Research Article Grinding Parameter Optimization of Ultrasound …downloads.hindawi.com/journals/mpe/2016/7896035.pdf · 2019. 7. 30. · rather limited. However, ultrasonic vibration-aided

Research ArticleGrinding Parameter Optimization ofUltrasound-Aided Electrolytic in Process Dressing forFinishing Nanocomposite Ceramics

Fan Chen, Bo Zhao, Xiao-feng Jia, Chong-yang Zhao, and Jing-lin Tong

School of Mechanics and Power Engineering, Henan Polytechnic University, Jiaozuo 454003, China

Correspondence should be addressed to Bo Zhao; [email protected]

Received 9 April 2016; Revised 26 June 2016; Accepted 15 August 2016

Academic Editor: Yuri Vladimirovich Mikhlin

Copyright © 2016 Fan Chen et al.This is an open access article distributed under theCreativeCommonsAttribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In order to achieve the precision and efficient processing of nanocomposite ceramics, the ultrasound-aided electrolytic in processdressingmethod was proposed. But how to realize grinding parameter optimization, that is, themaximum processing efficiency, onthe premise of the assurance of best workpiece quality is a problem that needs to be solved urgently. Firstly, this research investigatedthe influence of grinding parameters on material removal rate and critical ductile depth, and their mathematic models based onthe existing models were developed to simulate the material removal process. Then, on the basis of parameter sensitivity analysisbased on partial derivative, the sensitivity models of material removal rates on grinding parameter were established and computedquantitatively byMATLAB, and the key grinding parameter for optimal grinding process was found. Finally, the theoretical analyseswere verified by experiments: thematerial removal rate increaseswith the increase of grinding parameters, including grinding depth(𝑎𝑝), axial feeding speed (𝑓𝑎), workpiece speed (𝑉𝑤), and wheel speed (𝑉𝑠); the parameter sensitivity of material removal rate wasin a descending order as 𝑎𝑝 > 𝑓𝑎 > 𝑉𝑤 > 𝑉𝑠; the most sensitive parameter (𝑎𝑝) was optimized and it was found that the bettermachining result has been obtained when 𝑎𝑝 was about 3.73 𝜇m.

1. Introduction

Nanocomposite ceramics is composite that at least one of itsphases is at nanoscale size, and this substance has revealedthat it is suitable as an alternative to overcome limitations ofmicrostructure and being monolithic, while posing prepara-tion challenges related to the control of elemental composi-tion and stoichiometry in the nanocluster phase. They havebeen used for getting better physical properties, such as a highstrength at high temperatures, show low thermal expansion,have good wear resistance, and are chemically inert, whichare superior to conventional microscale composites and canbe synthesized using simple and inexpensive technique [1].As a result, this material has become a popular research topicinmilitary, aerospace, precise instruments, andmachine-toolindustries, but the applications for it have been impeded byhigh finishing costs and by damage caused during the finish-ing process due to the material’s brittleness, poor uniformity,

low reliability, and lowmalleability [2].Therefore, developingcost-effective nanocomposites ceramic machining techniquecan significantly broaden its possible applications. To solvethe problem, researchers have examined many ultrapre-cise machining methods, such as prestressed machining,ELID grinding, magnetic abrasive polishing, and ultrasonicvibration machining [3–7]. Currently, ELID grinding andultrasonic vibration-aided grinding are considered to befairly mature methods. ELID grinding can obviously increasegrinding efficiency, but in general the influence degree israther limited. However, ultrasonic vibration-aided grindingcan improve surface quality and grinding efficiency, but itsabrasive grains cannot retain sharpness during grinding. Sowe proposed the ultrasound-aided electrolytic in processdressing (U-ELID grinding) to combine the benefits of thesetwo methods [8].

A common problem for grinding is that the choiceof process plan still counts on traditional trial cutting and

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016, Article ID 7896035, 13 pageshttp://dx.doi.org/10.1155/2016/7896035

2 Mathematical Problems in Engineering

fa

Vs

A, f

Diamond grain

Diamond grain

Plastic deformationarea

Workpiece

Indentation zone

Vw

2CL

Brittle fracture area

2aOxidation film

Ch

hd

a pc

a pc

P

Workpiece

Figure 1: Motion state of a grain on diamond wheel in U-ELID grinding.

empirical method, which heavily rely on the field engineer’sexperiences, and is poor in processing efficiency and flexibil-ity [9]. The U-ELID grinding system is complex because ofinterdependence of ultrasonic vibration and ELID grinding,the processing can be affected by many conditions, andthe processing parameters have difficulty realizing real-timemonitoring precisely. So the manufacturer is always puzzledhow to choose a best process plan of grinding process.How to realize the overall improvement of grinding quality,the maximization of economic benefits, and the biggest useof machining capacity, that is, the maximum processingefficiency being realized on the premise of the assuranceof best workpiece quality, is a problem that cannot waitto be solved [10]. Therefore, the material removal rate andcritical ductile depth models for the U-ELID grinding weredeveloped based on the principle of grinding and the existingmaterial removal models, and the effects degree modelsof various grinding parameters were obtained by partialderivative. Finally the experiments have proved the reliabilityof these models, and the rational process parameters havebeen determined, which can be used to optimize otherparameters and guide machining in the U-ELID grinding fornanocomposite ceramics.

2. Theoretical Analysis about GrindingParameter Optimization

In the U-ELID grinding, the motion state of a grain ondiamond wheel and the interaction process of a grain andworkpiece were shown in Figure 1. Parameter optimizationis to realize the maximum processing efficiency on thepremise of the assurance of best workpiece quality, whichshould mainly include two parts: machining efficiency and

machining quality. As the critical ductile depth has a greaterimpact on both material removal rate and machining surfacequality, it was necessary to theoretically analyze it in detailwhen optimizing grinding parameter.

