ORIGINAL ARTICLE

Model of an abrasive belt grinding surface removal contourand its application

Y. J. Wang1 & Y. Huang1 & Y. X. Chen1& Z. S. Yang1

Received: 11 February 2015 /Accepted: 22 June 2015 /Published online: 17 July 2015# Springer-Verlag London 2015

Abstract Belt grinding technology is used for machining thecomplex surface of a blade; however, it is difficult to ensureprocessing accuracy. To solve this problem, a surface removalcontour (SRC) model for grinding the complex surface of ablade is proposed. First, this paper discusses why the normalcontact pressure between the grinding wheel and workpiecesurface accords with the Hertz contact theory, and further, thecalculation method for the pressure distribution of the Hertzcontact is given. Second, the SRC model is determined fromthe material removal rate (MRR) nonlinear model. To deter-mine the parameters of the MRR nonlinear and linear models,an abrasive belt grinding experiment was performed, whichshowed the relative error for the MRR nonlinear model was−1.1∼1.4 % and for the linear model was −12∼8 %. Third,combined with the Hertz contact theory, a SRC model basedon the MRR nonlinear model was built. The SRC experimentshowed the model’s accumulative error was only ±1 %, butthe accumulative error of the SRC model based on the MRRlinear model was −11∼5%. Finally, the application of abrasivebelt grinding on the blade showed the SRC model based onthe MRR nonlinear model was better in dimensional precisionand consistency of surface quality than the MRR nonlinearmodel. This led to more than 17.5 % surface roughness overthe processing requirement and, beyond a 30 % maximumerror, exceeded the standard. The residual stress on the bladesurface after grinding appeared as a tensile stress.

Keywords Abrasive belt grinding . Nonlinear . Surfaceremoval contour . Hertz contact theory

1 Introduction

With the improvement in performance of belt grinding, thescope for applying abrasive belts is expanding considerably,and belt grinding technology is now widely used for machin-ing workpieces with free surfaces, such as blades. Blades arethe key components of aircraft engines. Machining accuracyand quality plays an important role in whole machine perfor-mance and life [1–3]. After the NC-milling process, the allow-ance for machining varies across the surface [4, 5]. In addition,the pressure between the rubber contact wheel and blade isunevenly distributed during the grinding, which creates manyproblems in the precision removal of material.

Abrasive belt grinding is a very complex process. The ma-terial removal rate (MRR) is influenced by many factors, suchas belt speed, feed speed, and contact pressure distribution [6,7]. The linear model for the MRR was initially proposed byHamann [8], in which the material removal rate was propor-tional to the abrasive belt velocity, directly proportional to thepressure and inversely proportional to the feed speed. Later, amaterial removal rate model based on the Archard equationwas established by Zhang [9], but the model was essentiallythe same as Hamann’s theory, and it was inevitable thatZhang’s surface removal contour (SRC) model had large er-rors between the simulation and experimental results. Otherresearchers, however, considered the relationship between theMRR and influencing factors was exponential instead of lin-ear. Cabaravdic proposed the nonlinear model for MRR [10]using multivariate nonlinear regression analysis, which iswidely used in engineering and can better reflect the MRR[11, 12].

* Y. J. Wangwangyajieduck@163.com

1 The State Key Laboratory of Mechanical Transmissions, ChongqingUniversity, No.174, Shazhengjie, Shapingba, Chongqing 400044,China

Int J Adv Manuf Technol (2016) 82:2113–2122DOI 10.1007/s00170-015-7484-5

To resolve this problem in the precision belt grindingprocess of blades, the principal objective of this studywas establishing and applying the SRC model based onthe MRR nonlinear model. In practice, before buildingthe model, it should be clear what the distribution ofthe normal contact pressure in the contact area is be-tween the grinding wheel and workpiece surface, andconsequently which model is better for the SRC model.To determine the parameters of the MRR nonlinear andlinear models, an abrasive belt grinding experiment forthe MRR was implemented, and the relative errors ofthe two models were compared.

