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.
Resultado
—
Relação de tensões (correia em V)
A relação máxima de tensões de uma correia em V no limite do escorregamento é T₁/T₂ = e^(μ·θ ÷ sen β), a partir do coeficiente de atrito μ, do ângulo de abraçamento θ (radianos) e do semi-ângulo do canal da polia β. Esta é a equação de Euler-Eytelwein (capstan) com a correção para correias em V. Em uma correia plana, a relação limite de tensões é e^(μθ); mas a correia em V tem uma vantagem genial: ela se encaixa em um canal em V na polia, e ao ser tracionada, é puxada para dentro do canal, cunhando-se contra as duas paredes inclinadas. Esse efeito de cunha multiplica a força normal (e portanto o atrito) por um fator 1/sen β — como β é pequeno (tipicamente 17-19°, para um canal de 34-38°), sen β é pequeno e o atrito efetivo (μ/sen β) fica cerca de 3 vezes maior que o atrito real! É por isso que correias em V transmitem muito mais potência que correias planas do mesmo tamanho, com menor tração de instalação (poupando os mancais) e menos escorregamento — a razão de sua enorme popularidade em transmissões industriais e automotivas. A relação T₁/T₂ limite define a tração efetiva máxima (e portanto a potência) que a correia transmite antes de escorregar. Informe o coeficiente de atrito, o ângulo de abraçamento e o semi-ângulo do canal.
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.
Brake Contact Pressure
Calculate the contact pressure between the shoe/pad and the drum/disc of a brake, p = F ÷ A, from the normal force F (N) and the friction material contact area A (m²); the result is in kPa. Contact pressure is the normal force distributed over the friction surface area, and one of the most important parameters in a brake's or clutch's DURABILITY and PERFORMANCE. It must be below the friction material's ALLOWABLE pressure (linings, organic, semi-metallic, ceramic or sintered metallic pads — each with its limit). Pressures ABOVE the allowable lead to accelerated wear, overheating and friction loss (fading), reducing material life and impairing braking. Very LOW pressures underuse the material (a bigger, costlier brake than needed). Contact pressure also relates to the p·v product (pressure × velocity), the key indicator of the friction contact's thermal intensity — friction materials have a p·v limit above which they overheat, and that limit often governs design. This simple check — comparing contact pressure with the material's allowable — is essential in brake and clutch design and in choosing the right friction material for the application. Enter the normal force and the contact area.
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.