2.1. Critical Ductile Depth. From Figure 1, we can see that theinteraction process between a grain and workpiece is similarto an indentation experiment. So, assuming the workpiecematerial is rigid-plastic, the relationship between contactforce (𝑃) and feature size (2𝑎) on the indentation experimentcan be expressed as follows [11]:

𝑃 = 𝜉 ⋅ 𝐻V ⋅ 𝑎2. (1)

In Figure 1, the material damage is controlled by plasticdeformationwhen the external load (P) is less than the criticalductile depth (𝑃𝑐), and at the moment the ductile mode isthe main material removal method, as shown in the regionwhich was bounded by green circle. However, when the loadincreases more than the critical ductile depth, more portionsof material were removed by crack propagation. Moreover,Bifano et al. [12] found that there is a radial crack at thebottom of the plastic deformation zone, and it expands inreach; during unloading, under the combined action of localplastic deformation and the stress field, the transverse crackappears and extends forward until it reaches the workpiecesurface to form the partial peeling block when satisfyingthe transversal crack expanding condition, as shown theregionwhichwas bounded by green circle and carmine circle.Wilshaw et al. [13] also described that having an externalload that is higher than the critical ductile depth can lead

Mathematical Problems in Engineering 3

to crack propagation and brittle fractures, and the criticalductile depth can be expressed as follows:

𝑃𝑐 = 𝜆0𝐾𝐼𝐶 (𝐾𝐼𝐶

𝐻V)

3

. (2)

According to the grinding working principle, we learnedthe vertical load is determined by indentation depth orgrinding depth. From Figure 1, the actual grinding depth canbe written as

𝑎 = 𝑎

𝑝𝑐⋅ tan 𝜃. (3)

In an indentation experiment there are all the contactsurfaces of diamond indenter in close contact with specimen,but in machining there are only about half. So the criticalindentation depth or the critical ductile depth of singlediamond grit can be obtained.

𝑎

𝑝𝑐=

𝐾2

𝐼𝐶

𝐻2V tan 𝜃

√

2𝜆0

𝜉

. (4)

Equation (4) was obtained in the static condition. Indynamic grinding, it was subjected to the complicated inter-mitted machining and there was a great impact when thegrit hit the workpiece, so the wearing surface differed inshape and size compared with that in the static condition,and (4) cannot reflect the real response. Since the dynamiccharacteristic is influenced by many factors in the U-ELIDgrinding such as ultrasonic and grinding parameters, in orderto simplify the analytical process, the specific impacts ofdynamic parameters on dynamic fracture toughness have notbeen further analyzed, but the total impact was considered byintroducing one coefficient (𝐾𝑑). So, in the dynamic grinding,(4) can be rewritten as follows:

𝑎

𝑝𝑐= 𝐾𝑑 ⋅

𝐾2

𝐼𝐶

𝐻2V tan 𝜃

√

2𝜆0

𝜉

. (5)

ELID, namely, electrolytic in-process dressing, can ensurein-process diamond wheel dressing by the combined effect ofboth the wheel wear and electrolysis, which not only relatesto grindingwheel surface topography and grinding depth, butalso influences the shape accuracy and the surface quality ofworkpiece [14].Therefore, when the critical ductile depth wasanalyzed, it was necessary to consider the combined effectin ELID grinding. Because the combined effect can reach adynamic equilibrium, the wheel mass loss can be representedby the electrolyte content.Using the principle of Faraday’s law,through simple integration, the electrolyte content (𝑉V) can bewritten:

𝑉V = 𝜂𝑀 ⋅ 𝐼 ⋅ 𝑡

𝑧 ⋅ 𝐹 ⋅ 𝜌

. (6)

Oxidation film on grinding wheel surface was formedby the product produced in the electrolysis and plays animportant role in the ELID grinding [15]. The thickness ofoxidation film (ℎ𝑑) can be expressed as follows [8]:

ℎ𝑑 =𝑉V

𝐴𝑎

= 𝜂

𝑀 ⋅ 𝐼 ⋅ 𝑡

𝑧 ⋅ 𝐹 ⋅ 𝜌 ⋅ 𝐴𝑎

=

𝜂 ⋅ 𝑀 ⋅ 𝑡 ⋅ 𝑈 ⋅ 𝐴𝑐

𝑧 ⋅ 𝐹 ⋅ 𝜌 ⋅ 𝐴𝑎 ⋅ 𝑅

. (7)

From Figure 1, we could find the relationship betweengrinding depth and thickness of oxidation film. Based onthese formulas, the actual critical ductile depth can beexpressed as follows:

𝑎

𝑝𝑐= 𝑎𝑝𝑐 − ℎ𝑑

= 𝐾𝑑 ⋅

𝐾2

𝐼𝐶

𝐻2V ⋅ tan 𝜃

√

2𝜆0

𝜉

−

𝜂 ⋅ 𝑀 ⋅ 𝑡 ⋅ 𝑈 ⋅ 𝐴𝑐

𝑧 ⋅ 𝐹 ⋅ 𝜌 ⋅ 𝐴𝑎 ⋅ 𝑅

.

(8)

Similarly, the actual grinding depth can be written as

𝑎

𝑝= 𝑎𝑝 −

𝜂 ⋅ 𝑀 ⋅ 𝑡 ⋅ 𝑈 ⋅ 𝐴𝑐

𝑧 ⋅ 𝐹 ⋅ 𝜌 ⋅ 𝐴𝑎 ⋅ 𝑅

. (9)

2.2. Material Removal Rate. In summary, there were twokinds of material removal: ductile mode and brittle fracturemode [16]. From Figure 1, according to the reference materi-als, the material removal rate can be expressed as [8].

