Engineering question
How should a continuous casting machine convert encoder counts into billet length without hiding mechanical and timing errors inside one scale factor?
A common CCM arrangement uses a measuring roll in contact with the strand, an incremental encoder, a high-speed PLC counter and a length setpoint that initiates the shear or gas-cutting sequence. The arithmetic is simple; reliable measurement is not. Effective roll diameter, gearing, decoding mode, hot scale, slip, direction logic, counter capture and cutting delay all affect the final billet length.
A good implementation separates theoretical geometry from calibration and separates measured-length error from downstream cutting error. This makes troubleshooting possible: the team can decide whether the problem is in the encoder scale, the strand contact, the PLC capture event or the cutting machine response.
Calculation basis
Formulas and units
Counts per measuring-roll revolution
Croll = PPR × decode factor × encoder rev/roll rev
All terms must use the actual counter configuration and mechanical transmission ratio.
Theoretical linear scale
mm/count = π × Deffective / Croll
Use effective contact diameter, not only the nominal drawing diameter.
Target count
Ctarget = target length / (mm/count × calibration factor)
Define the calibration-factor convention once; this guide uses a multiplier on theoretical millimetres per count.
Worked example
Apply the formula
A 200 mm measuring roll drives a 1024 PPR encoder at 5 encoder revolutions per roll revolution, with X4 decoding and a 6000 mm target.
- 1Croll = 1024 × 4 × 5 = 20,480 counts.
- 2Roll circumference = π × 200 = 628.319 mm.
- 3Resolution = 628.319 / 20,480 = 0.03068 mm/count.
- 4Target count ≈ 6000 / 0.03068 = 195,570 counts.
Result: The theoretical target is about 195,570 counts. It must be verified with repeated physical measurements before production acceptance.
Open Encoder Length & Pulse CalculatorRecommended control architecture
- Encoder wired to a hardware high-speed counter with diagnostic access
- Signed count or direction state defined for casting and reverse/jog modes
- A captured count at the exact cut-command event
- Separate parameters for geometry, calibration and cut compensation
- Batch records containing target, measured count, command time and actual inspected length
Calibration method
Start with measured roll diameter and the documented PPR, decode and gear ratio. Run several billets at stable casting speed, measure cooled lengths using the agreed inspection method and compare the mean error. Apply a small calibration correction only after excluding slip and timing faults. Calibrating from a single billet can encode random shear response into the scale factor.
- Use several billets across the normal operating range.
- Record hot/cold measurement basis and thermal-shrinkage convention.
- Keep cut-delay compensation separate from scale calibration.
- Lock parameter changes behind authorization and record old/new values.
Common mistakes
- Using nominal diameter after resurfacing or wear
- Combining scale and shear-delay compensation
- Resetting the counter asynchronously during a capture
- Comparing hot target length with an undocumented cold measurement
Troubleshooting checks
- Constant percentage error: inspect circumference, PPR, decode and gear ratio.
- Constant millimetre offset: inspect command/capture point and cut delay.
- Error grows with casting speed: inspect response delay, slip and input-frequency margin.
- Random long/short billets: trend contact pressure, counter capture, shear-ready state and command timestamps.
Assumptions
- Measuring roll remains in positive contact with the strand
- Encoder ratio and counter mode are known
- Target and inspection length use an agreed temperature basis
Limitations
- Does not predict steel thermal shrinkage
- Does not model roller slip, runout or cutting-machine dynamics
- PLC scan-time calculations are insufficient when a hardware capture is required
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