Modeling of plasma spraying process to manufacture hybrid materials

Computer-Aided Design 39 (2007) 1120–1133www.elsevier.com/locate/cad

Modeling of plasma spraying process to manufacture hybrid materials

Feng Wanga, Ke-Zhang Chena,∗, Xin-An Fengb

a Department of Mechanical Engineering, The University of Hong Kong, Hong Kongb School of Mechanical Engineering, Dalian University of Technology, Dalian, China

Received 19 September 2006; accepted 6 September 2007

Abstract

A component, which has an optimized combination of different materials in its different portions for a specific application, is consideredas the component made of a multiphase perfect material. To fabricate such components, a hybrid layered manufacturing process was proposedand applies spraying, engraving, and refinishing technologies, among which the spraying step is the key technology for generating a coating ofhybrid materials with their required volume fractions in every unit volume. To manufacture such a coating, it is important to study the sprayingcharacteristics. This paper intends to establish the behavior model of plasma spraying, to implement the virtual manufacturing according to thebehavior model, to analyze the volume fraction error of material constituents and to optimize the related technological parameters to eliminate thevolume fraction error, thus providing the reliable basis for future real manufacturing.c© 2007 Elsevier Ltd. All rights reserved.

Keywords: Virtual prototyping; Virtual manufacturing; Behavior simulation; Plasma spraying; Hybrid layered manufacturing; Multiphase perfect material

1. Introduction

With the rapid development of high technology innumerous fields, some components/products are required topossess a range of special functionalities, which results fromthe materials exhibiting specific properties (e.g., negativePoisson’s ratio, zero thermal expansion coefficients, etc.). Sincehomogeneous materials cannot satisfy these requirements,attention has been paid to heterogeneous materials, whichmay include composite materials (CMs), functionally gradedmaterials (FGMs) and materials with a periodic microstructure(MPMs). However, different portions of a component may havedifferent special requirements. If the component is made of asingle homogeneous or heterogeneous material, the materialused may not meet all the special requirements in its differentportions, or may be redundant in some of its portions even if thematerial can meet all the requirements in some cases. To satisfyall the requirements, it would be necessary to use componentsmade of different materials, including homogeneous materialsand the three types of heterogeneous materials, thus meetingall the special requirements in different portions and also

∗ Corresponding author. Tel.: +852 2859 2630; fax: +852 2858 5415.E-mail address: [email protected] (K.-Z. Chen).

0010-4485/$ - see front matter c© 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.cad.2007.09.002

making the best use of different materials. Such componentscan be compared to certain natural organisms (e.g., bamboo,tooth and bone), which have perfect combinations of materialsand functions after a long time of evolution. It should beemphasized that the combination of different materials indifferent portions of a component must be optimized andshould be optimal for a special application [1]. Therefore,this can be considered as a “perfect” multiphase material,as a whole, for the special application. A component, whichhas an optimized combination of different materials (includinghomogeneous materials and different types of heterogeneousmaterials) in its different portions for a specific application, isthus considered as the component made of a multiphase perfectmaterial (CMMPM).

To design and represent such components according tothe requirements from high-technological applications, acorresponding computer-aided design method [1] (includingboth geometric and material design) and a corresponding CADmodeling method [2,3] (containing both geometric and materialinformation) have been successfully developed.

Currently, the researches about how to fabricate suchcomponents are rarely reported in the published literature.Shin et al. [4] proposed to apply layered manufacturingtechnology to fabricate heterogeneous object. However, the

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F. Wang et al. / Computer-Aided Design 39 (2007) 1120–1133 1121

existing layered manufacturing of heterogeneous objects[4–9] has some limitations and cannot satisfy the requirementfor manufacturing CMMPMs. For example, in the process ofdirect metal deposition (DMD) [4], the voids of microstructureson previous layers will be deformed due to high temperatureof laser when laser micro-cladding adds materials on thecurrent layer. Shape deposition manufacturing (SDM) [8]is not suitable to create very small and precise voidsfor periodic microstructures (at least down to less than0.1 mm) because it is difficult to fabricate the millingcutter with such small sizes. Three-dimensional printing(3DP) [9] cannot add different materials with variationalvolume fractions simultaneously for every unit volumeaccording to the specified material constituent compositionfunction. Therefore, a new hybrid layered manufacturingtechnology for fabricating such components was developed[10,11]. This 3-step hybrid manufacturing process appliesspraying (adding materials that may have different constituentswith their required volume fractions), engraving (removingmaterials from the layer to create very small and precise voidsfor periodic microstructures), and refinishing technologies(grinding/milling superfluous material to obtain required flatsurfaces and precise boundaries of the layer). Among thesesteps, the spraying is the key technology for generating the layerof multi-different materials with required volume fractionsin every unit volume. After investigations [12], atmosphericplasma spraying (APS) has been selected as the spray process,because it can control the extent of melting in various speciesand offers a unique method for composite fabrication [13,14].Currently, however, conventional plasma spraying cannot beapplied directly to manufacture the CMMPM and it needs majorimprovements to satisfy the basic requirements for spreadingtechnology. The new plasma spraying device was designedas shown in Fig. 1 and introduced in detail in a previouslypublished study [12]. To implement an accurate spraying (i.e.,the volume fractions of the sprayed material constituents cansatisfy the design requirements specified in a CAD model of thecomponent), it is important to investigate its characteristics interms of technological parameters and volume fraction errors.Since it would be risky and expensive to manufacture such aprototype machine, virtual manufacturing technology [15,16]was adopted to further study and optimize the hybrid layeredmanufacturing technology so as to provide a reliable foundationfor future real manufacturing with a much better prospect ofsuccess, a shorter lead time, and a much lower investmentcost.

