Example 21 - Features of Eigenvalues and Eigenvectors - Hydrodynamic Bearings

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Example 21 - Features of Eigenvalues and Eigenvectors - Hydrodynamic Bearings#

This example is based on Example 5.9.6 from [Friswell, 2010]. Example 7 from the documentation uses the BearingFluidFlow class to create a hydrodynamic bearing.

Here we are going to use the CylindricalBearing class, which is implemented based on [Friswell, 2010].

Hydrodynamic Bearings. Repeat the analysis of Example 5.9.1 when the bearings are replaced with hydrodynamic bearings. The oil-film bear ings have a diameter of 100 mm, are 30 mm long, and each supports a static load of 525 N, which represents half of the weight of the rotor. The radial clearance in the bearings is 0.1 mm and the oil film has a viscosity of 0.1 Pa s. These bearings have the same characteristics as Example 5.5.1.

import ross as rs
import numpy as np
import plotly.graph_objects as go
from IPython.display import display

# Make sure the default renderer is set to 'notebook' for inline plots in Jupyter
import plotly.io as pio

pio.renderers.default = "notebook"

Q_ = rs.Q_

steel = rs.Material("steel", E=211e9, G_s=81.2e9, rho=7810)

L = 0.25
N = 6
idl = 0
odl = 0.05

shaft = [rs.ShaftElement(L=L, idl=idl, odl=odl, material=steel) for i in range(N)]
bearings = [
    rs.CylindricalBearing(
        n=0,
        speed=Q_(list(range(0, 5000, 50)), "RPM"),
        weight=525,
        bearing_length=Q_(30, "mm"),
        journal_diameter=Q_(100, "mm"),
        radial_clearance=Q_(0.1, "mm"),
        oil_viscosity=0.1,
    ),
    rs.CylindricalBearing(
        n=len(shaft),
        speed=Q_(list(range(0, 5000, 50)), "RPM"),
        weight=525,
        bearing_length=Q_(30, "mm"),
        journal_diameter=Q_(100, "mm"),
        radial_clearance=Q_(0.1, "mm"),
        oil_viscosity=0.1,
    ),
]
disks = [
    rs.DiskElement.from_geometry(
        n=2, material=steel, width=0.07, i_d=odl, o_d=0.28, scale_factor="mass"
    ),
    rs.DiskElement.from_geometry(
        n=4, material=steel, width=0.07, i_d=odl, o_d=0.35, scale_factor="mass"
    ),
]

rotor = rs.Rotor(shaft_elements=shaft, disk_elements=disks, bearing_elements=bearings)
rotor.plot_rotor()

campbell = rotor.run_campbell(speed_range=Q_(list(range(0, 4500, 50)), "RPM"))

UserWarning:

Extrapolating bearing coefficients. Be careful when post-processing the results.

campbell.plot(frequency_units="RPM")

modal = rotor.run_modal(speed=Q_(4000, "RPM"))

for mode in range(6):
    display(modal.plot_mode_3d(mode, frequency_units="Hz"))

for mode in range(6):
    display(modal.plot_orbit(mode, nodes=[2, 4]))

References#

[Fri10] (1,2)

Michael I Friswell. Dynamics of rotating machines. Cambridge University Press, 2010.

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