NAMRCJohnson face Grinding Modeling

7/29/2019 NAMRCJohnson face Grinding Modeling

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DESIGN OF EXPERIMENTS BASED FORCE MODELINGOF THE FACE GRINDING PROCESS

Eric C. Johnson, Rui Li, and Albert J. ShihDepartment of Mechanical Engineering

University of MichiganAnn Arbor, Michigan

Hap HannaPowertrain Division

General Motors CorporationPontiac, Michigan

KEYWORDS

Bimetallic Grinding, Grinding Force Model,Electroplated CBN (ECBN), Response Surface

ABSTRACT

A grinding force model is developed to predictthe forces during the face grinding of cast ironand aluminum alloy 319. Design of experimentsmethods are used to create a response surfaceof four process parameters: feed rate, inclinationangle of the grinding wheel profile, offset anglebetween the grinding wheel and the workpiece,and the peripheral speed of the wheel. For eachmaterial, three polynomial equations aredetermined by regression analysis to representthe forces in three directions. The model shows

better accuracy for cast iron than aluminumalloy. The feed rate and inclination angle havethe most significant effect on the grinding forces.The model is simple and can be implemented inindustry quickly after a few test runs. However, ithas limited accuracy, generally within 10-20%on the prediction of grinding forces.

INTRODUCTION

Grinding is an important surface finishingprocess and has broad industrial applications.

One such case is the combustion deck surfaceof engine blocks and heads, as shown in Fig. 1.This deck surface seals against the head gasketto prevent the hot, high pressure gas fromescaping the combustion chamber. The function

of this seal is related to the roughness, flatness,and finish of the deck surface, and a high qualityfinishing process is essential. The task ofachieving this precision falls to either grinding ormilling processes. Although more expensive,grinding offers a better finish and is widelyapplied in such operation in automotivepowertrain manufacturing. This research studiesthe force modeling in face grinding of the enginecombustion deck surfaces.

FIGURE 1. FACE GRINDING PROCESS, USING ANENGINE BLOCK DECK SURFACE AS ANEXAMPLE.

Transactions of NAMRI/SME 241 Volume 36, 2008


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The grinding process can be characterized bycombining physical properties of the workpiecematerial, grinding wheel, and machine, with the

controllable parameters of the process. Thedistribution and shape of the grain cutting edgesstrongly influence the force and surface finish[Tonshoff et al. 1992]. The process parametersand wheel and workpiece geometry control thematerial removal rate and chip thickness. Thefriction force present at the cutting interface ispredominately determined by the materialproperties of the workpiece, as is the deflectionof the grinding wheel. As Brinksmeier et al.[2006] pointed out, the grinding process is thesum of the interactions among the wheeltopology, process kinematics, and the workpieceproperties. Most analytical force models arerelated to the topography of wheel, workpieceproperties, and chip thickness [Brinksmeier et al.2006; Malkin 1989; Tonshoff et al. 1992]. Inaddition to these physical/empirical models,many newly developed modeling techniques likeartificial neural network have been utilized tomodel the grinding process [Brinksmeier et al.2006; Lee and Shin 2004]. Most of these modelsare derived from the basic grinding operations:horizontal surface grinding and cylindricalgrinding, which are different from theconfiguration of vertical grinding the combustiondeck face.

Research on vertical surface grinding islimited. Lal and Srihari [1994] studied themechanics of chip formation in face grinding. Lal[1968] also investigated the effects that varyingtable speed, depth of cut, and workpiecematerial had on face grinding force, but nomodel was developed with these parameters.However, experiments involving more modern,electroplated superabrasive wheels, are absentfrom the current annals of face grindingknowledge. ECBN grinding wheels do notrequire periodic dressing and truing [Shi and

Malkin 2003], unlike a vitrified bond wheel. Oneaim of the present research, which utilized anelectroplated cubic boron nitrite (ECBN) grindingwheel, is to fill this gap.