This paper introduces the geometry of plasma-sprayeddeposits in Section 2, establishes the behavior modelof the spraying in Section 3, performs the behaviorsimulation of the spraying in Section 4, analyzes the volumefraction error of material constituents (i.e., the differencebetween the theoretical and the real volume fractions ofmaterial constituents) in Section 5 and optimizes the relatedtechnological parameters using simulations to eliminate thevolume fraction error in Section 6.

Fig. 1. Schematic diagram of the plasma spray system.

2. The geometry of the plasma-sprayed deposit

Plasma spraying is a versatile manufacturing technology, inwhich particles of virtually any material (if it can be synthesizedinto powder particles and if their melting temperature differsfrom their vaporization temperature by more than 200 K)are melted and accelerated in an enthalpic source (flame orplasma jet) on their high-speed path to the substrate wherethey impact and undergo rapid solidification forming a layer[12–14,17–22]. The reports from Herman et al. [13,14]showed that the chemistry of the thick layer is determinedby the composition of the feedstock, and, generally, if thespray temperature is kept to low values, minimal chemicalinteractions will occur at the interfacial layer during thedeposition process [14]. Therefore, the careful control ofthe feed rates of different material constituents can obtaindesired compositional variations [13,14], based on which theplasma spraying in this research adopted an axial, multi-feeder(i.e., three evenly distributed sub-feeders are set at 120◦ aroundthe jet axis of the main feeder system), and internal powderfeeding system, as shown in Fig. 1 [12]. The axial powderfeeding can lead to higher deposition efficiency and generate asymmetrically spread stream to form the uniform deposition nomatter how different the material constituents are. The multi-feeder system can realize multi-material deposition with therequired material composition, where each sub-feeder can feedone type of material powders by using a step motor, and its feedrate is easily controlled by changing the rotational speed of thestep motor individually. Such a design can generate the layerwith required volume fractions [12,13].

Before establishing a behavior model for plasma spraying,the geometry of plasma-sprayed deposits should be firstinvestigated since the component is built up by thesuperposition of deposits. During the spray process, thematerial distribution is not constant along the deposits. Thegeometry of plasma-sprayed deposits has been studied asa function of some plasma spraying parameters [23–25].Guessasma et al. [24] and Trifa et al. [25] validated that thecross-section profiles of deposits exhibit a Gaussian distribution

1122 F. Wang et al. / Computer-Aided Design 39 (2007) 1120–1133

Fig. 2. Gaussian distribution approximation of the deposit geometry [25].

(with correlation coefficients of the function fitting the depositmean cross-section varying from 0.83 to 0.998), as shownin Fig. 2. Due to the adoption of axial feeder systems, thedistribution of plasma-sprayed deposits is symmetrical [13,14,18,26]. Therefore, the spacial geometry of the deposits in thisresearch will be considered as presenting a Gaussian-shapeddistribution, as shown in Fig. 3, and its mathematical modelcan be expressed as follows [24]:

w(u, v) = hmaxe−(u2+v2)/2σ 2

, (1)

where u and v are the Cartesian coordinates of a point withinthe spray deposit (the center of the deposit is the origin ofthe Cartesian coordinate system), hmax expresses the highestpeak of the deposit and σ is its flattening [24]. Their valuesare dependent on the spraying parameters and can be obtainedby experiments. If the deposit width is taken as 4σ∼6σ , itsmathematical model is more accurate since about 95%–99.78%of the entire material distribution is encompassed [25], asshown in Fig. 3(b). To establish a precise deposition model, 6σ

is taken as the deposit width in this paper. The study of Trifaet al. [25] has also confirmed that the deposit has a homotheticgrowth, i.e. without changing its shape after several passes,as shown in Fig. 2. This linear deposit growth is of prime

importance because it means that deposits can be linearly addedin digital simulation and, thus, the mathematical model for thesuperposition of deposits is largely simplified.

