Example 4 - Anisotropic Bearings.

In this example, we use the rotor seen in Example 5.9.2 from [Friswell, 2010].

Both bearings have a stiffness of 1 MN/m in the x direction and 0.8 MN/m in the y direction. Calculate the eigenvalues and mode shapes at 0 and 4,000 rev/min and plot the natural frequency map for rotational speeds up to 4,500 rev/min.

import ross as rs
import numpy as np

# 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=0.8e6, cxx=0, cyy=0))
bearing_seal_elements.append(rs.BearingElement(n=6, kxx=1e6, kyy=0.8e6, cxx=0, cyy=0))

rotor592c = rs.Rotor(
    shaft_elements=shaft_elements,
    bearing_elements=bearing_seal_elements,
    disk_elements=disk_elements,
)

rotor592c.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=0.8e6, cxx=0, cyy=0))
bearing_seal_elements.append(rs.BearingElement(n=3, kxx=1e6, kyy=0.8e6, cxx=0, cyy=0))

rotor592fs = 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,
)
rotor592fs.plot_rotor()

# Obtaining results for speed = 150 rad/s (wn is in rad/s)

modal592c = rotor592c.run_modal(150.0)
modal592fs = rotor592fs.run_modal(150.0)

print("Normal Instantiation =", modal592c.wn)
print("\n")
print("From Section Instantiation =", modal592fs.wn)

Normal Instantiation = [ 82.60929602  86.68625235 251.70037114 276.87787937 652.85679897
 742.60864608]


From Section Instantiation = [ 82.6103125   86.68740438 251.75040613 276.94375838 654.32910577
 745.05999629]

# Obtaining results for w=4000RPM (wn is in rad/s)

speed = 4000 * np.pi / 30
modal592c = rotor592c.run_modal(speed)

print("Normal Instantiation =", modal592c.wn)

Normal Instantiation = [ 82.32547398  86.86369902 239.64228361 287.24958074 583.48782916
 806.8872843 ]

• Campbell Diagram

campbell = rotor592c.run_campbell(np.linspace(0, 4000 * np.pi / 30, 50))
# Plotting frequency in RPM
fig = campbell.plot(frequency_units="rpm")
fig.show()

• Mode Shapes

for i in np.arange(0, 5.1, 1):
    modal592c.plot_mode_3d(mode=int(i)).show()

References

Fri10

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