ORIGINAL ARTICLE

In-process prediction of the hardened layer in cylindricaltraverse grind-hardening

Unai Alonso & Naiara Ortega & Jose Antonio Sanchez &

Iñigo Pombo & Soraya Plaza & Borja Izquierdo

Received: 30 April 2013 /Accepted: 2 October 2013 /Published online: 20 November 2013# Springer-Verlag London 2013

Abstract Grind-hardening is an innovative manufacturingprocess that takes advantage of the high amount of heat gen-erated in the contact zone to produce a martensitic phasetransformation in the subsurface layer of the workpiece.However, for a successful industrial implementation of theprocess, the closed loop control of the hardening depth isessential. Firstly, in this paper, cylindrical traverse grindingtests andmetallographic analysis are conducted, and a grindingparameter that enables the in-process control of the hardnesspenetration depth (HPD) is proposed. Secondly, a nondestruc-tive method based on the Barkhausen noise technique is pre-sented as a quality control procedure for the HPD estimation.

Keywords Grind-hardening . Cylindrical traverse grinding .

Surface integrity . Barkhausen noise

AbbreviationsBN Barkhausen noiseHPD Hardness penetration depthRMS Root mean square

Nomenclature

ae Depth of cut (mm)a f Axial feed per revolution (mm/revolution)

bseff Effective width of cut (mm)de Equivalent diameter (mm)ec Specific grinding energy (J/mm3)Ec″ Area-specific grinding energy (J/mm2)f Frequency of the BN signal (Hz)F t Tangential force (N)lg Length of contact (mm)Pc″ Area-specific grinding power (W/mm2)vc Cutting speed (m/s)v f Axial feed rate (mm/min)v s Grinding wheel speed (m/s)vw Workpiece peripheral speed (m/s)σ Electrical conductivity (Ω−1 m−1)μ Magnetic permeability (T m A−1)

1 Introduction

Cylindrical traverse grinding is a widely used industrial pro-cess for finishing hard-to-cut materials such as hardened steel.During the previous stages of the manufacturing process,steel parts such as cams and bearing journals are surface-hardened by using thermal or case hardening, while the coreremains relatively soft. However, such processes are verydifficult to integrate in production lines and also have a highcost [1].

Grinding is a manufacturing process with a relatively highpower density input. Brinksmeier and Brockhoff proposed touse the enormous amount of heat generated in the contactzone to produce the austenization of the material on thesurface [2]. Subsequently, a hardened layer was generatedby rapid quenching (mainly due to the heat absorption fromthe workpiece).

At first, the viability of the process was questioned dueto various issues such as the control of the sparks generated(and the huge machine dirt caused by lack of coolant), lowrepeatability of the process, or the workpiece geometry.

U. Alonso (*) :N. Ortega : J. A. Sanchez : S. PlazaFaculty of Engineering of Bilbao, University of the Basque Country,Alameda de Urkijo s/n, 48013 Bilbao, Spaine-mail: unai.alonso@ehu.es

I. PomboFaculty of Technical Engineering of Bilbao, University of the BasqueCountry, Paseo Rafael Moreno “Pitxitxi” 3, 48013 Bilbao, Spain

B. IzquierdoFaculty of Technical Engineering of Eibar, University of the BasqueCountry, Avda Otaola 26, 20600 Eibar, Spain

Int J Adv Manuf Technol (2014) 71:101–108DOI 10.1007/s00170-013-5395-x

Furthermore, machines with high stiffness were required inorder to introduce large depths of cut needed for the heatgeneration.

It must also be taken into account that grind-hardeningmust be done in a single pass. Thus, it is much more difficultto apply the process to cylindrical plunge or traverse grindingdue to the boundary problems that may exist. For example,during a cylindrical plunge grinding, at the end of the work-piece rotation, there is not enough material to produce theheat, and a nonuniform hardness penetration depth (HPD) isgenerated. In order to avoid this effect, Kolwitz et al. [3]proposed that the outer diameter cylindrical plunge grindingshould be divided in two phases. Firstly, a radial infeedwithout workpiece rotation should be done, and then theprocess would proceed with constant depth of cut and work-piece rotation. In cylindrical traverse grinding, this type ofboundary effects has not been studied yet.

