Research Article Study on Effect of Ultrasonic Vibration

Research ArticleStudy on Effect of Ultrasonic Vibration on GrindingForce and Surface Quality in Ultrasonic Assisted Micro EndGrinding of Silica Glass

Zhang Jianhua Zhao Yan Zhang Shuo Tian Fuqiang Guo Lanshen and Dai Ruizhen

School of Mechanical Engineering Hebei University of Technology Guangrongdao Street Hongqiao Tianjin 300130 China

Correspondence should be addressed to Zhang Jianhua jhzhanghebuteducn

Received 28 February 2014 Revised 20 May 2014 Accepted 11 June 2014 Published 8 July 2014

Academic Editor Mohammad Elahinia

Copyright copy 2014 Zhang Jianhua et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Ultrasonic vibration assisted micro end grinding (UAMEG) is a promising processing method for micro parts made of hardand brittle materials First the influence of ultrasonic assistance on the mechanism of this processing technology is theoreticallyanalyzedThen in order to reveal the effects of ultrasonic vibration and grinding parameters on grinding forces and surface qualitycontrast grinding tests of silica glass with and without ultrasonic assistance using micro radial electroplated diamond wheel areconductedThe grinding forces aremeasured using a three-component dynamometerThe surface characteristics are detected usingthe scanning electronmicroscopeThe experiment results demonstrate that grinding forces are significantly reduced by introducingultrasonic vibration into conventional micro end grinding (CMEG) of silica glass ultrasonic assistance causes inhibiting effect onvariation percentages of tangential grinding force with grinding parameters ductile machining is easier to be achieved and surfacequality is obviously improved due to ultrasonic assistance in UAMEG Therefore larger grinding depth and feed rate adopted inUAMEG can lead to the improvement of removal rate and machining efficiency compared with CMEG

1 Introduction

Expanding requirements of microproducts with features andstructures at microscale and nanoscale such as micro opticalsystem micro robot micro motor and fuel injection noz-zle presents stimulation and challenges to micromachiningtechnology [1 2] Machining of micro parts made fromnonferrous metals and other materials which are not diffi-cult to machine can be reliably achieved by microturningmicromilling microdrilling and so forth [2] However thereare only limited methods existing for the process of 3Dmicrocomponents of hard and brittle materials Microgrinding isone of the most promising processing technologies in thisfield Ramesh et al [3] conducted high-table-reversal-speedmicrogrinding tests on different hard and brittle materialsin which fine slots with 01mm width and high aspectratio of 15 were produced The lowest surface roughnessobtained of WC Al

2O3 and BK7 are 016 120583m 032 120583m and

052 120583m respectivelyThe lowest average surface roughness of1297 nm was achieved in Rahmanrsquos experiment [4] in which

microgrinding of BK7 glass was carried out using micro-EDM-fabricated PCD tool

There are many challenges that lie in microgrindingHigh grinding forces in microgrinding result in high heatgeneration and rapid microwheel wear [3 5 6] In additionaccording to nanoindentation testing median crack willgenerate and grow inward in the material when the loadexceeds the critical value [7 8] It is always required toobtain fracture-free surface on which damage due to fracturecracks should not be achieved on the final machined surface[9] The experiments indicate that higher grinding forcewill lead to more residual crack on surface and subsurfaceTherefore in order to yield high surface integrity and surfaceaccuracy in microgrinding cutting depth and feed rate mustbe maintained in a quite low level to limit grinding forcewhich results in low removal rate and low efficiency

It is indicated by previous research onultrasonic vibrationassisted machining (UVAM) that machining quality can besignificantly improved by introducing ultrasonic vibrationStarting with the investigation of vibration assisted planning

Hindawi Publishing CorporationShock and VibrationVolume 2014 Article ID 418059 10 pageshttpdxdoiorg1011552014418059

2 Shock and Vibration

HQP Cutting

Gap

thicknessCutting

thickness

UAMEG CMEG

r

rr

y y

y

O xx

xO998400O

w

ws

Wheel

The cutting abrasive trajectoryThe former abrasive trajectory

Workpiece

z

o

A f

Figure 1 Machining process of UAMEG and conventional micro end grinding (CMEG)

Junichiro [10] initiated UVAM and conducted a series ofexperiments on it Comparedwith traditionalmicrogrindingthe cutting force was lowered by 30-50 the temperature incutting areawas lowered to the room temperature and highermachining accuracy and lower workpiece surface roughnesswere achieved Tawakoli et al [11] conducted comparativeexperiments of ultrasonic assisted dry grinding and con-ventional dry grinding of 42CrMo4 which demonstratedconsiderable advantages of UVAM up to 60 reductionof normal grinding force and significant improvement onthe Rz parameter Similar experiments were conducted on100Cr6 [12] and the results indicated that the aided ultrasonicvibration considerably eliminated the thermal damage ofworkpiece surface and subsurface increased the G-ratio andreduced the grinding forces (up to 60ndash70 of normal grind-ing forces and up to 30ndash50 of tangential grinding forces)Akbari et al [13] investigated the ultrasonic vibration effectson grinding process of alumina ceramic by experiments Thetestsrsquo results also indicated significant improvements surfaceroughness improved by 8 total grinding force reduced byup to about 22 and workpiece fracture strength increasedby approximately 10 on average Therefore UAMEG istreated to be a promising method to improve conventionalmicrogrinding of microparts made of hard and brittle mate-rials However research on the mechanism of this newprocessing method has not been reported so far

In this paper the influence of ultrasonic assistance onthe mechanism of this processing technology is theoreticallyanalyzed UAMEG is applied to silica glass for the first timeon amanual developedmachine tool to experimentally studythemechanism of grinding forces and surface characteristicsGrinding forces are measured by a three-component forcedynamometer unit and the surfaces are detected using scan-ning electron microscope (SEM)

2 Mechanism Analysis of UAMEG

21 Machining Process of UAMEG The machining processof UAMEG can be seen in Figure 1 The precision feed ofgrinding wheel V

119908is in the direction of 119909-axis along which

the workpiece operates simple harmonic motion with smallamplitude119860 and high frequency119891 (ultrasonic vibration)Thegrinding wheel rotates at high speed 120596

119904around the 119911-axis

which orients in cutting depth direction

From Figure 1 it can be seen that exterior marginabrasives on the grinding wheel end face firstly cut into theunmachinedmaterial which leads to shearing-forming chipsor brittle-fracture chips (here defined as the first grindingzone) inner margin abrasives only encounter the machinedmaterial whichmainly lead to sliding ploughing and repeat-edly ironing the machined material surface generated by theformer abrasives due to the spring back of material (heredefined as the second grinding zone) Therefore the cuttingthickness of exterior abrasives is much larger than cuttingthickness of inner abrasives So fracture cracks are morelikely to generate in the first grinding zone In other wordsif ductile grinding is achieved in the first grinding zone finalmachined surface free of cracks can be obtained

In Figure 1 the dashed curve refers to the trajectoryof the former abrasive which represents the profile of theunmachined regionmaterialThe solid curve is the trajectoryof the cutting abrasive In CMEG the cutting abrasivecontinuously cuts the unmachined material However thecutting mechanism is different in UAMEG When the solidcurve moves to the right of the dashed curve it indicatesthat the cutting abrasive cuts into the unmachined materialas from point 119875 to 119876 When the solid curve moves to theleft of the dashed curve as from point 119876 to 119867 the cuttingabrasive withdraws from unmachined material regionTherewill be a gap between the cutting abrasive rake face and theunmachined material Then a new cutting cycle commencesfrom point 119867 As this cutting cycle circulated at ultrasonicfrequency intermittent cutting is achieved in UAMEG

22 Instantaneous Abrasive Cutting Thickness in UAMEGIn the present paper the instantaneous abrasive cuttingthickness (ℎ) is defined as the distance between trajectories ofthe cutting abrasive and the former abrasive in the directionparallel to the surface Real abrasive cutting thickness isdetermined by the trajectories of several adjacent abrasivesBut considering the feasibility of modeling and gradual waneof the influence of the abrasives increasingly distant fromthe cutting abrasive only two adjacent abrasives are takeninto account in this work The geometrical schematic ofinstantaneous abrasive cutting thickness according to thetrajectories of the two adjacent abrasives is shown in Figure 2and is mathematically modeled in this sectionThemodelingis based on the following hypothesis abrasives are well