𝑀𝑟 = 𝑁𝑑 ⋅ 𝑉 ⋅ 𝑆 =

{{{{{{{{

{{{{{{{{

{

𝐶𝑠 ⋅ tan 𝜃 ⋅ 𝑓𝑎 ⋅ 𝑎2

𝑝⋅ √𝑎𝑝⋅ 𝑑𝑠𝑒 ⋅ (

𝑉𝑠

𝑉𝑤

)

𝐶𝑔

⋅[

[

tan−1(𝑉𝑤

𝑉𝑠

√

𝑎

𝑝

𝑑𝑠𝑒

)]

]

𝐶𝑔

⋅ √𝑉2𝑥+ 𝑉2𝑦

𝑎

𝑝< 𝑎

𝑝𝑐

𝐶𝑠 ⋅𝜋

2

⋅ 𝐶𝐿 ⋅ 𝐶ℎ ⋅ 𝑓𝑎 ⋅ √𝑎𝑝⋅ 𝑑𝑠𝑒 ⋅ (

𝑉𝑠

𝑉𝑤

)

𝐶𝑔

⋅[

[

tan−1(𝑉𝑤

𝑉𝑠

√

𝑎

𝑝

𝑑𝑠𝑒

)]

]

𝐶𝑔

⋅ √𝑉2𝑥+ 𝑉2𝑦𝑎

𝑝> 𝑎

𝑝𝑐.

(10)

Suppose the diamond grit was adequate stiff and the workmaterial was an isotropic composite during machining. Themovement track of one diamond grit on a part of workpiecewas established in theU-ELID grinding, as shown in Figure 2.The cutting trace of single diamond grit in U-EILD grindingwas marked in red curve and its velocity equation of the

diamond grit in U-EILD grinding can be represented asfollows:

𝑉𝑥 = 𝑉𝑠 − 𝑉𝑤,

𝑉𝑦 = 𝐴 ⋅ 𝜔 ⋅ cos (𝜔 ⋅ 𝑡 + 𝜑) + 𝑓𝑎.(11)


A, fWorkpiece

Grit

fa

ap

Vw

Cutting trace

Vs

O

y

x

Figure 2: Cutting trace of a diamond grit in U-EILD grinding.

In the U-ELID grinding, geometrically generating inter-action between grits and workpiece surface was differentfrom that in the ordinary ELIDgrinding.Thiswas because theeffect by the axial ultrasonic vibration of grinding wheel andthe interaction of adjacent grains had a proportionately largerimpact on it. According to movement equation under U-ELID grinding and ELID grinding, using MATLAB, Figure 3shows the difference.

From Figure 3, the movement track was a spiral line andnot to interfere with another in the normal ELID grinding,

Adjacent grit in U-ELID grindingAdjacent grit in ELID grinding

Single grit in U-ELID grindingSingle grit in ELID grinding

1020

A, ffa

−40−30

−20−10

0

0−10

−20

−0.08−0.07−0.06−0.05−0.04−0.03−0.02−0.01

00.010.02

Z(m

m)

Y (mm)X (mm

)

Figure 3: Cutting trace of single abrasive grains in axial directionwith ultrasonic vibration.

but it was a sinusoid along the spiral and intervened with thatof other adjacent grits in theU-ELID grinding. In theU-ELIDgrinding, many sinusoids overlapped seriously and formedthe interlaced situation, increasing the removal volume ofworkpiece, which was the fundamental reason for the ultra-sonic grinding being able to greatly increase the machiningefficiency. Therefore, the weight coefficient (𝐾𝑚) was intro-duced in order to consider the influence of the ultrasonicvibration, and the material removal rate can be rewritten as

𝑀𝑟 = 𝐾𝑚 ⋅ 𝑁𝑑 ⋅ 𝑉 ⋅ 𝑆

=

{{{{{{{{{{{{

{{{{{{{{{{{{

{

𝐾𝑚 ⋅ 𝐶𝑠 ⋅ tan 𝜃 ⋅ 𝑓𝑎 ⋅ 𝑎2

𝑝⋅ √𝑎𝑝⋅ 𝑑𝑠𝑒 ⋅ (

𝑉𝑠

𝑉𝑤

)

𝐶𝑔

⋅[

[

tan−1(𝑉𝑤

𝑉𝑠

√

𝑎

𝑝

𝑑𝑠𝑒

)]

]

𝐶𝑔

⋅ √(𝑉𝑠 − 𝑉𝑤)2+[

[

[

𝐴 ⋅ 𝜔 ⋅ cos(𝜔 ⋅√𝑎𝑝⋅ 𝑑𝑠𝑒

𝑉𝑠

+ 𝜑) + 𝑓𝑎

]

]

]

2

𝑎

𝑝< 𝑎

𝑝𝑐

𝐾𝑚 ⋅ 𝐶𝑠 ⋅𝜋

2

⋅ 𝐶𝐿 ⋅ 𝐶ℎ ⋅ 𝑓𝑎 ⋅ √𝑎𝑝⋅ 𝑑𝑠𝑒 ⋅ (

𝑉𝑠

𝑉𝑤

)

𝐶𝑔

⋅[

[

tan−1(𝑉𝑤

𝑉𝑠

√

𝑎

𝑝

𝑑𝑠𝑒

)]

]

𝐶𝑔

⋅ √(𝑉𝑠 − 𝑉𝑤)2+[

[

[


𝑉𝑠

+ 𝜑) + 𝑓𝑎

]

]

]

2

𝑎

𝑝> 𝑎

𝑝𝑐,

(12)

where 𝑎𝑝= 𝑎𝑝 − (𝜂 ⋅ 𝑀 ⋅ 𝑡 ⋅ 𝑈 ⋅ 𝐴𝑐)/(𝑧 ⋅ 𝐹 ⋅ 𝜌 ⋅ 𝐴𝑎 ⋅ 𝑅).

