Robust Design of Composites Manufacturing Processes

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International Journal of Production Research,

Vol. 46, No. 8, 15 April 2008, 2087–2104

Robust design of composites manufacturing processes

with process simulation and optimisation methods

J. LI, C. ZHANG*, R. LIANG and B. WANG

Department of Industrial and Manufacturing Engineering, Florida Advanced

Centre for Composite Technologies (FACCT), Florida A&M University,

Florida State University College of Engineering, 2525 Pottsdamer Street,

Tallahassee, FL 32310-6046

(Revision received May 2006)

Due to the increasing variations in raw materials and manufacturing processes,composite manufacturing processes have more part-to-part variations comparedwith the metal manufacturing processes. To improve part quality consistency,tooling design optimisation is an imperative step for addressing the stochasticbehaviour of composite manufacturing processes. This paper presents anoptimisation approach for the typical composite manufacturing technique of resin transfer moulding (RTM), which minimises the sensitivity of the moulddesign to uncertain material properties by choosing appropriate locations of injection gates and vents. This paper proposes a stochastic simulation basedapproach for the RTM processes. Normal distribution and Weibull distributionwere utilised as the statistical models for representing the permeability values for

the main region and race-tracking, respectively. Based on the statistical propertiesof the permeability, a graph-based two-phase heuristic (GTPH) was adopted tominimise the flow dispersion value (a quantitative measure for part qualityconsistency) such that the process design is not sensitive to the material andprocess parameter variations.

1. Introduction

Composite manufacturing processes, such as resin transfer moulding (RTM), have

more part-to-part variations compared with the metal manufacturing processes. Thisis primarily due to the larger variations existing in the raw materials and processing

parameters. Understanding how the stochastic nature of materials and process

parameters affects the final part quality will lead to consistency in part quality.

In RTM processes, the reinforcement is cut, formed to the shape of the part and

placed in a prepared mould cavity where the release agent is applied to allow easy

removal of the final part. After closing the mould, resin is injected through the

porous fibre preform, saturating the reinforcement and expelling the air from of the

mould cavity. The de-moulding process is performed after curing. Figure 1 shows

the schematic of a RTM process. The RTM process has been widely used in

automobile and aerospace industries and its applications are expanding.

*Corresponding author. Email: [email protected]



Locations of gates and vents are key to a sound RTM tooling design. Many

deterministic optimisation studies regarding RTM process designs have been

conducted (Mathur et al . 1999, Luo et al . 2001, Jiang et al . 2002). However,

preform permeability, the physical property of the fibrous material described by

Darcy’s law (Scheidegger 1974) and a crucial parameter in flow process simulation

and optimisation, possesses certain statistical properties. This makes the determin-

istic optimisation results unreliable. As statistical modelling of permeability values is

gaining more attention, this paper presents a neighbouring search approach utilising

finite element method (FEM) and statistical method to obtain optimal locations of

injection gates and vents in which case the optimal design is insensitive to the

permeability variation. Furthermore, applications of the statistical properties of

permeability values to the process simulation are presented.

2. Methodology

In the RTM process, the major factors that determine the resin flow process and final

part quality can be grouped into two classes: deterministic factors and stochastic

factors. Deterministic factors, such as injection pressure, flow rate and mould

temperature, can be measured or controlled as desired. The primary sources of

processing uncertainty come from the preform permeability, which is dominated by

the preform microstructure, variations in rheological and kinetic properties of theresin. These uncertainties occur in different magnitudes. For example, for different

mould sizes, race-tracking permeability occurring at the edges or sharp corners of a

preform can range from two to three, up to over hundreds of times of the main

region permeability. However, the rheological and kinetic characterisation of resin,

i.e. viscosity, does not change as much as race-tracking permeability if filling time is

not excessively long. Therefore, the sources of crucial uncertain input variables are

narrowed. Only the main region permeability and race-tracking were considered as

stochastic factors in this study.

