PRODUCTION PROCESS

Residual stress prediction in quick point grinding

Stefan Tonissen • Fritz Klocke • Bjorn Feldhaus •

Steffen Buchholz • Markus Weiß

Received: 22 December 2011 / Accepted: 5 April 2012 / Published online: 29 April 2012

� German Academic Society for Production Engineering (WGP) 2012

Abstract The paper investigates the dependency of

residual stresses on process parameters of grinding in the

quick point mode. It is evaluated whether the area-specific

grinding power or energy is correlated to the residual

stresses in the surface and to the maximum residual stresses

in the surface layer. Firstly, the paper derives an analytical

model for the area-specific grinding power and energy

based on models from literature. Secondly, the residual

stress distribution of workpieces machined under varied

cutting conditions is depicted for each process point. It is

found that the area-specific grinding energy is correlated to

residual stresses whereas the area-specific grinding power

is an unsuitable residual stress predictor. Due to the limited

experimental scope future research should seek to validate

the findings with a broader variation of process conditions

in quick point grinding.

Keywords Quick point grinding � Residual stresses �Surface integrity

1 Introduction and motivation

Grinding is an abrasive manufacturing process that is

broadly applied in industry to machine mostly hard-to-cut

materials like hardened steel or nickel alloys [1–3]. The

grinding wheel, which consists of bonded grains, is rotated

and the workpiece is fed tangentially in a linear or rota-

tional movement [4]. The quick point grinding mode is a

traverse grinding process characterized by a skew inclina-

tion of the grinding wheel axis with respect to the work-

piece axis. This skew inclination reduces the contact area

between the grinding wheel and workpiece and thus cutting

force. Quick point grinding is an established process for

many applications like gear box or turbine shafts as well as

rolling elements for bearings [5, 6].

The economic efficiency of any grinding process is

determined by its productivity, associated cost, and work-

piece quality [7]. Depending on functional requirements of

the workpiece the quality requirements may vary [8]. In

particular, if workpiece failure initiates from crack for-

mation and propagation the sub-surface integrity is a major

quality criterion [9].

The term surface integrity was introduced by Field and

Kahles and defines the ‘‘inherent or enhanced condition of

a surface produced in a machining or other surface gen-

erating operation’’. The conditions of the surface altered

through a machining process may include mechanical,

metallurgical, chemical and other changes [10, 11].

Residual stresses are counted among the mechanical

conditions of a surface, which contribute substantially to

the functional behaviour of a workpiece. These stresses act

in a body without external forces or moments. In general, a

machining process affects the equilibrium of residual

stresses in a workpiece through a variety of mechanisms. If

material is removed the equilibrium is disturbed and the

workpiece deforms. Furthermore, the mechanical forces

and the heat flux acting during a machining may lead to

compressive or tensile residual stresses [2].

The measurement of residual stresses is costly and time-

consuming. Thus, there is a strong interest of predicting

residual stresses based on process characteristics that are

easily accessible [12]. Three such grinding specific process

characteristics are broadly applied in industry and

S. Tonissen (&) � F. Klocke � B. Feldhaus � S. Buchholz �M. Weiß

Laboratory for Machine Tools and Production Engineering,

Steinbachstraße 19, 52074 Aachen, Germany

e-mail: s.toenissen@wzl.rwth-aachen.de

123

Prod. Eng. Res. Devel. (2012) 6:243–249

DOI 10.1007/s11740-012-0382-x

academia. The specific grinding energy proposed by

Malkin relates the cutting power to the material removal

rate (ec = Pc/Qw) [4]. The area-specific grinding power is

the ratio of cutting power and contact area between the

grinding wheel and the workpiece (Pc00 = Pc/Ac). This

characteristic is largely used by Brinksmeier [12]. More

recently, Kruszynski and Wojcik reported fairly good

correlation of the area-specific grinding energy Ec00 to the

residual stresses in plunge grinding (Ec00 = Pc

00 Dt). In

contrast to the area-specific grinding power the area-spe-

cific grinding energy also accounts for the contact time of

grinding wheel and a particular point on the workpiece

[13]. The good correlation of residual stresses and area-

specific grinding energy were confirmed by Zeppenfeld for

speed stroke grinding [14]. However, it is yet unclear

which process characteristic is most suitable to predict

residual stresses of grinding in quick point mode.