From (12), in the U-ELID grinding, the material removalrate was determined by ultrasonic parameters, ELID elec-trical parameters, and grinding parameters. Among them,ultrasonic parameters and ELID electrical parameters haddifficulty in realizing real-time control during processing. So,in order to verify the reliability of the model, these modeswere quantitatively analyzed by MATLAB under differentgrinding parameters, and the related parameters were shownin Table 1.

After calculation, the removal model changed from duc-tile removal to brittle fracture when grinding depth wasabout 3.73 𝜇m. Due to the fact that the brittle fracture modelremoves materials in the form of large size and irregu-lar shape, the machining surface quality was deteriorated

seriously. So it can be predicted that the surface quality wasgood only when the grinding depth was less than 3.73𝜇m.Moreover, the variation of material removal rate with grind-ing parameters was shown in Figure 4.

As can be seen from Figure 4, the material removal rateincreases overall within certain boundaries; it increases asgrinding depth, axial feed velocity, and wheel speed increase.However, the workpiece speed has no obvious influence,which suggests that further increasing the workpiece speedwill not effectively increase the material removal rate andneed to consider the grinding quality to determine the scopeof workpiece speed for parameter prioritizing.

2.3. Models of Grinding Parameter Sensitivity to MaterialRemoval Rate. Parameter sensitivity mathematic models on


material removal rate can be determined via parametersensitivity based on the partial derivative. By seeking thefirst order partial differential of material removal rate with

respect to these grinding parameters, the mathematic modelsof the parameter sensitivity to material removal rate can beexpressed as follows in the U-ELID grinding:

𝜕𝑀𝑟

𝜕𝑉𝑠

=

{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{

{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{

{

𝑎2

𝑝⋅ 𝐾1 ⋅ 𝑉 ⋅ 𝑓𝑎 ⋅ √𝑎

𝑝⋅ 𝑑𝑠𝑒

{{

{{

{

[tan−1 ((𝑉𝑤/𝑉𝑠)√𝑎𝑝/𝑑𝑠𝑒)]

𝑉𝑤

−

𝑉𝑠 ⋅ √𝑎𝑝⋅ 𝑑𝑠𝑒

𝑑𝑠𝑒 ⋅ 𝑉2𝑠+ 𝑉2𝑤⋅ 𝑎𝑝

}}

}}

}

+

𝑎2

𝑝⋅ 𝑉𝑠 ⋅ 𝐾1 ⋅ 𝑓𝑎 ⋅ [tan

−1((𝑉𝑤/𝑉𝑠)√𝑎

𝑝/𝑑𝑠𝑒)]

𝑉𝑤 ⋅ 𝑉

⋅ √𝑎𝑝⋅ 𝑑𝑠𝑒

⋅

{{

{{

{

𝑉𝑠 + 𝑉𝑤 +

𝐴 ⋅ 𝜔2⋅ √𝑎𝑝⋅ 𝑑𝑠𝑒 ⋅ sin (𝜔 ⋅ √𝑎𝑝 ⋅ 𝑑𝑠𝑒/𝑉𝑠)

𝑉2𝑠

⋅[

[

[


𝑉𝑠

)+ 𝑓𝑎

]

]

]

}}

}}

}

𝑎

𝑝< 𝑎

𝑝𝑐

𝐾2 ⋅ 𝑓𝑎 ⋅ 𝑉 ⋅ √𝑎𝑝⋅ 𝑑𝑠𝑒 ⋅

{{

{{

{


𝑉𝑤

−

𝑉𝑠 ⋅ √𝑎𝑝⋅ 𝑑𝑠𝑒


}}

}}

}

+

𝑉𝑠 ⋅ 𝐾2 ⋅ 𝑓𝑎 ⋅ √𝑎𝑝⋅ 𝑑𝑠𝑒 ⋅ [tan


𝑝/𝑑𝑠𝑒)]

𝑉𝑤 ⋅ 𝑉

⋅

{{

{{

{

𝑉𝑠 + 𝑉𝑤 +

𝐴 ⋅ 𝜔2⋅ √𝑎𝑝⋅ 𝑑𝑠𝑒 ⋅ sin (𝜔 ⋅ √𝑎𝑝 ⋅ 𝑑𝑠𝑒/𝑉𝑠)

𝑉2𝑠

⋅[

[

[


𝑉𝑠

)+ 𝑓𝑎

]

]

]

}}

}}

}

𝑎

𝑝> 𝑎

𝑝𝑐,

𝜕𝑀𝑟

𝜕𝑉𝑤

=

{{{{{{{{{{{

{{{{{{{{{{{

{

𝑎2

𝑝⋅ 𝐾1 ⋅ 𝑓𝑎 ⋅ 𝑉𝑠 ⋅ √𝑎


𝑉𝑤

⋅

{{

{{

{

𝑉 ⋅ 𝑉𝑠 ⋅ √𝑎𝑝⋅ 𝑑𝑠𝑒


−

𝑉 ⋅ tan−1 ((𝑉𝑤/𝑉𝑠)√𝑎𝑝/𝑑𝑠𝑒)

𝑉𝑤

+

tan−1 ((𝑉𝑤/𝑉𝑠)√𝑎𝑝/𝑑𝑠𝑒)

𝑉 ⋅ 𝑉𝑤

}}

}}

}

𝑎

𝑝< 𝑎

𝑝𝑐

𝐾2 ⋅ 𝑓𝑎 ⋅ 𝑉𝑠

𝑉𝑤

√𝑎𝑝⋅ 𝑑𝑠𝑒 ⋅

{{

{{

{

𝑉 ⋅ 𝑉𝑠 ⋅ √𝑎𝑝⋅ 𝑑𝑠𝑒


−

𝑉 ⋅ [tan−1 ((𝑉𝑤/𝑉𝑠)√𝑎𝑝/𝑑𝑠𝑒)]

𝑉𝑤

+

tan−1 ((𝑉𝑤/𝑉𝑠)√𝑎𝑝/𝑑𝑠𝑒)