3. Behavior modeling of the plasma spraying

If there are q material constituents (a kind of inclusionscan be regarded as a material constituent), the theoreticalvolume fraction (VFT ) of the kth material constituent, v̇k , atthe position (x, y, z) in a Cartesian coordinate system, can berepresented as:

v̇k = fk(x, y, z) (k = 1, 2, . . . , q). (2)

At every unit volume, the sum of the volume fractions of allmaterial constituents should be equal to one and can be writtenas:

q∑k=1

v̇k = 1 (k = 1, 2, . . . , q). (3)

Because Z -height is a constant in a sprayed layer, thesefunctions can be also simplified as:

fk(x, y) = { fk(x, y, z)|z = constant, k = 1, 2, . . . , q} . (4)

Theoretically, the materials of a sprayed deposit onto a substrateaccording to fk(x, y) are focused on a unit volume (x, y). If itsvolume for this unit volume (x, y) is V0, the volume of the kthmaterial constituent at this position is represented as:

Vk = fk(x, y)V0 (k = 1, 2, 3, . . . , q). (5)

These material constituent composition functions, fk , can beselected from many related literature [27] by designers basedon the requirements from applications, specified in a CADmodel of the component [2], and called theoretical spray (TS)functions. In real spraying process, when a particle strikesthe substrate, the particle may rebound from or stick on thesubstrate, i.e., the deposition efficiency is usually less thanone. For simplifying the complex problem, the deposition

Fig. 3. 3D and 2D Gaussian distributions of the spray deposit.


efficiency is usually assumed to be one in numerical studiesof plasma spraying [23,28], i.e., the particle is assumed to stickon the substrate when it strikes the substrate. Therefore, thisresearch also takes the deposition efficiency as one. Since eachsub-feeder can change its feed rate individually, the materialvolume calculated based on Eq. (5) can be fed accurately bycarefully controlling the feed rates of each sub-feeder. Thus,the required volume fractions of spayed material constituentscan be obtained.

However, since a plasma spraying deposit at the sprayingdistance is not a theoretic point or unit volume and is anarea, which is much larger than a point, its theoretical materialcomposition function, fk , specified in a CAD model of such acomponent cannot be used directly as real controlling functionof the spraying device. In order to implement accurate sprayingto generate a layer of multi-different materials with theirrequired volume fractions in every unit volume, it is necessaryto consider the real feed rate of different material compositionsin real configuration.

Since the mathematical model of the deposit is a Gaussian-shaped distribution, the unit volume V0 of the deposit can becalculated as:

V0 =

∫∫D

hmaxe−(u2+v2)/2σ 2

dudv, (6)

where the integral region D is the spraying deposit area. Inthis paper, since the radius of the integral region D is takenas 3σ (i.e., corresponding to about 99.78% of the materialdistribution), D can be expressed as:

D = {(u, v)|u2+ v2

≤ (3σ)2}. (7)

Based on Eq. (6), hmax can be written as:

hmax =V0∫∫

D e−(u2+v2)/2σ 2 dudv. (8)

By substituting Eq. (8) into Eq. (1), the distribution w can berewritten as:

w =V0e−(u2

+v2)/2σ 2∫∫D e−(u2+v2)/2σ 2 dudv

. (9)

When the nozzle moves to the position where its spray depositcovers the point (x, y) as shown in Fig. 4, the volume of thekth material constituent obtained at the point (x, y), i.e., theinfinitesimal area (du × dv), can be represented as:

dVk(x, y) = Fk[(x + u), (y + v)]w(u, v)dudv, (10)

where w, u, and v are the coordinates in a local Cartesiancoordinate system (U , V , W ); x , y and z are the globalCartesian coordinate system (X , Y , Z ) as shown in Fig. 4, Fk

is the real spraying (RS) function for controlling feed rate ofthe material constituents and varies with the changes of nozzlepositions.

During the real spraying, the total materials collected at onepoint are actually the sum of the materials sprayed onto the

Fig. 4. Reverse deduction of the real spray function.

point from the nozzle in the positions where its spraying depositcover the point, and can be obtained as:

Vk(x, y) =

∫∫D

Fk[(x + u), (y + v)]w(u, v)dudv. (11)

Substituting Eq. (5) into Eq. (11) leads to

fk(x, y)V0 =

∫∫D

Fk[(x + u), (y + v)]w(u, v)dudv. (12)

By substituting Eq. (9) into Eq. (12), Eq. (12) can be rewrittenas:

fk(x, y) =

∫∫D Fk[(x + u), (y + v)]e−(u2

+v2)/2σ 2dudv∫∫

D e−(u2+v2)/2σ 2 dudv. (13)

Eq. (13) shows the relationship between the TS functionfk(x, y) and the RS function Fk(x, y). If

k =1∫∫

D e−(u2+v2)/2σ 2 dudv, (14)

Eq. (13) is then rewritten as:

fk(x, y) = k∫∫

DFk[(x + u), (y + v)]e−(u2

+v2)/2σ 2dudv.

