stock removal rate and workpiece strength in multi-pass grinding of ceramics

Stock removal rate and workpiece strength inmulti-pass grinding of ceramics

Bi Zhang*, Fulun Yang, Jiexin Wang, Zhenqi Zhu1, Richard MonahanDepartment of Mechanical Engineering, Precision Manufacturing Institute, University of Connecticut at Storrs,

191 Auditorium Road, Storrs, CT 06269, USA

Received 4 January 1999

Abstract

Stock removal rate and workpiece strength are evaluated in terms of machine stiffness and grinding wheel parameters in multi-pass

grinding of silicon nitride ceramics. This paper presents theoretical analyses on normal grinding force, actual depth of cut (ADOC) of a

grinding wheel, stock removal rate and residual strength of ground workpieces, as well as experimental results to verify the analyses. In the

grinding experiments, silicon nitride workpieces are subjected to multi-pass grinding with four diamond wheels of three grit sizes and two

bond types, as well as a precision grinder of adjustable stiffness. The electrolytic in-process dressing (ELID) technique is adopted to

evaluate how wheel dressing can affect the workpiece strength and stock removal rate in multi-pass grinding. A discussion addresses the

issues of strength gain and strength loss for ground workpieces and a recommendation is provided to obtain higher residual strength of

ground workpiece. # 2000 Elsevier Science S.A. All rights reserved.

Keywords: Diamond grinding; Silicon nitride ceramics; Stock removal rate; Workpiece strength; Machine stiffness

1. Introduction

More and more ceramic parts are used to substitute for

metal counterparts due to their excellent physical, chemical

and mechanical properties. However, ceramics, especially

structural ceramics, are extremely dif®cult to machine

because of their high hardness and brittleness. Grinding

has become one of the primary methods used in machining

ceramics. Nevertheless, it has also encountered several

problems, such as low workpiece accuracy and material

removal rate due to machine de¯ection, and strength degra-

dation due to grinding damage. A large amount of research

has, therefore, been directed towards solving these problems

in the past years. For example, Xu et al. [1] reported material

removal and damage formation mechanisms in grinding of

silicon nitride. Zhang and Howes [2] found that material

pulverization takes place in the surface layer of a ceramic

workpiece in the course of grinding. Surface pulverization

makes ceramic grains much smaller than those in the bulk,

and the ground surface with smooth appearance. If the depth

of cut in grinding is larger than a critical value, cracks can be

induced in the subsurface. These cracks may be predicted

based on workpiece material properties as well as grinding

conditions [3].

Machine de¯ection may be one of the factors contributing

to surface and subsurface damage and strength degradation,

as well as dimensional inaccuracies of ground workpieces

[4±6]. In order to avoid surface and subsurface damage in

grinding of ceramics, high stiffness machines have been

recommended for commercial grinding in ductile mode to

obtain a damage-free workpiece [7].

In previous reports [8,9], workpiece strength and dimen-

sional accuracies were investigated both theoretically and

experimentally in single pass grinding of silicon nitride

ceramics. It was found that in single pass grinding, a

grinding wheel with a large grit size results in a large

damage depth to the ground workpiece. The normal grinding

force is proportional to the set depth of cut (SDOC) of the

grinding wheel. There exists a critical machine stiffness

below which chatter may occur and cause more damage to a

ceramic workpiece. The critical stiffness can be lowered by

using the electrolytic in-process dressing (ELID) technique

[10], or a larger grit size for the grinding wheel.

The objective of this study is to evaluate residual strength

and stock removal rate in multi-pass grinding of silicon

nitride ceramics under various machine stiffnesses and

grinding wheel conditions. Normal grinding force and actual

Journal of Materials Processing Technology 104 (2000) 178±184

* Corresponding author. Tel.: �1-860-486-1489; fax: �1-860-486-2269.

E-mail address: [email protected] (B. Zhang).1 Present address: Stevens Institute of Technology, Hoboken, NJ 07030,

USA.

0924-0136/00/$ ± see front matter # 2000 Elsevier Science S.A. All rights reserved.

PII: S 0 9 2 4 - 0 1 3 6 ( 0 0 ) 0 0 5 5 2 - 5

depth of cut (ADOC) of grinding are also assessed under the

same conditions. Theoretical analyses are conducted to

qualitatively show how machine stiffness can affect work-

piece strength, stock removal rate, normal grinding force

and wheel ADOC.

