effects of crystal elasticity on rolling contact fatigue
DESCRIPTION
Effects of Crystal Elasticity on Rolling Contact Fatigue. Neil Paulson Ph.D. Research Assistant. Outline. Motivation and Background Crystal Structure Definitions Polycrystalline Material Model Steel Material Stiffness Model Hertzian Contact Modeling RCF Relative Life Study Future Work. - PowerPoint PPT PresentationTRANSCRIPT
Slide 1
Effects of Crystal Elasticityon Rolling Contact Fatigue
Neil Paulson
Ph.D. Research Assistant
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
#
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
1
Title slide (option 2)
Outline
Motivation and Background
Crystal Structure Definitions
Polycrystalline Material Model
Steel Material Stiffness Model
Hertzian Contact Modeling
RCF Relative Life Study
Future Work
#
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
2
Background and Motivation
Material heterogeneity can play a role in rolling contact fatigue failure,
Microstructure Topology
Raje, Jalalahmadi, Slack, Weinzapfel, Warhadpande, Bomidi
Voids or inclusions
Microstructure anisotropy
Microstructures are composed of many grains of multiple crystal phases
The relation between stress and strain depend on how atoms are arranged in the crystal phase
Grain Micrograph from electron backscatter diffraction (EBSD) scan showing grain orientations1
1Bruker Quantax EBSD Analysis Functions Bruker Corp., 2013
Objective
Extend current RCF FE model to incorporate the effects of crystal elasticity on RCF
#
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
Homogenous & Isotropic Material Models
Model for the bulk material behavior
Material stiffness does not depend on the direction
Infinite planes of symmetry
Only two independent elastic constants are needed to define the stress strain response
Stress-Strain Equations
#
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
Cubic Crystal Structure
Most widely used to incorporate crystal elasticity
Elastic constants for many materials are available in literature
Orientation of the crystal becomes important
The shear modulus is decoupled from E and ; otherwise the equations remain identical to isotropic material model
3 elastic constants are needed to define the stress strain response
Stress-Strain Equations
Shear modulus is independent of E and
#
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
Modeling Polycrystalline Aggregates
Each individual crystal has a unique orientation
Isotopic Stiffness Matrix
Cubic Stiffness Matrix
Euler Angles rotate the local stiffness matrix into the global coordinate frame
Isotropic stiffness matrix is identical after rotation
Cubic stiffness matrix becomes fully anisotropic after rotation
#
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
Material & Model Verification
A representative model of polycrystalline material was developed using Voronoi cells to represent individual grains
The stiffness matrix of each grain was rotated to the global coordinates
Uniaxial Strain was applied
Reaction forces were measured
Global material properties of the model were evaluated1:
1 Toonder, J, Dommelen, J, Baaijens, F. The relation between single crystal elasticity and the effective elastic behaviour of polycrystalline materials: theory, measurement and computation, Modelling Simul. Mater. Sci. Eng.
#
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
Steel Material Model
Example Cases
FEA results match isotropic constants
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
#
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
Rolling Contact Fatigue Domain
Strong stress gradients inside grains require modifications to FE domain
Isotropic
Anisotropic
Linear Strain
Elements
Constant Strain
Elements
Voronoi Centroid
Discretization
Fixed Element Area
Discretization
Isotropic Domain
Anisotropic Domain
#
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
Anisotropic Hertzian Contact
Stress concentrations occur at grain boundaries due to orientation change
Anisotropic Material
Isotropic Material
Hertzian Centerline Stresses
Anisotropic stress profiles deviate from isotropic stresses
#
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
10
Rolling Contact Fatigue Life Equations
Microstructures models simulate randomness from experimental testing
Lundberg-Palmgren equation can be reduced for constant survivability and volume:
Three different numerical models have been proposed with Isotropic Voronoi Element microstructure
2D Discrete Element Model
2D Finite Element Model
3D Finite Element Model
3.36
2.65
4.55
the experiments of Lundberg and Palmgren
#
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
Modeling Rolling Contact
Hertzian Line Contact Load
21 Loading Steps
Load Transverses Anisotropic Region
was evaluated for each element
Maximum value and location recorded
#
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
12
Shear Stress Reversal Results
33 crystal orientation maps were run for a given topological model
Maximum Shear Stress on Voronoi Boundaries
Experimentally Observed -crack Bounds1
Isotropic Shear Stress independent of grain boundaries
Anisotropic shear stress increased by orientation mismatch
Isotropic shear stress matches theory
1 Chen, Q., Shao, E., Zhao, D., Guo, J., & Fan, Z. (1991). Measurement of the critical size of inclusions initiating contact fatigue cracks and its application in bearing steel. Wear, 147, 285294.
