Male and Female Rotor Profiles Explained – Screw Air Compressors Manufacturer

Rotor Profiles Field Engineering Reference

Male rotor has convex lobes, female has concave flutes. Conjugate through the Litvin mesh equation. 4/6 for oil-injected air (Atlas Copco GA series), 5/6 for oil-free (Atlas Copco ZR/ZT, GHH Rand), 5/7 in some Bitzer refrigeration screws. SRM A-profile symmetric circular arcs 1960s, D-profile asymmetric around 1982. SRM patents expired through the 1990s. Stosic, Smith, Kovacevic at City University London published the N-profile rack-generation method, documented in Stosic's 2005 Springer monograph "Screw Compressors: Mathematical Modelling and Performance Calculation." Rack generation decoupled the female root from the male tip, which had been the major constraint in earlier generation methods where adjusting the blow-hole forced simultaneous changes to the tip sealing, the leading flank, and the female undercutting limit.

The Leading Flank

The leading flank of the male lobe carries the full interlobe pressure differential during compression, around 7–8 bar in a single-stage oil-injected machine. Largest internal leakage path. Profile comparisons going back to Stosic and Hanjalic's 1997 paper in the Journal of Fluids Engineering and through many Purdue Compressor Engineering Conference cycles rank profiles by total sealing line length.

Compressor surging and pulsation hits centrifugals below 60 percent flow.

Clearance uniformity along the leading flank is a better predictor of field efficiency.

Leakage through a narrow gap scales with the cube of gap height in laminar conditions. A localized widening to 60 µm on a flank otherwise at 40 µm dominates the leakage integral. A different profile holding 42 µm everywhere, nominally worse by average clearance, leaks less in total. Sealing line length became the standard metric because it needs only the 2D geometry. Clearance uniformity needs the manufacturing tolerance field, which is shop-specific and proprietary.

One mid-tier European OEM switched profiles in the mid-2000s. The new profile was marginally worse on the test stand at nominal geometry. SER variance across the production run dropped. The old profile had a leading-flank zone where the clearance was sensitive to arc center positioning error during grinding. The new profile had a gentler curvature there. Nominal worse, fleet average better, worst-of-batch much better. No published comparison would rank the new profile ahead of the old.

The Blow-Hole

Stosic's own analyses in the 2005 monograph and in Purdue papers through the 1990s–2000s attribute 30–50% of total internal leakage in dry machines to the blow-hole. In oil-injected machines the oil fills the passage partially and the fraction drops. The blow-hole is a triangular gap at the high-pressure cusp where the contact line terminates before reaching the bore intersection.

The published blow-hole comparisons all use the maximum cross-sectional area over one meshing cycle. The area varies with angular position. A profile whose blow-hole peaks sharply and closes through most of the cycle leaks less per revolution than a profile with the same peak spread across a wider arc. Time-averaged area weighted by pressure difference is the quantity that predicts leakage. The comparisons that built the reputations of the D-profile and N-profile used the maximum-area method. It remains the standard in the Purdue proceedings, IMechE Part E, and the International Journal of Refrigeration.

The blow-hole has axial extent, not just cross-sectional area. Gas entering the triangle has to travel axially through a passage whose length depends on the wrap angle. Dry machines run 300°+ wrap partly for the longer blow-hole passage and partly for sealing line length. Oil-injected machines at 250–300° get less from the passage length because the oil provides its own flow resistance.

The trailing flank controls the blow-hole at the cusp. Steeper flanks shrink the triangle. OEMs will publish rotor OD, length, lobe count, wrap angle, L/D ratio in their marketing. They will not give the trailing flank curve. Two competing profiles can look identical on the leading side and diverge at the trailing flank near the cusp by tenths of a millimeter, and that divergence sets the oil-free efficiency ranking. The competitive distance between profiles, measured in SER, is encoded in maybe 15° of angular arc on the cross-section.

Steep trailing flanks push radial load onto the discharge bearing. Bearing L10 life goes with the inverse cube of dynamic load. Industrial machines need 40,000+ hours. Optimization papers in the Purdue proceedings from the 2000s–2010s produce trailing flanks steeper than anything on the market and do not include bearing life as a constraint. That is why those results stayed in the proceedings.

The lobe combination affects the blow-hole independently of the trailing flank. At 5/6, the thinner fifth male lobe sweeps closer to the cusp than the wider fourth lobe of a 4/6, and a mediocre 5/6 profile can have a smaller blow-hole than a well-tuned 4/6 because the lobe geometry closes the cusp. Part of why 5/6 displaced 4/6 in oil-free duty.