Shock and Vibration 3

Oi + 1

A

B

h

L

Oi

O

r

r

w

A f

N

M xQ

y

120596s

Figure 2 Geometrical schematic of instantaneous abrasive cuttingthickness

distributed with uniform size deformation and run out ofthe wheel are negligible the wheel end face is parallel toworkpiece surface ultrasonic amplitude and frequency keepsteady in machining process

The time when the former abrasive (here defined as the(119894 + 1)th abrasive) moves to point 119876 and the cutting abrasive(here defined as the 119894th abrasive) moves to point119873 is definedas start time 119905

119861is defined as the time when the 119894th abrasive

moves to point 119861 (119909119905119861 119910119905119861) along the dashed line At the same

time the center of the wheel moves to point119874119894 Point 119860 (119909

119905119860

119910119905119860) is the intersection of trajectory of the (119894 + 1)th abrasive

and the extension line of 119897119861119874119894

The (119894 + 1)th abrasive moves topoint 119860 at 119905

119860and the center of the wheel moves to point119874

119894+1

at the same timeBased on the principles of geometry instantaneous abra-

sive cutting thickness of the (119894 + 1)th abrasive at 119905119860can be

expressed as follows

ℎ119905119860

119894+1= radic1199032 + 1198712 minus 2119903119871 cos [120596

119904(119905119860minus Δ119905)] minus 119903 (1)

where Δ119905(Δ119905

= 1119898119899) is defined as the time differenceaccording to the phase difference of these two adjacentabrasives which is equal to the time that the (119894+1)th abrasivemoves from point 119873 to point 119872 119898 is the quantity of all theabrasives in themost exteriormargin ofmicrowheel end face119899is spindle speed and 119871 is the distance between 119874

119894and 119874

119894+1

Consider

119871 = 1199090119894+1

minus 119909119900119894 (2)

where 119909119905119861

119874119894and 119909

119905119860

119874119894+1are the 119909 position of the wheel center

at 119905119861and 119905119860 respectively which can be further expressed as

follows

119909119905119860

119874119894+1= V119908sdot 119905119860+ 119860 sdot sin (120596

119891sdot 119905119860)

119909119905119861

119874119894= V119908sdot 119905119861+ 119860 sdot sin (120596

119891sdot 119905119861)

(3)

Then the line 119897119861119874119894

can be given as follows

119897119861119874119894

119910119905119861

= (119909119905119861minus 119909119905119861

119874119894) tan (120596

119904sdot 119905119861) (4)

minus145 minus14 minus135 minus13 minus125 minus12

times10minus3

h gt 0 the abrasive cuts into material

h lt 0 the abrasive withdraws from uncut materialsminus5

0

5

h(120583

m)

tA (s)

Figure 3 Instantaneous abrasive cutting thickness (ℎ) about 119905

during half a wheel rotating cycle

Table 1 Simulation test parameters

Parameter A (120583m) f (kHz) n (rmin) V119908(120583ms) r (120583m)

Value 3 20 9 times 103 300 1500

The trajectory of the (119894 + 1)th abrasive in UAMEG can beexpressed by

119909119894+1

= V119908119905 + 119903 cos (120596

119904(119905 minus (119894 + 1) Δ

119905)) + 119860 sin (120596

119891119905)

119910119894+1

= 119903 sin (120596119904(119905 minus (119894 + 1) Δ

119905))

(119894 = 0 1 2 )

(5)

where 120596119891(120596119891= 2120587119891) is the angular frequency of ultrasonic

vibrationBecause the point 119860 (119909

119905119860 119910119905119860) is the intersection of the

trajectory of the (119894 + 1)th abrasive and the extension lineof 119897119861119874119894

the following simultaneous equations system can bederived

119909119905119860

= V119908sdot 119905119860+ 119903 sdot cos (120596

119904sdot (119905119860minus Δ119905)) + 119860 sdot sin (120596

119891sdot 119905119860)

119910119905119860

= 119903 sdot sin (120596119904sdot (119905119860minus Δ119905))

119910119905119860

= (119909119905119860

minus 119909119905119861

119874119894) sdot tan (120596

119904sdot 119905119861)

(6)

The relationship between 119905119860and 119905119861can be obtained by solving

(6) using MATLAB Substitute it into (3) (2) and (1) thenthe final model of instantaneous abrasive cutting thickness isdeveloped

The simulation test is conducted using MATLAB undercertain conditions in Table 1

The simulation result of the instantaneous abrasive cut-ting thickness about 119905

119860in several ultrasonic cycles is shown

in Figure 3 A positive ℎ value indicates that the abrasive cutsinto unmachined materials A negative ℎ value also indicatesthe abrasive withdraws from unmachined materials It canbe seen that ℎ repetitively oscillates as analogous sine wave


Tool +P Plastic deformationenclave

(a)

ToolPlastic deformation

enclave

Median crack

+P

(b)

Median crack

Tool minusPPlastic deformationenclave

(c)


enclave

Median crack

Lateral crack

minusP

(d)

Figure 4 Indentation process of brittle materials

at ultrasonic frequency which indicates that intermittentcutting is achieved in UAMEG from the point of view ofsingle abrasive and the average value of ℎ is to be cut downsignificantly

In the grinding process single abrasive grinding force canbe expressed as follows

119865 = 119870119860120583

(ℎ) (0 lt 120583 lt 1) (7)

where 119870 is grinding force per unit grinding area whichdepends on material properties 119860

(ℎ)is the grinding cross-

sectional area and 120583 is the coefficient of frictionGrinding cross-sectional area 119860

(ℎ)is proportional to ℎ

that is 119860(ℎ)

prop ℎ Therefore assisted ultrasonic vibrationwhich leads to low average value of ℎ is to cut down theaverage value of grinding cross-sectional area 119860

(ℎ)

Furthermore when the intermittent cutting is achievedthe instantaneous gap which will exist between the face ofabrasive and unmachined material is helpful to reduce thecoefficient of friction 120583 In addition the result of Cliftonrsquosresearch about the plate-impact tests for brittle materialsdemonstrates that the dynamic fracture toughness is less than30 of the static fracture toughness Therefore consideringthe impact effect in UAMEG the dynamic fracture tough-ness which is favorable to decrease the value of119870 should beconsidered in the grinding force model for single abrasive

As a result single abrasive grinding force and thus thewhole wheel grinding force are to effectively decrease due toassisted ultrasonic vibration in UAMEG

23 Undeformed Chip Thickness and Ductile Machining inUAMEG Themachiningmechanism is greatly influenced bythe ratio of the effective cutting edge radius of the tool tothe undeformed chip thickness in micromachining Becausethe edge radius of the abrasives tends to be in the samescale with the undeformed chip thickness a small changein undeformed chip thickness significantly influences the

grinding process [5] This ratio predominantly defines theactive material removal mechanism such as brittle-ductiletransition Therefore the abrasive is assumed to be hemi-spheric to take into consideration low undeformed chipthickness in UAMEG Then ductile machining by UAMEGis analyzed in this section

Indentation tests were conducted to investigate the plas-ticity of brittle material [8 14] Crack initiation and growthduring indentation process of brittle material are shown inFigure 4 As the indenter tip penetrates into the surface ofthe sample of brittle material under small load the materialexhibits elasticitywith formation of plastically deformed zonein the form of a hemispheric enclave The bottom of thisplastic zone is conserved under high residual stresses Withthe increase of the load a crack called median crack isinitiated from the bottom of plastic zone along the axialdirection of the load During unloading half cycle the lateralcrack is initiated oriented in the lateral direction to the loadaxe As unloading continues lateral crack grows towards thesurface

