International Journal of Automotive Technology, Vol. 12, No. 1, pp. 8392 (2011)DOI 10.1007/s1223901100112

Copyright 2011 KSAE12299138/2011/05611

83

DEVELOPMENT OF A FIBER-REINFORCED PLASTIC ARMREST FRAME FOR WEIGHT-REDUCED AUTOMOBILES

H. S. PARK* and X. P. DANG

Lab for Production Engineering, School of Mechanical and Automotive Engineering, University of Ulsan,Ulsan 680-749, Korea

(Received 16 March 2009; Revised 23 July 2010)

ABSTRACTThis paper presents the design optimization process of a short fiber-reinforced plastic armrest frame tominimize its weight by replacing the steel frame with a plastic frame. The analysis was carried out with the equivalentmechanical model and design of experiment (DOE) method. Instead of considering the whole structure, it is divided into threesimpler regions to reduce the complexity of the problem through examining its structural characteristics and load conditions.The maximum stress and deflection of the regions that carry the normal load are calculated by the analytical mathematicalform derived from an equivalent model. The other regions loaded by contact stress are handled by FEM (finite elementmethod), the DOE method, and the RSM (response surface model). To optimize the design variables in both cases, the objectfunctions derived from these calculations are solved with a CAE (computer aided engineering) tool. This method clearlyshows the mechanical and mathematical representation of structural optimization and reduces the computing costs. Afterdesign optimization, the weight of the optimum plastic-based armrest frame is reduced by about 18% compared to the initialdesign of a plastic frame and is decreased by 50% in comparison with the steel frame. Some prototypical armrest frames werealso made by injection molding and tested. The research results fulfilled all of the design requirements.

KEY WORDS : Armrest frame, Fiber-reinforced plastic, Design optimization, DOE, FEM

1. INTRODUCTION

Current automobile manufacturing requires a reduction ofweight not only to increase performance and decrease fuelconsumption but also to reduce manufacturing cost andstrengthen competitiveness (Kim and Yoon, 2007; Park andLee, 2007). Saving limited metallic natural resources isalso a trend in sustainable manufacturing. Therefore, usingalternative materials that are cheaper and lighter and thatcan be recycled is one practical solution. For automotiveaccessories, the armrest frame, which is conventionallymade of steel, is one object that could be constructed withplastic. This requirement originates from the demands ofthe automotive industry.

The advantages of plastic materials, especially fiber-rein-forced plastics, include being light-weight and well-adaptedto mass production methods as well as having low manu-facturing costs and superior mechanical properties (Fu etal., 2000; Thomason, 2002; Park and Pham, 2009). Theother important advantage is good molding characteristics,allowing the designer to design the product they desire interms of shape and structure.

In addition to choosing appropriate material, structuraloptimization is also an important task to minimize the re-

quired volume of material in design optimization. Intheory, the shape and structural optimization of a complexpart is very complicated, and it requires not onlyknowledge, experience, and effort of engineering designersbut also the application of appropriate scientificmethodology. Despite successes in the optimization fieldover the past several decades, these breakthroughs are stilldifficult to use in practical and industrial applications (Daiet al., 2007). In general, structural optimization can beclassified as follows: size optimization, shape optimizationand topology optimization. For size optimization, designvariables are the structural aspects such as thickness, width,height or the section properties of a cross-section in a givendomain. Shape optimization deals with the geometricalshape of structures. The geometry of the structure is variedto obtain the optimal structure shape. Topologyoptimization is different from size and shape optimization.This method seeks the optimum distribution of materials orthe existence of an element of the finite element method tominimize the volume of material and maximize thestiffness.

In practice, there is no general optimization method forall the structural optimization process, but various methodshave been adopted. With the recent advancement of thefinite element method to solve a structural optimizationproblem for a particular part, engineering designers andresearchers prefer to use FEM and computer-aided engi-*Corresponding author. e-mail: phosk@ulsan.ac.kr

84 H. S. PARK and X. P. DANG

neering (CAE) in conjunction with optimization strategies.One of the most popular methods is the design of experi-ment (DOE), in which design variables are considered asthe factors. In the DOE method applied to structuraloptimization, FEM code is utilized to implement thestructural analysis. After that, the approximation responsesurface is constructed from the design matrix and analysisresults by using the least squares method (Akbulut, 2003;Han et al., 2004; Schfer and Finke, 2007; Chen et al.,2008). The DOE method is easy to use and can be appliedto most design optimization problems. Researchers andengineering designers have tended to adopt DOE in designpractice (Park, 2007).

