NAFEMS Auto Unified CAE Analysis for a Leaf Spring Type
-
Upload
indranil-bhattacharyya -
Category
Documents
-
view
43 -
download
3
description
Transcript of NAFEMS Auto Unified CAE Analysis for a Leaf Spring Type
A UNIFIED CAE ANALYSIS FOR A LEAF SPRING TYPE
SUSPENSION VEHICLE
A UNIFIED CAE ANALYSIS FOR A LEAF SPRING TYPE SUSPENSION VEHICLE
Youngwon Hahn
Engineering Specialist, Dassault Systèmes Simulia Corp, USA
THEME
Multi-body simulation
KEYWORDS
Vehicle suspension, leaf spring, kinematics, compliance, vibration, durability,
unified CAE
SUMMARY
A vehicle suspension is an important subassembly connecting the vehicle body
with the tires. It requires high performance and durability since the road force
from the tires is transmitted through it to the vehicle body and passengers.
Commonly, CAE analyses for the suspension, such as kinematic, vibration, and
durability analyses, are performed separately due to the lack of a unified
analysis tool. Specifically, it is difficult to analyze the dynamic behavior of a
leaf spring type suspension with flexible panels because of nonlinear effects
such as those due to contact, residual stress caused by the U-bolt assembly, and
rigid body motion caused by the shackle. This flexible dynamic behavior
makes it difficult to perform a unified analysis for the handling, vibration, and
durability of the suspension. In this study, a unified CAE analysis for a leaf
spring type suspension vehicle is performed using Abaqus. The analysis
sequence includes a kinematic and compliance analysis to identify the
suspension characteristics, a modal and frequency response analysis to
determine the vibration behavior, and four post-load simulator analyses to
examine the durability response. Two models which have a flexible leaf spring
suspension are considered; one has a rigid frame and the other has a flexible
frame. The models are obtained from the archive of the National Crash
Analysis Center. Both models use a rigid upper body for convenience. In order
to easily create the models, a plug-in for Abaqus/CAE was developed. With
this plug-in, each analysis model can be generated using pre-existing finite
element models of the suspension components. The resulting Abaqus model
allows the user to consider the unloaded shape of the leaf spring and to position
the leaf spring after the U-bolt assembly. Various vehicle positions can also be
considered by changing the mass of the vehicle.
A UNIFIED CAE ANALYSIS FOR A LEAF SPRING TYPE
SUSPENSION VEHICLE
1: Introduction
CAE (Computer Aided Engineering) is one of the powerful design tools
available today given its ability to handle many complex engineering problems
in the automotive industry. However, CAE analyses, such as kinematic,
vibration, and durability analyses, are performed separately due to the lack of a
unified CAE analysis tool. Since this increases time and cost, automotive
product developers would benefit from a unified CAE procedure [1]: one
model for different analyses. In particular, it is difficult to find a unified CAE
tool for a vehicle suspension system due to its complexity.
A vehicle suspension is an important subassembly in an automotive vehicle.
Since the road load is transferred to the vehicle body through the suspension,
the suspension should be well designed with respect to handling, NVH, and
durability. There are many different types of suspension. The Macpherson type
or Double Wishbone type of suspension is commonly used for passenger
vehicles. This type of suspension can be modeled as rigid links in a CAE
analysis. However, a leaf spring type suspension (Hotchkiss type suspension),
which is used for trucks or heavy duty vehicles, requires that the flexibility of
the leaf spring panels be considered in the CAE analysis. As shown in Figure 1,
the leaf spring suspension consists of leaf spring panels, the axle, and other
components, such as bolts. The spring stiffness is based on the bending and
contact behaviors of leaf spring panels. In order to capture the physical
behavior of the leaf spring suspension, a flexible body should be modeled in
the CAE analysis.
In this paper, a unified CAE analysis using Abaqus is proposed for leaf spring
type suspension vehicles in order to check various vehicle performances, such
as handling, NVH, and durability.
Figure 1: Leaf spring type suspension.
A UNIFIED CAE ANALYSIS FOR A LEAF SPRING TYPE
SUSPENSION VEHICLE
2: Leaf Spring Type Suspension Model
A leaf spring type suspension consists of leaf spring panels, a center bolt, a U-
bolt, an axle, and a bushing. Multiple leaf spring panels are constrained by the
center bolt and the U-bolt. The U-bolt assembly process introduces preloading
stress and makes it difficult for the user to simulate leaf spring type
suspensions. The preloading effect from the center bolt is assumed small in
comparison with the effect from the U-bolt [2].
In order to easily build the complex leaf spring suspension system, an
Abaqus/CAE plug-in is used. The plug-in requires the presence of pre-existing
finite element component models such as for the U-bolt, leaf spring panels, and
axle. Once the user specifies the coordinates of the joint, the connecting area
information in the flexible component, and other suspension properties, the leaf
spring type suspension model is automatically generated in Abaqus/CAE.
