Analysis of grinding quantities through chip sizes

Pei-Lum Tso*, Shih-Huang Wu

Department of Mechanical Engineering, National Tsing Hua University, Hsinchu, Taiwan, China

Received 23 February 1997; received in revised form 30 September 1998

Abstract

Grinding chips obtained under different conditions represent a wide variety of morphologies. Observation of chips using a scanning

electron microscope leads to greater understanding of metal removal and the chip formation mechanism. An image processing method is

employed to measure the size of grinding chips and an equivalent chip-volume parameter is proposed to de®ne comparable chip sizes of

various grinding conditions. Grinding quantities such as surface ®nish, grinding force, and speci®c energy are investigated herein, to relate

to chip-volume. The results of this study con®rm that this chip-volume parameter is a useful index in accurately predicting and evaluating

the grinding quantities of particular grinding operations. # 1999 Elsevier Science S.A. All rights reserved.

Keywords: Chip-volume; Grinding chips;

1. Introduction

Chip formation and material removal depend primarily on

the microstructure of the grinding wheel, of the work

material, and the grinding kinematics. Fig. 1 shows the ¯ow

chart between chip formation and grinding quantities. The

chips produced in grinding are relatively small and their

sizes vary due to the randomly oriented cutting edges on the

grinding wheel. Six basic types have been classi®ed: ¯ow-

ing, shearing, ripping, knife, slice, and melting [1]. Previous

studies involving chip geometry have generally focused on

the undeformed chip thickness, in addition to proposing

some models based on a single-grain approach [2,3]. Those

models frequently assume that no plastic deformation and

plowing occur during chip formation and that the grinding

wheel has a uniform topography and grain shape: in addition

that, all of the grains in the contact area take part in chip

formation and no overlapping of traces occurs. Since the

shape of the chips are always deformed, investigating the

chip-volume is a more realistic task. In this work, experi-

ments are performed to survey chip sizes; an empirical

parameter `̀ equivalent volume of chip parameter'' being

established also. This parameter describes the actual mate-

rial removal, and is correlated to the grinding quantities of

grinding processes. The relationship between the chip-

volume and surface ®nish, as well as the speci®c grinding

energy are also investigated.

2. Experimental

The experimental apparatus consists of a horizontal spin-

dle surface grinder, a two component piezoelectric dynam-

ometer, and a personal computer equipped with an on-board

A/D card. The material of the specimen workpieces is a

water-hardening steel W1(SK3) of a hardness of 60 Rock-

well C after hardening, and of dimension 150�60�15 mm3.

Each series of grinding test consists of four passes, and

includes one spark-out pass. The type of grinding wheel

employed here is WA80K8V, of size 140�13�50.8 mm3.

Table 1 lists the grinding and dressing conditions, in which

the grinding wheels were dressed using a single-point

diamond dresser.

3. Chip formation and size measurement

With an extremely high strain rate, substantial heat is

generated at the shear zone and a certain portion of this heat

is transferred to the chips. As the chips leave the workpiece

and ¯y into the air, they undergo an exothermic reaction with

oxygen [4]. Without coolant, the common shapes of grinding

chips are spherical due to very high temperature, which

Journal of Materials Processing Technology 95 (1999) 1±7

*Corresponding author. Tel.: +886-3-5742919; fax: +886-3-5722840

E-mail address: pltso@pme.nthu.edu.tw (P.-L. Tso)

0924-0136/99/$ ± see front matter # 1999 Elsevier Science S.A. All rights reserved.

PII: S 0 9 2 4 - 0 1 3 6 ( 9 9 ) 0 0 2 9 7 - 6

continues to rise until they melt or explode [5]. Other smaller

portions are slender, bent and irregular. Chips were collected

during the grinding operation by a catcher made of paper,

after which the catcher was placed on a magnetic table and

chips then examined under a scanning electron microscope

at a magni®cation of 200, the micrographs were scanned as

black-and-white pictures as shown in Fig. 2. The majority of

the chips are spherical, although some messy dots and chips

that are too small were eliminated from the pictures. To

calculate the average chip size, the modi®ed pictures were

stored as bitmap image ®les which are composed of a series

of one and zero, which indicates that the pixel is black or

white respectively. By writing a program to count the

numbers of one and zero, the areas of both black and white

could be calculated. The area of black, i.e., the total area of

spherical chips, was then divided by the number of spherical

chips to obtain the average area of the chips. Dividing by the

magni®cation and transforming the area into volume yielded

the average volume of the chips.

As Figs. 3 and 4 the average volume of the chips increases

with respect to the increase in table speed (Vw); however, it

decreases with respect to the increase in wheel speed (Vs).

The reason for such an occurrence is that when the table

speed is faster or wheel speed is slower, the grit of the

grinding wheel produces a longer and deeper cutting path.

