EngOpt 2016 - 5th International Conference on Engineering OptimizationIguassu Falls, Brazil, 19-23 June 2016.

Topology optimization vehicle chassis: Software applied to optimization trucksand buses chassis stringer in automotive industry

LIXANDRAO FERNANDO, P. H.; SANTOS, G. A.; NAKAMOTO, F. Y.

Department of Mechanical Engineering, IFSP, SP, Brazil

e-mail: paulohlf@yahoo.com.br/givanildo@ifsp.edu.br/nakamoto@ifsp.edu.br

Abstract

The necessity to reduce production costs in the automotive industry is strongly investigated by productengineers. For this reason, engineers and designers search in other areas modern techniques that can beimproved or used in their projects, using computational methods for optimization applied to the part design.The application of this technique is a further step to the use of CAE software currently used on a large scalein the automotive industry. This actual technique is well-known with ”Topology optimization”.

As the vehicle chassis is the link between the cabin, engine, transmission and axles, it has a greatimportance in the construction of vehicle. For the development of production, engineering companies havehigh costs due to the time it takes to get a better product, and it is very difficult to develop and designa product with the lightweight of the material that suits to the application. The stringer chassis is one ofthe most important items of the vehicle because that is where it supports all parts of the structure in thepropellant vehicle.

Actually, the United States, Denmark, China, Japan, etc., use the optimization technology in the con-struction of their products, reducing the weight, size and final cost of production. This paper search toidentify such optimization technology, and applies it in the analysis of a chassis (trucks or buses), comparingsome commercial software for this analysis. It will be used for comparison some softwares that have some op-timization type incorporated such as Optistruct (Altair), SolidWorks (Dassault Systemes) with ParetoWorks(Sciart), ANSYS and Spaceclaim (ESSS) with Virtual PYXIS (Virtual CAE).

After this comparison, will be creat in a next article a new software through of the simplex algorithmtheory, which has the linprog (a routine MATLAB), specific software for weight reduction chassis. Byexperimental knowledge, this technology has never been used in Brazil specific in the automotive industry.

Nowadays, there are at least five broad classes of distinct optimization technology. They are: StructuralOptimization,Parameter Optimization, Multidisciplinary Optimization (MDO), Multi-objective or ParetoOptimization and Robustness and Reliability Optimization. These are broad classes commonly used formany applications in industry and academy. Depending of the nature of the design problem is used one orother optimization broad classes.

So, the proposal of this article find to identify the problems of the product engineers, searching to reducematerial for better distribution of weight x power ratio, with the use of the optimization topology. Theresults will contribute to a new application in academic and industrial use.

Keywords: Topology Optimization, ParetoWorks, Optistruct, Virtual PYXIS, ANSYS, Spaceclaim.

1 IntroductionAlmost of the companies of the vehicle chassis manufacturers try to reduce the weight of their structures. The

weight reduction occurs as an end result, with several positive factors such as decrease in vehicle consumption,possible higher of load in the axles, reducing weight and components of the front and rear axles, the possibilityof lowering the tread, allowing best tire costs, etc. Study or work related to the optimization of use to solve thevariables found in a design of a stringer chassis.

There are many technical literatures of engineering, however, specifically the optimization method is cur-rent, that is, there are not large developments in the project area in the national companies of the vehiclemanufacturer. The study is against this problem, and aims to establish the hole and positioning not only bycomputer-aided engineering (CAE) [1] systems, but also by optimization for the analysis of chassis and com-ponents manufacturing. The proposal would be to identify an existing chassis market to understand the forcesacting on the beam in relation to the permissible total gross weight (PBT), especially the torsional tensionforces in the element, check the current drilling plane of the stringer and through topology optimization methodknow with TOM, propose a new drilling plan and cuts to this stringer as a result of the developed software.

2 Literature Review2.1 Introduction and basic concepts in optimization

There are at least five broad classes [2] are many important for developing in industry. They are classifiedas (Figure 1):

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Figure 1: Optmization broad classes.

• Structural optimizationStructural optimization [3] is an optimization of a structure’s shape [4], size, topology, topometry ortopography. Topology optimization is only one kind of structural optimization. Size optimization consistsof modifying properties of structural elements. Shape optimization is to minimize volume surface shape ofa 2D or 3D solid. Topology optimization is the form for the reducing material with density, homogenization[5] or level-set methods. Topography and topometry optimization, like are applicable only to 2D or shellelements.

• Parameter optimizationParameter optimization find to solve problems such as minimization of a specified objective function overa defined data set.

