Engineering question
How is negative strip time calculated for sinusoidal mould oscillation, and which stroke and speed conventions cause the most errors?
Negative strip occurs during the part of a mould-oscillation cycle in which the downward mould velocity exceeds the downward casting speed. It is commonly discussed with oscillation marks, lubrication and shell behaviour, but a kinematic calculation alone does not prescribe safe or optimum casting practice.
The calculation is especially sensitive to unit and stroke definitions. This guide uses full peak-to-peak stroke S, frequency in cycles per minute converted to hertz, and casting speed converted to the same velocity units as the differentiated sinusoidal mould motion.
Calculation basis
Formulas and units
Frequency
f(Hz) = frequency(CPM) / 60
Cycles per minute cannot be inserted directly into an equation expressed in seconds.
Sinusoidal displacement and maximum velocity
x(t) = (S/2) sin(2πft); vmax = πfS
S is the full peak-to-peak stroke in metres.
Negative strip interval per cycle
tN = cos⁻¹[vc/(πfS)] / (πf)
The interval exists only when casting speed vc is less than the maximum downward mould speed.
Worked example
Apply the formula
Full stroke 6 mm, frequency 180 cpm and casting speed 1.2 m/min.
- 1f = 180/60 = 3 Hz; S = 0.006 m; vc = 1.2/60 = 0.02 m/s.
- 2vmax = π × 3 × 0.006 = 0.05655 m/s = 3.393 m/min.
- 3tN = cos⁻¹(0.02/0.05655)/(π × 3) ≈ 0.1283 s.
- 4Cycle time = 1/3 = 0.3333 s; negative strip fraction ≈ 38.5%.
Result: The analytical sinusoidal interval is about 0.128 s per cycle. It is not a recommendation for process settings.
Open Negative Strip Time CalculatorInterpretation in a control system
The PLC or motion controller may generate a sinusoidal reference, a modified waveform or a hydraulic/servo command whose actual motion differs from the reference. A kinematic screen should therefore be paired with position/velocity feedback, waveform definition, actuator performance and timestamped casting-speed data.
- Confirm whether the HMI stroke entry is full stroke or amplitude.
- Confirm whether frequency is CPM, Hz or a controller-specific unit.
- Trend actual mould position when suitable feedback exists.
- Keep formula version and approved settings under change control.
Engineering boundary
Negative strip time is one descriptor of mould motion. Final practice also depends on section size, steel grade, flux/lubrication, mould taper, cooling, withdrawal, oscillator mechanics and plant operating experience. Elexorn's calculator is a transparent reference tool and remains under named steel-process review.
Common mistakes
- Using amplitude where the equation expects full stroke
- Mixing CPM, Hz, m/min and m/s
- Using an unverified legacy subtractive formula
- Treating the analytical result as a process setpoint
Troubleshooting checks
- Unexpectedly large value: verify CPM-to-Hz and full-stroke convention.
- No negative interval: confirm whether casting speed exceeds calculated maximum mould speed.
- Calculated and observed motion differ: compare actual position feedback with reference waveform.
- Different tools disagree: normalize units and write each tool's displacement convention explicitly.
Assumptions
- Sinusoidal reference motion
- Full peak-to-peak stroke
- Constant casting speed during one cycle
- Ideal tracking of commanded motion
Limitations
- Does not model nonsinusoidal or asymmetric waveforms
- Does not include servo tracking error or mechanical compliance
- Does not set metallurgical practice or guarantee surface quality
Topic cluster