Summary: A belt answers to two different angular errors, and the published tolerance tables do not tell you which one you are reading. A skewed idler steers the belt at a drift rate equal to the belt speed times the tangent of the skew angle, so one degree of skew at 2 m per s moves the belt edge 34.9 mm per s, and the one degree squareness allowances that appear in the installation standards cannot be tracking limits. A cross level error instead shifts the belt through gravity to a new equilibrium, bounded by the superelevation tolerance of the belt width over 600, which is 1.67 mrad on every belt width. Of the whole published table only the level family is readable by a tilt channel, because every plan rotation, including the idler skew that does the steering, leaves both tilt axes unchanged. Settlement adds a third chain that the channel does read: differential settlement between idler stations becomes a local vertical curve, and once it exceeds gravity times the belt mass times the spacing squared over twice the tension the belt lifts off the idlers and the steering is lost.

1. The Two Ways an Angle Moves a Belt

A belt conveyor is the first structure in this series whose alignment error does not stay where it is made. The belt runs over idlers and pulleys, and the opening fact of the whole subject is stated in the consulting literature on misalignment: the belt moves in a perpendicular direction to the idler rolls and pulleys it is running on. An idler that is not square to the belt line is therefore not a support with a defect, it is a steering input. The belt leaves that roll travelling perpendicular to it, which is to say sideways relative to the conveyor, and it moves toward the end of the roll it meets first.

The kinematics of that steering are published in the mathematical modelling literature on belt tracking. For a belt approaching a roll under an entry angle alpha, the transverse belt velocity is the belt velocity times the tangent of alpha, and for the small angles involved the tangent is the angle itself in radians. The entry angle is affected by roller to roller misalignment, roller shape, belt tension and the belt deformation between rolls, and the models exist precisely because the entry angle is not simply the angle you would measure on the frame. But the relation itself is exact and unforgiving: an angle in the plan of the conveyor becomes a velocity of the belt, in metres per second of sideways travel per metre per second of belt speed, with no threshold and no equilibrium.

The second way an angle moves a belt is different in kind. Rotate the structure about the axis of belt travel, so that one stringer is lower than the other, and the belt and the material on it respond to gravity. The tracking literature describes the mechanism: the mass of the belt and the bulk material seeks the lowest available potential energy, the belt twists in the trough, and the whole belt shifts toward the low side. This is a force equilibrium, not a rate. The belt shifts, the trough geometry and the friction on the rolls build up a restoring effect, and the belt comes to rest in a new position. Nothing accumulates while nobody watches.

So the two families are a velocity and a position. A velocity is harmless for a stopped conveyor and unbounded for a running one, and it never stops itself. A position shift is bounded by the mechanics of the trough and it arrives complete. Every alignment figure ever published for a conveyor belongs to one of these two families or to a component that does not steer the belt at all, and the millimetre in which the figure is printed does not say which. Sorting the table is therefore the first job, and the sorting that worked for the crane runway article, where the blind items were positions and the readable ones were slopes, does not work here, because the plan family contains slopes too. The sort has to run on the axis of the rotation, not on the units of the number.

2. The Ladder of Published Figures, Converted

Three documents carry the numbers, and they agree in structure while differing in almost every value. The CEMA Conveyor Installation Standards, published also as Appendix D of Belt Conveyors for Bulk Materials, gives the stringer and idler erection family, and its figures are reproduced consistently in industry installation texts and in a consultants’ note on misalignment. The Indian steel plant acceptance norms IPSS 2-03-010-97, published as a free document by the Steel Authority of India, gives pulley, idler and take-up tolerances for commissioning. The Chinese national standard GB/T 10595 gives a third set, which circulates through industry sources rather than as a free text, so its figures should be confirmed against the specified edition before they enter an acceptance. The conversion into slopes is the only way the three can be read together.

The spread from the tightest tolerance to the loosest is seventy times, with the belt sag row excluded because it is a design figure built in on purpose rather than a tolerance, and that spread is wider than any single structure in this series has shown. But the pattern is the finding. Every loose rung is a plan angle: the idler squareness allowance of one degree, the take-up squareness of one degree, and the idler perpendicularity figure of one degree that circulates in the Chinese installation guidance. Every tight rung is a slope in the vertical plane: the stringer straightness of 0.25 mrad, the levelness of 0.5 mrad, the superelevation of 1.67 mrad, the adjacent idler vertical figures. The table is not one ladder of increasing care. It is two families printed side by side, one of which steers the belt through the running geometry and one of which moves it through gravity to a stop, and the loosest numbers in it belong to the steering family.

