What a Worn Sheave Groove Does to a New Belt

Why this matters

The sheave is a wear part and almost nobody treats it as one. A belt gets replaced, the drive runs, and the belt gets replaced again sooner, and at no point does anyone put a gauge on the groove. The uncomfortable part is that a new belt in a worn groove does worse than the old belt did in the same groove, which reads as a defective belt and gets returned as one. The old belt had spent years wearing its own sidewalls into the shape of the groove it lived in. The new one has not, so it touches in a narrow band at the top of each flank and carries the entire load there. This is what a shop is buying when it replaces belts on a schedule and sheaves never.

Isolate before any of this, and do not pry

Lock out and tag the motor at its disconnect. A blower wheel holds rotational energy after the power is off, which is stored mechanical energy under 29 CFR 1910.147: verify zero rotation by eye and block the wheel or close and secure the damper before reaching past the guard. Slacken the drive fully to remove or fit a belt; prying one over a sheave rim with a screwdriver cuts the tensile cords and can snap the belt and the tool back at you. If a sheave has to come off a taper bushing, keep the puller square, stand out of the line of the screw, and wear eye protection meeting 29 CFR 1910.133, because a jaw that slips under load throws. Clear rubber dust with a HEPA-filtered vacuum rather than blowing it around; compressed air used for cleaning must be reduced below 30 psi with effective chip guarding and personal protective equipment under 29 CFR 1910.242(b), and blowing a bank of belt dust into the air of a small mechanical room is an inhalation exposure you created for no reason. The guard goes back on before restart under 29 CFR 1910.219 in general industry or 29 CFR 1926.300(b) on a construction site.

Three weeks, then three more

A rooftop unit's supply blower, single B-section belt, nominal driver pitch diameter 4.0 in, driven 10.0 in, motor nameplate 1750 rpm. Predicted blower speed is 1750 x 4.0 / 10.0 = 700 rpm.

The belt was replaced on a routine visit. Correct section, correct length, tensioned with a tester to the maker's new-belt figure, alignment checked with a straightedge. Three weeks later the unit squealed on start. The tech re-tensioned it. Three weeks after that it was squealing continuously and the sidewalls were glazed hard and visibly narrower than the spare in the truck.

One new belt finished in six weeks, on a drive that had been going a year at a time.

What the readings said

Speed. With the drive running, guard closed, optical tach from outside the plane of rotation: 681 rpm against a predicted 700, a shortfall of 19 rpm, or 2.7 percent.

Slip, ruled out. Locked out, chalk marks on both rims, blower sheave barred over ten revolutions by hand from the rim with fingers clear of the groove entry: the driver came to rest at 25.7 revolutions, an effective ratio of 2.57 against a geometric 2.50. The hand-barred ratio matched the running ratio, and the gap between geometry and running is where slip lives. There was none. The drive was turning slow because it was geometrically slow.

What that implies about the belt's position. Treating the driven sheave as true at 10.0 in, the driver's effective diameter is 10.0 / 2.57 = 3.89 in against a 4.0 in pitch diameter. That is a radial drop of (4.0 - 3.89) / 2 = 0.055 in, just under a sixteenth of an inch. Nothing anyone would see by eye, and it had already cost 2.7 percent of the airflow.

The groove. A groove gauge for the section, held against the flank with a light behind it, showed daylight at the top of each flank and contact at the bottom. The flanks had dished. On the belt itself, the polished band on each sidewall was a narrow stripe near the top edge rather than the full flank height.

The belt. Top width measured 0.60 in against 0.656 in for a new B section, a loss of 0.056 in in six weeks.

The arithmetic of a belt sinking into its own groove

A V-groove is a wedge, so losing width means sinking. For a groove of included angle 36 degrees, which is inside the range V-sheave makers commonly publish for this section and diameter and is the as-manufactured value rather than the worn one, the width lost per unit of radial drop is 2 x tan(18 degrees), or 0.65. So a 0.056 in width loss corresponds to a radial drop of 0.056 / 0.65 = 0.086 in, which takes another 0.172 in off the effective diameter.

That is a lower bound and it is worth saying why: the groove has dished, so the effective included angle at the contact band is larger than the as-manufactured 36 degrees, and a wider angle means more sinking for the same width lost. The real drop is somewhat worse than 0.086 in.