The other aim of this paper is to develop aneffective face grinding force model. In theabsence of established analytical models, apractical solution is to empirically correlate theresponse to the input variables with a polynomialapproximation. This is known as responsesurface methodology [Cochran 1957]. For agiven polynomial degree, the number of

experiments required to fit the model growsexponentially with the number of factors.However, the number of experiments can often

be reduced by using design of experiments(DOE) techniques. DOE is a systematicapproach to experimental design in whichmultiple factors are varied simultaneously, whilecontrolling for variance. Properly implemented,DOE increases the efficiency of the informationgathering. When DOE methods are combinedwith regression modeling, a polynomialapproximation of the response is obtained [Box1951]. This technique is called response surfacemethodology (RSM). Alauddin et al. [2007]recently combined RSM with dimensionalanalysis to develop a grinding force model usingconventional abrasives. This study furtherexpands the RSM method for modeling ECBNface grinding forces.

In this research, the forces arising in facegrinding using an ECBN wheel are investigated.Cast iron and aluminum alloy 319 (AL319) arestudied. DOE methods were used to develop anempirical model to predict face grinding forces.First and second order regression models werederived to predict the normal, tangential, andlateral specific grinding forces. The model isvalidated by comparing forces at intermediategrinding conditions.

GRINDING KINEMATIC MODEL

The grinding forces can be represented in twocoordinate systems. One is a global coordinatesystem defined relative to the machine. Asshown in Fig. 2, the three force components inthe global coordinate system are: force normalto the ground surface FN; force against the feeddirection, FL; and force normal to the feeddirection and ground surface, FT. The grindingexperiments measured forces relative to this

global coordinate system.

Another coordinate system is a localcoordinate system, defined relative to the wheeland workpiece contact surface. As shown in Fig.2, forces Fn and Fl are normal and coincident tothe inclined contact surface, respectively, and liein a plane at angle to the feed direction andnormal to the ground surface. Force Ft is tangentto the wheel rotation axis. Angle is the offsetangle between the wheel and workpiece. Angle

is the inclination angle of the wheel profile withrespect to the ground surface.



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FIGURE 2. FN, FT, AND FL IN GLOBAL (MACHINE)COORDINATE SYSTEM AND Fn, Ft, AND FlINLOCAL (WHEEL/WORKPIECE) COORDINATESYSTEM.

For analysis, the measured forces FN, FT, andFL are transformed to the local coordinatesystem using the following equations:

= +cos sin sin sin cosn N T LF F F F [1]

= +cos sint T LF F F [2]

= + sin cos sin cos cosl N T LF F F F [3]

The contact surface between the wheel andworkpiece was discretized into several depthintervals along the wheel axis, as shown in Fig.3. Each depth interval was associated with acertain inclination angle . Since the profile wasdivided into a finite number of discrete intervals,

was approximated as the gradient of thestraight line connecting the end points of eachsegment. It is dependent on the grinding depth.The incremental force contribution of eachinterval was determined by subtracting the force

measured at the shallower interval thatpreceded it, if any existed. The number of

intervals tested was proportional to the modelorder. Thus for a second order model, there arethree depths and three force intervals.

Four input parameters were selected: feed perrevolution f (mm/rev), angles and , andperipheral cutting speed V (m/min). Theresponses were the local specific normal andtangential forces, kn and kt, respectively. Thelocal specific lateral force kl was negligible andwas not modeled. The local specific forces arecalculated from the local forces as:

= =tn

n t

FFk k

S S[4]

where S is the contact area between the tooland workpiece, and kn, kt are the normal andtangential grinding pressures, respectively. Sdepends on the depth of cut and offset angle .The wheel was plunge ground into a workpiece,and the resulting imprint measured on aprofilometer, to assist in the calculation of S. Themeasured wheel profile and profile fit are shownin Fig. 4. The local specific forces that arepredicted by the model can be converted to anaggregate global force by the followingprocedure:

1. Discretize contact surface into square

grid elements. Each element isassociated with a particular , , andmaterial. An example is given in Fig. 5,which uses a Cartesian system ofuniformly sized square grid elements.

2. Calculate local specific forces kn and ktfor each element using the predictionmodels of Eqs. [6-9]. The material type ofeach element will dictate which model touse. klmay be assumed to be zero.

