1 Präsentationstitel | Ort oder Vortragender | YYYY-MM-DD

Topology and Shape Optimization versus

Traditional Optimization Methods

Dr.-Ing. Elke Feifel, Dr.-Ing. Dietmar Mandt, Voith Turbo

2 Topology and shape optimization versus traditional optimization methods

Electric drive (E)

Diesel-Hydraulic drive (DH)

Diesel-Electric drive (DE)

traction motor

trolley wire diesel engine generator

electric converter

traction motor

diesel engine

hydrodynamic transmission

final drive

electric converter

Diesel-Hydromechanic drive (DHM)

diesel engine

gearbox final drive

Overview

Traction Principles of Railway Vehicles

3 Topology and shape optimization versus traditional optimization methods

Metro Pennsylvania

USA

Final Drives

Complete wheel sets

EMU Zagreb

High Speed Train CRH 3

MoR China

4 Topology and shape optimization versus traditional optimization methods

Adapt the speed of the output of an electric

motor or transmission to the speed of the

wheelset via one ore more gear ratios.

Mechanical power transmission with a

minimum of wear, high efficiency and a

minimum of noise and vibration.

Low weight and restricted space.

Final Drives, Values and Objectives

5 Topology and shape optimization versus traditional optimization methods

Production Technologies of Spur Gears

Zahnstange-

Bezugsprofil

Form - Fräser

- Schleif-

scheibe

Fingerfräser

Source: WZL, RWTH Aachen

technologies by hobbing

development in manufacturing

methods leads to wider variety

in geometry

by modifying tooth root

geometry critical stresses can

be reduced

profile grinding

technology

6 Topology and shape optimization versus traditional optimization methods

Optimization of a Spur Gear

Reduction of stress in root fillet

no collision with tooth of opposite gear

free-shape optimization in root fillet

most sever load positions

4 load cases due to 2 directions

dir 1

dir 2

root fillet

FLC1

(dir1)

FLC4 (dir2) FLC2

(dir1) FLC3

(dir2)

7 Topology and shape optimization versus traditional optimization methods

Stress in Root Fillet due to 4 Loadcases

s1,max

dir 1 dir 2

s1,max

s3,max s3,max

LC 1; dir 1 LC 2; dir 1 LC 3; dir 1 LC 4; dir 1

Principle Stress s1

Principle Stress s3

8 Topology and shape optimization versus traditional optimization methods

Shape Optimization of Root Fillet

Optimization task

No. Objective Constraints

2 mimimize max.

principle stress s1

s1 > s1,lim

3 mimimize max.

principle stress s1

4 mimimize max.

equivalent stress sv

9 Topology and shape optimization versus traditional optimization methods

Shape Optimization of Root Fillet

Shape change of optimized

contour

Original Contour

Optimization 2

Optimization 3

Optimization 4

10 Topology and shape optimization versus traditional optimization methods

Principle Stress in Root Fillet (LC4)

principle stress s1

(LC4) in root fillet

Reduction of tensile

stress of 35%

original contour

optimized contour

Original Contour

Optimization 2

Optimization 3

Optimization 4

sigma_1 (Original Contour)

sigma_1 (Optimized Contour 2)

sigma_1 (Optimized Contour 4)

sigma_1 (Optimized Contour 3)

11 Topology and shape optimization versus traditional optimization methods

0.0

0.5

1.0

1.5

2.0

2.5

3.0

sa

fety

fa

cto

r S

F

OriginalContour

OptimizedContour 3

SF(Original)

SF(OptimizedContour 4)

Safety Factor of Root Fillet

SFmin=1.17

SFmin=0.87

fatigue strength

considering mean stress

taken from Smith chart

Minimum safety factors:

0.87 original contour

1.17 optimized

contour No. 3

Increase of load capacity

of 35%

12 Topology and shape optimization versus traditional optimization methods

Safety Factor - Comparison with Bionic Root Fillet

Source: Roth, R.: Developing a Bionic Gear Root Fillet

Contour, VDI-Berichte 2108, 2010.

optimized root fillet

(„tension triangle“)

SFmin=1.17

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

-35 -30 -25 -20 -15 -10 -5 0

node

Safety Factor (Optimized Contour 4)

13 Topology and shape optimization versus traditional optimization methods

Conclusion – Optimization of Root Fillet

Free shape optimization in root fillet of spur gear leads to reduction

of tensile stress and increase of load capacity of more than 35%.

Good agreement with safety factor of bionic root fillet contour based

on the method of „tension triangle“

Speed up optimization process by using shape optimization

Shape optimization on fatigue strength instead of optimization on

stresses

14 Topology and shape optimization versus traditional optimization methods

Spring – Requirements on Design

Specific spring stiffness C0,min

Restriction of design space

Equivalent stress smaller than slim

Topology optimization

Shape optimization

15 Topology and shape optimization versus traditional optimization methods

Topology Optimization to reduce Stiffness

Topology Optimization

No. Objective Constraints Parameters

1 min.

compliance volfrac < Vlim

minimum

membersize

2 min.

compliance volfrac < Vlim

stress constraint

minimum

membersize

3 min. volume

spring

stiffness >

C0,min

stress constraint

minimum

membersize

4 max.

displacement volfrac < Vlim

stress constraint

minimum

membersize

1 2

3 4

16 Topology and shape optimization versus traditional optimization methods

Topology Optimization to Reduce Stiffness

optimization results differ from

design exspected

no feasible design

1 2

3 4

17 Topology and shape optimization versus traditional optimization methods

Topology Optimization

optimization results are framework structures

members are objected to tension or compression

small strain energy large stiffness of structure

large strain energy required

members subjected to bending small stiffness of structure

modifications of design space to force a structure objected to bending

4

mod1

4

mod2

4

mod3

4

mod4

18 Topology and shape optimization versus traditional optimization methods

Design Derived from Optimization Results

restrictions on stiffness C0,min

fulfilled

good agreement with design

from engineering department

allowable stress exceeded

no feasible design

shape optimization with

design derived from topology

optimization

4 mod4

design

proposal

sv

19 Topology and shape optimization versus traditional optimization methods

Freeshape Optimization

sv > sv,max sv < sv,max

Design proposal:

equivalent stress

Results of shape optimization:

shape change equivalent stress

20 Topology and shape optimization versus traditional optimization methods

Conclusion – Optimization of a Spring

OptiStruct optimized design differs strongly from expected design

Topology optimization on minimum compliance has no feasible

design

Modifying the design space leads to feasible design proposal which

fulfills the requirements

„Intelligent“ solutions might get lost in numerical optimization

process

21 Topology and shape optimization versus traditional optimization methods