𝑉 ⋅ 𝑉𝑤

}}

}}

}

𝑎

𝑝> 𝑎

𝑝𝑐,

𝜕𝑀𝑟

𝜕𝑎𝑝

=

{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{

{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{

{

1

2

𝑎

𝑝⋅ 𝐾1 ⋅ 𝑉 ⋅ 𝑓𝑎 ⋅ √𝑎


{{

{{

{

5𝑉𝑠 ⋅ [tan−1((𝑉𝑤/𝑉𝑠)√𝑎

𝑝/𝑑𝑠𝑒)]

𝑉𝑤

+

𝑉2

𝑠⋅ √𝑎𝑝⋅ 𝑑𝑠𝑒

(𝑑𝑠𝑒 ⋅ 𝑉2𝑠+ 𝑉2𝑤⋅ 𝑎𝑝)

}}

}}

}

−

𝑎2

𝑝⋅ 𝐴 ⋅ 𝜔

2⋅ 𝐾1 ⋅ 𝑓𝑎

2𝑉𝑤 ⋅ 𝑉

⋅ √𝑎𝑝⋅ 𝑑𝑠𝑒

⋅[

[

tan−1(𝑉𝑤

𝑉𝑠

√

𝑎

𝑝

𝑑𝑠𝑒

)]

]

⋅[

[

[


𝑉𝑠

)+ 𝑓𝑎

]

]

]

⋅ sin(𝜔 ⋅√𝑎𝑝⋅ 𝑑𝑠𝑒

𝑉𝑠

) 𝑎

𝑝< 𝑎

𝑝𝑐

1

2

𝐾2 ⋅ 𝑓𝑎 ⋅ 𝑑𝑠𝑒 ⋅ 𝑉𝑠 ⋅ 𝑉 ⋅

{{

{{

{


𝑉𝑤 ⋅ √𝑎𝑝⋅ 𝑑𝑠𝑒

−

𝑉𝑠


}}

}}

}

−

𝐴 ⋅ 𝜔2⋅ 𝐾2 ⋅ 𝑓𝑎 ⋅ [tan


𝑝/𝑑𝑠𝑒)] ⋅ 𝑑𝑠𝑒

2𝑉𝑤 ⋅ 𝑉

⋅[

[

[


𝑉𝑠

)+ 𝑓𝑎

]

]

]

⋅ sin(𝜔 ⋅√𝑎𝑝⋅ 𝑑𝑠𝑒

𝑉𝑠

) 𝑎

𝑝> 𝑎

𝑝𝑐,


𝜕𝑀𝑟

𝜕𝑓𝑎

=

{{{{{{{{{{{

{{{{{{{{{{{

{

𝐾1 ⋅ 𝑎2

𝑝⋅ 𝑉𝑠

𝑉𝑤

⋅ √𝑎𝑝⋅ 𝑑𝑠𝑒 ⋅

[

[

tan−1(𝑉𝑤

𝑉𝑠

√

𝑎

𝑝

𝑑𝑠𝑒

)]

]

⋅

{{

{{

{

𝑓𝑎 ⋅ [2𝐴 ⋅ 𝜔 ⋅ cos (𝜔 ⋅ √𝑎𝑝 ⋅ 𝑑𝑠𝑒/𝑉𝑠) + 𝑓𝑎]

2𝑉

+ 𝑉

}}

}}

}

𝑎

𝑝< 𝑎

𝑝𝑐

𝐾2 ⋅ 𝑉𝑠

𝑉𝑤

⋅ √𝑎𝑝⋅ 𝑑𝑠𝑒 ⋅

[

[

tan−1(𝑉𝑤

𝑉𝑠

√

𝑎

𝑝

𝑑𝑠𝑒

)]

]

⋅

{{

{{

{

𝑓𝑎 ⋅ [2𝐴 ⋅ 𝜔 ⋅ cos (𝜔 ⋅ √𝑎𝑝 ⋅ 𝑑𝑠𝑒/𝑉𝑠) + 𝑓𝑎]

2𝑉

+ 𝑉

}}

}}

}

𝑎

𝑝> 𝑎

𝑝𝑐,

(13)

where

𝑉

= √(𝑉𝑠 − 𝑉𝑤)2+[

[

[


𝑉𝑠

)+ 𝑓𝑎

]

]

]

2

,

𝑎

𝑝= 𝑎𝑝 −

𝜂 ⋅ 𝑀 ⋅ 𝑡 ⋅ 𝑈 ⋅ 𝐴𝑐

𝑧 ⋅ 𝐹 ⋅ 𝜌 ⋅ 𝐴𝑎 ⋅ 𝑅

,

𝐾1 = 𝐾𝑚 ⋅ 𝐶𝑠 ⋅ tan 𝜃,

𝐾2 = 𝐾𝑚 ⋅ 𝐶𝑠 ⋅𝜋

2

⋅ 𝐶𝐿 ⋅ 𝐶ℎ.

(14)

These mathematical models of parameter sensitivity tomaterial removal rate were calculated by MATLAB, and therelated parameters were shown in Table 1. The change ratesof material removal rate under different grinding parameterswere shown as in Figure 5.

Figure 5 shows that grinding parameters have variousinfluences on the material removal rate. Grinding depthwas the most important, followed by axial feed velocity,then wheel speed, and then workpiece speed. In order tovalidate the reliability of these models and the correctness oftheoretical analysis, the following relevant experiments werecarried out.

3. U-ELID Grinding Experiments

3.1. Equipment and Method. Experiments were carried outon a modified CNC machine center assisted with self-designed ultrasound and ELID devices. In order to make theresultsmore comparable, the experiment used the contrastiveanalysis method, and the absence or presence of ultrasoundand ELID devices was used to control the experiment state,as shown in Table 2, and the experimental setup was shownin Figure 6.

