Number of V-Belts
Calculate the number of V-belts needed in a drive, N = P_design ÷ P_belt, from the design power P_design (the power to transmit times the service factor, kW) and the power each individual belt can transmit P_belt (kW, corrected by the wrap-angle and length factors). When a single V-belt lacks capacity to transmit the needed power, SEVERAL belts are used in parallel, running in parallel grooves of the same pulleys (multi-groove pulleys). The belt count is the design power divided by one belt's capacity. The design power includes the SERVICE FACTOR (1.0 to 2.0+), amplifying the nominal power to cover real operating conditions — shocks, frequent starts, hours of daily use, type of driving and driven machine (a crusher has a high factor, a fan a low one). The power per belt comes from the maker's tables for each profile and speed, corrected by the wrap angle (less wrap → less capacity) and belt length. When several belts are used, they should be a MATCHED SET (with identical lengths) to share the load equally — belts of different lengths overload some and idle others. This is the final step of selecting a V-belt drive. Enter the design power and the power per belt.
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Number of V-belts
The number of V-belts required in a drive is N = P_design ÷ P_belt, from the design power P_design (the power to be transmitted multiplied by the service factor) and the power a single belt can carry P_belt. When one V-belt lacks the capacity for the required power, several belts run in parallel, riding in parallel grooves of the same sheaves (multi-groove pulleys). The belt count is the design power divided by the capacity of one belt. Design power includes the service factor (1.0 to 2.0+), which raises the nominal power to cover real operating conditions - shock loads, frequent starts, hours of use per day, type of driving and driven machine (a crusher rates high, a fan low). Power per belt comes from manufacturer tables for each cross section and speed, corrected for the arc of contact (smaller wrap gives lower capacity) and for belt length. When several belts work together, they must come from a matched set, with identical lengths, so the load splits evenly - belts of differing length overload some and leave others idle. This calculation is the final step in selecting a V-belt drive. Enter the design power and the power per belt.
Related Tools
Belt Transmission Ratio with Slip
Calculate a belt's real transmission ratio accounting for slip, i = (D ÷ d)·(1 − s/100), from the driving D and driven d pulley diameters (mm) and the slip percentage s (%). A belt's THEORETICAL transmission ratio is simply the pulley diameter ratio (D/d) — a large driving pulley turning a small driven one multiplies the rotation. But in practice, a belt drive is NOT exact like a gear drive (which has interlocking teeth): the belt transmits by FRICTION, and there is always a small SLIP between belt and pulleys. This slip has two components: ELASTIC slip (creep, inevitable, ~1-2%, from the belt stretching and contracting as tension changes between the two sides) and GROSS slip (occurring under overload, when the belt loses grip — undesirable and harmful). Slip makes the driven pulley's real rotation SLIGHTLY LOWER than theoretical, and the real transmission ratio a bit different from nominal. In applications needing exact synchronism (engine timing shafts, positioning), V-belt slip is unacceptable, and TIMING (toothed) belts or chains, which do not slip, are used. This calculation quantifies the slip effect on the transmission ratio. Enter the driving and driven pulley diameters and the slip percentage.
Belt Transmitted Power
Calculate the power transmitted by a belt, P = (T₁ − T₂)·v, from the tight-side tension T₁ (N), the slack-side tension T₂ (N) and the belt velocity v (m/s). In a belt drive, the driving pulley drags the belt by friction, creating a DIFFERENCE in tension between the two sides: the side that 'pulls' (tight side, T₁) is more tensioned than the side that 'follows' (slack side, T₂). This difference (T₁ − T₂), the effective tension or tangential force, is the net force that actually transmits motion; times the belt velocity, it gives the transmitted POWER. The larger the tension difference the belt can sustain without slipping (depending on friction, wrap angle and, in V-belts, the wedging effect of the pulley walls), the greater the transmissible power. Power also grows with belt velocity — so high-power drives use large pulleys and fast belts (up to a limit, since centrifugal tension reduces available friction at very high speeds). This is central in belt-drive design, present in almost every rotating machine: motors, fans, pumps, compressors, machine tools and vehicles. Enter the tight- and slack-side tensions and the belt velocity.
Stress Intensity Factor (K)
Calculate the stress intensity factor, K = Y × σ × √(π·a), from the geometry factor Y (dimensionless), the applied stress σ (MPa) and the crack size a (m). The result, in MPa·√m, quantifies the intensity of the stress field at a crack tip, the central concept of fracture mechanics. When K reaches the material's fracture toughness (K_IC), the crack propagates unstably and failure occurs — even at stresses well below the yield strength. It is the basis of damage-tolerant design. Enter the geometry factor, the stress and the crack size.
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.
Belt Wrap Angle
Calculate a belt's wrap (contact) angle on the smaller pulley, θ = π − 2·arcsin((D − d) ÷ (2·C)), from the larger D and smaller d pulley diameters (m) and the center distance C (m). The wrap angle is the angle of the arc over which the belt actually WRAPS the pulley, in contact with it — and it is a critical parameter, since it is along that arc that the friction (transmitting the force) acts. The LARGER the wrap angle, the greater the contact area and the greater the force the belt can transmit without slipping. In a drive between two DIFFERENT-DIAMETER pulleys, the belt wraps LESS around the smaller pulley (angle below 180°) and MORE around the larger — and slipping always starts on the pulley with LESS wrap (the smaller), which therefore limits capacity. The wrap angle decreases when the diameter difference grows or the center distance shrinks (close, very different pulleys 'wrap' little). So drives with large reduction (very different pulleys) or close centers have reduced capacity, and sometimes use an IDLER (tensioner) pulley to increase wrap. The wrap angle enters directly into the tension ratio (e^(μθ)) and the belt-count correction factors. Enter the pulley diameters and the center distance.
Belt Maximum Tension
Calculate a belt's maximum (tight-side) tension, T₁ = T_e·r ÷ (r − 1), from the effective tension T_e = T₁ − T₂ (the power-transmitting force, N) and the tension ratio r = T₁/T₂ (at the slip limit). Knowing the force the belt must transmit (the effective tension, from power and velocity) and the maximum tension ratio the belt sustains before slipping (from friction, wrap and, in V-belts, the wedge effect), the individual side tensions can be computed. The maximum tension T₁ (tight side) is the larger, and it SIZES the belt's strength (which must not break) and the load on the BEARINGS and pulley shafts (which feel the sum of both side tensions, bending the shaft). Knowing T₁ is essential to: check the belt resists (versus its tensile strength), size the bearings for the radial load imposed by the belt (which can be significant and shortens bearing life), and set the correct installation tension. The LOWER the tension ratio r (worse friction, less wrap), the HIGHER the T₁ needed for the same power — hence the advantage of V-belts (high r) in reducing loads. Enter the effective tension and the tension ratio.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.