Carry it through. Effective driver diameter goes from 3.89 in to 3.89 - 0.172 = 3.72 in, and blower speed to 1750 x 3.72 / 10.0 = 651 rpm. Against the design 700 rpm that is 7.0 percent low, up from 2.7 percent six weeks earlier. The process runs away from itself: the deeper the belt sits, the narrower the contact band, the faster the belt wears, the deeper it sits.

What the wedge loses on the way down

The V-groove's whole contribution is that the flanks push back harder than the radial load, by a factor of 1 divided by the sine of the half angle, so a 36 degree groove multiplies the effective coefficient of friction by 1 / sin(18 degrees) = 3.24. That figure is for contact on both flanks at the as-manufactured angle. Two things erode it:

• The angle opens. If the contact band has dished out to an effective 42 degrees, the multiplier falls to 1 / sin(21 degrees) = 2.79, about 14 percent of the wedge gone. Modest on its own.
• The belt bottoms out. Once the belt touches the groove floor, the radial load is carried there instead of on the flanks and the wedge is not reduced, it is deleted. Effective friction falls back toward the bare coefficient, roughly a factor of three.

The pressure story is worse than the friction story. Contact pressure is normal force divided by contact area, so when the polished band shrinks to a third of the original flank engagement, the same load runs at three times the pressure. That is what glazes a new belt in weeks: not slip, not heat from the drive, but a contact stress the belt was never designed to carry on a stripe that narrow.

Why the second belt failed faster than the first

The belt that ran a year in that sheave had, over that year, worn its own sidewalls to match the dished flank. Contact was spread. It was slow, because it was riding low, and nobody had ever measured its speed to know.

The replacement arrived with straight, full-angle sidewalls into a groove that no longer had a straight flank to meet them. All of the load went through the top edge, and the belt cut itself down to the groove's shape at a rate set by contact pressure rather than by normal wear. Then it did what the first belt had done, only in weeks.

That is the whole trap: a worn groove is invisible while the belt in it is old, and announces itself only after a correct repair. The tech who replaces the belt is the one who gets blamed.

The fix, and the two fixes that are not fixes

The sheave was replaced and a new belt fitted at the same time, because a belt that has been running in a worn groove has been cut to that groove's profile and will not sit correctly in a new one.

Do not dress the groove. Filing or grinding a cast sheave to restore a flank cannot reproduce the section's angle and finish, and it releases respirable dust from the casting and whatever coating is on it. There is no version of this that ends with a groove inside tolerance.

Do not fit a larger section. A belt that sits proud of the rim contacts on its outer corners, which is a smaller contact band than the one you were trying to escape, and it will cut itself down to the same place.

How to verify you got this right

• Gauge the groove before you fit the belt, not after. A groove gauge for the section, held against the flank with light behind it: daylight at the top of the flank with contact at the bottom is a dished groove and the sheave is finished. The maker publishes the wear limit for the section, and that number is the gate.
• Check where the new belt sits. With correct tension and the drive locked out, the belt's top surface should sit flush with or slightly above the sheave rim. Below the rim on installation day means the groove is worn, the section is wrong, or both.
• Tach and compare. Run the drive with the guard closed, take the driven speed from outside the plane of rotation, and compare it with what the pitch diameters predict. A drive that reads 2 to 3 percent slow with no slip present is riding low, and that reading is available on every drive you ever touch.
• Check the other sheave too. Grooves wear on both ends and the small one usually wears first, because it carries the same load on less arc. Gauging one and not the other is half a check.
• Write the sheave's condition on the ticket. A groove that gauges near its limit today is next season's two-belts-in-six-weeks call, and a note now is what turns it into a planned sheave change instead of a warranty argument about belts.

References

• 29 CFR 1910.147 for mechanical isolation and stored rotational energy; 29 CFR 1910.219 (general industry) and 29 CFR 1926.300(b) (construction) for guarding of belts, pulleys and sheaves
• 29 CFR 1910.242(b) for the 30 psi limit and required chip guarding when compressed air is used for cleaning; 29 CFR 1910.133 for eye protection during puller work
• Sheave manufacturer engineering data for groove included angle by section and pitch diameter, published groove wear limits, and groove gauge use
• Belt manufacturer data for nominal top width by section and for outside-to-pitch diameter corrections
• See related: How a Belt Drive Transmits Torque; How to Work Out a Drive Ratio From What Is on the Machine; Why a Belt Slips and What It Costs