2 Contact pressure model

2.1 Basic assumptions of the Hertz contact theory

Contact problems are nonlinear problems. In 1881, Hertz as-sumed that the contact between the contact wheel and themold free-form surface had a half elliptical sphere pressuredistribution and elliptical contact area, as shown in Fig. 1.He analyzed the surface contact stress and deformation

according to Hooke’s law, and adopted the following hypoth-esis [13, 14]:

1. Contact objects deform elastically in accordance withHooke’s law.

The process of blade grinding has a small machining allow-ance and low contact pressure, and the plastic deformation onthe contact wheel’s rubber surface will not exceed 1 % of thewheel’s radius. Because the flexibility of the belt’s substrateand the thickness of the base is generally only 0.1∼0.3 mm, theassumption is suitable for the grinding contact.

2. The load is perpendicular to the contact area, that is to say,the contact surface is completely smooth, without anycontact friction between the objects.

While the abrasive belt moves anti-clockwise with a con-stant velocity around point O, the abrasive belt and contactwheel do not incur relative sliding in cornerite α, as shown inFig. 2. The contact wheel connects with the bracket through abearing, so that its friction is very small and can be ignored. Ifthe abrasive belt in cornerite α and the contact wheel aretreated as a whole assembly, the forces on the assembly arethe abrasive belt tension F1 and F2, Fz from the bracket, thetangential grinding force Ft and the normal force Fn from theworkpiece surface, and the torque on the whole assembly isbalanced, and described by

F1⋅Rc ¼ Ft⋅Rc þ F2⋅Rc; ð1Þwhere Rc is the radius of the contact wheel.

Numerically

Ft ¼ F1−F2; ð2Þso that when the belt drives the rotating contact wheel, thecontact wheel bears only the radial pressure and not the torquefrom the abrasive belt.

If the contact wheel and the abrasive belt in cornerite α arestudied separately, there is no friction between them to spin thecontact wheel faster, and the normal force Fn acts on thecontact wheel through the abrasive belt.

Fig. 1 The half ellipsoid distribution of contact pressure

Fig. 2 Forces on abrasive belt in cornerite α and contact wheel

Fig. 3 Grinding depth at the intersection curve Li

2114 Int J Adv Manuf Technol (2016) 82:2113–2122

3. The contact area is small compared with the curvatureradius of the contact surface.

The hypothesis can simplify the geometry condition with-out causing great error. Strictly speaking, this assumption doesnot meet the grinding contact state for a concave surface of theblade body. However, some research found [15], where therolling bearing, steel ball and ring raceway were preciselyfitted, the size of the contact area was relatively close to theball radius. It was notable that the calculated results in thisassumption, including the relief stress and elastic approach,were in close accordance with the experimental results. There-fore, this assumption was also approximatively suitable for thegrinding contact state for the concave surface on a blade body.

To sum up, the status of normal contact pressure was inaccordance with the basic hypothesis of the Hertz contact the-ory. The normal force Fn acted on the contact wheel andthrough the abrasive belt, with its pressure on the contact wheelsurface conforming to a half ellipsoidal distribution. In turn, theforce from the contact wheel acted on the workpiece surfaceand through the abrasive belt, and its pressure on the workpiecesurface was also distributed in a half ellipsoidal form.

2.2 Pressure distribution model

Based on the Hertz contact theory, the surface pressureconformed to a half ellipsoid distribution under the two free-form contacts, as shown in Fig. 1. The pressure in the contactarea [14–17] can be expressed as

P x; yð Þ ¼ P0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1−

x

a

� �2−

y

b

� �2r; ð3Þ

where a and b are respectively the long and short half axes ofthe ellipse in the local coordinates on the contact area, asshown in Fig. 1, and P0 is the pressure of the ellipse center,calculated as

a ¼ ma

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3Fn

2X

ρ

1−ν12

E1þ 1−ν22

E2

� �3

vuut ; ð4Þ

Fig. 4 The formation process ofSRC

Fig. 5 Grinding mode of the MRR test

Table 1 Contact parameters forthe SRC tests Contact wheel Workpiece Principal planes

