International Journal of Engineering Trends and Technology (IJETT) – Volume 16 Number 6 – Oct 2014
Design and Optimization of Hydro Pneumatic Suspension System through
Structural Analysis
Ratna Babu Dondapati¹ P.V.Anil Kumar²
¹ M.tech student, ²Associate professor, dept of mechanical engineering, kits, markapur, A.P, INDIA
Dynamic analysis to analyze strength and
ABSTRACT
The aim of this project is to
develop a simulation model containing the
hydro pneumatic suspension system of the
rally truck. The model is validated by
dynamic
model can be used for further research
with respect to alive damping control or
implementing the system in other vehicles.
As the vehicle is designed without wheel
suspension, wheel loader drivers are
exposed to high levels of whole body
vibration which influences ride comfort
negatively. The work presented in this
thesis has the aim to investigate the
potential in adding an axle suspension to a
wheel loader in order to reduce vibrations
and increase handling quality.
In this project, the three-dimension
model
of
Hydro
suspension system
UNIGRAPHICS
is
and
pneumatic
modelled
imported
ANSYS software to perform static and
ISSN: 2231-5381
in
into
of
Hydro
pneumatic suspension system and optimize
if required.
INTRODUCTION
measurement data on both component
level as well as full vehicle level. The
characteristics
Hydro pneumatic suspension is a
type of automotive suspension system. The
purpose of this system is to provide a
sensitive,
suspension
dynamic
that
and
high-capacity
offers
superior ride
quality. A nitrogen reservoir with variable
volume yields a spring with non-linear
force-deflection characteristics. In this way
the resulting system does not possess any
Eigen frequencies and associated dynamic
instabilities, which need to be suppressed
through
extensive
damping
in
conventional suspension systems.
The nitrogen gas as spring medium
is approximately six times more flexible
than conventional steel, so self-leveling is
incorporated to allow the vehicle to cope
with
the
extraordinary
suppleness
provided.
http://www.ijettjournal.org
Page 268
International Journal of Engineering Trends and Technology (IJETT) – Volume 16 Number 6 – Oct 2014
Hydro-pneumatic system has been
 Perform Harmonic analysis to find
designed and optimized for static loads and
maximum deflections and stress on
vibration control. Hydro-pneumatic system
Hydro
is
system for operating frequencies.
to
develop
containing
a
the
simulation
hydro
model
pneumatic
suspension
pneumatic
suspension system of the rally truck.
DESIGN CALCULATIONS
PROBLEM DEFINITION &
Mathematics of the spring rate
METHODOLOGY
Spring rate is a ratio used to measure how
resistant a spring is to being compressed or
The purpose of this system is to
provide a sensitive, dynamic and highcapacity
suspension
that
offers
superior ride quality. A nitrogen reservoir
with variable volume yields a spring with
expanded during the spring's deflection.
The
magnitude of the spring
force
increases as deflection increases according
to Hooke's Law. Briefly, this can be stated
as
non-linear force-deflection characteristics.
In this way the resulting system does not
possess
any
Eigen
frequencies and
where
associated dynamic instabilities, which
F is the force the spring exerts
need to be suppressed through extensive
k is the spring rate of the spring.
damping
in
conventional
suspension
systems.
x is the deflection of the spring from its
equilibrium position (i.e., when no force is
The methodology followed in my project
applied on the spring).
is as follows:
Spring rate is confined to a narrow
 Perform the Design calculations of
the Hydro-pneumatic system.
 Perform Static analysis to find
max. Deflections and max. Stress
interval by the weight of the vehicle, load
the vehicle will carry, and to a lesser
extent
by
suspension
geometry
and
have
units
performance desires.
on Hydro pneumatic suspension
Spring
system
of N/mm (or lbf/in). An example of a
for
operating
loading
rates
typically
linear spring rate is 500 lbf/in. For every
conditions.
 Perform Modal analysis to find
inch the spring is compressed, it exerts
natural frequencies on the Hydro
500 lbf. A non-linear spring rate is one for
pneumatic suspension system.
which the relation between the spring's
ISSN: 2231-5381
http://www.ijettjournal.org
Page 269
International Journal of Engineering Trends and Technology (IJETT) – Volume 16 Number 6 – Oct 2014
compression and the force exerted cannot
characteristics were assumed for the series
be fitted adequately to a linear model. For
elements. Equation 3-4 shows the formula
example, the first inch exerts 500 lbf force,
used to calculate the spring force (F) as a
the second inch exerts an additional
function of displacement (x).