In this paper, the design process, as well as a new ap-proach for the optimization process, of a fiber-reinforcedplastic armrest frame are presented. In the conceptual designstate, best initial design was determined by a relative com-parison method and by considering the manufacturing attri-butes of the product. The structural optimization processwas then carried out by using a combination of the analy-tical equivalent mechanical model, DOE method, FEM andnumerical optimization.

2. DESCRIPTION OF AN ARMREST FRAME AND DESIGN SPECIFICATIONS

2.1. Description of an Armrest FrameAn armrest is a feature found in most modern and com-fortable cars and provides passengers a place to rest theirarms. Many cars have a broad armrest between the backseats, which may be folded out when the central (third)seating area is not required. Armrests in some vehicles maybe also equipped with further convenient accessories suchas cup holders, audio or air-conditioner controls, andstorage compartments. Today, the rear center armrest withcup holder is an important feature that some carmanufacturers highlight in their advertising, for example,the Sonata and Elantra from Hyundai, the Altima from

Nissan, the Lincoln Town from Ford, and the Civic fromHonda. The armrest has a steel frame that is surrounded bysoft polyurethane foam and an outer leather layer. Figure 1shows an armrest with a cup holder on the back seat of acar. In the armrest, the frame is the most important partbecause it carries the load, and it is often made by formingsheet metal.

2.2. Design SpecificationsFormerly, a steel armrest frame made of 2-mm-thick sheetmetal was used to carry the load. It was blamed for theheavy weight and high manufacturing cost because of itslong manufacturing process that includes punching, stamp-ing and welding. In an attempt to reduce the weight andmanufacturing cost, the steel frame should be redesignedwith plastics or plastic-based materials. With these newmaterials, the weight of the product will be reduced, andthe manufacturing productivity will be increased throughthe application of the injection molding process. Inaddition, another requirement is that the frame structureshould be optimized to fulfill the design conditions butminimize the volume of required material.

Figure 2 shows the loads that the frame carries. Thecritical working condition occurs when the armrest is laiddown in a horizontal position. In this case, it is fixed at theleft end by the four short pins, and the applied force acts onthe right end. To ensure the fail-safety of the armrestaccording to safety standards, the frame must be strongenough to support an 800-N distributed load located at adistance of 20 mm from the right free end.

The yield strength of steel is approximately five to tentimes higher than that of common plastics (250 MPa com-pared to 20~55 MPa). Therefore, the plastic frame must befive to ten times thicker than the steel one (approximately10~20 mm in thickness) if the structure is the same as thesteel frame. Of course, this thickness prohibits the use ofshell-type plastic products for this purpose, and, therefore,structural optimization should be carried out to reduce thethickness.

The region on the right side of the frame where the cupholder is assembled should be retained. However, the mainbody region in the middle can be modified to increase thestrength and stiffness of the frame. On the armrest frame,there are also two metal insert pins in each side at the left

Figure 1. Rear center armrest with a cup-holder. Figure 2. Steel armrest frame and its load condition.

DEVELOPMENT OF A FIBER-REINFORCED PLASTIC ARMREST FRAME FOR WEIGHT-REDUCED 85

end that are used to fit the armrest to the seat frame. Thus,it is an important region where contact stress occurs. Thecontact stress must be less than the yield stress to ensurethat the joins between the metal pins and plastics are notbroken. The deflection of the frame is also consideredbecause it affects the quality of the frame. Therefore, theseparameters should be reduced as much as possible.

In this research, structural optimization was the mostimportant task. The problem was how to minimize theweight and deflection of the frame while keeping the stressbelow an allowable value. The following sections presentthe optimization method applied to the design of the plasticarmrest frame.

3. PROPOSED DESIGN OPTIMIZATION METHOD

Optimization is a complicated procedure for most engi-neering designers, and this process always includes a com-plex algorithm and a number of iterations until conver-gence criteria are satisfied. As mentioned in Section 1,there are some practical methods that deal with structuraloptimization, and none of them are generally suitable andmulti-purpose. Each method has its own advantages anddisadvantages depending on particular circumstances ofstructure, load, and boundary conditions. Whicheverstructural optimization method is used, in general, FEM isalways an indispensable tool of structural analysis thatsupports the structural optimization process. For thisreason, FEM is applied in the proposed method.