(15)

Since the function fk(x, y) is known and can be obtained fromthe CAD model of the component, the function Fk(x, y) canbe reversely deduced from fk(x, y) using Eq. (15). Based onthe RS function Fk(x, y), the feed rates of different materialpowders can be controlled to ensure that the volume fractionsof sprayed materials satisfy the original design requirement.

Example 1. The TS function fk(x, y) specified in the CADmodel of a component is:

fk(x, y) = ax + by + c, (16)


where a, b, and c are constants. Eq. (15) can thus be written as:

ax + by + c = k∫∫

DFk[(x + u), (y + v)]

× e−(u2+v2)/2σ 2

dudv. (17)

From this equation, the RS function, Fk(x, y), can be reverselydeduced as follows:

Fk(x, y) = (ax + by + c). (18)

This is a special example, in which the TS function fk(x, y)

and the RS function Fk (x, y) have the same expression. In mostcases, the function fk(x, y) differs from the function Fk(x, y).

Example 2. The TS function fk(x, y) specified in the CADmodel of a component is:

fk(x, y) = a0 + a1x + a2x2, (19)

where a0, a1, and a2 are constants. According to Eq. (15),Eq. (19) can be rewritten as follows:

a0 + a1x + a2x2= k

∫∫D

Fk[(x + u), (y + v)]

× e−(u2+v2)/2σ 2

dudv. (20)

Therefore, the RS function Fk (x, y) can be reversely deducedfrom Eq. (20) as:

Fk(x, y) = a0 + a1x + a2x2−

a2σ2(2 − 11e−9/2)

2(1 − e−9/2)

≈ (a0 + a1x + a2x2− a2σ

2). (21)

4. Plasma spray behavior simulation

After establishing RS of the spraying device according to thetheoretical material constituent composition function specifiedin a CAD model of a CMMPM, behavior simulation of theplasma spraying based on the RS is performed to manufacturevirtually the CMMPM for verifying that the theoretical materialconstituent composition function specified in the CAD modelcan be achieved.

4.1. Digital model of the material distribution

If a square component made of an FGM as shown in Fig. 5(a)is manufactured, the layer to be sprayed is the hatching area.In order to minimize error, the best tool path should be alongthe direction in which the variation of constituent materialsis minimal [29]. For this component, the scan path of theboundary is determined by the component boundary and thenozzle will move along the tool path in a zigzag pattern asshown in Fig. 5(b). During the manufacturing, spraying iscontinuous. In the digital simulation, however, spraying has tobe discrete; i.e., the spray device sprays once after moving eachspraying-step p. If the spraying row scanning step Prow andthe spraying column scanning step Pcol both are equal to p as

Fig. 5. Tool path of the spraying process for a square component made of anFGM.

shown in Fig. 5(b) and the sprayed material for every spraying-step is focused on a square area of side length p, the volume V0of the sprayed material can be calculated as follows:

V0 = δp2, (22)

where δ is the required thickness of the layer.In order to ensure the uniform thickness of the layer, the

material volume V0 should be equal to a constant. Accordingto the Eqs. (3) and (5), V0 can be represented as:

V0 =

q∑k=1

Vk (k = 1, 2, . . . , q), (23)

where Vk is the volume of kth material sprayed every time.By substituting Eq. (9) into Eq. (23), Eq. (23) can be

rewritten as:

w =

q∑k=1

wk (k = 1, 2, . . . , q), (24)

where wk is the distribution height of the kth sprayed materialconstituent, which can be calculated as follows:

wk =Vke−(u2

+v2)/2σ 2∫∫D e−(u2+v2)/2σ 2 dudv

. (25)

Let us assume that the area of the spray deposit on thesubstrate is included within a circle of radius R = 0.5and height hmax = 0.1. The digital model of the materialdistribution is illustrated in Fig. 6(a), in which the depositcan be discretized into 88 grids by grid lines equally spacedfrom the spray scanning step p = 0.1. The material volumeat every grid is equal to the surface integral of the Gaussian-shaped distribution w over its corresponding grid region. If the


Fig. 6. Spray digital model (n = 88).

coordinate of the center of the i th grid is (ui,vi ), the materialvolume Vi (ui , vi ) of the Gaussian-shaped distribution w overits corresponding grid region can be expressed as:

Vi (ui , vi ) =

∫ ui +p2

ui −p2

∫ vi +p2

vi −p2

wdudv. (26)

By substituting Eq. (24) into Eq. (26), Eq. (26) can be rewrittenas:

Vi (ui , vi ) =

q∑k=1

Vik(ui , vi ) (k = 1, 2, . . . q), (27)

where

Vik(ui , vi ) =

∫ ui +p2

ui −p2

∫ vi +p2

vi −p2

wkdudv (k = 1, 2, . . . , q), (28)

where i is the serial number of the grids and k is the serialnumber of the material constituents.

