page or check for previous versions at the Internet Archive. Yahoo! is not affiliated with the authors of this page or responsible for its content.
Microsoft PowerPoint - Defense Draft 2-3 1
1
A Multi-Scale Iterative Approach for
Finite Element Modeling of
Thermal Contact Resistance
Mary Kathryn Thompson (mkt@mit.edu)
Mechanical Engineering Department
Massachusetts Institute of Technology
2
What are the Goals for Surface
Modeling in General?
Idealize Surface Geometry
Analytical or Numerical
Model of Surface Behavior
Understand and Predict
Surface Phenomena
Design Systems for
Improved Performance
Measure and Import
Surface Geometry
Multi-Scale FE Model of Thermal
Contact Resistance (TCR)
Predict Micro/ Macro Scale TCR
Understand Bolted Joint Systems
Improve Design for Power
Electronics Module
What are the Goals for
this Work? 2
3
Agenda:
Surface Importation
Multi-Scale Iterative Finite Element Modeling of
Thermal Contact Resistance
Case Study: Contact Analysis of Bolted Joints
Case Study: Factors Influencing Performance of
Bolted Joints
Conclusions and Recommendations
4
Surface Importation
Surface Importation
Multi-Scale Iterative Finite Element Modeling of
Thermal Contact Resistance
Case Study: Contact Analysis of Bolted Joints
Case Study: Factors Influencing Performance of
Bolted Joints
Conclusions 3
5
What are the Challenges for Modeling
Contact Systems?
Surface
Geometry (irregular, complex)
Chemistry (adhesion, adsorption)
Layers (coatings, oxides)
Imperfections (sub-surface cracks, voids)
Material
Located in interface (air, lubricants, wear particles)
Transfer across interface
Properties (scale, temperature dependent)
Loads
Sporadic contact
Very high localized loading (plasticity, fracture, creep)
Multiple physics regimes (electrical, thermal, structural, fluid, etc.)
6
What are the Traditional Methods for
Modeling Surface Geometry?
Ignore the surface details
Include the surface details as experimental coefficients
Model surface as having regular, geometric features
Use symmetry and similarity to only model 1 asperity or asperity pair
Model random surfaces with probability distributions
Model random surfaces with fractals
Blencoe, K. A., et al., The influence of lubricant rheology and
surface topography in modelling friction at concentrated
contacts Proc. Instn. Mech. Engrs. Vol. 212 Part J.
Chilamakuri, S. K., and Bhushan, B., Contact
analysis of non-Gaussian random surfaces. Proc.
Instn. Mech. Engrs. Vol. 212 Part J.
McRae, G. A. et al., A comparison of fractal dimensions
determined from atomic force microscopy and
impedance spectroscopy of anodic oxides on Zr02.5Nb.
Applied Surface Science 191 (2002) 94-105.
Time
Complexity
Accuracy 4
7
How Can We Improve Surface Modeling?
Make better assumptions
In the short term (this work):
Incorporate real (measured) surface
geometry into finite element models
Historically could not be done
Assumption dissuaded others from trying
In the long term (future work):
Evaluate surface modeling techniques by
comparing idealized surfaces with
imported surfaces
Surface Measurement and
Importation
Finite Element Model of
Contact Behavior at the
Surface
Understand Surface
Phenomena
Predict Performance and
Design Systems for
Improved Performance
8
How Can We Import Surface Geometry?
1.
Gather information about surface geometry
2.
Transfer information to an array
3.
Operate on array values (optional)
4.
Apply array values to modify finite element
model or to create solid model geometry 5
9
Creating Surfaces by Modifying Finite
Element Model
1.
Create a volume (solid model geometry).
2.
Mesh the volume to create nodes and
elements.
3.
Detach the finite element model from the
solid model.
4.
Select every node
1
(or every surface node)
and move the z coordinate of that node by
a fraction of the asperity height value (or
the full asperity height) for that (x,y)
location.
1. Hyun, S. et al. Finite element analysis of contact between elastic self-affine surfaces. Phys. Rev. E 70, 026117 (2004).
10
2L Sample
19,200 points
2.25 um apart
4L Sample
76,800 points
0.84 um apart.
8L Sample
76,800 points
1.14 um apart
360 um
267 um
364 um
Example Measured Surfaces
Gar S-22 Conventional Machining Microfinish Comparator
Consists of 22 Electroformed nickel replicas of original machined surfaces
Measured 2, 4 and 8 u lapped surfaces (0.05, 0.1, and 0.2 um) using
Zygo optical interferometer 6
11
Contact
Pressure
(MPa)
Contact
Gap (um)
Imported
Surface
(Resolution
3 um)
Measured
Surface
How Good are Imported Surfaces?
