MACHINE TOOL

Numerical modelling of ground surface topography: effectof traverse and helical superabrasive grinding with touch dressing

Shubham Kumar • S. Paul

Received: 18 April 2011 / Accepted: 10 February 2012 / Published online: 26 February 2012

� German Academic Society for Production Engineering (WGP) 2012

Abstract Grinding processes are often used for final

finishing of components because of their ability to satisfy

stringent requirements of surface roughness and dimen-

sional tolerance. Surface topography generated during

grinding depends upon many parameters like wheel

parameters, wheel velocity, downfeed, grit density etc. and

it also depends upon the type of grinding procedures (viz.

plunge grinding, traverse grinding, helical grinding, touch

dressing etc.) employed. Therefore, a correct examination

of the parameters and type of process employed to carry

out grinding are necessary. This paper is an attempt to

develop the relation between the different grinding

parameters and the grinding procedures like plunge, tra-

verse and helical superabrasive grinding with touch

dressing and the average surface roughness. For this pur-

pose, a numerical simulation technique has been imple-

mented to generate the grinding wheel topography. The

ground workpiece surface has also been generated by

simulating removal of work material depending upon the

trajectory of the abrasive grits on the grinding wheel

without taking rubbing and ploughing into consideration.

Keywords Grinding � Modelling � Surface topography �Surface roughness

List of symbols

a Semi apex angle of the square pyramidal grit

h Rotational angle of any grit

a Infeed or downfeed

b Base dimension of the grit

c Grit density per unit area

dg Average grit diameter

ds Diameter of the grinding wheels

h Height of the grit

ha Average grit depth of cut

x, z Coordinate of the grit tip

vg Grinding speed

vw Table speed in surface grinding

Ra CLA surface roughness

1 Introduction

Grinding is considered as a finishing operation in manu-

facturing and extensive studies have been carried out to

predict the surface roughness of the workpiece upon

grinding. This paper is concerned with the simulation of

wheel topography and the effect of various grinding

parameters and conditions on the roughness of the ground

workpiece. In this regard, research involving wheel

topography generation and surface roughness estimation

has been taken into consideration. The methods adopted for

estimation of surface roughness can be classified as

empirical and numerical [1]. The former method is based

on experimental results and the observations could only be

valid within the investigated experimental domain; there-

fore its universal usage is limited as the models developed

under a particular grinding condition that may not be

usable for roughness prediction under other conditions. The

numerical methods have been attempted to develop a

model which can be used universally.

S. Kumar (&) � S. Paul

Department of Mechanical Engineering, Indian Institute of

Technology, Kharagpur, West Bengal 721302, India

e-mail: shubhamkgpian@gmail.com

S. Paul

e-mail: spaul@mech.iitkgp.ernet.in

123

Prod. Eng. Res. Devel. (2012) 6:199–204

DOI 10.1007/s11740-012-0370-1

The methods reported in the literature for the estimation

of surface roughness using numerical techniques consist of

two processes [1–13]; namely, the simulation of the wheel

topography for a given grit density and grit size; and the

simulation of the surface topography involving the mod-

elling of the kinematic interaction of the wheel with the

ground surface. Pandit and Wu [2] have modelled grinding

wheel surface profile as a continuous autoregressive pro-

cess and validated the model by considering eight different

grinding wheels. They also concluded that the proposed

characterization can be used for surface roughness profiles.

Wang and Moon [3] proposed multi-resolution method to

simulate the grinding wheel, wherein the grinding wheel

and the grits are modelled as a convolution of random

waves. They have investigated plunge surface grinding.

Salisbury et al. [4, 5] have modelled the grinding wheel

surface as a set of Fourier spectrum and have studied the

effect of various levels of table speed, wheel speed, wheel

type and grinding wheel frequency characteristic i.e. the

amplitude on the surface roughness of the workpiece for

single pass surface grinding mode. Zhou and Xi [6]

developed a truncated model to simulate the grinding

wheel by taking into consideration the random distribution

of the grain protrusion heights and calculated the surface

roughness using this model for traverse surface grinding

mode. Cooper and Lavine [7] have studied the effect of

different grinding parameters on a cylindrical workpiece

using numerically assembled grinding wheel information.