Dividing Vi (ui , vi ) by the grid area, the total material heightof the i th grid can be obtained as follows:

hi = Vi (ui , vi )/p2. (29)

By substituting Eq. (27) into Eq. (29), the total height can bethen expressed as:

hi (ui , vi ) =

q∑k=1

hik(ui , vi ) (k = 1, 2, . . . , q), (30)

where

hik(ui , vi ) = Vik(ui , vi )/p2 (k = 1, 2, . . . , q). (31)

4.2. Data format of material distribution

According to the above analysis, when the nozzle movesto one spray step, the data format of the digital model of the

material distribution is designed as follows:

(ui , vi , hik |i = 1, 2, . . . , n; k = 1, 2, . . . , q), (32)

where ui and vi are the coordinates in a local coordinate system,i is the serial number of the grids in the local coordinate system,n is equal to 88 as indicated in Fig. 6(a) if the deposit is dividedinto 88 grids as mentioned previously, k is the serial number ofthe material constituents, hik is the height of the kth materialconstituent sprayed in the i th grid and can be calculated usingEq. (31).

The whole spray area (i.e., the hatching region as shown inFig. 5(b)) can also be divided by grid lines with step length p,so that N grids can be obtained. The file format of the sprayedmaterial distribution simulation is designed as follows:

(X j , Y j,h jk | j = 1, 2, . . . , N ; k = 1, 2, . . . , q), (33)

where X j and Y j are the coordinates in the global coordinatesystem, j is the serial number of the grid in the globalcoordinate, k is the serial number of the material constituentsand h jk is the height of the kth material constituent sprayed inthe j th grid.

The initialization of the simulation file is performed asfollows: (i) sort out the global coordinates X j and Y j of theN grids in an ascending order according to the value of X andthen in an ascending order according to the value of Y , (ii)fill them into the simulation file in the format as shown in Eq.(33), and (iii) let the height of each grid be h jk = 0 ( j =

1, 2, . . . , N ; k = 1, 2, . . . , q).

4.3. Algorithm for calculating the height and the real volumefractions of material constituents in each grid

During the spray process, the spray device moves along thespraying path from the start point to the end point as shown inFig. 5(b). When the spray torch moves to the next spray step,the heights of the accumulated materials on each grid can becalculated according to the following algorithm:

(1) j = 0;(2) j = j + 1, i = 0;(3) Set X p = X j , Yp = Y j,;(4) Renew the spray digital model (32) for the spray position

(X p, Yp) according to the following equation:

hik(ui , vi ) = hi (ui , vi )Fik(ui , vi ) k = 1, 2, . . . , q (34)

(5) i = i + 1;(6) Retrieve q values of hik(ui , vi ) for i th grid from the spray

digital model (32);(7) Set Ax = X p + ui , Ay = Yp + vi;(8) Calculate the accumulated height at the position (Ax , Ay)

in the simulation file (33) as follows:

h jk(Ax , Ay) = h jk(Ax , Ay)

+ hik(ui , vi ) (k = 1, 2, . . . , q) (35)

(9) If i < n (n = 88), go to (5);(10) If j < N , go to (2);(11) End


Fig. 7. Simulation for spraying and comparison with VFR and VFT curves (a) virtual component after spraying, (b) virtual component after milling, (c) userinterface of volume fraction of material compositions and (d) comparison with VFR and VFT curves.

Based on the above procedure and for a given grid (x j , y j ) inthe global coordinate system, the height of the sprayed materialconstituents in the grid can be calculated, according to Eqs. (30)and (35), as follows:

h j (x j , y j ) =

q∑k=1

h jk(x j , y j ) (k = 1, 2, . . . , q), (36)

where h j (x j , y j ) is the total height and h jk(x j , y j ) is theheight of the kth material constituents. The VFR of the sprayedmaterial constituents in the grid can be calculated as:

v̇k = h jk(x j , y j )/h j (x j , y j ) (k = 1, 2, . . . , q), (37)

where v̇k is the real volume fraction (VFR) of kth material.