• Multidisciplinary optimization (MDO)Multidisciplinary optimization (MDO) is the actual area that involves many disciplines, fluid, thermal,acoustic, NVH, multibody dynamics, crashworthiness, etc.

• Multi-objective or Pareto OptimizationMulti-objective or Pareto optimization is a method for numerically defined the Pareto frontier with baseon exogenous factors, with decision for human and not by computer model only.

• Robustness and reability optimizationRobustness and reliability optimization are methods for control of the measured in terms of a mean valueand its variance.

2.2 Introduction topology optimizationThe optimization has become a major theme in the aviation areas, where the reduction in weight of the

material was closely linked to the cost they could be manufactured. The method is know with TOM [6] [4] [7][8] [9].

There are various methods used to perform topology optimization: Homogenization, Solid Isotropic mate-rial without or with penalization (SIMP), Continuous, level-set, Evolutionary Structural Optimization (ESO),Topological derivatives, etc. There are already some software existing for optimization, but there is a greatfind for high-performance processing and calculation speed. The main purpose of this article is to analyse theexistence of software through TOM with application in automotive industry.

At the end of the 1980s, several studies of the optimization in universities and also in the airline industryhas had a good rise of the model, however, [4] proposed the application in optimization of continuous structureswith this possibility was a step for obtaining optimal structures have been carried out for many applications. Inthe method, there is the possibility to find the so-called empty positions (positions 0) or full positions (positions1), (Figure 2).

Topology optimization is a computational method for structural optimization. The method lets you set theoptimal topology structures, with the distribution of material within a project area, aimed at the removal orplacement of the material at each point of the domain, which can minimize (or maximize) the objective function

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specified. The method consists of collecting data, to define the function objective to find a maximum deflection,minimum mass, maximum hardness and others. Through these data and of the function objective is madeoptimization problem formulation.

Figure 2: Principle topology optimization[10].

Following define the objective function, and adopt a process such as minimizing the function. It is madeof a process function interactions, and each interaction, a further reduction rate is checked converging theframework for an optimal solution. Of course for the number of interactions is reduced, we have a large numberof calculations and should adopt such restrictions for the role. The TOM can involve several variables andsearch the optimal distribution of material within a project area, it removes and adds material on the fixed areain order to tend an objective function. Studies involving the current TOM are based on heat transfer, fluidflow or vibrations, continuous structures. Denmark and Germany, [11] since 1988, there are several studies ontopology optimization.

In Brazil the studies began by the year 2000 at USP (Universidade de Sao Paulo), and there are currentlylarge studies in Brazilian universities, UFRGS, PUC-RIO, UFRJ, UFSCAR, UNICAMP, UFABC, etc.

2.3 Mathematics Programming – Approach SimplexOne kind of optimization approach stemmed Linear Programming, formulated also for the use of non-linear

functions is the simplex method. It was developed by Dantzig [12] thus allowing the solution of linear program-ming problems more efficiently. MATLAB [13] has a routine that solves linear problems, called LINPROG [14].This routine is designed to help programmers in linear programming calculation because it is a robust programand widely used in solving engineering problems.

2.4 Criteria for design and manufacture of chassisThe product engineers in Brazil now use CAE, method to analyze continuous structures using software such

as Patran (Pre-processor) and Nastran (processor) and others. The chassis is specified exclusively for the vehicleto some improvements with respect to resistance aspects, comfort, handling characteristics and processing load.The chassis is based on the harmony of some aspects of the body intended, planned operating conditions andtype of transport. The chassis is designed to absorb contact on-chassis bodies in various applications such aswaste collector car, freight car truck, road freight transport car, etc., as shown in Figure 3.

Figure 3: Bodies kind applied in the chassis [15].

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Chassis settings depend on the type or model of equipment, ranging from 4x2, i.e. with 4-wheel contact withthe ground, but with traction on 2 wheels, through 4x4, 6x2, 6x6, 8x2 or 8x4. Some other conditions chassisconfiguration can be designed for special equipment, see Figure 4.

Figure 4: Chassi 4x4 [15].

Most of the implements made by coach builders requires diverse dimensions of distance between centers.The distance between axes is the distance from front axle to rear axle. This is due to the fact that vehicle man-ufacturers industries has in its sales catalog just a few standardized measures of wheelbase due to minimizationof cost of their manufacturing process. This demand for diverse dimension means that there is change in thepositioning of the rear axle changing holes in the chassis beam when they are not defined by the manufacturer,(Figure 5). Also for this fact is important that engineers know the detail stringer chassis applied to the vehicle.

