Architecture Optimisation applied to Gearboxes SIM@SYST. Level 2014, - - PowerPoint PPT Presentation

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Architecture Optimisation applied to Gearboxes

SIM@SYST. Level 2014, Carg` ese Steven Masfaraud 1 2 Fabrice Danes 1 Pierre-Emmanuel Dumouchel 1 Florian de Vuyst 2 Nicolas Vayatis 2

1PSA Peugeot Citro¨

en

2CMLA ENS Cachan

October 20, 2014

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 1 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

1

Architecture optimization of gearboxes Gearbox Architectures Milestones Specifications Criteria, Constraints State of art

2

Optimization of a given architecture Problem definition Framework for optimization of given architecture Formalization of architecture description Analysis: computation of criteria and constraints functions Optimization strategy

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Concluding remarks

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 2 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Gearbox Architectures

Architecture optimization of gearboxes

Create a software that find the best gearbox according to some specifications ⇒ Browse all architectures (technical solutions)

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 3 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Gearbox Architectures

Architecture optimization of gearboxes

Create a software that find the best gearbox according to some specifications ⇒ Browse all architectures (technical solutions)

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 3 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Gearbox Architectures

Architecture optimization of gearboxes

Create a software that find the best gearbox according to some specifications ⇒ Browse all architectures (technical solutions)

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 3 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Gearbox Architectures

Architecture optimization of gearboxes

Create a software that find the best gearbox according to some specifications ⇒ Browse all architectures (technical solutions) Components composing an architecture: Rotating shafts Connexions between shafts: Gears, epicyclic, CVT, freewheel... Selection components: synchronizers, clutches...

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 3 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Milestones

Milestones

Architecture Optimizer Architecture Generator Assemblate blocks Parametrization Architecture Viability tester Test viability: Results analysis Best representant architecture Valid architecture Invalid Optimization

• obtaining ratios
• commandable

Best representant Store best

• f best Arch

representants to create arch

1

Optimization of given architecture to find its best representative

2

Architecture generation

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Filtering architecture with automated engineer reasoning

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 4 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Milestones

Design Space

Once the engineer has selected an architecture, he must finds the best dimensions of the gearbox to meet the specifications

λ1 λ2 λ3 λ4 λ5 λ6 λ7 λ8 λ9 Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 5 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Specifications

Specifications

Ratio definition While engaged, a gear defines a ratio of rotational speed between the input (engine) and the output (wheels) ri = ωoutput ωinput , i = [1, ng] with ng the number of gears of the gearbox

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 6 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Specifications

Specifications

Ratio definition While engaged, a gear defines a ratio of rotational speed between the input (engine) and the output (wheels) ri = ωoutput ωinput , i = [1, ng] with ng the number of gears of the gearbox Adaptation of gearbox ratios on each couple car/engine Lower CO2 emissions on certification cycles Maximize the driveability

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 6 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Specifications

Specifications

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 6 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Criteria, Constraints

Criteria, Constraints

Criteria Minimize distance to ratios specifications Minimize mass Minimize production price Maximize efficiency

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 7 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Criteria, Constraints

Criteria, Constraints

Criteria Minimize distance to ratios specifications Minimize mass Minimize production price Maximize efficiency Constraints Imposed functional volume Non-collision of gearbox parts

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 7 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

State of art

State of art: at PSA

Constrained optimization for known architecture Parametrize the architecture: position of parts and shafts, diameters

• f gear

Writing on paper the objective function to maximize Writing on paper the (in)equations of constraints

Exceeding of functional volume No part collision

Writing them in a Matlab input file for optimization Issues Architecture is fixed A change in architecture means rewriting everything from scratch Functional volume must be simple to have analytical equations

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 8 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

State of art

State of art: Literature review

Yi-shih Lin (2009): A Method and Software Tool for Automated Gearbox Synthesis Associated with Engineers from Romax (Gearbox software editor) Automatic solving of ratios, graph-oriented Volume constraints simplified to 1D problems Set of elementary components limited (only gears) No other work related afterwards, no implementation known in Romax

