In REX, the following ratios are differentiated between different screw zones.
In REX/PSI, compression ratios are calculated both within the respective zones (compression zone and decompression zone) as well as in the overview section under „Dimensions,“ where the compression ratio of the zones before and after a (de-)compression zone is displayed.
The values may differ if the channel pitch, land width, channel radii, or flank angle are varied.
The compression ratio is calculated from the channel width $b$, the channel height $h$ (including screw clearance) and the nominal screw diameter $D$:
$$CR = \frac{(b_1 \cdot h_1)\cdot (D-h_1)}{(b_2 \cdot h_2) \cdot (D-h_2)}$$
With index 1 for the start of the zone and index 2 for the end of the zone.
For barrier screws, the compression ratio is calculated from the ratio of the cross-sectional area upstream of the barrier zone (index 1) to the total cross-sectional area of both channels (index F: solids channel, index S: melt channel) at the end of the barrier zone:
$$CR = \frac{b_1 \cdot h_1}{(b_F \cdot h_F)+(b_S \cdot h_S)}$$
The Pump Ratio indicates the ratio of the channel depth of the metering zone after degassing $h_{M,2}$ in relation to the channel depth of the metering zone before degassing $h_{M,1}$.
$PR = \frac{h_{M,2}}{h_{M,1}}$
Typically, a value of 1.5 to 1.6 is realised.
There is also a typical ratio for the channel depth of the degassing zone. This is typically 2.0 to 2.5 times the channel depth of the metering zone after degassing. In most cases, this successfully prevents the degassing opening from flooding.
Compression ratio of a (de)compression zone (CR)
The compression ratio of a compression or decompression zone is calculated from the channel cross-section at the beginning and end of the zone:
$CR = \frac{h_E*b_E}{h_M*b_M}$
with the channel depth $h_E$ and the channel width $b_E$ at the start of the (de)compression zone (the feed zone for a three-zone screw) and the channel depth $h_M$ and channel width $b_M$ at the end of the (de)compression zone (the metering zone for a three-zone screw).
Volume compression ratio (VCR)
As the ratio of the channel depths does not allow a meaningful comparison between two screw concepts, the volume compression ratio is used for a more precise description. It relates the channel cross-section of the feed zone to the channel cross-section of the metering zone. In REX, the screw clearance is also taken into account.
$VCR=\frac{[(h_E+s)*(t_E-i_E*e_E)]*(D-(h_E+s))}{[(h_M+s)*(t_M-i_M*e_M)]*(D-(h_M+s))}$
with the channel depth $h$, the screw clearance $s$, the pitch $t$, the number of flights $i$, the flight width $e$ and the diameter $D$. With the indices $E$ for the feed zone and $M$ for the metering zone.
Volume compression ratio for barrier screws (VCR)
For barrier screws, the volume compression ratio is also calculated from the ratio of the channel cross-section of the feed zone to the added channel cross-section of the solids and melt channel at the end of the barrier zone:
$VCR = \frac{B_E*h_E}{B_S*h_S+B_F*h_F}$
With the channel width $B$ and the channel height $h$ for the indices $E$ for the feed zone, $S$ for the melt channel and $F$ for the solids channel of the barrier zone.