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FunctionaldesignandoptimizationofparametricCADmodelsinaknowledge-basedPLMenvironmentARTICLEinINTERNATIONALJOURNALOFPRODUCTDEVELOPMENTJANUARY2009DOI:10.1504/IJPD.2009.026174

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60 Int. J. Product Development, Vol. 9, Nos. 1/2/3, 2009

Functional design and optimisation of parametric CAD models in a knowledge-based PLM environment

S. Gomes*, A. Varret, J.B. Bluntzer and J.C. Sagot SeT Laboratory Belfort-Montbeliard University of Technology (UTBM) 90010 Belfort Cedex, France E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] *Corresponding author

Abstract: The main purpose of this paper is to present our approach to automatically generating optimised 3D Computer-aided Design (CAD) models into which all the known expert design rules are integrated, by changing only functional requirements for the same product architecture. Through the requirement specifications integrated into our ACSP Product Lifecycle Management (PLM) system (functional and product architecture parameters), we are able to generate and automatically draft/produce/test/validate/optimise a parametric product architecture and its geometric skeleton, using a commercial CAD software program. A knowledge-based engineering software program, using constraint propagation with a first-order inference engine, and a multiobjective optimisation solver are used as an interface between the PLM system and the CAD software.

Keywords: functional design; knowledge-based engineering; multiobjective optimisation; Product Lifecycle Management; PLM; Computer-aided Design; CAD.

Reference to this paper should be made as follows: Gomes, S., Varret, A., Bluntzer, J.B. and Sagot, J.C. (2009) Functional design and optimisation of parametric CAD models in a knowledge-based PLM environment, Int. J. Product Development, Vol. 9, Nos. 1/2/3, pp.6077.

Biographical notes: After a PhD in Mechanical Engineering from Institut National Polytechnique de Lorraine (INPL) in 1999, S. Gomes is currently an Associate Professor at Belfort-Montbeliard University of Technology in the Mechanical Engineering and Design Department. His current research interest includes multidisciplinary optimisation to improve mechanical engineering design processes using collaborative and knowledge-based engineering.

Antoine Varret is a Teacher at Belfort-Montbeliard University of Technology in the Mechanical Engineering and Design Department. He also continues scientific studies with a PhD work in the Systmes et Transports (SeT) Laboratory. His research focuses on multidisciplinary optimisation in mechanical design.

After technical studies concluded by a Masters degree in Mechanical Engineering and Design from the Belfort-Montbeliard University of Technology in 2006, Jean Bernard Bluntzer began scientific studies with a

Copyright 2009 Inderscience Enterprises Ltd.

Functional design and optimisation of parametric CAD models 61

PhD work in partnership with an automotive supplier working on the bumper area. The main topic of the research, integrating collaborative design and knowledge management, is how to decrease the routine engineering time in the CAD area, and particularly on models based on complex shapes.

Jean Claude Sagot is a Professor in Ergonomics. He is the Director of the Mechanical Engineering and Design Department at Belfort-Montbeliard University of Technology. He is also responsible for the ERgonomie et Conception de Systmes (ERCOS) Search Unit at the SeT Laboratory. His research focuses on the intervention of ergonomics in the design process of products, with particular emphasis on the development of knowledge, methods and tools to recentre design on the end user, while preserving health, safety, comfort and the efficiency of the human-machine relationship.

1 Introduction

The engineering design of complex systems (Rechting, 1991) with a systematic approach (Pahl and Beitz, 1995) is a decision-making process with the purpose of choosing from among a set of options that leads to an irrevocable allocation of resources. It is inherently a multiobjective process. As products become increasingly complex, their design is usually on a large scale, typically with a significant number of design variables, parameters, requirements, constraints and objectives. Consequently, multiobjective optimisation is being used more often to provide one optimal solution.

The main trend, particularly in industrial companies, is to propose complex products whose design spans several engineering contexts and disciplines. At the same time, although companies have grown in complexity, they have also reduced the number of areas of competence, in order to be specialised in one (or several) discipline(s); thus, the use of subcontractors is now very common. In addition, besides the traditional cost considerations, more recent industrial requirements, such as robustness, reliability and design performance and also marketing criteria, have been identified and have quickly become important characteristics of the design and of the optimisation process. Nowadays, actual real-world engineering design problems involve simultaneous optimisation to meet several objectives and to ensure compliance with various constraints determined by the design team.

