Load generation and durability assessment of leaf springs ...

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


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.


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


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



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]


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]


-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



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]


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.



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


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


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


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


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


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.


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


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


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


Load generation and durability assessment of leaf springs ...

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