digital twin modeling via tribomechadynamics
TRANSCRIPT
Digital Twin Modeling via Tribomechadynamics
Matthew BrakeRice [email protected]
How Do We Model Joints?
Motivation:
Real structures have many joints
Between industrial decisions to move away from testing and other sectors not being able to test enough, data for modeling becoming scarce
Due to lightweighting, nonlinearities are significant
Thus, calibrated modeling is becoming less feasible…
What is Tribomechadynamics(aside from a portmanteau word)?
Tribomechadynamics Constituent Research Areas
Structural Dynamics• Vibration and nonlinear dynamics• Reduced order modeling• System level analysis (macroscale)• Simple, pointwise contact models;
usually heuristic in nature• Typical experiments use shakers,
impact hammers, accelerometers• Typical models are dynamic, finite
element or reduced order models
Contact Mechanics• Elasticity and plasticity solutions• Static stress analysis• Focus on the contact patches (spans
meso- and macroscale)• Contact models usually are large,
spatially distributed, and based on Coulomb.
• Typical experiments use MTS machines or fretting rigs
• Typical models are static, high fidelity finite element
Tribology• Wear• Surface evolution over time• Focus on micro- and nano-scale
features• Contact models usually are for
asperity on asperity contact• Typical experiments use tribometers
or other wear rigs in addition to profilometers
• No such thing as typical models (tribology spans many disciplines…from solids to fluids to chemistry)
Goal of Tribomechadynamics
• Given an assembly,– Predict response during design stage– Predict performance degradation over time– Use models to optimize joint designs (weight/properties/wear/etc)
Image courtesy of Rolls Royce
Big Claim: By the end of the year, we will have all of the technology necessary to model an entire satellite predictively.
Big Claim Details
Goal:• Given material properties (such as from tensile testing), estimates of what the surface finish is
like, and accurate models of subcomponents, predict the nonlinear dynamic characteristics of an assembled structure
Hurdles:1. Predictive friction or hysteresis models2. Model reduction techniques to scale up from academic structures to large structures3. Efficient and accurate simulation methods for analyzing more than modal response (e.g.,
transient, shock and random vib, etc.)4. Predictive Adequate wear models
Big Claim Details
Goal:• Given material properties (such as from tensile testing), estimates of what the surface finish is
like, and accurate models of subcomponents, predict the nonlinear dynamic characteristics of an assembled structure
Solutions/Smaller Claims:1. Elastic-plastic contact models with realistic surface models can yield predictive hysteretic
models2. Between hyper reduction techniques and modal derivatives, we have the necessary theories in
place3. Quasi-static methods are advancing quickly and simultaneously; should be ready when the
models are4. Wear models may need some calibration still…but enhanced Archard models are a good place
to start
Evidence (In Progress; Blind Prediction)
For our models, µ is the only free parameter. But, due to plasticity, predictions are relatively insensitive to it.
Shaded: experimental uncertaintyBlue, green: upper and lower bounds of physics-based simulations
J.H. Porter, N.N. Balaji, and M.R.W. Brake, “A Non-Masing Microslip Rough Contact Modeling Framework for Spatially and Cyclically Varying Normal Pressure,” IMAC XXXIX A Conference and Exposition on Structural Dynamics, Online, February, 2021.
What About A Real Structure?
• Salient details:– Subcomponents are still linear– Lots of nominally identical joints– Envelopes of excitation well defined
Image courtesy of Rolls Royce
• Highly detailed joint models could be used to develop lower fidelity, calibrated models.
• These could be constructed for a range of common joints• Ultimately, this could be a feature in NASTRAN, ABAQUS, or
SIERRA where you choose a joint model from a pre-populated list…
How? Future Goal: Libraries of Joint Models
Joint
Fully Integrated Modeling with
Libraries of Standard Joints for commercial FEA
Predictive Model
• Physics-Based• Computationally
Intensive• Standardization
could lead to a library of joint models
Calibrated Model
• Fast• Sufficiently
Accurate• Chosen based
on use case to minimize model form error
System Model
• Many DOFs• Composed of
many joint submodels
N.N. Balaji and M.R.W. Brake, “The Surrogate System Hypothesis for Joint Mechanics,” Mechanical Systems and Signal Processing, 126, pp 42-64, 2019.