4.4. Simulation of the layer thickness

According to the digital model and the algorithm forcalculating the height and real volume fractions of materialconstituents, components can be virtually manufactured usinga virtual manufacturing system written by C++ and OpenGL.Taking the component with the linearly changed materialcompositions along the y-axis (Material 1: f1(y) = F1(y) =

1 − y and Material 2: f2(y) = F2(y) = 1 − f1(y) = y)shown in Fig. 5(a) as an example, a dynamic manufacturingof the sprayed layer was simulated according to the tool pathshown in Fig. 5(b). The results are shown in Fig. 7. Fig. 7(a)shows the virtual component after spraying and Fig. 7(b) the

one after further milling. If the position of the point is input, thecorresponding volume fractions of material constituents at thisposition can be obtained automatically as shown in Fig. 7(c).Then comparing VFR with the VFT , their difference can bededuced as shown in Fig. 7(d).

5. Error analyses

The difference between VFR and VFT is called the error ofvolume fraction of material constituents, which includes twoaspects of errors: one results from simulation error, the otherfrom technological parameter error. In this study, the volumefraction error of Material 1 (M1) of the component shown inFig. 5(a) is taken as an example to be investigated, and meansquare deviation (MSD) σ is introduced to evaluate the error.The smaller the value of σ , the smaller the error of volumefraction.

5.1. Simulation error

Simulation error results from the spray deposit discretiza-tion. In the digital spray model, the deposit area is divided into ngrids by grid lines spaced by the scanning step. The volume V0covered by the Gaussian-shaped distribution can be correspond-ingly decomposed into n small columns. For the i th column,its theoretical volume fraction is replaced by the mean volumefraction shown as Fig. 6(b), which results from simulation error.This error can be greatly reduced by increasing the degree of


Fig. 8. Relationship between the MSD of discretization and the DOD.

discretization (DOD). However, as DOD increases, the digitalcalculation will proliferate and this cannot match the simulationinvestigation requirements. Therefore, it is necessary to selectthe suitable DOD in order to ensure the simulation accuracy andsatisfy the simulation requirement. The MSD of discretization,σD , is represented as:

σD =

√√√√1n

n∑i=1

(Vi1 + Vi2

p × p

)2

, (38)

where Vi1 and Vi2 are respectively the volumes of prisms shownin Fig. 6(c) and (p × p) is the base-area of i th column. If thediameter D of a deposit is divided into M spray-steps (p) (i.e.,D = Mp), the relationship between MSD of discretization andDOD can be obtained and plotted in Fig. 8, which shows thatthe σD will decrease to zero with the increase in M and begin toreach a plateau for M = 20. Therefore, M = 20 can be selectedas the DOD of spraying deposit, since simulation error causedby discretization has been controlled with a smaller value.

5.2. Technological parameter error

Theoretically, it is assumed that the sprayed material isfocused on a point or unit volume, and the material at theposition (x j , y j ) is obtained in one step. According to Eqs. (5)and (29), their theoretical heights can be calculated by:

h′

j1(x j , y j ) = V0 f j1(x j , y j )/p2. (39)

However, in real situation the materials sprayed onto thesubstrate are not focused on a point, and the total materialsaccumulated at one point result from materials sprayed indifferent successive steps with variational volume fractions, asshown in Fig. 10. For example, the VF of the upper deposit(red color) is different from that of the lower deposit (greencolor). Thus, the VFR of every point is the average valueof the deposits for these times. If the deposit is smaller orthe layer is thinner, the error is smaller. Secondly, in the realconfiguration, the powder feeders feed the feedstock materialswith defined volume fractions only at regular intervals as shownin Fig. 11(a), whereas theoretical spraying (TS) functionsspecified in the CAD model is continuously varied. If theinterval is small enough, the discrete function will be close tothe continuous TS function, as shown in Fig. 11(b), and VFerror will be greatly reduced.

Fig. 9. (a) Comparisons between the VFR and the VFT curves, (b) Error curvebetween VFR and VFT .

Table 1Effect of accumulated heights on the VFR of materials sprayed

1 2 3 4 5

h j 4.01 4.01 4.01 4.01 4.01h′

j1 4.01 3.79 2.00 0.22 0h j1 3.98 3.85 2.00 0.02 0.01v̇ 100% 94.44% 50% 5.56% 0%v̇ 99.29% 95.95% 50% 4.05% 0.33%|v̇ − v̇| 0.72% 1.51% 0 1.51% 0.33%

In order to investigate the effect of technological parameterson the errors between VFR and VFT , the calculated results(h′

j1) and the real ones (h j1) are compared in Fig. 9. It canbe seen that Point 1 and 5 are corresponding to the component’sverges, Point 2 and 4 present the maximal errors, and Point 3 theminimal one. The h′

j1 and h j1 values for the five selected pointsare listed in Table 1, which indicates the difference betweenh′

j1 and h j1. Although these errors are unavoidable due to thelarger spray deposit and the material feed at intervals, theycan be reduced by optimizing related technological operatingparameters.