rt E1 v1 ρ11 ρ12 E2 v2 ρ21 ρ22 ω

30 % 4.5 MPa 0.499 0 1/51 113 GPa 0.34 0 1/16 π2

Int J Adv Manuf Technol (2016) 82:2113–2122 2115

b ¼ mb

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3Fn

2X

ρ

1−ν12

E1þ 1−ν22

E2

� �3

vuut ; ð5Þ

P0 ¼ 3Fn

2π⋅a⋅b; ð6Þ

where E1 and E2 are respectively the elasticity modulus of thecontact wheel and blade, and μ1, μ2 separately are Poisson’sratio of the contact wheel and blade. ma and mb are respec-tively the coefficients associated with the elliptical eccentric-ity, ∑ρ is the sum of the principal curvatures of the contact

wheel and blade. ma, mb, and ∑ρ are calculated as

ma ¼ffiffiffiffiffiffiffiffiffiffiffiffi2L eð Þπ⋅k2

3

s; ð7Þ

mb ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2L eð Þ⋅k

π3

r; ð8Þ

Xρ ¼ ρ11 þ ρ12 þ ρ21 þ ρ

22; ð9Þ

where e is the elliptic eccentricity, L(e) the second type ofcomplete elliptic integral, ρ11 and ρ12 the principal curvaturesof the contact wheel, and ρ21 and ρ22 the principal curvaturesof blade. k, e, and L(e) are calculated as

k ¼ b=a; ð10Þ

e ¼ffiffiffiffiffiffiffiffiffiffi1−k2

p; ð11Þ

L eð Þ ¼Z π=2

0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1−e2sin2 αð Þ

qdα: ð12Þ

The principal curvature function F(ρ), in the general con-tact problem, is defined by

F ρð Þ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiρ11−ρ12ð Þ2 þ 2 ρ11−ρ12ð Þ ρ21−ρ22ð Þcos 2ωð Þ þ ρ21−ρ22ð Þ2

qX

ρð13Þ

where ω is the angle formed by the two principal planes of thecontact objects.

The relationship between the surface pressure and displace-ment can be determined using Eq. (13).

F ρð Þ ¼2þ b=að Þ2� �

L eð Þ−2 b=að Þ2K eð Þ1− b=að Þ2� �

L eð Þ; ð14Þ

where K(e) is the first type of complete elliptic integral.

K eð Þ ¼Z π=2

0

dϕffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1−e2sin2 ϕð Þ

q : ð15Þ

3 Model of the MRC

3.1 Model of the MRC based on the NMRR

If the MRR is not a function of the feed speed Vw, the nonlin-ear model [10] of the MRR can be expressed as

r ¼ Cg⋅Pb1 ⋅Vb2s ; ð16Þ

where, r is the grinding depth in unit time (per second), Cg=CA Ka Kt, CA the modified constant of the grinding process,Ka the resistance coefficient determined by the properties ofthe abrasive and removed material, Kt the durability coeffi-cient of the abrasive belt, P the uniform distribution pressure

Fig. 8 The relative error of r′

Fig. 6 The test results of material removal rate

Fig. 7 The relative error of r″

2116 Int J Adv Manuf Technol (2016) 82:2113–2122

in the contact area, Vs the belt velocity, and b1,b2 are constants.Figure 3 shows the simple grinding mode of the uniform

distribution of the contact pressure. The pressing block is acuboid, and the workpiece surface is a plane. So the pressurePon the contact area of the workpiece is uniform. Li is theintersection curve where the workpiece surface intersects theplane, which is perpendicular to the direction of the feed speedVw, and Lc is the contact length of Li. Thus, the contact timeTc of Li is

Tc ¼ Lc

Vw: ð17Þ

The grinding depth ht is proportional to the contact time Tc,expressed as

ht ¼ Cg⋅Pb1 ⋅Vb2s ⋅Tc: ð18Þ

Based on the Hertz contact theory, when grinding complexcurved surface parts, under the pressure caused by Fn, contactwheel deformation occurs. Take the short half axis b in linewith the direction of the feed speed Vw as an example. Theintersection curve Li is parallel to the x-axis, and enters thegrinding state where the point in the grinding state is xi=0 andthe time t= t1=0. When the point xi=0 on the intersectioncurve Li is out of the grinding state, time t=t5. The contactlength Lc(xi) means the contact length on the point x=xi,which is on intersection curve Li. The contact time Tc(xi) of

the different location is not the same on intersection curve Li,as shown in Fig. 4:

Lc xið Þ ¼ 2b 1−xi

a

� �2 !1=2

; ð19Þ

Tc xið Þ ¼ Lc xið ÞVw

: ð20Þ

The contact pressurePt (xi,t) of points on intersection curveLi change over time, and is expressed as

Pt xi; tð Þ ¼ 0xi

a

� �2

þ t⋅Vw−bb

� �2 !

