digital twin modeling via tribomechadynamics

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…


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


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


Summary of Hysteretic Model Results

Summary of Hysteretic Model Results


• 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


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


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.

mailto:[email protected]



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

digital twin modeling via tribomechadynamics

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