Line-shaft flat belt losing speed under full load
A coir-yarn spinning unit runs its main line shaft from a 7.5 kW, 1440 rpm three-phase motor through an open flat-belt drive. The motor pulley is 100 mm diameter, the line-shaft pulley is 400 mm, and the centre distance is 900 mm. The belt is 60 mm wide and 5 mm thick, laced endless. For two years the line shaft turned at about 360 rpm. Last month the spinners noticed the shaft running near 330 rpm whenever the ring frames are fully loaded, and the belt now smells hot and shows a shiny, glazed inner face. The fitter has already applied belt dressing twice, which helped for a day each time. Management wants the speed restored without buying a new motor, and the maintenance budget allows either a wider flat belt with a gravity take-up or a change to V-belts with new pulleys.
1. Calculate the line-shaft speed the drive should give, and the percentage slip implied by 330 rpm. Is slip alone an adequate explanation, and what does the glazed belt face tell you?
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Ideal driven speed: N₂ = N₁ × d₁/d₂ = 1440 × 100/400 = 360 rpm. Observed 330 rpm gives slip = (360 − 330)/360 × 100 = 8.3%, which is four to eight times the 1–2% expected of a well-laced flat belt.
Belt speed = π × 0.100 × 1440/60 = 7.5 m/s, well below the ~20 m/s limit for flat belts, so centrifugal lift is not the cause. Slip alone does not explain why the drive worked for two years, but the other symptoms point the same way: a glazed, polished friction face means the belt has been sliding continuously and has lost its grip, and the hot smell confirms it. Dressing raises friction temporarily, which is why speed came back for a day.
So the belt is running at its friction limit. Before spending money, confirm speed with a tachometer, check tension by deflection (roughly 10 mm per metre of span), check pulley alignment and crown, and look for oil or grease reaching the belt from the bearings.
2. Rank the three corrective options - retensioning, a wider flat belt, V-belt conversion - and show numerically why V-belts transmit more power at the same peak tension. Why is over-tightening not an answer?
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Ranking: (1) clean, deglaze, align and retension - cheapest, addresses the immediate cause; (2) wider flat belt plus gravity take-up if slip returns at full load; (3) V-belt conversion only if the drive is genuinely under-capacity, since it is the most expensive.
Why V-belts win. Arc of contact on the small pulley: sin α = (200 − 50)/900 = 0.167, α = 9.6°, so θ = 180 − 19.2 = 160.8° = 2.81 rad. Flat belt, μ = 0.3: T₁/T₂ = e^(0.3 × 2.81) = 2.3. V-belt, 38° groove, same μ: μ′ = 0.3/sin 19° = 0.92, T₁/T₂ = e^(0.92 × 2.81) = 13. With T₁ limited to 1000 N, the flat belt transmits (1000 − 435) × 7.5 = 4.2 kW, while the V-belt transmits (1000 − 77) × 7.5 = 6.9 kW. The 7.5 kW motor already exceeds the flat belt at this tension.
Over-tightening: doubling belt pull adds roughly 2 kN to both the motor and line-shaft bearings and deflects the shaft, trading belt slip for bearing failure. Tension must be set by deflection, not by feel.
3. If management chooses V-belts, what else must change on the drive, and what data do you need before ordering?
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Hardware changes. The crowned flat pulleys must be replaced by grooved pulleys of the correct section. The speed ratio must be worked out on pitch diameters, not outside diameters, because the belt sits down inside the groove; an A-section belt on a 100 mm outside-diameter pulley runs on a distinctly smaller pitch diameter, so the line shaft will not turn at 360 rpm unless the pitch diameters are chosen for the ratio. The 900 mm centre distance must also be checked against the minimum for the chosen section, and take-up travel provided for belt stretch.
Data needed before ordering: motor kW and duty hours per day (to fix the service factor, typically 1.2–1.4 for a spinning line shaft); design power and small-pulley speed (to select the belt section); rated power per belt (to fix the number of belts); standard belt lengths available; existing shaft diameters and keyway sizes at both pulleys; whether the line shaft and its bearings can carry the revised pull; and whether the motor slide rails give enough adjustment for alignment and tensioning.