To make the optimization process easier, flexible, andeffective, the proposed structural optimization method alsoadopts the DOE and FEM methods. However, instead ofapplying the DOE method for the whole model, as isusually done, DOE is only applied to a partial model, andanother method, called the equivalent mechanical modelmethod, is used for the remaining portion of the model.Thus, the combination of DOE and the equivalent mech-anical model method is applied to combine the advantagesof each method. To apply the proposed method, the design-ed part is divided into simpler sub-regions based on theirshape and load condition. The DOE method and equivalentmechanical model method are used simultaneouslydepending on the shape and load characteristics of eachregion. The optimization process is split into two branchesas shown in Figure 3.

In this design, for example, the armrest frame is dividedinto three main regions, including one contact stress regionand two bending stress regions. The contact stress occurs inthe region that has two insert pins. In this case, it is difficultto construct the explicit contact stress equation that servesas the constraint function for optimization. Thus, the bestway to perform optimization is to use the DOE method andpost DOE method, which includes approximating the re-sponse surface model and then conducting an optimizationsearch based on this approximate equation to find theoptimum design variables of this region. In contrast, the

main body region and cup-holder region that carry bendingload can be modeled as popular models in solid mechanicsby using an equivalent mechanical model. Then, explicitequations that describe stress and deflection can be easilyderived. This system of equations serves directly as objec-tive functions and constraint functions for the optimizationprocess.

The improvement of the proposed method compared tothe conventional method is its computing effectiveness.This method of structural optimization also shows themechanics and mathematics clearly based on basic andexplicit solid mechanical equations. The complexity of themodel is reduced significantly due to sub-region division.When using DOE on each region that has relativeindependence, the number of design variables or designpoints is significantly reduced, exploiting the advantages ofthe DOE method. For the region that can be transformedinto the equivalent mechanical model, the explicitequations that describe stress at critical cross-sectionpositions and deflection at concerned positions areformulated. Therefore, the optimization problem is solvedrapidly and precisely by the numerical method withoutrebuilding and reanalyzing the 3D model as a totally FEM-based method.

Figure 3. Systematic design optimization procedure.

86 H. S. PARK and X. P. DANG

The proposed structural optimization method has the ad-vantages of ease of use, reliability, and low computing cost.With these considerations, the systematic procedure fordesigning the plastic armrest frame is presented in Figure 3,and the main steps of this process are described in moredetail in the following section.

4. SYSTEMATIC PROCEDURE FOR DESIGN OPTIMIZATION

4.1. Material SelectionThe plastic material chosen must have light weight andreasonable cost. For this reason, polypropylene (PP) is thefirst candidate because it is the most popular and cheapplastic. However, according to preliminary analysis, the de-flection of the armrest made of PP plastics is extremelyhigh because of its low elastic modulus (about one hundredtimes smaller than that of steel). Material with a low elasticmodulus causes a high deflection. To satisfy the designspecifications, the thickness of the armrest must beincreased. Consequently, it wastes material. The deflectionis in an inverse ratio to the elastic modulus and momentinertia of the cross-section. The cross-section optimizationcan increase the moment of inertia, but it cannot compen-sate for the stiffness when the elastic modulus is too low.Table 1 shows the mechanical properties of some commonplastics and fiber-reinforced thermal plastics.

ABS and PA-6,6 have good mechanical strength and ahigh elastic modulus compared to PP, but they are expen-sive and, therefore, are not good choices. Fiber-reinforcedthermal plastics are the best solution because of their super-ior mechanical properties. The trend in the automotiveindustry is for car makers to increase their use of reinforcedplastics to reduce weight and manufacturing costs. Further-more, fiber-reinforced thermal plastics are easily recycledor re-used at the end of the service life of a vehicle toprotect the environment (Reinforced Plastics, 2004).

