Development of stiffness analysis

program for automotive wheel bearing

May 16, 2012

SIMULIA Comunity Conference, Providence, RI, USA

Inha Lee, ILJIN Global

Contents

2

I. Introduction

II. Wheel bearing stiffness analysis

III. Program development

IV. Verification

V. Conclusion

I. Introduction

3

+ Automotive wheel bearing; transmits engine power & supports vehicle weight

+ Stiffness of bearing; significant influence on the ride comfort and the steering feeling during the driving

+ Need for designer to analyze stiffness easily and quickly; shorter development period and reduced development cost

Configuration of corner module and wheel bearing

inner ring

outer ring

hub

ball

wheel assembly

knuckle

drive shaft

wheel bearing

Need of this study

author year summary

T. Numata 2005

The stiffness of the knuckle (including outer ring) and hub shaft was analyzed by FEM, the bearing stiffness was calculated by a program developed in-house, and the moment stiffness of the entire unit was obtained by adding the values computed for each component.

S.P. Lee et al. 2010Structural design and analysis of automotive wheel bearing was described. Parametric method was applied to get the optimal bearing design

S.P. Lee et al. 2011

The analysis model which can consider the stiffness behavior with ball contact angle change was developed. To verify the reliability of the results, experiment was carried out and compared with analysis results.

4

Previous studies

+ No bearing stiffness analysis program ever developed for designer

+ Half modeling or Full modeling

+ Element; C3D4 Tetra element, 1st order shape function

+ Material nonlinear analysis; stress-strain curve

+ Geometric nonlinear analysis; large displacement

+ Contact analysis; surface to surface contact, penalty method

+ Ball; compression only spring (CONN3D2)

+ Loading; kinematic coupling

5

II. Stiffness analysis

Analysis method

6

Design specification & Geometry

Vehicle specification Value

Axle load (Rs) 1150 kgf

Track width (Ts) 1540 mm

Tire radius (r) 320 mm

C.G. Height (h) 600 mm

Drum/Disc thickness 7 mm

Wheel offset 56 mm

Bearing specification Value

Ball diameter (Dw) 12.7 mm

Pitch center diameter (Dpw) 57 mm

Contact angle (a) 35 deg.

Ball pitch (Bp) 30 mm

No. of Balls 13

Ball center (Bc) 42.7935 mm

Bc

Dw

DpwBp

a

Bearing specification of wheel bearing

rh

Rfs Rrs

Tfs Trs

Vehicle specification

7

Material properties

Parts MaterialYoung’s modulus,

GPaPoisson’s

ratioYield strength,

MPa

Hub SAE 1055 207 0.3 456

Hub hardened Heat treatment

Outer ring SAE 1055 207 0.3 456

Outer ring hardened Heat treatment

Inner ring SAE 52100 239 0.3 1480

Material properties Stress strain curve

Strain

Str

ess (

MPa)

52100 1055

3D model of wheel bearing

8

Boundary conditions

rTaT

r

Boundary conditions

+ Outer ring tap holes; all DOF fixed

Contact conditions

+ Hub and inner ring

Boundary conditions and loadings

Ball

+ CONN3D2 axial connector

+ Spring constant; k=60kN/mm

Bo

9

Loading

+ Loading point; wheel center

+ kinematic coupling

+

+ (Bo=6.2065 mm)

Corneringacceleration, G

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Tr, kgf 575 620 665 709 754 799 844

Ta, kgf 0 62 133 213 302 400 506

M, Nm 38 236 461 715 996 1306 1644

ora BTrTM

ra

s

ssr TGT

T

GhRRT ,

2

+ Total bearing flange displacement, U

+ Bearing deflection,

+ Bearing moment, M

+ Bearing stiffness,

where,

; displacement at point A

; displacement at point B

D ; hub flange O.D(Ø130 mm)

10

U A B

Calculation the bearing stiffness

1 Utan

D

A

B

D

ora BTrTM

M

11

III. Program development

CATIA Template

Activate design CAD model

Apply the analysis conditions

Run Abaqus

Remove small fillets and faces

Make heat treatment part

Make springs

Apply load cases

Apply spring constant

Make analysis CAD model

AFC Template Report Template

Activate analysis result

Extract results

Activate analysis CAD model

Monitor analysis status

Make analysis report

Developed program’s process

Developed program’s UI

CATIA Template AFC Template Report Template

Input

1. Remove small fillet, small face

2. Rotate the model

Modification the model Output

1. Make analysis CAD

model

Full model Half model

CATIA Template

1. Set working directory

2. Set hub, outer ring, inner ring, ball

3. Set heat treatment parts

4. Set hole face, fillet face

Analysis CAD model

1. Activate analysis CAD model

2. Assign Material properties

3. Set the loading point

Assign analysis conditions

1. Input vehicle specification

2. Calculate loadings

3. Export the loadings

Set the loading case Set spring constant

1. Set the spring constant

2. Make analysis model

TaTr

AFC Template

Analysis model

1. Make analysis report1. Set bearing specification1. Activate analysis result

2. Recognize the model

information

3. Extract result

View result Set specification Make report

Report Template

Analysis report

IV. Verification

Comparison with experiment

Deflection

+ The analysis deflection and stiffness showed good

agreement with the experiment deflection and stiffness,

respectively.

Stiffness (

Nm

/deg.)

G

V. Conclusions

20

+ The BSAP(Bearing Stiffness Analysis Program) was developed.

It contains three templates; CATIA Template, AFC Template,

Report Template.

+ The bearing stiffness analysis was performed by BSAP.

+ To verify the reliability of developed BSAP, experiment was

carried out and compared with the analysis results. They

showed good agreement with analysis results.