Magnetic pull modeling with negative stiffness

[kouki3042]

Hello,

I'm working on modeling an electrical machine rotor and aiming to consider magnetic attraction by introducing a negative stiffness bearing.
However, in the static analysis, I don't observe any noticeable effect from the negative stiffness.
Do you have any recommendations or insights on how to properly model this behavior?
For reference, I used the following code for comparison:

import numpy as np
import ross as rs

# Materials
steel = rs.Material(name="Steel", rho=7810, E=211e9, G_s=81.2e9)  # SI units

L_total = 0.6          
od = 0.05              
id_ = 0.0              
n_elems = 6            

shaft_elems = [
    rs.ShaftElement(
        L=L_total / n_elems,
        idl=id_,
        odl=od,
        material=steel,
        shear_effects=True,
        rotary_inertia=True,
        gyroscopic=True,
    )
    for _ in range(n_elems)
]

disk = rs.DiskElement(n=n_elems // 2, m=12.0, Ip=0.15, Id=0.08, tag="IMP")

# Bearing
amb_left = rs.BearingElement(
    n=0, kxx=0, kyy=4e7, cxx=0, cyy=0  
)

amb_right = rs.BearingElement(
    n=6, kxx=0, kyy=4e7, cxx=0, cyy=0  
)

# Negative stiffness bearing
Magnetic_pull_neg = rs.BearingElement(
    n=3, kxx=0, kyy=-4e7, cxx=0, cyy=0 
)
# The same bearing but with positive value for comparison
Magnetic_pull_pos = rs.BearingElement(
    n=3, kxx=0, kyy=4e7, cxx=0, cyy=0  
)

# Rotors
rotor = rs.Rotor(
    shaft_elements=shaft_elems,
    disk_elements=[disk],
    bearing_elements=[amb_left, amb_right],
)


rotor_pos = rs.Rotor(
    shaft_elements=shaft_elems,
    disk_elements=[disk],
    bearing_elements=[amb_left, amb_right, Magnetic_pull_neg],
)


rotor_neg = rs.Rotor(
    shaft_elements=shaft_elems,
    disk_elements=[disk],
    bearing_elements=[amb_left, amb_right, Magnetic_pull_neg],
)

# Plots 
rotor.plot_rotor().show()

static_analysis = rotor.run_static()
static_analysis.plot_free_body_diagram().show()
static_analysis.plot_deformation().show()


static_analysis_neg = rotor_neg.run_static()
static_analysis_neg.plot_free_body_diagram().show()
static_analysis_neg.plot_deformation().show()

static_analysis_pos = rotor_pos.run_static()
static_analysis_pos.plot_free_body_diagram().show()
static_analysis_pos.plot_deformation().show()

modes = rotor.run_modal(speed=0)
modes.plot_mode_2d(mode=0).show()  
modes.plot_mode_3d(mode=0).show()  

modes_pos = rotor_pos.run_modal(speed=0)
modes_pos.plot_mode_2d(mode=0).show() 
modes_pos.plot_mode_3d(mode=0).show()

modes_neg = rotor_neg.run_modal(speed=0)
modes_neg.plot_mode_2d(mode=0).show()
modes_neg.plot_mode_3d(mode=0).show()

[jguarato]

Hi @kouki3042!

In ROSS, the run_static() function does not use the full bearing stiffness matrix when computing the static equilibrium. Internally, the method replaces the bearing stiffness with a very large axial stiffness (≈ 1e20) to “lock” the bearings in place and compute only the reaction forces.
Because of this, any negative stiffness you define in the bearing element is not included in the static solution, which is why you don’t see any effect from magnetic attraction in run_static().