As an example of rolling round profiles, a running pass schedule used at the Institute of Metal Forming is chosen. In the upcoming sections we will explain how the mill works and provide the basic implementation of the train in PyRolL.
The rolling train was built as a semi-continuous rolling train which means that it consists of a reversing mill representing the roughing train of a street and four finishing stands which represent the finishing train. The plant was built in a modular approach; that means that every rolling mill of the finishing train is adjustable in its position towards the other mills. Currently, there are various pass schedules to roll various profiles like rounds, squares, hexagons or rebars. In its most basic configuration, which will be presented here, the mill is operated in the following manner:
| # | Groove Type | Groove Width [mm] | Groove Height [mm] | Roll Gap [mm] | Nominal Roll Radius [mm] | Rolling Velocity [ms^-1] |
|---|---|---|---|---|---|---|
| R1 | Swedish Oval | 60 | 28.0 | 13.5 | 160.5 | 1.0 |
| R2 | Round | 36.6 | 36.5 | 1.5 | 160.5 | 1.0 |
| R3 | Swedish Oval | 60 | 16.0 | 1.5 | 160.5 | 2.0 |
| R4 | Round | 27.6 | 26.0 | 1.0 | 160.5 | 2.0 |
| R5 | Circular Oval | 34.0 | 13.4 | 5.4 | 160.5 | 2.0 |
| R6 | Round | 20.4 | 19.8 | 1.8 | 160.5 | 2.0 |
| R7 | Circular Oval | 34 | 8.8 | 0.8 | 160.5 | 2.0 |
| R8 | Round | 14.7 | 14.8 | 3.8 | 160.5 | 2.0 |
| R9 | Circular Oval | 20.1 | 8.5 | 3.5 | 160.5 | 2.0 |
| R10 | Round | 11.3 | 12.0 | 4.0 | 160.5 | 2.0 |
| F1 | Circular Oval | 15.6 | 8.1 | 2.3 | 107.5 | 7.8 |
| F2 | Round | 10.1 | 10.0 | 1.5 | 107.5 | 9.3 |
| F3 | Circular Oval | 12.8 | 6.2 | 2.0 | 107.5 | 12.1 |
| F4 | Round | 8.1 | 8.0 | 1.5 | 85.0 | 15.8 |
The distance between the reversing mill and the first finishing stand is 4.5 meters, and the distance between the single
finishing stands is 1.5 meters.
Drawings of the grooves are available when contacting the International Center for Groove Pass Design
using kalibrierzentrum@imf.tu-freiberg.de.
The presented pass schedule is used to roll a 48 millimeter (cold) round profile made from C45 to an 8-millimeter round profile.
The measurements are given in a cold state.
As already mentioned, the Initial Profile is a 48 mm round profile made from C45. Additional parameters represented in SI-Units can be seen in the following table:
| Material | C45 |
|---|---|
| Diameter | 50e-3 [m] (warm) |
| Temperature | 1473.25 K |
| Density | 7500 [kg/m^3] |
| Specific Heat Capacity | 690 [J/K] |
| Thermal Conductivity | 23 [W/mK] |
Implementation in PyRolL:
in_profile = pr.Profile.round(
diameter=50e-3,
temperature=1200 + 273.15,
strain=0,
material=["C45", "steel"],
freiberg_flow_stress_coefficients=pr.FreibergFlowStressCoefficients(
a=2731.39 * 1e6,
m1=-0.00268,
m2=0.31076,
m3=0,
m4=-0.00056,
m5=0.00046,
m6=0,
m7=-0.98375,
m8=0.000139,
m9=0,
baseStrain=0.1,
baseStrainRate=0.1
),
density=7.5e3,
specific_heat_capacity=690,
thermal_conductivity=23
)REVERSING_PAUSE_DURATION = 6.1
sequence = pr.PassSequence([
pr.RollPass(
label="K 02/001 - 1",
roll=pr.Roll(
groove=pr.SwedishOvalGroove(
r1=6e-3,
r2=26e-3,
ground_width=38e-3,
usable_width=60e-3,
depth=7.25e-3
),
nominal_radius=321e-3 / 2,
rotational_frequency=0.99
),
gap=13.5e-3,
back_tension=0,
front_tension=0
),
pr.Transport(
label="I->II",
duration=REVERSING_PAUSE_DURATION
),
pr.RollPass(
label="K 05/001 - 2",
roll=pr.Roll(
groove=pr.RoundGroove(
r1=4e-3,
r2=18e-3,
depth=17.5e-3
),
nominal_radius=321e-3 / 2,
rotational_frequency=0.99
),
gap=1.5e-3,
back_tension=0,
front_tension=0
),
pr.Transport(
label="II->III",
duration=REVERSING_PAUSE_DURATION
),
pr.RollPass(
label="K 02/001 - 3",
roll=pr.Roll(
groove=pr.SwedishOvalGroove(
r1=6e-3,
r2=26e-3,
ground_width=38e-3,
usable_width=60e-3,
depth=7.25e-3
),
nominal_radius=321e-3 / 2,
rotational_frequency=1.98
),
gap=1.5e-3,
back_tension=0,
front_tension=0
),
pr.Transport(
label="III->IV",
duration=REVERSING_PAUSE_DURATION
),
pr.RollPass(
label="K 05/002 - 4",
roll=pr.Roll(
groove=pr.RoundGroove(
r1=4e-3,
r2=13.5e-3,
depth=12.5e-3
),
nominal_radius=321e-3 / 2,
rotational_frequency=1.98
),
gap=1e-3,
back_tension=0,
front_tension=0
),
pr.Transport(
label="IV->V",
duration=REVERSING_PAUSE_DURATION
),
pr.RollPass(
label="K 03/001 - 5",
roll=pr.Roll(
groove=pr.CircularOvalGroove(
r1=6e-3,
r2=38e-3,
depth=4e-3
),
nominal_radius=321e-3 / 2,
rotational_frequency=1.98
),
gap=5.4e-3,
back_tension=0,
front_tension=0
),
pr.Transport(
label="V->VI",
duration=REVERSING_PAUSE_DURATION
),
pr.RollPass(
label="K 05/003 - 6",
roll=pr.Roll(
groove=pr.RoundGroove(
r1=3e-3,
r2=10e-3,
depth=9e-3
),
nominal_radius=321e-3 / 2,
rotational_frequency=1.98
),
gap=1.8e-3,
back_tension=0,
front_tension=0
),
pr.Transport(
label="VI->VII",
duration=REVERSING_PAUSE_DURATION
),
pr.RollPass(
label="K 03/001 - 7",
roll=pr.Roll(
groove=pr.CircularOvalGroove(
r1=6e-3,
r2=38e-3,
depth=4e-3
),
nominal_radius=321e-3 / 2,
rotational_frequency=1.98
),
gap=0.8e-3,
back_tension=0,
front_tension=0
),
pr.Transport(
label="VII->VIII",
duration=REVERSING_PAUSE_DURATION,
),
pr.RollPass(
label="K 05/004 - 8",
roll=pr.Roll(
groove=pr.RoundGroove(
r1=2e-3,
r2=7.5e-3,
depth=5.5e-3
),
nominal_radius=321e-3 / 2,
rotational_frequency=1.98
),
gap=3.8e-3,
back_tension=0,
front_tension=0
),
pr.Transport(
label="VIII->IX",
duration=REVERSING_PAUSE_DURATION
),
pr.RollPass(
label="K 03/002 - 9",
roll=pr.Roll(
groove=pr.CircularOvalGroove(
r1=6e-3,
r2=21.2e-3,
depth=2.5e-3
),
nominal_radius=321e-3 / 2,
rotational_frequency=1.98
),
gap=3.5e-3,
back_tension=0,
front_tension=0
),
pr.Transport(
label="IX->X",
duration=REVERSING_PAUSE_DURATION
),
pr.RollPass(
label="K 05/005 - 10",
roll=pr.Roll(
groove=pr.RoundGroove(
r1=0.5e-3,
r2=6e-3,
depth=4e-3
),
nominal_radius=321e-3 / 2,
rotational_frequency=1.98
),
gap=4e-3,
back_tension=0,
front_tension=0
),
pr.Transport(
label="->F1",
duration=REVERSING_PAUSE_DURATION
),
pr.RollPass(
label="F1 - K 3/50",
roll=pr.Roll(
groove=pr.CircularOvalGroove(
r1=2.5e-3,
usable_width=15.6e-3,
depth=(8.1e-3 - 2.3e-3) / 2,
),
nominal_radius=215e-3 / 2,
rotational_frequency=11.5
),
gap=2.3e-3,
back_tension=0,
front_tension=0
),
pr.Transport(
label="F1->F2",
duration=1.5 / 7.8
),
pr.RollPass(
label="F2 - K 9/24",
roll=pr.Roll(
groove=pr.RoundGroove(
r1=0.5e-3,
r2=5.1e-3,
depth=(10e-3 - 1.5e-3) / 2
),
nominal_radius=215e-3 / 2,
rotational_frequency=13.77,
),
gap=1.5e-3,
back_tension=0,
front_tension=0
),
pr.Transport(
label="F2->F3",
duration=1.5 / 9.3
),
pr.RollPass(
label="F3 - K3/51",
roll=pr.Roll(
groove=pr.CircularOvalGroove(
r1=2.5e-3,
usable_width=12.8e-3,
depth=(6.2e-3 - 1.96e-3) / 2,
),
nominal_radius=215e-3 / 2,
rotational_frequency=17.85,
),
gap=1.96e-3,
back_tension=0,
front_tension=0
),
pr.Transport(
label="F3->F4",
duration=1.5 / 12.06,
),
pr.RollPass(
label="F4 - K 9/23",
roll=pr.Roll(
groove=pr.RoundGroove(
r1=0.5e-3,
r2=4.1e-3,
depth=(8e-3 - 1.5e-3) / 2
),
nominal_radius=170e-3 / 2,
rotational_frequency=29.5,
),
gap=1.5e-3,
back_tension=0,
front_tension=0
)
])