There are several kinds of fiber-reinforced thermalplastics in terms of fiber length and fiber direction. Theyinclude short fiber-reinforced, long fiber-reinforced, fibermat-rein-forced, and continuous fiber-reinforced plastics.From the short fiber to continuous fiber reinforced plastics,the mechanical properties improve rapidly, but the timeconsumed and manufacturing cost increase while thedesign freedom decreases because of the moldingcharacteristics, such as the viscosity, molding pressure andfilling ability. Among these fiber-reinforced plastics, shortfiber-reinforced plastics that have an average fiber lengthof less than 1 mm can satisfy the injection moldingrequirement in mass production.

The popular short fiber-reinforced thermal plastics arecompound of polypropylene or PA-6,6 with glass fibers(GF) or carbon fibers. Although the compound of poly-propylene and short glass fiber offers lower tensile strengthand elastic modulus than other compounds (see Table 1), itis the least expensive. Moreover, short glass fiber-rein-

forced PP has excellent mechanical properties in com-parison with pure PP (tensile strength doubles and elasticmodulus triples). Short glass fiber-reinforced PP plasticsare the best choice of material for making the armrestframe.

The compound of short glass fiber and polypropylene isa kind of composite material; therefore, it is not isotropic.The tensile strength of PP with 30 wt% short glass fiber,shown in Table 1, was measured in the fiber direction.Many studies point out that the fiber direction coincideswith flow direction in the injection molding process (Fu etal., 2000; Zhou and Mallick, 2005). The strength of shortfiber-reinforced plastic in the direction normal to the flowdirection or in the weld line zone is lower than that in theflow direction. This characteristic must be taken into accountin the design optimization process of the armrest frame.Figure 4 shows the fiber direction and weld line position inthe armrest that was analyzed using Moldflow plasticsimulation. In addition, the mechanical properties of shortglass fiber-reinforced plastics vary with the production pro-cess conditions, the resin properties, and the average fiberlength. In other words, there are many factors that affect thereal strength of this material. These factors were taken intoconsideration when choosing the design safety factor.

4.2. Conceptual DesignTo choose the best initial design for the optimization step, aconceptual design was carried out. At first, some models ofthe armrest frames were built using parametric CAD basedon the function, performance requirements, dimensionalconstraints, and load conditions of the frame. These models

Table 1. Mechanical properties of some common plasticsand fiber reinforced plastics.

MaterialsTensile strength (MPa)

Elastic modulus

(GPa)

Density(g/cm)

Polypropylene (PP) 36 1.6 0.91PA-6,6 83 2.8 1.14PVC-rigid 44 2.7 1.40ABS 99 2.3 1.18PA-6,6 +33%GF 130 7.5 1.39PP+30%GF 72 4.9 1.12

Figure 4. Weld line position (a) and fiber direction (b) inthe armrest frame after injection molding.

DEVELOPMENT OF A FIBER-REINFORCED PLASTIC ARMREST FRAME FOR WEIGHT-REDUCED 87

were then analyzed to identify their volume, stress, anddeflection. Normally, these steps require the designers intui-tion and experience in the design, mechanics and strengthof materials to determine the best initial design. To over-come these disadvantages, analytic and relative compari-son methods were used in the conceptual design.

The manufacturing attributes such as the molding pro-cess and tooling cost were also considered in depth. Asimpler structure of the frame was preferred over a com-plicated one. Because of the characteristic of the product,the inside region of the main body of the frame should behollow to allow the insertion of polyurethane foam aroundthe frame. As mentioned in Section 2, the cup-holder regionmust be kept because of the cup-holder function. However,the main body in the middle of the frame (see Figure 2)could be constructed in any configuration in its design space.

It is true that, for plastic parts, the best way to increasestiffness is ribbing (Rosato, 2003). Increasing the numberof ribs can increase the stiffness of the model, but it alsoincreases the weight. Rib patterns or arrangement also affectthe stiffness and weight of the model. Figure 5 shows twelveframe models with various ribbing patterns. Based on theribbing principle, the twelve models were selected accord-ing to designers intuition and experience. After modelingvarious models with various structures, the next step is ana-lyzing the stress and deflection and calculating the volumeof each model by using FEM software. To determine whichmodel is the best in terms of strength, stiffness, and volumeof materials, the relative compare method was used. Althoughasymmetrical bending is not the load condition of the design,this new load case was added to assess the additional qualityof the frame under torsion. An arbitrary model was chosenas a benchmarking model - a model to which the others arecompared. The relative values of the volume, stress, anddeflection of other models that compare to the bench-marking model were calculated by the following formula:

(1)

where Ri is the relative value of the volume, stress, ordeflection. Vi and Vbm are the absolute values of the volume,stress, or deflection of the i-th model and benchmarkingmodel, respectively.

