Post on 24-Apr-2022
Mercedes-Benz Türk TP/EVT - Team CAE - Calculation and Simulation
Load generation and durability assessment of leaf springs with CAE methods 3rd International Conference
Dynamic Simulation in Vehicle Engineering
23.05.2014, St. Valentin, Austria
Mehmet Bakır, Murat Sıktaş, Serter Atamer
4 => 3
new thickness
profile
Weight and cost reduction of the pendulum leaf spring
Optimization of the leaf spring
Reduction of leaves from 4 to 3 with new thickness distribution
Because of the thickness profile increase in all leaves, the new designed leaf spring (k=0.32 mm/kN) is approx. 9%
stiffer than the original leaf spring (k=0.35 mm/kN).
Unloaded original leaf spring geometry is scanned and this exact
geometry is modelled by finite element modeling.
The new designed leaf spring geometry is designed by the
design team and this geometry data is modeled by finite
element modeling.
Dickenverlauf der originalen Pendelfeder
Mercedes-Benz Türk - TP/EVT - Team CAE 2
Mercedes-Benz Türk - TP/EVT - Team CAE 3
Calculation Steps
2. Elastokinematic-Calculations
3. MBS-Calculations
4. FEM-Calculations
5. FEMFAT-Calculations
Elastic Spring Model
Cutting Forces
Max-Stresses
Fatigue Life
Fo
rce-T
ime H
isto
ry
1. Basic-Checks with BLAFES
4
Methods for Load Collective Calculation with MBS
Calculation of the Load Spectra (Cutting Forces)
Simulation based on measured wheel forces MBS of complete vehicle on digital road profile
Simulation based on endurance track profiles Tire models
Objective Determination of the load spectra of cutting forces for testing and fatigue analysis
Digital road profile
Method 2 Method 1
• 2 different methods are available for durability analysis of components which are simulation of complete
vehicle and simulation of axle systems.
• In this study, rear axle system is used in order to calculate the load spectra of leaf spring cutting forces which
delivers more accurate results to be used in durability analysis of leaf spring.
Mercedes-Benz Türk - TP/EVT - Team CAE
Rear axle MBS Model
Rear axle CAD Model
5
Coil bush
Second rear axle
Triangular
control arm
MBS Model
Leaf spring
First rear axle
longitudinal control
arm
Suspension
damper
Based on the CAD model of the rear axle sub-
system, MBS model was built to calculate the
load spectra of the cutting forces acting on the
leaf spring using measured wheel forces.
Mercedes-Benz Türk - TP/EVT - Team CAE
6
•Force element is built-in for coil bush.
•Leaf springs are modelled as beam elements by the help of Abaqus
program and transferred to Simpack.
•Nonlinear characteristic curves are used for suspensions force elements.
•Stabilizer is modeled with beam elements for its flexible characteristics
Leaf springs as beam models
Force elements for
longitudinal and triangular
control arm
Force element for coil bush
Nonlinear characteristic
curves for suspension
MBS Model
Details of the rear axle multi body simulation model
Stabilizer as beam model
From Abaqus beam model to Simpack
Mercedes-Benz Türk - TP/EVT - Team CAE
7
Wheel force measurements
by force transducers
MBS Calculations Vehicle wheel force measurements for MBS calculations
Measured Wheel Forces
from the vehicle
2 x 13 t, Q3A, V48, Pen
3-Achser, 2 x 13 t
L964V048 6X4 SZM
Measured Forces & Moments in 6 directions
Measured wheel forces
are applied in MBS
Model as Input Values
time
Measu
red
Fo
rce in X
-dir
ecti
on
Application of
measured forces
Mercedes-Benz Türk - TP/EVT - Team CAE
Mercedes-Benz Türk - TP/EVT - Team CAE 8
MBS Calculations
For the original and weight-reduced leaf springs
2 different MBS models were built.