According to experimental results, an empirical model

relating the average volume of the chips to the wheel speed

and table speed was obtained using rigorous statistical

analysis and curve-®tting methods. The following relation-

ship is found for the surface grinding of a water-hardening

steel W1(SK3) of a hardness of 60 Rockwell C after hard-

ening. The grinding wheel was WA80K8V, used with a

grinding depth of 10 mm without coolant.

Previous studies [6] involving chip sizes were concerned

primarily with the undeformed chip thickness, on the basis

of the geometrical interaction of a grit moving path. The

undeformed chip thickness is theoretical and depends pri-

marily on the average distance of the grit cutting edges or the

cutting edge density of the grinding wheel:

Vol / Vÿ0:52s � V0:26

w : (1)

Eq. (1) is an empirical model from experiments (Fig. 5),

where the chip-volume has a ®rm relationship with the

workpiece speed (Vw) and the wheel speed (Vs). An equiva-

lent volume of chip parameter can be identi®ed for the

grinding conditions derived herein. This parameter not only

compares the relative chip-volume under different condi-

tions, but also considers the effect of the cutting edge

distribution. The equivalent volume of chips parameter

Veq is de®ned as follows:

Veq � � � Vÿ0:52s � V0:26

w ; (2)

where � is a constant and can be obtained from experiment.

Removal of the material in the form of chips not only

generates a new surface, but also consumes energy. Thus,

the size and shape of chips are somewhat related to the sur-

face ®nish. The change of chip-volume requires the variation

of the grinding force and grinding energy. Therefore, inves-

tigating the relationship between the volume of the chips and

other grinding quantities such as surface ®nish, grinding

force, and speci®c grinding energy, is a worthwhile task.

Fig. 1. The connection chart between grinding conditions and grinding characteristics.

Table 1

Grinding conditions

Wheel speed 1100±1900 m/min

Table speed 3, 4, 5 m/min

Depth of cut 10 mm

Coolant none

Dressing lead 0.1 mm/rev

Dressing depth 10 mm/pass

2 P.-L. Tso, S.-H. Wu / Journal of Materials Processing Technology 95 (1999) 1±7

Fig. 6 presents the correlation between the volume of

chips and the surface roughness ground under each condi-

tion. The surface roughness Rz (average peak±valley height)

increases with an increase in the equivalent volume of chip

parameter. Such a tendency becomes more signi®cant for a

larger Veq. The phenomenon indicates that the greater the

volume of the chips the worse the surface ®nish. This ®nding

clearly suggests that there is a suf®cient correlation between

the volume of chips and the surface roughness produced in

grinding. Another grinding parameter proposed by Inasaki

Fig. 2. SEM micrographs of chip types for different values of Vs: (a) Vs�3000 rpm, Vw�5 m/min, and a�10 mm; (b) Vs�2700 rpm, Vw�5 m/min, and

a�10 mm; (c) Vs�2400 rpm, Vw�5 m/min, and a�10 mm; (d) Vs�1800 rpm, Vw�5 m/min, and a�10 mm.

Fig. 3. The influence of the grinding wheel speed on the volume of the

chips. Fig. 4. The influence of the table speed on the volume of the chips.

P.-L. Tso, S.-H. Wu / Journal of Materials Processing Technology 95 (1999) 1±7 3

[7], the average cross-sectional area am of the chips, is

evaluated to compare with the parameter Veq. The average

cross-sectional area of the chips is calculated from:

am � w2 Vw

Vs

�����a

Ds

r; (3)

where w is the theoretical cutting edge spacing, a depth of

cut, and Ds is the equivalent wheel diameter. Fig. 7 depicts

the correlation between the surface roughness and average

cross-sectional area. These results follow a similar trend to

that in Fig. 6. A close relationship apparently does not exist

between Rz and am. Consequently, Veq is an appropriate

parameter correlated to surface roughness. Such a phenom-

enon might be because an increase in the volume of the chips

causes the cutting depth of the grit to increase. Thus, the

cutting action not only plays a major role in the grinding

process, but also in¯uences the surface roughness.

4. Grinding force and specific grinding energy

Speci®c grinding energy u is de®ned as follows:

u � Ft � Vs

a � b � Vw

; (4)

where Ft is the tangential grinding force, and b is the

grinding width. Fig. 8 shows the relationship between the

tangential force (Ft) and the normal (Fn) force and Veq.

Fig. 9 summaries the relationship between the speci®c

grinding energy and Veq. As Veq increases, u progressively

decreases, and then slowing decreases. Such a decrease

tends towards a minimum value of approximately 13.8 J/

mm3 in the limit. The limiting value of u is quite close to that

of a previous investigation into the grinding of a ferrous

material of 13.2 J/mm3 [8].

The speci®c grinding energy can be separated into three

components [8]: chip formation, plowing, and sliding

energy. This minimum u should correspond to the speci®c

chip formation energy, which is assumed to remain constant.

Speci®c chip formation energy refers to the energy expended

for actual material removal. Plowing energy is expended by

the deformation of workpiece material without actual mate-

rial removal, including side ¯ow from the grain cutting path

and plastic deformation under an abrasive grit cutting edge.