6. Optimization of the technological operating parameters

The technological operating parameters involve feedscheme, scanning step and spatial distributions of materialssprayed. In order to analyze the effect of the technologicalparameters on the volume fraction of the materials sprayed in alayer, the following virtual manufacturing were carried out withthe same simulation conditions: D = 20p, D = 1, h = 0.1,L = 120p, where D is the diameter of the spray deposit, p the


Fig. 10. Scheme of material accumulation. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of thisarticle.)

Fig. 11. Discretization of the TS function.

scanning step, h the height of the Gaussian-shaped distribution,and L the spray distance as shown in Fig. 12(a). The MSD ofthe material volume fraction, σVF, is represented as follows:

σVF =

√√√√ 1N

N∑i=1

(v̇i − v̇i )2. (40)

6.1. Feed scheme

The sprayed layer is accumulated by the materials fromthe spraying nozzle moving along the tool path as shown inFig. 5(b), in which the hatching area is the required area ofthe component but the region within the profiled outline is theactual sprayed area. The area beyond the hatching area is causedby spray deposit and does not satisfy the requirement in terms ofmaterial thickness. After the spray step simulation of spraying,the component with a square shape is virtually manufacturedas shown in Fig. 7(a). The cross-section of the component istrapezoidal as shown in Fig. 7(a), and the slope section will

be milled in a subsequent operation as shown in Fig. 7(b) sothat the verges of the component are at the positions ya andyb. The VFT curve of M1 is shown in Fig. 12(b) (100% M1at ya and 0% M1 at yb), for which there are two different feedschemes:

(a) M1 and M2 are simultaneously sprayed from the startingpoint y0. The VFT curve of M1 can be obtained as shownin Fig. 12(c). It can be seen from it that M1 at y0 is 100%,M1 at y1 is 0%, but M1 at ya is smaller than 100% and M1at yb is larger than 0%.

(b) M1 is sprayed alone in the range of y0 − ya, then M2 issprayed with M1 in the range of ya − yb, and finally M2 issprayed alone in the range of yb − y1. The VFT curve ofM1 for this spraying method is shown in Fig. 12(d). It canbe seen from it that M1s at y0 and ya are 100%, and M1s atyb and y1 are 0%.

According to the two feed schemes, the virtual manufac-turing processes were performed respectively. The simulation


Table 2Comparison of the volume fraction curves for different feed schemes

Fig. 12. Volume fraction curves of M1 for different feed schemes.

results are shown in Table 2, from which the following infor-mation can be obtained:

• for Scheme (a), the value σVF is smaller, and the VFR of theM1 at ya is 95.45% and that at yb is equal to 4.5%, whichcannot satisfy the design requirement;

• for Scheme (b), although its value σVF is larger, the VFR ofthe M1 at ya is 100% and that at yb is equal to 0%, whichcan satisfy the design requirement.

Fig. 13. Comparison of VFR and VFT curves and the error curve of VFR andVFT .

Therefore, it can be concluded that Scheme (b) is a morepertinent feed scheme because of its correct volume fractionof M1 at the verges, and should be adopted as the basis of thefurther investigation.

Fig. 13 shows the comparison of VFT and VFR behaviorsand the curve of their errors over a whole spraying area basedon Scheme (b). In Fig. 13, Point A and Point B are at thetwo verges of the component respectively, and Point M andPoint N have the maximal errors of volume fraction. If PointM would shift towards the left side and Point N would shifttowards the right side, the real curve could be closer to thetheoretical one, thus reducing or eliminating the errors. Thisresult can be realized by starting the spraying of M2 earlier inthe region of y0 − ya and stopping the spraying of M1 later inthe region of yb − y1. But this operation may affect the materialvolume fractions at the two verges of the component. To selectthe suitable position to feed materials M1 and M2, the virtual


Fig. 14. Feed schemes of M1 and M2.

Table 3Effect of feed schemes on the VFR of materials sprayed

D = 1, D = 20p, h = 0.1, L = 120p20p(100p) 22p(98p) 24p(96p) 26p(94p) 28p(92p) 30p(90p)

Point A (M1%) 0.987 0.993 0.997 0.999 0.999 1Point B (M1%) 0.007 0.007 0.003 0.001 0 0σVF 0.005 0.003 0.009 0.015 0.022 0.028

manufacturing process was simulated with six different feedschemes (i.e., different starting points and stopping points).These six new feed schemes were designed with the objectiveof improving the starting spray M2 when the nozzle is at thepositions: 20p, 21p, 22p, 23p, . . . , 30p, respectively, and,correspondingly, stopping spray M1 at the positions: 100p,99p, 98p, 97p, . . . , 90p, respectively, as shown in Fig. 14. Thesimulation results of VFR curves for M1 are shown in Fig. 15,and the values of σVF for the different feed schemes are listed inTable 3. It can be concluded from Table 3 that the feed schemefor 22p (called Scheme (c)) is the most suitable one (the VFRof M1 at position ya is 99.3%, that of M1 at position yb is0.007 %, and σVF is 0.003) and thus selected as the best feedscheme.