The main purpose of this work is to develop a design methodology and a direct multiobjective optimisation approach, integrating functional design and knowledge-based engineering features, such as expert rule definition or design experience feedback, in order to reduce costs, lead time and also improve product qualities and values. This methodology helps the designer to take parametric Computer-aided Design (CAD) models of an optimised product through functional requirements, design rules and design objectives that can be verified and reached using optimisation loops. This methodology is applied in a collaborative design process (Kvan, 2000) using ACSP (in French: Atelier Coopratif de Suivi de Projets) (Gomes and Sagot, 2002), a self-developed knowledge-based Product Lifecycle Management (PLM) environment (Shen, 2003; Gomes et al., 2005) based on internet technologies (Liu and Xu, 2001; Zhuang et al., 2000).

62 S. Gomes, A. Varret, J.B. Bluntzer and J.C. Sagot

As a first step, using the requirements specification and the technical characteristics of the product, integrated by the project members into our ACSP PLM system (functional and product architecture parameters), we are able to generate and automatically produce a parametric product architecture and its geometric skeleton, in a commercial CAD software program. CAD designers can then complete this 3D skeleton by using generic templates of parts stored in a shared database (Gomes et al., 2006).

In the second step, a knowledge management approach (Grundstein, 2000) including a knowledge-based engineering software program, using constraint propagation with a first-order inference engine, is used as an interface between the PLM system and the CAD software (Peltonen, 2000).

The last step is to develop an application for the optimisation of the product by using specific algorithms to minimise weight or number of parts or to achieve other objective functions with respect to various functional parameters, geometrical variables and design rules. As the objective functions are considered nonlinear functions, depending on the functional parameters, it is necessary to use a heuristic search method, such as Genetic Algorithms, in order to find the best solution in the design context.

Our methodology of coupling the Genetic Algorithm optimisation approach, constraint propagation, with the inference engine and the PLM environment will be presented. To validate our research hypotheses, an experimental case study is chosen: the ground-link suspension system of a racing car design and manufacturing project, including conceptual, embodiment and detailed design phases as well as manufacturing phases.

Before describing our functional, knowledge-based engineering (Sferro, 1999; Whitney et al., 1999) and optimisation design methodology, we will first present the main principles of multidisciplinary and multiobjective optimisation.

2 Multidisciplinary and multiobjective optimisation principles

Companies need to optimise their products and processes daily, hence optimisation plays a significant role in todays design cycle. Optimising a system means selecting the best available option from a wide range of possible choices. This specific approach can be a complex task as, potentially, a huge number of options should be tested. There are several sources of complexity, such as the computational difficulties in modelling physics problems, the potentially high number of free variables, or a high number of objectives and constraints/constraining factors.

A single optimisation approach is not sufficient to deal with real-life problems. Therefore, engineers are frequently asked to solve problems with several conflicting objective functions.

Multidisciplinary optimisation consists in finding the optimal design of complex engineering systems, which requires analyses that take into account interactions amongst the disciplines (or parts of the system) and which seek to synergistically exploit these interactions.

In order to help engineers and decision-makers, old and new optimisation techniques are studied and widely used in industry. Each optimisation technique is qualified by its search strategy, which determines the robustness, the reliability and/or the accuracy of the


method. Robustness means that the objective functions are met even when starting far from the final solution. On the other hand, accuracy measures the capability of the optimisation algorithm to get as close as possible to the functional desired limits.

There are hundreds or thousands of optimisation methods in scientific literature; each numerical method can solve a specific or more generic problem. Some methods are more appropriate for constrained optimisation, others for unconstrained continuous problems, or for solving discrete problems.

Many classical optimisation methods exist; these methods can be used provided that certain mathematical conditions are satisfied. Thus, for example, linear programming efficiently solves problems where both the objective and the constraints are linear with respect to all the decision variables. Other specific numerical methods can be useful for solving quadratic programming, nonlinear problems, nonlinear least squares, nonlinear equations and multiobjective optimisation.

Unfortunately, real-world applications often include one or more difficulties which make these methods inapplicable. Most of the time, objective functions are highly nonlinear or may not have an analytic expression in terms of the parameters.

