Is weight-per-meter control worth the investment?

Weight-per-meter control saves material, but which three parts of the material does it save?

Ask ten suppliers how much material a weight-per-meter control system saves and you will get ten different answers, and most of them sound better than reality. The amount saved is not a fixed percentage: it is the sum of three independent sources, and each one depends on the data from your own line. A percentage handed to you by someone else may not hold at all once it is moved onto your annual output, your material price and your tolerance requirements. So separate the three accounts first.

Part one: weight per meter running heavy over the long term is the part that keeps flowing away

When weight per meter sits for a long time at a level above the reference value, it means a thousand meters of cable has used the material that nine hundred-odd meters should have used. This loss is quiet: no alarm, no out-of-tolerance, and inspection will not necessarily catch it either, because it is still inside the tolerance — it is simply running steadily along the upper deviation.

There are usually three sources. The reference value was set conservatively. Manual adjustment lags, and operators mostly fine-tune only once they see the weight running light, so on average it always comes out heavy. And once the screw and barrel wear, the extrusion output drifts and nobody re-calibrates it.

What the system does is pin the reference value down, so that the measured value holds onto it instead of drifting above it. The closed-loop control process decides whether that can be done consistently.

Part two: the target value raised to protect the lower limit is usually the biggest item

The drawing specifies a minimum for the insulation and the sheath, but what really governs production is the lower limit: any meter that falls below it is a non-conforming product, to be reworked or downgraded, at a cost far higher than using a little more material. So nobody dares to set the target value exactly at the lower limit.

Let the half-band of the weight-per-meter fluctuation during stable production be B. To guarantee that it never falls below the lower limit L at any moment, the target value must satisfy target value ≥ L + B. Put in terms of wall thickness it is the same thing, with one extra geometric conversion in between: against one set of on-site readings, weight per meter 0.1413 kg/m, reference wall thickness 1.650 mm, wire diameter 17.50 mm and material density 1.42 g/cm³ are locked to one another, so moving one moves the others, and wall thickness compensation 0.020 mm sits on that same chain.

The key is B. The larger B is, the higher the target value has to be raised, and that raised portion of material is given away: it is not a product requirement and not a process necessity, it is purely insurance bought against fluctuation. It acts on every meter of cable and every minute of production, unlike an occasional out-of-tolerance, which is only a scattered loss. The real bulk is usually this insurance.

One thing also has to be made clear: B is not entirely within the control system's power to compress. Mechanical fluctuation of the equipment, discontinuous feeding and the accuracy of temperature control all contribute, so the sources of the fluctuation have to be investigated first before it is even possible to judge how small a B the system can achieve.

Part three: the transition section at start-up and at a construction change

At start-up and at a construction change, weight per meter takes a while to travel from out of control to stable. Of the material produced in that stretch, the light part can only be scrapped, and the heavy part can be used but has already consumed extra material; the more tangible loss is time — the machine is running but producing no conforming product.

The value of the system here is to shorten the transition section: reference values are stored by construction, so at a construction change one press of "construction confirmation" switches to the reference value for the new construction, instead of feeling your way with trial runs and manual sample weighing. This gain saves machine hours rather than material, so it has to be listed as an item of its own and must not be folded into the material saving.

Payback on a weight-per-meter control system: variables, where they come from and the formulas

The calculation uses only a few variables. The formulas are not the awkward part; where the values come from is.

Annual material saving

annual material saving ≈ annual output × reduction ratio of the weight-per-meter target value × material price

The three factors must be on the same basis: if annual output is in weight, the material price is the price per kilogram; if it is in length, convert it first into a price per meter. The relationship between the reduction ratio and the band is the core of it — to protect the lower limit, the target value does not go below the lower limit plus the half-band, so the room for reduction is the difference between the band before installation and the band after it; if the band cannot be pushed down, the reduction ratio is zero.

The capacity gain from construction changes

annual capacity gain ≈ number of construction changes per year × time shortened per change × margin per machine hour

It shares no factor with the item above, so it must be calculated separately. How trustworthy it is depends on whether the time shortened really turns into output.

Payback period

payback period (years) = investment ÷ annual gain

The annual gain is the sum of the material saving and the capacity gain, and the investment also has to include the labour taken up by installation and modification, commissioning and training. The payback period has to be compared with the remaining service life of the line, not with a number of years that feels comfortable.

A purely arithmetic example: putting the assumed values in

Every figure below is an assumed value set for the purpose of demonstrating the arithmetic. It is not measured data, and it does not represent the actual level of any production line.

• Assume annual output Q = 1000 tonnes = 1 000 000 kg
• Assume an all-in material price P = 10 yuan/kg
• Assume the half-band before installation B₁ = 2.0% of the target value, and after installation B₂ = 0.8% of the target value

Step one: r = 2.0% - 0.8% = 1.2%. Step two: 1 000 000 kg × 1.2% × 10 yuan/kg = 12 000 kg × 10 yuan/kg = 120 000 yuan, that is about 120 000 yuan a year. Against a construction with a weight per meter of 0.1413 kg/m, 1.2% is equivalent to using about 0.0017 kg less per meter (0.1413 × 1.2% = 0.0016956): on a single meter it is negligible, but multiplied by a full year's output it is a six-figure sum.

