Tilting pad bearing force mismatch with external load?

[6cvhycmwjr-cloud]

Hello,

When i run the tilting pad bearing example and I use the determine_eccentricity function, with the load below (884 N in x-direction and -2670 N in y-direction) and remove the eccentricity and attitude angle i get follow results for the pad forces in x and y-direction.

X = [-7.28544297e+02 2.76706082e-01 7.28851243e+02 1.16683225e+03 -1.16902545e+03]
Y = [-237.51226667 -456.52528266 -236.56528483 1607.61184037 1606.01794477]

When I make the sum of the forces in Y-direction I come to a value of 2283 N. For the X-direction the sum equals to approximately zero. Is there a reason why we see this deviation in values between bearing forces and external load?

bearing = TiltingPad(
n=1,
frequency=Q_([3000], "RPM"),
equilibrium_type="match_eccentricity",
model_type="thermo_hydro_dynamic",
journal_diameter=101.6e-3,
radial_clearance=74.9e-6,
pad_thickness=12.7e-3,
pivot_angle=Q_([18, 90, 162, 234, 306], "deg"),
pad_arc=Q_([60, 60, 60, 60, 60], "deg"),
pad_axial_length=Q_([50.8e-3, 50.8e-3, 50.8e-3, 50.8e-3, 50.8e-3], "m"),
pre_load=[0.5, 0.5, 0.5, 0.5, 0.5],
offset=[0.5, 0.5, 0.5, 0.5, 0.5],
lubricant="ISOVG32",
oil_supply_temperature=Q_(40, "degC"),
nx=30,
nz=30,
eccentricity=0.35,
attitude_angle=Q_(287.5, "deg"),
load=[8.8405e02, -2.6704e03],
)

[gsabinoo]

Hello @6cvhycmwjr-cloud! I hope you are doing well.

Thank you for reporting this issue. The discrepancy you're observing in the bearing forces is related to how the optimization initial values are handled in the current main branch. This behavior has already been addressed in a Pull Request #1245 that is currently under review.

When you use equilibrium_type="determine_eccentricity" and remove the eccentricity and attitude_angle parameters from the TiltingPad class initialization, the optimization process starts with undefined or uninitialized values, resulting in incorrect convergence.

In the current code on the main branch, the initial optimizer setup is:

elif self.equilibrium_type == "determine_eccentricity":
    # Initial guess: [eccentricity, attitude_angle, pad_angles...]
    if self.initial_pads_angles is not None:
        x0 = [self.eccentricity, self.attitude_angle] + list(
            self.initial_pads_angles
        )
    else:
        x0 = [self.eccentricity, self.attitude_angle] + [0.0] * self.n_pad

Without appropriate values for self.eccentricity and self.attitude_angle, the optimizer cannot find an equilibrium position compatible with the external load provided ([884, -2670] N), resulting in the discrepancy you observed in the forces.

How initial values are used

The optimization process requires initial guesses for the equilibrium position. Users have two options:

1. Provide eccentricity and attitude angle: these serve as the initial guess for the shaft position in the global reference frame
2. Provide initial pad angles (via initial_pads_angles): these represent the initial angular position of each pad in its own local reference frame

If initial_pads_angles is not provided, the optimizer uses default values for the pad angles.

About the changes in the PR under review

The open PR already fixes this problem in two ways:

1. Estimated default values in the TiltingPad class initialization

def __init__(
    self,
    ...
    yj=None,
    equilibrium_type=None,
    eccentricity=0.3,                    # Estimated default value
    attitude_angle=np.pi * 3 / 2,        # 270° as default
    load=None,
    initial_pads_angles=None,
    model_type="thermo_hydro_dynamic",
    **kwargs,
):

2. Initial values for optimization

elif self.equilibrium_type == "determine_eccentricity":
    # Initial guess: [eccentricity, attitude_angle, pad_angles...]
    if self.initial_pads_angles is not None:
        x0 = [self.eccentricity, self.attitude_angle] + list(
            self.initial_pads_angles
        )
    else:
        x0 = [0.3, np.deg2rad(270)] + [1e-4] * self.n_pad  # Initial pad angles different from zero

One possible temporary approach:

While the PR is not merged into main, you can work around the problem by explicitly providing the eccentricity and attitude_angle initial values.

---

Thank you for reporting! Please let me know if I understood the issue correctly

[6cvhycmwjr-cloud]

Thank you very much for your reply, I will try this out!