From a mathematical point of view, a multiobjective optimisation problem can be written as follows:

min [f1(X), f2(X), ... , fi(X)], Gj(X) 0, and G1(X) = 0, X = (x1, ..., xn+u) where:

X = (x1, ..., xn+u) is the vector of the variable generally integrating the n customers requirements and u technical design parameters of the product. These variables are considered as input data of the optimisation problem. These input parameters are the quantities that the designer can vary. It is by modifying these values that the search for an optimum is performed. The variables can be continuous or discrete. The problem may even contain a mixture of continuous and discrete variables.

f1,...,fi are the objective functions, the response parameters. When i > 1 and the different and conflicting functional requirements are observed, we speak about multiobjective optimisation. These are the quantities that the designer wishes to maximise or minimise. For example, the designer can maximise the efficiency and the performance, or can minimise the cost and the weight.

Gi(x1, ..., xn+u) 0, and G1(x1, ..., xn+u) = 0 are the constraints. Equality and inequality constraints directly connected to the requirements are imposed on the project. These constraints correspond to the limits that the designer must meet due to the need to comply with standards, or due to the particular characteristics of the environment, the functionalities, the physical limitations, etc. These constraints must be satisfied in order to be able to consider a certain solution as acceptable. All the constraints define a feasible region in a multidimensional solution space. For example, designers can impose some general constraints, such as the maximum admissible stress, the maximum deformation, or the minimum performance. The designer can even impose some special constraints on the variables such as the total volume, the thickness range and so on.

With a multiobjective problem, the notion of what is optimum changes as the aim is to find good compromises rather than a single solution. So, a multiobjective optimisation does not produce a unique solution but a set of solutions. These solutions are called


Pareto solutions. The set of solutions can be called trade-off surface or Pareto frontier. In the Pareto frontier, none of the components can be improved without the deterioration of at least one of the other components.

3 Functional, knowledge-based engineering and optimisation design methodology

The design activity involves many contributors and experts throughout the product lifecycle, which starts with project tasks, proceeds to functional definition, product modelling, manufacturing and ends with its destruction or recycling. Whether the design solution is a tangible product, service, software program, process, or something else, designers typically follow these main steps, applying a concurrent (Sohlenius, 1992) and distributed (Brissaud and Garro, 1996) engineering process:

understand their customers needs and requirements (Requirements vector R = [r1,, rn])

define the problem they must solve, and also the functions and subfunctions they have to develop in order to satisfy these needs (Functions vector Fu = [fu1,, fum])

create and select a product solution including one or several parts (Parts vector P = [p1,, pk])

analyse and optimise the proposed solution by finding optimal sets of technical characteristics or parameters for each part, subproduct or product assembly (Technical parameters vector T = [t1,, tu]), while maximising or minimising objective functions and verifying design constraints and rules (Rules vector Ru = [F1(X),, Fi(X)]). In this context, X is defined by the concatenation of both R (R = [r1,, rn]) and T (T = [t1,, tu]) vectors: X = [x1, ..., xn+u] = [r1,, rn, t1,, tu]

check the resulting design against the customers needs, by means of a validation loop.

3.1 Our design methodology

Our design approach offers a systematic and orderly way to proceed through the development process of optimised products (Eggers et al., 2002). This methodology ensures that designers:

integrate the customers requirements during the entire design process, applying the House of Quality principles (Mocquo, 2007)

store their design information during the design process in a PLM system, using the Multi-Domains and Multi-Viewpoints data model, based upon the Axiomatic design (Suh, 1998) and the Multi-Viewpoints Product Model (Tichkiewitch, 1996)

extract, reorder and validate engineering knowledge, using our KATRAS multiagent society (Monticolo et al., 2006), in a collaborative engineering context (Jin and Lu, 1998)


generate a well-structured and parametric product architecture, based on our

approach of functional constraint propagation in parametric CAD models (Bluntzer et al., 2006)

can combine the design parameters and make each of them evolve within the limits of the customer requirements while following all expert rules, using an inference engine in a knowledge-based engineering system (Whitney et al., 1999; Serrafero, 1998)

make the best possible design decisions due to multidisciplinary and multiobjective optimisation loops, involving metaheuristic algorithms such as genetic algorithms, for minimising and/or maximising objective functions.

As illustrated in Figure 1, our functional, knowledge-based engineering and optimisation design methodology has been developed in order to reduce the time devoted to routine design by connecting all these design tools, while keeping a traceability between the different viewpoints (functional, structural, geometric, etc.) on the product:

All designers can generate Project, Product, Process and Usability information in our PLM system, by integrating knowledge engineering features. At the same time, a continuous and automatic process of knowledge capitalisation, using the KATRAS multiagent society, is carried out (Monticolo et al., 2006).