On the other hand, the outcome of the process also dependson the grinding wheel type. The high temperatures generatedin the process could deteriorate the bond properties producinga big wear of the wheel. Experimentally, it has been indicatedthat resin bonded corundum wheels are more practical thanvitrified bonded corundum ones [1]. However, many authorshave successfully used vitrified wheels to carry out grind-hardening operations [3–7]. A study carried out by Salonitiset al. [8] also concluded that softer bonding material, coarserabrasive grains, and an open structure are more appropriatedto produce a deeper HPD.

Moreover, the power consumption during this process ismuch smaller than in conventional processes, because noenergy is consumed for the transportation. Salonitis et al. [9]used life cycle assessment methods for the environmentalanalysis of the grind-hardening process of raceways and tripodjoint production. They found that by replacing the conven-tional heat treatment method and rough grinding with thegrind-hardening process, the environmental damage wasreduced in approximately 40 %.

Due to the great interest generated by this new grindingoperation, investigations in this process have been conductedin many research centers, in order to improve the selection ofproper process parameters enabling the control of the HPD.Two different approaches have been identified within thisresearch.

The first one is based on the description of the physicalprocess by means of analytical and numerical thermo-metallurgical models. Several studies have focused on thestudy on surface grinding [4, 10, 11]; a few have studiedcylindrical plunge grinding [3, 6, 12], and cylindrical traversegrind hardening has only been studied by Nguyen and Zhang[7]. They developed a three-dimensional finite element modeland compared it to experimentally measured HPD. However,they only studied on the effect of one workpiece turn and

obtained a nonuniform microstructure at the two ends of theworkpiece. Whereas the results obtained with these modelsare promising, they are limited due to the complex calcula-tions and little knowledge about the behavior of material inextreme grinding.

The second approach is based on the empirical determina-tion of the appropriate process parameters [1, 2, 13, 14]. This,however a simple method, is time-consuming, expensive, andprovides little insight to the fundamentals of the physicalprocess taking place. Moreover, it is extremely difficult toextrapolate these results to different grinding methods andgrinding conditions.

Due to the fact that hardened depth and profile stronglyinfluence the contact fatigue properties, industry has beensearching for methods that are able to characterize thematerial quickly, accurately, and easily without damaging theworkpiece.

The detection of HPD with nondestructive methods hasbeen widely studied in recent years. Electromagnetic methodssuch as hysteresis, Barkhausen noise (BN), or eddy current-based methods have been developed.

When a variable external magnetic field is applied on aferromagnetic material, discontinuous flux changes appeardue to irreversible jumps during domain wall motion. Theseflux changes can be detected as voltage pulses in a pickup coilplaced on the surface forming a signal known as the BN. Thissignal is then amplified and filtered in order to establish thegraph of the BN versus the magnetic field strength (known asBN fingerprint).

BN is sensitive to various parameters that affect the domainwall configuration. On the one hand, magnetic domain wallmovement is strongly influenced by microstructural features(such as grain size and second-phase precipitations). Themaximum amplitude of the BN voltage decreases with grainsize due to reduced domain density [15, 16]. The influence oftempering temperatures has also been studied for case-carburized steel, and an excellent correlation has been foundbetween the hardness depth profile and root mean squarevalues BN [17].

The presence of different metallurgical phases on the sur-face of the hardened workpiece generates a BN fingerprintwith two peaks. Several authors have found a good correlationbetween the amplitude of these two peaks and the depth ofthe hardened layer up to 2 mm in depth [18–20]. On theother hand, the magnitude and sign of the applied or residualmacroscopic stresses have a strong influence on BN signal[21].

Magnetic Barkhausen noise has been shown to be a sensi-tive technique for characterizing ferromagnetic materials. It isa nondestructive economical technique and can be easily usedto evaluate samples of various shapes and sizes, and it can be agood alternative in terms of fastness and accuracy.

102 Int J Adv Manuf Technol (2014) 71:101–108

In the consulted literature, however, the value of the HPDhas always been obtained in grind-hardening tests throughmicrographs and microhardness profiles (after sectioning thespecimen), and to date, there is no method that can predict theHPD nondestructively in a production line.

The present study has two objectives: on the one hand, tofind a parameter that enables the online prediction of the HPDduring the cylindrical traverse grind-hardening process. Onthe other hand, this work is complemented with a simplequality control method for the HPD estimation, based on theBN technique.

2 Thermal damage control parameters in grinding

In the grinding process, the energy consumed per unit volumeof removed material is far superior to other processes. Thisenergy is almost entirely transformed into heat in the contactarea between the wheel and the workpiece. In the last decades,numerous studies have focused on predicting the high tem-peratures developed in the workpiece, because they can affectthe surface integrity by generating damages, such as cracks,phase changes, or tensile residual stresses, which reduce thefatigue life of the part.

Based on an analytical study on the temperature distribu-tion in the ground workpiece surface, Malkin and Lenz pro-posed relating the maximum surface temperature to a maxi-mum allowable specific grinding energy [22]:

ec ¼ e0 þ CTmax de1=4ae−3=4vw

−1=2 ð1Þ

where ec is the specific grinding energy, e0 is the 45 % ofthe chip formation energy, C is a constant dependent onmaterial properties, Tmax is the maximum surface temperature,de is the equivalent diameter, ae is the depth of cut, and vw isthe workpiece peripheral speed.

After making a long series of experiments for differentvalues of ae, d e, and vw, the authors identified a burningthreshold that related well to Eq. 1 (an example of a burnthreshold diagram can be seen in Fig. 1). This approach hasalso been used by Stephenson et al. to predict the burningdamage on Inconel workpieces [23] and by Meyer et al. [24]on hardened steel, amongst others.

Despite claiming that lines of constant maximum grind-ing temperatures could be obtained, they only distinguishbetween burned and nonburned workpieces. This proce-dure could also be used to relate the HPD to the specificgrinding energy. However, the workpiece diameter and theactual depth of cut must be known during the grindingprocess, making it difficult to implement in an in-processburn detection system.

Recently, Kolkwitz et al. [3] proposed the use of the spe-cific grinding power Pc″ for estimating the HPD in cylindricalplunge grinding:

P0 0c ¼ F t ⋅vc

bseff ⋅ lgð2Þ

where F t is the tangential force, vc is the cutting speed, bseff isthe effective width of cut, and lg is the geometrical length ofthe contact zone. However, a clear correlation between spe-cific cutting power and HPD was not found.

Brockhoff [1] studied separately on the effect of the varia-tion of the depth of cut and the feed speed on the HPD forsurface grind-hardening. Taking the time of contact betweenthe grinding wheel and the workpiece into account, he consid-ered the evolution of the energy entering the component basedon one area element (area-specific grinding energy, Ec″).

E0 0c ¼ P

0 0c ⋅Δt ¼ F t ⋅vc

bseff ⋅vwð3Þ

HPD and Ec″ showed a similar trend when the depth of cutwas increased; however, this tendency was not observed whenvarying the feed speed.

Kruzynski and Wójcik [25] reported that the time of con-tact between the grinding wheel and the workpiece had to betaken into account in order to predict the residual stresses inthe surface. They found a good correlation between area-specific grinding energy Ec″ and residual stresses in surfaceplunge grinding. This good correlation was confirmed byZeppenfeld [26] for speed stroke grinding and Tönissenet al. [27] for quick point grinding.

Thus, this energy-related parameter might be moreuseful than specific cutting power for predicting the HPD.

Specificenergy

(J/m

m3 )

de1/3a-3/4vw

-1/2

Fig. 1 Example of burn threshold diagram

Int J Adv Manuf Technol (2014) 71:101–108 103

Furthermore, it can easily be estimated online, since the pre-diction of the effective grinding depth and length of contact isnot necessary. In this work, the relationship between HPD andthe previous two key process parameters (Pc″ and Ec″) wasstudied for cylindrical traverse grind hardening.

3 Experimental setup

3.1 Test piece preparation

The test specimens where made from an AISI 1045 steelcold-drawn bar. The composition of this medium-carbon steelis shown in Table 1. The workpieces were turned and groundto its final dimensions (shown in Fig. 2) with the parameterslisted in Table 2. These parameters should be carefully chosenso as not to produce a microstructural change in the workpiecethat could affect the grind-hardening operation. Using theBarkhausen noise technique, it was checked that the partsdid not suffer significant changes during this previous grind-ing process.

3.2 Grind-hardening tests

The grinding tests were carried out on a Danobat FG-600-Sgrinder using a CS33A802HH4VK1 corundum grindingwheel (manufactured by TYROLIT) with a diameter of450 mm and a width of 18 mm. With the aim of increasingthe heat which was derived to the workpiece, all tests weredone without any coolant supply. Moreover, due to the severewear undergone by the grinding wheel, it was dressed prior toeach machining operation.