Figure 2 shows a screenshot of the plug-in and finite element component
models.
Figure 2: Screenshot of the plug-in (Left) and finite element component models (Right).
In this paper, the Silverado model, which can be downloaded from the National
Crash Analysis Center, is used for the leaf spring type suspension vehicle. Two
models which have a flexible leaf spring suspension are considered as shown in
Figure 3; one has a rigid frame and the other has a flexible frame. The joint and
bushing are modeled as connector elements in the Abaqus model. The tire and
upper body are defined as rigid for convenience. A contact interaction is also
defined between the leaf spring panels in order to prevent their
interpenetration. A rebound clip is defined as a coupling. Four posts are
generated in order to apply the load at the bottom of the wheel. Between the
wheel and the plate, “slide-plane” type connector element is used.
A UNIFIED CAE ANALYS
Figure 3: Rigid body frame model (Left) and
3: Analysis Procedure
After building the leaf spring suspension
procedure is required prior to
durability analyses:
1. U-bolt assembly procedure
The role of the U-
a bolt load. It can be
section surface of the U
the bushing center points at the ends of the leaf spring panels are fixed
and the bolt assembly load is applied to the U
the upper body is also
2. Positioning procedure
After the U-bolt assembly load is applied, the constraints at
center points at the end of the leaf spring panel
order to locate the wheel
position can be adjusted by moving
The mass center of the upper body is
3. Gravity procedure
After positioning the wheel,
after removing the boundary condition
procedure is not required in
Figure 4 shows the Von Mises
A UNIFIED CAE ANALYSIS FOR A LEAF SPRING TYPE
SUSPENSION VEHICLE
Rigid body frame model (Left) and flexible body frame model (Right).
leaf spring suspension vehicle, the following analysis
procedure is required prior to the kinematics and compliance, NVH, and
bolt assembly procedure
-bolt is to constrain the leaf spring panels by applying
bolt load. It can be modeled by applying a pre-section force on the
section surface of the U-bolt in the Abaqus model. In this procedure,
the bushing center points at the ends of the leaf spring panels are fixed
bolt assembly load is applied to the U-bolts. The mass center of
also fixed.
Positioning procedure
bolt assembly load is applied, the constraints at the bushing
center points at the end of the leaf spring panel should be released
the wheel in the equilibrium position. The vehicle
position can be adjusted by moving the wheel upward or downward.
The mass center of the upper body is also fixed.
After positioning the wheel, the gravity force is applied to the model
after removing the boundary condition on the upper body. This
procedure is not required in the kinematics and compliance analysis.
Von Mises stress contours from the U-bolt loading analys
TYPE
SUSPENSION VEHICLE
body frame model (Right).
leaf spring panels by applying
section force on the
. In this procedure,
the bushing center points at the ends of the leaf spring panels are fixed
bolts. The mass center of
bushing
released in
wheel upward or downward.
gravity force is applied to the model
kinematics and compliance analysis.
bolt loading analysis.
A UNIFIED CAE ANALYS
Figure 4: The Von Mises
After completing the above
conditions are applied:
Kinematics and compliance
The center of gravity in the upper body is fixed and the plate at the
bottom of the wheel is moved upward and downward.
double-bump test,
simultaneously moved in
study [3].
Vibration
The frequency response analysis is performed after
loading is applied.
front suspension
mode-based steady
Abaqus is used.
Durability
A random displacement is applied to the plate at the bottom of the
wheel after the
analysis proced
For the vibration and durability analys
the wheel and the plate in order to prevent free sliding
surface. If the wheel model
contact is defined between
are not needed.
The results from each analysis
A UNIFIED CAE ANALYSIS FOR A LEAF SPRING TYPE
SUSPENSION VEHICLE
The Von Mises stress result from U-bolt assembly loading analysis
the above procedures, the following loads and boundary
Kinematics and compliance
The center of gravity in the upper body is fixed and the plate at the
bottom of the wheel is moved upward and downward. Only a
test, in which the right and left wheels are
simultaneously moved in the same direction, is performed in this
The frequency response analysis is performed after the gravity
loading is applied. A unit load is applied at the right wheel in the
suspension and the left wheel in the rear suspension. The
based steady-state dynamic analysis procedure available
Abaqus is used.
random displacement is applied to the plate at the bottom of the
the gravity loading is applied. The implicit dynamic
procedure available in Abaqus is used in this study.
vibration and durability analyses, additional springs are added between
the wheel and the plate in order to prevent free sliding of the wheel on the plate
model is replaced with a flexible FE tire model and
between the flexible tire and the plate, the additional spring
from each analysis are discussed next.