The Taguchi methodology indicates that by conducting planned experiments

under some assumptions that uncontrollable or noise variable can be preciselycontrolled, the designer can choose the levels of controllable variables to accomplish

a robust system that is insensitive to inevitable changes of the noise variables

Pump

Resin Catalyst

Fiber preform

Injection gateMixer

Vent

Figure 1. RTM process.

2088 J. Li et al.



(Fowlkes et al . 1995, Montgomery 2001, Myers et al . 2002). However, this traditional

robust design approach is not applicable to RTM mould-filling process design, even

though locations and numbers of gates and vents can be considered as controllable

variables, and race-tracking permeability can be considered as a noise variable,

since race-tracking permeability cannot be controlled in the experiments.The proposed stochastic simulation based approach for statistical characterisa-

tion of composites manufacturing processes scheme is depicted in figure 2.

The following steps are involved:

1. Statistical modelling of fibre preform permeability. Two types of statistical

distributions, normal and Weibull, are used to model the main region

permeability and race-tracking, respectively. Monte Carlo simulation

techniques are used to provide samples for stochastic simulation and tooling

optimisation.

2. RTM processes flow simulation. A major component in the methodology is

the RTMSim, a flow simulation software package developed by the authors.The RTMSim is a finite element solver for simulating the resin flow inside the

clamped mould. RTMSim visualises the resin advancement progress and

calculates the mould pressure profile and mould-filling time. By providing

the boundary conditions, such as resin viscosity, permeability values, gates

and vents locations, the flow pattern and the pressure distribution can be

obtained. An example is shown in figure 3. The seat is manufactured by the

RTM process, the injection gate is positioned at the top and the resin vent

is located at the bottom. The contour plot shows the predicted resin

advancement process.

RTMSim flow

simulation

Statistical variables

Process parameters

• Preform permeability• Resin viscosity• Injection pressure

Robust process design

• Flow process

• Part quality modeling

Optimal design

Graph-based, two-phaseheuristic algorithm

Figure 2. RTM processes robust design scheme.

Resin injection gate

Resin vent

Figure 3. Part design and flow simulation.

Robust design of composites manufacturing processes 2089



3. Robust tooling design. Since some of noise factors are not normal variables,

the traditional robust design methodology is not applicable in this study.

A simulation-based optimisation approach is proposed to achieve the design

goal. As the single flow simulation cannot provide reliable information for

the design engineers, stochastic flow simulation could serve as an alternative.Based on the permeability analysis, statistical models of permeability values

are proposed. With quantified part quality, the stochastic simulations

are performed extensively with different geometries and permeability

distributions. In this study, design variables are input into the RTMSim

program to calculate the objective function for the robust design model.

Based on the objective values and the FEM meshed geometry, a graph-based,

two-phase heuristic (GTPH) determines the searching direction and generates

new design variables to be used in the next iteration until the maximum

robustness is found. The following sections describe the details of the

proposed approach.

2.1 Statistical modelling of fibre preform permeability

In a previous research study by the authors, statistical models were used to describe

the statistically distributed permeability values. Many factors, such as material

handling, fabric structure variation and working environment, contribute to the

variation of fibre preform permeability values. However, different flow conditions

may lead to different statistical properties for the permeability values. These methods

provided the statistical insight into the RTM processes, which is important for parts

quality prediction and process control. Pan et al . (2000) and Hoes et al . (2002)

conducted experimental investigations and concluded that normal distribution issuitable for modelling average permeability values. In a recent work by the authors

(Li et al . 2005), the Weibull distribution was utilised for modelling race-tracking, also

known as channel effect, which results from misfit between the fibre preform and the

mould. The resin with faster speed at edges drags the flow in the main region and

speeds the flow advancement. The reason the Weibull distribution outperforms

the normal distribution in terms of describing the race-tracking is that Weibull

distribution has the ability to model the variables with the following properties:

(1) continuous; (2) positive; and (3) asymmetrically distributed. In the for main

region permeability, all factors contribute randomly to the permeability. Normal

distribution is appropriate as confirmed in other research work.The next logical issue is determining the distribution spreads. Wong et al .

