Example 6 - Isotropic bearings with damping.

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Example 6 - Isotropic bearings with damping.#

In this example, we use the rotor seen in Example 5.9.5 from [Friswell, 2010].

The isotropic bearing Example 3 is repeated but with damping in the bearings. The, x and y directions are uncoupled, with a translational stiffness of 1 MN/m and a damping of 3 kNs/m in each direction.

import ross as rs
import numpy as np
import plotly.graph_objects as go

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

pio.renderers.default = "notebook"

# Classic Instantiation of the rotor
shaft_elements = []
bearing_seal_elements = []
disk_elements = []
steel = rs.steel
for i in range(6):
    shaft_elements.append(rs.ShaftElement(L=0.25, material=steel, n=i, idl=0, odl=0.05))

disk_elements.append(
    rs.DiskElement.from_geometry(n=2, material=steel, width=0.07, i_d=0.05, o_d=0.28)
)

disk_elements.append(
    rs.DiskElement.from_geometry(n=4, material=steel, width=0.07, i_d=0.05, o_d=0.35)
)
bearing_seal_elements.append(rs.BearingElement(n=0, kxx=1e6, kyy=1e6, cxx=3e3, cyy=3e3))
bearing_seal_elements.append(rs.BearingElement(n=6, kxx=1e6, kyy=1e6, cxx=3e3, cyy=3e3))

rotor595c = rs.Rotor(
    shaft_elements=shaft_elements,
    bearing_elements=bearing_seal_elements,
    disk_elements=disk_elements,
)

rotor595c.plot_rotor()

# From_section class method instantiation.
bearing_seal_elements = []
disk_elements = []
shaft_length_data = 3 * [0.5]
i_d = 3 * [0]
o_d = 3 * [0.05]

disk_elements.append(
    rs.DiskElement.from_geometry(n=1, material=steel, width=0.07, i_d=0.05, o_d=0.28)
)

disk_elements.append(
    rs.DiskElement.from_geometry(n=2, material=steel, width=0.07, i_d=0.05, o_d=0.35)
)
bearing_seal_elements.append(rs.BearingElement(n=0, kxx=1e6, kyy=1e6, cxx=3e3, cyy=3e3))
bearing_seal_elements.append(rs.BearingElement(n=3, kxx=1e6, kyy=1e6, cxx=3e3, cyy=3e3))

rotor595fs = rs.Rotor.from_section(
    brg_seal_data=bearing_seal_elements,
    disk_data=disk_elements,
    leng_data=shaft_length_data,
    idl_data=i_d,
    odl_data=o_d,
    material_data=steel,
)
rotor595fs.plot_rotor()

# Obtaining results for w=0

modal595c = rotor595c.run_modal(0)
modal595fs = rotor595fs.run_modal(0)

print("Normal Instantiation =", modal595c.wn * 60 / (2 * np.pi), "[RPM]")
print("\n")
print("From Section Instantiation =", modal595fs.wn * 60 / (2 * np.pi), "[RPM]")

Normal Instantiation = [ 834.32208726  834.32208726 2890.6574236  2890.65742361 8223.63465095
 8223.63465117] [RPM]


From Section Instantiation = [ 834.33341919  834.33341919 2891.57258897 2891.57258897 8174.61783178
 8174.61783186] [RPM]

# Obtaining results for w=4000RPM

modal595c = rotor595c.run_modal(4000 * np.pi / 30, num_modes=14)  # speed input in rad/s
print("Normal Instantiation =", modal595c.wn * 60 / (2 * np.pi), "[RPM]")

Normal Instantiation = [ 821.83844862  845.51158264 2616.47783213 3130.72229886 6210.9376164
 7341.91366704 8988.36233905] [RPM]

# The input units must be according to your unit standard system
campbell = rotor595c.run_campbell(np.linspace(0, 4000 * np.pi / 30, 50), frequencies=7)
# Plotting frequency in RPM
campbell.plot(frequency_units="RPM")

References#

[Fri10]

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

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