The product architect creates a parametric product architecture and skeleton in the PLM environment, and the same features can be automatically generated in the CAD software, using a Visual Basic script file, exported directly from the PLM system. At the same time, he/she generates a table of parameters (X = [x1, ..., xn+u]) with various acceptable domains for continuous variables (for example : x1 [8,10.5]) or discrete variables (x2 {steel, aluminium, carbon}).

Then, the CAD designers can begin to build solid features directly on the previous parametric product architecture and skeleton, with a limited access control on the parameters.

As proposed by the KnoVa-Sigma model (Serrafero, 2002), expert designers first validate expert knowledge extracted by the artificial agents from the PLM database. They perform a voting process in a knowledge management environment system in order to validate the engineering knowledge such as expert rules (Fi(X), Gj(X), if-then-else rules, etc.), and define the project-product-process context in order to be able to reuse this knowledge in future projects.

Then, with a knowledge-based engineering platform, using an inference engine based on constraint propagation (Yannou et al., 2003), the expert designers set up the design parameters (X = [x1,, xn+u]) with values relating to the acceptable domains, according to the customers requirements. In this step, we see that the knowledge-based engineering application computed by the inference engine is automatically generated from the knowledge-based PLM system.

In order to ensure quality-cost-time requirements on the project programme, expert designers have to proceed to optimisation loops on the product definition, taking into consideration design constraints (Gj(X)0) and objective functions Fi(X) to be minimised or maximised, as described in the previous paragraph. They have to build


and compute an optimisation model, using a multidisciplinary and multiobjective optimisation processor, computing input/output parameters (X = [x1,, xn+u]) imported from the previously presented table of parameters

Finally, product architects and expert designers can choose various vectors of optimal solutions (input/output parameters Xi = [x1,, xn+u]i) situated on the Pareto frontier of the optimisation problem. After a last checking loop in the knowledge-based engineering platform, these optimal solutions, defining various optimal design alternatives, are then archived in the CAD model table of parameters, in order to verify the compatibility with the other nonalgebraic expert rules.

CAD designers, expert designers and product architects can finally visualise the optimal design alternatives by opening the CAD model synchronised with the table of parameters.

Figure 1 Functional, knowledge-based engineering and optimisation design methodology (see online version for colours)

PLM environment

KM environment

KBE applicationwith an inference

engine forconstraintspropagation

KBE applicationwith an inference

engine forconstraintspropagation

Multi-Disciplinaryoptimizationprocessor

Multidisciplinaryoptimisationprocessor

ParametricCAD modeler

Dynamictable ofparameters

PRODUCT DOMAIN Requirements (R) Functions (Fu) Parts (P) Technicalcharacteristics (T),

PRODUCT DOMAIN Requirements (R) Functions (Fu) Parts (P) Technicalcharacteristics (T)

PROJECT DOMAINTasksResourcesMilestonescosts,

PROJECT DOMAINTasksResourcesMilestonescosts,

PROCESS DOMAINPlants,Assembly facilitiesManufacturingmeans ,

PROCESS DOMAINPlants,Assembly facilitiesManufacturingmeans ,

EXPERTPROCESSEXPERT

PROCESSEXPERT

EXPERIENCEEXPERT

EXPERIENCEEXPERT

RULES (Ru)EXPERT

RULES (Ru)EXPERT

VOCABULARYEXPERT

VOCABULARY

2. Generation of a parametric product architecture and skeleton (*.catvbs script file)2. Generation of a parametric product architecture and skeleton (*.catvbs script file)

4. Generation of a parameters table X with validity domain (x1 [10,35])4. Generation of a parameters table X with validity domain (x [10,35])

synchronisation

8. CAD model

5. Set up of parameters (X=[x1, ,xn+u ]), validity domains (x2{ steel, a luminum , carbon }) and design objectives (Gi (X) 0)

5. Set up of parameters (X=[x1, ,x +u validity domains (x2{ steel, a luminum , carbon }) and design objectives (G

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7. Vectors of optimalinput/outputparameters

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7. Vectors of optimal

parameters(Xi = [x1,, xn+u ]i on

Pareto Frontier )

