Presented By (Sahadeo Ramjatan) Sahadeo Ramjatan

Problem Description Investigate 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 joints
Objective is to develop an empirical relationship for the pressure as a function of the cylinder’s rotational speed and film thickness
Compare the pressure when using the full circular film thickness and the parabolic approximation TFAWS 2016 – August 1-5, 2016 4<br>

Literature Review using Parabolic Film TFAWS 2016 – August 1-5, 2016 5<br>

Reynolds Equation TFAWS 2016 – August 1-5, 2016 6 Net flow rates due to pressure gradients within the lubricated area Net entraining flow rate due to surface velocities Side Leakage<br>

Film Thickness TFAWS 2016 – August 1-5, 2016 7<br>

Computational Domain ANSYS CFX (Version 14.5) to find the pressure at different rotational speeds and film thickness
CFD allows coupling of fluid dynamics and rotor dynamics
Boundary conditions
Rotating Wall and Non-slip wall
Model 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 forces
Radius is .0762m or 3in
Hydrodynamic Lubrication TFAWS 2016 – August 1-5, 2016 8<br>

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

Empirical Equation TFAWS 2016 – August 1-5, 2016 10 The 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<br>

Empirical Equation TFAWS 2016 – August 1-5, 2016 11 The 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<br>

Comparing with Analytical Solution TFAWS 2016 – August 1-5, 2016 12 As 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 pressure
As the rotational speed increases there is also greater differences in pressure<br>

Preloaded Bearing Application Consider designing a passive release mechanism for a configuration consisting of a shaftless system suspended by hydrodynamic pressure
The preload force imparted by the springs is significant for stabilizing the rotor TFAWS 2016 – August 1-5, 2016 13<br>

Non-Newtonian Model Simulation TFAWS 2016 – August 1-5, 2016 14 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<br>

Dynamic Moving Mesh Simulation TFAWS 2016 – August 1-5, 2016 15 A 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<br>

Conclusion Investigated 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 thickness
As the film thickness or speed increased, there was a greater difference in maximum pressure from the analytical (parabolic) and empirical (full circular film) expression
Considered 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, 2016 16<br>

Acknowledgements We 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 travel TFAWS 2016 – August 1-5, 2016 17<br>

References P. Kapitza, Collected Papers of Kapitza, London: Pergamon Press, 1965
R. Snidle and J. Archard, "Theory of Hydrodynamic Lubrication for a Spinning Sphere," in Proc Instn Mech Engrs , Leicester, 1969-70
D. 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, 1995 TFAWS 2016 – August 1-5, 2016 18<br>