Considering analogous sine waved instantaneous abra-sive cutting thickness crack initiation and growth during sin-gle abrasive cutting process in UAMEG can be interpreted asshown in Figure 5When ℎ is negative the abrasivewithdrawsfrom the uncut shoulder and only slides on the machinedsurface As ℎ increasing the abrasive cuts gradually into uncutshoulder material the material exhibits elasticity followedby formation of plastically deformed zone in the form ofa hemispheric enclave When the maximum undeformedchip thickness (119905max) exceeds the critical undeformed chipthickness (below which chips will not form) the abrasiveremoves the material via plastic deformation At some ℎ

values where 119905max and cutting force are in excess of the criticalvalues median cracks initiate and grow with increasing ℎ Asthe abrasive passed which is analogous to the unloading halfcycle the residual stresses beneath the plastic zone propagatelateral cracks Then the lateral cracks grow towards surface


Workpiece

Uncut shoulder

h lt 0

raw

(a)

Workpiece

Uncut shoulder

h = 0

raw

(b)

Uncut shoulder

Workpiece

h gt 0

raw

(c)

Workpiece

Uncut shoulder

Lateral crack

Median crack

h gt 0

raw

(d)

Figure 5 Abrasive cutting process under intermittent machining in UAMEG

of uncut shoulder and thus a part of uncut shoulder materialis to be removed via brittle pattern

According to Arif et alrsquos [9] research it is fair enoughassumed that even if median cracks and lateral cracks aregenerated the cracks can still get clear of the final machinedsurface under some certain conditions as is shown inFigure 6

Arif et al [9] demonstrate that fracture of final machinedsurface is predominantly influenced by themedian crackThelength of median crack is equal to seven times of the radiusof lateral crack that is 119862

119898= 7119862119871[15]

The critical condition that both of these two crack systemsapproach the final machined surface can be given as follows

119862119898sdot cos 120579 = 119862

119871

120579 = arccos(1

7) = 8179

∘

(8)

As the 120579 range from 0 to 8179∘ depth of damage due tomedian crack remainsmore than damage depth due to radiusof lateral crack Beyond this limit of 120579119862

119871is too small to reach

the final machined surface Thus if median cracks do notapproach the final machined surface ductile machining canbe achieved

From the geometry of Figure 6 critical condition whichobtains final fracture-free machined surface can be writtenas follows

119862119898sdot cos120601

119888+ 119903119886sdot cos 120579

119888= 119903119886 (9)

(119903119886minus 119905119888) sdot cos120601

119888= 119903119886cos 120579119888 (10)

1199032

119886+ ℎ2minus 2 sdot 119903

119886sdot ℎ119888sdot sin 120579

119888= 119903119886minus 119905119888 (11)

where 119905119888is the critical undeformed chip thickness for ductile

brittle transition 119903119886is radius of the abrasive and ℎ

119888is the

critical instantaneous abrasive cutting thickness for ductilegrinding

Then substituting (8) into (9) ℎ119888can be expressed as

follows

ℎ119888= 119903119886sdot sin 120579

119888minus radic1199032119886sdot (sin2120579

119888minus 1) + (

cos 120579119888sdot 119862119898

1 minus cos 120579119888

)

2

(12)

It can be seen from (12) that the critical median crack length119862119898leads to a limit to the critical instantaneous abrasive cut-

ting thickness ℎ119888under given abrasive radius 119903

119886and cutting

speed This defines the upper limit of material removal ratefor ductilemachining Critical instantaneous abrasive cuttingthickness increases with the decrease of critical median

Abrasivecenter

Uncut shoulder

h

h

CL

ap

Cm

tc

120579c

120601c

O

z

ra

ra

fw

Final machined surfaceSurface machined bycutting abrasive

Surfacemachinedby formerabrasive

x

Figure 6 Geometry of critical undeformed chip thickness (119905119888) of

ductile machining

crack length That means lower critical median crack lengthimproves material removal rate under ductile machining

From Lawn and Marshallrsquos [8] research the criticalmedian crack length 119862

119898can be expressed as follows

119862119898

= 1205830[1198702

119868119862

1198672] (13)

where 1205830is the geometrical constant which depends on

material properties 119867 is material hardness and 119870119868119862

ismaterial static fracture toughness

Assisted ultrasonic vibration will lead to high levelof dynamic impact load between abrasives and workpiecematerial In addition as mentioned above dynamic fracturetoughness 119870

119868119863reduces to less than 30 of 119870

119868119862for brittle

materials under impact load Thus critical median cracklength 119862

119898is to be decreased due to the assisted ultrasonic

vibration In other words ductile machining is easier tobe achieved in UAMEG Therefore higher abrasive cuttingthickness and thus higher grinding depth and feed rate whichcan be allowed for ductile machining in UAMEG comparedwith CMEG improve the material removal rate under theguarantee of high machining quality

3 Experimental Details

31 Experimental Set-Up The ultrasonic vibration assistedmicro end grinding of silica glass is conducted on a manualdevelopedmachine tool as is shown in Figure 7 which is builtfor the purpose of realizing three crucialmotions inUAMEGworkpiece ultrasonic vibration high speed grinding wheelrotation and high-accuracy feed motion


Control cabinet

Dynamometer Wheel

Motor Spindle

Workpiece

Piezoceramics

UltrasonicgeneratorHornMicrofeed

stagesAir line kit

Control unit

(a) The machine tool

z y

xo

Fixture Horn

A f

s

fGrinding wheel

Workpiece

(b) Amplified drawings

Figure 7 Experimental set-up

Ultrasonic vibration of the silica glass sample which isactually reciprocation harmonic motion with high frequencyand low amplitude is created by a piezoelectric actuator withthe input of sine voltage signal derived from an ultrasonicgenerator The vibration amplitude is amplified by a speciallydesigned acoustical waveguide booster to attain desirablevibration amplitude values on sample The silica glass sampleis adhered and fixed onto a fixture which is designed to bethe minimum dimension and weight to limit distortion ofultrasonic waveform and loss of ultrasonic energy Ultrasonicvibration of the sample with tunable amplitudes (from 3 to85 120583m) at frequency 20KHz can be achieved by changing theinput power from 02 to 08 kW

High-speed and reliable rotating motion of microdia-mond grinding wheel is supported by a high-performancespindle system The microelectroplated diamond grindingwheel (radius 1500120583m) is installed on a high speed spindle(up to 50000 rpm) with high spindle accuracy (within 1 120583m)

High-accuracy micro feed motion is created by a triaxialmicro feed system It is assembled with two precision gradelinear motor horizontal stages with position accuracy 3 120583mand bidirectional repeatability plusmn04 120583m and a precision gradeservo motor vertical stage resolution with accuracy plusmn1 120583mand bidirectional repeatability plusmn075 120583m

A three-component force dynamometer unit (Kistler9256-C2) is used for the measurement of the grinding forcesas is shown in Figure 8 The grinding forces generated ingrinding zone are to be converted into charge signal bythe piezoelectric dynamometer The multichannel chargeamplifier receives the charge signal from the dynamometerand converts it into a proportional voltageThe built-in high-pass filter is used to filter interference signal from spindlerotation A data acquisition and analysis system (DynoWare)is used for data collection and display

32 Experimental Conditions and Preparation To investi-gate particularly and contrastively the influence of aidedultrasonic vibration and grinding parameters on variationtendency of grinding forces and surface characteristics thesingle factor experiment is set up and the experimentalgrinding parameters are shown in Table 3 The dimension ofthe silica glass sample is 50 times 20 times 3mm and its materialproperties are shown in Table 2 The radius and grain size

Chargeamplifier

Wheel

Sample

Dynamometer

Data acquisition board

Dynoware

Figure 8 Schematic of force measurement instrument

Table 2 Material properties of silica glass sample

Property name ValueHardness (GPa) 62Young modulus (GPa) 820 times 10

3

Fracture toughness (MPam12) 12

of the electroplated diamond grinding wheel are 15mm and270 respectively To minimize the influence of parallelismerror of wheel end face and sample surface the experimentalsystem is adjusted using a gradienter during assembling andclamping process and repeated fine grinding is conducted onsample surface before every recorded test

4 Results and Discussion

41 Influence of Ultrasonic Vibration and Grinding Parameterson Grinding Forces Figure 9(a) shows the grinding forces incontrastive experiments with and without ultrasonic vibra-tion under the grinding conditions of 119899 = 18 times 10