This paper investigates the relationship between residual

stresses and key process parameters in quick point grind-

ing. In particular, it is evaluated, whether the area-specific

grinding power Pc00 or the area-specific grinding energy Ec

00

can be used as a residual stress prediction parameter in

quick point grinding.

Section 2 derives a model of the area-specific grinding

energy based on two existing models of contact area and

tangential cutting forces. Section 3 describes the experi-

mental setup and the residual stress distribution of the test

specimens. Section 4 evaluates the hypothesis and Sect. 5

discusses the results and concludes with an outlook.

2 Model development

Figure 1 shows the relationship of residual stresses over

area-specific grinding power Pc00 qualitatively as proposed

by Brinksmeier [12]. Brinksmeier depicts a progressive

increase of residual stresses over the area-specific grinding

power Pc00 in zone 3, which is most relevant to practical

grinding operations [12]. Kruszynski and Wojcik point out

that contact time between the grinding wheel and a par-

ticular point on the workpiece play an important role in the

formation of residual stresses. They relate residual stresses

to area-specific grinding energy Ec00 [13].

In quick point grinding the contact time Dt between a

particular point on the workpiece and the grinding wheel

may vary largely through process parameter selection.

Therefore, it is investigated whether the area-specific

grinding power Pc00 or the area-specific energy Ec

00 is a

suitable process characteristic to predict residual stresses.

The area-specific grinding energy Ec00 is linked to the

area-specific grinding power Pc00, which can be determined

by the relationship

P00

c ¼Ft � vc

Ac: ð1Þ

The area-specific grinding energy Ec00 is then calculated

by

E00

c ¼ P00

c � Dt; ð2Þ

where Dt is the contact time. In surface grinding the contact

time of a particular point on the workpiece is determined

by

Dt ¼ lg

dw � p � nw; ð3Þ

where lg is the contact length between workpiece and

grinding wheel, dw the workpiece diameter and nw the

revolutions per minute of the workpiece.

It can be seen that for the prediction of area-specific

grinding power and energy the impact of process parame-

ters on the contact area Ac and the tangential cutting force

Ft needs to be determined.

2.1 Contact area and force model

Figure 2 depicts the contact area of down grinding in the

quick point mode. The skew inclination aq of the grinding

wheel axis with respect to the workpiece axis leads to a

thermoelastic material deformation

thermoplastic material deformation

thermomechanic and thermoplasticmaterial deformation

thermomechanic and thermoplasticmaterial deformation plus deformationdue to microstructural transformation

1

2

3

4resi

dual

str

ess

[MP

a]

area specific grinding power Pc´´

0

< 0

> 0

therm

res

mech

1 2 3 4

Fig. 1 Residual stresses as a

function of area-specific

grinding power

244 Prod. Eng. Res. Devel. (2012) 6:243–249

123

pivoting angle c. Due to that pivoting angle the workpiece

is not in contact with the side face of the wheel but

exclusively with the circumferential face in contrast to

conventional traverse grinding.

Models for the contact area and the cutting forces are

derived by Bucker [5] and Gerent [6]. Equation (4) shows

Gerent’s model for the contact area Ac, which incorporates

the wear angle u of the grinding wheel, which is typical for

traverse grinding. The wear angle is not considered by

Bucker’s model. The parameter ds represents the diameter

of the grinding wheel, fa the axial feed and ae the infeed.

The constants a1 to g1 (Table 1) were determined through a

CATIA simulation based on algorithms developed by

Gerent and documented by [6]. The particularity of the

algorithm is that it maps the impact of wear on the contact

area.

Ac ¼ a1 � aq þ 2� �b1 �uc1 � dd1

s � de1

w � ff1

a � ag1e : ð4Þ

In Eq. (5) Gerent’s cutting force model for quick point

grinding is given. The coefficients of the force model a2 to

e2 (Table 2) were determined through grinding experi-

ments on a Junker Quickpoint 5002/20 and the forces were

measured by a cutting force dynamometer. The material

cut is hardened 100Cr6 (62 HRC).

Ft ¼ a2 � f b2

a � vc2

c � nd2

w � ae2

e : ð5Þ

The following Table 3 lists the process parameters of

the cutting experiments which were applied to derive the

coefficients of the force model.