2. Theoretical analyses

2.1. Normal grinding force

Based on the experimental observations and the existing

literature, e.g. [11,12], a relationship between normal grind-

ing force Fz and ADOC aa of a grinding wheel can be

established:

Fz � F0 � Caaa (1)

where Ca is a constant determined by grinding conditions, F0

is the break-in force under which ADOC is zero. Wheel

ADOC can be presented for the ith pass as [13]

aai � a0 1ÿ kw

ks � kw

� �i( )

(2)

where a0 is wheel SDOC, ks is machine stiffness and kw is

cutting stiffness. Substituting Eq. (2) into (1), the normal

grinding force Fz in the ith pass is given as

Fzi � F0 � Caa0 1ÿ kw

ks � kw

� �i( )

: (3)

For given grinding conditions, F0, Ca, a0 and kw are non-

negative constants. The following relationship is obtained:

dFzi

dks

� iCaa0

kw

kw

ks � kw

� �i�1

> 0: (4)

Eq. (4) shows that normal grinding force Fzi monotonically

increases with the increase of machine stiffness. However, as

there exists kw/(ks�kw)<1, kw/(ks�kw) approaches zero for a

highly stiff machine. In this case, normal grinding force Fzi

becomes a constant, Fz�F0�Caa0. In addition, if the number

of grinding passes i is large enough, i.e. [kw/(ks�kw)]i

approaches zero. Normal grinding force Fzi can again

become constant. Moreover, wheel ADOC approaches

wheel SDOC if machine stiffness or the number of grinding

passes is large enough. It should be noted that any difference

between wheel ADOC and SDOC will directly contribute to

the dimensional inaccuracies of a ground workpiece.

2.2. Stock removal rate

For feedrate fe and width of grinding bw, stock removal

rate Qw is given as

Qw � aaibwfe � a0bwfe 1ÿ kw

ks � kw

� �i( )

(5)

For given grinding conditions, a0, fe, bw and kw are constants,

then

dQw

dks

� ia0bwfe

kw

kw

ks � kw

� �i�1

> 0 (6)

Eq. (6) shows that stock removal rate Qw monotonically

increases with the increase of machine stiffness. Similar to

the normal grinding force, under a given grinding condition

stock removal rate Qw approaches a constant, Qw�a0 febw.

On the other hand, if the number of grinding passes i is large

enough, stock removal rate Qw also becomes a constant.

According to the above analysis, stock removal rate Qw in

multi-pass grinding can be a constant if machine stiffness or

the number of grinding passes is large enough. A stable

stock removal rate will contribute to the dimensional accura-

cies of ground workpieces.

2.3. Workpiece strength

Based on the previous analyses [8] and Eq. (3), the normal

grinding force per grit in the ith pass can be expressed

as

fgni � 2kfFzi

pkrbwCatÿhai

� 2kf

pkrbwCF0 � Caa0 1ÿ kw

ks � kw

� �i" #( )

� a0 1ÿ kw

ks � kw

� �i" #( )hÿt

(7)

where kf is a dimensionless constant, kr is a constant

determined by grinding conditions, C is the number of

active cutting points per unit area, exponent h is a constant

related to contact frequency, and t is an exponent describing

the in¯uence of contact pressure. An analytical model is thus

derived to predict the residual strength of a ground work-

piece, based on the work reported by Malkin and Hwang

[14]:

sf � Zfÿmgni

� Z

(2kf

pkrbwCF0Caa0 1ÿ kw

ks � kw

� �i" #( )

� a0 1ÿ kw

ks � kw

� �i" #)hÿt

8<:9=;ÿm

or

sf � Z2kf

pkrbwC

� �ÿm(

F0ahÿt0 1ÿ kw

ks � kw

� �i" #hÿt

� Caa1�hÿt0 1ÿ kw

ks � kw

� �i" #1�hÿt)ÿm

(8)

B. Zhang et al. / Journal of Materials Processing Technology 104 (2000) 178±184 179

where Z and m are non-negative constants. Thus, under

general grinding conditions

dsf

dks

� ÿmZiahÿt

0

kw

2kf

pkrbwC

� �ÿm

�(

F0ahÿt0 1ÿ kw

ks � kw

� �i" #hÿt

� Caa1�hÿt0 1ÿ kw

ks � kw

� �i" #1�hÿt)ÿmÿ1

� F0�hÿ t� 1ÿ kw

ks� kw

� �i" #ÿ1

�Caa0�1� hÿ t�8<:

9=;� kw

ks � kw

� �i�1

1ÿ kw

ks � kw

� �i" #hÿt

< 0 (9)

Eq. (9) demonstrates that residual strength of ground silicon

nitride sf decreases with the increase of machine stiffness. If

the number of grinding passes i is large enough, kw/(ks�kw)

approaches zero as kw/(ks�kw)<l. In this case, strength sf

will become stabilized. In other words, as the number of

grinding passes increases, residual strength of ground work-

pieces approaches a certain value and is not affected by

machine stiffness.