6.2. Spray scanning step

During spraying, if the spray scanning step following rowsand columns correspond both to the spraying-step p, themanufacturing efficiency (i.e., the quantity of manufacturedproducts at unit time) is lower. The diameter of a sprayingdeposit is divided into 20p as optimized in the Section 5.1.The p is a unit of discretization for digit simulation, notthe step length of numerical controlling (NC). If the sprayscanning step is larger than 20p, a material layer cannotbe formed. Within 20p, the spray scanning step could belarger than p to reduce the whole spraying time. The spray

scanning step thus adopts multispraying-step, i.e., Prow =

mp (m is an integer). After spraying a layer, the top surfaceis ground to obtain required thickness and flatness of thematerial layer for the next operation. But increasing the sprayscanning step, the undulation of the surface will be enhancedas shown in Fig. 16(a), so that the grinding operation willremove thicker layer to level off the top surface, which canaffect the accuracy of volume fraction. In order to selectsuitable scanning step, the virtual manufacturing processeswere implemented using Scheme (c) with different values ofProw (i.e., Prow = D/20, 2D/20, . . . , 12D/20). The errorcurves of volume fraction with different Prow are shown inFig. 16(b), in which the error of volume fraction increases withincreasing Prow. The relationship between σVF and Prow hasbeen plotted in Fig. 16(c). It can be seen from Fig. 16(c) thatthe value of σVF is still not increased drastically when m isincreased to 10. Therefore, the Prow should be selected equal to0.5D, thus ensuring higher manufacturing efficiency and lowererror.

6.3. Distribution of sprayed materials

The previous analyses are based on the assumption thatthe distribution of the spray material exhibits a symmetricalGaussian shape. However, during plasma spraying, thedistributions of sprayed materials are not symmetrical whenthe plasma torch adopts a non-axial feed [14,26]. In order


Fig. 15. (a) Effect of feed schemes on VFR, (b) enlarged diagram for the areaincluding Point A and (c) error curves of different feed schemes.

to find out the difference from non-axial feeds, the virtualmanufacturing process was implemented with five differentmaterial deposit distributions. The results are shown in Table 4,in which column (a) represents axially symmetrical feedand column (b)–(e) non-axially symmetrical feed. When thedistribution is not axially symmetrical, the change trendsof the real volume fraction curves are basically similar tothose observed in axially symmetrical distribution, but thereexists difference for error curves. When the distributions areequivalent to those shown in Table 4(b) and (c), the absolutevalues of the peak and bottom of the volume fraction errorcurve are identical. When the distributions follow those shownin Table 4(d) and (e), the absolute values of the peak andbottom of the volume fraction error curve are different. Fromthe σVF listed in Table 4, it can be found that the non-symmetrydistributions of materials sprayed can lead to the incrementof the error between VFR and VFT, Distributions (d) and (e)

Fig. 16. (a) Virtually fabricated component, (b) comparison of error curves ofVF for different spray scanning steps and (d) σVF for different spray scanningsteps.

have a larger increment of volume fraction error. Therefore, itappears more appropriate to select the axial feed. If non-axialfeeds are adopted, nevertheless Distributions (b) and (c) arebetter choices than any others since the values of their σVF arelower than those of Distributions (d) and (e).

7. Conclusions

In this paper, behavior modeling of the plasma sprayingin a hybrid layered manufacturing process for CMMPMs isestablished. Based on the behavior model, the real sprayfunctions for controlling the feed rates of different constituentpowders can be reversely deduced from the theoretical materialconstituent composition functions specified in a CAD modelof a CMMPM for implementing accurate spraying. By meansof virtual manufacturing for a square component made of anFGM with the linear composite change, the error between VFTand VFR is analyzed, and the related technological parametersare optimized to eliminate the errors. The simulation resultsshow that the reasonable selections for the feed scheme, thespray scanning step and the distributions of materials sprayedcan effectively reduce the error of volume fractions, and willprovide reliable bases for future real manufacturings.


Table 4Effect of the distribution of materials sprayed on the VFR of materials sprayed

Acknowledgements

The reported research is supported by CompetitiveEarmarked Research Grant of Hong Kong Research GrantsCouncil (RGC) under project code: HKU 7062/00E andUniversity Research Committee Grants (CRCG) of theUniversity of Hong Kong. The financial contribution isgratefully acknowledged.

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Modeling of plasma spraying process to manufacture hybrid materials