(in press) proposed numerical methods to predict permeability based on the fabric

structure. In their research also investigated statistical variations. The ends of the

vectors representing the crossover of the towpaths were simulated according to a

normal distribution with a mean 3.86 Â 10À9 m2 and a standard deviation of

0.12 Â 10À9 m2. Other factors, such as nesting of layers also affect the scatter in

permeability values significantly. The above research work focused on the material

aspect of the permeability distribution. While in actual production, other factors,

such as working conditions, can contribute to the permeability variables that

may lead to inconsistent part quality. The relationship between permeability andits components is rather complex. Mathematical methods, such as probability

theory, cannot be used to obtain answers for the questions defined, even though the

2090 J. Li et al.



analytical solutions were derived. In this work, the objective is to seek the optimal

tooling design that is insensitive to the parameter variations. Thus, the spread of the

process parameter distribution is not a concern.

2.2 Robust design implementation

The concept of simulation before production has been utilised in almost every field

of industry. However, in the realm of RTM processes the process parameter

uncertainty impedes the broader application of simulation to the real production.

Dry spots that form by trapped air bubbles while resin is saturating the preform are

responsible for major defects in the RTM process. Positioning the vent where the

flow ends to entrap the air will ensure consistent part quality. Moreover, tooling

design cannot be changed during the course of manufacturing. In fabricating a batch

of specific parts, the permeability variations and the variations of race-tracking effect

of the fibre preforms make the ending locations of the flow diverse. Due to theuncertain process parameters, the flow does not end where desired. Therefore,

the strategy of utilising the simulation program should be investigated to resolve

the problems discussed above.

Current mathematical models for quantifying RTMed part quality have been

discussed in a previous work by the authors (Li et al . 2005). The proposed flow

ending location dispersion value method was utilised in this study. Placing the vent at

the location where the flow ends will prevent dry spot formation. Due to the fact that

permeability values possess certain statistical properties, the flow will not end at the

same position from part to part. The locations where the flow ends also possess

certain statistical properties that can be utilised to quantify the part quality.Therefore, the vents should be placed at locations that minimise the ending location

variations due to uncertainties in process parameters to maintain the consistent part

quality.

A flow ending location dispersion value D is defined to quantify the ending

location variation. As shown in figure 4, the variance of distances between locations

to the centre point of the location set is the value being evaluated.

D ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPpj ¼1 ðd j À d Þ2

p À 1

s ð1Þ

where D is dispersion value; j is j th location; p is total number of locations; d j isdistance from the j th location to the centre point of location set; d is average distance

from locations to the centre point of location set.

Using this flow dispersion value, RTM process performance can be quantified.

Generally speaking, the tooling design resulting in a smaller flow dispersion value is

better than that resulting in a larger flow dispersion value. This can be generalised for

Figure 4. Illustration of the flow ending location dispersion value.




multi-vent situations: for each vent there is an associated dispersion value.

Regardless of how complex the part is, the ending locations of the flow can be

obtained through flow simulation. Therefore, for multi-vent cases, the ending points

can be grouped into a multi-set of points as desired. Obviously, the vent should be

positioned at the centre of the points set to minimise the flow dispersion value.In the flow simulation, the finite element method was implemented for solving the

governing equations. Specifically, a control volume/FEM method was utilised because

of the moving boundary conditions. The geometry (domain) was partitioned into

many sub-domains, and the partial differential equations were solved by linear or

nonlinear approximations. Therefore, obtaining the flow dispersion value through

mathematical modelling and calculation is difficult and depends on the permeability

distribution for different regions involving normal and Weibull distributed variables.

However, regardless how complex the profile distribution of permeability values, the

flow dispersion value converges to a certain point based on its definition. Monte Carlo

simulation and the flow simulation were combined to obtain the flow dispersion value.For a complex part with statistically distributed permeability values as shown in

figures 5 and 6, 20 simulation runs is a safe lower bound to achieve the convergence.

Figure 6. Convergence plot of dispersion value.

Race-tracking regions

Main region

Figure 5. Car door FEM model.

2092 J. Li et al.



Each selected injection gate location has a minimised dispersion value. Therefore,

the optimisation problem for robust design is to seek the location or locations of

gates with smallest minimised dispersion values according to the number of gates and

vents. The smaller the dispersion value, the more robust the tooling design.