2.2 Residual stress prediction parameter

The parameters varied within the design of experiments

(see Sect. 3.2) are the axial feed rate vfa and the number of

revolutions per minute of the workpiece nw, which are

linked to the axial feed through the following relationship:

fa ¼ vfa=nw: ð6Þ

By combining the abovementioned equations the

relationship between the axial feed fa, the revolutions per

minute of the workpiece nw, and the area-specific grinding

power Pc00 can be obtained. A measure for the area-specific

grinding power m(Pc00) written in terms of the axial feed fa

and the revolutions per minute of the workpiece nw can be

introduced, which describes the parameters varied within

the experimental design. All other parameters are kept

constant and described by the proportionality constant c:

vfa

workpiecegrinding wheel

contact area Ac

vfa

αq

nw

Fig. 2 Contact area in quick

point grinding [5, 6]

Table 1 Regression parameters for contact area model

Parameter a1 b1 c1 d1 e1 f1 g1

Value 4.2135 -0.0454 -0.2481 0 0.4695 0.4965 0.9790

Table 2 Regression parameters for force model

Parameter a2 b2 c2 d2 e2

Value 110.1627 0.9940 -1.3067 0.9892 0.9338

Table 3 Process parameters for derivation of coefficients of force

model

Parameter Unit Variation

range

Axial feed fa mm/rev 0.04…0.12

Grinding wheel speed vs m/s 60…140

Infeed ae mm 0.10…0.25

Workpiece diameter dw mm 20…60

Grinding wheel B126 N11

V D47 ST140

Lubricant Mineral oil

Prod. Eng. Res. Devel. (2012) 6:243–249 245

123

P00c ¼Ft � vc

Ac¼ a2 � vc2þ1

c � ae2�g1

e

zfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflffl{c

a1 � aq þ 2� �b1 �uc1 � dd1

s � de1w

� fb2�f1

a � nd2

w

zfflfflfflfflfflffl}|fflfflfflfflfflffl{mðP00c Þ

¼ c �m P00c� �

:

ð7Þ

An equivalent measure can be introduced for the area-

specific grinding energy Ec00 by multiplying the area-

specific grinding power Pc00 with the contact time.

E00c ¼ P00c � Dt ¼ P00c � lgdw � p � nw

¼ ~c � fb2�f1

a � nd2�1w

zfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflffl{m E00cð Þ

¼ ~c �m E00c� �

:

ð8Þ

The hypothesis evaluated by this paper is that the area-

specific grinding energy Ec00 is a more suitable prediction

parameter for residual stresses in quick point grinding than

the area-specific grinding power Pc00. If the hypothesis is

true, the measure for the area-specific grinding energy

m(Ec00) must show better correlation to residual stresses

than the measure for the area-specific grinding energy

power m(Pc00).

3 Experimental

3.1 Specimen preparation

The specimens for the experiment were made from 1.4108

(DIN-code) hardened to 62 HRC. The composition of this

iron-chromium-molybdenum-steel is listed in Table 4.

Figure 3 shows the dimensions of the specimens.

3.2 Machining parameters

Grinding in the quick point mode is a traverse grinding

process, where the wheel is engaged in an angle aq with

regards to the workpiece axis. Five different combinations

of machining conditions varying the axial feed rate vfa and

the revolutions per minute of the workpiece nw were

determined through design of experiments [15], that was

employed to distribute the effect of machining conditions

on residual stresses. These parameters were chosen since

they influence the cutting forces Ft, the contact area Ac and

the workpiece feed rate vw, which all have a potential

impact on the area-specific grinding energy Ec00.

The grinding wheel was dressed in advance of each

machining operation to minimize the influence of tool

wear.

3.3 Residual stress measurement

The residual stress distribution in the surface layer was

measured by the X-ray diffraction principle. A Diffrak-

tometer Xstress 3000 was used for the measurement and

the residual stresses were calculated based on the sin2 wtechnique. A concise elaboration of the sin2 w technique is

given by Noyan and Cohen [16]. Residual stresses were

measured in parallel and perpendicular to the axial feed in

the depths 0, 10, 26, 53, 100, and 305 lm. The removal of

layers to measure at different depths was carried out by

etching. According to the producer Stresstech measurement

results of the XStress 3000 may deviate by 2 % in repeti-

tive measurement of the same surface.

The measured residual stresses under the different

machining conditions are depicted in Fig. 4. The axial feed

rate has a great impact on the residual stress distribution for

nw = 200 min-1 whereas its impact is considerably smal-

ler nw = 800 min-1. Factor combination B induces the

greatest compressive stresses in the surface; however pro-

ductivity at this point is low due to the small axial feed

rate. The results show, that an increase of axial feed rate

needs to be accompanied by a proportionate increase of

revolutions per minute to avoid tensile stresses in the sur-

face layer (Fig. 4).

