determination of screw groove depth and pump ratio of exhaust screw

among the parameters of the exhaust screw, the screw groove depth h1 and h2 are the most important, because these two values directly affect the working state of the exhaust screw
we know that when the screw parameter d of the extruder ф the productivity of the exhaust screw is determined by the screw groove depth h1 of the first metering section when the speed and speed n are fixed. the determination method of its value is not much different from that of ordinary screw, but because the length diameter ratio l/d of the exhaust screw is large, the value of h1 can also be larger. according to equation (8-10) h1=kd, it can be seen from the statistics table 11-3 of the existing screw that under the same diameter, a larger length diameter ratio corresponds to a larger k value, so there is also a larger screw groove depth h1
when h1 is determined, h2 cannot decide at will. it is known from the theory of fluid dynamics that the screw groove depth directly affects the slope of the screw characteristic line. the possibility of the inclination or fluctuation of the characteristic line of the two screw sections.
therefore, the concept of pump ratio Ω is introduced. the so-called pump ratio refers to the ratio of the screw groove depth of the second metering section to the screw groove depth of the first metering section, namely:
Ω=h2/h1    （11-10）
the pump ratio Ω is a very important parameter of the exhaust screw. the closer Ω is to 1, the closer h2 and h1 are, and the closer the characteristic lines of the two screws are, the greater the possibility of material spilling is. although the possibility of material spilling is reduced, the instability of extrusion will increase when the head pressure is low.
viscosity under isothermal condition when the molten material is newtonian liquid η is the same. when dpmax/d Ω=0, it can be calculated that the maximum working pressure is only Ω=1.5, which is the so-called optimal pump ratio in theory. table 11-2 calculates the p/pmax values for different pump ratios. if the productivity q1 of the first metering section will be different diagonal lines, it can be analyzed that the maximum working pressure pmax is exactly the pressure at the intersection of the envelope of these diagonal lines and the horizontal line of q1
when considering plastics as a non newtonian fluid, it is tried to prove that the maximum head pressure can be obtained when the pump ratio Ω is 1.75 for polyethylene with mi=0.2-5.0. it can be seen from the statistics of exhaust screws in various countries in table 11-3 that the pump ratio of most exhaust screws is between 1.5-2.0. when the pump ratio Ω is small, the output fluctuation is small and the extrusion quality is high, but colleagues also increase the possibility of bleeding
after the pump ratio Ω is determined, the groove depth of the second metering section can be calculated from formula (11-10). some data suggest that the exhaust screw has a second compression ratio, which is wrong, because it is known that the compression ratio is the ratio of the volume of the first screw groove in the feeding section to the volume of the last screw groove in the metering section. when the discharge period of the exhaust screw is short, l, the screw groove is not full, so there is no volume ratio