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Design of Blood-Lubricated Bearings Using Fluent Presentation to the 2003 Fluent User Group Meeting Cambridge Technology Development, Inc. CTD Edward Bullister, Ph.D. eb@alum.mit.edu

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Overview Physics of Thin-Film Lubrication Governing Equations of the Lubrication Approximation Numerical Implementation in Nekton Fluent Example Problems Steady Unsteady

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Physics of Lubrication Outflow < Inflow Couette Flow Becomes Unbalanced when Plates are not Paralllel UU

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Approximation to N-S Equations Assumptions: Laminar Flow, Re Small (no inertia) L/B - Large (reasonable; typically ~1000) No Slip Incompressible Case Presented Here

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Lubrication Analogues Physical VariableComputational Analogue PressureTemperature Gap 3 / Thermal Conductivity K RHSHeat Source Q Fluid FluxHeat Flux Note: μ

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Implementation in Fluent UDFs for: Material Properties Heat Source In Nonplanar Bearings, Integration of Pressure x- and y- Components

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Computational Work Comparison Direct SolutionLubrication Approximation Dimensions:32 Equations:Full (Navier)-StokesEnergy

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Force Predictions Comparison With Long–Bearing (L/D >> 1) Theory L/D110100 Fluent Force Prediction (Newtons) 103386042550 Exact Solution(Newtons) Infinitely Long 428428442840 Difference76%10%0.6% Conditions: No cavitation (continuous film) D = 40 mm; 3500 RPM; Gap = 2 mils; ε = 0.1; μ = 5 cp Close Agreement where exact Solution is valid

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Details of Journal Bearing at L/D = 1 Pressure (Pascal)

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Cavitating Journal Bearing at L/D = 1 Pressure (Pascal)

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Thrust Bearing D = 40mm ω = 3500 RPM h = 1- 10 mils 4 Contoured Quadrants

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Thrust Bearing – Steep Contours Pressure Footprint Beneath Rotating Thrust Bearing (Plotted via its Temperature Analogue) Computational Grid

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Stiffened Thrust Bearing

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Example: Unsteady Bearing

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Bearing Stability Continuous vs. Cavitating

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Trajectories in Stable and Unstable Bearings

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Stability Problem Eigenvalue Analysis Predicts continuous film bearing neutrally stable: = 0 + i /2 Simulations Use unsteady time stepping procedure Simulate with initial bearing eccentricity not at equilibrium with steady applied load Track motion of piston in response to net forces

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Unsteady Simulation Results Bearing takes Circular Orbit around equilibrium position Period of Orbit about ½ that of cylinder rotation consistent with: Eigenvalue Analysis Experimentally Observed “whirl” instability Trajectory of Simulated Bearing

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Recommendations Design for sufficient load capacity to maintain allowable gaps at operating speeds For continuous film bearings, avoid symmetry For unstable bearings, avoid symmetry

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Design of Fluidic Devices Design Support and Analysis CFD Analysis Brought to you by… CTD @ attbi.com 781-790-1177

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