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 9 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Problem definition

Respect of specifications

Objective function to maximize f (x) = −µ1

i=nr

• i=1

(ri(x) − rit)2 − µ2m(x)

• Criteria

−µ3Vext(x) − µ4Vc(x)

• Constraints

ri(x) Actual Ratio rit Targeted Ratio ng Number of gears m(x) Actual mass Vext(x) Overflow volume of parts outside of functional volume Vc(x) Collision volume between parts µ1,µ2 Balance coefficients given by the engineer µ3,µ4 Very high penalty coefficients

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 10 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Problem definition

Respect of specifications

Objective function to maximize f (x) = −µ1

i=nr

• i=1

(ri(x) − rit)2 − µ2m(x)

• Criteria

−µ3Vext(x) − µ4Vc(x)

• Constraints

It is possible to imagine configurations that does not respect the constraints Constraints violation= low function value The optimizer can find its way in order to reduce constraints violation

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 10 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Framework for optimization of given architecture

Optimization workflow

General Mechanics Architecture Analyser Ratios Models Forces Parameters set up Compute Speeds Forces Architecture Sizer

Function

Mass Volumic Analyser Optimizer Specifications point parameters Models Generator function evaluator Compute mass, volumes Parts Catalog Volumes Function Value

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 11 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Formalization of architecture description

Description by a graph

Idea Describe in a simple way the technical solution Shafts connected by functions ⇒ graph Mechanical point of view: Energy paths in the gearbox Handle assembly constraints for parametrizing Graph analyser writes geometrical assembly constraints These constraints are solved in a constructive way

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 12 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Analysis: computation of criteria and constraints functions

Analysis: computation of criteria and constraints functions

Evaluating criteria and constraints functions To evaluate the objective function, specific analysis package were developed: Ratios: General mechanics model Mass, volumes: Volume models Volume model General Mechanics model

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 13 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Analysis: computation of criteria and constraints functions

Analysis: computation of criteria and constraints functions

Evaluating criteria and constraints functions To evaluate the objective function, specific analysis package were developed: Ratios: General mechanics model Mass, volumes: Volume models Volume model General Mechanics model

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 13 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Analysis: computation of criteria and constraints functions

Analysis: computation of criteria and constraints functions

Evaluating criteria and constraints functions To evaluate the objective function, specific analysis package were developed: Ratios: General mechanics model Mass, volumes: Volume models Volume model General Mechanics model

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 13 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Optimization strategy

Genetic Algorithms (GA)

Advantages of GA Global search Adaptation to the specificities of the problem by defining adapted mechanisms (mutation, crossover) Sensitivity to noise limited

Figure : Collision Volume function Figure : Exceeding volume function

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 14 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Optimization strategy

Sub-problems

To accelerate convergence, we use the specificities of the problem Parameters are separated in different sets: Almost independent problems Transversal position of shafts Transversal positions of blocks Axial position of blocks on shafts Axial positioning on shafts is the most difficult one to solve for the

• ptimizer

→ Information of parts width was not given to the optimizer

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 15 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Optimization strategy

Axial Pre-optimisation

1D optimization for axial positioning Defining position and width of blocks by functions

x p1(x) p2(x) p3(x) w1(x) w2(x) w3(x)

Minimizing distance between parts Writing non collision constraints minimize

x

|pi(x) − pj(x)| , i = j subject to |pi(x) − pj(x)| > wi(x) + wj(x) 2 , i = j

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 16 / 17

Architecture optimization of gearboxes Optimization of a given architecture Concluding remarks

Concluding remarks

Work done Framework developed to evaluate Gearbox fitness function and constraints Optimizer developed using specificities of the problem Pre-Optimization to increase convergence Future Work Explore architectures using graph theory Filter these architecture with automated engineer reasoning

Steven Masfaraud (PSA/CMLA) Architecture Optimisation of Gearboxes October 20, 2014 17 / 17