The superelevation rule deserves its own paragraph, because it is the pile article’s taper wearing different clothes. The tolerance is written as the belt width over 600, so the denominator is the object itself, and the consequence is exactly the one the pile article derived: the absolute offset grows with the width, 1.33 mm on an 800 mm belt, 2.0 mm on a 1200 mm belt and 3.33 mm on a 2000 mm one, while the slope stays constant at 1.67 mrad for every belt ever built. A schedule of cross level readings carries no information until the belt widths are beside it, and a conversion performed at one width is wrong at another.

One caveat belongs in this section rather than in a footnote, because it is the standard’s own. The CEMA installation text states that these tolerances are guidelines to facilitate proper idler and belt alignment, and that the overriding issue is idler and belt alignment as opposed to structural alignment. The structure numbers are means. The end is where the belt runs, and the next section shows why the loosest numbers in the table cannot be the end.

3. Why the Loosest Numbers Cannot Be Tracking Limits

Take the drift relation literally for a moment and price every rung of the ladder in the only unit that matters to a running belt, which is how fast the edge approaches the structure. The table below uses a belt speed of 2 m per s, an edge allowance of 50 mm from the belt edge to the trip zone, and one revolution of a 150 m conveyor, which is a 300 m loop and 150 seconds of running. The relation is the published one, the lateral velocity is the belt speed times the tangent of the entry angle, and it is stated here as the no slip upper bound, because the real entry angle differs from the frame angle and the self centering hardware opposes the drift.

Read the last row twice, because it is the whole argument. The tightest published slope in the entire table, the stringer straightness of 3 mm in 12 m, produces seventy five millimetres of sideways travel in a single revolution of a modest conveyor, if nothing opposes it. At five metres per second, which is an ordinary overland speed, one degree of skew is 87 mm per s. There is no figure in any of the three documents at which a belt would sit quietly inside its allowance for one revolution. A conveyor that runs centered does not run centered because its geometry is inside tolerance.

It runs centered because the geometry is opposed. Crowned pulleys, the trough itself, the self centering weight of the load and the training idlers supply a restoring steering input on every revolution, and the belt sits at the point where the sum of the steering inputs and the sum of the restoring inputs cancel. That is a dynamic equilibrium, and the published tolerances are the bound on the disturbance that the centering hardware has to absorb, not a window the belt is held inside. The correct reading of the table is the opposite of the naive one: the tighter the structure is built, the less work the centering hardware has to do, and the tolerance is a budget for the restoring hardware, not a margin for the belt.

The one degree figures now make sense, and their name is the finding. Idlers are mounted with bolts in the slotted holes of their brackets, and the commissioning process deliberately skews them to steer the belt onto the centre line. A component that is meant to be rotated during commissioning cannot carry a tolerance of a fraction of a milliradian, so the standard gives it a degree, which is a range the slot can deliver, and hands the tracking job to the adjustment rather than to the erection. The same logic explains the take-up: the take-up pulley exists to move, so its squareness gets a degree while every fixed component gets millimetres. The loosest numbers in the table are assembly allowances, and the industry’s own cure for mistracking is the same quantity as the disease, because a training idler is an idler skewed on purpose.

The honest correction to the arithmetic in the table is the one the modelling literature insists on, and it should be stated rather than hidden. The entry angle is not the frame angle. Belt tension stretches the belt longitudinally, the belt deforms between rolls, and the angle at which the belt actually meets the roll differs from the angle at which the roll sits on the frame. The drift rates above are upper bounds, reached when nothing deforms and nothing centers, and a real conveyor sits below them by the amount the equilibrium absorbs. What survives the correction is the structure of the argument: the plan angle enters the problem as a velocity, the velocity has no equilibrium of its own, and the equilibrium that holds the belt is maintained by hardware that must be allowed to work.

4. The Equilibrium Side: Cross Level and Gravity

The cross level family is weaker, and the weakness is worth a number. At exactly the superelevation tolerance, one stringer higher than the other by the belt width over 600, the lateral component of gravity on the belt is the tangent of 1.67 mrad, which is 0.17 percent of the weight of the belt and everything on it. A belt resting on a steel roll has a friction coefficient of the order of 0.3 to 0.5, so the belt does not slide on a flat roll at the tolerance or at a hundred times it. The drift mechanism on the tilted side is not sliding. It is the trough and the belt twist: the mass seeks the low point, the belt shifts within the trough until the geometry builds a restoring effect, and it stops.

