Andreas Almqvist, Luleå University of Technology
Tribology Days
Ö-vik
6-8 Nov 2012
• Why is modelling & simulation important?
• The Luleå mixed lubrication model
– Surface Topography
– Computing Flow factors
– Component simulation
• Current activities
• Future work
2
3
Understanding
Ranking Optimisation
Testing new ideas
𝛻 ⋅𝜌ℎ3
12𝜂𝛻𝑝
= 𝛻 ⋅1
2𝐔𝑠𝜌ℎ +
𝜕
𝜕𝑡𝜌ℎ
𝜂?
𝜂1, 𝜂2, 𝜂3…
Model
Component
Full-
scale
A complement to:
4
Few commercially available packages
AVL
Ricardo Suite
MIT Consortium
COMSOL Multiphysics
Lubrication Shell
Excite
Piston&Rings
5
Delveloped by: The division of
Award2010
– Flow between asperities
– Asperity deformation
– Utilizing the Flow Factors
– All regimes considered
– Coarse grid = fast
– Pressure
– Load
– Friction
– Leakage
Topography representation
Flow Factor computations Component Simulation
u+
1
u
u
u y1
y2
6 PhDs 5 Lics
60+ publications 40+ Tribology 20+ Mathematics
I II III
at LTU
2004-
Local scale; describing the Surface Topography
Global scale; describing Geometry - Incorporating the effects of roughness
Local
Global
7
through homogenization
8
1. Representative roughness – # of realizations / measurements
– Resampling, interpolation
– Filtering, mirroring
2. Flow factors – Contact mechanics
• Material model - Linear Elastic Perfectly Plastic
• # Loads (=> separations)
– Local problems
• Core of the homogenization
• # Separations
3. Component simulation – Interpolate ff’s onto global domain and
solve for homogenized pressure
p u
*
0minV
p
u+
1
u
u
u y
1
y2
AFM VSI • Artificial surfaces measured with AFM and VSI • Anomalies created from measurement technique observed • Effect on tribological parameters investigated…
Sa (μm) Sk (μm) Spk (μm) Svk (μm)
AFM 39.0 10.9 45.1 101.0
VSI 91.6 64.3 220.0 521.0
• Large differences in roughness parameters for artificial surfaces • Far smaller differences for ’real’ surfaces • However, care must be taken with ’extreme’ surfaces, i.e. laser textured
Paper by Andrew Spencer et al. - Trib. Int. Vol. 57
I
9
• Mirroring => Perfect periodicity
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11
12 Matlab GUI by Dr. Fredrik Sahlin
• Resampling
• Revamped!
• Was – Matlab 2007 + COMSOL Multiphysics 3.5a
• Is – MATLAB code only!
• Mini-courses / tutorial sessions on the usage of the code will be given.
II
(http://www.python.org/ code under construction)
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How to achieve a physically acceptable result?
– Representative contact mechanics model
– Clearance measure defining direct contact
– Full film computation over the non-contact area only
Rigid point
II
Contact mechanics BEM model
Local problems Homogenization
14 Contact spot
Topography rep.
In contact
Patir and Cheng Homogenization
Paper by Almqvist et al. – ASME Journal of Tribology, Vol. 133
---> Incorrect modelling of the so called micro-bearing problems
15
[mm]
[ m ]
[mm]
- Include inter-asperity coupling - Have a deterministic representation of the surface
p
u
16
We want to:
Average interfacial separation (Å)
Con
tact
pre
ssu
re (
-)
Almqvist and Persson et al. – Journal of the Mechanics and Physics of Solids, Vol 59. 17
• Cavitation
• Asperity collision
• Wear modelling
• Piston ring - Cylinder liner lubrication
VR
SSF
VR, SSF, Sauer-Danfoss
II
SSF, Scania
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• Universal equation (Non-linear)
– Elrod – “Incompressible HL”
– Vijayaraghavan Compressible
• Linear Complementarity Problem
– Dini - Incompressible
– Almqvist & Wall - Compressible
𝐴 𝜃 𝜃 = 𝑏,
𝐴𝑝 + 𝐵 1 − 𝜃 = 𝑏,
𝑝 1 − 𝜃 = 0
𝑔 𝜃 = 1, 𝜃 ≥ 10, 𝜃 < 1
II
19
• Friction contribution to deformation included
• FFT accelerated solution procedure
Frictionless Friction included N N
F f=N
II
20 PhD Student - Joel Furustig
• After the first component scale simulation, new flow
factors can be computed and then incorporated to
compensate for possible plastic deformations
21
II
PhD Students - Joel Furustig & Andrew Spencer
Mesh convergence studies &
Optimisation of geometries
have been conducted to verify the accuracy of the model.
PhD Student - Shaojie Kang
3
4
2
4
2
1
80 μm
60μm
ᵟ
Y
X
3
4
2
4
2
1
80 μm
60μm
ᵟ
Y
X
Interference:
Thermoelasto-plastic, time dependent simulations in LS DYNA
22
II
Stress Plastic strain Temperature
PhD Student - Shaojie Kang
Interference Friction Velocity
23
II
• Stress grows from zero to the maximum value, then decreases to the residual stress after collision.
• The distorted stress profile is due to the existence of friction. • Maximum stress is observed near the surface and large plastic
deformation are observed.
A B
C D
24 PhD Student - Shaojie Kang
II
• Maximum plastic strain is found close to the surface • Wear model could be established -> plastic strain is larger
than a critical value means seizure.
A B
C D
25 PhD Student - Shaojie Kang
II
• Maximum temperature is found at the smaller(top) asperity • Max temp rise ≈40°
A B
C D
26 PhD Student - Shaojie Kang
II
III
PhD Student - Andrew Spencer 27
II
28 PhD Student - Andrew Spencer
III II
• Piston ring - Cylinder liner lubrication
• Power losses in hydraulic motors
• Lubrication of cam – roller systems
Energimyndigheten, Scania, Volvo
VR, Hägglunds Drives
Scania, Bosch, HD
III
• Cavitation
• Asperity collision
• Wear modelling
• Piston ring - Cylinder liner lubrication
VR
SSF
VR, SSF, Sauer-Danfoss
SSF, Scania
II
29
30
PhD Student - Markus Söderfjäll
Energy agency Volvo Powertrain AB
Scania
III
31
- Out of roundness - Ring twist & dynamics
- Floating liner test rig
- Effect of laser texture
More than 50% reduction of power losses
Bosch Rexroth (Hägglunds drives AB)
III
32 PhD Student - Patrik Isaksson
PhD Student - Mohammad Shirzadegan
Hägglunds drives AB (Bosch Rexroth), Sweden
Robert Bosch GmbH, Germany
Scania AB, Sweden
Aim
A fast and reliable tool for prediction of slippage in cam - roller contacts
III
33
III
34 PhD Student - Mohammad Shirzadegan
Conformal contact
Non-conformal contact
Are the scales separable? Reaction forces?
Global
Local
The dynamic behaviour can be predicted if the physics can represented by a mathematical model:
Cam
Roller
Spring
Follower
𝑥, 𝑥 , 𝑥
𝑘 𝑐
𝑓𝑐(𝑡) 𝑓𝑐(𝑡)
𝑓𝑠 𝑓𝑑
𝑚 𝑚
System Lumped model Free body
diagram
𝑭𝒙 = 𝒎𝒙
35
36
• Inter-asperity cavitation
• Micro-EHL
• Non-Newtonian Rheology
Questions?
Tribology Days
Ö-vik
6-8 Nov 2012
Andreas Almqvist, Luleå University of Technology [email protected]