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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