That is why no published document gives a drift threshold for cross level, and why none is needed. A threshold is a property of a mechanism that runs away, and this one runs to a position and stops. What the documents publish instead are erection limits, the level tolerance of plus or minus 3 mm between the two idler support members in the CEMA text and the width over 600 in the stringer practice, which are the same family at slightly different figures, 2.5 mrad against 1.67 mrad on a 1200 mm belt. The CEMA figure is absolute and therefore looser as a slope on a narrow belt and tighter on a wide one, at 3.75 mrad on an 800 mm belt, which is another instance of the rule from the pile article: convert at the width in use before comparing anything.

For monitoring, the two families ask for two different instruments. A cross level error is meaningful as a level, because the equilibrium displacement of the belt grows with it and holds steady, so a reading of the level is a reading of a state. A skew error is not meaningful as a level at all, because the consequence of a skew is a rate, and a stopped conveyor hides it while a running one spends it. The practical sentence is that a cross level channel supports a threshold and a skew does not, and that a tilt channel is on the cross level side of that divide from the moment it is mounted.

5. What a Tilt Channel Reads on a Conveyor, and What It Cannot

Sort the published table by the axis of the rotation rather than by the units, and the result settles the scope question in one pass. A tilt channel reads rotations about horizontal axes: the cross level, which is the rotation about the line of travel, and the grade, which is the rotation about the transverse axis. A rotation about the vertical axis is invisible to it, because gravity does not change when a structure yaws, and every plan quantity in the table is a rotation about the vertical axis or a position in the plan. The table below is the whole sort.

The first row is the refinement this family adds to the sorting rule from the crane runway article. The stringer straightness of 3 mm in 12 m is a slope, 0.25 mrad, and on the runway the slopes were the readable subset. Here it is plan, and it is as unreadable as any position in the plan. A tilt channel does not sort the world into slopes and positions, it sorts it into rotations about horizontal axes and everything else, and a slope in the plan belongs to everything else. An article or a specification that converts the whole table into angles without performing this second sort will claim a scope it does not have.

What remains is still a real scope, and it is the one settlement actually attacks. The cross level and the grade of the stringers are the vertical geometry of the structure, and they are exactly the quantities that foundation movement, gallery deflection and differential settlement change over the life of the conveyor. The instrument on a conveyor is a structure instrument, not a steering geometry instrument, and the honest specification says so in the first line rather than being discovered saying something else in the last.

The outcome, where the belt actually runs, belongs to a different device, and the industry has already built it. The misalignment switch is mounted at the belt edge with its roller set about 20 mm out from the edge, it actuates when the wander exceeds about 20 mm, and it is built in two stages, an alarm at the first contact point and a trip at the second, with the roller arm angles at 20 and 35 degrees. Chinese field practice sets the alarm offset by belt width, 30 to 50 mm below 800 mm, 50 to 80 mm from 800 to 1400 mm, and 80 to 120 mm on wide or fast conveyors, which is an explicit trade of sensitivity against nuisance tripping. The division of labour on a conveyor is three way: the switch watches the belt, the tilt channel watches the structure, and the plan survey owns everything in the horizontal plane.

One mounting rule follows from the commissioning process itself. The sensor belongs on the stringer, not on the idler frame. The idlers are the adjustable element, the bolts sit in slotted holes, and the tracking process skews them on purpose, so a datum bolted to an idler frame is a datum that the tracking crew moves by design. The stringer is the element the standard tolerances are written for, it is the element the settlement acts on, and it is the element nobody adjusts after handover.

6. The Grade Side: Settlement, the Vertical Curve and Belt Lift

The grade channel earns its place through one chain of consequences that starts at a quantity it can read and ends at a tracking symptom. A support settles. The stringer follows, because the installation texts require the support structure to be mounted on stable foundations that will not shift under the design loads, which is a requirement the ground does not always honour. The belt path between the neighbouring idler stations acquires a local vertical curve, and the question is when that curve takes the belt off the rolls.

The criterion is classical mechanics and it closes in three lines. The belt under tension runs as a straight chord between its contact points, and it stays on a low idler only if its own weight bends it down by at least the settlement offset over the span between the untouched neighbours. Write the tension as T, the belt and load mass per metre as m, and the idler spacing as a, and the belt lifts off when the settlement exceeds g times m times a squared over twice T, where g is 9.81 m per second squared. The same statement as a radius is that the local curve of the path, a squared over twice the settlement, falls below the gravity radius, the tension over g times m, and both forms are the standard concave curve reasoning that the design stage performs once on the drawn profile.

