Presented By (Sahadeo Ramjatan) - PowerPoint Presentation

1. Presented By(Sahadeo Ramjatan)Sahadeo Ramjatan Graduate Student - University of FloridaSpace Systems GroupAlvin YewAerospace Engineer, NASA GSFCThermal & Fluids Analysis WorkshopTFAWS 2016August 1-5, 2016NASA Ames Research CenterMountain View, CA TFAWS Interdisciplinary Paper SessionHydrodynamic Pressure Generated in Lubricant Film Around Shaftless Reaction Wheel

2. Outline Background Problem DescriptionLiterature ReviewMethodology and ApproachSpring Loaded Application Conclusions TFAWS 2016 – August 1-5, 20162

3. BackgroundConformal BearingsHigh Degree of Geometrical Conformity Load is carried over a large area Journal BearingsNon-conformal BearingsContacting surfaces do not conform well together Full burden of load is carried by a small contact areaMating Gear Teeth and Rolling Element Bearings Rolling Element BearingsBall Bearings where load is primarily radial with some thrust load presentRoller Bearings where load is purely radial in most applications TFAWS 2016 – August 1-5, 20163

4. Problem DescriptionInvestigate the line contact problem of a rolling cylinder on a plane Applications include cylindrical roller bearings used in jet engines and electric motors and similar motion can be seen in flywheels and synovial jointsObjective is to develop an empirical relationship for the pressure as a function of the cylinder’s rotational speed and film thicknessCompare the pressure when using the full circular film thickness and the parabolic approximationTFAWS 2016 – August 1-5, 20164

5. Literature Review using Parabolic FilmTFAWS 2016 – August 1-5, 20165Kapitza (1965)Analytical equations for the pressure when a cylinder or ball is rolling on a surfaceSnidle & Archard (1969)Derives a solution for the hydrodynamic pressure for lubricated sphere spinning on a curved surface Brewe (1978)The parabolic approximation resulted in an overestimate of the minimum film thickness of 1.6% and 0.7% for a thickness ratio (h/R) of 10-4 and 10-5

6. Reynolds EquationPressure is governed by Reynolds Equation In many conventional lubrication problems, side leakage can be neglected resulting in analytical solutions to Reynolds EquationHamrock presents a 1D integrated form of Reynolds Equation for a rolling cylinder on a plane  TFAWS 2016 – August 1-5, 20166Net flow rates due to pressure gradients within the lubricated areaNet entraining flow rate due to surface velocities Side Leakage is where the pressure gradient is zero such as the point of maximum pressure 

7. Film Thickness Based on the geometry of the rotating surface and is needed to solve for the pressure distribution If the region of pressure generation is sufficiently less than the curvature of the rotating body then we can use a parabolic film approximation to get an analytical solutionTo solve the 1D Equation, CFD Post-processing was used to determine xm, the maximum pressure location along the wall TFAWS 2016 – August 1-5, 20167

8. Computational DomainANSYS CFX (Version 14.5) to find the pressure at different rotational speeds and film thicknessCFD allows coupling of fluid dynamics and rotor dynamics Boundary conditions Rotating Wall and Non-slip wallModel Assumptions Laminar flow, constant viscosity, no-slip at the boundary faces, isothermal conditions, incompressible fluid, inertia and surface tension forces are negligible compared with viscous forcesRadius is .0762m or 3inHydrodynamic LubricationTFAWS 2016 – August 1-5, 20168

9. Validation of Computational Model TFAWS 2016 – August 1-5, 20169Pressure gradient along the wall is found to be in good agreement with the analytical relationshipω =100 rpm h0 =500 µm.

10. Empirical Equation TFAWS 2016 – August 1-5, 201610The maximum pressure is graphed as a function of the minimum film thickness at various operating speeds. Each operating speed demonstrated an excellent fit with a power law regression

11. Empirical Equation TFAWS 2016 – August 1-5, 201611The power law regression is further investigated by graphing the coefficients and exponents of the power law equations as a function of angular speed. This can then be used to develop an empirical equation for the pressure. P =C∙h0E

12. Comparing with Analytical SolutionTFAWS 2016 – August 1-5, 201612As the film thickness increases, there is a greater difference in maximum pressure because the pressure distribution spreads out more evenly as opposed to being localized. As the pressures spread out more evenly away from the point of minimum film thickness the parabolic assumption might no longer be valid resulting in greater differences in hydrodynamic pressureAs the rotational speed increases there is also greater differences in pressure

13. Preloaded Bearing ApplicationConsider designing a passive release mechanism for a configuration consisting of a shaftless system suspended by hydrodynamic pressureThe preload force imparted by the springs is significant for stabilizing the rotorTFAWS 2016 – August 1-5, 201613

14. Non-Newtonian Model Simulation TFAWS 2016 – August 1-5, 201614 Rheological model parameters for an aerospace lubricant (Braycote) was then fitted with experimental data (Prat, 2010) using the Carreau-Yasuda non-Newtonian model. As the rotational speed increases, the Non-Newtonian model approaches the isoviscous model

15. Dynamic Moving Mesh SimulationTFAWS 2016 – August 1-5, 201615A dynamic moving mesh simulation is used to demonstrate the case where a lateral spring is imposed on a 2D cylinder and the resulting deflection is plotted as a function of time. Using the empirical equation and the analytical solution resulted in a 4.7% difference in the deflection

16. ConclusionInvestigated the hydrodynamic pressure of a rolling cylinder on a plane Reviewing literature, we saw that the parabolic approximation could result in an overestimate of the film thickness with larger errors for thicker films Developed an empirical relationship for the pressure as a function of the cylinder’s rotational speed and film thicknessAs the film thickness or speed increased, there was a greater difference in maximum pressure from the analytical (parabolic) and empirical (full circular film) expressionConsidered a passive release mechanism for a shaftless system working with a non-Newtonian lubricant which resulted in a 4.7% difference in the deflection between the empirical and analytical equation TFAWS 2016 – August 1-5, 201616

17. AcknowledgementsWe would like to thank Dr. Norman Fitz-Coy, Associate Professor, Mechanical & Aerospace Engineering, University of Florida, for all of his guidance and support We would like to thank Mr. Russell Roder, NASA GSFC, for his guidance and support We would like to thank the John Mather Nobel Scholarship Program for funding our travelTFAWS 2016 – August 1-5, 201617

18. References P. Kapitza, Collected Papers of Kapitza, London: Pergamon Press, 1965R. Snidle and J. Archard, "Theory of Hydrodynamic Lubrication for a Spinning Sphere," in Proc Instn Mech Engrs , Leicester, 1969-70D. E. Brewe, B. J. Hamrock and C. M. Taylor, "Effect of Geometery on Hydrodynamic Film Thickness," NASA, Virginia, 1978.P. Prat, M. Vergne, M. Pochard and J. Sicre, "Optimization of the Rheological Behavior of Thickened Liquid Lubricants for Spacecraft Applications," in Lubricants and Lubrication, 1995TFAWS 2016 – August 1-5, 201618