The cutting forces and moments acting on
the leaf springs are calculated with the help of
measured wheel forces for both models.
Measured Wheel Forces
2 x 13 t, Q3A, V48, Pen
3-Achser, 2 x 13 t
Force-Time Table
Critical time-point with Max-Fz
For the original leaf spring
Fo
rce [
N.]
Torq
ue [
Nm
m.]
Für die originale Pendelfeder
Max-Forces
L964V048 6X4 SZM
Samples from the results: Tables of the max forces
[N/mm2]
Mercedes-Benz Türk - TP/EVT - Team CAE 9
FEM Calculations using MBS cutting forces & moments
New designed leaf spring vs original leaf spring – max stresses
-0.82
0.87
-0.87
0.82 0.86
-0.82
Principal stress distribution on the upper (last) leaf:
The maximum stress values on the upper leaf of the new designed leaf spring decreases approx. 10% in comparison with the original leaf spring.
0.81
-0.87
Highest stress
-1.08
0.94
-0.93
1.00 0.93
-1.20
0.93
Highest stress
-0.88 -1.06
0.88 0.93
-1.02
New design
Original
The stress values
are scaled to the
maximum value in
the corresponding
figure showing the
maximum as 1.00
and all the others
as percentage (%)
values in relation
to the maximum.
[N/mm2]
Mercedes-Benz Türk - TP/EVT - Team CAE 10
-0.67
0.72
-0.71
0.69 0.73
-0.67
Principal stress distribution on the lower (first) leaf:
0.69
-0.71
Highest stress
-0.77
0.99
-0.95
0.83 1.00
-0.79
0.82
Highest stress
-0.95
New design
Original
FEM Calculations using MBS cutting forces & moments
New designed leaf spring vs original leaf spring – max stresses
The maximum stress values on the lower leaf of the new designed leaf spring decreases approx. 20% in comparison with the original leaf spring.
The stress values
are scaled to the
maximum value in
the corresponding
figure showing the
maximum as 1.00
and all the others
as percentage (%)
values in relation
to the maximum.
[N/mm2]
Mercedes-Benz Türk - TP/EVT - Team CAE 11
Principal stress distribution on the mid-leaves:
Die Max-Spannungen auf den Zwischenblaetter der Gewichtsreduzierte Feder verringern sich ca.15% im Vergleich zur Feder-A9483201505.
-0.73 -0.81 -0.87
-0.79
0.56 0.81 0.86
0.75
-0.89 -0.91
-0.85 -0.95 -1.01 -0.95
-0.86 -0.78
0.91 0.95 0.86 0.91 1.00 0.95
0.85 0.79
Highest stress
Highest stress
New design
Original
The maximum stress values on the mid-leaves of the new designed leaf spring decreases approx. 15% in comparison with the original leaf spring.
FEM Calculations using MBS cutting forces & moments
New designed leaf spring vs original leaf spring – max stresses
The stress values
are scaled to the
maximum value in
the corresponding
figure showing the
maximum as 1.00
and all the others
as percentage (%)
values in relation
to the maximum.
Calculated Force-Time
Histories from MBS
Mercedes-Benz Türk - TP/EVT - Team CAE 12
Force acting on Spring front left Fz
Force acting on Spring Rear left Fz
Fo
rce
–T
ime
His
tory
Fo
rce
–T
ime
His
tory
Ra
ng
e P
air
Ra
ng
e P
air
MBS Calculations
The load spectra of
the both spring variants
are calculated
with the help of
multi body simulation. Measured Wheel Forces
2 x 13 t, Q3A, V48, Pen
3-Achser, 2 x 13 t
15
10
5
20
L964V048 6X4 SZM
Fx
Fy
Fz
Mx
My
Mz
Mercedes-Benz Türk - TP/EVT - Team CAE 13
MBS Load Spectra as input for FEMFAT Calculations
Weight reduced leaf spring vs original spring
Weight reduced spring
Original Spring
Example Force-Time-Curve / Fz
Time
Force
Due to the difference between the load spectra (not only the max. Forces but also all load collective) FEMFAT-Calculations were performed in order to achieve a comparison based on the damage values.