Step three, the construction-change item calculated on its own: assume 200 construction changes a year and a transition shortened by 0.5 hour each time, which saves 100 machine hours a year. What those 100 hours are worth depends on the margin per machine hour; it is not filled in here, only noted as an independent additional item.

Step four, the payback period. Take the material-saving part as 120 000 yuan and the investment as I (in yuan): payback period (years) = I ÷ 120 000. This expression is more useful read backwards: if the acceptable payback period is 2 years, the case holds as long as the investment is below 240 000 yuan; if only 1 year is acceptable, the ceiling is 120 000 yuan. The critical investment equals the acceptable payback period multiplied by the annual gain, and has nothing to do with a supplier's quotation.

Cases where the value of a weight-per-meter control system is open to question

• The output is too small. The material saving is proportional to annual output, so if output falls by an order of magnitude the gain falls by an order of magnitude too, while the fixed costs of installation, commissioning and maintenance do not fall with it. Below a certain size, the payback period becomes longer than the remaining service life of the line.
• The material price is low and the weight-per-meter tolerance is itself wide. With either of the two missing there may still be a case to calculate; with both present at once there is basically nothing to calculate: a cheap material gives a small price factor, and a wide tolerance means the target value never had to leave much margin for the lower limit in the first place, so the reduction ratio is close to zero.
• The fluctuation comes mainly from downstream rather than from the total material used. The total weight per meter is steady, and the trouble lies in eccentricity or an uneven conductor dimension, so the thin side of the wall thickness still reaches the lower limit. The system measures the total material used per unit length, so it cannot suppress a distribution problem, and installing it does not solve the problem you started with.
• The line is about to be retired, or the process is changed substantially and often. A payback period is only meaningful if it is shorter than the remaining life of the equipment; and frequent major process changes also mean the reference value has to be set again and again, and the labour that takes is a cost as well.

The fifth case has to be put separately: the existing fluctuation is already very small, with a stable machine and an experienced shift team holding the band very narrow, so the room for reduction is close to zero. The order in which a selection is judged should look at the band first and at the accuracy specification second; the other way round, it is easy to pay for capability you will never use.

Before you do the calculation, measure a baseline once

Every gain estimate starts from the same number: with no system installed, how wide is the fluctuation band of the existing weight per meter? That number can only be measured, not estimated; without a baseline, the formulas above are just assumptions dressed up as conclusions.

The readings from the inline weight-per-meter measuring device are exactly the raw material for a baseline. Taking the stable section on site as the reference — screw speed 41.24 rpm, haul-off speed 60.013 m/min and extrusion output 508.70 kg/h — what the baseline has to record is how far these quantities, together with the weight per meter 0.1413 kg/m, swing along the time axis, not their instantaneous values.

1. Record continuously rather than sampling at intervals, and cover at least several complete shifts in the stable section, so that the differences between shift teams and between times of day enter the sample.
2. Count the start-up section and the stable section separately. The former swings far more, and mixing the two together computes the band too high and inflates the gain.
3. Count by construction, and state the basis of the statistics — half-band, standard deviation and range are three different quantities, and the same one has to be used before and after.

If the shop floor already has a weight-per-meter display unit that is simply not yet closed-loop, the "material usage statistics" on the interface give segmented data for each reel, denser than cutting samples by hand; "under automatic control" tells you whether the line is currently running closed-loop or manual, and the two have to be separated when the baseline is taken, otherwise the drift of the manual stretches gets charged to the equipment.

Frequently asked questions

Prices for weight-per-meter control systems vary quite a lot — does the price have anything to do with how much material is saved?

The link is indirect. The material saving is decided only by how narrow the band can be compressed, by the annual output and by the material price, and is unrelated to how much was spent; the price only affects the denominator of the payback period. The sensible order is to work out how much can be saved first, and then look at how large an investment that annual gain can carry.

How narrow does the fluctuation band have to be before it counts as narrow enough?

There is no universal answer; it depends on how much margin the lower limit has been given. The better question is: how far above the lower limit is the target value now, and how much of that is margin kept against fluctuation? That difference is the upper bound on the room for compression, and how far it can actually be compressed still depends on the equipment and the process conditions.

Can the material saved be treated directly as cash gain?

In most cases yes, because it is the same material that is being saved and purchases really do fall. Two situations call for a discount: the margin saved is eaten up by the next process step or by a customer requirement; or the plant is not running at full output, in which case the material saving shows up as a lower cost rather than as more cash.

Is a line with small batches and many constructions always a bad case?

Not necessarily. A small annual output does hold the first account down, but when construction changes are frequent the third account takes a clearly larger share of the total gain, and can even overtake the material saving. For this kind of line the calculation should focus on the transition section: how many construction changes a year, and how long each transition lasts.