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.
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Relação D/d (polia-cabo)
A relação D/d entre o diâmetro da polia D e o diâmetro do cabo d é r = D ÷ d (ambos na mesma unidade). É o parâmetro mais importante para a vida à fadiga de um cabo de aço que trabalha sobre polias e tambores. Cada vez que o cabo passa por uma polia, ele é flexionado (dobrado e desdobrado), e essa flexão repetida fadiga os fios — quanto menor o diâmetro da polia em relação ao cabo (menor D/d), mais apertada a curva, maior a deformação de flexão dos fios e mais rápido o cabo fadiga e rompe. Por isso as normas exigem relações D/d mínimas: tipicamente 18 a 25 para guindastes, e valores ainda maiores (40 ou mais) para elevadores de pessoas e aplicações de alta durabilidade. Uma relação D/d pequena demais reduz drasticamente a vida do cabo — dobrar a relação D/d pode multiplicar a vida do cabo por várias vezes. Há um compromisso de projeto: polias maiores (D/d alto) prolongam a vida do cabo mas aumentam o tamanho, o peso e o custo do equipamento. A relação D/d, junto com a pressão de contato e a tração, define a durabilidade do cabo. Verificar que a relação D/d atende ao mínimo normativo é essencial no projeto de qualquer máquina de içamento. Informe os diâmetros da polia e do cabo.
Related Tools
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.
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.