7. Design choicesdefinition7. Design choicesdefinition

3. Model solidfeatures

3. Model solidfeatures

4. Validate expertknowledge

4. Validate expertknowledge

1. Generate Project, Product,Process and Usability information

1. Generate Project, Product,Process and

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ExpertDesigners

ExpertDesigners

CADDesigner

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Designers

3.2 Software tools applied in our design methodology

Software-supporting concurrent engineering, such as PLM systems, is needed to help design team members to manage data, information and knowledge during their project tasks. ACSP is a web-based PLM platform which helps the design team members to carry


out cooperative activities in product-process-design projects (providing the right data, to the right person at the right moment) and, by the integration of expert rules, to accelerate and optimise routine design processes in order to give more time to the innovative design tasks.

To carry out this objective, we have developed knowledge-based engineering features, such as expert rule definition or design experience feedback, in the ACSP PLM system, in order, first, to store this knowledge in a knowledge management system, and then to pilot parametric CAD models of the product (in our case CATIAv5), after one or several constraint propagation and optimisation loops using KADVISER, a knowledge-based engineering development environment and ModeFRONTIER, a multidisciplinary optimisation software program.

A knowledge-based engineering solver is a system which allows the routine design process to be accelerated by guiding designers through their choices and their thinking. It uses expert rules extracted from a knowledge database or formalised by human experts.

KADVISER includes a knowledge-based engineering solver which enables the development and running of expert applications, taking into consideration the subject to change and specific character of the company know-how. KADVISER includes a reasoning module based on an inference engine which gives data entry assistance, helps in decision-making and manages the data inexactitude. It can also communicate with the other main software families (PLM database, CAD modellers, MS Excel spreadsheet, etc.).

Constraint propagation is the mechanism in KADVISER which makes it possible to deduce the remaining fields of solutions at any moment during the application of a set of constraints. The main principles of the KADVISER inference engine with a constraint propagation mechanism are:

reversible constraint propagation the reversibility is the mechanism of the inference engine which makes it possible to suppress the constraints created by the input/output concepts. This spares designers from writing the various equivalent reversed formulas. To illustrate the reversibility mechanism, we consider the input/output vector X = [x1, x2, x3, x4] where x1, x3, x4 are real, and x2 is a chain of characters. If we have a constraint G1(X): x1 = x3 + x4, this constraint is also considered by the inference engine as (x3 = x1 x4) or (x4 = x1 x3). These reversibility properties have some limitations depending on the mathematical expression of the constraint

management of assumptions allowing the exploration of all the possible solutions reduction of the possible fields of solutions, starting from a numerical interval (for

example: x1[8,10.5]) or a list of discrete values (x2{steel, aluminium, carbon}). In order to illustrate the constraint propagation in the KADVISER inference engine, the following example is given, using numerical fields:

x1, x3, x4 are real: x1 [8.0, 10.5], x3 [22.0, 41.3] and x4 is unknown 1st computed constraint: (x4 = x3 11.0) then x4 [11.0; 30.3] 2nd computed constraint: (x4 = x1 + 6.0) then x4 [11.0; 16.5] 3rd computed constraint: (x4 12.0) then x4 [12.0; 16.5].


ModeFRONTIER is a tool for multidisciplinary optimisation problem solving, and it includes the most widely used methods, in fact, both standard and metaheuristic methods, for single and multiobjective optimisations.

Before 1980, multiobjective optimisation problems were solved only by means of weighted functions, with which the problem was transformed into a single objective problem using problem-dependent weightings wi, empirically defined by the user:

F(x) = w1*F1(X) + w2*F2(X) ++ wk*Fk(X).

Metaheuristic methods are a new type of method that has been developed since 1980. These methods have the ability to solve even difficult optimisation problems in the best way possible and aim to optimise several objectives simultaneously, thus generating various points in the Pareto set. This class of methods includes, among others, simulated annealing, genetic algorithms, particle swarm, ant colonies, evolutionary strategies and tabu search. This group of methods has significantly contributed to the renewal of multiobjective optimisation and has been applied in our experimental case study.