Figure 5: Shortening or lengthening t0 wheelbase [16].

The shortening of the chassis is very harmful to the vehicle due to the cut promoted under the chassis intractor and dump trucks without sub-frame that isn’t recommended by the manufacturer. The drilling or re-moval of material in the chassis is one of the most important elements regarding the application of effectiveness.A fact that not is recommended by vehicle manufacturers is the perforation of the tab stringer, it is these flapshave the highest stresses in the chassis beam, which can cause rupture around the punched holes, (Figure 6).Technically one should therefore examine the drilling and removal of material wherever possible using the soulof the C profile to the removal of materials.

Figure 6: Rules and drilling conditions in the chassis. Unit:mm [17].

The chassis manufacturer predicting the problem originate in relation drilling of a stringer, it recommendsby designers that whenever possible may be used the standard pre-drilled holes in the structure, however if itis making new holes are adopt as Figure 7 for drilling (Standard norm in accordance with 2007/46/EC.) [18].

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Where the letter A shows the minimum distance between the orifice and the flange delimiting this dimensionshould be three times the hole diameter greater than 40 mm, since the dimension B should also be three timesthe diameter but larger than 50 mm. The manufacturer sets the hole between the front axle and the rear axlemust be maximum 30 mm.

Figure 7: Standard allowed drilling in the stringer [17].

As much as this pattern drilling stringer was adapted, there is always a doubt whether that point of thestringer may be holed or not by the body builders, without this critically affects the structure of the stringer.This question will be found in the expected results of this work.

3 Technical backgroundThe constant difficulty of design engineers who dimensioning bodies on chassis and are faced with excess

weight on the axles of the vehicle by limiting the load is considerable. In order to minimize these impacts, aproposal that aims to demonstrate the use of topology optimization method for the minimization of specificmaterial for the construction of vehicle stringer will be prepared. Demonstrate through literature review thatthe topology optimization is one of the best methods for analysis of rigid structures that may suffer somedeformation, for it will be used this method to the study. This method can be studied in the future and tobe applied to other parts of the vehicle as the cabin, and drive powertrain, body, etc. It will be mathemati-cally demonstrated the topological optimization method for this application, with parallel use of HyperWorkssoftware company, which has a topology optimization analysis module called OptiStruct [19] and also with thesoftware Solidworks [20] with add-in ParetoWorks[21] [22] and also ANSYS [23] with add-in Virtual PYXIS[24]. All the analysis will be done in this module. Later analysis of the model will be compared with resultsCAE system, will can be demonstrated the effectiveness of TOM and proposed the creation of a software viaLINPROG routine (MATLAB), used by the Simplex method.

4 MethodologyThe project engineering companies present developments in various segments. In Brazil there are still few

companies searching to meet the needs of customers for product development through the TOM. Thus, thesubject of study can be presented as follows: ”Topology optimization vehicle chassis: Software applied to opti-mization trucks and buses chassis stringer in automotive industry”. The work aims to make a contribution tothe area in question in the context of proposing a structure for tasks or activities cycles, for carrying out theTOM applied to the car chassis product, causing the project to become profitable, with low density material,etc. It is useful, therefore, that the knowledge gained through this work, you may cause the reader to under-stand what is a structure built through a methodology, which may be not only specific activities in question,but some idea suggested by one or through the relationship of these. The concepts developed in this area searchto understand the structure of tasks for the validation of a product through the TOM, and through this searchsolutions so there is a demystification of the difficulty of using CAE systems by the designers of engineeringcompanies. To achieve the objectives should be a study of a car chassis through OptiStruct, ParetoWorks andVirtual PYXIS module, and through linear programming functions of mathematical model. The purpose of themethodology is to help us understand the incomprehensible, in the broadest terms, not only the products of sci-entific research, but the process itself, therefore, any successful scientific research implies certain methodologicalconsciousness Kaplan [25]. The path that has been founding for scientific methodology is given in accordancewith the execution of studies of reference bibliographies that exist with regard to similar cases, and from thesestudies, measure, or quantify the studies regarding the application of the TOM in engineering companies. Thisrun will search first set the foundation of the what is this, and how to work the engineering companies in thevarious organizations of this medium in Brazil, with respect to product development through the TOM fromthis definition will be explored the types of tasks that have been through TOM of the study and after thiswas related to the study manufacturing a prototype vehicle chassis. Was adopted a methodology that can be

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structured by the sequence of steps shown graphically in Figure 8.

Figure 8: Search Structure. Source: The author.

