How do you calculate the motor power for a vibrator screen?

Calculating the motor power required for a vibrating screen involves understanding several key parameters and using specific formulas. Here's a basic outline of the process:

1. Determine Basic Parameters:

   • Screen area (A): The total area of the screen (in square meters).
   • Screening material properties: Including bulk density (ρ), particle size, etc.
   • Capacity (Q): The amount of material to be screened per hour (in tons per hour or tph).

2. Assess Motion Parameters:

   • Amplitude (A_m): The peak deviation of the screen mesh from its original state (in millimeters).
   • Frequency (f): The number of oscillations per second (in Hertz).

3. Calculate Acceleration:

   • The acceleration (a) can be calculated with: \[ a = (2 \pi f)^2 \cdot A_m \]

4. Calculate Power Requirements:

   • Assuming a linear motion machine (for simplicity), the force required to move the screen can be estimated as: \[ F = m \cdot a \] where ( m ) is the mass of the screen and material on it.

5. Calculate Motor Power:

   • The mechanical power (P_m) required can be calculated using: \[ P_m = F \cdot v \] where ( v ) is the velocity, which can be approximated as ( v = 2 \pi f \cdot A_m ).
   • Therefore, \[ P_m = F \cdot 2 \pi f \cdot A_m \]

6. Convert Mechanical Power to Electrical Power:

   • To find the electrical power (P_e) needed by the motor, you have to consider the efficiency (( \eta )) of the motor: \[ P_e = \frac{P_m}{\eta} \]

Example Calculation

Suppose you have the following data:

• Screen area (A): 2 m²
• Bulk density (ρ): 1.5 tons/m³
• Capacity (Q): 100 tph
• Amplitude (A_m): 5 mm (0.005 m)
• Frequency (f): 15 Hz
• Motor efficiency (η): 90% or 0.9

Steps:

1. Calculate the required force:

   • Velocity (v): \[ v = 2 \pi \cdot 15 \cdot 0.005 \approx 0.471 m/s \]

   • Acceleration: \[ a = (2 \pi \cdot 15)^2 \cdot 0.005 \approx 44.42 m/s² \]

2. Estimate the mass (m) of the material on the screen: \[ m = \text{Screen area} \times \text{Bulk density} = 2 \times 1.5 = 3 \text{ tons} = 3000 kg \]

   • Calculate force: \[ F = 3000 \times 44.42 \approx 133260 N \]

3. Mechanical power needed: \[ P_m = 133260 \times 0.471 \approx 62706 W \approx 62.7 kW \]

4. Considering efficiency: \[ P_e = \frac{62.7}{0.9} \approx 69.67 kW \]

Thus, a motor with a power rating of around 70 kW would be required.

Note

This is a simplified calculation, and actual requirements may vary based on additional factors such as screen efficiency, material characteristics, and specific configuration. Always consult with equipment manuals or engineering services for accurate motor sizing.