3. Experimental procedures

Grinding experiments were carried out in the mode of

cup-type surface grinding on a precision grinder (Dover

Model 956-S), as shown in Fig. 1. The grinder had a rigid

structure due to the use of granite for its column and bed.

Because of aerostatic bearings for its spindle unit and x, y

and z-slides, the motion accuracies of the grinder were very

high. The grinder used a laser interferometer of a resolution

of 75 nm to form feedback controls in its x, y and z-axes. An

especially designed compliant workholder was used to vary

the loop stiffness between the wheel and workpiece. Fig. 2

shows the workholder with adjustable stiffness. A loop

stiffness of 5±40 N/mm was obtainable by adjusting the

distance between the two sliding blocks underneath the

¯exural plate. A three component force transducer (Kistler

Model 9617A1.5) was used to measure the grinding forces in

three directions. Four diamond wheels of two different

bonds and three grit sizes were employed. For convenience,

these wheels are later on called by their given notations

shown in Table 1. In order to investigate how different bond

types affect grinding results, wheels 600V and 1kC were

chosen to have approximately the same mean grit size but

different bond types, i.e. vitri®ed bond and cast iron bond.

All the diamond wheels were trued with a brake truer of a

silicon carbide wheel. The vitri®ed bond wheels were

dressed with alumina sticks, whereas the cast iron bond

wheels were dressed in process with an ELID unit as shown

in Fig. 2. After truing and dressing, the wheels were arranged

Fig. 1. Precision grinder for surface grinding with a cup-type wheel.

Fig. 2. Workholder with adjustable compliance.

180 B. Zhang et al. / Journal of Materials Processing Technology 104 (2000) 178±184

to grind a cast iron block in 10 passes at a feed of 2 mm/pass

to stabilize their cutting faces before they were actually used

for grinding. Each speci®c grinding cycle was repeated ®ve

workpieces and the results were processed using the statis-

tical methods. The silicon nitride (AlliedSignal GS-44) bars

had dimensions of 45 mm�4 mm�3 mm as speci®ed by the

ASTM Standard C1161-94, con®guration B. Wheel ADOCs

were experimentally measured by using the multi-pass

grinding technique combined with the laser interferometer

of the grinder. Off-line con®rmation of wheel ADOCs were

made using Surfanalyzer (Federal Products Model 5000)

and the stock removal rates were calculated based on the

measurements of wheel ADOCs. All the bars ground under

different grinding conditions were tested using a four-point

bending machine (Instron Model 8511) for their residual

strength information according to the ASTM Standard

C1161-90 [15].

4. Experimental results

4.1. Stock removal rate and grinding force

Grinding of silicon nitride was conducted in multi-pass

grinding mode and the results are compared with single pass

grinding. Grinding forces and stock removal rates are pre-

sented in Figs. 3 and 4 for multi-pass grinding, and for the

purpose of comparison, in Fig. 5 for single pass grinding.

The parameters for ELID device were as follows, square

waveform on/off time 2 ms, voltage 60 V, peak current 10 A.

Figs. 3 and 4 show experimental results on normal

grinding force and stock removal rate in multi-pass grinding

using wheel 600V at an SDOC of 2 mm/pass. Fig. 3 depicts

that as the number of grinding passes increases, the normal

grinding force also increases. The force increase is more

quickly in the beginning passes, and slows down as the

number of grinding passes increases, which is more evident

under a high machine stiffness condition. Normal grinding

force was smaller under lower machine stiffness, a phenom-

enon caused by machine de¯ection. In the ninth pass, for

example, the normal grinding force was around 30 N for the

machine stiffness tested. It turns out that the normal grinding

force, regardless of machine stiffness, eventually approaches

a limit value, if the number of grinding passes is large

enough. Meanwhile, similar to the case of normal grinding

force, stock removal rate increases with the increase of

number of grinding passes, as shown in Fig. 4. A relatively

high stock removal rate was obtained for higher machine

stiffness, and vice versa. Under the same grinding condi-

tions, larger machine stiffness results in smaller machine

de¯ection, and thus, a higher wheel ADOC and a higher

stock removal rate and wheel ADOC. Stock removal rate

reaches a limit value as the number of grinding passes is

large enough.