Timeline for Adoption
Today
Predictability of Academic Structures
High Fidelity Characterization of
Individual Joints to Feed into System Models or to
Provide Data to Calibrated Models
Fully Integrated Modeling with Libraries of Standard Joints for
commercial FEA
2022 2024 (with investment)
God created solids, surfaces were invented by the devil
–Wolfgang Pauli
Energy Dissipation in the Interface• What is friction?
– A set of mechanisms that dissipate energy when two surfaces are in contact with relative tangential motion
• The damage caused during tribological interactions is termed wear; not all wear is created equally• More than 182 wear models published between 1957 and 1992 in two tribology journals
Fretting = Adhesive Wear + Abrasive Wear + Corrosive Wear
• Adhesive wear leads to debris formation• Debris is trapped in the interface due to
lack of macroslip• Debris causes third body abrasive wear,
and generates heat• Heat + newly exposed surface leads to
oxidation• Corrosive wear occurs when oxidation
layer destroyed quicker than it can grow• Results in significant softening of the
interface, usually
Tribosystem
• Hysteretic models:– Bouc-Wen– Iwan– Valanis– Etc.
• Rate dependent models:– Coulomb– Stiction– Elasto-Plastic – LuGre– Leuven– Etc.
SD Friction Models Do Not Represent The Physics of Friction/Wear
A.T. Mathis, N.N. Balaji, R.J. Kuether, A.R. Brink, M.R.W. Brake, D.D. Quinn, “A Review of Damping Models for Structures with Mechanical Joints,” Applied Mechanics Reviews, 2020.
Hysteresis Quiz
• What hysteresis should we expect in a bolted joint?
A B
C D E F
Measured Hysteresis During Fretting
• Would anyone have guessed these for the system level hysteresis?
• Change over time due to fretting wear and fatigue wear
4 hours 8 hours 12 hours
Many hysteretic elements in parallel though…
A B F
+ + … +
So, if we get the hysteresis right, is that sufficient?
No…
Revisiting Assumptions (circa 2012)• Contact patch is fixed (i.e. constant
size/pressure distribution)• Even if edges of contact patch vary,
middle is definitely fixed → can be rigidly attached
• No measureable motions across the interface
• Energy dissipation due to microslip• Minimal (no) mode coupling• Higher bolt torques → larger contact
areas• Symmetrical behavior across the interface• Pressure cone of bolts is approximately
30 degrees• No macroslip at nominal loads
No. Varies significantly with time
No. Varies significantly with time too
No!
No…subsurface plasticity, wear, clapping… No. Very strong coupling under right conditions
No. Poisson effects mean the opposite
No. Highly dependent on fabrication
No. Dependent on mesoscale
No. Observed for higher modes at low excitations
Even Newer Observations from Tribomechadynamic Analysis
• Interface asperities are ellipsoidal– This results in more plasticity than hemispherical asperities
• Elastic contact models are softer than elastic-plastic for joint applications– Why? Because of the unloading curve and work hardening effects
• Fretting fatigue can be fast and severe– Significant dependence on excitation magnitude
• Predictive modeling looks possible without tuning parameters– Asperities treated in a statistical sense– Plasticity in tangential models removes sensitivity of friction coefficient
How can we predictively model a jointed structure?
(and thus, optimally design it)
Macroscale
Meso- and Microscale
Nanoscale
Taxonomy of Issues – Multiscale Interface Dynamics!
Nanoscale Ramifications
• Hall-Petch effect: as the grain size increases, the strength decreases as the stress necessary to move a dislocation across a grain boundary is decreased.