4 rmin119886119901

= 2 120583m and V119908

= 100 120583ms 119865119899 119865119905 and 119865

119888denote

the normal tangential and cross feed directional grindingforce respectively It can be seen that the normal grindingforce and the tangential grinding force in experiments withultrasonic vibration are much less than those in experimentswithout ultrasonic vibrationThey reach theminimumvaluesat ultrasonic amplitude of 75120583m and then increase withultrasonic amplitude increasing to 85120583m The influence ofultrasonic assistance on cross feed direction is only minute

The influences of grinding conditions on grinding forcesin UAMEG are shown in Figures 9(b) 9(c) and 9(d)


Ft

Fc

Fn

Grin

ding

forc

e (N

)

15 25 35 45 55 65 75 85

3

25

2

15

1

05

00

Ultrasonic amplitude (120583m)

(a)

Ft-UAMEG Ft-CMEGFn-UAMEG Fn-CMEG

Wheel speed (rmin) times104

Grin

ding

forc

e (N

)

08 18 27 36

3

25

2

15

1

05

0

(b)

Grin

ding

forc

e (N

)

35

252151

3

25

2

15

1

05

Depth of cut (120583m)


(c)

40 50 60 70 80 90 100 110 120 130

Feed rate (120583ms)

Grin

ding

forc

e (N

) 3

4

25

35

45

2

15

1

05

0


(d)

Figure 9 Effects of ultrasonic amplitude and grinding parameters on grinding forces (a) Effects of ultrasonic amplitude (V119908

= 100 120583ms119886119901= 2 120583m 119899 = 18000 rmin) (b) Effects of wheel speed (V

119908= 100 120583ms 119886

119901= 2 120583m 119860 = 85 120583m) (c) Effects of depth of cut (V

119908= 100 120583ms

119899 = 18000 rmin 119860 = 85 120583m) (d) Effects of wheel feed rate (119886119901= 2 120583m 119899 = 18000 rmin 119860 = 85 120583m)

In both UAMEG and CMEG the normal grinding forcedecreases rapidly and the tangential grinding force decreasessmoothly when wheel speed increases from 8000 rmin to36000 rmin The normal grinding force increases with theincrease of depth of cut and feed rate rapidly meanwhile thetangential grinding force increases rapidly with depth of cutbut smoothly with feed rate

It is indicated from Table 4 that the variation percentagesof tangential grinding forces with the increase of wheelspeed depth of cut and feed rate in UAMEG are smallerthan those in CMEG The variation percentages of normalgrinding forces with the increase of wheel speed and feed

rate in UAMEG are larger than those in CMEG Meanwhilethe variation percentages with the increase of wheel speedin UAMEG are smaller than those in CMEG It can beconcluded that aided ultrasonic vibration weakens the effectof the increase of wheel speed on variation percentage ofnormal grinding force but strengthens the effect of theincrease of depth of cut and feed rate The aided ultrasonicvibration enhances the effect of the increase of all the threegrinding parameters on variation tangential grinding force

Considering the inhibiting effect of ultrasonic assistanceon variation percentages of the tangential grinding force withincreasing of grinding parameters larger depth of cut and


Table 3 Parameters of microgrinding experiment

Ex number A (120583m) n (rmin) 119886119901(120583m) V

119908(120583ms)

1 0 18000 2 1002 65 18000 2 1003 75 18000 2 1004 85 18000 2 1005 85 8000 2 1006 85 27000 2 1007 85 36000 2 1008 85 18000 15 1009 85 18000 25 10010 85 18000 1 10011 85 18000 1 4012 85 18000 1 7013 85 18000 1 13014 0 8000 2 10015 0 27000 2 10016 0 36000 2 10017 0 18000 15 10018 0 18000 25 10019 0 18000 1 10020 0 18000 1 4021 0 18000 1 7022 0 18000 1 130

Table 4 Variation percentages of the grinding forces withwithoutultrasonic assistance

Ex number Variation percentage ()UAMEG CMEG

Wheel speed 119865119899

minus396 minus523119865119905

minus159 minus174

Depth of cut 119865119899

1790 992119865119905

619 962

Feed rate 119865119899

2705 2583119865119905

329 420

feed rate can be adopted in UAMEG compared with CMEGwhich is helpful to improve removal rate and machining effi-ciency However ultrasonic vibration contributes to negativeaction on variation percentage of normal grinding force withthe increase of grinding parameters compared with CMEG

42 Influence of Ultrasonic Vibration andGrinding Parameterson Machined Surface It is very important to study thequality of machined surface to further investigate the effectof assisted ultrasonic vibration and grinding parameters onmachining mechanism in UAMEG Images of microtopog-raphy of the machined surfaces under six sets of conditionstaken by SEM are shown in Figure 10

In Figure 10(a) the darkness region represents complexfracture on the surface It is indicative of brittle-regimeremoval and severe surface damage It points to the factthat cracks penetrated into the final machined surface leadto complex fracture in CMEG under high instantaneous

abrasive cutting thickness and undeformed chip thicknessContrast result in UAMEG is shown in Figure 10(b) A squa-mous structure is formed on machined surface under ultra-sonic assistance with amplitude of 65 120583m which indicatesa complex process of brittle and ductile removal It can beinterpreted that intermittent cutting due to assisted ultrasonicvibration leads to the decrease of instantaneous abrasivecutting thickness and undeformed chip thickness As isinvestigated above instantaneous abrasive cutting thicknessrepetitively oscillates as analogous sine wave at ultrasonicfrequency When the instantaneous abrasive cutting thick-ness increases from zero material is removed in the form ofplastic deformationmeanwhile the plastic deformation accu-mulates and enlarges with the instantaneous abrasive cuttingthickness increasing When the maximum undeformed chipthickness is more than the critical value 119905

119888 cracks initiate and

grow As the instantaneous abrasive cutting thickness exceedsthe critical ℎ

119888value determined by (12) and (13) cracks

achieve to the final machined surface However surfacedamage and surface roughness are significantly improved dueto ultrasonic assistance

The comparison between the characteristics of surfacein Figures 10(b) 10(c) and 10(d) shows the influence ofultrasonic amplitude on machined surface It can be seenthat when the ultrasonic amplitude increases from 65 120583m to75 120583m there exists little evidence of fracture crack remainingon surface It can be explained that ultrasonic effect becomesmore significant with ultrasonic amplitude increasing Butwhen the ultrasonic amplitude increases to 85120583m fracturecracks occurring again become evenmore severe than that inFigure 10(b) as shown in Figure 10(d)This may be due to theexcessive impact power between the abrasive and materialswhen the ultrasonic amplitude increases to 85120583m

When the grinding depth decreases from 2120583m to 1 120583mas is shown in Figures 10(d) and 10(e) a squamous structuretakes the place of fracture on machined surface It indicatesthat more materials are removed in ductile region and theremaining fracture cracks are reduced with lower grindingdepth

Comparing Figures 10(d) and 10(f) it can be seenthat machined surface is improved with the wheel speedincreasing from 18000 rmin to 27000 rmin Obvious plasticploughing grooves and trivial fractures are observed onthe surface in Figure 10(f) which indicates that abrasivecutting thickness and undeformed chip thickness declinewith the increase of wheel speed and thus brittle fracture issignificantly reduced

In conclusion adding ultrasonic vibration can signif-icantly improve the quality of machined surface due tointermittent cutting which leads to the reduction of abrasivecutting thickness and undeformed chip thickness But ultra-sonic vibration with excessive amplitude is disadvantageousfor surface quality Low grinding depth and high wheel speedare beneficial to the machined surface

5 Conclusions

In this paper the promising processing method UAMEGfor hard and brittle materials is researched The effect of


(a) (b)

(c) (d)

(e) (f)

Figure 10 Surface machined at (a) 119860 = 0120583m 119886119901

= 2 120583m 119891119908

= 100 120583m 119899 = 18000 rmin (b) 119860 = 65 120583m 119886119901

= 2 120583m 119891119908

= 100 120583m119899 = 18000 rmin (c) 119860 = 75 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (d) 119860 = 85 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (e)

119860 = 85 120583m 119886119901= 1 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (f) 119860 = 85 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 27000 rmin

ultrasonic assistance on grinding forces and surface char-acteristics is theoretically and experimentally studied Thefollowing can be concluded from this study