Warnecke and Zitt [8] modelled the macro and micro

geometry of the grinding wheel using synthetic 3D-mod-

eling wherein the structure of grinding wheel was analyzed

using scanning electron microscopy (SEM). They also

studied the kinematic interaction between grinding wheel

and workpiece for different grinding processes such as

surface grinding, cylindrical grinding and internal cylin-

drical traverse and plunge grinding. Koshy et al. [9] in their

research paper concluded that the percentage of projected

area due to protruding abrasives is independent of the

abrasive grit size. Chen and Rowe [10, 11] generated

grinding wheel surface by single point diamond dressing

and studied the effect of dressing condition on the grinding

wheel and the generated workpiece after helical grinding.

The result was validated using the experimental result

available in the literature. Gong et al. [12] applied virtual

reality technology to simulate the grinding wheel and

studied the effect of cutting depth, axial feed and wheel

velocity on the surface roughness.

The different grinding parameters like grit density,

downfeed, wheel velocity, work speed etc. have significant

effect on the surface topography generated [1–13]. The

grinding procedures viz. plunge grinding, cross-feed

grinding, helical grinding and touch dressing also play an

important role in deciding the final surface finish of the

workpiece. Ghosh and Chattopadhyay [14, 15] have stud-

ied the effect of touch dressing on the surface roughness

using single layer brazed cBN wheels and they concluded

that a substantial improvement of transverse surface

roughness could be achieved on touch dressing. Vickerstaff

[16] has studied the effect of cross-feed on wheel wear and

surface roughness during surface grinding of hardened and

tempered Ni-Cr-Mo alloy steel by vitrified bonded alumina

grinding wheel. Iwai et al. [17] have studied the effect of

helical grinding on the surface finish and have inferred that

the better surface finish is achieved due to interference of

the trajectories of the multiple grits. Zhang and Uematsu

[18] have also studied the effect of helical grinding on

surface finish and found out that the surface roughness

value in case of helical grinding nearly becomes one-sev-

enth of the value in case of plunge grinding.

The work carried out by Chakrabarti and Paul [1]

involves the prediction of surface roughness for different

grinding parameters under plunge surface grinding. They

did not carry out any analysis for other grinding procedures

viz. traverse or cross-feed grinding, and helical grinding

with touch dressing. The aim of the present work is to

develop and implement numerical models for the predic-

tion of surface roughness for different surface grinding

operations namely plunge grinding, traverse or cross-feed

grinding and helical grinding with touch dressing. The

effects of different grinding parameters (grit density and

grit size) on the surface finish of the ground workpiece are

also studied. Further, the trend of the predicted results is

compared with experimental data available in the literature.

2 Simulation methodology

2.1 Generation of the wheel topography

The interaction between the abrasive grits and the work-

piece depends on the wheel topography and the grinding

parameters, thus affecting the surface roughness. The grits

distributed on the wheel surface differs in terms of their

shape, size, orientation and grit distribution density over

the wheel surface, which results in random variations in the

protrusion heights from the wheel surface. Chakrabarti and

Paul [1] have discussed different methods adopted by

various researchers to model the grinding wheel topogra-

phy. In grinding, it has been observed that the average rake

angle during chip formation can be taken as -60� [13].

Therefore, in this paper the grits have been modelled as

square pyramidal objects having an included angle of 120�.

The grit heights (h) were made to vary and the base

diameter of grits (dg) were changed in order to keep the

included angle constant. The grits have been placed ran-

domly on the periphery of grinding wheel of diameter ds

200 Prod. Eng. Res. Devel. (2012) 6:199–204

123

with a given grit density c. Figure 1 depicts the modelled

shape of an abrasive grit. The grit heights have been

assumed to vary by 5% and follow the relationship as

reported by Chakrabarti and Paul [1].

dg

2ffiffiffi

3p � 0:05dg \h \

dg

2ffiffiffi

3p þ 0:05dg ð1Þ

where, dg is the average diameter of the grits.

