Screw diameter is a critical parameter for screw compressors. In accordance with requirements for standardization and generalization across product series, the principle for determining the range of screw diameters is to cover the widest possible range of discharge capacities using the fewest possible diameter sizes, all while maintaining optimal peripheral speeds. In my country, the standardized series of screw diameters (in mm) is: (63), (80), (100), 125, 160, 200, 250, 316, 400, 500, 630, (800). Diameters in parentheses apply only to asymmetric profile designs; among these, the sizes 160, 200, 250, and 316 are the most commonly used.
Since discharge capacity is proportional to the square of the screw diameter, there are significant differences in capacity between adjacent sizes in the series—a disparity that becomes particularly pronounced at larger diameters. To address this, multiple length-to-diameter ratios are specified for each screw diameter to adjust the capacity range, allowing the capacities of adjacent diameter sizes to overlap effectively.
1. Length-to-diameter ratio: This refers to the ratio of the compressor screw's axial length ($L$) to its (nominal) diameter ($D_0$), denoted as $\lambda = L/D_0$. Design values typically range from $\lambda = 0.9$ to $1.5$, with a trend toward shorter relative lengths. For a given discharge capacity, a machine with a lower $\lambda$ ratio features a larger screw diameter and larger intake/discharge port areas, resulting in lower gas flow losses. A lower $\lambda$ ratio yields a shorter, thicker screw with a higher moment of inertia; this enhances rotor rigidity and improves operational reliability. Furthermore, regarding overall configuration, shorter screw rotors allow for the tandem arrangement of two screw sections on a single shaft, resulting in a compact overall structure.
It should be noted that higher $\lambda$ values are generally adopted only for compressors with high discharge capacities. This point is particularly evident in oil-injected machines, as the screw diameter cannot be made excessively large. To achieve the required discharge capacity, some machines even have to employ an extra-long lead (with a length-to-diameter ratio exceeding 2.0).
2. Screw wrap angle: The screw wrap angle is essential for ensuring adequate intake into the inter-lobe volume and achieving internal compression. To ensure the inter-lobe volume is fully charged, the screw wrap angle ($r_{1z}$) should not exceed the intake angle ($a_{1s}$). For the male rotor, this means $r_{1z} \le a_{1s}$. The intake angle can be determined by the fundamental relationship: $a_{1s} \approx 2\pi(1 - 1/Z_1) - \beta$. If the screw features a symmetric circular-arc profile, then $\beta \approx 0$ in the formula above; for a standard profile with $Z_1=4$, the male rotor intake angle is $a_{1s} \approx 270^\circ$. When the screw lead is short, the male rotor wrap angle ($r_{1z}$) often exceeds the intake angle; an excess of up to $30^\circ$ is permissible.
If the screw features an asymmetric profile, then $\beta = \beta_{01} \approx 35^\circ$. For a standard profile with $Z_1=4$, the male rotor intake angle is $a_{1s} \approx 235^\circ$ and the female rotor wrap angle is $r_{2z} = 160^\circ$. Adopting a smaller wrap angle for asymmetric profiles is advantageous for achieving a high actual wrap angle coefficient. Generally, the ranges for screw wrap angles are:
$r_{1z} = 240^\circ \sim 300^\circ$
$r_{2z} = 160^\circ \sim 200^\circ$
Table 4-5 lists the lead ($T$), length-to-diameter ratio ($\lambda$), and wrap angle ($r_z$) for my country's standard screw series. From the table, one can observe the screw diameter, length, relative length, lead, length-to-diameter ratio, and wrap angle:
a. Once the screw diameter and lead are determined, the length-to-diameter ratio ($\lambda$) and wrap angle ($r_z$) are established. ...are directly proportional;
b. The variation range of the screw's twist angle is $240^\circ$ to $300^\circ$. For a fixed screw diameter, there are only a limited number of combinations of lead and length-to-diameter ratio that yield the aforementioned twist angle values. This explains why multiple lead values are required for a single screw diameter.
To facilitate manufacturing and reduce the variety of cutting tools required, the number of lead options for each screw diameter is restricted. Chinese standards for screw compressor series specify two lead options—long and short—for each screw diameter; however, in specific cases (such as two-stage oil-injected machines or the low-pressure stage of oil-free machines), a "special long" lead is permitted to avoid the need for an excessively large screw diameter.