55 60 65 70 75

0

100

200

300

400

500

600

Radial position [m m]

Elevation[m]

Valid regionMeas. Prof ile

Prof ile Fit

FIGURE 4. PROFILE OF ELECTROPLATED CBNGRINDING WHEEL IN THIS STUDY.

FIGURE 3. DEPTH OF CUT INTERVALS ANDASSOCIATED INCREMENTAL CONTACT ANGLES.



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FIGURE 5. DISCRETIZATION OF CONTACTSURFACE INTO GRID ARRAY. EACH GRIDELEMENT IS ASSOCIATED WITH A PARTICULAR

, , AND MATERIAL.

3. Obtain local forces Fn and Ft for eachelement by multiplying that elements knand kt by its area S. For the example inFig. 5, Sis the same for all elements.

4. Transform local forces into globalcoordinate system using angles andof each element.

5. Sum elemental global forces to obtain theaggregate global force.

EXPERIMENTAL METHODS

Design of Experiments

A factorial experiment, in which the effects ofmultiple factors are tested simultaneously, canbe used to develop a polynomial responsesurface model. Given N levels of each factor,and k factors to be studied, a total of N

kunique

combinations of experimental conditions arepossible. In a full factorial design all N

k

combinations are tested; this provides estimatesof each factors main effect, and also allowsinteractions between factors to be examined infull. Testing each factor at two levels will

produce a first order model. The second ordermodel that accounts for curvature can bedeveloped by testing factors at three levels. Thenumber of experiments required by a fullfactorial design quickly becomes impractical tohandle as the model order and number offactors increase. Fractional factorial designs,which consist of a systematically selectedsubset of the full factorial design, are effectivemethods of reducing the number of tests [Finney1945]. Many fractional factorial designs havebeen enumerated: half-replicate, quarter-replicate, central composite, and rotatable

composite designs to name a few [Cochran1957].

This work used a central compositedesign toincrease efficiency. A visual representation ofthe design is shown in Fig. 6. In a centralcomposite design, midpoints are added to a firstorder model to create a second order model. Itallows curvature of the main effects to bestudied. The modeling process is divided intotwo steps:

Screening Test. The screening test was anexploratory 24

factorial experiment used to fit afirst order response surface. This forms thecorner points of the cube in Fig. 6, andcorresponds to trials 1 to 16 in Table 1.

Second Order Response Model. Midpointswere added to the 2

4factorial model to create a

second order response model. All factors werefound to be significant in the screening test, thus

TABLE 1. EXPERIMENTAL DESIGN.

Trial f V Trial f V Trial f V1 -1 -1 -1 1 14 1 1 -1 1 27 0 -1 0 02 1 -1 -1 -1 15 -1 -1 1 1 28 0 1 0 0

3 -1 1 -1 1 16 -1 1 1 1 29 0 0 -1 0

4 1 1 -1 -1 17 -1 0 -1 1 30 0 0 1 0

5 -1 -1 1 -1 18 1 0 -1 -1 31 0 0 0 -1

6 1 -1 1 1 19 -1 0 1 -1 32 0 0 0 1

7 -1 1 1 -1 20 1 0 1 1 33 0 0 0 0

8 1 1 1 1 21 -1 0 -1 -1 34 -1 0 0 0

9 -1 -1 -1 -1 22 1 0 1 -1 35 1 0 0 0

10 -1 1 -1 -1 23 1 0 -1 1 36 0 0 -1 0

11 1 -1 1 -1 24 -1 0 1 1 37 0 0 1 0

12 1 1 1 -1 25 -1 0 0 0 38 0 0 0 -1

13 1 -1 -1 1 26 1 0 0 0 39 0 0 0 1

FIGURE 6. CENTRAL COMPOSITE DESIGN.ACTUAL COMPOSITE DESIGN INCLUDES ANDIS FOUR DIMENSIONAL.



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a midpoint was added for each of the fourfactors. The entire second order experimentaldesign includes the first order trials from thescreening test, plus trials 17 to 39 in Table 1.

