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University of Notre Dame Outline Introduction Three-Dimensional Thermoelastic Rough Surface Contact Model for Isotropic Materials Three-Dimensional Asperity Contact Model for Anisotropic Materials with General Boundary Condition Future Work

University of Notre Dame Introduction

University of Notre Dame Contact Problem for Elastic Material Governing Equation:

University of Notre Dame Total area: A=∑A i Three-Dimensional Asperity Contact Model Analysis Flowchart Discretize the brake surface region Read characteristic data for each separate region Solve 3D rough surface thermoelastic problem using CGM technique. Obtain subsurface stress/strain … etc. based on contact pressure Analysis and graph the result AiAi

University of Notre Dame Rough Surface Contact

University of Notre Dame Why Need Analytical Solution Numerical Method (FEM, BEM, etc) Analytical Method Problem TypeComplex CaseSimple Case ResultTransient/Steady StateSteady State Solving TimeSlowRelatively Faster AccuracyGoodRelatively worse Can numerical methods handle rough contact problem? No!

University of Notre Dame Three-Dimensional Thermoelastic Rough Surface Contact Model for Isotropic Materials

University of Notre Dame  Deflection ( ) of B when pressure is applied at A (elastic effect) 3D Thermoelastic Asperity Contact Model for Isotropic Materials Normal pressure applied to circular region x=(x(B)-x(A)); y=(y(B)-y(A));a=dx/2;b=dy/2; z A B y [m] x [m] [m]

University of Notre Dame 3D Thermoelastic Asperity Contact Model for Isotropic Materials Normal pressure applied to circular region  Deflection (u z ) of B when pressure is applied at point A (thermal effect). z A B ω x [m] y [m] [m] ω : rotational velocity (rad/s) r1,r2,r3,r4 : the distance from B to each corner of rectangle A c = a (1+v) : a is thermal expansion coefficient

University of Notre Dame 3D Thermoelastic Asperity Contact Model for Isotropic Materials z ω P0P0 Smooth Surface Contact Force Surface Displacement (ω = 0 rad/s ) y [m] x [m] [m] P [N] [m] x [m] y [m] x [m] y [m]

University of Notre Dame 3D Thermoelastic Contact Model Verification P ij (contact force) u z (numerical result)u z (theory result) 3D Hertz problem P 0 = 2×10 5 N E = 72×10 9 Pa = 0.2 R sphere = 0.25 m u z (0,0) = 2.44×10 -4 m uz(0,0) = 2.52×10-4 m (theory) P(0,0) = 9.26×10 3 N P(0,0) = 9.47×10 3 N (theory)

University of Notre Dame 3D Thermoelastic Asperity Contact Model for Isotropic Materials 3D Hertz problem P 0 = 2×10 5 N E = 72×10 9 Pa n = 0.2 R sphere = 0.25 m Subsurface von-Mises stress (x-z plane) [Pa] [m] 1 [m]

University of Notre Dame 3D Thermoelastic Asperity Contact Model for Isotropic Materials Thermoelastic Hertzian result (smooth surface)

University of Notre Dame 3D Thermoelastic Asperity Contact Model for Isotropic Materials Thermoelastic Hertzian result (rough surface)

University of Notre Dame 3D Thermoelastic Asperity Contact Model for Isotropic Material (Ring Surface) (Original profile)(smooth)(rough) (Surface Displacement ) (Contact Force ) (ω = 10) y [m] x [m] h[m]u z [m] P ij [N] h[m] x [m] y [m]

University of Notre Dame Three-Dimensional Thermoelastic Rough Surface Contact Model for Anisotropic Materials

University of Notre Dame Asperity Contact Model for Anisotropic Material  Basic Equations of Anisotropic Elasticity  Type of Anisotropic Material (Based on Symmetry Planes)  Triclinic Materials (21)  Monoclinic Materials (13)  Orthotropic Materials (9)  Trigonal Materials (6)  Tetragonal Materials (6)  Transversely Isotropic (or Hexagonal) Materials (5)  Cubic materials (3)  Isotropic Materials (2)

University of Notre Dame 3D Contact Model for Anisotropic Material  3D Green’s function for infinite anisotropic medium: Idea: obtain the result in term of a line integral on an oblique plane in the three-dimensional space  General deformation: Note: f will be calculated due to different conditions

University of Notre Dame 3D Anisotropic Contact Model Verification P ij (Contact Force) u z (numerical result)u z (theory result)3D Hertz problem P 0 = 2×10 5 N E = 72×10 9 Pa = 0.2 R sphere = 0.25 m xy u z (0,0) = 2.48×10 -4 m u z (0,0) = 2.52×10 -4 m (theory) P(0,0) = 9.61×10 3 N P(0,0) = 9.47×10 3 N (theory)

University of Notre Dame 3D Contact Model for Anisotropic Material Anisotropic Application E1=144x10 9 pa, E2=E3=72x10 9 pa, v=0.2, G=E2/[2*(1+v)] Normal pressure distribution [pa] Contour for the normal pressure distribution

University of Notre Dame Future Work Investigate on the case that have different fiber property on the different region. Improve the algorithm to reduce the calculation time.

University of Notre Dame Thank you