(1) Ultrasonic assistance changes the machining mech-anism of micro end grinding from the point of viewof instantaneous abrasive cutting thickness (ℎ)Whenintermittent cutting is achieved ℎ repetitively oscil-lating as analogous sine wave at ultrasonic frequencyleads to reduction of average value of instantaneousabrasive cutting thickness

(2) Grinding forces can be significantly reduced (up to656 of normal grinding force up to 477 of tan-gential grinding force and up to 422 of cross feeddirectional grinding force) by introducing ultrasonicvibration into micro end grinding of silica glass

(3) Ultrasonic assistance gives rise to positive influencesof the variation percentage of tangential grindingforce with increase of grinding parameters because of

which larger depth of cut and feed rate can be adoptedin micro end grinding of silica glass to improvematerial removal rate and machining efficiency

(4) Intermittent cutting in micro grinding processachieved by introducing ultrasonic vibration leadsto the reduction of abrasive cutting thickness andundeformed chip thickness Therefore comparingwith CMEG the ductile machining is easier toachieve meantime the surface quality is significantlyimproved in UAMEG

(5) The aided ultrasonic vibration contributes muchinfluence to the machining mechanism of micro endgrinding which has the nature of complexity andintricacy Comprehensive models of grinding forcesurface damage and surface roughness need to beresearched for further study on the mechanism ofUAMEG


Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the Natural Science Foundationof Hebei Province of China (project nos E2012202088 andE2012202112) and Innovation Fund for Outstanding Youth ofHebei University of Technology (project no 2012011)

References

[1] T Masuzawa ldquoState of the art of micromachiningrdquo CIRPAnnalsmdashManufacturing Technology vol 49 no 2 pp 473ndash4882000

[2] E Brinksmeier Y Mutlugunes F Klocke J C Aurich P Shoreand H Ohmori ldquoUltra-precision grindingrdquo CIRP AnnalsManufacturing Technology vol 59 no 2 pp 652ndash671 2010

[3] K Ramesh H Huang L Yin and J Zhao ldquoMicrogrinding ofdeep micro grooves with high table reversal speedrdquo Interna-tional Journal of Machine Tools and Manufacture vol 44 no1 pp 39ndash49 2004

[4] A Perveen M P Jahan M Rahman and Y S Wong ldquoA studyon microgrinding of brittle and difficult-to-cut glasses usingon-machine fabricated poly crystalline diamond (PCD) toolrdquoJournal of Materials Processing Technology vol 212 no 3 pp580ndash593 2012

[5] D Dornfeld S Min and Y Takeuchi ldquoRecent advances inmechanical micromachiningrdquo CIRP AnnalsmdashManufacturingTechnology vol 55 no 2 pp 745ndash768 2006

[6] J Feng B S Kim A Shih and J Ni ldquoTool wear monitoring formicro-end grinding of ceramic materialsrdquo Journal of MaterialsProcessing Technology vol 209 no 11 pp 5110ndash5116 2009

[7] B Lawn and R Wilshaw ldquoIndentation fracture principles andapplicationsrdquo Journal of Materials Science vol 10 no 6 pp1049ndash1081 1975

[8] B R Lawn and D B Marshall ldquoHardness toughness andbrittleness an indentation analysisrdquo Journal of the AmericanCeramic Society vol 62 no 7-8 pp 347ndash350 1979

[9] M Arif M Rahman and W Yoke San ldquoAnalytical model todetermine the critical feed per edge for ductilebrittle transitionin milling process of brittle materialsrdquo International Journal ofMachine Tools and Manufacture vol 51 no 3 pp 170ndash181 2011

[10] K JunichiroPrecisionMachiningandVibrationAssistedCuttingBase and Application China Machine Press Beijing China1982

[11] T Tawakoli B Azarhoushang and M Rabiey ldquoUltrasonicassisted dry grinding of 42CrMo4rdquoThe International Journal ofAdvanced Manufacturing Technology vol 42 no 9-10 pp 883ndash891 2009

[12] T Tawakoli and B Azarhoushang ldquoInfluence of ultrasonicvibrations on dry grinding of soft steelrdquo International Journal ofMachine Tools and Manufacture vol 48 no 14 pp 1585ndash15912008

[13] J Akbari H Borzoie and M H Mamduhi ldquoStudy on ultra-sonic vibration effects on grinding process of alumina ceramic(Al2O3)rdquo World Academy of Science Engineering and Technol-

ogy vol 41 pp 785ndash789 2008

[14] D BMarshall and B R Lawn ldquoIndentation of brittlematerialsrdquoin Microindentation Techniques in Materials Science and Engi-neering P J Blau and B R Lawn Eds pp 26ndash46 AmericanSociety for Testing and Materials Philadelphia Pa USA 1986

[15] T G Bifano and S C Fawcett ldquoSpecific grinding energy as anin-process control variable for ductile-regime grindingrdquo Preci-sion Engineering vol 13 no 4 pp 256ndash262 1991

International Journal of

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Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

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Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



HQP Cutting

Gap

thicknessCutting

thickness

UAMEG CMEG

r

rr

y y

y

O xx

xO998400O

w

ws

Wheel

The cutting abrasive trajectoryThe former abrasive trajectory

Workpiece

z

o

A f

Figure 1 Machining process of UAMEG and conventional micro end grinding (CMEG)

Junichiro [10] initiated UVAM and conducted a series ofexperiments on it Comparedwith traditionalmicrogrindingthe cutting force was lowered by 30-50 the temperature incutting areawas lowered to the room temperature and highermachining accuracy and lower workpiece surface roughnesswere achieved Tawakoli et al [11] conducted comparativeexperiments of ultrasonic assisted dry grinding and con-ventional dry grinding of 42CrMo4 which demonstratedconsiderable advantages of UVAM up to 60 reductionof normal grinding force and significant improvement onthe Rz parameter Similar experiments were conducted on100Cr6 [12] and the results indicated that the aided ultrasonicvibration considerably eliminated the thermal damage ofworkpiece surface and subsurface increased the G-ratio andreduced the grinding forces (up to 60ndash70 of normal grind-ing forces and up to 30ndash50 of tangential grinding forces)Akbari et al [13] investigated the ultrasonic vibration effectson grinding process of alumina ceramic by experiments Thetestsrsquo results also indicated significant improvements surfaceroughness improved by 8 total grinding force reduced byup to about 22 and workpiece fracture strength increasedby approximately 10 on average Therefore UAMEG istreated to be a promising method to improve conventionalmicrogrinding of microparts made of hard and brittle mate-rials However research on the mechanism of this newprocessing method has not been reported so far

In this paper the influence of ultrasonic assistance onthe mechanism of this processing technology is theoreticallyanalyzed UAMEG is applied to silica glass for the first timeon amanual developedmachine tool to experimentally studythemechanism of grinding forces and surface characteristicsGrinding forces are measured by a three-component forcedynamometer unit and the surfaces are detected using scan-ning electron microscope (SEM)

2 Mechanism Analysis of UAMEG

21 Machining Process of UAMEG The machining processof UAMEG can be seen in Figure 1 The precision feed ofgrinding wheel V

119908is in the direction of 119909-axis along which

the workpiece operates simple harmonic motion with smallamplitude119860 and high frequency119891 (ultrasonic vibration)Thegrinding wheel rotates at high speed 120596

119904around the 119911-axis

which orients in cutting depth direction

From Figure 1 it can be seen that exterior marginabrasives on the grinding wheel end face firstly cut into theunmachinedmaterial which leads to shearing-forming chipsor brittle-fracture chips (here defined as the first grindingzone) inner margin abrasives only encounter the machinedmaterial whichmainly lead to sliding ploughing and repeat-edly ironing the machined material surface generated by theformer abrasives due to the spring back of material (heredefined as the second grinding zone) Therefore the cuttingthickness of exterior abrasives is much larger than cuttingthickness of inner abrasives So fracture cracks are morelikely to generate in the first grinding zone In other wordsif ductile grinding is achieved in the first grinding zone finalmachined surface free of cracks can be obtained