Fx
Fy
Fz
Mx
My
Mz
6 Channels 6 Channels
FEMFAT-Calculations with 12 Channels
Range Pair Spectra
Forces acting on Spring
front left Fz
Mercedes-Benz Türk - TP/EVT - Team CAE 14
FEMFAT Calculations
Damage results of the original leaf spring
Damage values in critical areas:
• 3 critical damage areas are shown as samples
• Max Damage => 0.0163
0.0163
Highest-
damage
value
Mercedes-Benz Türk - TP/EVT - Team CAE 15
Damage values in critical areas:
• 3 critical damage areas are shown as samples
• Max Damage => 0.0144
• Similar damage values like the original leaf spring
• Comparable lifetime values are expected
0.0144
FEMFAT Calculations
Damage results of the new designed leaf spring
Highest-
damage
value
Mercedes-Benz Türk - TP/EVT - Team CAE 16
0.86
0.81
1.00
1.00
0.75
0.75
Max-Stresses Max-Damage
0.88 0.94
# Order of the critical areas
1
3
2
4
1
2
3
4
Comparison – Stress & Damage Results
Original leaf spring Damage values in the mid-areas of
each leaf are ignored because of
the modeling
The spots with the maximum stress values
and maximum damage values are matching
each other in general for the original leaf
spring. However, the order of the maximum
stress values and maximum damage values
are different.
Mercedes-Benz Türk - TP/EVT - Team CAE 17
Comparison – Stress & Damage Results
New designed leaf spring
1.00
0.96
0.95
1.00
0.63
0.21
Max-Stresses Max-Damage
In case of the new design, both the spots and
the order of the maximum stress and damage
values are similar, and the most critical point
is observed on the last (uppermost) leaf
spring
Damage values in the mid-areas of
each leaf are ignored because of
the modeling
1
3
2
1
3
2
# Order of the critical areas
Summary
Mercedes-Benz Türk - TP/EVT - Team CAE 18
Within the scope of this project, a specified calculation flow is followed in order to reach an accurate comparison
between the original and new designed leaf spring.
After the stiffness and stress results under vertical loading of the leaf spring is calculated with in-house software
(BLAFES) based on mathematical calculations, elastokinematic analysis is performed to compare the stiffness values
and to prepare a base model for MBS.
Two separate MBS models are prepared both for the original and new designed leaf spring. The cutting forces and
moments on the leaf springs are calculated based on the wheel force measurements from a test vehicle at the torture
track.
FEM calculations show that, compared to the original design the maximum stresses on the new designed leaf spring
decreases up to 20 %.
Fatigue life calculations with FEMFAT show on the other hand similar damage results on both original and new designed
leaf springs, which means, comparable fatigue life values are to be expected.
The results show that with the new designed leaf spring with reduced number of leaves the aimed weight and cost
reduction can be achieved without worsening the durability characteristics.
For a comprehensive durability assessment of leaf springs which work under highly variable loading conditions, a multi-
channel fatigue life calculation should be performed.
Results & Conclusions
Acknowledgements
Mercedes-Benz Türk - TP/EVT - Team CAE 19
We wish to express our gratitude to Mr. Basaran Özmen for his helpful guidelines in finite element modeling,
Mr. Caner Dönertas for his valuable contribution through BLAFES.
We would also like to express our special apprecition and thanks to our colleages Dr. Stefan Öxl and
Mr. Volker Sing from TP/PCS Department of DAIMLER AG. Stuttgart for their support.
A special thanks to our colleage Mr. Jürgen Mehlhase from Klatt-Engineering Stuttgart for his help and
suggestions.
Thank you for your attention
Mercedes-Benz Türk - TP/EVT - Team CAE 20