Extruded rope diameter measurement with machine vision

An extruder pushes out rope at line speed and the PLC needs the live diameter, not a lab report. The classic tool for that job is a laser micrometer; a smart camera or vision sensor does the same work with one backlit image per trigger and hands the controller a switched pass/fail line plus a 0-10 V or 4-20 mA value it scales directly. This guide gives the decision by tolerance, the optics math (field of view, pixel size, focal length), the lighting and strobe numbers for a moving rope, the PLC signal scaling, and the cases where a micrometer or a line scan camera wins. The worked example: 8 mm rope, ±0.05 mm tolerance, 60 m/min.

The decision, up front

Backlight the rope and measure the silhouette. That one choice does most of the work: both edges carry the measurement, surface gloss and color drop out, and subpixel edge detection holds about 1/1000 of the field of view in production — 25 µm on a 25 mm field.

The LS-SMC-0063 is the shape of the simplest build: a 1.6 MP, 60 fps smart camera with a 16 mm lens and polarized white light including a transparent-light mode for backlit parts.

From there, buy by tolerance:

• ±0.1 mm or looser: an integrated smart camera with its own backlight, switched and analog outputs to the PLC.
• ±0.02 to ±0.05 mm: a mono smart camera behind a telecentric or fixed-magnification lens from the machine vision lenses range, calibrated with pin gauges.
• Tighter than ±0.02 mm, or every millimetre of length: a laser micrometer or a line scan camera with an encoder. Area cameras sample; those two do not miss.

Overhead mounting reads one axis. Drawn rope is rarely perfectly round, so plan a second sensor at 90° when ovality is a specified characteristic. The smart cameras finder carries both integrated-lens sensors and C-mount models.

What one pixel is worth

Two numbers set the whole gauge: pixels across the sensor, and the field of view they cover.

A backlit edge localizes to about 1/10 of a pixel with ordinary subpixel interpolation. A 1.6 MP-class sensor puts roughly 1,600 pixels across a 25 mm field: 15.6 µm per object pixel, and about 2 µm of algorithm repeatability on the diameter. Production never sees that number, because rope wander, lens distortion, backlight drift and scale calibration all consume margin. Budget 1/1000 of the field of view for a calibrated gauge and treat anything better as headroom. Object space pixel size from magnification derives the same relationship from the magnification side.

Run mono if the choice exists: the Bayer mosaic on a color sensor subsamples the edge and gives away contrast. The HK-TD032-12-WBN is a 1.6 MP mono vision sensor with a global shutter and an M12 lens.

Worked example: 8 mm rope at ±0.05 mm

1. Spec: 8 mm nominal, ±0.05 mm tolerance, line speed 60 m/min = 1 m/s.
2. Field of view = 3 × 8 = 24 mm; build 25 mm. The ×3 rule leaves ±8.5 mm of wander window around the rope.
3. With about 1,600 pixels across: 25 mm ÷ 1,600 = 15.6 µm per object pixel.
4. Two edges at 1/10 pixel each: 1.6 µm per edge, √2 combined ≈ 2.3 µm of algorithm repeatability.
5. Production budget at 1/1000 of field: 25 µm. That meets ±0.05 mm with 2:1 margin.
6. Calibrate with three pin gauges — 7.000, 8.000 and 9.000 mm — to set the scale and expose lens linearity error.

Decision: an integrated vision sensor holds ±0.05 mm on this part with room to spare. Go telecentric when the tolerance halves, not before.

Lens: focal length, coverage, telecentric

Standard lens first. With a 7.2 mm-wide 1/1.8" sensor covering a 25 mm field, magnification m = 7.2 / 25 = 0.288.

At a 200 mm working distance, f = 200 × 0.288 / 1.288 ≈ 45 mm. Mount the nearest standard focal length, 50 mm, and solve backwards for the working distance: 50 × 1.288 / 0.288 ≈ 224 mm.

Before resolution, check coverage: the image circle must span the sensor diagonal, the question lens sensor format explained settles. The lens finder filters by format, mount and resolution band.

Now the error that motivates telecentric. A standard lens scales with distance: at that 224 mm working distance, a 3 mm wander toward the camera shifts magnification by 3 / (224 − 50) ≈ 1.7 %, so the 8.00 mm rope reads 8.14 mm — nearly 3× the tolerance, with no real change in diameter. A fixed-magnification (object-side telecentric) lens holds scale through millimetres of wander and brings distortion down with it. Read when you need a telecentric lens for gauging for the full argument, and telecentric depth of field: validate measurement accuracy before trusting the stated range.

For the telecentric route, pair a C-mount smart camera with a fixed-magnification lens. The LS-SMC-0017 is an 8.8 MP smart camera with a C-mount, a 1" sensor and a global shutter, in color or mono. The LS-TCL-0574 is a 0.4x fixed-magnification C-mount lens with a 227 mm working distance and a 1.2" image circle.

At 0.4x, a 12.8 mm-wide sensor sees a 12.8 / 0.4 = 32 mm field, and 3,200 pixels across put the object pixel at 10 µm. With a stable bracket and calibration, 10-15 µm repeatability holds — half the integrated-sensor number. On the standard-lens wide route, the LS-FFL-0602 is an 8.5 mm, 1", 10 MP C-mount lens that matches a 1" sensor.