In Figure 1 the dashed curve refers to the trajectoryof the former abrasive which represents the profile of theunmachined regionmaterialThe solid curve is the trajectoryof the cutting abrasive In CMEG the cutting abrasivecontinuously cuts the unmachined material However thecutting mechanism is different in UAMEG When the solidcurve moves to the right of the dashed curve it indicatesthat the cutting abrasive cuts into the unmachined materialas from point 119875 to 119876 When the solid curve moves to theleft of the dashed curve as from point 119876 to 119867 the cuttingabrasive withdraws from unmachined material regionTherewill be a gap between the cutting abrasive rake face and theunmachined material Then a new cutting cycle commencesfrom point 119867 As this cutting cycle circulated at ultrasonicfrequency intermittent cutting is achieved in UAMEG

22 Instantaneous Abrasive Cutting Thickness in UAMEGIn the present paper the instantaneous abrasive cuttingthickness (ℎ) is defined as the distance between trajectories ofthe cutting abrasive and the former abrasive in the directionparallel to the surface Real abrasive cutting thickness isdetermined by the trajectories of several adjacent abrasivesBut considering the feasibility of modeling and gradual waneof the influence of the abrasives increasingly distant fromthe cutting abrasive only two adjacent abrasives are takeninto account in this work The geometrical schematic ofinstantaneous abrasive cutting thickness according to thetrajectories of the two adjacent abrasives is shown in Figure 2and is mathematically modeled in this sectionThemodelingis based on the following hypothesis abrasives are well


Oi + 1

A

B

h

L

Oi

O

r

r

w

A f

N

M xQ

y

120596s







119905119860





119894+1




ℎ119905119860

119894+1= radic1199032 + 1198712 minus 2119903119871 cos [120596

119904(119905119860minus Δ119905)] minus 119903 (1)

where Δ119905(Δ119905


119894and 119874

119894+1

Consider

119871 = 1199090119894+1

minus 119909119900119894 (2)

where 119909119905119861

119874119894and 119909

119905119860



follows

119909119905119860

119874119894+1= V119908sdot 119905119860+ 119860 sdot sin (120596

119891sdot 119905119860)

119909119905119861

119874119894= V119908sdot 119905119861+ 119860 sdot sin (120596

119891sdot 119905119861)

(3)

Then the line 119897119861119874119894


119897119861119874119894

119910119905119861

= (119909119905119861minus 119909119905119861

119874119894) tan (120596

119904sdot 119905119861) (4)


times10minus3



0

5

h(120583

m)

tA (s)





Value 3 20 9 times 103 300 1500


119909119894+1

= V119908119905 + 119903 cos (120596

119904(119905 minus (119894 + 1) Δ

119905)) + 119860 sin (120596

119891119905)

119910119894+1

= 119903 sin (120596119904(119905 minus (119894 + 1) Δ

119905))

(119894 = 0 1 2 )

(5)






119909119905119860

= V119908sdot 119905119860+ 119903 sdot cos (120596


119891sdot 119905119860)

119910119905119860


119910119905119860

= (119909119905119860

minus 119909119905119861

119874119894) sdot tan (120596

119904sdot 119905119861)

(6)









(a)


enclave

Median crack

+P

(b)

Median crack


(c)


enclave

Median crack

Lateral crack

minusP

(d)




119865 = 119870119860120583

(ℎ) (0 lt 120583 lt 1) (7)





that is 119860(ℎ)


(ℎ)









Workpiece

Uncut shoulder

h lt 0

raw

(a)

Workpiece

Uncut shoulder

h = 0

raw

(b)

Uncut shoulder

Workpiece

h gt 0

raw

(c)

Workpiece

Uncut shoulder

Lateral crack

Median crack

h gt 0

raw

(d)





119898= 7119862119871[15]


119862119898sdot cos 120579 = 119862

119871

120579 = arccos(1

7) = 8179

∘

(8)





119862119898sdot cos120601

119888+ 119903119886sdot cos 120579

119888= 119903119886 (9)

(119903119886minus 119905119888) sdot cos120601

119888= 119903119886cos 120579119888 (10)

1199032

119886+ ℎ2minus 2 sdot 119903

119886sdot ℎ119888sdot sin 120579

119888= 119903119886minus 119905119888 (11)



119888is the



follows

ℎ119888= 119903119886sdot sin 120579


119888minus 1) + (

cos 120579119888sdot 119862119898

1 minus cos 120579119888

)

2

(12)



119886and cutting


Abrasivecenter

Uncut shoulder

h

h

CL

ap

Cm

tc

120579c

120601c

O

z

ra

ra

fw



x


ductile machining




119862119898

= 1205830[1198702

119868119862

1198672] (13)













Control cabinet

Dynamometer Wheel

Motor Spindle

Workpiece

Piezoceramics


stagesAir line kit

Control unit


z y

xo

Fixture Horn

A f

s

fGrinding wheel

Workpiece








Chargeamplifier

Wheel

Sample

Dynamometer


Dynoware




3





4 rmin119886119901

= 2 120583m and V119908

= 100 120583ms 119865119899 119865119905 and 119865

119888denote




Ft

Fc

Fn

Grin

ding

forc

e (N

)

15 25 35 45 55 65 75 85

3

25

2

15

1

05

00


(a)



Grin

ding

forc

e (N

)

08 18 27 36

3

25

2

15

1

05

0

(b)

Grin

ding

forc

e (N

)

35

252151

3

25

2

15

1

05



(c)

40 50 60 70 80 90 100 110 120 130


Grin

ding

forc

e (N

) 3

4

25

35

45

2

15

1

05

0


(d)



119908= 100 120583ms 119886


119908= 100 120583ms









119908(120583ms)

1 0 18000 2 1002 65 18000 2 1003 75 18000 2 1004 85 18000 2 1005 85 8000 2 1006 85 27000 2 1007 85 36000 2 1008 85 18000 15 1009 85 18000 25 10010 85 18000 1 10011 85 18000 1 4012 85 18000 1 7013 85 18000 1 13014 0 8000 2 10015 0 27000 2 10016 0 36000 2 10017 0 18000 15 10018 0 18000 25 10019 0 18000 1 10020 0 18000 1 4021 0 18000 1 7022 0 18000 1 130




minus396 minus523119865119905

minus159 minus174


1790 992119865119905

619 962

Feed rate 119865119899

2705 2583119865119905

329 420













5 Conclusions



(a) (b)

(c) (d)

(e) (f)


= 2 120583m 119891119908

= 100 120583m 119899 = 18000 rmin (b) 119860 = 65 120583m 119886119901

= 2 120583m 119891119908

= 100 120583m119899 = 18000 rmin (c) 119860 = 75 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (d) 119860 = 85 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (e)

119860 = 85 120583m 119886119901= 1 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (f) 119860 = 85 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 27000 rmin











Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Oi + 1

A

B

h

L

Oi

O

r

r

w

A f

N

M xQ

y

120596s







119905119860





119894+1




ℎ119905119860

119894+1= radic1199032 + 1198712 minus 2119903119871 cos [120596

119904(119905119860minus Δ119905)] minus 119903 (1)

where Δ119905(Δ119905


119894and 119874

119894+1

Consider

119871 = 1199090119894+1

minus 119909119900119894 (2)

where 119909119905119861

119874119894and 119909

119905119860



follows

119909119905119860

119874119894+1= V119908sdot 119905119860+ 119860 sdot sin (120596

119891sdot 119905119860)

119909119905119861

119874119894= V119908sdot 119905119861+ 119860 sdot sin (120596

119891sdot 119905119861)

(3)

Then the line 119897119861119874119894


119897119861119874119894

119910119905119861

= (119909119905119861minus 119909119905119861

119874119894) tan (120596

119904sdot 119905119861) (4)


times10minus3



0

5

h(120583

m)

tA (s)





Value 3 20 9 times 103 300 1500


119909119894+1

= V119908119905 + 119903 cos (120596

119904(119905 minus (119894 + 1) Δ

119905)) + 119860 sin (120596

119891119905)

119910119894+1

= 119903 sin (120596119904(119905 minus (119894 + 1) Δ

119905))

(119894 = 0 1 2 )

(5)






119909119905119860

= V119908sdot 119905119860+ 119903 sdot cos (120596


119891sdot 119905119860)

119910119905119860


119910119905119860

= (119909119905119860

minus 119909119905119861

119874119894) sdot tan (120596

119904sdot 119905119861)

(6)









(a)


enclave

Median crack

+P

(b)