Experimental Setup

The grinding experiments were conducted ona Fadal CNC vertical machining center. A 150

mm diameter, 60-grit electroplated CBN grindingwheel was used. A Kistler 9273A piezoelectricdynamometer was used to measure three forcecomponents during grinding. A 5% concentrationof water based cutting fluid, Hocut TR2000-C,was used. Although CBN wheels generallyperform best with oil-based coolants, industry ismoving towards water-based coolants forenvironmental considerations [Carius 1989].Dimensions of the workpieces used are given inTable 2.

The wheels rotational velocity was converted

to linear cutting speed, V, in the model. Theinclination angle was calculated based onincremental depth of cut as illustrated in Fig. 3.The model was based on rather than directlyon depth of cut. The angles and werenormalized by taking their sine for use in themodel.

Cast Iron. A cleanup pass and spark out wereperformed prior to each test. For each testcondition, five passes were made, to approachthe steady state depth of cut described byMalkin [1989]. The physical parameter rangesare given in Table 3.

AL319. Grinding aluminum is complicated bythe fact that the aluminum alloy tends to build up

on the wheel, due to its high ductility. Thebuildup was managed in the experiments bygrinding cast iron alongside the aluminum alloy,to scrape the aluminum build-up from wheelsurface. The cast iron workpiece was positionedat the high and low offset angles listed in Table2, = 0 and = 45. The aluminum plateswere placed directly adjacent to the cast ironplates, at = 6.8 and = 36.1, as illustratedin Fig. 7B. The aluminum force was calculatedby subtracting the cast iron force from themeasured bimetallic force, using values found incast iron response surface experiments. Therest of the experimental procedure was identical

to that of the cast iron experiments, with theparameter values listed in Table 3. The AL319experiments consisted of the first orderconditions, trials 1 to 16 in Table 1.

RESULTS

The ratio of the normal and tangential cuttingpressures, kt/kn, is considered to be arepresentation of the frictional behavior, f, that

TABLE 3. LEVELS OF CODED FACTORS

CodingFactor Units ModelFactor? 1 0 -1

f (mm/rev) Y 0.125 0.0875 0.050

(rpm) N 12000 8000 4000V

(m/min) Y 5742 3828 1914

0.707*

0.382*

0.000*

sin - Y0.589

**N/A -0.118

**

a

(m) N 150 65 20

0.035

N/A

0.005

sin

- Y0.078

0.017

0.005

*Cast iron.

**AL319.

is dependent upon depth of cut, a. Both parameters are

given, however sin is used in the model.

First order model.Second order model.

FIGURE 7. WORKPIECE ORIENTATIONS.(A) CAST IRON AND (B) BIMETALLIC

TABLE 2. WORKPIECE DIMENSIONS

Material Thickness Length

Cast iron 6 mm 60 mmAL 319 12 mm 60 mm



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is material dependent. They can be related by:

=t f nk k [5]

The friction coefficients for cast iron andAL319 are the slope of two lines plotted in Fig.8, 0.25 and 0.44, respectively. Lal [1968] found

f = 0.27 for cast iron, which is close to the valuefound in this study. The ratio of kt for cast iron

(kt,CI) to AL319 (kt,Al) was found to follow a linearrelationship, plotted in Fig. 9.

Response Model

The dominant factors were fand , which arerelated to the equivalent chip thickness. Fig. 10shows the response of kt to fat varying levels of

for cast iron material. Because the secondorder model did not include all full factorialterms, the effects of all factors and interactionscould not be independently discerned usingANOVA. Rather, terms were manually selectedbased on previously developed analyticalmodels, minimization of the PRESS statistic[Allen 1971], and visual inspection of theprediction surfaces vs. experimental data.

