The 14th IFToMM World Congress, Taipei, Taiwan, October 25-30, 2015 DOI Number: 10.6567/IFToMM.14TH.WC.OS12.009

The Reliability of Assembly Steel Wheels With Using FEM Analysis

I. Demiyanushko1

E. Loginov2

V. Mironova3

Moscow Automobile and Road Moscow Automobile and Road Moscow Automobile and Road

Construction State Technical Construction State Technical Construction State Technical

University (MADI), Russia University (MADI), Russia University (MADI), Russia

Abstract: The subject of the following article is the

problem of predicting fatigue strength and durability of

wheels constructed as an assembly of a rim and a disc, for

large dimension wheels. Such wheels are widely applied

to supersize cars, tractors, combine harvesters and other

agricultural and road machines Considered are the main

problems occuring when creating a FEA model for

various loading conditions, including bench test and

technological ones.

3 versions of the item production, depending on the

contact conditions of the disc and the rim during the

interference fit assembly followed by welding, have been

analyzed. Recommendations on decreasing of stress-strain

state in the most unsafe points of the construction have

been given. Keywords: Wheels of a modular design, Reliability, Fatigue

I. Introduction

The experience of automotive and tractor wheels

operation shows necessity of predicting fatigue strength

depending on the materials, loads applied, and production

technology [1,2]. Depending on the driving conditions,

certain testing methods for evaluating wheel durability

have been standardized. As regarded to the construction

operation mode under alternating loads (e.g. bending with

rotation), the fatigue strength evaluation is performed via

rotary bending fatigue tests (dynamic cornering fatigue

tests, as referred in EUWA), which are considered to be

the most informative fatigue tests.

In order to minimize testing and further construction

optimization costs, it is offered to perform FEM analysis

[2] and determine wheel stress-strain state, occurred under

the action of loads which correspond to dynamic

cornering fatigue tests performed in quasi-static problem

statement. When evaluating fatigue strength, the material

fatigue characteristics are examined, taking into account

the dispersion occurred due to the technology of

processing the interference fit, and welding between the

disc and the rim. The examination is performed by testing

the samples cutout from the wheel.

II. Problem statement

The chosen research object is a typical design tractor

wheel of high dimensionality, 26”, which is produced as

an assembly (Fig. 1). During the assembly process the disc

is fixed into the rim under interference fit with the

welding followed.

1demj-ir@mail.ru 2evgeny.m.loginov@gmail.com 3violettmir@gmail.com

During the operation and fatigue bench testing of

separate items, fatigue cracks in the welding joint have

been frequently detected, which is unacceptable according

to EUWA ES 3.12 [3] standards

(standards covering tests

for agricultural vehicles’ wheels). One of the features of

wheels of given type is rather rough production

technology which may lead to significant fatigue

characteristics dispersion of the construction and decrease

of reliability.

Fig. 1. Fatigue crack initiation in the wheel

Investigation of the defect appearance reasons and

analysis of the wheels’ fatigue strength and reliability was

performed by combination of up-to-date methods: FEA

stress-strain state analysis, and fatigue strength analysis

based on experimental research data [4]. In order to

perform FEA stress-strain state analysis MSC. Software

instruments have been used [5-7]. The analysis has been

performed for the case of loading the wheel on a vertical

rotary bending moment stand. In order to create a FEA-

model required it is necessary to create a model not only

for the wheel itself, but also for the stand load-applying

units.

Quasi-static stress-strain state analysis under various

assembly versions allows evaluation of stress amplitudes

σa in unsafe regions of the wheel under bending loads

applied during rotation. Evaluation of stress-strain state of

the wheel under influence of the interference fit between

the disc and the rim allows determination of the static

component σm of the loading cycle depending on the value

of the interference closure. Received parameters of the

stress cycle have been compared with the results of the

templates fatigue tests. The templates were cut out of the

wheel and included the welding joint. Comparative

analysis allows evaluating the parameters of fatigue

strength and durability of the wheels, detecting the reasons

of fatigue damage initiation. This analysis allows to

evaluate the reliability of the wheel during operation [4]

Fatigue crack

initiation zone

and provide recommendations on improving the

technology of wheel production.