Median crack


(c)


enclave

Median crack

Lateral crack

minusP

(d)




119865 = 119870119860120583

(ℎ) (0 lt 120583 lt 1) (7)





that is 119860(ℎ)


(ℎ)









Workpiece

Uncut shoulder

h lt 0

raw

(a)

Workpiece

Uncut shoulder

h = 0

raw

(b)

Uncut shoulder

Workpiece

h gt 0

raw

(c)

Workpiece

Uncut shoulder

Lateral crack

Median crack

h gt 0

raw

(d)





119898= 7119862119871[15]


119862119898sdot cos 120579 = 119862

119871

120579 = arccos(1

7) = 8179

∘

(8)





119862119898sdot cos120601

119888+ 119903119886sdot cos 120579

119888= 119903119886 (9)

(119903119886minus 119905119888) sdot cos120601

119888= 119903119886cos 120579119888 (10)

1199032

119886+ ℎ2minus 2 sdot 119903

119886sdot ℎ119888sdot sin 120579

119888= 119903119886minus 119905119888 (11)



119888is the



follows

ℎ119888= 119903119886sdot sin 120579


119888minus 1) + (

cos 120579119888sdot 119862119898

1 minus cos 120579119888

)

2

(12)



119886and cutting


Abrasivecenter

Uncut shoulder

h

h

CL

ap

Cm

tc

120579c

120601c

O

z

ra

ra

fw



x


ductile machining




119862119898

= 1205830[1198702

119868119862

1198672] (13)













Control cabinet

Dynamometer Wheel

Motor Spindle

Workpiece

Piezoceramics


stagesAir line kit

Control unit


z y

xo

Fixture Horn

A f

s

fGrinding wheel

Workpiece








Chargeamplifier

Wheel

Sample

Dynamometer


Dynoware




3





4 rmin119886119901

= 2 120583m and V119908

= 100 120583ms 119865119899 119865119905 and 119865

119888denote




Ft

Fc

Fn

Grin

ding

forc

e (N

)

15 25 35 45 55 65 75 85

3

25

2

15

1

05

00


(a)



Grin

ding

forc

e (N

)

08 18 27 36

3

25

2

15

1

05

0

(b)

Grin

ding

forc

e (N

)

35

252151

3

25

2

15

1

05



(c)

40 50 60 70 80 90 100 110 120 130


Grin

ding

forc

e (N

) 3

4

25

35

45

2

15

1

05

0


(d)



119908= 100 120583ms 119886


119908= 100 120583ms









119908(120583ms)

1 0 18000 2 1002 65 18000 2 1003 75 18000 2 1004 85 18000 2 1005 85 8000 2 1006 85 27000 2 1007 85 36000 2 1008 85 18000 15 1009 85 18000 25 10010 85 18000 1 10011 85 18000 1 4012 85 18000 1 7013 85 18000 1 13014 0 8000 2 10015 0 27000 2 10016 0 36000 2 10017 0 18000 15 10018 0 18000 25 10019 0 18000 1 10020 0 18000 1 4021 0 18000 1 7022 0 18000 1 130




minus396 minus523119865119905

minus159 minus174


1790 992119865119905

619 962

Feed rate 119865119899

2705 2583119865119905

329 420













5 Conclusions



(a) (b)

(c) (d)

(e) (f)


= 2 120583m 119891119908

= 100 120583m 119899 = 18000 rmin (b) 119860 = 65 120583m 119886119901

= 2 120583m 119891119908

= 100 120583m119899 = 18000 rmin (c) 119860 = 75 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (d) 119860 = 85 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (e)

119860 = 85 120583m 119886119901= 1 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (f) 119860 = 85 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 27000 rmin











Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











(a)


enclave

Median crack

+P

(b)

Median crack


(c)


enclave

Median crack

Lateral crack

minusP

(d)




119865 = 119870119860120583

(ℎ) (0 lt 120583 lt 1) (7)





that is 119860(ℎ)


(ℎ)









Workpiece

Uncut shoulder

h lt 0

raw

(a)

Workpiece

Uncut shoulder

h = 0

raw

(b)

Uncut shoulder

Workpiece

h gt 0

raw

(c)

Workpiece

Uncut shoulder

Lateral crack

Median crack

h gt 0

raw

(d)





119898= 7119862119871[15]


119862119898sdot cos 120579 = 119862

119871

120579 = arccos(1

7) = 8179

∘

(8)





119862119898sdot cos120601

119888+ 119903119886sdot cos 120579

119888= 119903119886 (9)

(119903119886minus 119905119888) sdot cos120601

119888= 119903119886cos 120579119888 (10)

1199032

119886+ ℎ2minus 2 sdot 119903

119886sdot ℎ119888sdot sin 120579

119888= 119903119886minus 119905119888 (11)



119888is the



follows

ℎ119888= 119903119886sdot sin 120579


119888minus 1) + (

cos 120579119888sdot 119862119898

1 minus cos 120579119888

)

2

(12)



119886and cutting


Abrasivecenter

Uncut shoulder

h

h

CL

ap

Cm

tc

120579c

120601c

O

z

ra

ra

fw



x


ductile machining




119862119898

= 1205830[1198702

119868119862

1198672] (13)













Control cabinet

Dynamometer Wheel

Motor Spindle

Workpiece

Piezoceramics


stagesAir line kit

Control unit


z y

xo

Fixture Horn

A f

s

fGrinding wheel

Workpiece








Chargeamplifier

Wheel

Sample

Dynamometer


Dynoware




3





4 rmin119886119901

= 2 120583m and V119908

= 100 120583ms 119865119899 119865119905 and 119865

119888denote




Ft

Fc

Fn

Grin

ding

forc

e (N

)

15 25 35 45 55 65 75 85

3

25

2

15

1

05

00


(a)



Grin

ding

forc

e (N

)

08 18 27 36

3

25

2

15

1

05

0

(b)

Grin

ding

forc

e (N

)

35

252151

3

25

2

15

1

05



(c)

40 50 60 70 80 90 100 110 120 130


Grin

ding

forc

e (N

) 3

4

25

35

45

2

15

1

05

0


(d)



119908= 100 120583ms 119886


119908= 100 120583ms









119908(120583ms)

1 0 18000 2 1002 65 18000 2 1003 75 18000 2 1004 85 18000 2 1005 85 8000 2 1006 85 27000 2 1007 85 36000 2 1008 85 18000 15 1009 85 18000 25 10010 85 18000 1 10011 85 18000 1 4012 85 18000 1 7013 85 18000 1 13014 0 8000 2 10015 0 27000 2 10016 0 36000 2 10017 0 18000 15 10018 0 18000 25 10019 0 18000 1 10020 0 18000 1 4021 0 18000 1 7022 0 18000 1 130




minus396 minus523119865119905

minus159 minus174


1790 992119865119905

619 962

Feed rate 119865119899

2705 2583119865119905

329 420













5 Conclusions



(a) (b)

(c) (d)

(e) (f)


= 2 120583m 119891119908

= 100 120583m 119899 = 18000 rmin (b) 119860 = 65 120583m 119886119901

= 2 120583m 119891119908

= 100 120583m119899 = 18000 rmin (c) 119860 = 75 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (d) 119860 = 85 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (e)

119860 = 85 120583m 119886119901= 1 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (f) 119860 = 85 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 27000 rmin











Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Workpiece

Uncut shoulder

h lt 0

raw

(a)

Workpiece

Uncut shoulder

h = 0

raw

(b)

Uncut shoulder

Workpiece

h gt 0

raw

(c)

Workpiece

Uncut shoulder

Lateral crack

Median crack

h gt 0

raw

(d)





119898= 7119862119871[15]


119862119898sdot cos 120579 = 119862

119871

120579 = arccos(1

7) = 8179

∘

(8)





119862119898sdot cos120601

119888+ 119903119886sdot cos 120579

119888= 119903119886 (9)

(119903119886minus 119905119888) sdot cos120601

119888= 119903119886cos 120579119888 (10)

1199032

119886+ ℎ2minus 2 sdot 119903

119886sdot ℎ119888sdot sin 120579

119888= 119903119886minus 119905119888 (11)