2.2 Simulating the grit interaction with the workpiece

Simulation of grit interaction with the workpiece involves

the simulation of the trajectory of a particular grit for a

period of time and to remove whatever workpiece material

is interfering with the trajectory of the grit. A detailed

kinematic analysis of the grit interaction with the work-

piece can be found in standard literature [13]. For com-

pleteness of the paper, a brief review is provided. First, an

x–z coordinate system is set with its origin O0 fixed on the

workpiece and coinciding with the grit G at the lowest

point, as shown in Fig. 2. Then, the trajectory of grit G,

which is a trochoid, can be described as:

x ¼ ds

2sin h� dsvw

2vgh ð2Þ

z ¼ ds

2ð1� cos hÞ ð3Þ

where, x and z are the coordinates of grit G after it has

rotated by angle h, vw is the velocity of the workpiece and

ds is the nominal diameter of the grinding wheel. To reduce

complexity during the simulation, the rubbing and

ploughing effects during grinding have been neglected

along with wear and tear of the grit during grinding.

The whole simulation process can be assumed to be

comprised of the two processes discussed above. The first

step is simulating the wheel topography and the second is

simulating the grit interaction with the workpiece. The

simulation is run in such a way that the trajectories of all

the grits are calculated and the interfering material is

removed in each run of the iteration. The simulation pro-

cess is carried out by discretizing workpiece surface into

very small rectangular areas and the entire surface infor-

mation (i.e. the depth of the workpiece at each of these

rectangular locations) is stored in a matrix whose dimen-

sions are equal to the number of rectangles along the length

and width of the workpiece. The surface roughness of the

simulated ground surface is calculated using Ra parameter.

3 Simulation results and discussion

The grinding process has been simulated by taking the

following parameters, viz. vg, vw, c, dg and a into consid-

eration. The effect of different surface grinding operations,

viz. plunge grinding, traverse or cross-feed grinding and

helical grinding with touch dressing, on the surface

roughness of the ground workpiece has been studied.

3.1 Plunge grinding

In plunge surface grinding, typically the width of the

grinding wheel is more than the width of the workpiece and

downfeed is given per stroke. The workpiece reciprocates

under the grinding wheel and the entire surface of the

workpiece is ground by the peripheral surface of the

grinding wheel. The surface roughness changes with

change in the input parameters like wheel speed, workpiece

speed, grit density etc. Similar work has been done by

Chakrabarti and Paul [1] and therefore, only the grit den-

sity and the grit size have been varied to study their effect

on surface roughness.Fig. 1 Modelled shape of an abrasive grit

Fig. 2 Trajectory of a single grain in grinding process

Prod. Eng. Res. Devel. (2012) 6:199–204 201

123

3.1.1 Variation in grit density (c)

Material removal in grinding can be thought of as collec-

tion of repetitive unit events. In grinding the unit event is

the generation of a grinding chip by the cutting action of an

abrasive grit and it can be quantified by the average grit

depth of cut (ha). Increase in grit density leads to reduction

in chip volume which results in the average grit depth of

cut (ha) becoming smaller. However, grit density cannot be

increased indefinitely for a given grit size. Moreover, high

grit density leads to less chip accommodation space

between grits, increasing probability of wheel loading.

Figure 3 depicts the effect of grit density on ground surface

finish. Expectedly, the increase in grit density provided

finer average grit depth of cut, i.e. finer chip volume

leading to improvement in the surface finish. A two fold

increase in grit density from 4 to 8 grits/mm2 provided

improvement in surface finish (Ra) from 0.46 to 0.30 lm

under plunge surface grinding.