Workpieces were held in place on the working table andrevolved under the rotating abrasive wheel, as shown in Fig-ure 6(a). Before experiments were conducted, the workpieceswere preciselymanufactured to ensure that they had the sameinner diameter. Each experiment was performed on eachparameter group and repeated ten times, and the averagevalue of the ten groups of experimental data was the finalresult. Before and after experiments, workpieces were washedwith acetone and dried in a drier for about 30 minutes, andthen the quality of workpiece was weighed with a precision

electronic balance, as shown in Figure 6(b).The experimentalconditions were described in detail in Table 3.

3.2. Results and Discussion. Under experimental conditions,grinding depth was greater than the critical ductile depthbecause it was 7 𝜇m in most experiments, so the theoreticalanalysis in the case of 𝑎𝑝 < 𝑎𝑝𝑐 can be ignored. Figures 7 and8 show the comparison between the theoretic analysis andexperimental result after data processing.

From Figures 7 and 8, the material removal rate increasesas the grinding parameters increase. Grinding depth has thegreatest impact, followed by axial feed velocity, then wheelspeed, and then workpiece speed. In addition, the change ofmaterial removal rate with the increase of grinding depthwas shown in Figure 7, and there is a prominent change inthe range of 3∼5 𝜇m, whether in theoretical or experimentalresults.Thismay be because the critical ductile depth is about3.73 𝜇m according the computational result in Section 2; themanner of material removal may transform from ductileto fracture in that range. Although the experimental databasically coincides with the theoretical analysis either inmaterial removal rate or in parameter sensitivity, there isclear difference between them.This is because, to simplify theanalysis, the theory analysis was merely to scratch the largerfactors and ignore these less important factors. Moreover,these larger factorswere described bymathematical formulas,which cannot fully express all the characteristics of thesefactors. So the theoretical analysis was just at the ideal state,and it cannot completely represent the realistic situations.But it captures the main contradiction, and we can havea deeper understanding of the U-ELID machining processand a guiding significance for the actual processing by thetheoretical analysis. To examine the accuracy of the analysis,at the same time, the surface roughness was measured underdifferent grinding depths by the White-Light Interferometryprofilometer, and the machined surface was shown in Fig-ure 9.

Figure 9 shows that when grinding depth was less than3 𝜇m, although there were some micro concavoconvex fea-tures and clear grinding traces on the machined surface,the overall surface quality was fairly good, so it can beconcluded that the manner of material removal was domi-nated by the ductile mode at this point. Along with grindingdepth increases, plowing ridges and grain traces weaken,and the workpiece surface becomes matte. This situationgradually intensifies, especially when the grinding depthwas 7 𝜇m; the surface quality decreases prominently, and


ap > apc

ap < apc ap > apcap < apc

ap > apcap < apc

ap > apcap < apc

1.00E − 05

1.00E − 04

1.00E − 03

1.00E − 02

1.00E − 01

1.00E + 00

Mat

eria

l rem

oval

rate

(mm

3/s

)

300 350 400 450 500 550 600250

fa : 2mm/sVs: 5200mm/s

Vs: 5200mm/s

1.00E − 06

1.00E − 05

1.00E − 04

1.00E − 03

1.00E − 02

1.00E − 01

1.00E + 00M

ater

ial r

emov

al ra

te (m

m3/s

)

1800 2300 2800 3300 3800 4300 48001300

Wheel speed Vs (mm/s)

ap: 7m/pass

ap: 3m/pass

ap: 7m/pass

ap: 3m/pass

ap: 3m/pass

fa : 2mm/sap: 7m/pass fa : 2mm/s

fa : 2mm/s

Vw : 500mm/s

Vw : 500mm/s

1.00E − 05

1.00E − 04

1.00E − 03

1.00E − 02

1.00E − 01

1.00E + 00

Mat

eria

l rem

oval

rate

(mm

3/s

)

2 3 4 5 6 71Grinding depth ap (m/pass)

fa : 2mm/sVs: 5200mm/s Vw : 50mm/s

1.00E − 05

1.00E − 04

1.00E − 03

1.00E − 02

1.00E − 01

1.00E + 00

Mat

eria

l rem

oval

rate

(mm

3/s

)

1.2 1.4 1.6 1.8 21

Axial feed velocity fa (mm/s)

Vs: 5200mm/s Vw : 500mm/s


Workpiece speed Vw (mm/s)

Figure 4: Comparison of theoretical analysis for material removal rate under grinding parameters.

the tiny broken particles and the scaly traces can be seenstarkly on the machined surfaces. Therefore, the materialremoval method was brittle fracture mode at this time.Based on above experimental analysis, it can be predictedthat the critical ductile depth must be in the range of 3∼5 𝜇m, which was just coinciding with the calculated resultsin Section 2. In order to make the results of evaluation morecomparable, the surface roughness, under different grindingdepths in different machining processes including ELIDgrinding (ELID), ultrasonic vibration-aided grinding (U),and U-ELID grinding (U-ELID), was measured and shownin Figure 10.

Figure 10 shows that in the U-ELID grinding the averageheight of the profile (𝑅𝑎) and the point height of irregularities(𝑅𝑧) were obviously lower than those in ELID grinding,but there was little difference compared with the ultrasonicvibration-aided grinding.Thismay be because the ultrasoundproduced the softening effect [17], and workpiece hardnessdecreases to some degree, while the electrolytic in-processdressing had less effect. So, the critical depth increases, andthe machined quality was greatly improved. Moreover, theU-ELID grinding was proved to be an efficient method ofductile machining for nanocomposite ceramics, comparedwith ELID grinding and ultrasonic vibration-aided grinding.


