Homework 3
Lubricating Flows
problems 2, 3, and 4 were created in excel.
1 Go the the class weblinks page (www:ewp:pri:edu= ernesto=F2003=FWLM=BooksLinks=other:html)
and view and study the videos on:
Fluid Film Lubrication,
The lecturer was hard to understand due to his foreign accent and frequent pauses. He discussed different fluid film lubrication as the title suggests. The tilted thrust bearing is one example. Hydrostatic film has oil pressure to promote separation of the bearing surfaces.
The lecture initially explained Reynolds initial analysis for pressure distribution between two parallel plates.
He then moved on to talk about conservation of momentum in a Newtonian fluid. Those equations led to a force balance, which led to finding the flow velocity profiles by integrating and using boundary conditions.
Next, he used the continuity equation to get the pressure distribution dependent on the velocity.
Surface Chemistry
This video was impossible to understand due to the lecturer’s foreign accent
He discussed surface atomic interactions
Then he discussed colloidal solutions and properties.
The connection to tribology was not understood from this specific video.
Surface Metrology.
The full title of the video is Roughness Height Parameters & Surface Metrology. As the title suggests, he examined the parameters of roughness. The parameters for describing a surface were divided into vertical z dependent, spatial x y dependent, and hybrid parameters.
For vertical parameters, “extreme height” parameters isRz is average surface height, Rt is max peak to valley, Rv is valley and rp is peak. “average” height parameters: Ra is surface roughness which is the average absolute different in surface height, and Rq is the root mean square surface difference. These are more useful values used to know the surface finish.
He then discussed actual surface roughness measuring techniques. Ra is not sufficient for predicting critical load behavior, but is still useful for a control value.
2 An tilted pad thrust bearing has an inlet gap hi = 2x10−3 m, an outlet gap ho = 10−3
m and a length L = 10−2 m. While the tilted pad is fixed, the velocity of the horizontal
slider is V = 1 m/s. Assume the properties of the working fluid are density = 103 kg/m3 and mu = 10−2 Pa.s and determine the pressure distribution and the volumetric flow rate of fluid in the bearing.
The equation given for a tiled bearing is
where m=(hi/ho)-1
Graphing this equation gives the following pressure distribution:
The peak pressure is 25.0 Pa at x=0.665x10-2 or 66.5% along the bearing.
The volumetric flow rate, q is calculated from the following equation:
Calculating at the peak pressure reduces terms since dp/dx=0. Then volumetric flow per unit width is q=Uh/2, where U=1, and h=(hi -ho)*(L-x)/L+ho=1.335x10-3,
The volumetric flow is q=6.68x10-4 m3/s /m (width)
3 A hydrostatic thrust bearing has an outer radius of 0.2 m, a recess radius of 0.1 m, a gap of 0.005 m and a recess cavity height of 0.05 m. Assume the same fluid properties as above. If the fluid if forced to flow into the bearing at a rate Q = 0.01 m3/s, estimate the recess pressure distribution.
The pressure distribution is derived by combining the following two equations:
And knowing q=Q/(2πr), pr=Q6μπh3ln(ror). Graphing gives the following plot:
Where the max pressure in the land area is p=106 Pa at r=0.1
4 A journal bearing consists of a shaft (journal) with radius rj = 0.0254 m and a sleeve
(bearing) with radius rb = 0.0250 m. Under certain operating conditions, the journal rotates at omega = 100 RPM and the excentricity is e = 0.0002 m. Assume the same fluid properties as above and determine the pressure distribution in the journal bearing.
The pressure distribution is given in Shaw analysis lubrication bearings as
Note: the lecture 5 notes equation have an extra factor of 6 added which is a typo.
In the above equation, Po is take as 0, mu=1e-2, U=omega*r, omega=100*2Pi/60=10.5rad/s, r=rj, c=rb-rj, n=e/c.
Where the max pressure is p=1524 at theta=2.30,