The relative comparison results of twelve models interms of the conceptual design, in which the Model 1 is thebenchmarking model, are shown in Figure 5. The modelwhose weighted sum of relative volume, deflection, andvolume is smaller than the others is the best one. Theweight factors are determined depending on the function ofthe designed part and the optimization target. In this designoptimization research, the volume of material is moreimportant in making the design economical. Therefore, theweighting of volume should be higher than stress or deflec-tion. Figure 5 shows that the Models 7 and 8 are the twocandidates that need to be considered thoroughly todetermine the best model at the end. Although Model 8 hasa smaller relative stress and deflection than Model 7, itsrelative volume is greater. If the weight factor is assigned tobe 2.0 for the relative volume and 1.0 for the relative stressand deflection, the weighted sum of all relative specifi-cations of Model 7 is smaller than those of Model 8 (619compared to 625). Thus, Model 7 is the best initial modeland is ready for the next steps in design optimization.

4.3. Equivalent Model ConstructionTo make the optimization process more convenient, anequivalent model is built and analyzed instead of the originalmodel. The geometry of the equivalent mechanical modelmay not be the same as the real one, but the stress and de-flection at critical cross sections and positions are similar.The load and moment acting on these critical cross-sectionsof the equivalent model must be the same as those of thereal model. In addition, the real model is also divided intosimpler regions or sub-domains, and the optimization pro-cess is carried out progressively. This approach can changea complex structural optimization problem into a simple one.In this design optimization, the armrest frame was dividedRi = 100% +

Vi VbmVbm

----------------- 100%

Figure 5. Relative stress, deflection, and volume of variousribbing and structures in the conceptual design. Figure 6. Regional divisions of the armrest frame.

88 H. S. PARK and X. P. DANG

into three regions: the cup-holder region, main body regionand inserted pin region as shown in Figure 6. This divisionwas done based on examining the shape, structure, andload condition of the frame.

4.3.1. Equivalent models of the main body region and cup-holder regionThe load characteristics of the cup-holder region and mainbody region are the same because they both carry bendingload. These regions can be replaced by an equivalent modelas a cantilever beam with equivalent cross-sections in theaspect of stress at critical cross-sections (Section A-A forthe main body region and Section B-B for the cup-holderregion) and deflection at load position (Figure 7). Thebending stress reaches the maximum value at these cross-sections in each region; therefore, ensuring the structuralstrength at these important positions will satisfy the strengthof both regions. As the result, structural optimization focuson the size optimization of the cross-section, and the optimi-zation problem becomes less complicated.

The design variables are determined based on geometri-cal parameters of important cross-sections. The stress iscalculated as

(2)

where M, y1, and I are the bending moment, the distancefrom the neutral axis to the upper edge of cross-section,and the second moment of inertia, respectively. For thecross-section A-A of the main body region in Figure 7,intermediate parameters are computed by the followingequations:

M = PL (3)

(4)

(5)

(6)

(7)

where A and Ix are the area of cross-section and the secondmoment of inertia to the axis at the upper edge of the cross-section, respectively.

The coefficient in Equations (4), (5), and (6) is addedto adjust the role of the two longitudinal ribs in carrying thebending moment. The reason is that the frame is only fixedat the left end by two short metal pins instead of long rigidpins through both sides. This coefficient ensures the equi-valence between the real model and equivalent model, andit is calculated by solving one unknown Equation (2) inwhich the value of on the left hand side comes from thestress analysis result of the initial model using FEM ( =

0.52). For the cross-section of the cup-holder, the mechani-cal equations are similar to the equations above.

The displacement is computed based on the equivalentmodel of deflection at the load position. Because the cross-section of the beam varies not only with the height but alsowith the shape, the discrete method is used to calculatedeflection. The construction of this model assumes that theeffect of the cross ribs on the deflection of the model in thelongitudinal direction is insignificant. The function of theseribs is to increase the buckling strength and stiffness in thetransverse direction. Figure 7 shows the discrete model todetermine the deflection of the model. The maximum de-flection at the bending force position of the armrest frameis computed as follows:

(8)

where E and Ii are the Youngs modulus and second momentof inertia of segment i, respectively.