• Applies to hardness, and thus plastic deformation, too
• Implication: perfect predictivity requires some information about the grain sizes of a material…
• However, consistent manufacturing processes can help us avoid this
M.R.W. Brake, “Contact Modeling Across Scales: From Materials to Structural Dynamics Applications,” About to be submitted to the Journal of Structural Dynamics.
Mesoscale and Higher
Claim: predictive joint modeling can/must begin at the meso-scale
– Grain structure controlled for via manufacturing processes; this allows us to treat the material properties as known constants
– Asperities can be handled in a statistical sense– Meso-scale curvature from machining/residual stresses is paramount– Necessitates a multi-scale analysis still
How Can We Model Meso-Scale Features?
• High fidelity approaches are intractable for real joints (let alone multiple joints)
• Example: Wang, An, Xu, and Jackson, “The Effect of Resolution on the Deterministic Finite Element Elastic-Plastic Rough Surface Contact Under Combined Normal and Tangential Loading,” Tribology International, 144, art. 106141, 2020.
11,514 elements
868,806 elements
64 um x 64 um
Proposed Approach: Zero Thickness Elements
• Advantages:– Can be superimposed on top of a non-coincident mesh– Can incorporate local topography as an internal height
function– Internal constitutive model can use almost any contact
model– Compatible with hyper-reduction techniques
N.N. Balaji, W. Chen, and M.R.W. Brake, “Traction-Based Multi-Scale Nonlinear Dynamic Modeling of Bolted Joints: Formulation, Application, and Trends in Micro-Scale Interface Evolution,” Mechanical Systems and Signal Processing, 139, art. 106615, 2020
Hyper Reduction Framework
Two major needs:
N.N. Balaji, T. Dreher, M. Krack, and M.R.W. Brake, “Reduced Order Modeling for the Dynamics of Jointed Structures Through Hyper-Reduced Interface Representation,” Mechanical Systems and Signal Processing, 149, art. 107249, 2021
Non-Stiffening Virtual Node Formulation
Mesh Coarsening Procedure
Mesh Coarsening Approaches
Uniform
Displacement Pressure & Displacement
• Objective functions can lead to dramatically different meshes…
N.N. Balaji, T. Dreher, M. Krack, and M.R.W. Brake, “Reduced Order Modeling for the Dynamics of Jointed Structures Through Hyper-Reduced Interface Representation,” Mechanical Systems and Signal Processing, 149, art. 107249, 2021
Preferred Hyper Reduction Approach
• Mesh selection based on pressure and displacement values from a static simulation of the high fidelity model
• Uniform meshes work fairly well too
• Full interface contained 2053 DOF
N.N. Balaji, T. Dreher, M. Krack, and M.R.W. Brake, “Reduced Order Modeling for the Dynamics of Jointed Structures Through Hyper-Reduced Interface Representation,” Mechanical Systems and Signal Processing, 149, art. 107249, 2021
Pressure & Displacement, 152 Elements
What About Simulation Techniques? RQNMA.