Ghosh and Chattopadhyay [14] have studied the effect of

grit density on surface roughness in grinding using single

layer cBN wheels and have observed that choice of densely

packed wheels over regular grit density provided improve-

ment in surface finish. The effect of grit density has also been

observed by Heo et al. [19]. They observed that use of finer

grits (Mesh#100 to #500), i.e. higher maximum possible grit

density, yielded reduction in surface roughness (Ra) from

0.40 to 0.15 lm. Thus, it may be inferred that the proposed

model could capture the generation of surface roughness in

grinding and the effect of grit density in particular.

3.1.2 Variation in grit size

Increase in the grit size leads to an increase in its effective

height and, the grit density typically decreases with

increase in the grit size. Thus, with an increase in the grit

size, the unit event in grinding becomes larger. Figure 4

depicts the effect of grit size on ground surface finish.

Surface roughness (Ra) increases by two fold from 0.20 to

0.40 lm when the diameter of grit is increased from 150 to

300 lm. The other grinding parameters were kept same

during simulation and they were taken as: vg = 150 m/s,

vw = 150 mm/s, c = 6 grits/mm2, and a = 25 lm. Thus it

may be deduced that the proposed model could capture the

effect of grit size on surface roughness correctly.

3.2 Simulation results for touch dressing

Grinding wheels possess an inherent weakness of having

unequal distance of the grit tips from the wheel substrate

surface [14]. Certain percentage of the grits always remains

over-protruded which do not allow the underlying ones to

participate during grinding. It results into less overlapping

cuts of grit leading to transverse surface roughness, sub-

stantially higher than the acceptable value [15]. Further, the

single layer cBN wheels tend to produce rougher surface

due to high sharpness of the abrasive grits [14, 15]. Such

high workpiece surface roughness associated with the use

of single-layer cBN wheel needs to be reduced and this

problem can be appropriately solved by controlled dressing

of the overlying cBN grits with a suitable diamond tool.

The process is popularly known as touch-dressing [14, 15].

Touch dressing allows participation of large number of

grits, which remain inactive before the dressing. The touch-

dressed wheel not only reduces the roughness of the ground

surface markedly but also maintains roughness value

almost constant over a long span of grinding. Figures 5 and

6 shows the variation of the surface roughness with the

level of the dressing of the wheel. The grits used are square

pyramidal and dressing is done in steps. X-axis (abscissa)

Fig. 3 Variation in surface roughness with grit density for plunge

grinding

Fig. 4 Variation in surface roughness with grit size for plunge

grinding

202 Prod. Eng. Res. Devel. (2012) 6:199–204

123

shows the level of dressing, which is basically the amount

of material removed or dressed from the top of the grits,

which is a percentage of the diameter of the grit and is

varied from 0 to 7% for simulation. 0% implies that no

touch dressing has been done. The base diameter of the grit

is 250 lm and thus the dressing has been done up to 17.5

micron. The surface roughness was calculated for two

different grit density values viz. 6 and 16 grits/mm2. Ghosh

and Chattopadhyay [14, 15] have studied the effect of

touch-dressing on surface roughness in grinding using

single layer cBN wheels with 252 lm abrasive grits. They

have studied the effect of touch dressing on three different

wheels and have observed that after each step of touch

dressing of the brazed wheels, the surface roughness value

decreases. They have varied the cumulative dressing depth

from 0 to 22 lm. Initially, up to 13 lm, the rate of

reduction in surface roughness is high and gradually the

rate diminishes. With further dressing, there is negligible

effect on the surface roughness because the rate of reduc-

tion in surface roughness is very low in the final stages of

the dressing as most of the grits participate in grinding after

critical depth of dressing. Similar reduction in surface

roughness has been captured by the proposed model as

shown in Figs. 5 and 6. Also, it can be observed that the

surface roughness value for higher grit density is low

which is apparent and has been discussed above.