4.3.2. Equivalent models of the contact stress regionThe contact stress is difficult to analyze, and it requires alarge amount of time to calculate. The contact stress onlyappears in material zones around the metal pins, so there isno need to calculate the contact stress using Abaqus FEMcode for the whole model. To accelerate the computingspeed, an idealized equivalent model was built to reducethe geometrical complication and the number of elements.The method of transforming a real model into idealizedequivalent model based on the principle of the force andmoment acting on the metal inserts in the real model andthe mechanical behavior of the idealized model are thesame as that for the real model. Figure 8 illustrates theequivalent contact stress model of the armrest frame. Thereare two design variables, the width b and radii R, that affect

= My1I---------

y1=4t1

h122----+2t3 b 2t1( ) h1 h4 t32--- +2t2h2 h1 h3

h22----

A--------------------------------------------------------------------------------------------------------------------

A=2 2t1h1+t2h2+ b 2t1( )t3[ ]Ix=43

---t1h13+23--- b 2t1( ) h1 h4( )3 h1 h4 t3( )3[ ]

+23---t2 h1 h3( )3 h1 h3 h2( )3[ ]

I=IxAy12

= Pl 33E-------- i 1=n i3 i 1( )3 Ii-----------------------

Figure 7. Equivalent model for calculating the stress atcritical cross-sections and the deflection at the load position.

DEVELOPMENT OF A FIBER-REINFORCED PLASTIC ARMREST FRAME FOR WEIGHT-REDUCED 89

the maximum contact stress and deformation or deflectionin this region. This method significantly reduces the com-puting cost in analysis, and computer simulation time isreduced when the design optimization method with FEMand DOE is employed.

4.4. Optimization ProcessAs demonstrated in Section 3, the structural optimizationprocess is divided into two sections: DOE is employed to systematically organize the experi-

ments. FEM is then used to analyze the results, followedby building a response surface model. Finally, mathe-matical optimization is carried out.

Direct explicit mechanical equations that serve as objec-tive functions and constraint functions are derived, andthe optimization problem is subsequentially solved bythe numerical method.The DOE method is applied for the optimization of the

contact stress region, and the direct equivalent mechanicalmodel approach is used for the optimization of the mainbody and cup-holder regions progressively.

4.4.1. Optimization of the contact stress regionFor contact stress regions where two steel pins are insertedin plastics, there are two design variables, r and b (seeFigure 8), that are called factors in DOE (Park, 2007).Because the number of factors is low, the full-factorialtechnique was used to carry out the simulation. The designmatrix for two factors with three levels is shown in Table 2.Nine design points, in other words, nine models in designspace, were constructed and were then analyzed by FEM todetermine the contact stress and deformation in the jointbetween the steel pins and plastic material.

The approximate response surface models for volume( f1), displacement ( f2) and stress ( f3) with two factors r andb are in the form of quadratic polynomials:

(9)

The coefficients of the response equations were calculatedby the least squares method. Table 3 shows the value of thecoefficients of Equation (9). R squared, which is called thecoefficient of the determinant, is displayed in the last columnand is based on the following formula:

(10)

where , and fi are the observed values, mean ofobserved values, and approximative values, respectively.

R squared is close to 1, which means that the goodnessof fit of the approximate models is very high.

To observe the influence of factors on the response morevisually, the graphs of the response surface model areshown in Figure 9. The optimization process was carriedout based on a system of equations from the responsesurface model. The optimization problem for the contactstress region is

fi = i 0, +i,1r+i,2b+i,3r2+i,4b2+i,5rb

R2 = 1

i yi fi( )2

i yi yi( )2-------------------------yi, yi

Figure 8. Equivalent model for analyzing the contact stressand deformation in the region around the inserted pins.

Table 2. Design matrix of inputs r and b and analysis results.