4 Experimental design case study

In order to illustrate our proposals, an experimental design case is chosen. Every year, the Mechanical Engineering and Design Department at Belfort-Montbeliard University of Technology has to develop and prototype an entire new racing vehicle. To simplify the demonstration, we choose to limit the experimental case study to a subproduct of the racing car: the ground-link suspension system. This subproduct of the racing car includes many mechanical parts linking the wheel to the chassis. The design and optimisation process will be focused on the suspension triangles (from the diagrams, this component looks like the one called the wishbone in English, an A-frame component linking the chassis to the wheel-hub) of the ground-link system. The main steps of our previously presented methodology are applied in this experimental case. For the optimisation study, the technical characteristics of external systems in interaction with the ground-link suspension (chassis, hubs, brakes, wheels) have been considered as requirements (R), as described in Table 2.

To complete the requirements, the mechanical characteristics of the ground-link suspension are considered as technical parameters (T), the continuous or discrete variables of our design and optimisation case study (Table 3).

As presented in Table 1 and Table 4, describing objective functions, constraints and expert rules, the equations for the optimisation problem are defined in two steps. First, we apply traditional mechanical analysis of nondeformable solids, allowing the definition of the maximum deceleration acceptable to the vehicle and loads generated at the various link points of the suspension triangles (wishbones). Then we define a standard material strength calculation in order to identify the stresses and deformations corresponding to these loads.

The first step allows the highest load applied to the lower triangle at point A to be identified (the respective values of the load vectors in X and Y directions: 1792 N; 1482 N, in a constant deceleration phase, value = 10 m/s corresponding to an emergency braking condition). However, this calculation identifies the front tie-rod of the lower triangle as the most highly stressed component.


Table 1 Requirements defined as constants of our design and optimisation case study

(see online version for colours)

Requirements (R)

{wheel/hub/brake} set geometry

A 865.25

0

B 96108

0

RS 5.26200

C 225.46

124

Coordinates of the different points in orthonormal basis O (X, Y, Z), in millimetres, are the following (with point (O) at the centre of the wheel):

Track width of the vehicle 1600 mm

Castor angle, camber angle, toe-out

0 (simplified configuration of the sets)

{wheel/hub/brake} set mass m = 15 kg

Vehicle suspended mass M = 460 kg

Front/Rear allocation of the suspended mass

front: Mv = 160 kg

rear: Mr = 300 kg

Vehicle centre of gravity height/the ground

h = 0,35 m

Vehicle wheel base e = 2,495 m

Suspension inclination angle in relation to the ground

am = 45

Friction factor of the tyre on dry road

0,85

Note: Lower triangles included in horizontal planes. For each triangle, bisectrix of the angle formed by the two tie-rods and the vehicle axis are perpendicular.

Table 2 Technical parameters defined as continuous or discrete variables of our design and optimisation case study (see online version for colours)

Technical parameters (T)

Continuous variables

Angle between the tie rods [20; 120] External diameter (or side) value H [10 mm; 40 mm] Thickness e [1 mm; 3 mm] Tie-rod length L = 300 mm

A

X

Y

D

EL

A

X

Y

D

EL


Table 2 Technical parameters defined as continuous or discrete variables of our design and optimisation case study (see online version for colours) (continued)

Technical parameters (T)

Discrete variables

Section type square shape: B = H

or

round shape: H = 2R

Material item material cost (/T) (kg/m3) E (Gpa) Re (MPa) n 1 steel 700 7850 210 235 4

2 aluminium 4000 2900 75 180 4

3 stainless 4500 8700 203 185 4

4 carbon 5000 1530 50 555 1.5

Table 3 Objective functions and constraints defined for our design and optimisation case study

Objective functions (Fi(X))

Tie-rod mass (to be minimised) m = .S.L Global stress (to be minimised) max tc f = + Global strain (to be minimised) f = f dl+

Constraints (Gj)

Maximum stress allowed in normal section Remax

n

Notes: Units: Lengths (mm), Loads (N), Youngs Modulus (N/mm or MPa), Moment of inertia (mm4), Sag (mm), Stress (N/mm or MPa), elastic limit (Re; N/mm or MPa), density (; kg).

Table 4 Expert rules defined for our design and optimisation case study

Rules (Ru)

Axial load (wheel/lower triangle) at point A (in O(X;Y;Z) basis)

Tix: 1792 N

Lateral load (wheel/lower triangle) at point A (in O(X;Y;Z) basis)

Tiy: 1482 N

Normal load in front tie-rod ( )1 1.cos 2 .sin( 2)2 2

Dn Tix Tiy = Tangential load in front tie-rod ( )1 1 1sin 2 .cos( 2)

2 2sin( 2) 2Dt Tix Tiy

= + +

Sag resulting from Dn 3.3

Dn Lf

EI=


Table 4 Expert rules defined for our design and optimisation case study

Rules (Ru)

Maximum stress resulting from Dn . .2

fDn L H

I =

round section: 4 4( ( 2 ) )I H H e= 64

Normal section moment of inertia

square section: 4 41

( ( 2 )12

)I H H e= Extension/Retraction resulting from Dt .

