.5sa0.25p v

0.5w

(10)

Now,

Ft,ch = uchvwapb

Vs

= K1vwbap

vs+ K2

vwbap

vsln

v1.5sa0.25p v

0.5w

(11)

In equation (11), the first term is static tangential chipformation force and the second term is dynamic tangentialchip formation force. Setting1and 2as ratio of static nor-mal chip formation force to static tangential chip formation

force and the ratio of dynamic normal chip formation forceto dynamic tangential chip formation force respectively,considering,K3 = K11 and K4 = K22, equation (11)yields,

Fn,ch =

K3+ K4ln

vs

a0.25p v0.5w

vwapb

vs

(12)

B. Sliding force

In geometric dynamic analysis of grinding grains, usingparabolic function to approximate cutting path, deviationbetween grinding wheel radius and radius of curvature of

cutting path, Hahn [15] defines,

= 4Vwdevs

(13)

Positive sign is for up grinding and negative sign is for downgrinding. Experimental data as indicated by Kannappanand Malkin [16] shows that the average contact pressurep between workpiece and abrasive grains approximatelylinearly increases as deviation of radius of curvature. So,the relationship is given by

P =p0 =4p0vwdevs

(14)

where,p0 is a constant and can be determined from experi-ments. There may be elastic, elastoplastic or plastic contactbetween workpiece and abrasive grains. So, frictional co-efficient, varies with average contact pressure. Accordingto friction binomial theorem, frictional co-efficient is,

=A0

W + =

p+ (15)

where, W is the normal load, A0 is the contact area, and and are coefficients which are determined by physical



3/4


4/4

[12] Malkin, S., 2002, Grinding Technology Theory and Application ofMachining with Abrasives (Translated by Cai G., Cong Y., Song G.)North Eastern University Press, Shenyang pp. 76-88 (in Chinese).

[13] Shinji, K., Kawamura, S., Kiato M., 1985, Academic cutting dynam-ics (translated by Gao X., Liu D.) National Defense Industry Press,Beijing, pp.98-107 (in Chinese).

[14] Liu, L., Fu, J., New Cutting Mechanics. Dalian University of Tech-nology, Dalian, pp.125-133 (in Chinese)

[15] Hahn, R.S., 1955. The effect of wheelwork conforming in precisiongrinding. Trans. of ASME, Journal of Engineering for Industry 77,1325-1329.

[16] Kannappan, S., Malkin, S., 1972. Effect of grain size and operationparameters on Mechanics of grinding. Trans. of ASME, Journal ofEngineering for Industry 94, 833-842.

[17] Vathire M. De, Delamare, F., Felder, E., 1981. An upper bound modelof ploughing by pyramidal indenter, Wear 55-64.

ABOUT THE AUTHORS

Biswajit Das was born in Hooghly, West Bengal India,on October 4, 1987. He received his B.E. and M.E. degreein Mechanical Engineering from Kalyani Govt. EngineeringCollege (WBUT) in 2009 and in 2013, respectively. Hejoined Indian Institute of Technology Kharagpur, as anInstitute Research Scholar. His research interests includeMetal cutting, Grinding and Surface coating.

Purnendu Daswas born in Kolkata, India, on December12, 1989. He received his B.E. degree in Production Engi-neering from Jadavpur University, in 2011, and M. Tech.degree in Mechanical Engineering from Indian Institute ofTechnology Delhi in 2013. He joined Indian Institute ofTechnology Kharagpur, as an Institute Research Scholar.His research interests include Metal cutting, Grinding, Metalforming and Thermal coating.

Soumyajit Roy was born in Barddhaman, West Bengal,India, on November 29, 1989. He received his B.E. degree inProduction Engineering from Jadavpur University, in 2011,and M. Tech. degree in Mechanical Engineering from IndianInstitute of Technology Delhi, in 2013. At present he is asan Institute Research Scholar in Indian Institute of Technol-ogy Kharagpur. His research interests include Dynamics ofMachine, Mechanism and Robotics, and Applied Mechanics.

Priyankar Dattawas born in Mahishadal, West Bengal,India, on March 20, 1988. He received his B.E. and M.E.degree in Mechanical Engineering from Jadavpur Universityin 2009 and in 2013, respectively. At present he is as anInstitute Research Scholar in Indian Institute of TechnologyKharagpur. His research interests include Composite Mate-rial, Dynamics of Composite Structure and Finite ElementAnalysis.


comparative study of force analysis and heat generation in grinding

Documents