The robust design problem using optimisation method can be formulated asfollows: Let S ¼ {s1, s2, . . . , sn} be the index set that denotes the mesh node of the

mould FEM geometry, where si , i 2 {1, 2, . . . , n} denotes the i th node in finite element

mesh. This forms the search domain. Let gj 2 S ( j ¼ 1, 2, . . . , ng) be the location of the

gates, where ng is the number of gates. Let vk 2S (k ¼ 1, 2, . . . , nv) be the locations

of vents, where nv is the number of vents.

Let ’ represent the sensitivity of the current system and define as follows:

’ ¼ f ðgj ,vkÞ ð2Þ

Furthermore, other constraints exist. The values of filling time and performance

index should be as low as possible to shorten the cycle time and obtain a quality part.Thus, the optimal tooling design is the one that has short average filling time, low

average performance index and narrow range, as well as variance of performance

indices for 100 simulated filling experiments. To minimise the sensitivity, ’, with

other constrains, the following optimisation expressions were formulated:

min’ ¼ f ðgj ,vkÞ ð3Þ

s.t.

min Dðgj ,vkÞ ¼ min ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPpl ¼1 vk À nl k k À aveð vk À nl k kÞð Þ2

p À 1s for all k ¼ 1, 2, . . . , nv ð4Þ

gj 2 V , j ¼ 1,2, . . . , ng ð5Þ

vk 2 V , k ¼ 1, 2, . . . , nv ð6Þ

To test the effectiveness of the above analysis and true characteristics of the

model, a statistical sampling simulation technique was employed (Law and Kelton

1991). The Monte Carlo simulation was used to provide the statistical permeability

inputs. Specifically, Weibull and normal distributions for race-tracking and average

permeability values were used. The permeability varied each time, even though the

production condition was consistent, which made a single simulation result

unreliable. The optimisation problem described above seeks the locations of

injection gates and vents in which case the dispersion value is minimised. Since the

dispersion value is a quantity indicating the sensitiveness of the process to

the parameter variations, the optimal solution is a robust tooling design that fulfils

the design goal.

2.3 Graph-based two-phase heuristic

The model (3)–(6) is a black box optimisation problem because of the FEM

approximation. Thus, an efficient heuristic algorithm to search for satisfactorysolutions is highly desirable. Typically, a ‘Black box’ optimisation problem refers to an

optimisation problem with objective function analytically unknown. Several general




techniques are available, including general branch and bound, local search by multi-

starts, pattern search by multi-starts, sequential constructive algorithm, Tabu search,

recursive sampling, simulated annealing, and genetic algorithm (Pardalos and

Resende 2002). The advantage of these techniques is that they are independent of

problem properties. Therefore, for the model (3)–(6), all the above techniques can beimplemented to obtain a satisfactory solution. However, the large number of

simulation runs required in the problem makes implementing impractical. Ye et al .

(2004) developed an effective algorithm, known as graph-based two phases heuristic,

for this type of problem. The algorithm consists of the following steps:

1. Mould geometry simplification. A method of directed weighted graph (DWG)

is used to approximately analyze the mould geometry such that the search

domain is narrowed. The example is illustrated in figures 7 and 8.

2. Optimisation in graph. Once the graph is constructed, the optimisation

problem formulation remains the same but search domain is reduced. Since

the constructed DWG is much simpler than the original finite element mesh of the mould geometry, the computational cost is dramatically decreased. After

exhaustive enumeration search is finished, the search domain is neighboured

around the optimised vertex. A pattern search algorithm follows. This

method initially finds a search direction along the principle axes of the design

variables, and marches in that direction until no further improvement is

found. If the search does not yield improvement, a smaller search radius is

used. This search is repeated until the convergence criterion is met.

3. Case studies

In this section, different case studies are investigated using the filling process

simulation and numerical optimisation. Each case is studied with a statistically

sampled permeability values.

Figure 7. Mould geometry.

Figure 8. Graph representation.

