Example 31 - Isotropic Bearings with Damping

This example is based on Example 5.9.5 from {cite}friswell2010dynamics

The isotropic bearing Example 5.9.1 (Example 17) 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 pandas as pd

from ross.units import 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, cxx=3e3, cyy=3e3, scale_factor=2),
    rs.BearingElement(n=len(shaft), kxx=1e6, kyy=1e6, cxx=3e3, cyy=3e3, 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()

Plotting the Campbell Diagram

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

campbell.plot(frequency_units="RPM", frequencies=8)

Plotting the Mode Shapes and Damped Natural Frequencies

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

for mode in range(7):
    display(modal.plot_mode_3d(mode, frequency_units="Hz"))