vibrating screen design calculation

Designing a vibrating screen involves several key calculations to ensure optimal performance, efficiency, and durability. Below is a step-by-step guide to the essential design calculations:

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1. Basic Parameters

Before calculations, define the following inputs:

• Material Properties: Bulk density (ρ), particle size distribution, moisture content.
• Capacity Requirement (Q): Tons/hour or m³/hour.
• Screen Dimensions: Length (L), width (W), and deck inclination angle (θ).
• Vibration Parameters: Frequency (f) in Hz or RPM, amplitude (A) in mm.

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2. Screen Area Calculation

The required screening area depends on capacity and material characteristics:
\[
A_s = \frac{Q}{F \cdot \rho \cdot C \cdot K \cdot M}
\]
Where:

• \(A_s\) = Screen area (m²).
• \(Q\) = Feed capacity (tons/hour).
• \(F\) = Basic feed rate per unit area (from empirical tables; e.g., 10–25 t/h/m² for coarse screening).
• \(C\) = Correction factor for deck inclination.
• \(K\) = Correction factor for moisture/fines.
• \(M\) = Material shape factor.

Note: Empirical values vary based on material type (e.g., sand vs. gravel).

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3. Stroke Length & Vibration Frequency

Stroke Length (S):

• Typically ranges from 2–12 mm for linear screens.
• Larger strokes for heavier materials; smaller strokes for fine particles.

Frequency (f):
\[
f = \frac{\text{RPM}}{60} \quad (\text{Hz})
\]
Common frequencies:

• Linear Screens: 700–1000 RPM (~12–16 Hz).
• Circular Motion Screens: 1200–3000 RPM (~20–50 Hz).

Tip: Ensure the product of amplitude and frequency squared meets material transport needs:
\[
G-force = A \cdot (2\pi f)^2 / g
\]
Where \(g\) = gravitational acceleration (\(9.81 \, \text{m/s}^2\)). Aim for 3–5 G’s for most applications.

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4. Material Travel Velocity

For a linear vibrating screen:
\[
v = N \cdot A \cdot f \cdot C_\theta \cdot C_m
\]
Where:

• \(v\) = Material velocity (m/s).
• \(N\) = Number of directional reversals per cycle (\(N=1\) for linear vibration).
• \(C_\theta\) = Incline factor (\(\approx 1 + 0.8\sin\theta\), where \(\theta\) is deck angle).
• \(C_m\) = Material factor (~0.8–1.2).

Adjust deck angle (\(\theta\)) to control velocity:

Typical angles:

15°–30° for inclined screens; 0°–5° for horizontal screens.

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5. Power Calculation

Motor power (\(P\)) depends on screen mass and dynamics:
\[
P = \frac{m_e \cdot A^2 \cdot f^3}{k}
\]
Where:

• \(m_e\) = Effective vibrating mass (screen + material) in kg.
• \(k\) = Empirical constant (~1–10 × 10⁶ depending on design).

Alternatively, use practical estimates:
\[
P \, (\text{kW}) ≈ C_r \cdot L \cdot W / 1000
\]
Where \(C_r ≈ 0.25–1 \, (\text{kW/m²})\) based on screen type.

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6. Natural Frequency Avoidance

Ensure operating frequency (\(f_{\text{op}}\)) avoids resonance with the screen’s natural frequency (\(f_n\)):
\[
f_n ≈ \frac{1}{2\pi} \sqrt{\frac{k_{\text{spring}}}{m}}
\]
Design springs/stiffness (\(k_{\text{spring}}\)) such that \(|f_{\text{op}} – f_n| > 20\%\).

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7. Deck Selection & Open Area

Choose mesh aperture size (\(a\)) based on separation needs (rule of thumb):
\[
a ≥ 1.25 × d_{\text{max}}
\]
Open area (%) affects throughput—higher % reduces blinding but weakens the panel.

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Key Design Considerations

1. Material Stratification: Higher G-forces improve separation but may damage fragile particles.
2. Durability: Use fatigue-resistant materials for decks and springs.
3. Dust Control: Enclosed designs may require reduced airflow calculations.

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Example Calculation

Given:
+ Capacity (\(Q\)) = 200 t/h of dry sand (\(\rho\) = 1.6 t/m³).
+ Desired separation at 10 mm aperture with moderate fines (<5%).

Steps:
1. Select screen area (\(A_s\)) using empirical rate (\(F ≈ 15 \, t/h/m²\)), correction factors (\(C ≈ 0.9\), \(K ≈ 1\), \(M ≈ 1\)).
\[ A_s ≈ Q/(F·C·K·M) ≈ 200/(15×0.9×1×1) ≈ 14.8 \, m² → Choose L=5m, W=3m.\]

2. Select stroke (\(A=6mm\)), frequency (\(f=15Hz\)), G-force:
\[ G ≈ [6×10^{-3}] × [2π×15]^2 /9.81 ≈ 5.\]

3.Calculate power assuming effective mass=3000kg:
\[ P≈3000×(6×10^{-3})^2×15^3/4×10⁶≈18 \, kW.\]

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For precise designs, use manufacturer software or standards like ISO/DIN norms tailored to vibrating screens.

Would you like help with specific components like spring selection or dynamic analysis?