Transcript CTD Design of Blood-Lubricated Bearings Using Fluent

CTD
Cambridge Technology Development, Inc.
Design of
Blood-Lubricated Bearings
Using Fluent
Presentation to the 2003 Fluent User Group Meeting
Edward Bullister, Ph.D.
[email protected]
Overview
 Physics of Thin-Film Lubrication
 Governing Equations of the Lubrication Approximation
 Numerical Implementation in Nekton Fluent
 Example Problems


Steady
Unsteady
Physics of Lubrication
Outflow < Inflow
U
U
Couette Flow Becomes
Unbalanced when
Plates are not Paralllel
Approximation to N-S Equations
 Assumptions:




Laminar Flow, Re Small (no inertia)
L/B - Large (reasonable; typically ~1000)
No Slip
Incompressible Case Presented Here
Lubrication Analogues
Physical Variable
Computational Analogue
Pressure
Gap3/
RHS
Fluid Flux
Temperature
Thermal Conductivity K
Heat Source Q
Heat Flux
Note:
μ
Implementation in Fluent
 UDFs for:



Material Properties
Heat Source
In Nonplanar Bearings,
Integration of Pressure
x- and y- Components
Computational Work Comparison
Direct Solution
Lubrication
Approximation
Dimensions: 3
2
Equations:
Full (Navier)-Stokes Energy
Force Predictions Comparison With
Long–Bearing (L/D >> 1) Theory
 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
L/D
1
Fluent Force Prediction 103
(Newtons)
Exact Solution(Newtons) 428
Infinitely Long
Difference
76%
10
100
3860
42550
4284
42840
10%
0.6%
Details of Journal Bearing at L/D = 1
Pressure (Pascal)
Cavitating Journal Bearing at L/D = 1
Pressure (Pascal)
Thrust Bearing
D = 40mm
ω = 3500 RPM
h = 1- 10 mils
4 Contoured Quadrants
Thrust Bearing – Steep Contours
Computational Grid
1.63e+06
1.55e+06
1.47e+06
1.39e+06
1.31e+06
1.22e+06
1.14e+06
1.06e+06
9.80e+05
8.98e+05
Pressure Footprint Beneath Rotating
Thrust Bearing
(Plotted via its Temperature Analogue)
8.16e+05
7.35e+05
6.53e+05
5.71e+05
4.90e+05
4.08e+05
3.27e+05
2.45e+05
1.63e+05
8.16e+04
0.00e+00
Contours of Static Temperature (k)
Apr 09, 2003
FLUENT 6.1 (2d, segregated, lam)
Stiffened Thrust Bearing
Example: Unsteady Bearing
Bearing Stability
Continuous

vs.
Cavitating

Trajectories in Stable and
Unstable Bearings
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
Unsteady
Simulation Results
 Bearing takes Circular
Orbit around
equilibrium position
 Period of Orbit about ½
that of cylinder rotation
consistent with:
Trajectory of Simulated Bearing
• Eigenvalue Analysis
• Experimentally Observed “whirl”
instability
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
CTD @ attbi.com
781-790-1177