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How to calculate horsepower of crusher

Calculating the horsepower of a crusher involves understanding several parameters that contribute to the overall energy requirements needed to crush material. Here is a step-by-step method to calculate it:

  1. Determine the Work Index (Wi): The Work Index is a standard measure of the energy required to crush a specific material. It needs to be known or obtained through testing or literature for the specific type of material being crushed.

  2. Measure the Feed Size (D): This is the size of the material before crushing, usually expressed in millimeters (mm) or inches.

  3. Determine the Product Size (d): This is the desired size of the material after crushing.

  4. Calculate the Reduction Ratio (RR): This is the ratio of the feed size to the product size. \[ RR = \frac{D}{d} \]

  5. Use Bond’s Law (or Energy Formula): The Bond's Law formula is: \[ E = W_i \left( \frac{1}{\sqrt{d}} - \frac{1}{\sqrt{D}} \right) \] Where:

    • ( E ) is the energy in kilowatt-hours per ton (kWh/ton)
    • ( W_i ) is the Work Index of the material (in kWh/ton)
    • ( D ) is the feed size (in micrometers)
    • ( d ) is the product size (in micrometers)

  6. Calculate the Total Energy Consumption: Multiply the energy consumption per ton by the total throughput (in tons per hour). \[ E_{total} = E \times \text{Throughput} \]

  7. Convert Energy to Power: Since horsepower is a measure of power, convert the total energy per hour into horsepower. \[ \text{Horsepower} = \frac{E_{total} \times 0.7457}{\text{hours}} \]

    Here, 0.7457 is the conversion factor from kilowatts to horsepower.

Example Calculation:

  • Work Index (Wi) of the material = 10 kWh/ton
  • Feed size (D) = 200 mm
  • Product size (d) = 50 mm
  • Throughput = 100 tons/hour

  1. Reduction Ratio (RR): \[ RR = \frac{200}{50} = 4 \]

  2. Using Bond's Law formula: \[ E = 10 \left( \frac{1}{\sqrt{50}} - \frac{1}{\sqrt{200}} \right) \]

  3. Calculate energy consumption (E):

    • Convert mm to micrometers: ( 50 \text{ mm} = 50,000 \mu m ) and ( 200 \text{ mm} = 200,000 \mu m )
    • ( E = 10 \left( \frac{1}{\sqrt{50000}} - \frac{1}{\sqrt{200000}} \right) )
    • ( \approx 10 \left( 0.00447 - 0.00224 \right) )
    • ( \approx 10 \times 0.00223 )
    • ( \approx 0.0223 \text{ kWh/ton} )

  4. Total energy consumption: \[ E_{total} = 0.0223 \times 100 = 2.23 \text{ kWh/hour} \]

  5. Convert to horsepower: \[ \text{Horsepower} = \frac{2.23 \times 0.7457}{1} \approx 1.66 \text{ HP} \]

Thus, the horsepower required to operate the crusher, under the given conditions, is approximately 1.66 HP.