For cast iron, the following models were foundto characterize the normal and tangentialgrinding pressures (units are in kPa):

= + +

+

2

2

71 8691 23453 sin

40048 sin 3476 sin sin

nk f f

[6]

= + +

+

2

2

20 1988 13300 sin 0.0351

7133 sin 876 sin sin

tk f f fV

[7]

The normal and tangential grinding pressuremodels for AL319 were (units are in kPa):

= +

+

+

48 236 1916sin 0.0041

16117 sin 358 sin

0.2727 sin

nk f V

f f

V

[8]

= + +

+ +

32.3 26.3 21.7 sin 4.9 sin

21.4 sin 5.6 sin 4.4 sin

tk f

f f V[9]

Model Validation

A set of experiments was performed usingparameter combinations that were not included

0 20 40 60 80 1000

10

20

30

40

50

60

kt, cast iron [kPa]

kt,

AL319

[kPa]

ratio kt,Al

/ kt,CI

= 0.511

FIGURE 9. RATIO BETWEEN TANGENTIALPRESSURES OF CAST IRON AND AL319.

0 200 400 600 8000

50

100

150

200

250

300

kt

[kPa]

kn

[kPa]

Cast iron, kt= 0.254k

n

AL319, kt= 0.443k

n

FIGURE 8. RATIO OF NORMAL AND TANGENTIALFORCES FOR CAST IRON AND AL319.

0.02 0.04 0.06 0.08 0.1 0.12 0.140

50

100

150

200

250

300

f [mm/rev]

Predictedk

t(castiron),

[kPa]

= 0

= 0.02

= 0.04

= 0.06

= 0.08

= 0.1

V= 3828 m/min

= 0

FIGURE 10. TANGENTIAL PRESSURE RESPONSELINES, CAST IRON MATERIAL



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in the 39 tests defined in Table 1. Thepredictions of the cast iron and AL319 modelswere validated by comparison with these tests.The parameter values used in the validationexperiments were interpolative, that is, they fellwithin the high and low parameter boundaries

defined in Table 3. The measured global forceswere used for comparison; the predicted globalforces were derived from the predicted localgrinding pressures using the procedureillustrated in Fig. 5.

Five validation experiments, V1 to V5 in Table4, were performed for cast iron. Results ofpredicted and measured FN and FT are plotted inFig. 11.

Three validation experiments, V6, V7, and V8in Table 5, were performed for AL319. Cast ironwas ground simultaneously. The cast ironworkpiece was positioned at the same offsetangles listed in Table 4, so that the data fromthose tests could be subtracted from themeasured aggregate bimetallic force. TheAL319 workpieces were placed adjacent to the

cast iron. The validation test parameters forAL319 are given in Table 5 and the results areplotted in Fig. 12.

Discussions

For cast iron, the experimental vs. predicted FTin Fig. 11B shows the accuracy is within 13.1% 5.1%. For FN in Fig. 11A the accuracy falls to

TABLE 5. AL319 VALIDATION TESTS.

Test Width f a V(mm) (mm/rev) (m) (deg) (m/min)

V6 12 0.05 85 -6.8 1914V7 12 0.075 75 8.1 4785V8 12 0.1 100 22.5 2781

TABLE 4. CAST IRON VALIDATION TESTS.

Test Width f A V(mm) (mm/rev) (m) (deg) (m/min)

V1 6 0.05 85 0 1914V2 6 0.075 75 15 4785V3 6 0.1 100 30 2781V4 18 0.06 20 0 2393V5 18 0.08 65 0 4307

(A)

V1 V2 V3 V4 V50

5

10

15

20

Validation test (cast iron)

FN

[N]

Measured

Predicted

(B)

V1 V2 V3 V4 V50

1

2

3

4

Validation test (cast iron)

FT

[N]

MeasuredPredicted

FIGURE 11. PREDICTED AND MEASURED (A)FN, AND (B) FT, FOR CAST IRON VALIDATION.

(A)

V1 V2 V30

2

4

6

8

10

Validation test (AL319)

FN

[N]

Measured

Predicted

(B)

V1 V2 V30

1

2

3

Validation test (AL319)

FT

[N]

MeasuredPredicted

FIGURE 12. PREDICTED AND MEASURED (A)FN, AND (B) FT, FOR AL319 VALIDATION.