> 1

!

Pt xi; tð Þ ¼ P0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1−

xi

a

� �2

−t⋅Vw−b

b

� �2s

elseð Þ:

8>>>><>>>>:

ð21Þ

Based on Eq. (17), the SRC on the intersection curve Li is:

h0h0xið Þ ¼ 2

Z Tc xið Þ=2

0Cg⋅Pt xi; tð Þb1Vb2

s dt: ð22Þ

The SRC is parabolic, with its symmetrical point xi=0 onintersection curve Li, where the grinding depth is h′(0). Thewidth of the SRC w is 2a and h′(a)=0.

The MRR r″ derived from the Archard equation and h″(xi)based on r″ are respectively

r″ ¼ 2kabr V s � Vwð ÞPHV

; ð23Þ

h″ xið Þ ¼ 2kabr V s � Vwð ÞHVVw

Z Tc xið Þ=2

0Pt xi; tð Þdt; ð24Þ

where kabr is the wear coefficient and HV the surface hardnessof the workpiece. When Vs and Vw are in the same direction,Vw in Eqs. (22) and (23) takes the sign “+”; When Vs and Vware in opposite directions, Vw in Eqs. (22) and (23) takes thesign “−”.

Fig. 9 Grinding mode of the SRC test

Fig. 10 Analysis of the SRCtests. a Fn=5 N, Vs=10 m/s, Vw=1 mm/s; b Fn=10 N, Vs=20 m/s,Vw=2 mm/s

Int J Adv Manuf Technol (2016) 82:2113–2122 2117

3.2 Determining the parameters of the MRR r′ and r″

To calculate the value of the parameters in Eqs. (16) and (23),the grinding test for the MRR was carried out on Tc4 titaniumalloy with an A16 abrasive belt (Fig. 5). The radius of thecontact wheel Rc was 140 mm, the ratio rt of thickness ofthe rubber and Rc was 30 %, the workpiece width Wp was8 mm, and the workpiece length Lp was 30 mm. The grindingtest did not start until the arc ACB was formed on the contactend of the workpiece. The height of the arc CD was

CD ¼ Rc−Rc⋅cos asinW p

2Rc

� �� �: ð25Þ

The width-height ratio of the arc ACB rh/w was

rh=w ¼ CD

Wp: ð26Þ

rh/w<1 %, so the contact pressure Pu was seen as a uniformdistribution, approximate to

Pu ¼ Fn

W p⋅Lp: ð27Þ

The results of the tests are shown in Table 1. The arc A ′C ′B′ formed on the contact end of the workpiece after a grindingtime Tg of 60 s, and the arcs ACB and A ′C ′B ′ were the sameshape. The length of the workpiece was measured with a mi-crometer. The material removal rate (MRR) r is

r ¼ A0ATg

: ð28Þ

Figure 6 shows the test results of the grinding depth. Withthe regression analysis of the test results, we obtain Kabr/HV=1.1813, Cg=1.4599, b1=0.8987, and b2=0.9486. The linearMRRmodel r″ has one parameter kabr/HV with a relative errorof −12∼8%, as shown in Fig. 7. However, the nonlinear MRRmodel r′ has three parameter Cg, b1, and b2 and its relativeerror was only −1.1∼1.4 %, as shown in Fig. 8.

3.3 Comparing h′(xi) with h″(xi)

The cylindrical workpiece was made of TC4 titanium alloy,with the cylindrical contact wheel going along the direction ofthe axis of the workpiece and perpendicular to its surface, asshown in Fig. 9. Table 1 provides the contact parameters forthe SRC tests. The ratio of the rubber thickness rt and Rc is

Fig. 11 Experimental equipment

Fig. 12 Device diagram of normal contact force control Fig. 13 The control system of grinding pressure

2118 Int J Adv Manuf Technol (2016) 82:2113–2122

30 %. The surface contour graph of the workpiece before andafter grinding is recorded using a FTSintra surface contour-graph, and the test MRC hTest is obtained by extracting fromthe former data. The process is calculated using Matlab soft-ware. Figure 10 shows the analysis of the MRC.