4 Results

The residual stresses in the surface as well as the maximum

residual stresses in the surface layer are depicted over the

measures m(Pc00) and m(Ec

00) in Fig. 5. The respective

values of m(Pc00) and m(Ec

00) are shown in Fig. 6. A qua-

dratic polynomial is fitted to evaluate the correlation of

residual stresses with both measures. The diagram shows

that very poor correlation exists between m(Pc00) and

residual stresses, whereas m(Ec00) seems to provide good

potential to predict residual stresses. This finding is inde-

pendent of errors that may have occurred during residual

stress measurements. The measurement error of 2 % is

depicted in the first diagram for machining combination

‘‘C’’.

Table 4 Composition (%) of specimens

Mass (%) C Si Mn Cr Ni Mo N

Min. 0.25 – – 14,00 – 0,85 0,30

Max. 0.35 1.00 1.00 16.00 0.50 1.10 0.50

246 Prod. Eng. Res. Devel. (2012) 6:243–249

123

The correlation between m(Pc00), m(Ec

00) and the residual

stresses in the surface and the maximum residual stresses in

the surface layer have to be put into question, because

the m(Pc00) and m(Ec

00) values were calculated based on the

exponential parameters f1, b2, and d2, which describe the

curvature of formula (4) and (5).

Although Gerent’s cutting experiments were carried out

on the same grinding machine, using the same lubricant

and almost the same grinding wheel, the parameters f1, b2,

and d2 may differ due to some deviant conditions. Firstly,

distinct bearing steel was cut, which was hardened to 62

HRC in both cases. Secondly, the hardness of the grinding

wheel deviates, although the same grain size and bonding

type was used. Thirdly, process parameters differ slightly,

however there is large overlap with regards to the respec-

tive process windows.

C D

A B

E

nw

v fa

200 min-1 800 min-1

100 mm/min

500 min-1

55 mm/min

machining parametersvs = 80 m/sdw = 46 mmae = 20 µm

q = 0,5°

grinding wheel:B126VSS2804J1SCV36down grindinglubricant: oil

dressing parametersaed = 2 µmvs = 80 m/svf = 4 mm/minqd = 0,5

experimental designworkpiece

2010

mm/min

ø46±0,5

ø28H7

hardened to: 62 HRC

α

Fig. 3 Dimensions of

specimens, experimental design,

and machining parameters

parallel perpendicular

-1000

-500

0

500

1000

1500

0,00 0,10 0,20 0,30

resi

dual

str

ess

[MP

a]

depth z [µm]

C*

-1000

-500

0

500

1000

1500

0,00 0,10 0,20 0,30

resi

dual

str

ess

[MP

a]

depth z [µm]

B*

-1000

-500

0

500

1000

1500

0,00 0,10 0,20 0,30

resi

dual

str

ess

[MP

a]

depth z [µm]

A*

-1000

-500

0

500

1000

1500

0,00 0,10 0,20 0,30

resi

dual

str

ess

[MP

a]

depth z [µm]

D*

-1000

-500

0

500

1000

1500

0,00 0,10 0,20 0,30

resi

dual

str

ess

[MP

a]

depth z [µm]

E*

A 76 46 -402 -630

B 45 41 -743 -942

C 1195 914 748 447

D 149 -2 -297 -584

E 112 38 -409 -684

surface [MPa]max [MPa]factor variation

* factor combination (Fig. 3)

Fig. 4 Residual stress

distribution of test specimens

and factor combinations

Prod. Eng. Res. Devel. (2012) 6:243–249 247

123

To account for possible deviations in the parameters f1,

b2, and d2 the impact of a relative variation of 15 % in each

parameter on the results are evaluated in Figs. 6 and 7.

Figure 6 shows that this relative variation of b2 and f1accounts for a variation of 44.9 % within the exponent

b2-f1 of the axial feed fa.

Although such broad variation is induced to the

parameters f1, b2, and d2, the poor correlation of residual

stresses with m(Pc00) can still be observed for both

minimum and maximum deviations (Fig. 7). On the other

hand m(Ec00) remains to be a good indicator for residual

stresses.

