Rope-Pulley Contact Pressure
Calculate the contact pressure between a wire rope and a pulley (or drum) groove, p = 2·T ÷ (d·D), from the rope tension T (N), the rope diameter d (m) and the pulley diameter D (m); the result is in kPa. When a tensioned wire rope wraps a pulley, it presses the pulley groove with a contact pressure depending on tension and geometry. This pressure is a critical WEAR factor of the rope and pulley: high pressures (highly tensioned rope, small-diameter pulley, thick rope) accelerate abrasive wear of the rope's outer wires and the pulley groove wear, shortening both lives. Contact pressure is INVERSELY proportional to pulley diameter — so larger pulleys and drums extend rope life (besides reducing bending fatigue). Codes and makers specify allowable pressures per pulley material (steel, cast iron, polymer) and rope. With the D/d ratio (governing bending fatigue), contact pressure sets the rope-pulley system durability. Controlling contact pressure — using adequate pulleys and keeping tension within limits — is essential for the service life and safety of cranes, elevators and cableways. Enter the rope tension, the rope diameter and the pulley diameter.
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Pressão de contato cabo-polia
A pressão de contato entre um cabo de aço e a garganta de uma polia (ou tambor) é p = 2·T ÷ (d·D), a partir da tração no cabo T, do diâmetro do cabo d e do diâmetro da polia D; o resultado é em kPa. Quando um cabo de aço tracionado contorna uma polia, ele pressiona a garganta com uma pressão que depende da tração e da geometria. Essa pressão é um fator crítico de desgaste do cabo e da polia: pressões altas (cabo muito tracionado, polia de pequeno diâmetro, cabo grosso) aceleram o desgaste por abrasão dos fios externos do cabo e o desgaste da garganta da polia, reduzindo a vida de ambos. A pressão de contato é inversamente proporcional ao diâmetro da polia — por isso polias e tambores maiores prolongam a vida do cabo (além de reduzir a fadiga de flexão). As normas e os fabricantes especificam pressões admissíveis conforme o material da polia (aço, ferro fundido, polímero) e do cabo. Junto com a relação D/d (que governa a fadiga de flexão), a pressão de contato define a durabilidade do sistema cabo-polia. Controlar a pressão de contato — usando polias adequadas e mantendo a tração dentro dos limites — é essencial para a vida útil e a segurança de guindastes, elevadores e teleféricos. Informe a tração no cabo, o diâmetro do cabo e o diâmetro da polia.
Related Tools
D/d Ratio (Pulley-Rope)
Calculate the D/d ratio between the pulley diameter D and the rope diameter d, r = D ÷ d (both in the same unit). The D/d ratio is the most important parameter for the FATIGUE LIFE of a wire rope working over pulleys and drums. Each time the rope passes a pulley, it is FLEXED (bent and unbent), and this repeated bending fatigues the wires — the SMALLER the pulley diameter relative to the rope (lower D/d), the TIGHTER the curve, the greater the wire bending strain and the faster the rope fatigues and breaks. So codes require MINIMUM D/d ratios: typically 18-25 for cranes (each bend costs life), and even higher (40+) for people elevators and high-durability applications. Too small a D/d ratio drastically reduces rope life — doubling the D/d ratio can multiply rope life several times. There is a design trade-off: larger pulleys (high D/d) extend rope life but increase the equipment's size, weight and cost. The D/d ratio, with contact pressure and tension, sets the rope durability. Checking that the D/d ratio meets the code minimum is essential in designing any lifting machine. Enter the pulley and rope diameters.
Wire Rope Working Load Limit (WLL)
Calculate a wire rope's allowable working load, WLL = MBL ÷ SF, from the minimum breaking load (MBL, N) and the required safety factor. The working load (WLL — Working Load Limit, or SWL — Safe Working Load) is the MAXIMUM load that can be safely applied to a rope, fitting or lifting equipment — the information STAMPED on slings, shackles, hooks and equipment plates, and what the operator uses to decide whether a given load can be lifted. It is obtained by dividing the breaking load (the real strength that would break the component) by the code safety factor (5 for general lifting, more for special situations). Respecting the WLL is an absolute safety rule in lifting and material-handling: exceeding the working load dangerously approaches the component to rupture, eliminating the safety margin covering dynamic effects, wear and uncertainties. The WLL is not the rope's strength — it is the SAFE fraction of it. Every rigging operation starts by checking that the load to lift is below the WLL of each component in the load line (rope, slings, shackles, hook, eye), since the chain is only as strong as its weakest link. Enter the breaking load and the safety factor.
Cable Tension in Accelerated Lift
Calculate the dynamic tension in a cable while lifting a load with acceleration, T = W·(1 + a/g), from the load weight W (N), the vertical lift acceleration a (m/s²) and gravity g. When a load is lifted with ACCELERATION (at lift start, when accelerating the rise), the cable must provide not only the force to support the weight (W) but ALSO the force to accelerate the mass upward — by Newton's second law, the total tension is the weight times the factor (1 + a/g). This means the DYNAMIC tension is GREATER than the static weight: an acceleration of g/2 (5 m/s²) raises the tension by 50%! That is why ABRUPT lifts (fast start, or worse, lifting an already-moving load or stopping abruptly) generate dangerous dynamic OVERLOADS in the cable, which can break it even with the static load within capacity. The effect is worse in abrupt STOPS and in loads 'snatching off the ground' (cable slack suddenly removed, generating an impact). So experienced operators lift SMOOTHLY (low acceleration), and the cable safety factors (5 or more) exist precisely to cover these inevitable dynamic overloads. This calculation quantifies the tension increase due to acceleration, essential in the safety analysis of dynamic lifts. Enter the load weight and the lift acceleration.
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.