Grinding Energy (Bond Work Index)
Calculate the specific comminution (grinding/crushing) energy by Bond's law, W = 10 × Wi × (1/√P₈₀ − 1/√F₈₀), from the ore's Bond work index Wi (kWh/t), and the particle sizes passing 80% of the product (P₈₀) and feed (F₈₀), in micrometers. The result, in kWh per tonne, is the energy needed to reduce the ore from feed to product size. Comminution is mining's largest energy consumer (up to 50% of the plant). The Wi index characterizes the ore's resistance to fragmentation. It is the basis for sizing mills and energy consumption. Enter the Wi, P₈₀ and F₈₀.
Resultado
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Energia de moagem (lei de Bond)
A cominuição — britar e moer o minério para liberar os minerais valiosos — é o maior consumo de energia de uma planta de mineração, podendo representar 30 a 50% de toda a eletricidade usada. Estimar essa energia é, portanto, crucial, e a referência clássica é a lei de Bond: W = 10 × Wi × (1/√P₈₀ − 1/√F₈₀). Aqui Wi é o índice de trabalho de Bond (kWh/t), uma propriedade do minério determinada em laboratório que mede sua resistência à fragmentação (minérios duros como quartzitos têm Wi alto, ~15-20; minérios brandos, baixo); F₈₀ e P₈₀ são os tamanhos pelos quais passam 80% da alimentação e do produto, em micrômetros (a granulometria de referência). O resultado, em kWh por tonelada, é a energia específica de moagem. A lei de Bond expressa uma verdade física importante: a energia para moer cresce desproporcionalmente à medida que se busca finura — moer até partículas muito finas (P₈₀ pequeno) consome muito mais energia (o termo 1/√P₈₀ dispara). Por isso a moagem fina é tão cara, e há um equilíbrio entre liberar bem o mineral (moer fino) e gastar energia razoável. A lei de Bond é uma das três 'leis da cominuição' (com Kick, para britagem grosseira, e Rittinger, para moagem fina); Bond é a mais usada na faixa intermediária e industrial. É a base do dimensionamento de moinhos (potência instalada), da estimativa de custo operacional e da comparação de circuitos. Informe o Wi, o P₈₀ e o F₈₀.
Related Tools
Total Reduction Ratio
Calculate the total reduction ratio of a three-stage comminution circuit, RR_total = RR₁ × RR₂ × RR₃, multiplying the reduction ratios of each crusher/mill in series. The dimensionless result is the circuit's overall size reduction — from bench rock blocks (hundreds of mm) to fine particles (mm or µm). Since each stage has a limited reduction ratio (4 to 10 for crushers), large total reductions (100, 1000 or more) require several stages in series: primary, secondary, tertiary crushing and milling. Enter the reduction ratios of the three stages.
Punching Work
Calculate the work (energy) consumed in punching or sheet cutting, W = (k·F·t) ÷ 1000, from the penetration factor k (~0.3-0.6, the fraction of thickness the punch travels shearing before fracture), the cutting force F (N) and the sheet thickness t (mm); the result is in joules. While the cutting FORCE sets the press tonnage, the WORK sets the ENERGY the press must deliver in the stroke — a distinct and equally important parameter, especially in eccentric and friction presses that store energy in a flywheel. The factor k appears because the cut does not consume maximum force over the full thickness: the punch penetrates shearing, force rises to a peak, then drops as the material FRACTURES abruptly (the fracture propagates and separates the material before the punch crosses the whole thickness). So the work is only a fraction (k) of the maximum-force × thickness product. Knowing the work is essential to size the press flywheel and motor (which must replenish the energy between strokes) and to avoid heavy cuts 'stalling' the press from lack of stored energy. Enter the penetration factor, cutting force and thickness.
Crushing Reduction Ratio
Calculate the reduction ratio of a crusher or mill, RR = F ÷ P, dividing the feed size F by the product size P (usually F₈₀/P₈₀ or crusher openings). The dimensionless result shows how many times the material was reduced in size in one stage. Each equipment type has a typical reduction ratio range: jaw crushers 4-7, cone crushers 5-8, ball mills up to 100 or more. Since each stage has a limited ratio, reducing large blocks to fine powder requires several stages in series, whose product of ratios gives the total reduction. Enter the feed and product sizes.
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.