550 lbf (for a total of 1050 lbf), the third
inch exerts another 600 lbf (for a total of
1650 lbf). In contrast a 500 lbf/in linear
With
spring compressed to 3 inches will only
F - Spring force [N]
exert 1500 lbf.
k - Constant (function of static volume and
The spring rate of a coil spring may be
pressure)
calculated by a simple algebraic equation
A - Accumulator floating piston area [m2]
or it may be measured in a spring testing
x - Floating piston displacement [m]
machine. The spring constant k can be
n - Polytropic exponent
calculated as follows:
DESIGN
PNEUMATIC
OF
HYDRO
SUSPENSION
SYSTEM
Where
d is the wire diameter,
G is the spring's shear modulus (e.g., about
12,000,000 lbf/in² or
80 GPa for
steel),
and N is the number of wraps and D is the
diameter of the coil.
Although linear spring and damper
characteristics in this model also produce a
Fig. shows the 3D modelling of hydro
hysteresis loop, the characteristics are not
pneumatic suspension system
progressive, as with a hydro-pneumatic
MATERIAL PROPERTIES:
spring. It was therefore decided to use a
All the components of the Hydro
polytrophic process to model the main
pneumatic suspension are made using hot-
spring. Since the volume and pressure of
rolled structural steel IS: 2062-1999,
the accumulators are known, the one
Grade A, Fe 410WA.All the components
unknown parameter (for the main spring)
of the Hydro pneumatic suspension are
is the polytrophic constant. In order not to
assigned as per the below material
over
properties.
complicate
ISSN: 2231-5381
the
model,
linear
http://www.ijettjournal.org
Page 270
International Journal of Engineering Trends and Technology (IJETT) – Volume 16 Number 6 – Oct 2014
Tensile Strength =
CALCULATIONS
Steel
IS:
2062-1999
410 Mpa
Mechanical
Properties:
Young’s modulus = 200Gpa
Yield Strength
= 250 Mpa
INPUT PARAMETERS
DIMENSIONAL PARAMETERS
Parameter
Symbol
Wire diameter
d
Spring outer diameter - [OD]
Value
Unit
15
155
mm
Spring free height (length)
Lf
566
Height 1
L1
460
Height 2
L2
---
Load 1 @ height 1
F1
14715000
N
Load 2 @ height 2
F2
---
Spring rate
k
---
End types for compression spring
N/mm
Squared (Closed) and Ground
SPRING MATERIAL & STRESS RELEATED PARAMETERS
Parameter
Symbol
Value
Material selectionx
ISSN: 2231-5381
http://www.ijettjournal.org
Unit
User defined
Page 271
International Journal of Engineering Trends and Technology (IJETT) – Volume 16 Number 6 – Oct 2014
GPa
Elastic modulus
E
200
Poisson's ratio
v
0.3
---
Material tensile strength
Sut
1400
MPa
Unprestressed (Set Not Removed) - Default
Prestressing (Set romoval)
Allowable torsional strength (% of Sut) +
Design factor at solid height against
torsional stress
ns
45
%
1.2
---
SPRING STABILITY (BUCKLING)
Parameter
Symbol
Value
Spring stability (buckling) check
Unit
Stability control
Ends are fixed with flat parallel surfaces
End condition*
End condition constant
α
0.5
---
Design factor for buckling
nb
1.5
---
OUTPUT RESULTS:
OUTPUT RESULTS
DIMENSIONAL PARAMETERS
Parameter
Symbol
Value
Number of active coils
Na
0
Number of total coils
Nt
2
Spring index
C
9.33
Spring rate
k
138820.75
Wire diameter
d
15
Spring outer diameter
OD
155
Spring mean diameter
D
140
ISSN: 2231-5381
http://www.ijettjournal.org
Unit
---
N/mm
mm
Page 272
International Journal of Engineering Trends and Technology (IJETT) – Volume 16 Number 6 – Oct 2014
Spring inner diameter
ID
125
Outer diameter at solid length
ODat solid***
133527.52
Spring free length (height)
Lf
566
Spring solid height
Ls
30.02
Maximum deflection (Lf to Ls)
Δx
535.98
Pitch at free length
p**
419441.69
SPRING MATERIAL & STRESS RELEATED PARAMETERS
Parameter
Symbol
Value
Load at solid height
Fs
74405264
Shear stress at height 1
τ1
1796686.12
Shear stress at height 2
τ2
---
Shear stress at solid height
τs
9084805
Ultimate tensile strength of material
Sut
1400
Allowable torsional strength
Sall
630
Factor of safety against torsional
foss
yielding at solid height
(Sall / τs )#
Modulus of rigidity
G
0
Unit
N
MPa
---
76.92
GPa
Elastic modulus
E
200
Material ASTM No.
--SPRING STABILITY (BUCKLING)
Parameter
Symbol
Value
Unit
Factor of safety against buckling
fosb+
1.296
---
Material shear modulus,
G
75,680,933,852.140 Pa
---
Ʈmax
657,828,793.341
---
Maximum shear stress possible, :
ISSN: 2231-5381
http://www.ijettjournal.org
Page 273
International Journal of Engineering Trends and Technology (IJETT) – Volume 16 Number 6 – Oct 2014
Static Analysis of Hydro
Pneumatic Suspension
Table.1 shows the max. Deflection and
Boundary conditions applied on the
S.no.