.Dt L

dlE S

= Maximum stress resulting from Dt

SDt

tc =

round section: 2 2( ( 2 )S H H e= 4 )

)

Tie-rod normal section

square section: 2 2( ( 2 )S H H e= Notes: Units: Lengths (mm), Loads (N), Youngs Modulus (N/mm or MPa),

Moment of inertia (mm4), Sag (mm), Stress (N/mm or MPa), elastic limit (Re; N/mm or MPa), density (; kg).

During the second step, we determine the normal and tangential load components in the front tie-rod and the resulting strain and stress.

As defined previously, during the project, these requirements, technical parameters, objective functions, constraints and expert rules are integrated by the expert designers into the ACSP PLM environment, directly associated to the product part list (Figure 2). The data are then extracted and structured in order to create:

knowledge archives associated with ACSP in a knowledge management system script files which automatically generate a CATIAv5 parametric CAD model,

describing the product parametric architecture, without any solid features. These solid features will then be created by CAD designers, using the previous product architecture

scripts for automatic generation of a knowledge-based engineering application via the KADVISER platform.

Figure 2 Example of an ACSP interface describing parameters and rules associated with the product part list (see online version for colours)


The KADVISER software, linked with the ACSP PLM environment, enables the expert designer to quickly generate specific knowledge-based engineering applications, as shown in Figure 3.

Figure 3 Screenshot of KADVISER application generated from ACSP database (see online version for colours)

With the KADVISER inference engine, it is possible to manipulate different types of elements: continuous variables (; H; e; L), discrete variables (material, section type), coupled variables (material: the material choice modifies cost, density, Youngs modulus, elastic limit and safety factor values), noncoupled functions (Dn; Dt) and coupled functions. For instance, S and I parameters are linked with section type and with all other functions using I and S parameters.

The specific, generated Knowledge-based Engineering (KBE) application allows the reduction of the domain of acceptable fields to be seen, when a value is assigned to one or several parameters, applying constraint propagation and the reversibility properties of the inference engine.

The next step is to carry out the optimisation with three contradictory objectives: minimise mass, max and strain. We apply the ModeFRONTIER optimisation software and declare, by importing the CAD parameter table, the following: input data (; section type; e; H; material), output data (mass; global stress; global strain) and rules. The optimisation was carried out in four steps:

Step 1 definition, through a random design of experiment approach, of a few sets of vectors (X) which are representative of the whole design space (input data)


Step 2 choice of a metaheurisric algorithm (we select in ModeFRONTIER a

Multi-Objective Genetic Algorithm) as a first base for calculation, analysis of mass, strain and stress values on the whole design space

Step 3 elimination of the vectors outside the Pareto frontier Figure 4. On the left-hand diagram, these vectors are all points on the right of the curves (we can identify four curves, which represent the Pareto frontiers for the four materials)

Step 4 selection of several optimal solutions and exportation of their values in an MS Excel spreadsheet.

Figure 4 Results of our optimisation application including the Pareto frontier graph and CAD model table of parameters, when analysing the results of contradictory objective functions: mass and strain (see online version for colours)

Design ID e H section material stress Re/n strain mass cost

142 1.0 30.0 120 1 4 34.6 370.0 0.36 0.042 0.209

214 1.4 34.0 120 1 4 21.5 370.0 0.19 0.066 0.329

252 1.0 16.0 120 2 1 58.7 58.8 0.34 0.141 0.099

298 1.0 28.0 120 2 2 27.9 45.0 0.18 0.094 0.376

318 1.0 24.0 120 1 1 46.5 58.8 0.16 0.170 0.119

367 1.2 40.0 120 2 2 15.2 45.0 0.07 0.162 0.648

1351 2.6 34.0 120 1 4 12.2 370.0 0.11 0.118 0.589

Notes: Section type is: 1 = round; 2 = square.

The last step is to visualise the results obtained directly, by opening the CAD model and selecting the desired optimal design. As explained previously, the MS Excel spreadsheet containing the optimal Xi vectors is also declared as a parameter table for the parametric CAD model.