As mentioned above, although there is extensive work inthe cylindrical grind-hardening process, there is a lack ofinformation regarding the suitable process parameters for thecylindrical traverse grind-hardening. Thus, different parameter

combinations were tested based on the authors' experience.Table 3 lists the process parameters which were finally con-sidered for the traverse grind-hardening operation.

The parameters that were varied during the tests were theworkpiece speed and the infeed. Two different values of theworkpiece speedwere considered in order to analyze the effectof the contact time of the grinding wheel at a particular pointof the workpiece.

Even if deeper HPD could be obtained with higher levels ofmaterial removal rates, too high infeed values could lead to anunstable process. On the one hand, if the machine tool is notstiff enough, dynamic problems may show up. Furthermore,due to the fact that the grind-hardening process was carried outwithout any coolant supply, high temperatures might acceler-ate grinding wheel wear, and chips could clog the grindingwheel pores or stick to the surface of the workpiece.

The grinding process was divided in two phases. Firstly, anOD-plungee operation was carried out with two-thirds of thegrinding wheel width on the right side of the workpiece.Afterwards, the process proceeded with a single grinding passalong 200mm. During the tests, the power consumption of thegrinding wheel spindle was measured.

After the tests, BN was measured on the surface of theworkpiece on the periphery of three cross sections located at adistance of 20 mm from each edge and at the center of theground length. Measuring procedure and equipment will bedescribed thoroughly in Section 5.

After the BN measurements, the ground workpieces weresectioned perpendicular to the rotation axis. Then, an angularsector of 60° of each slice was hot-mounted in a specimen byphenolic resin powder using an IPA40 REMET Evolutionmounting press. The molded specimens were subsequentlypolished with successively finer emery papers and then cloth-

Table 1 Composition ofspecimens (percentage) Mass (%) C Mn P S

Min 0.43 0.60 – –

Max 0.50 0.90 0.04 0.05

Fig. 2 Test piece dimensions

Table 2 Process parameters for test pieces preparation

Parameter Unit

Grinding wheel speed vs m/s 45

Workpiece speed vw rpm 110

Axial feed rate v f mm/min 560

Depth of cut ae mm 0.020

104 Int J Adv Manuf Technol (2014) 71:101–108

polished with alumina paste until a mirror-like surface wasobtained. Finally, the samples were etched using a 4 % HNO3

solution for about 15 s.In order to quantify theHPD, firstly, micrographs of the grind-

hardened area of these specimenswere taken bymeans of a LeicaDCM 3D microscope and a ×20 lens. Afterwards, the HPD wasmeasured in each micrograph using Leica Map software.

Microhardness was measured radially using a Future-TechFM-800 microhardness tester with a 500-g (4,900 N) load andaccording to ISO 6507-1 procedures. However, in some spec-imens, the heat-affected zone was so narrow that the recom-mended distance from the indentation center to the edge of thespecimen (in order to avoid interaction between the work-hardened regions and effects of the edge) could not be kept.Therefore, some hardness values of the grind-hardened layercould have been underestimated. The average value of thehardness of this layer was considered for analysis.

4 Results

In Fig. 3, the grinding wheel is shown after the test with theslowest workpiece speed (40 rpm) and the highest infeed

(0.180 mm). The appearance of the wheel after the test indi-cates that the wear along the width of the wheel is not uniform(three different zones are presented with a width approximate-ly equal to the axial feed per revolution). This effect wasshown to a greater or a lesser extent in all the tests that werecarried out.

It has to be taken into account that in the absence of wheelwear, the total infeed (ae) would be removed by the zoneclosest to the leading edge over a width a f. However, due towheel wear, a part of the infeed remains behind, so as to beremoved in the following workpiece rotation by a wheelportion of the same width. This effect produces a steppedprofile in the wheel (Fig. 4).

As it can be seen in Fig. 3, the grinding wheel surface of thetwo-thirds of the wheel closer to the leading edge is blunt. Thiscan be explained regarding the following two effects. Firstly,the highest amount of material is cut by this zone. Secondly, ithas to be considered that the material to be ground is nothardened, and the wheel blunts more easily.

Therefore, friction between wheel and workpiece is stron-ger in these zones, and high amounts of heat are generated(during the tests, it was observed that the incandescent chipswere focused on this area). As a result, it was consideredthat the effective grinding wheel width for the calcula-tions of the parameters described in the previous sectionshould be bseff=2/3·bs=12 mm.