Experi-ment No.

r(mm)

b(mm)

Volume(cm3)

Displacement(mm)

Stress(MPa)

1 15.0 15.0 50 1.01 44.22 15.0 20.0 58 0.78 37.83 15.0 25.0 86 0.71 36.74 18.5 15.0 60 0.84 38.85 18.5 20.0 82 0.63 34.76 18.5 25.0 104 0.51 34.07 22.0 15.0 71 0.75 36.78 22.0 20.0 96 0.56 33.59 22.0 25.0 122 0.54 31.2 Figure 9. Graph of displacement and stress responses.

Table 3. Coefficients for inputs of the DOE model forresponse displacement ( f1), volume ( f2), and stress ( f3).

Out-put

Inter-cept r b r

2 b2 r b R squaredf1 81.88 14.17 21.83 0.17 0.17 3.75 0.999f2 0.59 0.11 0.13 0.06 0.10 0.01 0.952f3 34.76 2.88 2.96 0.85 1.60 0.50 0.977

90 H. S. PARK and X. P. DANG

minimize f1 and f2 (11a)subject to f3 38 (11b)15 r 22; 15 b 25 (11c)

This problem is a multi-objective optimization processthat minimizes the volume ( f2) and displacement ( f1) of thecontact region model while keeping the stress below theallowable value of 38 MPa. The permitted design strengthof the material in the direction that is perpendicular to fiberdirection was chosen for the contact stress region with asafety factor of 1.25.

Multi-objective optimization was solved using the multi-objective genetic algorithm (MOGA) (Osyczka, 2002). Tosolve this MOGA conveniently, the iSight tool was used.For multi-objective optimization, there are many trade-offsolutions before choosing the one that best suits the designrequirements. The volume is the most important objectivefunction that affects the economical effects of the optimi-zation results. For this reason, the preferred optimum pointwas selected to minimize the volume rather than the de-flection. The optimum values of the design variables werechosen as r = 16.9 mm and b = 16.7 mm, and they wererounded to r = 17 mm and b = 17 mm.

4.4.2. Optimization of the main body and cup-holder regionThe structural optimization of the main body and cup-holder region were changed to cross-section optimizationwith the equivalent mechanical model. The cup-holderregion at the free end of the frame is simpler than the mainbody region because its cross-section has a U-shaped form.Its design variables include t, t4, h, and b (see Figure 7), inwhich t4 = 2.5 mm, h = 40 mm, and b = 170 mm are pre-determined and fixed according to the reasonable size and

shape of the frame. The thickness t is derived and roundedup to 3.5 mm without a special optimization procedure.Therefore, the main optimization task focuses on the optimi-zation of cross-section of the main body region. Wheneverthe area of cross-section is minimized, the material is alsominimized. The deflection is another design specificationfor which there is no given critical value. However, it shouldbe minimized to improve the quality of the frame. Themaximum stress at the critical cross-section must be lessthan the allowable stress of the material (41 MPa) in thefiber direction with a safety factor k. The optimization pro-blem is stated as follows:

Minimize (12a)

and (12b)

subject to

(12c)

2.5 t1 4.5; 2.0 t2 4.0; 50 h1 58;20 h2 30; 10 h3 15; 10 h4 20 (12d)t3 = 2.5; b = 17 (12e)

The problem described by Equations (12) is a multi-objective optimization problem, so it was also solved usingthe MOGA method to obtain engineering data mining.Figure 10 shows the Pareto plots or trade-off between thestress and area as well as between the deflection and area.Darker points (blue points in color printing) are possibleoptimum points. However, decreasing the area of cross-section, in other words, reducing the volume of material, ismore important than reducing the deflection. Therefore, thefinal optimum point (the small square point in Figure 10)was chosen. At this point, the values of the design variablesare t1 = 2.5 mm, t2 = 2.0 mm, h1 = 57.5 mm, h2 = 21 mm, h3= 15 mm, and h4 = 10 mm. The outputs (responses) are themaximum stress at the critical cross-section A-A = 34.3MPa and the deflection at the load position = 10.6 mm.4.5. Verification Results The results of mathematical optimization are, of course,reliable. However, there are always some errors whenchanging from the real model to the equivalent model dueto some simplified assumptions and the method of choos-ing design variables. As a result, it is necessary to verify

A=2 2t1h1+ t2h2+ b 2t1( )t3[ ] = Pl 33E-------- i 1=

n i3 i 1( )3 Ii-----------------------

My1I--------- 41=

Figure 10. Pareto plots used to determine the final optimumdesign variables for the main body region. Figure 11. Stress analysis result of the armrest frame.