TYPE
SUSPENSION VEHICLE
bolt assembly loading analysis.
and boundary
The center of gravity in the upper body is fixed and the plate at the
a
in this
gravity
in the
The
procedure available in
random displacement is applied to the plate at the bottom of the
The implicit dynamic
added between
of the wheel on the plate
flexible tire and the plate, the additional springs
A UNIFIED CAE ANALYSIS FOR A LEAF SPRING TYPE
SUSPENSION VEHICLE
Kinematics and Compliance
For the double-bump test, the suspension characteristics can be extracted.
Figure 5 shows the toe, camber and vertical force change versus vertical
displacement of the wheel for the rigid frame model. For the rear toe
result, hysteretic behavior is observed due to the contact interaction.
However, it is not significant since the toe value is small.
Figure 5: Toe at double-bump mode (Left: Front, Right: Rear).
Vibration
After a frequency extraction step using the AMS eigensolver, a mode-
based steady state dynamic analysis is performed. As shown in Figure 6,
the wind-up mode can be observed at around 43 Hz in the rigid frame
model. The flexible frame model shows the wind-up mode at
A UNIFIED CAE ANALYSIS FOR A LEAF SPRING TYPE
SUSPENSION VEHICLE
approximately 47 Hz, as shown in Figure 7. The flexible frame effects
can also be observed in the wind-up mode in Figure 7.
Figure 6: Vibration result from rigid frame model.
Figure 7: Vibration result from flexible frame model.
Durability
For the durability analysis, random displacement history is generated
with MATLAB and applied to the plate attached to the post at the bottom
of the wheel. The stresses on the leaf spring panel can be observed in the
rigid body model, as shown in Figure 8 (Top). In the flexible frame
model, a small local area of high stress is also observed at the front
suspension as shown in Figures 8 (Bottom) and 9 (Top (black arrow)).
A UNIFIED CAE ANALYS
Figure 10 shows the
in the high stress area
Figure 8: Stress contourframe models.
A UNIFIED CAE ANALYSIS FOR A LEAF SPRING TYPE
SUSPENSION VEHICLE
Figure 10 shows the time history of the Von Mises stress around a point
in the high stress area (indicated as point A in Figure 9 (Bottom)).
Stress contours at time = 0.53 sec in the rigid (Top) and flexible (Bottom
TYPE
SUSPENSION VEHICLE
point
(Bottom)
A UNIFIED CAE ANALYS
Figure 9: Stress contour
flexible frame model.
A
A UNIFIED CAE ANALYSIS FOR A LEAF SPRING TYPE
SUSPENSION VEHICLE
Stress contours at the front (Top) and rear (Bottom) suspension in
A
TYPE
SUSPENSION VEHICLE
in the
A UNIFIED CAE ANALYS
Figure 10: Stress history
indicated in Figure 9).
4: Conclusions
A unified CAE analysis is
using Abaqus. With one model, three different analyses (kinematics and
compliance, frequency, and durability
vehicle performance. The
high stress area/stress time history can be obtained for each analysis
In this paper, a rigid tire model
that more reliable results can be obtained if
5: Acknowledgments
The author would like to express his gratitude to the NHTSA for
Silverado finite element model and a
Carranza of SIMULIA for their kind advice.
REFERENCES
1. El Khaldi, F., Ni, R., Culiere
“Recent Integration Achievements in Virtual Prototyping for the
Automobile Industry,”
2. Qin, P., Dentel, G., and Mesh, M.,
Hotchkiss Suspension
3. Hahn, Y., 2010, “Kinematics and Compliance (K&C) S
Nonlinear Finite Element Model
4. Abaqus 6.10 Analysis User’s Manual, Dassault
A UNIFIED CAE ANALYSIS FOR A LEAF SPRING TYPE
SUSPENSION VEHICLE
tory at point “A” on the 3rd
leaf spring panel (point “A”
A unified CAE analysis is performed for a leaf spring type suspension vehicle
ith one model, three different analyses (kinematics and
, and durability) are performed in order to evaluate
The toe suspension parameter, the wind-up mode, and
high stress area/stress time history can be obtained for each analysis.
model is used for convenience. The author expects
that more reliable results can be obtained if a flexible tire model is used.
The author would like to express his gratitude to the NHTSA for use of the
Silverado finite element model and also thank Pierre Burgers and Fernando
for their kind advice.
Culiere, P., Ullrich, P., and Terres Aboitiz, C., 2010,
“Recent Integration Achievements in Virtual Prototyping for the
” FISITA, May 31.
Qin, P., Dentel, G., and Mesh, M., 2002, “Multi-Leaf Spring and
Hotchkiss Suspension CAE Simulation,” Abaqus Users’ Conference
“Kinematics and Compliance (K&C) Simulation Using a
Nonlinear Finite Element Model,” SAE 2010-01-0951
Abaqus 6.10 Analysis User’s Manual, Dassault Systèmes, 2010.
TYPE
SUSPENSION VEHICLE
leaf spring type suspension vehicle
evaluate the
up mode, and the
convenience. The author expects
the
Pierre Burgers and Fernando
2010,
imulation Using a