III. Dynamic cornering fatigue test procedure

Fatigue strength bench testing under bending loads

applied during rotation reproduce the combined influence

of the moments which occur under vertical load and side

force applied during turns or motion along an inclined

surface. The value of the vertical load applied to the wheel

is constant. And the vector of the moment applied, is

rotated relative to the wheel according to such pattern that

all the wheel spots are consecutively loaded by moments

with the values changing from one extreme to another.

Load appliance scheme is given on Fig. 2.

Fig. 2. Dynamic cornering fatigue test stand

The cyclic form of bending moment action is created

by rotating the wheel. When carrying out tests, the wheel

rim is fixed to the rotating stand bench. A cantilever arm

is fixed to the wheel via standard mounting holes, which

allows simulating the fastening of the wheel to the hub.

The load is applied to another end of the arm. During the

tests the wheel is rotated around the axis together with the

arm.

Depending on the arm position and the direction of

load application, necessary conditions of loading the

wheel relative to the respective axes are achieved.

Appearance of the testing stand is given on Fig. 3.

Fig. 3. Fixing the wheel to the dynamic cornering fatigue testing stand

IV. Modeling the test and fatigue strength evaluation

The process of creating a wheel model in assembly with

testing stand loading elements consists of several stages.

Due to construction symmetry the initial FEA model is

created being based on 1/8 part of the assembly. The

whole model is acquired by symmetrical mirroring of the

initial FEA mesh.

A. Creation of the wheel FEA model

The process of creating a FEA-mesh of a stamped wheel

is not complicated. Certain difficulties appear when

meshing the nipple hole zone. In order to receive proper

mesh, it is necessary to merge all surfaces with linear

dimensions less than the size of the element. As regarded

to the other surfaces, good quality mesh can be received

by using an automatic mesher.

Fig. 4 shows a transitional result for a 90˚ sector

directly after the first mesh mirroring against the

symmetry axis. The disc and the rim are created separately

and have no jointed nodes. It is accepted for an

insignificant amount of nodes to be coincident only. In

addition, it is recommended for the disc mesh to be of

greater size as compared to the rim mesh, in order to

ensure high quality of contact recognition.

Fig. 4. Wheel 90˚ segment FEA model

B. Creation of the testing stand FEA model

The bearing surface for the disc is the hub with given

parameters: height H = 40 mm; diameter D = 318 mm.

When creating the hub model, it requires a mesh seed

around the circumference with a diameter equal to the

diameter of the cantilever arm.

When creating the bolts model, the size of the

elements should be chosen 1,3 times smaller than the size

for the hub. The difference in the mesh size ensures better

quality contact detection between the parts.

Fig. 5. Hub and cantilever arm connection

Hereafter, 1 m cantilever arm simulation is performed.

In order to facilitate the analysis, the model is created by

10 Beam elements. The end of the arm coincident with

central hub node, is connected with the hub nodes located

within the closest surface to the arm. The connection is

performed via rigid RBE2 elements and includes the

nodes located within the circumference of a diameter

equal to the actual diameter of the arm (Fig. 5).

FEA model of the wheel assembled with the testing

stand is shown on Fig. 6. Then material properties data

with elastic-plastic constitutive model and stress-strain

curves are applied to all elements of the construction

(different properties for the rim and the disc). As regarded

to the Beam elements there should be additional

parameters specified, in particular cross-section

parameters with the circumference diameter.

Fig. 6. Assembled wheel and test stand FEA model

C. Loads & Boundary conditions

When simulating the load the following sequence of load

application shall be considered:

(1) Fixing the external rim flange and applying the bolts

tightening torque.

(2) The previous step is complemented by the force,

applied to the end of the testing stand cantilever arm.

In the pre-postprocessor software the stepwise loading

is simulated via a special “Load Cases” function. Since

the arm length is equal to 1 m, the force applied is equal

by absolute value to the bending moment and totals 16,14

kN.