Lighting: make the rope a silhouette

Light behind the rope, camera in front — machine vision lighting angles: surface or silhouette? covers why the silhouette wins for edges. The geometry adds the one number that matters: edge gradient. A diffuse backlight spreads light over tens of degrees; take ±20° as typical, and the silhouette softens over roughly gap × tan(20°) ≈ 0.36 × gap. At 20 mm of clearance between rope and light that is a 7 mm grey band, useless next to 1.6 µm edges. Keep the rope within a few millimetres of the panel where access allows, or specify a collimated backlight, which holds the edge transition on the order of 10 µm at any workable gap.

Lock the exposure. A backlit scene plus auto exposure is a drift generator: the loop chases brightness as the rope wanders or a splice passes, and the edge walks with it. Fix exposure and gain, strobe the light, and the scene is identical frame to frame — the failure mode behind auto exposure ROI instability.

Clear and translucent rope refracts the beam instead of blocking it, so you read a bright core with dark boundary bands; cross-polarizing cleans the internal scatter. The refraction and polarization handling for measuring clear extruded polymer width is close enough to rope work to read before specifying the light.

For the light itself, a light controller with constant-current outputs gives a dimmable steady level and clean strobe edges. The LS-CTL-0180 is a 4-channel constant-current controller rated 120 W, sized for 24 V lights. When the PLC should own the strobe timing over a serial line, the LS-CTL-0070 is a 4-channel, 200 W digital control box with strobe output and RS-232. Match the pulse duty to the light's rating as covered in LED strobe duty cycle: matching lights and controllers.

Line speed, strobe width and sampling

At 1 m/s: a 1 ms exposure smears 1,000 µm, 100 µs smears 100 µm, a 20 µs strobe smears 20 µm. Set the pulse from the tolerance — exposure ≤ tolerance ÷ line speed — so 0.05 mm at 1 m/s sets 50 µs, with the backlight overdriven to keep brightness at that width. High speed barcode verification: size the strobe pulse shows the same arithmetic on LED current and pulse width; exposure time vs shutter speed for moving-part inspection covers the full blur story, including why travel direction matters under an overhead camera.

Sampling is the honest limit of an area camera. Spacing between measurements = line speed ÷ frame rate: 1 m/s at 60 fps is one measurement per 16.7 mm, and anything shorter can pass unread between frames. When the spec says every millimetre, you need 1,000 profiles per second — line scan camera plus encoder territory (line scan camera field of view: how to calculate it) or a laser micrometer.

Wiring the result to the PLC

Three paths; use them together:

• Switched lines: opto-isolated outputs for undersize, oversize and sensor-fault, wired straight to digital inputs.
• Analog: 0-10 V inside a panel, 4-20 mA for longer runs or cabinets near drives.
• Ethernet: measurement and image for logging and trending, while the hardwired lines stay the control path.

Scale the analog span to the tolerance band, not the field of view, so the resolution lands where the spec lives. Mapping 6-10 mm onto 4-20 mA: 4 mm of span over 16 mA = 0.25 mm per mA, and a 7.60 mm rope reads 4 + (7.60 − 6.00) / 0.25 = 10.4 mA at the input card. For wiring, addressing and tags from the controller side, start with getting started with machine vision for PLC programmers.

Vision sensor, telecentric camera or laser micrometer

For extruded rope at ±0.05 mm or wider, buy the integrated smart camera and backlight: simplest mount, fewest parts, and a signal path the PLC already understands. Between ±0.02 and ±0.05 mm, the telecentric pair pays for itself in scrap avoided. Below ±0.02 mm, or with a mandate to see 100% of the length, the laser micrometer is the right tool and the camera is not.

Checks before you order

• Log the rope's centre wander for ten minutes; the field of view must exceed diameter plus twice the peak excursion.
• Order pin gauges at nominal −1, nominal and nominal +1 mm, and calibrate at running temperature.
• Add the 90° second sensor if ovality is specified.
• Confirm global shutter when strobing.
• Mount after the cooling trough; vision sensor housings are commonly rated to 50 °C.
• If the line is washed down, settle the housing question — NEMA 4X versus IP66 ratings — before the bracket is cut.
• Size the backlight with margin for wander, and specify collimation when the gap exceeds about 10 mm.
• Leave one spare switched output and one spare controller channel.

When a vision sensor is the wrong tool

Below ±0.02 mm, buy the laser micrometer: single-digit-micrometre repeatability and kHz-rate sampling are its home ground, and round product is exactly what two-axis scanner heads were built for.

Measuring in the hot zone before cooling buys feedback speed at the price of thermal drift and haze; at the trough exit the diameter is stable and the reading means something. And when wander outruns the field of view, fix the guiding first — widening the field only spends resolution you already committed to the tolerance.

Next step: size the rest of the cell — camera, lens, backlight, controller and stand — in the configurator, or bring the line drawing to the applications desk and we will spec it with you.