For ®ne grinding, the chip removal mechanism involves

micro-extrusion. In the mechanism, a relatively large

volume of material must be brought to a fully plastic state

for a relatively small amount of material to escape as a chip

[3]. Such an occurrence accounts for why the exponential in

u increases with a decrease in the volume of the chips. A

critical volume of chips apparently controls the plowing

process. Plowing action likely occurs when the volume of

chip removal exceeds the critical volume. Therefore, mate-

rial removal at the side of grit by plowing and plastic

deformation under the sub-surface of the material both

consume some amount of speci®c grinding energy.

Fig. 5. Experimental volume of chips versus the `equivalent volume of

chips' parameter.

Fig. 6. The influence of the `equivalent volume of chips' parameter on the

surface roughness.

Fig. 7. The influence of the cross-sectional area of the chips on the

surface roughness.

4 P.-L. Tso, S.-H. Wu / Journal of Materials Processing Technology 95 (1999) 1±7

5. Observation of grinding chips

As an abrasive grain passes through the grinding zone, the

grain initially plows, but this is then followed by cutting to

form the chip. Some of the plowing energy, the major part of

the grinding energy, goes into the chips. Plowing and cutting

processes are responsible for the topography of the tool±chip

contact surface. The total energy that is transmitted into

chips causes different states of chips. More cutting and less

plowing leads to apparent cutting traces on the chip surfaces.

On the other hand more plowing action causes more energy

to go into the chips and may cause the temperature of the

chips to increase.

Fig. 10(a)±(h) present a series of topographies of tool±chip

contact surfaces, with variation of the volume of the chips

examined under SEM. Visible micro-grooves are left on these

surfaces by the grit cutting edges. From the ®rst three pictures,

Fig. 10(a)±(c), the surfaces of the chips are smooth and ¯at

without valid cutting traces and micro-grooves. Notably, these

surfaces seem to have melted, with some micro-melting

particles on them. In reality, these surfaces are not very ¯at.

However, visible cutting traces and micro-grooves start to

appear in Fig. 10(d). The cutting traces and micro-grooves

become more evident in Fig. 10(g) and (h).

These micro-grooves were made by the grit cutting edges,

and they grow along the cutting direction. These areas are

elongated and run parallel to the direction of the micro-

grooves when the chip removal volume increases. Variation

in the tool±chip contact surfaces indicates that the amount of

cutting and plowing actions in¯uences the state of the

surfaces. Both actions affect a portion of the speci®c energy,

which consists primarily of speci®c plowing and chip for-

mation energy. More speci®c energy not only produces

melting of the surfaces of chips due to higher temperature,

but also reduces the cutting traces and micro-grooves on the

contact surfaces. The plowing action controls the primary

part of the speci®c energy.

Discussion of speci®c grinding energy and the volume of

chips stipulates that the speci®c grinding energy increases

progressively as the volumes of the chips decrease. The

speci®c plowing energy plays a major role in the total

energy, particularly when the volume of the chips is low.

When the volume of chips is low, more plowing action

occurs with more speci®c energy transmitted into the chips,

making a smooth but melting surface. When the volume of

chips is high, less plowing action occur with less speci®c

energy transmitted into the chips, making the cutting traces

and micro-grooves increase.

6. Conclusions

This study has analyzed the volume of grinding chips and

the correlation with the grinding quantities. Based on the

results presented herein, the following can be concluded.

Fig. 9. Specific grinding energy versus the `equivalent volume of chips'

parameter.

Fig. 8. The influence of the `equivalent volume of chips' parameter on the tangential (Ft) and normal (Fn) grinding force.

P.-L. Tso, S.-H. Wu / Journal of Materials Processing Technology 95 (1999) 1±7 5

Fig. 10. SEM micrographs of chip surfaces for different values of Veq: (a) 0.0165; (b) 0.0216 (c) 0.0264 (d) 0.0296; (e) 0.0318 (f) 0.0338 (g) 0.0393 (h)

0.0485.

1. Through image process methods, the volume of the chips

can be measured and quantified. An empirical `volume of

chip' model is identified to be the equivalent volume of

chip parameter Veq. This parameter describes the influ-

ence of the grinding inputs on the volume of the chips.

2. The surface roughness increases with an increase in Veq,

and then becomes more significant for a larger value of

Veq. The smaller the chip size, the better the surface

finish.

3. The specific grinding energy increases exponentially

with decrease in Veq. A critical volume of chips appar-

ently determines the occurrence of the plowing action.

4. Cutting traces and micro-grooves, as contributed by

plowing, appear in the tool±chip contact surfaces. They

elongate and expand when Veq is increased. However,

they might disappear as Veq becomes small: the surfaces

become smooth once melted, with some melting protru-

sion.

The observation of chips implies that appropriate guidelines

are correlated to grinding quantities and results during

grinding processes. A more thorough understanding of chip

formation requires further study, particularly in the removal

of fine and brittle material such as ceramics and semicon-

ductors.

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