DEVELOPMENT OF A FIBER-REINFORCED PLASTIC ARMREST FRAME FOR WEIGHT-REDUCED 91

the outcome of the equivalent model method by finiteelement analysis. After solving the mathematical optimi-zation problem, the optimum values of design variableswere used to update the model, and this model wasanalyzed again by FEM to check the stress distribution,deflection, and error between the equivalent and realmodels. Figure 11 illustrates the stress analysis result of theoptimum model. The stress is distributed uniformly alongthe length of the main body region, and the maximumstress is allowable.

The stress, deflection, and error analysis results betweenthe equivalent model based on solid mechanics and the realmodel based on FEM are shown in Table 4. The errors areless than 2.9%, and these errors are acceptable in practicalmechanical engineering. Therefore, the loop of the struc-tural optimization process terminated without iteration (seeFigure 3), and the computing time was reduced, which isthe advantage of the equivalent mechanical model method.It is clear that the structure of the armrest frame hasreached its optimum state for three reasons: the stress isdistributed uniformly, the model was built from the optimumdesign parameters, and the errors between the equivalentmodel and the real model are small.

The volume of the initial model decreases significantlyfrom 381 cm3 to 311 cm3 (a reduction of 18.3%), and the

stress and deflection are reduced from 38.7 MPa and 11.7mm to 34.9 MPa and 10.3 mm, respectively, after optimi-zation. Compared to the former steel armrest frame, thetotal weight of the plastic-based frame, which includes themetal inserted pins, decreases from 1.0 kg to 0.498 kg (areduction of 50%).

Some prototypical armrest frames were made by injec-tion molding to check the manufacturability and to verifytheir strength (see Figure 12). A simple method of testingthe strength of the armrest frames was carried out by usinga jig to fix the pins and a set of weights to create thebending load. Perceptible observation and the estimation ofthe manufacturing expenditure were also conducted. Theresults showed that the new plastic armrest frame meetseconomical and technical requirements. Mass productionwill be launched soon.

5. CONCLUSION

The development of a short fiber-reinforced polypropylenearmrest frame contributes to the reduction of the weightand manufacturing cost of automobiles. Analyzing the ro-bust structure of the armrest frame, establishing equivalentmodels, developing explicit objective functions and con-straints, solving mathematical optimization, and engineer-ing data mining were carried out to minimize the volumeand increase the strength of the frame. Estimated using theshort-term amortization of the tooling cost, the manu-facturing cost was reduced by 5% when the material waschanged from steel to short glass fiber-reinforced poly-propylene. This reduction will generate an enormous profitdue to mass production.

In addition to the economical and technical benefit ofdesign optimization, this study introduces a new structuraloptimization approach based on the conventional methodand advanced CAE tools. The flexible combination of DOE,FEM, the equivalent mechanical model, and numericaloptimization tools makes the structural design optimizationprocess much easier, more precise, and more reliable. Thecomputation cost is also reduced by eliminating some ofthe iteration steps due to the application of an appropriateanalytical equivalent model.

Finally, as mentioned in the introduction, there is nogeneral method for solving all optimum design problems,and this proposed method is not an exception. Because theoptimum design of a plastic armrest frame is a case studyof this proposed method, more applications should bedeveloped for other optimum design processes in futureresearch to confirm the effectiveness of this method.Developing more convenient and accurate methods forsolving shape and structure optimization must be continuedto improve the quality of the structural optimization pro-cess. Making a seamless interaction between commercialoptimization software and CAD/CAE systems in the auto-mated design-evaluate-redesign cycle is a potential approachthat will be the object of further research.

Table 4. Comparison of results between the equivalentmodel method and FEM analysis.

OutputsEquivalent

model method result

Finiteelement

analysis resultRelative

error

Stress (MPa) 34.3 34.9 1.7%Deflection (mm) 10.6 10.3 2.9%

Figure 12. Prototypical model of a short carbon fiber-reinforced PP plastic armrest frame.

92 H. S. PARK and X. P. DANG

ACKNOWLEDGEMENTThis work was supported by Businessfor Cooperative R&D between Industry, Academy, and ResearchInstitute funded Korea Small and Medium Business Administration.

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