2094 J. Li et al.



3.1 Case study I

For the seat part shown in figure 9, all edges contact the mould cavity. Ten Weibull

distributed independent permeability values were required for modelling the

race-tracking along the edges, while the permeability values for other region

remain normal variables. For each simulation run, required permeability values

are sampled from the distributed variables, ten from Weibull variables and one

from normal variables. The sample populations are shown in figure 10. Weibull

(1.638, 7.6829) and normal (1.655, 0.348) distributed variables were generated based

on previous experimental data (Li et al . 2005). Then the RTMSim was utilised for

cycle time and part quality prediction with the stochastic parameters.

The directed weighted graph approach was applied for mould geometry

simplification according to the permeability distribution. For example, race-tracking

Regions with race-tracking

Main region

Figure 9. Meshed geometry of sample part.

(a) Race-tracking (b) Average permeability

Figure 10. Permeability values generated by the specified distributions.




is present along the edges of the mould, which means points on the edge have more

weight than the points at the main regions. In addition, the search domain can be

further reduced due to part symmetry. The optimisation algorithm first evaluates all

the intersection points of the half directed weighted graph. Once an optimum is

found, the pattern search algorithm is utilised to search the neighbouring pointsaround the optimum from the first phase.

Twenty simulation runs were performed to obtain the point set. By positioning

the vent at the centre of the point set, the optimised dispersion value can be obtained.

Figure 12(a) plots the minimised dispersion values for each DWG intersection points

for the first phase. From the plot, point 2 and point 15, which are located at the

upper and lower corners, have relatively close minimised dispersion values.

Second phase optimisation started with these two points. The fine search

domain was restricted to the triangles formed by points 2 and 15 with their

neighbouring points on the DWG, shown in figure 12(b) by bold lines. The pattern

search algorithm was performed. However, for their neighbouring points on theFEM model, no improvement was achieved. Therefore, the optimisation

was stopped. The optimised tooling designs for one gate and one vent are shown

in figure 13(a) and (b).


(a) Dispersion values vs. locations of injection gate (b) Optimal solution domain

2

15

Figure 12. First phase optimisation.

2096 J. Li et al.



To evaluate the optimal tooling design, more simulation runs were performed

with statistically distributed permeability values. Due to the uncertainty of

permeability values, the mould-filling times for resin saturation were not uniform,

which led to difficulty in production scheduling and inconsistency in part quality.

The flow simulation results for the initial mould design and optimal tooling design,shown in figure 14, revealed that the filling time variation was reduced dramatically

up to 40%, indicating the optimal design is more robust and capable of maintaining

consistent part quality.

3.2 Case study II

A helicopter manifold lid was designed and evaluated for the proposed RTM flow

and Monte Carlo simulation, as shown in figure 15. The race-tracking was present

along the edge of the part and at the locations where the fabric was deformed.

The same materials were used in the simulation study. Therefore, it was assumed that

the average permeability values were statistically distributed as normal random

variables and the race-tracking effects were statistically distributed as Weibull

variables (see figure 10). The part was larger with more complex geometry than that

in the previous section.

(a) Before optimization (b) After optimization

Figure 14. Robust design evaluation.

(a) (b)

Injection gate

Vent

Injection gate

Vent

Figure 13. Robust tooling designs.




The directed weighted graph approach was applied. The mould geometry

simplification according to the permeability distribution is shown in figure 16.Due to part symmetry, placing two injection gates and two vents symmetrically on

the part may be more appropriate, which can also lead to shorter production

times. Therefore, a symmetry constrain applies in the optimisation problem. The

optimisation algorithm first evaluates all the two-point sets on the directed

weighted graph. Once an optimum is found, the pattern search algorithm is utilised

to search the neighbouring candidates around the optimum from the first phase

optimisation.

Twenty simulation runs were performed to obtain the point set. By positioning

the vent at the centre of the point set, the optimised dispersion value can be obtained.

Figure 17(a) plots the minimised dispersion values for 27 two-point sets for the firstphase optimisation. From the plot, regions formed by bold lines are identified as

potential domain for better solutions (see figure 17b).