ap > apc

ap < apc

ap > apc

ap < apc

1900 2500 3100 3700 4300 49001300


ap: 7m/pass fa : 2mm/sVw : 500mm/s

ap: 3m/pass fa : 2mm/sVw : 500mm/s

2 3 4 5 6 71

Grinding depth ap (m/pass)

fa : 2mm/sVs: 5200mm/s Vw : 500mm/s

1.00E − 08

1.00E − 07

1.00E − 06

1.00E − 05

1.00E − 04

1.00E − 03

1.00E − 02

1.00E − 01

1.00E + 00Ra

te o

f cha

nge o

f mat

eria

l rem

oval

rate

ap > apc

ap < apc

300 350 400 450 500 550 600250

ap: 3m/pass

ap: 7m/pass fa : 2mm/sVs: 5200mm/s

fa : 2mm/sVs: 5200mm/s


1.00E − 07

1.00E − 06

1.00E − 05

1.00E − 04

1.00E − 03

1.00E − 02

1.00E − 01

1.00E + 00

Rate

of c

hang

e of m

ater

ial r

emov

al ra

te

1.00E − 02

1.00E − 01

1.00E + 00

1.00E + 01

1.00E + 02

1.00E + 03

1.00E + 04

Rate

of c

hang

e of m

ater

ial r

emov

al ra

te

ap > apc

ap < apc

1.2 1.4 1.6 1.8 21


ap: 3m/passVs: 5200mm/s Vw : 500mm/s

ap: 7m/passVs: 5200mm/s Vw : 500mm/s

1.00E − 05

1.00E − 04

1.00E − 03

1.00E − 02

1.00E − 01

1.00E + 00Ra

te o

f cha

nge o

f mat

eria

l rem

oval

rate

Figure 5: Comparison of theoretical analysis for parameter sensitivity under grinding parameters.

Ultrasonic vibration-aidedacoustic system

Electrolysis deviceof ELID

(a) Experimental setup (b) Measuring equipment

Figure 6: Experimental setup.


1.00E − 08

1.00E − 06

1.00E − 04

1.00E − 02

1.00E + 00

Mat

eria

l rem

oval

rate

(mm

3/s

)

2 3 4 5 6 71Grinding depth ap (m/pass)

3800 43002800 33001800 23001300 4800


ap: 7m/pass fa : 2mm/s

fa : 2mm/s

Theoretical resultsExperimental results


Vw : 500mm/s


0

0.2

0.4

0.6

0.8

1

Mat

eria

l rem

oval

rate

(mm

3/s

)

600250 400 450 500 550300 350



Vs: 5200mm/s


0

0.2

0.4

0.6

0.8

1M

ater

ial r

emov

al ra

te (m

m3/s

)

1.2 1.4 1.6 1.8 21


ap: 7m/pass



0

0.2

0.4

0.6

0.8

1M

ater

ial r

emov

al ra

te (m

m3/s

)

Figure 7: Comparison of theoretical and experimental analysis for material removal rate under grinding parameters.

4. Conclusions

In this study, some new formulas including material removalrate and sensitivity models of material removal rates ongrinding parameter had been proposed, calculated, andexperimented in U-ELID grinding, compared with ELIDgrinding and ultrasonic vibration-aided grinding. From thisstudy the following conclusions can be drawn:

(1) The U-ELID grinding was analyzed to create math-ematic models for material removal rate and param-eter sensitivity, which were proved reliably and have

greater significance for further optimizing otherparameters.

(2) The removal rate increases as the grinding parametersincrease. In order, the most important parameterswere grinding depth, axial feed velocity, wheel speed,and workpiece speed. Considering the machiningsurface quality, the optimal comprehensive perfor-mance was obtained when grinding depth (keyparameter) was about 3.73𝜇m.







1.00E − 06

1.00E − 05

1.00E − 04

1.00E − 03

1.00E − 02

1.00E − 01

1.00E + 00Ra

te o

f cha

nge o

f mat

eria

l rem

oval

rate

1800 2300 2800 3300 3800 4300 48001300


Vw : 500mm/s ap: 7m/pass fa : 2mm/s

1.00E − 06

1.00E − 05

1.00E − 04

1.00E − 03

1.00E − 02

1.00E − 01

1.00E + 00

Rate

of c

hang

e of m

ater

ial r

emov

al ra

te

300 350 400 450 500 550 600250

Vs: 5200mm/s

fa : 2mm/s

1.00E − 02

1.00E − 01

1.00E + 00

1.00E + 01

1.00E + 02

1.00E + 03

1.00E + 04

Rate

of c

hang

e of m

ater

ial r

emov

al ra

te

2 3 4 5 6 71

Grinding depth ap (m/pass)


ap: 7m/pass

1.00E − 06

1.00E − 05

1.00E − 04

1.00E − 03

1.00E − 02

1.00E − 01

1.00E + 00Ra

te o

f cha

nge o

f mat

eria

l rem

oval

rate

1.20 1.40 1.60 1.80 2.001.00




Figure 8: Comparison of theoretical and experimental analysis for parameter sensitivity under grinding parameters.

(3) The U-ELID grinding has a wider efficient duc-tile machining range which makes it a highly effi-ciency, ultra-precise mirror processing technologyfor nanocomposite ceramics, compared with ELIDgrinding and ultrasonic vibration-aided grinding.