Figure 5 presents three different optimal solutions computed from the same parametric CAD model, when selecting the optimal design number 142, 298 and 318 from the parameter table resulting from the application of our methodology in a racing car experimental design project.


Figure 5 Visualisation of the results of or functional design and optimisation using a knowledge-based PLM environment (see online version for colours)

Design ID: 142

Design ID: 298

Design ID: 318

5 Conclusion

In this paper, we presented our functional, knowledge-based engineering and optimisation design methodology, which has been defined to accelerate routine design in order to leave more time available to innovation. This methodology uses various software tools in different research fields: PLM, Knowledge-based Engineering, multidisciplinary optimisation and advanced parametric CAD modelling. In order to validate our assumptions, we launched an experimental design case study: the design and build of a racing car. In this paper, we limited the application to a small part of the system: the suspension triangle (wishbone) of the ground-link suspension system. This experimental case study helps us to assess the methodology by identifying the main positive and also negative points to improve. In this context, the main positive points of our methodology are:

ensuring that the product design remains within the limits set out by the customers requirements, in so far as a true functional analysis and design is applied

ensuring that the design developed is verified using all the expert rules, which must be frequently updated and validated by various expert designers

archiving the data and information from the project, and also accumulating knowledge (expert rules, expert vocabulary, expert experiences, etc.)

defining several design parameter sets corresponding to optimal solutions and good compromises between different contradictory objectives. The multiobjective genetic algorithm allows us to eliminate classical analysis-synthesis-evaluation loops of a traditional design process (Yannou et al., 2003), and to go farther than a just acceptable solution. This approach is performed without reconsidering the performance of the optimisation algorithm used

immediate visualisation of the different optimal solutions by automatic update of the parametric CAD model.


Our methodology shows a few lacks that must be addressed in the future. First, the application field of this methodology is limited to routine design. Product architecture and technical principles must be determined before the beginning of the optimisation loop, as an input of the illustrated process.

In our example, we use explicit mathematical functions, making the application of optimisation algorithms faster and easier, considering the very simple shapes used for the product (simple solids with constant section tubes) and also well-known mechanical analysis models. Future work will consist in considering more complex shapes and solid features and integrating data coming from other fields. These data can be measurements resulting from numerical simulations and analyses performed in Computer Aided Engineering (stress, strain, Young Modulus, etc.) or CAD (volume, centre of gravity, material density, etc.) systems.

Another issue we intend to address in further work consists in reducing the number of steps of our methodology, which can introduce a lack of traceability of the design choices during the feedback loops.

During the whole design process, the traceability between the different choices made about the product will be implemented through a matrix-based modelling and system analysis method, describing product design information: requirements (Rn vector of n requirements), functions (Fum vector of m functions), parts (Pk vector of k parts) and technical parameters (Tu vector of u technical parameters). Our traceability method will use several matrices:

Requirements-Functions matrix: Rfu = (rfuij), 1 i n, 1 j m Functions-Parts matrix: FuP = (fupij), 1 i m, 1 j k Parts-Technical parameters matrix: PT = (ptij), 1 i k, 1 j u. Each matrix contains a binary quotation (0 or 1) representing the relationships between the four information domains. This approach allows basic multiplication of adjacent matrices to analyse interaction propagation between the different choices concerning the systems and helps to proceed to a reverse engineering approach to visualise the impact of each modification. For instance, the RFu and FuP matrices are multiplied together to produce the Requirements-Parts matrix (RP = (rpij), 1 i n, 1 j k), which provides a means for understanding what requirements are related to product parts. Next, the RP is multiplied with the PT matrix to define the Requirements-Technical parameters (RT = (rtij), 1 i n, 1 j u) to determine how the requirements are related to the technical parameters.

The analysis performed on the matrices uses simple mathematical functions, including the summation of rows and columns and sorting. The methods, similar to the Axiomatic design (Suh, 1990; 1998) and Design Matrix System (Browning, 2001), provide useful insights into system requirements, functionality and components by focusing attention on important requirements, functions and components. This will be a great challenge for our next piece of research work.


Acknowledgements

The authors would like to thank the Metropolitan Community of the region of Montbliard, the Franche-Comt Region Council, OSEO Innovation, the French Ministry of Industry and the Automotive of the Future cluster, for their funding of this research activity.

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