Second phase optimisation search domains were restricted to the identified

regions, shown in figure 17(b) by bold lines. The pattern search algorithm began to

evaluate the neighbour point on the FEM model and if an improvement was found,

the continuing direction can be determined. For the circle domain, the principal

direction was determined toward the centre of the round portion. The optimal design

was found by placing two injection gates at the centres of the left and right portions

of the part and positioning two vents at the two bottom ends (see figure 18a).

In another sub-domain, when the search began from the bottom, a slightimprovement was observed along the principal direction, which is toward the

centre of the whole part. The final solution was found where two injection gates were


Main region

Figure 15. Meshed geometry with varying permeability of the lid.


2098 J. Li et al.



positioned adjacently at the centre of the part and the vents were located at the two

bottom ends (see figure 18b).

In figure 19, simulated mould-filling times for resin saturation with the

distributed process parameter are plotted in histogram. Initially, the filling timesranged from 410 seconds to 600 seconds. After optimizing with the new of gate and

vent locations, the filling time range narrowed significantly from 450 seconds to 530

seconds. The robust design was successfully achieved.

3.3 Case study III

A more complex part for a boat deck was designed, as shown in figure 20(a). The

race-tracking distribution is shown in figure 20(b), which was along the edge of the

part and sharp corners. The same materials were used in the simulation study.

Therefore, the average permeability values were assumed to be statisticallydistributed as normal random variables and the race-tracking effects were

statistically distributed as Weibull variables (see figure 10). The part geometry



(a) (b)Vent

Gate

Vent

Gate

Figure 18. Robust tooling designs.




involving mostly asymmetric features was more complex than that described in the

previous section.

The mould geometry simplification according to the permeability distribution is

shown in figure 21. Due to part asymmetry, optimisation for placing more than one

injection gate will result in extremely long computational time. Therefore, one gatedesign was adopted for this optimisation problem.




Main region

Figure 20. Meshed geometry with varying permeability of the ship part.


2100 J. Li et al.



Figure 22(a) plots the first phase optimisation result for one vent design. The

dispersion values for the gate locations at two longer ends had smaller values than

those in the interior region. The reduced search domain is shown in figure 22(b) with

bold lines. During the second phase search, the performance was not remarkably

improved and outliers were observed due to large race-tracking effect and complexgeometric features, which indicate a multi-vent design, may be more appropriate.

As shown in figure 23(a), separating the ending points into two sets decreased

the minimised dispersion values dramatically from 2.5 to 0.8 and the potential

optimum search domain moved from the two ends to the centre of the part, as shown

in figure 23(b) with bold lines. During the second phase optimisation, the

marching directions were confined along the DEG boundary in order to reduce




Figure 23. First phase optimisation for two-vent scenario.




the computation load. The optimal designs are shown in figure 24 with a typical resin

flow process and the presence of flow disturbance.

The tooling evaluation study was performed. Plots in figure 25 simulated

mould-filling times for resin saturation with the distributed process parameter.

From figure 25(a) and (b), it was found that the filling time variation was reduced byabout 40%, which is the same level as in the case studies I and II. The optimisation

approach for robust design shows consistency for various part complexities, which

can be generalised for more applications.

3.4 Discussion

In this study, a heuristic algorithm was used to seek solutions for nonlinear

optimisation problems in the field of composite manufacturing. Since the flow

prediction simulation utilises FEM, an approximation method to actual process,the heuristic that finds satisfactory solutions with less computational efforts tends to

perform better for this type of ‘black box’ problem. The key point that makes the

graph-based two phases heuristic promising is its uniqueness of mould geometry

simplification, which quickly locates the potential optimal solution domain and



Vent

Gate

Figure 24. Robust tooling design.

2102 J. Li et al.



significantly shortens the necessary computational time. For a typical optimisation

problem of over 1000 search points, only about 30 to 40 points should be evaluated.

4. Conclusions

The optimal process design and process automation have been the focus of the

current research. However, a key factor in RTM process—preform permeability—is

stochastic in nature, which makes these current methods hard to implement. Taking

into account the statistical properties of permeability, a robust design with an

optimisation method was proposed. The following steps are involved:

. Generate permeability values by the Monte Carlo simulation based on the

fabric structure.