In Fig. 10a, h″(0) is greater than the test SRC hTest; how-ever, in Fig. 10b, h″(0) is less than hTest; This is because, whenVs=10 m/s, the relative error of the linear MRR model isbetween −12 and −9%, as shown in Fig. 6, and the cumulativeerror of h″(0) is about 11 %, which is caused by the timeintegration of the relative error of the linear MRR model.Similarly, when Vs=20 m/s, the relative error of the linearMRR model is between −1.5 and 1.5 %, and the cumulativeerror of h″(0) is about −5%. The relative error of the nonlinearMRR is between −1.1 and 1.1 %, as shown in Fig. 7, and thecumulative error of h′(0) is only ±1 %, so that h′(xi) is veryclose to the test SRC hTest, as shown in Fig. 9.

4 Application

4.1 Experimental setup

The abrasive belt grinding of the blade experiment is carriedout using a CNCmachine [18, 19]. The machine tool includesthe N-axis to control the normal contact force, three movingaxes X, Y, Z, and rotating axes A, B,C as shown in Fig. 11. The

direction of the X-axis is along the length of the machiningblade. The Y-axis is perpendicular to the length of the machin-ing blade and along its width. The Z-axis is vertical to thecontact wheel. The A, Y, and Z axes are the rotation axesrespectively around the X, Y, and Z axes. The N-axis is alongthe normal direction of the blade.

To achieve precise control of the contact pressure, the N-axis is adopted as the adjustable pressure belt grinding devicewith feedback, as shown in Fig. 12. In the device, the spring isin a compressed state acting on the nut with a thrust Fs, whichoffsets the effect of the weight G, so the normal contact forceFn is approximately equal to the output force of the cylinderFc.

Figure 13 shows the device schematic for the control of thenormal contact force [20–22]. The system controller, an in-dustrial computer (IPC), collects and deals with the feedbacksignal from the normal contact force, and sends out a control-ling signal. The proportional valve receives the control signal,and controls the gas flow into the cylinder which controls theoutput force of the cylinder’s piston. The output force signal,which is detected in real-time by a high-precision force sensoron the guide pillar, transmits the grinding pressure to the IPCvia an A/D converter. This system adjusts the PID controller’sparameters on line using a fuzzy algorithm and has a veryquick response output, good stability, and tracking perfor-mance. The system has strong anti-interference ability andcan satisfy the real-time request of the grinding controlsystem.

Fig. 14 Method for the surface precision belt grinding

.baltaMni(b)XNscihparginUni(a)

Fig. 15 The machiningallowance distribution

Table 2 Parameters and process for the blade abrasive belt grindingexperiment

Process Belt Beltspeed Vs

Feed speedVw

Contact forceFn

Roughgrinding

Pyramid belt,237AA

20(m/s) 2(mm/s) Real-timeadjusting

Int J Adv Manuf Technol (2016) 82:2113–2122 2119

4.2 Experimental method

Figure 14 shows the surface precision abrasive beltgrinding method. First, the blade surface was testedusing a 3D coordinate-measuring-machine, and aVC++ and UG/OPEN API were adopted as secondarydevelopment tools. The geometry of the machiningblade [23, 24] was refactored in Unigraphics NX ac-cording to the testing point data, and the bases of therefactored and theoretical models matched. As a result,the machining allowance was the distance between thesurfaces of the refactored and theoretical models, asshown in Fig. 15. The maximum depth of the SRCwas then equal to the machining allowance, and thecontact force was calculated combined with the givengrinding and contact parameters. Table 2 provides thegrinding parameters and Table 3 the contact parameters.To compare the SRC models based on the nonlinear andlinear MRRs, the contact force Fn′ was calculated using

the nonlinear model in the region of the surface param-eter v=[0.05, 0.5], u=[0.05, 0.95], and the contact forceFn″ was calculated using the linear model in the regionv=[0.05, 0.5], and u=[0.05, 0.95], as shown in Fig. 16.Finally, with real-time pressure control on the CNCabrasive belt grinding equipment, the high-precisiongrinding process on the blade surface was realized.