• A quasi-static approach that accounts for non-Masing models is RQNMA• Gold standard for cyclic behavior: Malte Krack’s Extended Periodic Motion Concept• Gold standard for transient behavior? Doesn’t exist yet
N.N. Balaji and M.R.W. Brake, “A Quasi-Static Non-Linear Modal Analysis Procedure Extending Rayleigh Quotient Stationarity for Non-Conservative Dynamical Systems,” Computers and Structures, 230, art. 106184, 2020
Q: What do you do with a really fast solver and reduction method?A: Run 100,000,000 simulations and see what happens!(AKA, due to the pandemic, we couldn’t go outside)
Benchmark System
• The Brake-Reuß beam is a structural dynamics benchmark adopted by approximately 20 institutions
• Multiple version exist to assess the effects of interface design, and influence of the structure on joint properties
Hysteretic Modeling, Pareto Optimization, and Model Form Error
Mode 1, 5 Patch Joint Models Mode 1, 152 Element Joint Models
J.H. Porter, N.N. Balaji, C.R. Little, and M.R.W. Brake, “A Quantitative Assessment of the Model Form Error of Friction Models Across Different Interface Representations for Jointed Structures,” Mechanical Systems and Signal Processing, Under Review
Application of Pareto Optimal Models to Other Modes
Mode 2, 5 Patch Joint Models Mode 2, 152 Element Joint Models
J.H. Porter, N.N. Balaji, C.R. Little, and M.R.W. Brake, “A Quantitative Assessment of the Model Form Error of Friction Models Across Different Interface Representations for Jointed Structures,” Mechanical Systems and Signal Processing, Under Review
Summary of Hysteretic Model Results
Summary of Hysteretic Model Results
J.H. Porter, N.N. Balaji, C.R. Little, and M.R.W. Brake, “A Quantitative Assessment of the Model Form Error of Friction Models Across Different Interface Representations for Jointed Structures,” Mechanical Systems and Signal Processing, Under Review
• Including viscous damping is necessary to capture low amplitude dissipation
• The 4 parameter Iwan model works very well for this system
• For systems with some evidence of gross slip, a post slip stiffness is necessary
• Applying Masing assumptions to models that are not formulated with them in mind results in dramatically different results than simulations without the Masing assumptions enforced
• The more physical models have higher error than the less physical models (due to fewer parameters for calibration), but tend to do better on predicting the response of higher modes
• Overall, five patch models can be accurately calibrated to high fidelity data just as well as higher fidelity models
Statistical Approaches Useful in Determining Sensitivities
• Using a simplified model (elastic, dry friction), we can statistically explorethe sensitivity to different parameters…
10 0 10 1 10 2-1
0
1
2
3
4
5
6
10 0 10 1 10 2130
140
150
160
170
180
190
Sensitivities to Small Perturbations
179.5
180
180.5
181
• Indication that friction model and properties is important to capture
• Prestress standard deviation was ~25% of nominal prestress
• Topology relegated to relativeslope between interfaces fornow
Normal Contact Models: Rough Contact, Elastic Material Model
J.H. Porter, N.N. Balaji, and M.R.W. Brake, “A Non-Masing Microslip Rough Contact Modeling Framework for Spatially and Cyclically Varying Normal Pressure,” IMAC XXXIX A Conference and Exposition on Structural Dynamics, Online, February, 2021.
Normal Contact Models: Rough Contact, Elastic-Plastic Material• Preliminary results (not accounting for
ellipsoids)
• Elastic-plastic material models stiffen the system due to preloading of interface
• Coefficient of friction has small effect as plasticity accounts for tangential dissipation too
• Rough contact based on Cattaneo-Mindlinsolution
• Hysteresis model used to synthesize a new Iwan model formulation
• Implemented via an Augmented Lagrange formulation
J.H. Porter, N.N. Balaji, and M.R.W. Brake, “A Non-Masing Microslip Rough Contact Modeling Framework for Spatially and Cyclically Varying Normal Pressure,” IMAC XXXIX A Conference and Exposition on Structural Dynamics, Online, February, 2021.
Predictive Modeling is Almost There…
• Model Fidelity– Predictive modeling capabilities are just about here.– How to capture wear mechanisms accurately?
• Model Reduction– Hyper reduction techniques suitable for single joints in high fidelity– What about large, multi-joint structures?
• Solvers– Quasi-static and frequency domain solvers in good shape– Transient solvers desperately need attention
Outlook and Discussion Points
• Tribomechadynamics – confluence of nonlinear mechanics, nonlinear dynamics, and tribology is a rich research field
• Major open question 1 – how can we rigorously include wear in these models?
• Major open question 2 – what types of multi-fidelity analyses will be necessary to scale these techniques to large structures?
• Major open question 3 – what about thermal effects? How do other nonlinearities couple?
• Major open question 4 – how can we enable transient and random vibration simulations tobe efficient for large structures?