12
What Have We Learned About Surface
Modeling?
Historically surfaces modeled with idealizations
Now possible to import real surface data and create
surface geometry using surface data
Qualitatively shown that surface importation is viable
surface modeling option 7
13
Multi-Scale Iterative Finite
Element Modeling of Thermal
Contact Resistance
Surface Importation
Multi-Scale Iterative Finite Element Modeling of
Thermal Contact Resistance
Case Study: Contact Analysis of Bolted Joints
Case Study: Factors Influencing Performance of
Bolted Joints
Conclusions
14
What Is Thermal Contact Resistance (TCR)?
Temperature drop across the interface due to
imperfect heat transfer across contacting
asperities and gaps in between
Electrical analogy for heat transfer
Quasi-1D (averaged) approximation for 3D
problem
Q = (1 / R
total
) T
R
total
= R
1
+ R
contact
+ R
2
q = Q / A = (1 / r
total
) T
T = T
11
- T
22 8
15
What are the Challenges
for Modeling TCR?
1D approximation for a 3D problem
Heat transfer mechanisms and material properties depend on
temperature and length scale of features (surface layers, gaps, etc.)
parallel to heat flow
Requires thermal / structural model
Requires analysis over multiple length scales
Load applied on shorter length scales (micro) depends on mechanical
contact at longer length scales (macro)
Thermal behavior at longer length scales (macro) depends on the
behavior at shorter length scales (micro)
Still lack computational capability to model multiple length scales
simultaneously
16
What are the Traditional Methods to Model
TCR?
Model surface and perform deformation analysis to determine contact pattern
Same traditional surface assumptions
Sometimes contact pattern assumed instead of predicted
Thermal analysis of single constriction (heat channel or asperity pair)
Combine results to predict TCR for multiple constrictions arranged in the predicted
contact pattern using symmetry, similarity or probability arguments
Interstitial heat transfer often neglected
Resistance to solid/solid conduction between contacting asperities often neglected
Heichal, Y. and Sanjeev, C., Predicting
Thermal Contact Resistance Between
Molten Metal Droplets and a Solid
Interface. J. Heat Transfer, Vol. 127,
(2005)1260-1275.
Degiovani, A. et al., Thermal Resistance of
a Multi-Constrictions Contact: A Simple
Model. Int. J. Heat and Mass Transfer 46
(2003) 3727-3735.
Kumar, S., and Ramamurthi, K., Prediction of
Thermal Contact Conductance in Vacuum
Using Monte Carlo Simulation. J.
Thermophysics and Heat Transfer, Vol. 15, No.
1, (2001) 27-33.
Tio, K. and Sadhal, S., Thermal
Constriction Resistance: Effects of
Boundary Conditions and Contact
Geometries. Int. J. Heat Mass Transfer,
Vol. 35, No. 6 (1992) 1535-1544. 9
17
How Can We Improve TCR Modeling?
Full 3D model
Incorporate real or realistic surface geometry
Solve for true contact pattern
Include interstitial heat transfer
Include solid/solid resistance between contacting
asperities (TBR)
Iterate micro/macro solutions to include thermal
and structural scale dependence
18
Multi-Scale Model of TCR
1.
Import surface geometry,
guess r
contact
and solve
macro scale thermal /
structural problem to
determine micro scale
load(s) and average
temperatures at interface
2.
Import surface geometry
and solve micro scale
thermal/structural
problem to determine
r
contact
3.
Apply r
contact
to macro
scale thermal/structural
problem to determine
total thermal resistance
A
real
Micro Scale
Thermal/Structural
Contact Model
Macro Scale
Thermal/Structural
Contact Model
R
r
contact
r
boundary
f
applied
F
applied
a
real
TCC
Q
applied T
applied
P
contact 10
19
Multi-Scale Model of TCR
Limitations:
Systems with micro scale gaps near room temperature*
No convection, radiation in the gaps
Neglected surface layers (oxides, etc.) *
Nano scale effects estimated based on experimental data
Linear elastic material properties *
Non-temperature dependent material properties *
No thermal expansion*
Macro scale average contact pressure = applied load *
Micro scale average TCR = applied TCC *
20
Contact Analysis of Bolted
Joints
Surface Importation
Multi-Scale Iterative Finite Element Modeling of
Thermal Contact Resistance
Case Study: Contact Analysis of Bolted Joints
Case Study: Factors Influencing Performance of
Bolted