Through the technical proposal initially, a literature reference will be finding, focusing on areas of TopologyOptimization, Structural Mechanics and Manufacturing Processes, (Figure 9). Shall be deemed these areasbecause they are more associated with delimitation of the subject. The concepts addressed these three areasinclude the interests of research.

Figure 9: Area of research interest. Source: The author

Thus, a search of the bibliography was done, getting up the main items related to the research question (sub-ject matter). It will also be defined as aspects of product features to structure the study. As the main techniqueto achieve the objectives of this study, had used the documentary research, which according to Godoy,[26], isthe examination a lot of materials, which have not yet received an analytical treatment, or may be re-examined,searching for new interpretations or complementary. This documentary part will be generated through theresults of OptiStruct, ParetoWorks and Virtual PYXIS module.

5 Numerical Implementation of the topology optmization algorithmThe code of the topology optimization algorithm is implemented in MATLAB using the LINGPROG (a

routine of the MATLAB). At each iteration of the topology optimization algorithm, a structural analysis iscarried out by using Finite Element Method (FEM)[1], to account for the calculation of the output displacementof the structure. The gradients of the objective function and constraints are calculated. The optimizer generatesa new set of design variables after each iteration and the optimization continues until convergence is achievedfor the objective function.[27]

The PLS solves several linear sub problems sequentially find the solution of the non-linear problem. ThePLS has been applied successfully in Topological optimization in several papers in the literature and is thereforethe method of choice for this job.

Numerical methods require the continued dominance of the structure is discretized. Thus we have, forexample, instead of a continuous distribution density inside the field structure, density values of the elementscomposing the field of discretized structure. It is considered as a variable density element which is a continuousvariable, you can take any value within the element. In this work, the domain structure is discretized into finiteelements. The TOM software proposed in this paper can be implemented using the MATLAB programminglanguage. Figure 10 describes the software algorithm procedure.

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Figure 10: Flowchart TOM procedure. Source: Adapted: [28]

6 ResultsThis project is premised development through topology optimization reducing material of a stringer vehicle

chassis (truck and bus) with mathematical model and Optistruct, ParetoWorks and Virtual PYXIS software,which can be used in the automotive industry, mainly serving design engineers the chassis area vehicle. Inthis work we see the confrontation of topological optimization method front of the CAE system in relationto its better efficiency due to minimization function via an interaction cycle. It made possible the productivecapacity of this material on an industrial scale with a new drilling plan in the chassis beam, and software that cansimulate this plan, because the project has industrial support of Scania companies in Brazil (Chassis builder) andLavrita Engineering (construction of several implemented bodies), form of the provision of resources, availabilityof information, among others.

6.1 The Stringer ChassisThe stringer chassis is existing in the industry. The model of the truck that receiving the stringer chassis

is Scania P440 CB 4x4. This chassis is made for attending special vehicles with firetrucks, and others, (Figure11).

Figure 11: Courtesy Lavrita Engenharia [29].

The stringer chassis have many hole for to fix all components of the structure. The designers and engineersof the Scania finding developing the stringer putting this hole between of the simulation CAE. But not is utilizedTOM for design the holes in stringer. The design of the chassis is accordance with Figure 12.

Figure 12: Stringer Scania P440 CB 4x4 Source: The autor

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6.2 The Loads and constrainsThe stringer chassis of the firetruck has the max load of the 100.000N and 6 fixed points in structure . The

material of this structure is LNE 380 that is a carbon steel with the tensile strength limit with 440 MPa, thatis a isotropic material. To see Figure 13.

Figure 13: Loads and constrains of the structure Source: The autor

6.3 Criteria of the analyses CAE and TOMFor to simplified of the analyses we adopt the two-dimensional phase. The formula of the TOM for elements

of the two-dimensional phase is.

6.4 Results of the CAEThe analyses post-processing were make only with structural static, with the Software PartoWorks, ANSYS

and Optistruct. Was observed the max. stress (critery of the Von Misses) ant the max. Displacement, (Figure14,15 and 16).

Figure 14: ParetoWorks: Maxim Stress Source: The autor

Figure 15: ANSYS: Maxim Stress Source: The autor

Figure 16: OPTISTRUCT: Maxim Stress Source: The autor

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Figure 17: ParetoWorks: Maxim Displacement Source: The autor

Figure 18: ANSYS: Maxim Displacement Source: The autor

Figure 19: OPTISTRUCT: Maxim Displacement Source: The autor

Between this results we have a comparative table. To see table 1.

Table 1: Results numerical.