Acknowledgements
Support from the National Science Foundation, Sandia National Laboratories, Rice University, the NOMAD Research Institute, the TRC, Altair, SIEMENS,
South Central Imaging, Polytec, SIMULIA, and the TMD Lab
Tribomechadynamics Research Challenge 2021
• Goal is to assess the current state of the state-of-the-art methodologies
• Challenge: make a blind prediction of the nonlinear dynamic response of a system that has not yet been fabricated.
• Provided: CAD model, technical drawings, including material and surface specifications required to manufacture and assemble the system, and accurate information about the bolts used and their torque.
• This challenge corresponds to an engineering task typical of the daily work within industry, and is distinctly different from recent research thrusts, which have focused on calibrating models against measured properties of a fabricated prototype.
Email [email protected], [email protected], or [email protected] for more information.
Questions?
Backup Slides for Experimental Studies
Case Study: Benchmark System
• The Brake-Reuß beam is a structural dynamics benchmark adopted by approximately 20 institutions
• Multiple version exist to assess the effects of interface design, and influence of the structure on joint properties
Fun fact: the Brake-Reuß beam dimensions were chosen based on scrap metal in the University of Stuttgart’s machine shop
Experimental Discovery 1: Damage Observations
• In some assemblies, we have observed significant changes in frequency and damping
• Occurred in both shaker and impact hammer testing
• Designed an experiment to test whether this was settling or wear
0
2
4
6
8
10
12
157 158 159 160 161 162 163 164 165
Ampl
itude
[g/N
]
Frequency [Hz]
Peak frequency evolution
Seat 1aSeat 1a returnSeat 1bSeat 1b returnSeat 2Seat 2 returnSeat 3Seat 3 return
Solid line: high amplitude excitationDashed line: low amplitude return
Low amplitude tests
Low amplitude tests
Damage Observations: Wear/Fretting
• Direct observation of wear at high-low pressure transitions
Experimental Discovery 2: Electronic Pressure Film
• Electronic pressure films modified to measure contact pressure within a bolted interface duringdynamic excitation
Second BRB Fun fact: Christoph Schwingshackl (wisely?) declined the opportunity for it to be called the Brake-Reuß-Schwingshackl beam
Electronic Pressure Film: Normal Force Variation
Torque: 5 NmAmpl.: 4 gFreq.: 151 Hz
Torque: 20 NmAmpl.: 4 gFreq.: 155 Hz
Electronic Pressure Film: Variation of Contact Force & Area
1
2
3
4
1
2
3
4
Electronic Pressure Film: Variation of Contact Area
1
2
3
4
1
2
3
4
5 Nm 20 Nm
Experimental Discovery 3: High Speed Imaging
High speed camera
measurements of the beam under
vibration
Applying Digital Image Correlation
technique
Post processing and & analysis to
extract local interface behaviour
-5
40
0
30
Interface [subset]
5
20
10
Time [frame]
100908070605040302010
Fun fact: We used a toothbrush to make that speckle pattern
High Speed Imaging: First Bending Mode
LOWER BEAM
UPPER BEAM
Vertical displacements at the horizontal interface
Excitation direction
-150
-100
-50
0
50
100
150
20
504010 30
20100
-150
-100
-50
0
50
50
20
100
40
150
3010
20
100
25
-5
20
0
5015 45
403510 30
5
25205 15
1050
Upper beam Lower beam
Difference
Clear evidence of local kinematics during steady
state excitation
For 4 N excitation
Curved Interface Configurations
Conformal Edge Gap Center Gap
0-0 \ \
250-250 0-250 250-0
1000-1000 0-1000 1000-0
5000-5000 0-5000 5000-0
unit: μm Configuration
Concave Convex
Convex Flat Flat Concave
• Shaker driven up to 5 g’s• Smaller curvatures intended to be representative of manufacturing tolerances; larger curvatures
for purpose of experimental parameter study/understanding
Mode 1: Significant slip and separation at outsides, but not middle
Left region Right regionCenter region
Conformal, flatConformal, curvedEdge gapCenter gap
Mode 2: Macroslip observed!
Left region Right regionCenter region
Conformal, flatConformal, curvedEdge gapCenter gap