TRANSPORT PROBLEMS 2010

PROBLEMY TRANSPORTU Volume 5 Issue 4

stabilizer bars, calculation, construction

Adam-Markus WITTEK*, Hans-Christian RICHTER
ThyssenKrupp Bilstein Suspension GmbH
Oeger St. 85, 58095 Hagen, Germany
Bogusaw AZARZ
Silesian University of Technology, Faculty of Transport
Krasiskiego St. 8, 40-019 Katowice, Poland
*Corresponding author. E-mail: adam.wittek@thyssenkrupp.com



STABILIZER BARS: Part 1. CALCULATIONS AND CONSTRUCTION

Summary. The article outlines the calculation methods for stabilizer bars. Modern
technological and structural solutions in contemporary cars are reflected also in the
construction and manufacturing of stabilizer bars. A proper construction and the selection
of parameters influence the strength properties, the weight, durability and reliability as
well as the selection of an appropriate production method.



STABILIZATORY SAMOCHODOWE: Cz 1. OBLICZENIA I KONSTRUKCJA

Streszczenie. W artykule przedstawiono zarys metod obliczeniowych stabilizatorw
samochodowych. Nowoczesne rozwizania technologiczno-konstrukcyjne we
wspczesnych samochodach znajduj rwnie odzwierciedlenie w konstrukcji i
produkcji stabilizatorw. Prawidowa konstrukcja i dobr parametrw maj wpyw na
cechy wytrzymaociowe, ciar, trwao oraz niezawodno jak i wybr waciwej
metody produkcyjnej.


1. INTRODUCTION

The function of stabilizer bars in motor vehicles is to reduce the body roll during cornering. The
body roll is influenced by the occurring wheel load shift and the change of camber angle. Decisive is
the steering performance which may be purposefully adjusted towards understeer or oversteer when
designing the stabilization. So the stabilizer bars increases the travelling comfort and to a considerable
extent the driving safety [10].
Stabilizer bars are non-bearing spring elements in vehicles. In contrast to all bearing springs, which
are loaded by the static forces also in resting condition, the stabilizer bars are normally loaded during
the driving phases only [4]. As resilient components of the chassis, stabilizer bars are connectors
between axle and body as well as between the wheels of an axle. The position of stabilizer bars is
selected in such a way that the anti-roll suspension stiffens the rotation of the body about the
vehicles longitudinal axis is made difficult without simultaneously hindering the vertical
suspension, i.e. motion of the body towards the vertical axis. For this purpose, the stabilizer bar is
arranged in the axle in such a way that the back comes to rest approximately at the level of the wheel
centers across the driving direction. The bearings of the stabilizer bar support themselves against the
body; stabilizer bars do not contribute to static support of the weight of the body against the axle and
remain unloaded during synchronistic downward or upward deflection of the spring.
136 A.-M. Wittek, H.-Ch. Richter, B. azarz

When the body leans due to centrifugal forces acting in the transverse direction of the vehicle, the
so-called reciprocal suspension comes about. This means that at the bend of the road the bend-external
wheel deflects downwards and the bend-internal wheel deflects upwards. As a result of this, the
stabilizer bar arms are deflected in the opposite direction and the back is twisted [9, 10].
The body roll during cornering could be reduced also by the selection of a harder vertical
suspension, but it would have a negative impact on the driving comfort. The stabilizer bars contribute
thus considerably to the improvement of comfort of the motor vehicles.


2. CALCULATION AND CONSTRUCTION

Stabilizer bars for the chassis of motor vehicles are usually U-shaped bars of spring steel with
circular or circular ring cross-section, so they form a bow with the back and the arms. As few as
possible kinks preferably in a single plane should be planned when constructing stabilizer bars.























Fig. 1. Form of stabilizers
Rys. 1. Ksztaty stabilizatorw

This makes the manufacturing of the parts easier. However, as a rule, the stabilizer bars do not lie
in a single plane, but for the purpose of avoidance of other chassis parts are arranged spatially
bent, angled and cranked in a partly bizarre way (fig. 1, 2). Their U-shape is principally maintained
[1, 3, 4]. Fig. 2 contains examples of different shapes of stabilizer bars.
As large bending radii as possible should be selected. The inner bending radius must have at least
the size of the bar diameter. The arm ends are shaped differently for the purpose of force transmission
and steering. Generally, when constructing stabilizer bars, effort must be made to minimize the
weight, e.g. by shortening the arms while maintaining constant stabilizer bar action (fig. 4) [1, 3, 4].
Most commonly, stabilizer bars are mounted in rubber or plastic (fig. 3), and each shape of bearing
requires an appropriate shape of the bar end. The plastic bearing, the rubber stiffness and the rubber
strain have an influence on all stabilizer bars or the wheel rate, respectively.
Stabilizer bars: Part 1. Calculation and construction 137

Fig. 2. Shapes of stabilizer bars - examples
Rys. 2. Ksztaty stabilizatorw samochodowych przykady














Fig. 3. Plastic bearings for stabilizer bars
Rys. 3. Przykady oysk stabilizatorw samochodowych

Stabilizer bars are manufactured mostly of round stock with rolled, drawn, peeled or ground
surface. Bars that additionally take over the axle location functions are manufactured principally of
ground or peeled primary material. Stabilizer bars are loaded only in turns. In contrast to the load-
bearing spring elements, there are no requirements in respect of the relaxation performance. Therefore,
also considering the notch sensitivity, the heat treatment strength is selected lower than in case of
load-bearing spring elements [1, 3, 4].
138 A.-M. Wittek, H.-Ch. Richter, B. azarz

Fig. 4. Optimization of the weight of stabilizer bars by shortening the arm length with unchanged stabilization
effect
Rys. 4. Redukcja ciaru stabilizatorw poprzez skrcenie ramion przy niezmienionej sztywnoci

The curb weight of a car has been increasing steadily in the course of years due to increased
requirements with regard to safety and convenience equipment. In order to counteract the tendency,
components with substantial weight saving potential have been identified. The consideration of the
load of stabilizer bars has shown that the max. load is on the outer edges of the diameter. The load
decreases inwards to the neutral stage to a mean stress of
vm
= 0. Theoretically, the solid stabilizer bar
could be hollowed out without affecting the function. Therefore, the tubular stabilizer bars come into
question with increasing frequency. In case of a tubular stabilizer bar, the weight may be reduced in
comparison with the solid stabilizer bar of equal shape, with equal stabilization effect and adequate
maximum stress [10].
The concern of the stabilizer bar calculation is to consider the numerous influences and various
requirements based on the strain and stress relations in such a way that the designed stabilizer bar
satisfies the requirements of
the strength test within the scope of which the compliance with the permitted stress, safety, load
capacity or endurance limits are tested
and the requirements of
the function test within the scope of which the compliance with the requested stabilizer bar rate,
the forces and stabilizer bar travels within the specified tolerances, the vibration performance and
other requirements are tested [6].

2.1. Strength test

A force applied on the bar ends of a U-shaped bent solid stabilizer bar causes bending stress as well
as torsional stress at the bar. While torsional stresses prevail at the back of the bar, the bending stresses
are particularly great in the area of the arms [1, 3, 4, 6].
Stabilizer bars: Part 1. Calculation and construction 139

The permitted equivalent stress

V
may be calculated according to the equation

2 2
3t o o + =
V
(1)
where: - bending stress, torsional stress.
From the permitted torsional and bending stress values. In most cases, during stress analysis it will
be found that the maximum equivalent stress and consequently the vulnerable cross-section is at the
transition radius from the back to the arm. The position (stress maximum) is determined by the shape
of the arm and the relationship bending radius/arm length [1, 3, 4].
The torsional stresses may be calculated from

p
t
W
M
= t
,
(2)
were: M
t
torque moment, W
p
modulus of twist.
For bar backs with round profile

3
16
d
Ft
t
t = , (3)
where: t lever arm (fig. 5), F - force, d diameter of stabilizer bar.
And the bending stresses from

W
M
b
= o
,
(4)
where: M
b
bending moment, W modulus of section.
For bar backs with round profile

3
32
d
Fb
t
o =
,
(5)
where: b lever arm (fig. 5).
The equivalent stress
v
may be calculated according to the equation

2 2
3
3 4
16
t b
d
F
V
+ =
t
o
.
(6)
The value of strains at the transition radius depends on the distances h
1
+r and h
2
fig. 6 [3] shows
different arm shapes of a stabilizer bar with circular profile.
Depending on the angle w
o
defined in (fig. 7), the torsional and bending stresses as well as the
equivalent stress resulting from the summing-up may be calculated:




Fig. 5. Exemplary embodiment and transmission of forces
Rys. 5. Przykadowy model zastpczy do oblicze wytrzymaociowych stabilizatora

140 A.-M. Wittek, H.-Ch. Richter, B. azarz

1
2
2
1
2
1
) 1 / 3 arccos(
h
h
arctg
h
h
h r w
o
+
|
|
.
|

\
|
= (7)

2
2
1
2
1 max
3 1 r
h
h
h
W
F
V
+
(
(

+
|
|
.
|

\
|
= o (8)
The equations describe the place and size of the maximum equivalent stress in the transition area
between the back and the arms [3] is the angle at which the transfer of equivalent stress is zero.
0 =
dw
d
V
o
(9)
The equivalent stress reaches its maximum at these points.



Fig. 6. Load ,
b
and
v
at the transition radius from the shaft to the arm of a stabilizer bar
Rys. 6. Naprenia ,
b
und
v
w przejciu promienia z czci prostej do ramienia prta stabilizatora



Fig. 7. Change in shape of the arm in the transition area
Rys. 7. Zmiany geometrii ramion stabilizatora w strefie promienia

Due to different requirements on stabilizer bars and numerous influences on the strength of
materials, the characteristic value of the planned material is not always used in full value when
dimensioning.
[degree]
Stabilizer bars: Part 1. Calculation and construction 141

Permitted stresses which result as a quotient from the strength value regarded as ultimate stress
) , , , , , (
01 . 0 2 . 0 tF bE p p e m
R R R R t o and the required safety
erf
S S = are taken into account [6, 7, 8].
S
ertr zul
/ o o = (10)
S
ertr zul
/ t t = (11)
In some cases, characteristic values as shear modulus G and shear-spring limit (torsional elasticity
limit)
tE
t are required for the design of torsionally strained stabilizer bars, but they are usually
missing. Using approximation notations,

( ) u +
=
1 2
E
G (12)
where: u - Poisson ratio, E modulus of elasticity.

bE
bE
tE
o
o
t 578 , 0
73 , 1
= =
(13)
a calculation is possible (
10
3
= u set). When the abovementioned material data is missing, the tensile
strength
m
R is used as a basis for the calculation of permitted stress
zul
t [6, 7, 8].

2.2. Function test

2.2.1. Rough determination of the total spring travel 2s

The rough calculation assumes that a part of the stabilizer bar is stressed only by twisting and the
other only by bending. Participation of the back in the total spring travel:

( )
F
GI
l r h
s
p
T
T
2
1
1
2
2
+
= (14)
where: I
p
polar moment of inertia.
Participation of the arm in the total spring travel:

F
EI
l
s
s
B
3
2
2
3
2
= (15)
where: I moment of inertia about axis.
The total spring travel results from:
( )
2 1
2 2
B T
s s s + = (16)
F
EI
l
GI
l r h
s
s
p
T
(
(

+
+
=
3
) (
2 2
3 2
1
(17)
The force F is calculable from the equation (17). Generally, the rough calculation yields greater forces
than the measurements. This can be also traced back to the fact that the straining of rubber bearing is
left out of consideration. Therefore, it is recommended to reduce the calculated force by about 10%. In
case of simple geometries of stabilizer bar arms, the errors are of the order of 5%, however, in case of
arms which, due to their shaping, allows assuming high torsion rates, the error may increase
considerably [3, 4].

2.2.2. Exact determination of the total spring travels 2s

In case of an exact calculation, strains occurring in each profile are taken into consideration. Here, too,
simplifying assumptions are made:
- The flexibility of the arms is small in relation to their length,
- In unloaded condition, the stabilizer bar lies in a single plane,
- The bearings are rigid,
142 A.-M. Wittek, H.-Ch. Richter, B. azarz

- The stabilizer bar is symmetrical,

- As a result, only one side of the stabilizer bar is calculated.
Participation of the back in the total spring travel resulting from torsion:

( )
F
GI
l r h
s
p
T
T
2
1
1
+
=
(18)
Resulting from bending:

( ) ( )
( )
)

(
(

+
+
+ +
+
=
2
2
2 0 2
2
2
1
2
1
3
h l
h l h
l l
EI
h l F
s
c
c a
c
B
(19)
Participation of the arm in the total spring travel resulting from torsion:

}
= =
s
l
p
T
p
dl t
GI
F
s dl
GI
Ft
ds
0
2
1
2
(20)
Participation of the arm in the total spring travel resulting from bending:

}
= =
s
l
B
dl b
GI
F
s dl
GI
Fb
ds
0
2
1
2
(21)
The total spring travel 2s for the entire bar gives then (16)(17)(18)(19):
( )
2 2 1 1
2 2
T B T B
s s s s s + + + = (22)

3. CONCLUSIONS

The engineering data for stabilizer bars are specified by car manufacturers. These physical
characteristics must not be altered by the stabilizer bar manufacturers. The described calculation
methods serve thus the purpose of determining the following:
1. Whether the most important physical characteristics such as stabilizer bar rate, geometrical
data (such as bending radii and planes) have been chosen correctly.
2. Whether the stress concentration, in particular in radii areas, remains comparable to the other
stabilizer bar constructions within permitted limits.
3. Whether the chosen, possible method of production guarantees that the stresses in critical
areas remain under the permitted limit.
4. Whether the geometrical requirements of the car manufacturer for bars are feasible in the
series production.


References

1. Von Estorff H.-E.: Technische Daten Fahrzeugfedern Teil:3 Stabilisatoren. Stahlwerke
Brninghaus GmbH, Werk Werdohl, Hang Druck KG, Kln 1969.
2. Technische Daten Fahrzeugfedern. Stahlwerke Brninghaus GmbH, Werk Werdohl, E.Anding
KG, Herborn 1965.
3. Ulbricht J., Vondracek H., Kindermann S.: Warm geformte Federn Leitfaden fr Konstruktion
und Fertigung. Hoesch Werke, Hohenlimburg Schwerte AG, W.Stumpf KG, Bochum 1973.
4. Fischer F., H.Vondracek H.: Warm geformte Federn - Konstruktion und Fertigung. Hoesch
Werke, Hoesch Hohenlimburg AG, W.Stumpf KG, Bochum 1987.
5. Mitschke M.: Teoria samochodu Dynamika samochodu tom 2/ Drgania. Wydanie 2
Wydawnictwa Komunikacji i cznoci, Warszawa 1989.
6. Meissner M.,.Schorcht H.-J.: Metallfedern Grundlagen, Werkstoffe, Berechnung, Gestaltung
und Rechnereinsatz. 2. Auflage, Springer Verlag, Ilmenau 2007.
7. Muhs D., Wittel H., Jannasch D., Voiek J.: Roloff / Matek Maschinenelemente Normung,
Berechnung, Gestaltung. 18. Auflage, Viewegs Fachbcher der Technik, Wiesbaden 2007.
Stabilizer bars: Part 1. Calculation and construction 143

8. Jakubowicz A., Orlo Z.: Wytrzymao materiaw. Wydanie 6, Wydawnictwa Naukowo-

Techniczne, Warszawa 1984.
9. Reimpell J., Betzler J.W.: Fahrwerktechnik Grundlagen. 5. Auflage, Vogel Verlag, Wrzburg
2005.
10. Dziemballa H., Manke L.: Gewichtsreduzierung durch hochbeanspruchte Rohrstabilisatoren.
ThyssenKrupp Technoforum 2004, Essen 2004.
11. Topac M., Kuralay N.S.: Computer aided design of an anti-roll bar for a passenger bus.
http://www.turkcadcam.net/rapor/otobus-stab-cae/index.html,23.10.2010
12. Tschtsch H., Dietrich J.: Praxis der Umformtechnik. 9. Auflage, Vieweg + Teubner, Wiesbaden
2008.
13. Klocke F., W.Knig W.: Fertigungsverfahren 4 Umformen. 5. Auflage, Springer Verlag. Berlin
Heidelberg 2006.
14. Krist T.: Handbuch fr Techniker und Ingenieure. 12. Auflage, Hoppenstedt Technik Tabellen
Verlag, Darmstadt 1991.
15. Klein B.: FEM Grundlagen und Anwendungen der Finite-Element-Methode im Maschinen- und
Fahrzeugbau. 7. Auflage, Vieweg Studium Technik, Wiesbaden 2007.
16. Meissner M., Fischer F., Wanke K., Plitzko M.: Die Geschichte der Metallfedern und
Federtechnik in Deutschland. 1. Auflage, Universittsverlag Ilmenau. Ilmenau 2009.
17. Heiing B., Ersoy M.: Fahrwerkhandbuch Grundlagen, Fahrdynamik, Komponenten, Systeme,
Mechatronik, Perspektiven. 2. Auflage, Vieweg + Teubner, Wiesbaden 2008.
18. Prochowski L.: Mechanika ruchu. Wydanie 2 Wydawnictwa Komunikacji i cznoci, Warszawa
2008.

Received 11.10.2009; accepted in revised form 9.12.2010
TRANSPORT PROBLEMS 2011
PROBLEMY TRANSPORTU Volume 6 Issue 1


stabilizer bars, calculation, model

Adam-Markus WITTEK*, Hans-Christian RICHTER
ThyssenKrupp Bilstein Suspension GmbH
Oeger St. 85, 58095 Hagen, Germany
Bogusaw AZARZ
Silesian University of Technology, Faculty of Transport
Krasiskiego St. 8, 40-019 Katowice, Poland
*Corresponding author. E-mail: adam.wittek@thyssenkrupp.com



STABILIZER BARS: Part 2. CALCULATIONS - EXAMPLE

Summary. The article contains the further outline of the calculation methods for
stabilizer bars. Modern technological and structural solutions in contemporary cars are
reflected also in the construction and manufacture of stabilizer bars. A proper
construction and the selection of parameters influence the strength properties, the weight,
durability and reliability as well as the selection of an appropriate production method.



STABILIZATORY SAMOCHODOWE: Cz 2. OBLICZENIA - PRZYKAD

Streszczenie. W artykule przedstawiono dalsz cz zarysu metod obliczeniowych
stabilizatorw samochodowych. Nowoczesne rozwizania technologicznokonstrukcyjne
we wspczesnych samochodach znajduj rwnie odzwierciedlenie w konstrukcji
i produkcji stabilizatorw. Prawidowa konstrukcja i dobr parametrw maj wpyw
na cechy wytrzymaociowe, ciar, trwao oraz niezawodno jak i wybr waciwej
metody produkcyjnej.


1. INTRODUCTION

The stabilizer bars in vehicles have the following functions:
1. Pure rolling motion (cornering) without stimulating the wheels. The reduction of rolling motion
during cornering is achieved that way.
2. Stimulation of the wheels in the same direction.
The secondary spring rates occurring in practice in the bearings lead to stiffening of the body
suspension (mechanical parallel connection of secondary spring rate and body rigidity)
3. One-sided stimulation.
Due to the stabilizer bar occurs one-sided stiffening of the body (comfort deterioration).
Additionally, the stabilizer bar strengthens the waddling motion of the body (waddling: rolling
caused by the road surface).

One of the most important criteria when calculating a stabilizer bar (function test) is the spring rate
of the stabilizer bar the stabilizer bar rate. The stabilizer bar rate results from the sum of deflections
at the ends (axle articulation) and the stabilizer bar force. Only the vertical portions of the
displacement and the force are considered. The rate is stated in the N/mm unit.

138 A.M. Wittek, H.Ch. Richter, B. azarz

2. CALCULATION OF THE STABILIZER BAR RATE



Fig. 1. Arrangement and principle of operation of stabilizer bars in a motor vehicle
Rys. 1. Rozwizania i funkcje stabilizatorw w pojazdach samochodowych

In case of the calculation of cornering ability, the transmission ratios and from wheel to spring or
stabilizer bar are specified [1]. They are understood as quotients from the spring travel of the wheel
and from the spring or stabilizer bar end [1, 10]:
and (1)

Whereas the forces are transmitted in the reversed ratio as compared to the travels from wheel to
spring or to stabilizer bar, and are adopted square in the transmission ratio of the spring or
stabilizer bar rate which are indeed quotients from force and spring travel:
and (2)

The stresses and in the stabilizer bar can be calculated with the given dimensions as a function of
forces acting on the arm ends:
[N] (3)

Characterizing feature of the typical stabilizer bar (fig. 2) is the double mounting of its back on the
vehicle frame or body, or on the axle or the wheel suspension arms, respectively, and fastening of its
arm ends on the axle or the wheel suspension arms, or on the vehicle frame or body, respectively.
These stabilizer bars can be designed for all wheel suspensions.
Stabilizer bars: Part 2. Calculations example 139



Fig. 2. Equivalent system for stabilizer bar calculation
Rys. 2. Model zastpczy obliczeniowy stabilizatora
(4)
(5)
With the given longitudinal dimensions, the bar diameter may be calculated [1, 7, 8, 10]:
(6)
where for Ushaped, fulllength round stabilizer bar (constant diameter)
Calculation of a stabilizer bar with circular crosssection and pure torsional strain [510]:

Fig. 3. Equivalent system for stabilizer bar calculation
Rys. 3. Model obliczeniowy stabilizatora
140 A.M. Wittek, H.Ch. Richter, B. azarz

Twisting moment of the stabilizer bar:
[MPa] (7)

where , [] (8)

[MPa] (9)

The stabilizer bar rate is then:

[N/mm] (10)

3. INFLUENCE OF THE FLEXIBLE STABILIZER BAR BEARING

Each stabilizer bar has either four or, when the longitudinal displaceability of the back or the arm
ends over connecting links is achieved, six bearing surfaces which in general are flexible and as a
result reduce the stabilizer bar rate. The extent of this bearingrelated rate decrease depends, apart
from the flexible bearing surfaces, also on their position on the stabilizer bar as well as the shore
hardness and the volume of bearing material used [1, 11]. Back bearing function and requirements:
connection / fixing of the stabilizer bar to the vehicle body,
transmission of forces and moments,
Realization of the degree of torsional freedom
- frictionless/lowfriction,
- generation of a defined twisting rigidity (secondary spring rate),
Axial protection during shear force transmission.
Considering that the resilient rubber bearings are connected in series with the stabilizer bar, the
calculation of the rate of complete system and consequently of the stabilizer bar with resilient rubber
bearing gives [1, 7, 8, 10]:

(11)




4. STRENGTH TEST AND FUNCTION TEST (EXAMPLE)

4.1. Drawings and general design data
Stabilizer bars: Part 2. Calculations example 141

Table 1
stabilizer geometry (points of intersection)













Bar geometry:
bar diameter d [mm]: 28.000
lenght [mm]: 1711.490


Fig. 4. Stabilizer bar / production drawing / bar geometry
Rys. 4. Rysunek wykonawczy stabilizatora prtowego, wsprzdne
point [-] X [mm] Y [mm] Z [mm] radius [mm]
1 335,000 -541,000 0,000
2 225,000 -541,000 -51,300 51,000
3 124,800 -400,200 -80,700 51,000
4 0,000 -395,000 0,000 51,000
5 0,000 -228,200 0,000 51,000
6 105,600 -223,400 -85,900 51,000
7 105,600 0,000 -85,900 51,000
8 0,000 265,000 0,000 51,000
9 0,000 410,000 0,000 51,000
10 105,000 410,000 0,000 51,000
11 210,000 541,000 0,000 51,000
12 335,000 541,000 0,000
142 A.M. Wittek, H.Ch. Richter, B. azarz

4.2. Warehousing, forces and tensions:
Table 2
stabilizer with back bearings:
bearing X [mm] Y [mm] Z [mm] F
x
[N] F
y
[N] F
z
[N]
point No.: [-]
1 335,000 -541,000 0,000 0 0 2127 1
2 0,000 -326,147 0,000 0 0 -3528,5 2415
3 0,000 326,093 0,000 0 0 3528,5 6291
4 335,000 541,000 0,000 0 0 -2127 8557

deflection (wanted) 2s [mm]: 77.000
tangent force [N]: not defined
Table 3
bearing spacing
bearing X [mm] Y [mm] Z [mm] distance
3-2 0,000 652,240 0,000 632,24
4-1 0,000 1082,000 0,000 1082
2-1 -335,000 214,853 0,000
3-4 -335,000 -214,907 0,000

lenght of leg [mm] : 335.0 3
leg distance [mm] : 1082.0 3
bearings distance [mm] : 326.0


Fig. 5. Stabilizer bar spring travel / warehousing
Rys. 5. Droga sprysta stabilizatora, oyskowanie - mocowanie
Stabilizer bars: Part 2. Calculations example 143

maximum equivalent stress at 0 [MPa]: 390 at length 631.9mm
maximum corrected equivalent stress [MPa]: 465 at length 713.1mm Pos. 0

4.3. Results of calculation
Maximum bar diameter [mm]: 28.00
lenght theor. (for pipe stabilizers) [mm]: 1711.5
lenght theor. (for rod stabilizers) [mm]: 1728.2
lenght before / after [mm]: 0.00
mass theor. / actual [kg]: 8.27
calculated deflection [mm]: 71.30
rate [N/mm]: 29.83
roll angle [] : 3.77
leg angle (bearing 1-4) [] : 12.15
stress / roll angle [MPa/] : 103.42

