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Bernhard BettigMechanical Design Research Lab

Mechanical Engineering - Engineering Mechanics Dept.Michigan Technological UniversityWeb site: http://www.me.mtu.edu/~mdrl

Rotordynamics Unit 5:Modeling Journal Bearings

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Journal Bearing review The journal bearing appears in the

dynamic finite element equations as a linear spring and damper.

=

+

y

x

yyyx

xyxx

yyyx

xyxx

FF

v

u

kkkk

v

u

cc

cc

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Journal Bearing review In order to determine the c and k coefficient

values, we must consider the fluid pressures in the bearing.

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Journal Bearing reviewThe fluid pressures can be calculated using Reynolds equation:

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Perturbation Solution To determine the dynamic coefficients,

we can assume that the pressure is the sum of the static pressure and variations due to small motions of the shaft about the static equilibrium position.

where:

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Perturbation Solution

and:

47

Fluid Pressure Calculations The boundary conditions for a

journal bearing are:

boundary pressure static at the 0condition)boundary s(Reynold

edge trailingfilm at the 0

grooves,supply at pressure feeding theequals , and 0at 0

=

=

=

=

===

p

Zppp

pLzzp B

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Fluid Pressure Calculations The fluid pressure distribution looks like:

Static (p0)

Perturbation (px)Perturbation (py)

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Fluid Pressure Calculations The pressure distribution varies as a

function of e0/c, , and .

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Fluid Pressure Calculations

611

Fluid Pressure Calculations

The bearing force is assumed to be comprised of the static force and dynamic forces due to small shaft motions.

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Fluid Pressure Calculations The static force and dynamic coefficients

are found through integration:

713

Fluid Pressure Calculations

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Numerical Calculations The pressures are solved numerically

using the finite difference method.

Control Volume

Neighboring Control Volumes

815

Numerical Calculations

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Numerical Calculations

917

Numerical Calculations

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Numerical Calculations

10

19

Numerical Calculations

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Numerical Calculations The integrations are performed by

summation of each control volume.

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21

Numerical Calculations

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Sample Questions1. The bearing from last week is discretized into a 20 x

20 grid of control volumes. The shaft is displaced 3 mm in the +X direction.

Consider a control volume centered at = 0 and Z = LB/2. What is the new pressure, after the next iteration, if the static pressure in this cell is 1.5 MPaand the neighboring pressures are 1.2 MPa (east), 1.3 MPa (south), 0.7 MPa (west), and 0.8 MPa (north)?

2. What contribution (in Newtons) does the pressure of this control volume make to the total force (a) in the X direction, (b) in the Y direction.