The contact bodies defined are the disc, the rim, the

upper and lower bolt heads (16 contact bodies for the bolts

total).

The nodes which are in the immediate vicinity to the

transition edge from the bolt head to its body are excluded

from contact since the original construction includes a

washer between the disc and the bolt. Thus, contact

actually takes place at insignificant distance from the hole

which is considered to be a stress concentrator.

Bolts tightening torque is simulated by applying the

load equal to 78,45 kN via 3D Bolt Preload function. The

action of this force is equivalent to the tightening torque

of 600 Nm.

Fig. 7. Defining bolts as contact bodies

D. Solver options

The analysis has been performed in the elastic-plastic

constitutive model using Sol 400 [6] solver. The friction

model chosen in the solver contact task options is Bilinear

Coulomb model.

Contact pairs are determined on a condition that the

body with greater-size mesh is considered Master, and the

body with coarser mesh is considered Slave. Contact

search is performed from Slave to Master.

E. Results analysis and post processing

3 possible versions of item production under various

conditions of the technological assembly of the rim and

the disc have been considered for stress-strain state

analysis:

(1) Diametric dimensions of the disc and the rim equal to

nominal dimensions. Neither interference fit, nor

clearance is formed.

(2) The construction is assembled with a clearance

between the disc and the rim.

(3) The construction is assembled with an interference fit

between the disc and the rim. Analysis is performed

for 2 interference closure values: 0,25 mm and 0,4

mm.

In consequence of the wheel stress-strain state analysis

it has been determined that maximal stress in the bolting

zone is significant (Fig. 8). But since the bolted

connection during the analysis under conditions of stand

testing is chosen conventionally, the stress distribution in

the bolting zone is not of concern, and it shall not be

considered during the fatigue strength evaluation. In this

case the most loaded zone for the wheel is the rim in the

region of the rim well close to the welding joint.

Force

Cantilever

arm

Fig. 8. Von Mises stress distribution around bolt holes

Under conditions of tight contact between the disc and

the rim without a clearance or interference fit (Case 1),

maximum equivalent von Mises stress σi in the welding

joint zone result in σi = σa =73 MPa (Fig. 9).

During loading the construction according to “bending

during rotation” testing stand layout according to Case 2,

the model is created suggesting initial absence of contact

between the contiguous surfaces of the disc and the rim,

except for the welding zone (Fig. 10). Thus, faces of the

welding joint are the only surfaces transferring loads from

the disc to the rim.

Fig. 9. Von Mises stress distribution around the rim under the conditions

of no clearance or interference fit

.

Fig. 10. Clearance between the disc and the rim (scaled model)

The calculation has been performed in order to

evaluate maximal stress in the welding joint zone without

any interference fit. Fig. 11 shows the stress distribution in

this calculation round the rim surface. Maximal von Mises

stress equals σi = σa= 172 MPa.

Fig. 11. Von Mises stress distribution around the rim under conditions of

non-zero clearance

It should be mentioned that though the analysis has

been performed in the elastic-plastic constitutive model,

the stress-strain state in the welding joint zone under

“bending with rotation” load layout is elastic. This

provides a possibility to analyze stress-strain state

occurring independently from cyclic load to determine

stress amplitudes σa and from interference fit (Case 3) to

determine a static component of the stress cycle σm.

In order to evaluate the construction behavior under

the conditions of an interference fit, the wheel stress-strain

state FEA analysis under two values of interference

closure has been performed: 0,4 mm (maximum value as

referred to engineering documentation) and 0,25 mm.

The analysis of the outcomes shows that under greater

interference closure of 0,4 mm great stress occurs in the

welding joint zone. Besides, maximum stress, equals to

σi = σm = 228 MPa, provided distributed contact is

displayed (please refer to Fig. 12).

Considering that the yield strength of the material

equals 255 MPa, it should be considered that under cyclic

load of the disc during bending with rotation, the static

component of the stress resulting from interference fit,

may in some unfavorable cases achieve the values, close

to the yield strength.