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7.9% 16.1%. One explanation may be that FNis affected by vertical deflection of the grindingwheel. This can be caused by deflection of the

workpiece, machine, and grinding wheel. Thedeflection will directly relate to the depth of cut a.In the model presented in this paper, theinclination angle was used, rather than aitself.Thus, a possible improvement may be tointegrate adirectly into the model.

For AL319, Fig. 11B shows a reasonableprediction of FT, with an error of 17.9% 5.8%.The FN predictions in Fig. 11A are only within26.1% 5.2% of the measured values. Inadditional to the possibility of deflectiondiscussed above, the AL319 forces are moresusceptible to experimental uncertainty becausethey are obtained by subtracting the cast ironforces from the bimetallic data. The uncertaintyof both measurements is compounded. By usinga cast iron workpiece that is longer than thealuminum workpiece, the aluminum results canbe improved by directly measuring the cast ironforce during each aluminum experiment.

CONCLUSIONS

This study predicted the specific forces in theECBN face grinding of cast iron and AL319. On

the basis of DOE, a second order polynomialresponse surface model was built for cast iron,and a first order model was constructed forAL319. Among four grinding parameters studied,the feed rate and inclination angle had the mostsignificant effect on the grinding forces. Themodel demonstrated more accurate grindingforce prediction for cast iron than AL319. Thelocal specific forces may be integrated over anarbitrary workpiece geometry to calculate theaggregate global grinding force. These simplemodels are very suitable for industrialapplications, however accuracy is limited to 10-

20%. For a given grinding wheel and workpiecematerial, DOE methods can be used to quicklycharacterize and predict grinding performance.

REFERENCES

Alauddin, M., L. Zhang, and M.S.J. Hashmi(2007). Grinding Force Modelling: CombiningDimensional Analysis with Response SurfaceMethodology. Int. J. Manufacturing Technologyand Management, Vol. 12, pp. 299310.

Allen, D.M. (1971). Mean Square Error ofPrediction as a Criterion for Selecting Variables.Technometrics, Vol. 13(3), pp. 469-475.

Box, G.E.P. and K.B. Wilson (1951). On theExperimental Attainment of OptimumConditions. Journal of the Royal StatisticalSociety Series B, Vol 13(1), pp. 1-45.

Brinksmeier E., J.C. Aurich, E. Govekar, C.Heinzel, H.W. Hoffmeister, F. Klocke, J. Peters,R. Rentsch, D.J. Stephenson, E. Uhlmann, K.Weinert, and M. Wittmann (2006). Advances inModeling and Simulation of GrindingProcesses. Annals of the CIRP, Vol. 55(2), pp.667-696.

Carius, A.C. (1989). Effect of Grinding FluidType and Delivery on CBN Wheel Performance.presented at Society of ManufacturingEngineers, Modern Grinding Technology, Novi,Michigan.

Cochran, W.G. and G.M. Cox (1957).Experimental Designs. Wiley, New York.

Finney, D.J. (1945). The Fractional Replicationof Factorial Arrangements. Ann. Eugen. Vol 12,pp. 291-301.

Lal, G.K. (1968). Forces in Vertical SurfaceGrinding. International Journal of Machine ToolDesign Research, Vol. 8, pp. 33-43.

Lee, C.W. and Y.C. Shin (2004). Modeling ofComplex Mfg. Processes by Hierarchical FuzzyBasis Function Networks with Application toGrinding Processes. J. Dyn. Sys., Meas.,Control, Vol. 126, pp. 880-890.

Malkin, S. (1989). Grinding Technology: Theoryand Application of Machining with Abrasives.Wiley, New York.

Shi, Z., and Malkin, S., 2003, An Investigationof Grinding With Electroplated CBN Wheels,Annals of the CIRP, 52(1), pp. 267270.

Srihari G. and G.K. Lal (1994). Mechanics ofVertical Surface Grinding. Journal of MaterialsProcessing Technology, Vol. 44, pp. 14-28.

Tonshoff H.K., J. Peters, I. Inasaki, and T. Paul(1992). Modeling and Simulation of GrindingProcesses. Annals of the CIRP, Vol. 41(2), pp.677-688.


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NAMRCJohnson face Grinding Modeling