spread equation with residual stress instead of using pillar_spread_correction_coefficients

[QiangF]

Physically pillars will have the same elongation set by the long product rolling boundary condition.
Look like in the current solving algorithm, that boundary condition is not enforced, which result in using pillar_spread_correction_coefficients to mitigating the differences.

Is it possible to enforce the same elongation on all pillars and solve the spreading equation by add residual stress between pillars?
That would also enable the spring back and stress relaxation creep effect after the roll piece get out of the groove.

[RollingTechSupport]

Currently one can set the 'Elongation_Correction' flag to basically include the spread correction. This correction is the result of the material cohesion.
This still results in different local elongations but enforce the same mean elongation per pillar.

To include a residual stress calculation this could be further expanded your right.
A similar approach was used in a simulation for cladding of two or more sheets where one has a similar problem with the elongation and therefore velocity distribution inside the workpiece.
Still I would doubt that a empirical spread model would yield good results but if so it would be awesome. Do you plan to integrate something like this or how is this of your interest?

[QiangF]

I am trying to build a shape reference table for our rolling mill. I use the wusatowski spreading. I have tried wusatowski_material_coefficient=0.995, even such a small change will result in a huge difference in groove filling and lead to contact problems. But with the default value, it looks like the spread is much bigger than expected, it looks like this
https://ibb.co/7Nn5mZfz

I just want to make it smaller, is there any other parameter that I can adjust?

[RollingTechSupport]

Well to me it looks like the pass design has pretty significant overfill in some grooves.
To my experience, the wusatowski spread equation tends to underestimate the real spread of the material by around 10%.
Therefore I'm wondering how this results comes to place in the first place.

So there are some possibilities to change the behavior of the model.
There is the wusatowski_temperature_coefficient, the wusatowski_material_coefficient and the wusatowski_friction_coefficient.
Further what would be also interesting, do you use the pyroll.lendl_equivalent_method?
Can you share the pass design then one could help you more easily.

[QiangF]

The snippet is here https://gist.github.com/QiangF/667b8a26d7b6424b26889ed31b0512c3
This is how it looks like when run on my computer, you can see significant overfill
https://ibb.co/mFgKhhdv

I have not done too much customization. It looks like wusatowski_material_coefficient and wusatowski_friction_coefficient are equivalent in the equation. These two are extremely sensitive, you can try by setting either one to 0.995, 1, and 1.001.

pyroll.lendl_equivalent_method does not seem to affect the spreading in this case.

[RollingTechSupport]

Okay, thank you.
So the "problem" here is the pyroll.pillar_model plugin. The way this model is designed, the type of spread equation used, so also the formulation of the formula is affecting the result quite heavily.
From personal experience, the most stable and also good matching results for almost all steel grades can be achieved by using the pyroll.lendl_equivalent_method plugin without the pyroll.pillar_model and pyroll.wusatowski_spreading.
If you want to use the pillar model I suggest you switch to pyroll.sparling_spreading, it's a similar formula than the orig. wusatowski formula but runs more stable.
There you could use the sparling_material_coefficient if you want to alter the spreading behavior.

Further:

max_radius=stand['r0'], min_radius = stand['r0'] - groove.depth,

is calculated per default so you don't have to set this explicitly.
Also this:

rotator = pyroll.core.Rotator( # parent=roll_pass, label=f"Rotator:{i}", duration=0, length=0, )

Is created automatically and is normally not needed to be defined, or you want to change something explicitly here.
Your manuel_solve method is pretty much copying the behavior of the original solve method as also here the out_profile becomes the new in_profile and so on.

[QiangF]

Thank you for the clarification, I am starting to appreciate the design of Pyroll now. With regard to the spreading model, what is the best method to fit the spreading parameters? How to measure the roll spreading of the material accurately? Do you use a rectangular profile as a test piece?

We have a continuous bar rolling mill for special steel. I have noticed that the spreading difference can be quite large. I think we can fit the shape change, make an accompany spreading coefficient database for PyRoll, and some real world application show cases.

[RollingTechSupport]

Well you can use every profile, in the end rectangular ones are the easiest to measure.
In the mill I work, we use hot sampling from laser gauges.
Well from a material point of view, one could say that austenitic steels have a tendency to spread less that ferritc steels.
But I don't know which kinds of steels you use.
There is also a table for the freiberg-spread-model one can look into to get an idea.

Regarding the fitting, I used the lmfit package and in there the method cobyla as it works very robust for these kinds of problems.

import pyroll.core as pr
import pyroll.pillar_model
import pyroll.freiberg_flow_stress
import pyroll.ring_model_thermal
import pyroll.sparling_spreading
import numpy as np
from lmfit import Parameters
from lmfit import minimize, fit_report

measured_material_width = [
    56.3e-3,
    36.4e-3
]

in_profile_imf = pr.Profile.round(
    diameter=50e-3,
    temperature=1100 + 273.15,
    material=["C45", "steel"],
    density=7.5e3,
    thermal_conductivity=23,
    specific_heat_capacity=690
)

def create_pass_sequence(material_coefficient: float):
    return pr.PassSequence([
        pr.RollPass(
            label='K02/001',
            roll=pr.Roll(
                nominal_diameter=321e-3,
                groove=pr.SwedishOvalGroove(
                    r1=6e-3,
                    r2=26e-3,
                    depth=7.25e-3,
                    usable_width=60e-3,
                    ground_width=38e-3
                ),
                temperature=25 + 273.15
            ),
            gap=13.5e-3,
            velocity=1,
            disk_element_count=30,
            sparling_material_coefficient=material_coefficient,
        ),

        pr.Transport(
            label="K02/001 -> K05/001",
            duration=8,
            disk_element_count=30,
        ),
        pr.RollPass(
            label='K05/001',
            roll=pr.Roll(
                nominal_diameter=321e-3,
                groove=pr.FalseRoundGroove(
                    r1=4e-3,
                    r2=18e-3,
                    depth=17.5e-3,
                ),
                temperature=25 + 273.15
            ),
            gap=1.5e-3,
            velocity=1,
            disk_element_count=30,
            sparling_material_coefficient=material_coefficient,
        ),
    ])

def solve_pass_sequence_and_return_spread_error(params):
    act_width_errors = []
    sparling_material_coefficient = params['sparling_material_coefficient'].value
    print(f'Current Material Coefficient: {sparling_material_coefficient}')
    sequence = create_pass_sequence(sparling_material_coefficient)
    sequence.solve(in_profile_imf)

    for i, roll_pass in enumerate(sequence.roll_passes):
        print(f'Roll Pass {i}: {roll_pass.label}')
        print(f'Calculated Width: {roll_pass.out_profile.width}')
        act_width_errors.append(measured_material_width[i] - roll_pass.out_profile.width)

    rms_error = np.sqrt(np.mean(np.array(act_width_errors) ** 2))
    print("RMS error: ", rms_error)
    return np.array(rms_error)


spread_coefficient = Parameters()
spread_coefficient.add('sparling_material_coefficient', value=0.8, min=0.7, max=0.9, vary=True)

result = minimize(
    solve_pass_sequence_and_return_spread_error,
    params=spread_coefficient,
    nan_policy='omit',
    max_nfev=100,
    method="cobyla"
)

print(fit_report(result))