Belt Conveyor Capacity
Calculate the mass flow capacity of a belt conveyor, Q = A × v × ρ × 3600, from the cross-section area of the load on the belt A (m²), the belt speed v (m/s) and the material's bulk density ρ (t/m³). The result, in tonnes per hour, is the conveyor's transport capacity — essential equipment in handling ore, gravel, grain and coal. The load area depends on the belt width, the material's surcharge angle and the idler configuration. Wider, faster belts and denser materials raise the capacity. It is the basis of conveying system design. Enter the load area, the speed and the density.
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Belt conveyor capacity
The belt conveyor is the workhorse of bulk solids handling — ore, crushed stone, coal, grain, cement — continuously moving huge quantities of material over long distances at low cost. Its capacity (mass flow rate) is Q = A × v × ρ × 3600, where A is the cross-sectional area of the load on the belt (m²), v the belt speed (m/s), ρ the material's bulk density (t/m³, accounting for the voids between grains), and 3600 converts seconds to hours. The result comes out in tonnes per hour. It is essentially the continuity equation: flow = area × velocity × density. Each factor is a design lever. The load area depends on the belt width, on the material's dynamic surcharge angle (how much it 'piles up' without sliding, forming a triangular or trapezoidal profile on the belt), and on the idler configuration (belts with V-shaped or three-roll troughing idlers form a trough that carries far more than a flat belt). Typical speed ranges from 1 to 5 m/s (faster raises capacity but also wear and dust). The density is a material property. Belts at large mines move tens of thousands of tonnes per hour. Sizing the capacity is the starting point of conveyor design, which then involves the drive power (to overcome friction and lifting), the belt strength, and the tensioning and cleaning systems. Enter the load area, the speed, and the density.
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V-Belt Tension Ratio
Calculate the maximum tension ratio of a V-belt at the slip limit, T₁/T₂ = e^(μ·θ ÷ sin β), from the friction coefficient μ, the wrap angle θ (radians) and the pulley groove half-angle β (degrees). This is the Euler-Eytelwein (capstan) equation with the V-belt correction. In a FLAT belt, the limit tension ratio is e^(μθ); but the V-belt has a clever advantage: it fits into a V-shaped GROOVE in the pulley, and when tensioned, is pulled INTO the groove, wedging against the two inclined walls. This WEDGE effect multiplies the normal force (and thus the friction) by a factor 1/sin β — since β is small (typically 17-19°, for a 34-38° groove), sin β is small and the EFFECTIVE friction (μ/sin β) is about 3 times the real friction! That is why V-belts transmit much more power than flat belts of the same size, with lower installation tension (sparing the bearings) and less slip — the reason for their huge popularity in industrial and automotive drives. The limit T₁/T₂ ratio sets the maximum effective tension (and thus power) the belt transmits before slipping. Enter the friction coefficient, the wrap angle and the groove half-angle.
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