Screw Feeder capacity calculation

Calculating the capacity of a screw feeder involves understanding the material properties, screw geometry, and operational parameters. Below is a step-by-step guide to determine the theoretical capacity:

1. Basic Formula for Screw Feeder Capacity (Theoretical Volumetric Flow Rate)
The volumetric flow rate (\(Q_v\)) in m³/h or ft³/h is given by:

\[
Q_v = 60 \cdot A \cdot v \cdot n \cdot \eta
\]

Where:
– \(A\) = Cross-sectional area of material flow (m² or ft²)
– \(v\) = Pitch of the screw (distance between flights, m or ft)
– \(n\) = Rotational speed (RPM)
– \(\eta\) = Efficiency factor (typically 0.6–0.9, depending on material and design)

2. Cross-Sectional Area (\(A\))
For a screw with an outer diameter (\(D\)) and inner shaft diameter (\(d\)):

\[
A = \frac{\pi}{4} \left( D^2 – d^2 \right)
\]

3. Mass Flow Rate Calculation
To convert volumetric flow to mass flow (\(Q_m\) in kg/h or lb/h):

\[
Q_m = Q_v \cdot \rho \cdot C_f
\]

Where:
– \(\rho\) = Bulk density of material (kg/m³ or lb/ft³)
– \(C_f\) = Fill factor (typically 0.25–0.75, depends on material flowability)

4. Adjustments for Material Type
– Cohesive materials (e.g., powders): Lower fill factor (~0.25–0.5).
– Free-flowing materials (e.g., grains): Higher fill factor (~0.6–0.75).
– Inclined or vertical screws: Reduce capacity due to backflow.

5. Example Calculation
Given:
– Screw diameter (\(D\)) = 0.2 m
– Shaft diameter (\(d\)) = 0.05 m
– Pitch (\(v\)) = 0.15 m
– Speed (\(n\)) = 50 RPM
– Bulk density (\(\rho\)) = 800 kg/m³
– Fill factor (\(C_f\)) = 0.6
– Efficiency (\(\eta\)) = 0.8

Step 1: Calculate cross-sectional area: