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
Bogusław ŁAZARZ
Silesian University of Technology, Faculty of Transport
Krasińskiego 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: Część 2. OBLICZENIA - PRZYKŁAD

Streszczenie. W artykule przedstawiono dalszą część zarysu metod obliczeniowych
stabilizatorów samochodowych. Nowoczesne rozwiązania technologiczno–konstrukcyjne
we współczesnych samochodach znajdują również odzwierciedlenie w konstrukcji
i produkcji stabilizatorów. Prawidłowa konstrukcja i dobór parametrów mają wpływ
na cechy wytrzymałościowe, ciężar, trwałość oraz niezawodność jak i wybór właściwej
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. Łazarz

2. CALCULATION OF THE STABILIZER BAR RATE

Fig. 1. Arrangement and principle of operation of stabilizer bars in a motor vehicle

Rys. 1. Rozwiązania i funkcje stabilizatorów 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 zastępczy – obliczeniowy stabilizatora

(4)

(5)
With the given longitudinal dimensions, the bar diameter may be calculated [1, 7, 8, 10]:

(6)
where for U–shaped, full–length round stabilizer bar (constant diameter)
Calculation of a stabilizer bar with circular cross–section and pure torsional strain [5–10]:

Fig. 3. Equivalent system for stabilizer bar calculation

Rys. 3. Model obliczeniowy stabilizatora
140 A.M. Wittek, H.Ch. Richter, B. Łazarz

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 bearing–related 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/low–friction,
- 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)

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

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 prętowego, współrzędne
142 A.M. Wittek, H.Ch. Richter, B. Łazarz

4.2. Warehousing, forces and tensions:

Table 2
stabilizer with back bearings:
bearing X [mm] Y [mm] Z [mm] Fx [N] Fy [N] Fz [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 sprężysta stabilizatora, łożyskowanie - 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. Końcówki stabilizatora

4.5. Aterial and production requirements

Table 4
144 A.M. Wittek, H.Ch. Richter, B. Łazarz

Fig. 7. Stabilizer bar - stress distribution

Rys. 7. Wykresy naprężeń w stabilizatorze

material: SAE 5160 or DIN 55Cr3

E-modulus, G-modulus [MPa]: 206000, 78500
spec. gravity [MPa]: 7.85 kg/m³
surface condition: black bar bar diameter [mm]: 28.00±0.28
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 Brüninghaus

GmbH, Werk Werdohl, Hang Druck KG, Köln, 1969.
2. Technische Daten Fahrzeugfedern. Stahlwerke Brüninghaus GmbH, Werk Werdohl, E.Anding KG,
Herborn, 1965.
3. Ulbricht J., Vondracek H., Kindermann S.; Warm geformte Federn – Leitfaden für 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.
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Wydawnictwa Komunikacji i Łączności, 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., Voßiek J.: Roloff / Matek Maschinenelemente – Normung,
Berechnung, Gestaltung. 18. Auflage, Viewegs Fachbücher der Technik, Wiesbaden, 2007.
8. Jakubowicz A. Orloś Z.: Wytrzymałość materiałów. Wydanie 6, Wydawnictwa Naukowo-
Techniczne, Warszawa, 1984.
9. Reimpell J., Betzler J.W.: Fahrwerktechnik – Grundlagen. 5. Auflage, Vogel Verlag, Würzburg,
2005.
10. 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.
11. Brendecke T., Götz O., Schneider F., Brust B.: Präsentation Wissenmanagment Stabilisatoren
ThyssenKrupp Bilstein Suspension GmbH, Hagen, Dezember, 2006.

Received 11.10.2009; accepted in revised form 20.03.2011