119888is the



follows

ℎ119888= 119903119886sdot sin 120579


119888minus 1) + (

cos 120579119888sdot 119862119898

1 minus cos 120579119888

)

2

(12)



119886and cutting


Abrasivecenter

Uncut shoulder

h

h

CL

ap

Cm

tc

120579c

120601c

O

z

ra

ra

fw



x


ductile machining




119862119898

= 1205830[1198702

119868119862

1198672] (13)













Control cabinet

Dynamometer Wheel

Motor Spindle

Workpiece

Piezoceramics


stagesAir line kit

Control unit


z y

xo

Fixture Horn

A f

s

fGrinding wheel

Workpiece








Chargeamplifier

Wheel

Sample

Dynamometer


Dynoware




3





4 rmin119886119901

= 2 120583m and V119908

= 100 120583ms 119865119899 119865119905 and 119865

119888denote




Ft

Fc

Fn

Grin

ding

forc

e (N

)

15 25 35 45 55 65 75 85

3

25

2

15

1

05

00


(a)



Grin

ding

forc

e (N

)

08 18 27 36

3

25

2

15

1

05

0

(b)

Grin

ding

forc

e (N

)

35

252151

3

25

2

15

1

05



(c)

40 50 60 70 80 90 100 110 120 130


Grin

ding

forc

e (N

) 3

4

25

35

45

2

15

1

05

0


(d)



119908= 100 120583ms 119886


119908= 100 120583ms









119908(120583ms)

1 0 18000 2 1002 65 18000 2 1003 75 18000 2 1004 85 18000 2 1005 85 8000 2 1006 85 27000 2 1007 85 36000 2 1008 85 18000 15 1009 85 18000 25 10010 85 18000 1 10011 85 18000 1 4012 85 18000 1 7013 85 18000 1 13014 0 8000 2 10015 0 27000 2 10016 0 36000 2 10017 0 18000 15 10018 0 18000 25 10019 0 18000 1 10020 0 18000 1 4021 0 18000 1 7022 0 18000 1 130




minus396 minus523119865119905

minus159 minus174


1790 992119865119905

619 962

Feed rate 119865119899

2705 2583119865119905

329 420













5 Conclusions



(a) (b)

(c) (d)

(e) (f)


= 2 120583m 119891119908

= 100 120583m 119899 = 18000 rmin (b) 119860 = 65 120583m 119886119901

= 2 120583m 119891119908

= 100 120583m119899 = 18000 rmin (c) 119860 = 75 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (d) 119860 = 85 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (e)

119860 = 85 120583m 119886119901= 1 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (f) 119860 = 85 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 27000 rmin











Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Control cabinet

Dynamometer Wheel

Motor Spindle

Workpiece

Piezoceramics


stagesAir line kit

Control unit


z y

xo

Fixture Horn

A f

s

fGrinding wheel

Workpiece








Chargeamplifier

Wheel

Sample

Dynamometer


Dynoware




3





4 rmin119886119901

= 2 120583m and V119908

= 100 120583ms 119865119899 119865119905 and 119865

119888denote




Ft

Fc

Fn

Grin

ding

forc

e (N

)

15 25 35 45 55 65 75 85

3

25

2

15

1

05

00


(a)



Grin

ding

forc

e (N

)

08 18 27 36

3

25

2

15

1

05

0

(b)

Grin

ding

forc

e (N

)

35

252151

3

25

2

15

1

05



(c)

40 50 60 70 80 90 100 110 120 130


Grin

ding

forc

e (N

) 3

4

25

35

45

2

15

1

05

0


(d)



119908= 100 120583ms 119886


119908= 100 120583ms









119908(120583ms)

1 0 18000 2 1002 65 18000 2 1003 75 18000 2 1004 85 18000 2 1005 85 8000 2 1006 85 27000 2 1007 85 36000 2 1008 85 18000 15 1009 85 18000 25 10010 85 18000 1 10011 85 18000 1 4012 85 18000 1 7013 85 18000 1 13014 0 8000 2 10015 0 27000 2 10016 0 36000 2 10017 0 18000 15 10018 0 18000 25 10019 0 18000 1 10020 0 18000 1 4021 0 18000 1 7022 0 18000 1 130




minus396 minus523119865119905

minus159 minus174


1790 992119865119905

619 962

Feed rate 119865119899

2705 2583119865119905

329 420













5 Conclusions



(a) (b)

(c) (d)

(e) (f)


= 2 120583m 119891119908

= 100 120583m 119899 = 18000 rmin (b) 119860 = 65 120583m 119886119901

= 2 120583m 119891119908

= 100 120583m119899 = 18000 rmin (c) 119860 = 75 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (d) 119860 = 85 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (e)

119860 = 85 120583m 119886119901= 1 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (f) 119860 = 85 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 27000 rmin











Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Ft

Fc

Fn

Grin

ding

forc

e (N

)

15 25 35 45 55 65 75 85

3

25

2

15

1

05

00


(a)



Grin

ding

forc

e (N

)

08 18 27 36

3

25

2

15

1

05

0

(b)

Grin

ding

forc

e (N

)

35

252151

3

25

2

15

1

05



(c)

40 50 60 70 80 90 100 110 120 130


Grin

ding

forc

e (N

) 3

4

25

35

45

2

15

1

05

0


(d)



119908= 100 120583ms 119886


119908= 100 120583ms









119908(120583ms)

1 0 18000 2 1002 65 18000 2 1003 75 18000 2 1004 85 18000 2 1005 85 8000 2 1006 85 27000 2 1007 85 36000 2 1008 85 18000 15 1009 85 18000 25 10010 85 18000 1 10011 85 18000 1 4012 85 18000 1 7013 85 18000 1 13014 0 8000 2 10015 0 27000 2 10016 0 36000 2 10017 0 18000 15 10018 0 18000 25 10019 0 18000 1 10020 0 18000 1 4021 0 18000 1 7022 0 18000 1 130




minus396 minus523119865119905

minus159 minus174


1790 992119865119905

619 962

Feed rate 119865119899

2705 2583119865119905

329 420













5 Conclusions



(a) (b)

(c) (d)

(e) (f)


= 2 120583m 119891119908

= 100 120583m 119899 = 18000 rmin (b) 119860 = 65 120583m 119886119901

= 2 120583m 119891119908

= 100 120583m119899 = 18000 rmin (c) 119860 = 75 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (d) 119860 = 85 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (e)

119860 = 85 120583m 119886119901= 1 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (f) 119860 = 85 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 27000 rmin











Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119908(120583ms)

1 0 18000 2 1002 65 18000 2 1003 75 18000 2 1004 85 18000 2 1005 85 8000 2 1006 85 27000 2 1007 85 36000 2 1008 85 18000 15 1009 85 18000 25 10010 85 18000 1 10011 85 18000 1 4012 85 18000 1 7013 85 18000 1 13014 0 8000 2 10015 0 27000 2 10016 0 36000 2 10017 0 18000 15 10018 0 18000 25 10019 0 18000 1 10020 0 18000 1 4021 0 18000 1 7022 0 18000 1 130




minus396 minus523119865119905

minus159 minus174


1790 992119865119905

619 962

Feed rate 119865119899

2705 2583119865119905

329 420













5 Conclusions



(a) (b)

(c) (d)

(e) (f)


= 2 120583m 119891119908

= 100 120583m 119899 = 18000 rmin (b) 119860 = 65 120583m 119886119901

= 2 120583m 119891119908

= 100 120583m119899 = 18000 rmin (c) 119860 = 75 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (d) 119860 = 85 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (e)

119860 = 85 120583m 119886119901= 1 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (f) 119860 = 85 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 27000 rmin











Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)

(c) (d)

(e) (f)


= 2 120583m 119891119908

= 100 120583m 119899 = 18000 rmin (b) 119860 = 65 120583m 119886119901

= 2 120583m 119891119908

= 100 120583m119899 = 18000 rmin (c) 119860 = 75 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (d) 119860 = 85 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (e)

119860 = 85 120583m 119886119901= 1 120583m 119891

119908= 100 120583m 119899 = 18000 rmin (f) 119860 = 85 120583m 119886

119901= 2 120583m 119891

119908= 100 120583m 119899 = 27000 rmin











Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Acknowledgments


References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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