#
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
13
RCF Relative Life
Relative life equation was used to determine bearing fatigue life
Shear Stress results from crystal orientations were used to create Weibull plot of RCF life
33 Different topological microstructures
#
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
14
RCF Relative Life
All topological domain results combined into one RCF relative life plot
ModelModel Type2-Weibull SlopeLundberg-PalmgrenExperimental1.125Harris and KotzalasExperimental Bounds0.7-3.5Raje2D DEM3.36Jalalahmadi2D FEA2.65Weinzapfel3D FEA4.55Current Model2D FEAAnisotropy1.174Weibull Distribution Function
2-Parameter Weibull
3-Parameter Weibull
#
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
15
Current Model Development
Implement damage mechanics coupled with crystal elasticity to model both crack initiation and propagation
Develop a multi-phase representative model for bearing steel microstructure
Model a nonuniform distribution of crystal orientations (texture)
-phase
-phase
#
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
16
Measurement of Skidding in Cam and Roller Follower
Skidding in Cam and Followers causes wear and premature failure
A test rig has been developed to study the causes of skidding
An analytical model is under development to model the causes of skidding
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
#
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
17
Title slide (option 2)
Cam and Follower Test Rig
Flywheel 700 mm flywheel to maintain constant shaft speed under alternating load conditions
Shaft Coupling rigidly connects the driven shaft and camshaft
Drive Motor 55 HP provides power to camshaft with speeds up to 1800 RPM
Test Cell Assembly contains the camshaft, tappet, lubrication pathways and speeds sensor
One way Clutch Allows deceleration under flywheel inertia for Stribeck curve data
- Tappets are machined to hold
optical sensor
- Rollers are laser etched with
20-60 divisions
- Time between divisions is
measured with optical sensor
- Sensor is sealed from
environment with sleeve
Speed Measurement
#
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
18
Test Rig Roller Skidding
Rolling Region
Skidding Region
Intermittent
Skid
Cam shows initial stages of skidding wear
Skidding created with modified roller follower
Skidding only apparent at low loads
Results show a transition from skidding into a pure rolling regime
Short skidding regions are seen after the transition to rolling regime
#
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
Analytical Roller Skidding Model
cam
I roller
W axle
W cam
W
2D roller skidding model under development
EHL of cam and roller interface (
HL of roller and pin joint
Kinematics of cam and follower
Torque Balance to find angular velocity (
EHL &
Mixed EHL
Cam Kinematics
Torque
Balance
HL
#
November 14, 2013
Mechanical Engineering Tribology Laboratory (METL)
0
50
100
150
200
250
300
Young's Modulus (GPa)
Voigt Bound
Reuss Bound
FEM
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Poisson's Ratio
Voigt Bound
Reuss Bound
FEM
-1.5-1-0.500.511.52
-3
-2.5
-2
-1.5
-1
-0.5
0
Stress Profile (/P
max
)
Distance Below Surface (z/b)
x, iso
y, iso
z, iso
max, iso
x, aniso
y, aniso
z, aniso
max, aniso
0123456789101112131415161718192021
-1
-0.5
0
0.5
1
Load Step Number
xy
(GPa)
0369121518
0
50
100
150
200
250
300
Time (s)
Roller Velocity (RPM)
0369121518
0
1000
2000
3000
Normal Load (N)