Figure 5 shows the evolution of the hardened layer for agrinding test with a workpiece speed of 40 rpm and an infeedof 0.130 mm. As the grinding wheel moved along the work-piece, the power consumption increased due to the progressivewear and dulling of the grinding wheel. As a result, the heatderived to the workpiece was higher, and the HPD increased.Themean value of the hardnessmeasurements associatedwiththe indentations within the hardened layers was 665 HV,similar to the one obtained with an ordinary quenching with99 % of martensite (655) [28].

The HPD values are depicted over the calculated parametersPc″ and Ec″ in Figs. 6 and 7. The HPD varies approximately

Table 3 Grind-hardening conditions

Parameter Unit

Grinding wheel speed vs m/s 45

Workpiece speed vw rpm 40–75

Axial feed v f mm/rev 6

Infeed ae mm 0.075–0.180

Fig. 3 Grinding wheel surface after the grind-hardening test (ae=0.180 mm;vw=40 rpm)

af af af

workpiece

wheel

Machined materialae

vf

vw

Fig. 4 Stepped wheel wear in cylindrical traverse grinding

Int J Adv Manuf Technol (2014) 71:101–108 105

linearly with the area-based specific grinding power (Pc″) iftests with the same workpiece peripheral speed are considered.However, results show high dispersion. This effect may be dueto the fact that in the calculation of the parameter Pc″, thecontact area has been estimated considering the geometricaland not the real contact length. In fact, nowadays, it is widelyknown that due to the deflection of the wheel and workpiece,the real value can be substantially larger than the geometricalone [29]. Even if Pc″ might be useful to compare experimentswith the same workpiece peripheral speed, the actual depth ofcut, workpiece, and grinding wheel diameters and cuttingforces must be known in-process in order to estimate the reallength of the contact zone. Thus, the use of this parameter isdifficult if a closed loop control of the HPD is needed.

Likewise, HPD also varies approximately linearly witharea-based specific grinding energy (Ec″), but in this case,there seems to be a unique relationship between this parameterand the HPD for any machining condition (the coefficient ofdetermination indicates that approximately 87.5 % of theexperiments fit this linear correlation). Moreover, area-basedspecific grinding energy may be used with the aim of control-ling the HPD during the grind-hardening process, because the

parameters for its calculation (cutting power, workpiece pe-ripheral speed, and effective width of cut) can be easilymeasured.

5 HPD prediction with Barkhausen noise technique

Although the HPD can be predicted in-process from the Ec″parameter, there is a need of utilizing nondestructive testsduring the quality control, in order to ensure that the layerhas been properly generated.

HPD determination with BNmeasurements is based on thedifference in magnetic properties between the hardened layerand base material. Usually, case-depth studies using the BNmethod rely on a two-peaked behavior of the BN signal [30].However, other methods such as noise magnetizing sweepshave been proposed [31].

In this work, values of BN on the surface of the sampleswere taken using a commercially available Rollscan 300system (Stresstech Group, Finland) and a general purposeprobe (Stresstech S1-18-12-01) with a pickup coil at the center

0 0.2 0.4 0.6 mm0

0.1

0.2

0.3

0.4

1

2

0 0.2 0.4 0.6 mm

mmmm

0

0.1

0.2

0.3

0.4

1

2

Cursor 1 Cursor 2

Horizontal distance

X = 0.346110 mm X = 0.346110 mm

Y = 0.207500 mm Y = 0.078020 mm

0.129765 mm

1

Cursor 1

X = 0.331170 mm

Y = 0.173470 mm

Horizontal distance

Cursor 2

X = 0.331170 mm

Y = 0.066400 mm

0.106960 mm

0 0.2 0.4 0.6 mm

mm

0

0.1

0.2

0.3

0.4

1

2

Cursor 2

X = 0.350260 mm

Y = 0.076360 mm

0.0358345 mm

Cursor 1

X = 0.350260 mm

Y = 0.112050 mm

Horizontal distance

Fig. 5 Evolution of heat transformed layer along the workpiece (left side, center, and right side)

y = 1 4399x-84 471 R² = 0 5816

y = 0 5801x-47 524 R² = 0 6806

0

20

40

60

80

100

120

140

160

180

50 00 100 00 150 00 200 00 250 00 300 00

HP

D (

µm

)

P (W/mm2)