The numbers move in the direction intuition does not expect, and the direction is the useful part. Tighter belts lift sooner, and lighter belts lift sooner, so the vulnerable conveyor is the one that is heavily tensioned and running light, which is exactly the empty return after a shutdown or the low load condition after a feed cut. On a 30 kN belt carrying 50 kg per m at 1.2 m spacing, the threshold is 11.8 mm of differential settlement, and doubling the tension to 60 kN cuts it to 5.9 mm. As a slope between the neighbouring stations, 11.8 mm over 2.4 m is 4.9 mrad, or 0.281 deg, which is more than fifty times the 0.005 deg accuracy of the instrument and more than two hundred and eighty times its resolution. The event is loudly readable before it happens.

The published relatives put the threshold in proportion. The joint alignment limit in the stringer practice is 3 mm, which is a quarter of the 30 kN threshold and most of the 60 kN one, so an as built conveyor inside its erection tolerance is already spending a serious fraction of the distance to belt lift. And the consulting literature states that concave radii should be calculated on the worn belt weight, because a lighter belt lifts sooner, which is the design stage acknowledging the same sensitivity that settlement exploits later. The design radius is computed once, on the profile as drawn. Settlement is the mechanism that moves the as built profile after the design is frozen, and it moves it exactly where the supports are.

What belt lift does when it happens is published in the first principles of the subject: a belt that is not in full contact with its idlers cannot be steered by them, and loss of contact is listed among the root causes of mistracking. So the chain is complete, and every link in it is checkable. Settlement at the support, a grade change between stations that a tilt channel reads as a fraction of a degree, a local vertical curve, the belt running as a chord above the low idler, the loss of steering at exactly the station that settled, and the mistracking that follows. It is the one consequence chain in the whole conveyor family that begins at a quantity a tilt channel reads, and it ends at the symptom the switch at the belt edge watches for.

7. The Datasheet Against the Readable Criterion

The instrument is the same dual axis RS485 unit the last two articles used, the ZCT2xxM-LBS-Ax-H5-460x, with a plus or minus 15 deg range, 0.005 to 0.01 deg accuracy, 0.001 deg resolution, a zero deviation of 0.05 deg, a zero temperature drift of 0.002 deg per degree Celsius typical and 0.13 deg maximum over the full working range, an IP67 seal and a minus 40 to plus 85 degrees Celsius working range. The criterion is the readable one, the superelevation of the belt width over 600, which is 0.0955 deg, and the ranking below sets the same datasheet against the crane runway cross level of 1.0 mrad and the pile taper of one percent for comparison.

The conveyor criterion sits between the runway and the pile, and the ranking lands between them in the same order, with the resolution and the accuracy comfortably inside, the zero deviation at half of the budget and the two drift figures at most of it and beyond it. The statement that follows is the one the crane runway article already established and this family re lands rather than re derives: on a criterion of the order of a milliradian the instrument is a comparator in time, permanently mounted, read against its own baseline with the temperature beside every reading, and the specification has to be written on zero stability because the accuracy line cannot decide anything. The conveyor adds one line to that result, which is the movement of the ranking itself. The last column of the table is the same five datasheet numbers against the pile criterion, and they land at 0.2 to 22.7 percent. Nothing on the datasheet changed between the columns. The criterion did, and it is the criterion that decides whether a specification term matters, which is the statement the pile article made and this table is the third confirmation of.

8. What to Specify

Name the document before quoting the number. The same quantity differs by nearly an order of magnitude across the three documents: the idler plan angle is 1.5 mrad in the steel plant acceptance norms and one degree in the CEMA erection text, and the level figures differ in kind, absolute in one and proportional to the belt width in another. The first act of specification is naming which document governs, and the second is confirming the edition, because the Chinese standard’s figures circulate through secondary sources that should be checked before an acceptance is written around them.

Sort by the axis of rotation, not by the units. Convert every figure into a slope and then sort the slopes into rotations about horizontal axes and everything else. The readable subset on a conveyor is the level family and the grade family, and the specification should say structure monitoring, not tracking monitoring, because the steering geometry lives in the plan and no tilt channel reaches it.