Table 1

Speci®cations of the cup-type diamond wheels

Wheel SD120N100V SD600N100V SD1000N100C SD10000N100C

Notation 120V 600V 1kC 10kC

Wheel diameter (mm) 180 180 180 180

Bond type Vitrified Vitrified Cast iron fiber Cast iron fiber

Mesh # 120 600 1000(Japanese) 10000(Japanese)

Mean grit size (mm) 110 15 15 1.5

Dressing Dressing sticks Dressing sticks Electrolytic in-process dressing Electrolytic in-process dressing

Wheel surface speed 25 m/s(82 ft/s) 25 m/s(82 ft/s) 25 m/s(82 ft/s) 25 m/s(82 ft/s)

Feedrate 5 mm/s (0.2 in./s) 5 mm/s (0.2 in./s) 5 mm/s (0.2 in./s) 5 mm/s (0.2 in./s)

Workpiece material High pressure sintered silicon

nitride (GS-44, AlliedSignal)

High pressure sintered silicon






Fig. 3. Grinding force vs. machine stiffness in multi-pass grinding at

SDOC 2 mm with wheel 600V.

Fig. 4. Stock removal rate and wheel ADOC vs. machine stiffness in

multi-pass grinding at SDOC 2 mm with wheel 600V.


Fig. 5 shows single pass grinding results on normal

grinding force and stock removal rate in terms of machine

stiffness and grinding wheels. The results demonstrate that

both normal grinding force and stock removal rate increase

with the increase of machine stiffness. In the range of the

machine stiffness tested, wheel 1kC resulted in the largest

stock removal rate, but the smallest normal grinding force,

which was followed by wheels 120V and 600V, and 10kC. In

addition, for the grinding wheels of the same bond type, the

wheel of a large grit size generated a large stock removal rate

but a small grinding force, and vice versa. On the other hand,

for the grinding wheels of the same bond type, the cast iron

bond wheel 1kC gave a much larger stock removal rate yet a

much lower grinding force if compared with the vitri®ed

bond wheel 600V. It was found that wheel ADOC is always

smaller than wheel SDOC in single pass grinding. In multi-

pass grinding, however, wheel ADOC can be very close

to wheel SDOC. In this case, normal grinding force

approaches a certain value as the number of grinding passes

increases.

4.2. Residual strength of ground workpieces

Since the effect of machine stiffness on the residual

strength of ground silicon nitride in single pass grinding

has been reported in another paper [8], this paper deals with

the effect of machine stiffness on strength of ground silicon

nitride in multi-pass grinding.

Fig. 6 presents the residual strength of silicon nitride bars,

each subjected to 20 grinding passes at wheel SDOCs of 1

and 2 mm. In-house four-point bending tests showed that the

baseline strength of the silicon nitride bars was 846 MPa.

The residual strength of the bars ground with wheel 600V

was around 1100 MPa at wheel SDOCs of either 1 or 2 mm,

although different machine stiffnesses resulted in slightly

different workpiece strength. With the application of wheel

600V, workpiece strength was actually enhanced by approxi-

mately 30%. On the other hand, under the same grinding

conditions, both wheels 1kC and 120V resulted in ground

workpiece strength of around 770 MPa, a 9% drop from the

baseline strength. Machine stiffness did not show an obvious

effect on the ground workpiece strength when wheels 1kC

and 120V were used.

From Fig. 6, it is obvious that under multi-pass grinding

conditions, machine stiffness has little effect on the residual

strength of ground silicon nitride. This may be attributed to

the effect of wheel ADOC on ground workpiece strength. As

the number of grinding passes increases, wheel ADOC

approaches wheel SDOC regardless of machine stiffness.

In this case, the grinding forces under different machine

stiffness conditions approach the same limit value, which

does not signi®cantly alter ground workpiece strength.

5. Discussion

The results of this study demonstrate that in grinding of

silicon nitride, normal grinding force, stock removal rate and

wheel ADOC vary with machine stiffness. Under the same

grinding conditions, a machine of lower stiffness results in

smaller grinding forces, a lower stock removal rate and

wheel ADOC, which is in contrast to a higher stiffness

machine. Consequently, the lower wheel ADOC can directly

affect workpiece accuracies and dimensional tolerances,

which may not be what one expects. On the other hand,

the results on multi-pass grinding indicated that the in¯u-

ence of machine stiffness diminishes as the number of

grinding passes increases. Both theoretical analyses and

Fig. 5. Presenting (a) normal grinding force; and (b) stock removal rate vs.

machine stiffness, in single pass grinding at SDOC 10 mm.

Fig. 6. Residual strength of ground silicon nitride vs. machine stiffness

under the condition of 20 grinding passes for different grinding wheels.


experimental results have a good agreement on the effect of

machine stiffness on grinding force, stock removal rate and

wheel ADOC.