Fig. 12. Von Mises stress distribution around the rim under conditions of

0,4 mm interference fit

The analysis performed at smaller value of

interference closure of 0,25 mm reveals that the stress

around the welding joint zone decreases up to the value of

σi = σm = 136 MPa (Fig. 13).

Welding

joint

Fig. 13. Von Mises stress distribution around the rim under conditions of 0,25 mm interference fit

V. Wheel templates fatigue testing

Since the main problem area is the junction of the disc and

the rim, special templates considering the welding

technology have been manufactured to determine fatigue

parameters of the material in the construction. The

templates have been cut out of the finished wheel via 2

parallel cross-sections, normal to the wheel plane.

Template solid model is shown on Fig. 14.

Fig. 14. DW20Ax26 tractor wheel template sketch

Applying bending momentum to the template allows

evaluating the endurance limit of the material used in the

construction, considering structural and technological

factors, determining the peculiarities of the rim cross-

section and its junction with the disc. It should be

mentioned that under these tests, the static load

component occurring as a result of interference fit

influence, is not reproduced.

As opposed to standard methods of fatigue testing, the

following method is based on the template forced

oscillation. The main advantage of such method lies in the

simplicity of load application and sufficient reduction in

test time[8]

.

The tests have been performed by using an

electrodynamics vibration stand with cantilever template

fixation. Equipment overview is shown on Figure 15. The

template (3) is fixed on a mobile stand of the oscillator (1)

by means of a special screw clamp (2).

Stand oscillation parameters (frequency and excitation

amplitude) have been measured with the use of an

accelerometer (7), installed on a vibration stand, and an

optical displacement controller (5).

The template’s rim oscillations have been measured by

means of an optical measuring device (6). Stresses have

been measured by resistance strain gauges (4), installed

close to the zone of disc-to-rim junction (Figure 16).

Fig. 15. Overview of electrodynamics vibration stand with a template mounted

Calibration of the stress initiated in the template has

been run with the use of strain-gaging, measuring the

propelling force with the oscillation frequency

corresponding with the greatest deformations in the

junction zone between the disc and the rim, and measuring

oscillations spread by means of an optical displacement

controller. Before running the tests all the elements of the

measuring circuit have been calibrated on the basis of test

signals (with known values of amplitudes and stress).

To achieve maximum oscillation amplitudes and,

respectfully, maximum stresses, the template oscillation

has been performed with a frequency, equal to the

frequency of its main mode, which has been preliminary

determined via free oscillations method and equals 690 Hz.

Fig. 16. Mounting resistance strain gauges to the template

In order to evaluate stress-strain state of the template

and choose the locations for the resistance strain gauges, a

template FEA analysis using MSC. Nastran has been

performed.

The first mode oscillations analysis with simulating

the template fixation on the vibration stand has shown

(Fig. 17) that the stress distribution of the FEA model

coincides with the one received within the experiment.

Fig. 17. Stress distribution during the template oscillations under 1st mode (FEA analysis using MSC. Software).

The maximal stress is detected in the fatigue crack

initiation zone around the welding joint, which allows

determining the resistance strain gauges mounting layout

(Fig. 16).

Templates testing on a vibration stand have been

performed via a step-by-step load increase method under

various values of the excitation amplitude.

During the test runs gauges #1 and #3 have been

mounted in the places of maximal stress initiation

according to the earlier performed analysis. The control

has been performed in terms of measuring the template’s

corner point oscillations amplitude by means of optical

displacement controller.

The base quantity of load cycles totals 2 х106

cycles.

The results are shown on Fig. 18 in the form of an S-N

curve. There is a distinct linear pattern of stress amplitude

decrease with the increasing quantity of cycles observed. Average value of the templates’ endurance limit on the

basis of 2 х106 cycles totals σv =160 MPa with the

minimal value being σv =150 MPa and the maximal value

being σv =180 MPa.

Fig. 18. S-N curve for templates tested

The location of the fatigue crack is shown on Fig. 19.

The crack is distributed from the leg of the welding joint

deep into the rim well. The number of cycles prior to the

damage was set to as amount of cycles prior to a 10%

decrease in the loading frequency.