5 Discussion and outlook

The paper shows that the area-specific grinding energy Ec00

seems to be a useful predictor for residual stresses in quick

maximum residual stress in surface layer

max,parallel

max,perpendicular

residual stress in surface layer

surface,parallel

surface,perpendicular

R2max,parallel = 0,9985

R2max,perpendicular = 0,9914

R2surface,parallel = 0,9809

R2surface,perpendicular = 0,9746

-1000

-500

0

500

1000

1500

0 0,2 0,4 0,6 0,8

resi

dual

str

ess

σ[M

Pa]

m(Ec'')

-1000

-500

0

500

1000

1500

0 0,2 0,4 0,6 0,8re

sidu

al s

tres

s σ

[MP

a]m(Ec'')

maximum residual stress in surface layer

max,parallel

max,perpendicular

residual stress in surface layer

surface,parallel

surface,perpendicular

R2max,parallel = 0,2550

R2max,perpendicular = 0,2794

R2surface,parallel = 0,1811

R2surface,perpendicular = 0,1672

-1000

-500

0

500

1000

1500

0 100 200 300

resi

dual

str

ess

σ[M

Pa]

m(Pc'')

-1000

-500

0

500

1000

1500

0 100 200 300

resi

dual

str

ess

σ[M

Pa]

m(Pc'')

748

+2%

-2%

763

733

Fig. 5 Correlation of residual

stresses and area-specific

grinding power and energy

fa nw

[mm] [min-1]0,050 200 43 182 10 0,213 0,912 0,0500,013 800 84 604 12 0,105 0,755 0,0150,500 200 134 343 52 0,669 1,714 0,2610,125 800 265 1135 62 0,331 1,419 0,0770,110 500 156 642 38 0,312 1,285 0,076

m(Ec'')(min)m(Ec'')(max)m(Ec'')m(Pc'')(min)m(Pc'')(max)m(Pc'')

relative absolutef1 0,4965 ± 15% ± 0,0745 maximal (abs.) minimal (abs.)

b2 0,9940 ± 15% ± 0,1491 0,7211 0,2739

d2 0,9892 ± 15% ± 0,1484 maximal (rel.) minimal (rel.)

b2 - f1 0,4975 44,9% -44,9%

force model coefficients

induced variationoriginal value resulting variation of exponent b2 - f1

Fig. 6 Variation of force model coefficients and resulting values for m(Pc00) and m(Ec

00)

248 Prod. Eng. Res. Devel. (2012) 6:243–249

123

point grinding. In contrast, the area-specific grinding power

Pc00 cannot be used to forecast residual stresses. The find-

ings confirm the importance of Ec00 that was already pro-

posed by Kruszynski and Wojcik for plunge grinding [13]

and Zeppenfeld for speed stroke grinding [14]. The influ-

ence of an energy based process characteristics on residual

stress emphasizes the critical role of contact time in the

quick point mode.

The scope of experiments was limited to a relatively

small process window because it covers only five

machining combinations. Although the area-specific

grinding power can be excluded from the set of possible

residual stress predictors based on the experiments, it

remains unclear whether the area-specific grinding energy

may be used to predict residual stresses for any process

parameter combination in quick point grinding. Future

analysis should intend to verify the importance of the area-

specific grinding energy Ec00 for a broader variation of other

critical process parameters like the cutting speed, the wear

angle of the grinding wheel, or the depth of cut. Further-

more, such a study should clarify, whether the assumption

of a progressive curvature, which was described by the

quadratic polynomial, is suitable to describe the correlation

between residual stresses and area-specific grinding

energy.

Acknowledgments This research and development project is

funded by the German Federal Ministry of Education and Research

(BMBF) within the Framework Concept ‘‘Research for Tomorrow’s

Production’’ and managed by the Project Management Agency

Karlsruhe (PTKA). The authors are responsible for the contents of

this publication.

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surface,parallel,min surface,perpendicular,minsurface,parallel,max surface,perpendicular,max

-1000

-500

0

500

1000

1500

0,00 0,50 1,00 1,50 2,00

resi

dual

str

ess

[MP

a]

m(Ec'')

all R2 values > 0,89all R2 values < 0,38

-1000

-500

0

500

1000

1500

0 400 800 1200

resi

dual

str

ess

[MP

a]

m(Pc'')

σ σ

Fig. 7 Residual stresses versus area-specific grinding power and energy for varied force model coefficients

Prod. Eng. Res. Devel. (2012) 6:243–249 249

123