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.
Result
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Ângulo de abraçamento da correia
O ângulo de abraçamento (de contato) de uma correia na polia menor é θ = π − 2·arcsen((D − d) ÷ (2·C)), a partir dos diâmetros da polia maior D e da menor d e da distância entre centros C. É o ângulo do arco em que a correia efetivamente contorna a polia, em contato com ela — e é um parâmetro crítico, porque é ao longo desse arco que o atrito (que transmite a força) atua. Quanto maior o ângulo de abraçamento, maior a área de contato e maior a força que a correia pode transmitir sem escorregar. Em uma transmissão entre duas polias de diâmetros diferentes, a correia abraça menos a polia menor (o ângulo é menor que 180°) e mais a polia maior — e o escorregamento sempre começa na polia de menor abraçamento (a menor), que por isso limita a capacidade. O ângulo de abraçamento diminui quando a diferença de diâmetros aumenta ou a distância entre centros diminui (polias próximas e muito diferentes 'abraçam' pouco). Por isso, transmissões com grande redução ou centros próximos têm capacidade reduzida, e às vezes usam uma polia tensora (esticadora) para aumentar o abraçamento. O ângulo de abraçamento entra diretamente na relação de tensões (e^(μθ)) e nos fatores de correção do número de correias. Informe os diâmetros das polias e a distância entre centros.
Related Tools
Belt Contact Arc
Calculate the contact-arc length of a belt on the smaller pulley, L_arc = (d ÷ 2)·θ, from the smaller pulley diameter d (mm) and the wrap angle θ (radians). The contact arc is the length of the belt portion actually in contact with the pulley (touching it), along the wrap angle — simply the pulley radius times the angle (in radians), the arc-length formula. This length matters for several reasons: it sets the CONTACT AREA between belt and pulley (with the width), governing contact pressure and friction distribution; it influences heating (friction × area) and wear of both belt and pulley; and it is relevant to elastic slip (creep), where the belt, changing tension from T₁ to T₂ along the arc, elastically stretches and contracts, sliding microscopically over the pulley — a small INEVITABLE slip (1-2%) occurring even without gross slipping, making the output speed always slightly below theoretical. A larger contact arc (bigger pulley or more wrap) distributes friction better and reduces the slip tendency. This calculation complements the geometric and friction analysis of a belt drive. Enter the smaller pulley diameter and the wrap angle.
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 Centrifugal Tension
Calculate the centrifugal tension in a belt, T_c = m·v², from the mass per unit length m (kg/m) and the belt velocity v (m/s). When the belt wraps a pulley at high speed, its own mass, making the turn, generates a CENTRIFUGAL force tending to 'throw' the belt outward, LIFTING it off the pulley. This creates an additional tension throughout the belt (the centrifugal tension), the same at all points and not contributing to power transmission — it only 'steals' part of the belt's gripping capacity against the pulley. Centrifugal tension grows with the SQUARE of velocity, so it is negligible at low speeds but becomes important in fast belts. The effect is harmful: by lifting the belt off the pulley, centrifugal tension REDUCES the normal contact force and thus the friction available to transmit power — there is an OPTIMAL velocity above which increasing speed reduces transmissible power (the belt starts to 'float'). So belt speed has a practical limit (typically 25-30 m/s for conventional V-belts, more for special belts). Centrifugal tension must be added to the tensions to get the total tight- and slack-side tensions. Enter the mass per unit length and the velocity.
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.