Vw=0.1m/s

Vw=0.2m/s

Fig. 6 Correlation of HPD and area-specific grinding power

No burn Grind-hardening

y = 50,759x-3,4007 R² = 0,8747

0

20

40

60

80

100

120

140

160

180

0,000 0,500 1,000 1,500 2,000 2,500 3,000 3,500

HP

D (

µm

)

E'' (J/mm2)

Fig. 7 Correlation of HPD and area-specific grinding energy

106 Int J Adv Manuf Technol (2014) 71:101–108

that applies the excitation field and receives the response ofthe material (Fig. 8). For each studied cross section, the rootmean square (RMS) voltage was recorded (after passing thesignal through a low-pass and high-pass filter) at four posi-tions on the periphery of the cross section (separated 90° fromeach other). The average value of these four measurementswas considered for analysis.

However, before making BN measurements, some consid-erations must be taken into account. On the one hand, theoptimal magnetization voltage amplitude and frequency mustbe determined in order to have a maximum sensitivity in ourmaterial. In this case, a magnetization voltage amplitude of1 Vpp and an excitation frequency of 125 Hz were selected.

On the other hand, it must be considered that the BN signalgenerated in the layers beneath the surface is damped by theeddy current opposition due to the material that the signal hasto pass. High-frequency content of BN signal is attributed tothe near-surface magnetization, and low-frequency compo-nents will be associated to greater depths below the surface.The depth corresponding to each frequency of the BN signalcan be calculated using the skin depth formula [32]. Thisequation of the penetration depth is strictly valid for only the

case of a material of infinite thickness under a plane magneticfield. Therefore, the depth calculated by the equation shouldbe taken as an approximate value.

δ ¼ffiffiffiffiffiffiffiffiffiffi

1

πfσμ

s

ð4Þ

where δ is the depth of penetration, f is the frequency of theBN signal, σ is the electrical conductivity, and μ =μ0μ r is themagnetic permeability.

In order to correlate the BN with the HPD, the frequencyrange of the filter has to be adjusted to have maximumsensitivity in the depth range of the expected hardened layers.

The analyzer used in this work allows the study on BN inthree frequency ranges: 10–70, 70–200, and 200–450 kHz.After measuring the HPD destructively in the first tests, the70–200-kHz range was selected. Considering that the electri-cal conductivity of martensite for AISI 1045 steel is approx-imately 0.41·107Ω−1 m−1 and the relative permeability 75, themaximum depth associated with the analyzed signal is110 μm. This depth is adequate to compare hardened layerswith a lower width or close to this value. It must be noted, thatthe importance of the selection of the filter frequency rangebecomes crucial when HPD must be estimated.

Figure 9 reports the measured BN values for each analyzedHPD. As it can be observed, it suggests that there is anapproximately lineal relationship between these two parame-ters. After calibration for each process and material, thisprocedure could be used as a nondestructive method to esti-mate the HPD.

6 Conclusions

This paper discusses the cylindrical traverse grind-hardeningof a medium carbon steel. It has been evaluated whether theEc″ and the Pc″ could be used as predictors of the HPD. Theresults suggest that an approximately linear correlation exists

Fig. 8 Experimental arrangement for BN measurements with a Rollscan 300 system

y = -0 4976x + 127 05R² = 0 8169

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120 140 160 180

BN

(V

pp

1 f

=125

Hz)

HPD ( m)

Fig. 9 Correlation of BN RMS values and HPD

Int J Adv Manuf Technol (2014) 71:101–108 107

between Ec″ and the HPD for any machining parametercombination. Therefore, this parameter may be used for in-process estimation of the HPD.

Conversely, results for Pc″ suggest that this parametercould only be used to predict the HPD for tests with the sameworkpiece peripheral speed. This reinforces the hypothesisthat the grinding power is not sufficient to predict changes inthe workpiece due to temperature rise for any grinding param-eter combination. Hence, contact time must be taken intoaccount. However, results show big dispersion, and the con-sideration of the real contact length in the definition of Pc″would provide better results.

Furthermore, it has been observed that there is a correlationbetween the RMS of the Barkhausen noise signal and thedepth of hardened layer in the workpiece. Thus, this methodcould be used as a nondestructive test to approximately predictthe HPD.

Acknowledgments The authors gratefully acknowledge the fundingsupport received from the Spanish Ministry of Science and Innovationfor funding the project “Integración de modelos numéricos y técnicasexperimentales para el aumento del valor añadido en el rectificado decomponentes de precisión” (DPI-2010-21652-C02-00).

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