Moreover, the results also demonstrate that machine

stiffness did not seem to have a signi®cant in¯uence on

the residual strength of ground workpieces in multi-pass

grinding, although the strength was different for the wheels

of different grit sizes and bond types. Theoretically, the

residual strength of ground workpieces monotonically

decreases with the increase of machine stiffness. When

wheel 600V was used, higher strength of ground workpieces

was obtained at machine stiffness of 5 and 40 N/mm, which

does not fall into the theoretical prediction.

In previous reports [8,9,17], it was identi®ed that the

residual strength of ground silicon nitride can be enhanced

by the compressive residual stress in the ground surface

layer, but may be reduced by the introduction of grinding

induced damage to the workpiece. It is, therefore, agreed

that residual strength sr is expressed in the following

equation:

sr � sb � Dsc ÿ Dsd (10)

where sb is the baseline strength of workpieces, Dsc strength

gain through the introduction of compressive residual stress,

and Dsd is the strength loss due to grinding damage.

Eq. (10) presents that the ground workpiece strength is

determined by the baseline strength of the workpiece as well

as possible strength gain Dsc and strength loss Dsd that are

related to the grinding process, which is consistent with Xu

et al. [16]. If neither strength gain nor strength loss is

induced to a workpiece, the workpiece should retain its

baseline strength, which can also be obtained by lapping or

polishing the workpiece. Under a normal grinding condition,

both strength gain and strength loss may occur simulta-

neously, which can make the prediction of the ground

workpiece strength sr somewhat dif®cult.

To further address this point, Fig. 7 presents measurement

results on residual strength and stress as well as damage

depth of silicon nitride workpiece subjected to single pass

grinding at wheel SDOC 10 mm, and machine stiffness 40 N/

mm. Under the grinding conditions, wheel 600V bestowed

the highest strength on the ground workpieces while wheels

1kC and 120V resulted in the almost equally low strength,

although wheels 600V and 1kC shared the same mean grit

size. Obviously, there must be some important factors other

than grit size that affect workpiece strength. On the other

hand, the measurement results on ground workpiece damage

showed that wheel 600V results in a much smaller damage

depth than did the other wheels. It may be speculated that

strength loss Dsd could be much less for the workpieces

ground with wheel 600V than with the other two wheels due

to possibly less damage induced. Furthermore, compressive

residual stress of ground workpieces was the highest for

wheel 120Vand the lowest for wheel 1kC. Strength gain Dsc

could be very high for the workpieces ground by wheel

120V, high for wheel 600V and low for wheel 1kC. The

ground workpiece strength is determined by the combined

effect of strength gain and strength loss. Generally, more

compressive residual stress can be induced with a dull

grinding wheel, or a wheel with large grit size, or a wheel

with stiff and strong bond material, while less damage may

be generated with small grit depth of cut. Since ELID

grinding allows a more aggressive cutting, it may not be

bene®cial to workpiece strength although it is good for

workpiece accuracies. High workpiece strength can be

obtained using a high compressive stress yet low damage

grinding. In this regard, grinding wheels of a higher con-

centration and a larger grinding width are recommended for

grinding ceramics. In this case, grinding machines of higher

stiffness should be utilized.

6. Conclusion

This study provides theoretical analyses to predict the

general trends of ground workpiece strength, stock removal

rate and grinding force in terms of machine stiffness and

grinding wheel parameters in multi-pass grinding of ceramic

materials. The study concludes that in multi-pass grinding of

ceramics, machine stiffness becomes less important than in

single pass grinding in terms of stock removal rate and wheel

ADOC. The effect of machine stiffness diminishes as the

number of grinding passes increases. In addition, machine

stiffness does not seem to have a signi®cant effect on ground

workpiece strength. It has been made clear that the residual

strength of ground workpiece is determined by the baseline

strength of the workpiece material and the strength gain due

to grinding-induced compressive residual stress, as well as

strength loss due to grinding-induced damage.

Acknowledgements

The authors gratefully acknowledge the research supports

from the US Department of Energy under contract #19X-

SU366C with Lockheed Martin Energy Research Corpora-

tion and from the US National Science Foundation under

Fig. 7. Measurement results on residual strength and stress as well as

depth of grinding damage of silicon nitride subjected to single pass

grinding at wheel SDOC 10 mm and machine stiffness 40 N/mm.


Grant #DMI-9500223. The authors wish to thank Dr.

Xianghe Peng of Chongqing University in China and senior

students Mr. Khon Lam and Mr. Hoang Phung for their

assistance in the experimental work.

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stock removal rate and workpiece strength in multi-pass grinding of ceramics

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