Nomenclature

𝐴: Amplitude of ultrasonic vibration (𝜇m)𝐴𝑎: Effective conducting area on anode (mm

2)𝑎: Feature size on indentation (mm)𝑎𝑝: Grinding depth (mm)

𝑎

𝑝: Actual grinding depth (mm)

𝑎𝑝𝑐: Nominal critical grinding depth (mm)𝑎

𝑝𝑐: Actual critical grinding depth (mm)

𝐶𝑔: Constant caused by dynamic performanceof wheel

𝐶ℎ: Depth of transversal crack (mm)𝐶𝐿: Length of transversal crack (mm)𝐶𝑠: Static effective grains’ number per unit area

(/mm2)𝑑𝑠𝑒: Equivalent diameter of wheel (mm)𝐹: Faraday’s constant𝑓: Frequency of ultrasonic vibration (Hz)


0.450.4

0.350.3

0.250.2

0.150.1

0.050

(mm

)

0 0.1 0.2 0.3 0.4

(mm)

0

2

4

6

8

10

12

(m

)

(a) 1𝜇m

0.450.4

0.350.3

0.250.2

0.150.1

0.050

(mm

)

0 0.1 0.2 0.3 0.4

(mm)

02468101214

(m

)

(b) 3𝜇m

0.90.80.70.60.50.40.30.20.10

(mm

)

0246810121416182022

(m

)

0 0.2 0.4 0.6 0.8

(mm)

(c) 5𝜇m

0 0.2 0.4 0.6 0.8

(mm)

05101520253035

(m

)

0.90.80.70.60.50.40.30.20.10

(mm

)

(d) 7𝜇m

Figure 9: Surface topography under different grinding depths.

0

0.03

0.06

0.09

0.12

0.15

0.18

Surfa

ce ro

ughn

ess (

m

)

71 4 5 62 3

Grinding depth (m/pass)

Ra-ELID Rz-ELIDRa-U Rz-URa-U-ELID Rz-U-ELID

Figure 10: Surface roughness under different grinding depths.

𝑓𝑎: Axial feed velocity of wheel (mm/s)𝐻V: Hardness of workpiece (Pa)ℎ𝑑: Thickness of oxidation film (mm)𝐼: Current of electrolysis (A)𝐾𝐼𝐶: Fracture toughness of workpiece (Pa⋅mm)𝐾𝑚: Impact coefficient of ultrasonic vibration

on movement state

Table 1: Relevant parameters.

Objects Parameters Value

Workpiece

MaterialNano-zirconia

toughened aluminananocomposite

ceramicDensity (𝜌) 4.9 g/cm3

Fracture toughness (𝐾𝐼𝐶) 7.9Mpa⋅m1/2

Vickers hardness (𝐻V) 10.9GpaElasticity modulus 315GpaPoisson’s ratio 0.3

Average grain size 50 nmInner diameter (𝑑𝑤) 35mm

Wheel

Material Cast iron bonddiamond wheel

Concentration 100%Model W40

Outer diameter (𝑑𝑠) Φ25mmWidth 17mm

Half taper angle (𝜃) 60∘

Grindingparameters

Wheel speed (𝑉𝑠) 1.3m/s–5.2m/sWorkpiece speed (𝑉𝑤) 0.28m/s–0.5m/sAxial feed velocity (𝑓𝑎) 1mm/s-2mm/sGrinding depth (𝑎𝑝) 1 𝜇m/pass–7𝜇m/pass

Ultrasonic frequency (𝑓) 35000HzUltrasonic amplitude (𝐴) 10𝜇m


Table 2: Experiment methods.

Experiment state Ultrasonicgenerator Special power source of ELID

U-ELID grinding Open OpenELID grinding Close OpenUltrasonic grinding Open Close

Table 3: Conditions of experiment.

Parameters Conditions

Wheel truingVoltage: 120V; duty ratio:5 𝜇s : 5 𝜇s; wheel speed:1000 r/min

Wheel sharpeningTruing wheel speed: 1000 r/min;voltage: 120V; duty ratio:5 𝜇s : 5 𝜇s; electrode gap: 1mm;wheel speed: 1000 r/min

Workpieces

Nano-zirconia toughenedalumina nanocomposite ceramic,outer diameter: Φ60mm, innerdiameter: Φ35mm, height:40mm

Diamond wheelDiameter: 25mm, height: 17mm,particle size: 280#, cast ironbond, concentration: 100%

Wheel speed 1.3m/s, 2.6m/s, 3.9m/s, 5.2m/s

Workpiece speed 0.28m/s, 0.37m/s, 0.43m/s,0.5m/s

Axial feed velocity 60mm/min, 80mm/min,100mm/min, 120mm/min

Grinding depth 1 𝜇m/pass, 3𝜇m/pass, 5 𝜇m/pass,7𝜇m/pass

Grinding fluids Ratio of mother liquor todistilled water: 1 : 50

Special power supply voltage 90VDuty ratio 5 𝜇s : 5 𝜇sInterelectrode gap 0.3mm

Ultrasonic parameters Frequency: 34.835 kHz,amplitude: 10𝜇m

“#” is the grain size unit of Japan.

𝐾𝑑: Impact coefficient of dynamic parameterson dynamic fracture toughness

𝑀: Molecular weight of metal bond (g/mol)𝑁𝑑: Dynamic effective grains𝑃: External load (N)𝑃𝑐: Critical load (N)𝑅: Total resistance in ELID circuit (Ω)𝑆: Cross-sectional area (mm2)𝑡: Valid time of electrolysis (s)𝑈: Electrode voltage (V)𝑉: Relative velocity between wheel and work

piece (mm/s)𝑉𝑤: Linear velocity of work piece (mm/s)𝑉𝑠: Linear velocity of wheel (mm/s)

𝑉V: Electrolyte content (mm3)

𝑧: Valence of metallic element𝜉: Geometrical factor of diamond indenter𝜂: Current efficiency𝜃: Half-angle of indenter or grain (rad)𝜆0: Correlation coefficient𝜌: Density of metal bond (g/mol)𝜑: Initial angle of ultrasonic vibration (rad)𝜔: Angular velocity (rad/s).

Competing Interests

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

Acknowledgments

The authors sincerely acknowledge the National ScienceFoundation of China (Contract nos. 51175153 and 51475148)and the Fostering Foundation of Henan Polytechnic Univer-sity for the Excellent Ph.D. Dissertation, for their financialsupport of this research project.

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Research Article Grinding Parameter Optimization of Ultrasound …downloads.hindawi.com/journals/mpe/2016/7896035.pdf · 2019. 7. 30. · rather limited. However, ultrasonic vibration-aided