Mount on the stringer, not on the idler frame. The idlers are the adjustable element, mounted in slotted holes and deliberately skewed during commissioning. A datum bolted to an idler frame is a datum the tracking process moves on purpose, and the standard’s own instruction is that the idlers are the tool used to perform the tracking while the structure tolerances are the framework they work inside.

Alarm on the rate, and say why. This family publishes no operational doubling of the erection tolerances, unlike the crane runway standard, which doubles its vertical allowance from construction to service and thereby publishes a life budget. On a conveyor the only published service criterion is where the belt runs, which the switch watches, so the cause side signal has to be a trend, in millimetres of cross level per metre per year, and the specification should state the reasoning rather than leave the number looking arbitrary.

Keep the record the installation standard already asks for. The installation text requires that suitable records be kept of the installed misalignment values, which is a one time commissioning record on paper. A permanent channel produces that record continuously, with a clock and a temperature beside every line, and the commissioning survey becomes the first entry in it rather than a document that ages in a drawer.

Pair the channel with edge monitoring. The tilt channel sees the causes that live in the structure and the switch sees the belt. The plan survey owns the geometry that steers. A monitoring plan that contains only one of the three is answering one third of the question, and the failure that crosses the missing thirds is the one that looks like a mystery in the data afterwards.

Bound the lift threshold with the numbers actually in use. The belt lift threshold is the belt and load mass times the idler spacing squared over twice the tension, and without the tension and the mass per metre it is indicative only. A specification that sets a settlement alarm without those two numbers has set a number with no mechanism behind it, and the tension in particular moves the threshold by a factor of two across the ordinary range.

9. Limits

This article is an argument about geometry, standards and one datasheet, and its boundaries are the following. It is not a tracking survey and does not replace the plan survey that the steering geometry belongs to. It does not monitor the belt, the splices, the idler rolls or the condition of any component, and it does not measure belt tension, without which the lift threshold is indicative rather than exact. Readings taken while the conveyor runs carry the dynamic response of the structure, belt vibration and wind on an exposed gallery among them, so the cross level and grade trends should be read from stationary windows or with the running periods removed. The drift rates in section 3 are upper bounds from the published kinematic relation, not field measurements, and the real entry angle differs from the frame angle by the amount the belt deforms. No belt conveyor deployment is claimed here: the nearest published company work is warehouse racking, an indoor steel frame measured for plumb, which is a different structure measured for a different quantity. The arithmetic is reconstructed from public standards, published industry literature and classical mechanics, and where a figure depends on a document it is attributed to that document.

Frequently Asked Questions

1. Can a tilt sensor detect belt mistracking? No. The angle that steers the belt is a rotation about the vertical axis, the skew of an idler or a pulley in plan, and gravity does not change when a structure yaws, so no tilt channel sees it. What a tilt channel reads on a conveyor is the vertical geometry of the structure, the cross level and the grade, which drive the weaker gravity mechanism and the settlement chain. Where the belt actually runs is watched by the edge misalignment switch, and the plan geometry belongs to the survey.
2. Why is the idler squareness allowance one degree if one degree of skew moves a belt 35 mm per second? Because it is an erection allowance rather than a tracking limit. Idlers are mounted with bolts in slotted holes and are then skewed on purpose during commissioning to steer the belt onto the centre line, so the standard gives the adjustable component a range the slot can deliver. A belt runs centered as a dynamic equilibrium between the steering inputs and the restoring hardware, crowned pulleys, the trough and the training idlers, and the tolerances bound the disturbance that hardware absorbs. The drift relation is the no slip upper bound of what an unopposed angle would do.
3. How much differential settlement before the belt lifts off the idlers? The threshold is g times the belt and load mass per metre times the idler spacing squared, divided by twice the belt tension. On a conveyor tensioned to 30 kN carrying 50 kg per m at 1.2 m spacing that is 11.8 mm of differential settlement between the neighbours, and doubling the tension halves it to 5.9 mm. As a slope between the stations it is 0.281 deg, which the instrument reads many times over, and the chain continues from there, because a lifted belt is a belt the idler below it can no longer steer.
4. Which alignment figures should an acceptance cite? Whichever document the contract names, cited with the edition, because the three published sets disagree: one degree of idler squareness in the CEMA erection text against 1.5 mrad of idler angular misalignment in the steel plant acceptance norms, and an absolute level tolerance in one against a width proportional superelevation in another. The figures should be converted into slopes for comparison and then sorted by axis of rotation, so that the readable subset, the level and grade family, is specified as structure monitoring and the plan family is left to the survey that can actually see it.