# Example 20 - Features of Eigenvalues and Eigenvectors - Cross-Coupling in the Bearings#

This example is based on Example 5.9.4 from .

Cross-Coupling in the Bearings. This system is the same as that of
Example 5.9.1 except that some coupling is introduced in the bearings between
the x and y directions. T he bearings have direct stiffnesses of 1 MN/m and cross
coupling stiffnesses of 0.5 MN/m.

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

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.BearingElement(
n=0, kxx=1e6, kyy=1e6, kxy=0.5e6, kyx=0.5e6, cxx=0, scale_factor=2
),
rs.BearingElement(
n=len(shaft), kxx=1e6, kyy=1e6, kxy=0.5e6, kyx=0.5e6, cxx=0, scale_factor=2
),
]
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"))

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

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