a unified cae analysis for a leaf spring type suspension ... filea unified cae analysis for a leaf...

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.


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.


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


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,


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,


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.


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


SUSPENSION VEHICLE

The Von Mises stress result from U-bolt assembly loading analysis

the above procedures, the following loads and boundary

Kinematics and compliance


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


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


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


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)).


Figure 10 shows the

in the high stress area

Figure 8: Stress contourframe models.


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)


Figure 9: Stress contour

flexible frame model.

A


SUSPENSION VEHICLE

Stress contours at the front (Top) and rear (Bottom) suspension in

A

TYPE

SUSPENSION VEHICLE

in the


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


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

a unified cae analysis for a leaf spring type suspension ... filea unified cae analysis for a leaf...

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