Π_Q - Measuring the Efficiency of an Extruder Screw & Barrel Combination

Based on the following model:

The output of a single screw extruder depends on a drag flow mechanism, i.e., it is assumed that there is no slip at the die and barrel walls.  If there is any slip at the barrel wall as the screw rotates then, of course, the downstream component of the flow of the melt is diminished and the efficiency of the screw decreases.  Also, if there is any wear of the screw, the clearance between the screw flight and the barrel is increased and the back-flow over the flights is likewise increased, so again the efficiency of the screw decreases.

It can be shown that the volumetric flow rate, Q, in a single screw extruder is given by the following equation:

                              (1)

Where:

                 D is the diameter of the screw (m)

                 N is the screw speed (revs/s)

                 H is the Channel depth in the metering section (m)

                  θ is the helix angle ( º ),  17.7º  for a square pitched screw,  pitch = D

                  η is the polymer melt viscosity (Pa s)

                  is the pressure gradient (Pa/m)

                  δ is the clearance between the screw and barrel (m)

                  e is the flight width (m)

Equation (1) simplifies to:

                                                                                          (2)

δ in equation (1) is extremely small compared with the screw diameter, D, so that the leakage flow is negligible compared with the downstream flow and can be effectively ignored.  Similarly, the channel depth, H, is small compared with the screw diameter and, if the die and screw are properly balanced, the pressure gradient approaches zero, so the pressure flow, which acts in the opposite direction to the drag flow, is small and can likewise be ignored.

This being the case it is possible to establish the efficiency of the screw using a dimensionless number:

Where :

             W is the channel width in the metering section (m) 

              V_z is the downstream velocity of the melt at the barrel wall (m/s). But,

Assuming pure drag flow, it is possible to estimate the output of a single screw extruder using the dimensions of the screw in the metering section according to the equation:

(Remember to keep your units consistent - if you want your output in kg/hr and your melt density is in kg/m³, then lengths should be in metres and the screw speed should be in revolutions per hour)

Example: