Longitudinal thickness variations: what Fourier analysis reveals about rolls and bearings

The problem: visible in the complaint, invisible in the cross profile

Inline thickness measuring systems traverse across the web. They deliver an excellent cross profile, but in the machine direction only a sample: at each point across the width, the film is captured only every few meters. Variations with a period of a few decimeters – exactly the order of magnitude of a roll circumference – slip through this grid. The converter notices them nonetheless: as winding defects, as streaks in printing, as scrap in die-cutting.

Measuring: thickness over the film length

Longitudinal thickness measurement captures the film continuously at a fixed cross position over several meters of length, offline on a sample or inline with a stationary sensor. The resolution is decisive: it must be significantly finer than the smallest roll circumference in the line. At the same time, the diameters and rotational speeds of all rolls are recorded – from the calender through the take-off and cooling rolls to the winder.

Evaluating: Fourier analysis assigns the cause

Fourier analysis decomposes the measured thickness profile into its frequency components. In the case of run-out error, imbalance or bearing damage, each roll leaves behind a variation at its own rotational frequency – which can be calculated from web speed and roll diameter. A peak in the spectrum at exactly this frequency identifies the roll unambiguously. If multiples of the frequency also appear, this points to a local defect (impact mark, bearing damage) rather than uniform out-of-roundness.

Frequencies that do not match any roll lead to other causes: pulsating melt feed from the extruder or kneader, fluctuating temperature control, web tension controller in a limit cycle.

Acting: from measured value to maintenance

• Incipient bearing damage shows up in the spectrum long before it becomes audible or measurable as a temperature rise. The bearing replacement is scheduled for the next maintenance window.
• Run-out errors of individual rolls are quantified; this decides between regrinding and continuing to run.
• Complaints can be substantiated or refuted with the spectrum of the affected reel.

As a recurring inspection – for instance at every recipe or format change – longitudinal thickness measurement becomes an early warning system that needs no additional sensors on the bearings: the film itself is the sensor. Case study: Bearing damage detected before the roll failed.

Quick checklist, machine direction

1. Determine the period of the variation in meters – does it match a roll circumference?
2. Convert roll diameter and web speed into a frequency and compare with the spectrum.
3. Multiples of the fundamental frequency present? Then a local defect rather than out-of-roundness.
4. No roll frequency? Check melt feed, temperature control and web tension.
5. Rule out the measuring system itself: calibration, sensor distance, vibrations on the measuring frame.

The detailed list with characteristics and inspection steps: Checklist “12 causes of thickness variations”.