3.3 Touch dressing with cross-feed grinding

In case of plunge grinding no cross feed is provided to the

table, while in case of cross-feed grinding a cross feed is

provided to the table at the end of each stroke. Cross-feed

is common when the workpiece width is more than the

width of the grinding wheel. Figures 5 and 6 show the

variation of ground surface roughness in the case of cross-

feed grinding with the level of touch dressing done and are

for two different values of grit density viz. 6 and 16 grits/

mm2 respectively.

The other grinding parameters were kept unchanged

during simulation and they were vg = 150 m/s, vw = 150

mm/s, a = 25 lm. Cross feed of 1 mm/stroke was pro-

vided to the grinding wheel at the end of each stroke. It can

be inferred from Figs. 5 and 6 that for the same set of input

parameters, average surface roughness in case of cross-feed

grinding is less as compared to plunge grinding.

Vickerstaff [16] has studied the effect of cross-feed

grinding on surface roughness of the workpiece and has

observed that cross-feed grinding leads to reduction in the

average surface roughness values. Similar effects have been

demonstrated by the proposed numerical simulation. In case

of traverse or cross-feed grinding also, the effectiveness of

touch dressing has been effectively captured by the pro-

posed numerical model as can be seen in Figs. 5 and 6.

3.4 Helical grinding

In case of helical grinding, the table is provided with a

constant transverse speed, unlike in cross-feed grinding in

which the cross-feed is provided at the end of each stroke.

The table transverse speed used for simulation was 15 mm/

s and the other grinding parameters were kept unchanged.

Figure 7 shows the variation of ground surface roughness

with grit density in case of helical grinding and also pre-

sents a comparative picture between helical grinding and

plunge grinding for the same set of grinding parameters. It

can be observed that for the same set of grinding param-

eters surface roughness is less in case of helical grinding as

compared to the surface roughness in plunge grinding.

Zhang and Uematsu [18] have claimed reduction in surface

roughness upon helical grinding by a factor of seven.Fig. 5 Variation in surface roughness with touch dressing for plunge

and cross-feed grinding for low grit density (6 grits/mm2)

Fig. 6 Variation in surface roughness with touch dressing for plunge

and cross-feed grinding for high grit density (16 grits/mm2)

Prod. Eng. Res. Devel. (2012) 6:199–204 203

123

Though, in the present work, the improvement in surface

finish on helical grinding seems to be by a factor of two.

Iwai et al. [17] have observed improvement in surface

finish upon helical grinding due to the interference of the

trajectories of the multiple grits, which has been effectively

modelled in the present work as seen in Fig. 7.

Figure 5 indicates that plunge surface grinding without

touch dressing with a grit density of 6 grits/mm2, provided

a surface roughness (Ra) of around 0.33 lm, which reduced

to 0.20 lm on traverse or cross-feed grinding. Helical

grinding produced almost similar surface roughness (Ra) of

around 0.21 lm. Helical grinding does not require incre-

mental cross-feed after each stroke, which is the charac-

teristics of cross-feed grinding and thus helical grinding

would require much less cycle time enhancing the pro-

ductivity simultaneously providing improved surface finish

as compared to plunge surface grinding.

Further, Fig. 5 indicates that touch-dressing brings down

the surface roughness in case of traverse or cross-feed

grinding to around 0.17 lm, which is not much improved

from surface roughness of around 0.21 lm (refer Fig. 7)

achieved under helical grinding. Touch-dressing introduces

another operation prior to employing the single-layer cBN

wheels for grinding and in the process further increases the

cycle time. Over and above, touch dressing may lead to

increase in grinding forces [14, 15].

4 Conclusions

A model for generating the surface topography based on

the cutting conditions, wheel topography and initial

workpiece geometry has been developed. The model

developed has been implemented to study the effect of

different grinding parameters and operations, viz. plunge

surface grinding, traverse or cross-feed grinding with touch

dressing and helical grinding, on ground surface topogra-

phy. The proposed methodology captures the parametric

effect on surface roughness successfully both in degree and

nature as has been verified against experimental results

from previously published literature.

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