Max. Von mises stress
Hydro pneumatic suspension
The basic vehicle masses of the rally truck
Deflection
Von mises
(mm)
stress (Mpa)
0.22
221
1
is 6000 kg which is divided over the front
and rear axle by 60 percent and 40 percent
respectively. Gravity = 9.81m/s. The
summed mass of the axles including rims
and tyres is approximately 1500 kg per
axle.
MODEL ANALYSIS OF HYDRO
PNEUMATIC SUSPENSION
From the modal analysis, a total of 6
natural frequencies are observed in the
frequency range of 0-10Hz. The mass
participation of each of these 6 frequencies
1. Pressure load is applied on top of the
suspension system
are listed in the below table. The mode
shapes of these frequencies are shown in
2. Hydro pneumatic suspension system
the below figures.
bottom connecter is arrested in all Dof.
Table.2 Shows the natural frequencies
in the range of 0-10Hz
Fig. uniform deflection of Hydro
pneumatic suspension
Mode
1.
2.
3.
4.
5.
6.
Frequency [Hz]
3.4475
3.8879
4.2731
4.3062
6.8699
7.5621
HARMONIC RESPONSE
ANALYSIS OF HYDRO
PNEUMATIC SUSPENSION
Harmonic analysis was carried out
to determine the operating frequencies,
Fig. Max Von mises stress in Hydro
pneumatic suspension
ISSN: 2231-5381
deflections and stress of a structure in the
frequency range of 0 -10 Hz.
No. Of sub steps = 10
http://www.ijettjournal.org
Page 274
International Journal of Engineering Trends and Technology (IJETT) – Volume 16 Number 6 – Oct 2014
Table.2 Deflections and VonMises stress
The Hydro pneumatic suspension was studied for 3
different cases:
for operating frequencies
 Static Analysis
S.no FRQ
Def.
VON MISES
(mm)
STRESS (MPa)
 Modal analysis
 Harmonic Analysis
From the above analysis it is concluded that that
1
1
0.2
2.2
2
2
0.3
2.3
deflections within the design limits of the material
3
3
0.8
2.5
used. The deflections and stresses obtained in the
4
4
0.7
2.4
harmonic analysis are also under the design limits
5
5
0.2
2.5
6
6
0.24
2.6
7
7
0.8
3.3
8
8
0.31
2.9
9
9
0.34
3.2
REFERENCES
10
10
1.9
9.4
1. John C. Dixon, “The Shock Absorber Handbook”, SAE
the Hydro pneumatic suspension has stresses and
of the material.
Therefore it concluded that the Hydro pneumatic
suspension is safe under the given operating
conditions.
International, 1999, ISBN 0-7680-0050-5
2. Arthur Akers a.o., “Hydraulic Power System Analysis”, Iowa
From the above results it is observed that the
operating frequencies are very less than the yield
strength of the material. The yield strength of the
material used for Hydro pneumatic suspension is
250 MPa.
State University, 2006, ISBN 0-8247-9956-9
According to the VonMises Stress Theory,
the VonMises stresses of Hydro pneumaticsuspension operating frequencies are less than the
yield strength of the material.
Dynamics”, fifth edition, Virginia Polytechnic Institute and
3. M. Pinxteren, “Development of a multi-body model of a
Dakar Rally truck with independent suspension”, Eindhoven
University of Technology, June 2007, DCT2007.043
4. J.L. Meriam and L.G. Kraige, “Engineering Mechanics
State University, 2003, ISBN 0-471-26606-x
5. G.R. Siau and T.L. Spijkers, “Development of a multi-body
simulation model of the DAF Dakar rally truck”, Eindhoven
University of Technology, August 2006, DCT2006.092
Hence Hydro pneumatic suspension is safe under
the operating loads, and the design of Hydro
pneumatic suspension is safe and having more
FOS.
suspension
has
been
for
structural
behaviour well designed model by using design
calculations.
ISSN: 2231-5381
7. Modelling of the hydro-pneumatic suspension system of a
rally truck by J.A. Razenberg,
loaded
a Hydro pneumatic
studied
and damper system by CHRISTIAAN LAMBERT GILIOMEE,
8. Ride a- roll performance analysis of a vehicle with spring
CONCLUSION
In the present project
6. Analysis of a four state switchable Hydro- pneumatic spring
interconnected
Hydro-pneumatic
suspension
by
SANJEEV CHAUDHARY,
9. Analysis of Hydro pneumatic interconnected suspension
struts in the roll plane vehicle model by Liwen wu,
10. Anela-stic Model of a Twin Accumulator Hydro-pneumatic
Suspension
System
http://www.ijettjournal.org
by
J.L.
van
Niekerk
Page 275
,