. Quantify part quality by mathematical modelling.

. Conduct the flow simulation with stochastic parameters.

. Optimise the process parameter for a robust design.

Applying the optimisation method for robust design is the key concept of the

work. In this way, the uncertainty of the actual production, such as process

performance, part quality, and the most important parameters regarding process

design, production scheduling and cost estimation, can be analysed more accurately

than the traditional deterministic approach. This will result in properly designed

moulds that maintain consistent part quality and stable production process.

Case studies involving three parts of various complexities were investigated.

The objective was to determine the numbers and locations of the injection gates and

vents, which could lead to a design insensitive to the process uncertainties, such as

race-tracking effects. The graph-based, two-phase heuristic algorithm was found to

obtain satisfactory solutions. The optimal gate/vent configuration achieves the

design goal. Future work will be extended toward developing sensor locations

optimisation, and automatic control methodology for reducing the part quality

variation, such that the global optimal process design solution for RTM processes

can be obtained.

References

Fowlkes, W.Y. and Creveling, C.M., Engineering Methods for Robust Product Design UsingTaguchi Methods in Technology and Product Development, 1995 (Addison WesleyLongman, Inc.: New York, USA).

Hoes, K., Dinescu, D., Sol, H., Vanheule, M., Parnas, R., Luo, Y. and Verpoest, I.,New set-up for measurement of permeability properties of fibrous reinforcements forRTM. Composites: Part A, 2002, 33(7), 959–969.

Hoes, K., Dinescu, D., Sol, H., Parnas, R.S. and Lomov, S., Study of nesting induced scatterof permeability values in layered reinforcement. Composites: Part A, 2004, 35(12),1407–1418.

Jiang, S., Zhang, C. and Wang, B., Optimum arrangement of gate and vent locations for RTMprocess design using a mesh distance-based approach. Composites: Part A, 2002, 33(4),

471–481.Law, A.M. and Kelton, W.D., Simulation Modeling and Analysis, 2nd ed., 1991

(McGraw-Hill: New York, USA).




Li, J., Zhang, C., Liang, Z. and Wang, B., Statistical characterization and robust design of RTM processes. Composites: Part A, 2005, 36(5), 564–580.

Luo, J., Liang, Z., Zhang, C. and Wang, B., Optimum tooling design for resin transfermolding with virtual manufacturing and artificial intelligence. Composites: Part A, 2001,32(6), 877–888.

Mathur, R., Fink, B.K. and Advani, S.G., Use of genetic algorithm to optimize gate and ventlocations for the moulding process. Polym. Comp., 1999, 20(2), 167–178.

Montgomery, D.C., Design and Analysis of Experiments, 5th ed., 2001 (John Wiley & SonsInc.: Hoboken, USA).

Myers, R.H. and Montgomery, D.C., Response Surface Methodology Process and ProductOptimisation Using Designed Experiments, 2nd ed., 2002 (John Wiley & Sons Inc.:Hoboken, USA).

Pan, R., Liang, Z., Zhang, C. and Wang, B., Statistical characterization of fiber permeabilityfor composite manufacturing. Polym. Comp., 2000, 21(6), 996–1006.

Pardalos, P.M. and Resende, M., Handbook of Applied Optimization, 2002 (Oxford UniversityPress: New York, USA).

Pardalos, P.M. and Romeijn, E., Handbook of Global Optimization, Volume 2: HeuristicApproaches, 2002 (Kluwer Academic Publishers: Norwell, USA).

Wong, C.C., Long, A.C., Sherburn, M., Robitaille, F., Harrison, P. and Rudd, C.D.,Comparisons of novel and efficient approaches for permeability prediction based on thefabric architecture. Composites: Part A, 2006, 37(6), 847–857.

Ye, X., Zhang, C., Liang, Z and Wang, B., A heuristic algorithm for determination optimalgate and vent locations for RTM process design. J. Manuf. Proc., 2004, 23(4), 267–277.

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