1. No category

THE CONSULTANCY UNIT OF THE TUN ABDUL RAZAK RESEARCH CENTRE (TARRC)
Predicting the Performance of Hydromounts
Judith Picken
[email protected]
www. rubberconsultants.com
Introduction
 Rubber research centre
in Hertfordshire
 Seven units:
Engineering Design
Product Evaluation &
Testing
Industrial Support
Materials
Characterisation
Advanced Materials &
Product Development
Biotechnology
Market Intelligence &
Promotion
Outline
 What are hydromounts, and why do we need them?
 Main source of non-linearities
 Non-linear model for rubber
 Viscoplastic model
 Effect of frequency
 Effect of amplitude
 Effect of scragging
 Resistance to flow
 Vacuum effect
Structure of a Hydromount
Rubber spring
First chamber
Inertia track
Second chamber
Rubber diaphragm
900
800
Variation of a hydromount’s
dynamic properties with
frequency for different strain
amplitudes
700
600
500
400
300
200
100
0
0
10
20
30
Frequency / Hz
40
50
800
700
Amplitude
Hydromounts are non-linear
with respect to both
frequency and amplitude
K'' / Nmm-1
K' / Nmm-1
1000
600
0.05mm
500
0.1mm
0.2mm
400
0.3mm
300
0.5mm
200
1mm
100
0
0
10
20
30
Frequency / Hz
40
50
Non-linearities





Resistance to flow in the inertia track: The linear equation
underestimates the resistance and does not include
turbulent flow
Stiffness and damping of the rubber spring
A preload results in a mean displacement, altering the pump
area of the rubber spring
Compliances of the two chambers are assumed to be elastic,
but there is a frequency and amplitude dependent phase
difference between the change in pressure and the change in
volume
The vacuum effect: when the pressure in the first chamber
falls below atmospheric air can come out of solution leading
to a rise in the compliance
Non-linear model for rubber
We need to predict the stress-strain behaviour of a filled rubber subjected
to time-varying inputs – quasi-static, cyclic, creep suitable for engineering
applications
The model should:
Be simple to implement in commercial FEA codes
Have as few parameters as possible
• Ideally related to the compound formulation
Be related to physical processes
• used outside characterisation test regime
• helps to achieve small number of parameters
Be based on simple characterisation tests
Predict the effect of temperature
Predict the response to strain history (Mullins Effect)
One-Dimensional ‘Viscoplastic’ Model
VE
HE
EP
Incorporating three different terms:
• Hyperelastic – underlying behaviour
• Viscoelastic – rate effects
• Elastoplastic – rate-independent
hysteresis
Hyperelastic part
Viscoelastic part
  he  ep   ve
Elastoplastic part
HR Ahmadi et al, 2008, Rubber Chemistry and Technology, 81(1): 1-18.
7
EDS14
EDS15
EDS16
EDS19
EDS14 model
EDS15 model
EDS16 model
EDS19 model
T = 248K
6
4
3
2
1
0
0.1
1
Material
EDS19
EDS14
EDS15
EDS16
Frequency/Hz 10
N330/[phr]
0
15
30
45
100
2
T=373K
1.8
1.6
1.4
G'/MPa
G'/MPa
5
Temperature- and frequencydependence can be modelled
with a simple viscoplastic
model
N.B. EDS compounds have
defined formulations and wellestablished physical properties
1.2
1
0.8
0.6
A.H. Muhr, 2009, pp131-136
in Constitutive Models for
Rubber VI, ed Heinrich G et
al., publ. CRC press/Balkema.
0.4
0.2
0
0.1
1 Frequency/ Hz 10
100
A viscoplastic model can also be used to model the
amplitude dependence.
model
experimental
HR Ahmadi et al, 2008, Rubber Chemistry and Technology, 81(1): 1-18.
Scragging (cyclic pre-straining) of rubber changes the measured modulus.
This can be approximated with a viscoplastic model if the maximum
scragging strain is known.
JGR Kingston and A.H. Muhr, 2011, Plastics, Rubbers and Composites, 40(4):161-168
Compliance of rubber diaphragms
Pressure volume relation for different diaphragms
0.00006
circular c=30mm
annular d=25mm, c=5mm
annular d=20mm, c=10mm
annular d=15mm, c=15mm
annular d=23.5mm, c=5.5mm
Volume / m
3
0.00005
0.00004
0.00003
0.00002
0.00001
0
0
50000
100000
150000
200000
Pressure / Pa
250000
300000
350000
2
1.6
1.2
.
experimental
simulation
Pressure difference, Δ p 12 (Bar)
The linear equation widely used to model resistance to flow in the inertia
track underestimates the resistance and does not include turbulent flow. The
resistance to flow is dependent on flow rate which is amplitude dependent.
0.8
0.4
0
0
0.2
0.4
0.6
0.8
Volumetric flow rate, q i (L/s)
1
6
Pressure, p 1 (Bar)
0.6
0.4
0.2
0
-0.2
The Vacuum Effect
4
2
0
-2
0
0.2
0.4
0.6
Time (s)
0.8
1
1.2
0
0.2
0.4
Time (s)
0.6
0.8
• Pressure in the first chamber
falls below atmospheric
when the mount is excited
sinusoidally at frequencies
around the peak stiffness.
1.2
0.8
0.4
0
-0.4
5
10
15
20
Frequency (Hz)
2
Pressure, p 1 (Bar)
K ' and K '' (kN/mm)
Pressure, p 1 (Bar)
0.8
1.5
1
0.5
0
-0.5
-1
0
0.2
0.4
Time (s)
0.6
0.8
• The pressure reaches a
plateau when the gases
dissolved in the liquid comes
out of solution, providing a
cushion.
K' / Nmm-1
1000
900
Non-linear model results
800
700
600
500
400
300
200
100
0
0
10
20
30
Frequency / Hz
40
50
Concluding Remarks
 A viscoplastic model for non-linear behaviour of rubber agrees
reasonably well with experiment when accounting for the
effects of:
• Frequency
• Strain amplitude
• Scragging
 Resistance to flow:
• Good agreement found between experimental
measurements and model
• Found to be dependent on flow rate
 The effects of vacuum formation during operation were studied
 This model for hydromounts can be extended to include
adaptive mechanisms such as multiple inertia tracks etc.
THE CONSULTANCY UNIT OF THE TUN
ABDUL RAZAK RESEARCH CENTRE (TARRC)
Thank you
Judith Picken
Engineering Design Unit
[email protected]
www. rubberconsultants.com