Example 22 - Features of Eigenvalues and Eigenvectors - The Effect o f Axial Load and Follower Torque

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Example 22 - Features of Eigenvalues and Eigenvectors - The Effect o f Axial Load and Follower Torque#

This example is based on Example 5.9.7 from [Friswell, 2010].

The Effect o f Axial Load and Follower Torque. Investigate the effect on the model of Example 5.9.1 of axial loads of —10,10, and 100 kN and torques of 50 and 100 kNm.

import ross as rs
import numpy as np
import pandas as pd
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
num_freq = 6

bearings = [
    rs.BearingElement(n=0, kxx=1e6, cxx=0, scale_factor=2),
    rs.BearingElement(n=N, kxx=1e6, 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"
    ),
]

results = pd.DataFrame(
    {"speed": [0 for _ in range(num_freq)] + [4000 for _ in range(num_freq)]}
)

for speed in Q_([0, 4000], "RPM"):
    for axial in Q_([0, 10, 100, -10], "kN"):
        shaft = [
            rs.ShaftElement(L=L, idl=idl, odl=odl, material=steel, axial_force=axial)
            for i in range(N)
        ]
        rotor = rs.Rotor(
            shaft_elements=shaft, disk_elements=disks, bearing_elements=bearings
        )

        modal = rotor.run_modal(speed=speed)

        results.loc[results.speed == speed.m, f"Axial Load {axial.m}"] = (
            Q_(modal.wd[:6], "rad/s").to("Hz").m
        )

    for torque in Q_([50, 100], "kN*m"):
        shaft = [
            rs.ShaftElement(L=L, idl=idl, odl=odl, material=steel, torque=torque)
            for i in range(N)
        ]
        rotor = rs.Rotor(
            shaft_elements=shaft, disk_elements=disks, bearing_elements=bearings
        )

        modal = rotor.run_modal(speed=speed)

        results.loc[results.speed == speed.m, f"Torque {torque.m}"] = (
            Q_(modal.wd[:6], "rad/s").to("Hz").m
        )

display(rotor.plot_rotor())
display(results)
speed Axial Load 0 Axial Load 10 Axial Load 100 Axial Load -10 Torque 50 Torque 100
0 0 13.792067 13.935788 15.020440 13.642635 13.661623 13.233779
1 0 13.792067 13.935788 15.020440 13.642635 13.661623 13.233779
2 0 43.658247 43.913150 46.132265 43.401542 43.307680 42.238874
3 0 43.658247 43.913150 46.132265 43.401542 43.307680 42.238874
4 0 114.080085 114.759565 120.620287 113.394556 113.826845 113.060004
5 0 114.080085 114.759565 120.620287 113.394556 113.826845 113.060004
6 4000 13.590156 13.739728 14.867629 13.434622 13.439273 12.943261
7 4000 13.973146 14.111493 15.156882 13.829336 13.860259 13.491418
8 4000 40.072764 40.330147 42.570013 39.813547 39.718828 38.646459
9 4000 46.905083 47.154123 49.325073 46.654356 46.569549 45.543484
10 4000 95.521512 96.087639 100.969101 94.950323 95.179280 94.143329
11 4000 131.633132 132.403364 139.063735 130.856441 131.621534 131.621623

References#

[Fri10]

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

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