c. kalavrytinos - fea of a steering knuckle

2012

[

Finite Element Analysis of a Steering Knuckle

]

MSc Mechanical Engineering

Finite Element Analysis PG

Christos Kalavrytinos


ABSTRACT

This report investigates the stresses caused on a steering knuckle component. A

physical test with strain gauge readings is compared to a Finite Element Analysis

model in Ansys and also validated by hand calculations. The test and Ansys results

were found to have a 5% error which is well within a 10% reasonable value. The

hand calculations showed a 70% error which was attributed to the simplifications and

assumptions made to make the calculations possible as well as the geometry

complexity. The component was then redesigned to remove material from low stress

area in order to reduce its mass.

Christos Kalavrytinos Page i


CONTENTS

ABSTRACT............................................................................................................................... I

CONTENTS.............................................................................................................................. II

1.0 INTRODUCTION................................................................................................................1

1.1 OBJECTIVES.....................................................................................................................1

2.0 DETERMINATION OF LOADINGS....................................................................................2

2.1 ROAD BUMP CASE.............................................................................................................2

2.2 BRAKING CASE.................................................................................................................3

2.3 CORNERING CASE.............................................................................................................3

3.0 SOLID MODELING.............................................................................................................4

4.0 VALIDATION...................................................................................................................... 5

4.1 PHYSICAL TEST................................................................................................................. 5

4.2 HAND CALCULATIONS........................................................................................................6

4.3 FINITE ELEMENT SIMULATION OF TEST................................................................................8

4.4 RESULTS........................................................................................................................ 11

5.0 FINITE ELEMENT MODELING........................................................................................12

5.1 ROAD BUMP FEA............................................................................................................13

5.2 BRAKING FEA................................................................................................................15

5.3 CORNERING FEA............................................................................................................17

5.4 RESULTS........................................................................................................................ 18

6.0 DISCUSSION.................................................................................................................... 19

7.0 REDESIGN....................................................................................................................... 20

8.0 CONCLUSION.................................................................................................................. 21

9.0 RECOMMENDATIONS.....................................................................................................21

REFERENCES:...................................................................................................................... 22

APPENDIX.............................................................................................................................. 22

Christos Kalavrytinos Page ii


1.0 Introduction

The aim of this report is to redesign the steering knuckle (i.e. upright) of an off-road

buggy in order to reduce its mass while retaining a satisfactory safety factor. In order

for this to be achieved, the component will be subjected to structural analysis with

different methods; finite element analysis (FEA) on Ansys, physical test and hand

calculations. According to the analysis results, material can be added to parts that

are subjected to higher stress than the safety factor permits. Material can also be

removed from low stress areas, thus, helping to reduce the component mass. In

order to allow for a validation with hand calculations, certain simplifications and

assumptions have to be made and justified.

1.1 Objectives

In order to successfully complete the project, the following objectives have to be

achieved:

Finite Element Analysis:

Determination of loads in three different load cases (i.e. bump, braking,

cornering) as provided in the brief.

Simplify and make assumptions necessary to perform the finite element

analysis.

Refine mesh at points of interest and show converged results.

Experimental Test:

Observe the physical testing conditions (e.g. supports used, loading

arrangement, etc.) and relate that to the FEA model.

Observe and record values of elastic strains and deflections.

General:

Perform simplified calculations based on mechanics of solids theory to

determine stress and strain values in order to compare them to the physical

test and FEA model.

Redesign the component to reduce weight where possible and ensure a

safety factor of 5 on this critical component.

Christos Kalavrytinos Page 1


2.0 Determination of Loadings

In this section, the loadings for three different cases of road bump, braking and

cornering are calculated. For all calculations the mass of the vehicle was split

according to the distribution at each corner. For the front left wheel, the mass is

163.125 kg.

2.1 Road bump case

The vehicle travels at a constant speed of 50 km/h (13.9 m/s) and hits a bump (Fig.

1) of total length of 2 m and maximum height of 0.25 m at the centre (1 m).

Figure 1, Road bump.

u= xt

t=xu= 113.9

=0.072 sec

Uvertical= Xverticalt

= 0.250.072

=3.47m /sec

Avertic al=Vverticalt

= 3.470.072

=48.2m / s2

Wheel AccelerationForce=mass×acceleration=163.125×48.2=7863N

There is also an inertia force created by the unsprung mass which is calculated using

only the rim and tyre weight (10kg). This might not be realistic since the unsprung

mass consists of other suspension components, but in this case it is an assumption

for the sake of simplification. This is how it is calculated.



Wheel Inertia=48.2×10=482N

2.2 Braking case

In this case the vehicle decelerates (i.e. brakes) at a constant 0.5G. The weight

transfer to the front wheels cannot be calculated due to lack of data (e.g. roll centre,

etc.). Thus, a simplified approach is applied.

Braking Force=mass×decceleration=mass×0.5×9.81=800.1N

This force will also be applied on the hub plate opposite to the direction of travel.

This force acts at a distance from the centre of the hub and is therefore a moment.

The distance is the dynamic radius R of the wheel at approximately 0.305m.

Brakingmoment=Braking Force×R=244N

This force is transferred to the two brake calliper fixing holes which are at a 94.7 mm

distance from the centre of the hub and at a 40° angle from the vertical axis. The

force is split in half to be applied equally on both holes and analysed to two

components.

Fb=2440.0947

=2577N F1/2=25772

=1288.5N

Resolving the components:

Fx=1288.5×cos (50 )=828.23N

Fy=1288.5×sin (50 )=987.05N

2.3 Cornering case

In this loading case, the vehicle travels around a corner of 10 m radius (r) at a

constant speed of 20 km/h (u=5.56 m/s). The case is again simplified due to lack of

weight transfer data. The centripetal force is calculated as follows:

F cent=m×u2

r=163.125×5.56

2

r=504.3N



Since this force also acts at a distance it is considered as a moment:

F corn=Fcent×0.305m=153.8N

3.0 Solid modeling

Due to the complexity of the geometry of the component, the CAD files were

provided in an STP file format. They are illustrated in Fig. 2 in the Catia CAD

package.

Figure 2, Knuckle part in Catia.

4.0 Validation



The model is validated by hand calculations and strain gauge measurements during

a load test. This allows for a comparison between the three sets of results to see if

the FEA model is accurate.

4.1 Physical test

In this test, the part was secured as shown in Fig. 3 (provided by Lahr J.) using a

type of support that can be described as frictionless. A vertical load was applied on

the central surface of the hub. The load was increased in steps of 1kN from 0kN to

5kN and the part was allowed to settle before the strain and deflection

measurements were taken. The rest of the setup details can be found in the

Appendix section. The results can be seen in Table 1.

Figure 3, Steering knuckle setup.



Table 1, Strain and displacement results.

4.2 Hand calculations

In order to allow for hand calculations, the problem was simplified and basic

principles from the theory of Mechanics of Solids were used. Certain assumptions

were made to make this possible. One assumption is that the hub can be analysed

as a beam so that the stress and strains can be calculated for any particular point

along that length. The beam starts and finishes at the centres of the connecting balls.

A second assumption is that, during bending, the shape of the cross sectional area

does not change. Finally, all strain gauge readings appear linear, however, for this

case only strain gauges parallel to the beam length were considered. Strain gauge 6

was chosen since it is placed in a convenient point and calculating the second

moment of area was easier due to the geometry of the section.

Figure 4 illustrates the section at strain gauge 6 location along with the values for

second moment of area for the x and y axes.

Known data:

Beam length (L) = 0.222 m

Point load at center (P) = 5000 N

Distance of strain gauge from centre (x) = 0.0611 m (measured in Catia)

Young's modulus (E) = 210 GPa

Moment of Inertia (Iyy) = 31276×10−6m4



Bending moment:

As shown in the schematic in Fig. the bending moment at a particular point x where

the strain gauge no. 6 is positioned, is:

Maximum= P×L4

=5000×0.2224

=277.5N

Moment at x=P×x2

=5000×0.06112

=152.75Nm

Figure 4, Bending moment diagram (www.awc.org)

Deflection:

Δx= P×x48×E×I

× (3 L2−4 x2 )

¿ 5000×0.222

48×210×109×3.1276×10−6× (3×0.2223−4×0.06112 )=6.3×10−4mm

Stress in Y direction:



σ y=MYyIyy

=152.75×4.4×10−3

3.1276×10−6 =2.44MPa, where y is the distance from centroid

(60.063, 35.559mm from Catia)

Strain in Y direction:

ε y=σ yE

=2.44×106

210×109=1.16×10−5=11.6 με

Figure 5, Section at strain gauge 6 location.

4.3 Finite element simulation of test

The geometry was imported to Ansys Workbench where all the components were

bonded together using a Boolean operation as shown in Fig. 6. Imprint faces were

added at the positions of the strain gauges also visible in Fig. 6. They allow for a

strain reading to be taken from the whole active are of a strain gauge.

Then the material properties (provided in the brief) were changed to a Young's

modulus of 210 GPa and maximum tensile strength to 430 MPa as shown in Fig. 7.

The setup used was as close as possible to the physical test rig.



Figure 6, Geometry model in Ansys with strain gauge imprint faces.

Figure 7, Material properties.

The setup used in the validation model is shown in Fig. 8 where frictionless supports

were used as the closest representation of the original supports used in the test. A

force of 5000 N was applied at the same surface as in the test.

Figure 9, shows the geared hole which added more geometrical complexity, thus,

increasing the number of nodes to a point with no interest. The geometry was



simplified and the mesh was refined in general and also at the position of the strain

gauge as shown in Fig. 10. Mesh statistics show a total of 98439 nodes with 56221

elements. A close inspection of the mesh reveals that the elements are correctly

placed at their boarders without any large differences in side lengths.

Figure 8, Validation model setup.

Figure 9, Geared hole detail.



Figure 10, Mesh at strain gauge.

4.4 Results

The model was solved and straight away it is visible (Fig. 11) that there is a high

stress concentration at the ball shafts. However, in this case they are not of particular

interested and the focus is on the knuckle only. The strain gauge number 6 reading

was exported to Excel and the strain values were averaged with a result of -39 με

(Fig. 11). The strain component used was the normal elastic strain to the Y axis,

since this is the direction that the gauge measures strain on. Table 2 shows the

comparison between the strain gauge reading and the Ansys result. The percentage

error at 5% is well within a reasonable 10% limit.

Figure 11, Stress result.



Figure 12, Strain gauge 6 result.

Table 2, Physical test and Ansys result comparison.

The theoretical result from calculations at 11.6 με compared with the Ansys test at 39

με is within a 70.3% error.

5.0 Finite Element Modeling

The model used in the FEA simulation was validated with the strain gauge test and is

well within a reasonable 10% error. For the three different loading cases (i.e. road

bump, braking, cornering) the Engineering Data and Geometry fields were linked so

that all Static Structural analyses would run with the same data. The Supports used

in all the cases were the Frictionless Support type as they allow for rotation of the

connection balls. This is closer to reality that the fixed support. A frictionless support

was also added to the connection with the steering control arm since it also provides

some support. The meshing was carefully refined to ensure that the elements

matched with their adjacent ones.



5.1 Road bump FEA

For the road bump, the forces that were calculated in section 2, were used. They

consist of the wheel acceleration force and the inertia load of the wheel. As the wheel

moves up it compresses the spring, which in turn loads the knuckle. Assuming slow

reaction for the chassis to the wheel the spring force is equal to the body accelerating

with the acceleration of the wheel. The inertia load from the wheel can be added to

that. Figure 13 illustrates the setup used. The default mesh can be seen in Fig. 14

Figure 13, Road bump case setup.



Figure 14, Default mesh.

The mesh was then refined twice until result convergence was evident. The first

refinement was a general Body Sizing method where element size was set to 3mm

for the whole part. The second refinement (2mm face sizing) was done on the front

face where the stress was found to be higher than the original mesh as well as at the

point of the strain gauge where the first measurement was taken (10 MPa). The two

refinements can be seen in Figures 15 and 16.



Figure 15, First refinement (3mm element size).

Figure 16, Second refinement (2mm face sizing).

5.2 Braking FEA

In the braking case, the same supports as previously were used. The forces were

added at the at the brake calliper mounting points and the deceleration force on the

hub plate (Fig. 17). Note the components of the force that add up to 1288.5 N as in

the calculations. The first and second mesh refinements can be seen in Figures 18

and 19.



Figure 17, Braking case setup.

Figure 18, First mesh refinement (3mm body sizing).



Figure 19, Second mesh refinement (2mm face sizing).

5.3 Cornering FEA

The same principles were applied to the cornering setup (Fig. 20) with the forces

consisting of a force and a moment. The mesh was also refined at high stress points

twice in this analysis. The first refinement was like the previous cases with a body

sizing with 3mm elements. The second refinement can be seen in Fig. 21.

Figure 20, Cornering case setup.



Figure 21, Second refinement (Face sizing 2mm elements).

5.4 Results

Table 3 shows the results of stress at points of interest on the knuckle. It is clearly

evident that the road bump case causes the highest stress on the knuckle. Figure 22

illustrates the stress measures in Ansys. Results seem to converge after two

refinements.

Table 3, FEA stress results.



Figure 22, Road bump stress result.

6.0 Discussion

The maximum tensile strength for the material as given by the brief is 430 MPa. The

minimum safety factor is also given as a minimum of 5. Therefore the maximum

stress in any of the cases must not be more than 86 MPa. Even at the road bump

case, the stress does not exceed 86 MPa with the highest stresses being on the front

plate where the hub boss is connected.

The physical test results and FEA results are within a 5% error which means that the

results for the three cases will be close in an actual driving test with road bumps,

braking and cornering.

However, the hand calculations are within a 70% error. This can be attributed to the

simplifications made to make the calculations possible. Simple mechanics of solids

approaches were used. Even though the calculations are simple, there are many

things that could influence the stress results. The assumptions made also play a

major role in the outcome of the calculations.

The goal now is to redesign the part so that its mass is reduced by removing material

from low stress areas.



7.0 Redesign

The geometry was redesigned to reduce weight from where possible. A total of 60

grams were reduced from the part with the introduction of some holes illustrated in

Fig. 23. The stress results can be seen in Fig. 24 and are within the safety factor.

There could be further material removal to reduce mass without affecting the safety

factor. However, the redesign process is an iterative task and can take a long time

and simulations to ensure that each change does not increase the stress beyond the

specified point, in this case, 86 MPa.

Figure 23, Redesigned geometry and mesh.



Figure 24, Redesign stress results.

8.0 Conclusion

The model was successfully validated with the use of strain gauges during the

physical test. However the hand calculations showed a high error (70%). This can be

attributed to the assumptions and simplifications made during the calculations. These

were essential due to the complexity of the geometry.

The redesigned component helps to show low stress areas where material can be

removed from to reduce the mass.

9.0 Recommendations

This work can be improved further with an investigation into more accurate hand

calculations. Moreover, using more realistic model constrains for the physical test in

the FEA such as remote displacements could provide more accurate results. This is

due to the fact that the supporting brackets used were made of aluminium which is

elastic compared to steel and could have displaced during the test.



The component mass can be further reduced if time is spend finding low stress areas

and carefully and gradually applying and measuring design changes and how they

affect the stress.

References:

Walker N., Mechanics of Solids Lecture Notes, Birmingham City University website

http://www.awc.org/pdf/DA6-BeamFormulas.pdf (Last accessed on 26/05/2012)

Appendix

Figure 25, Strain gauge location.



Figure 26, Steering knuckle.


c. kalavrytinos - fea of a steering knuckle

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