4.4. End configuration
left right
inner eye diameter [mm]: 12.3 3 12.3 3
outer eye diameter [mm]: 40.0 1 40.0 1
thickness at eye [mm]: 9.0 0.5 9.0 0.5

Fig. 6. Stabilizer bar - end configuration
Rys. 6. Kocwki stabilizatora

4.5. Aterial and production requirements
Table 4



144 A.M. Wittek, H.Ch. Richter, B. azarz


Fig. 7. Stabilizer bar - stress distribution
Rys. 7. Wykresy napre w stabilizatorze


material: SAE 5160 or DIN 55Cr3
E-modulus, G-modulus [MPa]: 206000, 78500
spec. gravity [MPa]: 7.85 kg/m
surface condition: black bar bar diameter [mm]: 28.000.28
bar lenght (pipe) [mm]: 1711.00 bar lenght (rod) [mm]: 1728.00
temper strength: HB- diameter [mm] 0.00 0.00 hardness (Rockwell) [HR] 45.0 49.0
tensile strength: [MPa] 1444 1625


5. CONCLUSIONS

The described calculation methods should be instrumental in designing the stabilizer bars. If the
calculated stresses in the bearing / bend are too high ( ), there are two ways to solve it when
constructing the stabilizer bar [11]:
1. Use of a steel of higher strength (possibilities limited).
2. Stabilizer bar with variable diameter:

Stabilizer bars: Part 2. Calculations example 145

If the maximum permissible stress is exceeded even using high-strength steel, a transfer of
the deformation work to less stressed areas must follow. Consequence stabilizer bar with
non-constant diameter / wall thickness (rotary swaging).
Large diameters / wall thicknesses in critical areas (e.g. bends, bearing surfaces).
Thinner diameters / wall thicknesses at the back / arms.
The required rate may be achieved only by reducing the diameter/wall thickness in the less
stressed areas may.


Refeferences

1. von Estorff H.-E.:Technische Daten Fahrzeugfedern Teil:3 Stabilisatoren. Stahlwerke Brninghaus
GmbH, Werk Werdohl, Hang Druck KG, Kln, 1969.
2. Technische Daten Fahrzeugfedern. Stahlwerke Brninghaus GmbH, Werk Werdohl, E.Anding KG,
Herborn, 1965.
3. Ulbricht J ., Vondracek H., Kindermann S.; Warm geformte Federn Leitfaden fr Konstruktion
und Fertigung. Hoesch Werke, Hohenlimburg Schwerte AG, W.Stumpf KG, Bochum, 1973.
4. Fischer F., H.Vondracek H.: Warm geformte Federn Konstruktion und Fertigung. Hoesch
Werke, Hoesch Hohenlimburg AG, W.Stumpf KG, Bochum, 1987.
5. Mitschke M.: Teoria samochodu Dynamika samochodu tom 2/ Drgania. Wydanie 2
Wydawnictwa Komunikacji i cznoci, Warszawa, 1989.
6. Meissner M.,.Schorcht H.-J .: Metallfedern Grundlagen, Werkstoffe, Berechnung, Gestaltung und
Rechnereinsatz. 2. Auflage, Springer Verlag, Ilmenau, 2007.
7. Muhs D., Wittel H., J annasch D., Voiek J .: Roloff / Matek Maschinenelemente Normung,
Berechnung, Gestaltung. 18. Auflage, Viewegs Fachbcher der Technik, Wiesbaden, 2007.
8. Jakubowicz A. Orlo Z.: Wytrzymao materiaw. Wydanie 6, Wydawnictwa Naukowo-
Techniczne, Warszawa, 1984.
9. Reimpell J ., Betzler J .W.: Fahrwerktechnik Grundlagen. 5. Auflage, Vogel Verlag, Wrzburg,
2005.
10. Topac M., Kuralay N.S.: Computer aided design of an antiroll bar for a passenger bus.
http://www.turkcadcam.net/rapor/otobus-stab-cae/index.html, 23.10.2010.
11. Brendecke T., Gtz O., Schneider F., Brust B.: Prsentation Wissenmanagment Stabilisatoren
ThyssenKrupp Bilstein Suspension GmbH, Hagen, Dezember, 2006.

Received 11.10.2009; accepted in revised form 20.03.2011