4.3 Results and analysis

Figure 17 shows the microscopic analysis of the bladesurface. Before grinding, the blade surface showed sig-nificant milling grain; the surface texture was improvedunder the grinding force Fn″ and consequently the mill-ing grain and defects were completely eliminated underthe grinding force Fn′.

Figure 18 shows the surface roughness of the blade beforeand after grinding. Before grinding, the roughness values wererespectively 0.34∼0.52 μm and 0.5∼0.62 μm in the u and vdirections. Under the normal contact force Fn″, the roughnessvalues were 0.22∼0.37 μm and 0.34∼0.47 μm, which did notmeet the requirement of less than 0.4 μm, and while the nor-mal contact force was Fn′, the value became 0.14∼0.22 μmand 0.17∼0.39 μm.

After grinding, the surface of the blade was measuredusing a 3D coordinate-measuring-machine, and the datawere analyzed using Matlab. The processing errors areshown in Fig. 19. In the grinding process, the forcesacting on the baffle were the tension forces F1 andF2, the tangential grinding force Ft and the componentforce of G generated from the incline of the microboard. The frictional force was generated between theguide pillar and the baffle in the opposite direction tothe cylinder output force Fc, so that the frictional forcehad a machining error for the whole machine region of(v=[0.5, 0.95] and u=[0.05, 0.45]), which was greaterthan zero. As Fig. 4b shows, h″(0) was below the hTestwhen the belt speed Vs was 20 m/s; therefore, the cal-culated Fn″ was less than the theoretical force. In thev=[0.5, 0.95] region, owing to the grinding phenome-non, the machining error was between 8 and 26 μmwhich did not meet the processing requirements (ma-chining accuracy 20 μm). That is to say, the maximum

Table 3 Contact parameters for the blade abrasive belt grindingexperiment

Contact wheel Blade Principal planes

rt E1 v1 ρ11 ρ12 E2 v2 ω

0.3 4.5 MPa 0.499 0 1/16 113 GPa 0.34 0

Fig. 16 Normal force distribution of Fn′ and Fn″

Fig. 17 Blade microscopicsurface. a Milling surface; bsurface under Fn″; c surface underFn′

2120 Int J Adv Manuf Technol (2016) 82:2113–2122

precision error would exceed the processing require-ments by over 30 %. The h′(0) was very close to thehTest, and the calculated Fn′ was also approximately thesame as the theoretical pressure. Under these circum-stances, the machining error was between 0 and20 μm in the v=[0.05, 0.5] region.

Figure 20 shows the surface residual stress after grinding.In this figure, the value was the average of three measure-ments, because of the “rubbing” and “ploughing” action ofthe abrasive grains. The residual stress on the blade’s surfaceappeared as a tensile stress with a value between −140 and0 MPa. Along the surveying depth direction, the residualstress reduced initially and then increased.

5 Conclusions

1. The normal contact pressure of abrasive belt grinding sat-isfies the assumptions of Hertz contact theory, and thepressure between contact wheel and workpiece surface,through the belt, was distributed as a half ellipsoidalpattern.

2. The proposed SRC model was based on the nonlinearMRR, and the values of Cg, b1, and b2 were determinedusing a grinding test. The results of the SRC tests, usingthe model built in this paper, accorded well with the testdata, with an error of only ±1 %. However, the maximumerror for the SRC model based on the linear MRR was11 %.

3. Compared with the SRC model based on the linear MRR,the nonlinear MRR model had greater prediction accura-cy. The results from the blade grinding experimentshowed that, in the grinding area under Fn′, which wascalculated using the SRC model based on the nonlinearMRR, the processing level can meet the requirements andthe roughness value was less than Ra 0.4 μm. The max-imum error for the grinding accuracy was less than20 μm. In the grinding area under Fn″, the surface rough-ness of 17.5 % exceeded the machining accuracy require-ment, and the maximum error was 30% over the standard.The residual stress on the blade surface after grindingappeared as a tensile stress.

Acknowledgments This work was supported by the National NaturalScience Foundation of China “Research on CNC Abrasive Belt Grindingfor Aeronautical Engine Blades” (NO.51275545) for which we aregrateful.

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