Fig. 19. Fatigue crack in the template tested

VI. Fatigue strength evaluation

As a result of bending during rotation under conditions of

stand testing, cyclic harmonic stress alteration. Besides,

when the interference fit occurring as a result of the

assembly between the disc and the rim is not considered,

the stress alteration is executed via asymmetric cycle.

Given the presence of interference fit as a result of an

assembly, interference fit stress is considered constant

average cycle stress, and the loading cycle itself changes

to asymmetric. The influence of cycle asymmetry on the

endurance limit can be considered by using the

Goodman’s criterion (1):

(1)

To evaluate the durability of the wheel the value of в

has been taken according to the reference data and equals

в = 420 MPa. The endurance limit has been evaluated

from the experimental diagram on the basis of 106 cycles

considering the dispersion and cycle asymmetry under

various interference closure values (Figure 20).

An

aly

sis

cond

itio

ns

Str

ess

amp

litu

de

а

Av

erag

e

inte

rfer

ence

fit

stre

ss

m

En

du

tan

ce l

imit

con

sid

erin

g c

ycl

e

asy

mm

etry

аv

Res

ult

Units MPa MPa MPa -

Clearance

between the disc

and the rim.

Contact via

welding joint only

172 0 150-

180

Possible

breakdown in

the welding

joint zone

Interference

closure between

the disc and the

rim =0,25 mm

73 136 125-

105

Endurance

margin ca. 1,7

Interference

closure between

the disc and the

rim =0,4 mm

73 228 70-90

Possible

breakdown in

the welding

joint zone

TABLE I. Wheel fatigue strength analysis results

Listed in the table are the results of the expected wheel

endurance according to the data from the wheel stress-

strain state analysis and template testing experimental data.

Fatigue Crack

𝜎𝑎𝜎𝑣

+𝜎𝑚

𝜎в

= 1

average values

Fig. 20. Endurance limits evaluation considering cycle asymmetry

It should be considered that semiautomatic welding

process and insufficient margin of durability (Table 1), as

well as contact absence or maximal interference closure,

lead to crack initiation after smaller amount of cycles.

VII. Conclusions

In order to increase the reliability of the wheels

manufactured, strict control of diametric dimensions of

the discs and rims is required. Considering the production

volumes it is possible to group discs and rims into pairs in

order to ensure a secure minimal interference fit and

absence of a clearance. It is recommended to production

engineers to pay special attention to tolerances

specification process in items production. Therewith,

automatic welding technology ought to be supplied in

order to minimize fatigue characteristics dispersion for the

given construction.

Acknowledgment

Authors are grateful to their colleagues, i.e.

Doct. Alexander M. Vakhromeev and Eng. Iliya A.

Karpov for participation in this work.

References [1] Demiyanushko I.V., Cast aluminum wheels for cars: development,

manufacture, design, Demiyanushko I.V, Esenovsky Y.K.,

Vakhromeev A.M., Avtomobilnaya Promyshlennost, Moscow,

No.9, 2002, p.35 - 39. [2] Demiyanushko I.V., Yudin M.N., Information technologies and

creation of automobile wheels designs, Avtomobilnaya

Promyshlennost, No.9, 2003, p.3 - 5. [3] EUWA ES 3.12. Test requirements for agricultural wheels. 2004

[4] Irina V. Demiyanushko, 'State-of-the-Art and Trends of

Development of Reliability of Machines and Mechanisms', Mechanisms and Machine Science, 2011, pp. 173-183.

http://dx.doi.org/10.1007/978-94-007-1300-0_14

[5] Zienkewich О. The Finite Element Method. Moscow Mir

publishing, 1975. 544 pages.

[6] MSC.Patran 2012 User’s Guide. www.mscsoftware.com

[7] MSC.Nastran 2012 Quick Reference Guide. www.mscsoftware.com.

[8] Batrak N.I., Vakhromeev A.M. Methodical aspects of fatigue

testing for passenger car wheels // Questions of structural mechanics and construction reliability: Collection of MADI

scientific works. – Moscow, MADI, 2010. – p. 5-19.