Software No.Elements Maxim Stress(MPa) Maxim Displacement(mm)ParetoWorks 1000 470.000 1900

ANSYS 986 254.920 0.565OPTISTRUCT 1224 385.100 1.661

Is possible to observe that the maxim stress is approximately similar between the software ANSYS andsoftware OPTISTRUCT. This fact it happens because the type of the analysis is by OC (Optimization criteria)with material law SIMP, and without penalization of the material. Already ParetoWorks the TOM is by Pareto.Is other form of the analysis.

6.5 Results of the analys TOMWas adopted by criteria of the designer, the condition of the minimization of the volume until 70 percent of

the structure volume. This criteria was adopted because before was analysed of the structure per maximizingstiffness, and this other criteria the reduction was between 50-55 percent, but with criteria, the structure wasseparated in more that two parts. Then, this criteria wasn’t adopted. Now how stayed the structure withvolume minimization until 70 percent (Figure 20,21,22).

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Figure 20: PARETOWORKS: TOM. Source: The autor

Figure 21: VIRTUAL PYXIS: TOM Source: The autor

Figure 22: OPTISTRUCT: TOM. Source: The autor

6.6 Superposition with the stringer chassis existentIn accordance with the propose this article, is possible to put the design of the TOM in stringer chassis

existent, and after remove the holes existent where not is correct to put holes. We have analysis differentbetween ParetoWorks, Virtual PYXIS and Optistruct, was analysed the three cases. This Figure 23 has thefirst case with ParetoWorks, In Figure 24 has the second case with Virtual PYXIS or Optistruct. In Figure 25is third case. In Figure 26, 27 and 28 is propose new stringer chassis in the three cases.

Figure 23: PARETOWORKS: Superposition with Stringer chassis. Source: The autor

Figure 24: VIRTUAL PYXIS: Superposition with Stringer chassis. Source: The autor

Figure 25: OPTISTRUCT: Superposition with Stringer chassis Source: The autor

6.7 New Stringer chassisThis is the final result with the propose. The designers and engineers of the automotive industry has a new

form for to know if is possible to hole in anywhere position in stringer chassis, (Figure 26, 27 and 28).

Figure 26: PARETOWORKS: New stringer chassis. Source: The autor

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Figure 27: VIRTUAL PYXIS: New Stringer chassi. Source: The autor

Figure 28: OPTISTRUCT: New Stringer chassi. Source: The autor

6.8 Comparing between softwareThe three software were analysed with same loads and constrains and materials. ParetoWorks have problems

for processes up of 10.000 elements in this application , but with 1.000 elements was the faster for configuration ofthe conditions of the boundary. However by little structures is possible configure more than 1.000.000 elementseasily. Virtual PYXIS is very good by TOM, have many functions, and by to work with the solver (ANSYS) isfaster by to solver problem. Optistruct is a good software that together with the software Hypermesh is easyconfigure many options of the meshes. Then is possible to generate a mesh with good quality.

The different results for a new stringer chassis is normal, because each software has a specific algorithm. Theoptimization with Virtual PYXIS for this application was the best (chassis with large up 6.000mm), becauseonly reduce holes in parts really possible in practice in accordance with the draftsman of the structure. TheOC is material law SIMP without penalization was the more possible to do a good application. However thesoftware ParetoWorks and Optistruct can be tested in many others parts of the vehicle, then all software arepossibles by to use for TOM.

7 ConclusionsIt is seen that the optimization area is new and that we should look for it to reduce costs into the automotive

industry. This article aims to research the bibliographic proposed for comparison, and promove the possibilityof the developing an specific algorithm for optimization of the holes in stringer chassis, the theme is possibledeveloping in other future article.How possibility for developing this article it is proposes two studies: developing the reducing of the holes instringer chassis with structural analysis of the three-dimensional fase and developing news analysis for stringerchassis as dynamic structural, vibrations, and others areas.

8 AcknowledgementsThe present study was supported by Altair Brazil (Mr. Valdir Cardoso); ESSS ANSYS (Mrs. Mariana

Buchner Linard); Virtual PYXIS Brazil (Mr. Leandro Garbin and Mr. Paulo Nigro); Sciart (Mr. PraveenYadav); University of Winconsin (Dr. Krishnan Suresh and MBA Liz Christenbury), Lavrita Engenharia (Mr.Wilson Molina and Mr. Roberto Molina), and Scania (Mr. Hugo) and also Mr. Dr. Cicero Ribeiro de Lima(UFABC-SP) by the incentive developments in area of the topology optimization and MSc Kelly Cristina deLira Lixandrao (UFABC-SP), my wife by incentive and comprehension. To all colleagues a big thanks.

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