The blow-hole interaction with lobe combination is something the profile optimization community tends to underweight. Stosic's monograph treats lobe combination selection and profile optimization as largely sequential steps: pick the lobe count, then optimize the profile. In practice the interaction is strong enough that optimizing a 4/6 profile and a 5/6 profile to the same trailing-flank aggressiveness will produce very different blow-hole areas, and no amount of trailing-flank optimization on the 4/6 can close the gap. The lobe combination is doing thermodynamic work that the profile cannot replicate. This has implications for manufacturers who have invested heavily in 4/6 rotor tooling and are trying to compete in oil-free markets by profile improvement alone. The tooling investment creates inertia. Some manufacturers stayed with 4/6 longer than the thermodynamics warranted because switching to 5/6 required new rotor blanks, new grinding setups, new balancing fixtures, and new casing bores.

Screw compressor engineering at the profile level is a field where the interaction between thermodynamic optimization and manufacturing capital investment is unusually tight. A profile that is optimal in the abstract is only useful if the factory can make it. A factory that has optimized its grinding process around one profile family faces a real cost to switch, even if the new profile is measurably better. This tension between what the geometry wants and what the installed base of manufacturing equipment can deliver shapes the profile landscape more than any purely thermodynamic consideration. The profiles on the market at any given time are as much artifacts of manufacturing history as they are of engineering optimization.

Manufacturing

The grinding wheel has to fit into the female root. Minimum wheel diameter is fixed by spindle and guard geometry. One European OEM hardcodes this constraint in its optimization code after a profile could not be ground on the production equipment. Circular-arc profiles dominate mass production because the rotor-to-wheel transformation is predictable. Splines gain marginal SER at nominal.

Dressing errors on the wheel reproduce on every lobe. Same wheel, every groove. A deviation of several microns at one angular position appears at the corresponding meshing position on every lobe of every rotor ground with that wheel until the next dress. Random scatter averages out over the meshing cycle. Systematic dressing error does not. Standard dimensional inspection does not catch it. Angular profile measurement on a rotor checking instrument does. A rotor can pass all checks and carry a persistent seal weak spot for its entire life.

The connection between dressing error and field performance is underexplored in the literature because rotor grinding is a manufacturing discipline and screw compressor thermodynamics is a fluid mechanics discipline, and the two communities do not talk to each other much. The OEMs bridge them internally because they have to. The gap in the open literature is a gap in institutional structure, not a gap in knowledge.

Clearance Setting

The male rotor grows radially faster than the casing on start-up. Cold clearance at the male tip has to accommodate the worst thermal transient. VSD machines ramping slowly need less excess cold clearance than fixed-speed machines hitting full load in seconds. The tighter cold clearance means better SER at steady state for the life of the machine, which is a permanent full-load efficiency benefit from VSD that gets overlooked in VSD sales literature because VSD is sold on part-load savings.

VSD screw compressor operation varies motor speed from 25 to 100 percent.

Female tips deflect inward under gas pressure. Cold clearance is set larger than a rigid calculation to let the deflection close the gap. Both rotors deflect at midspan under gas load. Above single-stage pressure ratios around 5:1, midspan contact at full load leaves polished wear tracks visible at disassembly. The N-profile tolerates center distance drift from thermal cycling and bearing wear.

Oil-Injected

Oil fills clearances, partially seals the blow-hole, absorbs heat. Above about 40 m/s tip speed, oil churning becomes a significant parasitic. Oil viscosity at the contact depends on oil inlet temperature from the circuit and cooler. Oil-injected profile optimization is a system problem involving the whole oil circuit, and profile differences in oil-injected machines are smaller than in dry machines because the oil masks geometric imperfections.

Oil-injected machines are where most of the global compressor fleet sits. The GA series from Atlas Copco, the ASD/BSD series from Kaeser, the EG/EP series from Kobelco, and dozens of Chinese manufacturers building on N-profile derivatives or older SRM-derived geometries, all compete in this segment. The profile contributes to the efficiency differences between these machines, and it is not the only contributor and probably not the largest contributor. Motor efficiency, drive efficiency, oil separator pressure drop, cooler sizing, and the control algorithm for capacity regulation all affect the package SER that the customer sees. A manufacturer with a profile 1% worse than a competitor's but a separator with 0.3 bar less pressure drop and a better VSD algorithm can come out ahead on the ISO 1217 Annex C test. Profile gets the marketing emphasis because it is the most defensible IP and the hardest for a competitor to reverse-engineer from external measurements. Separator design and control algorithms are easier to replicate.

That said, within a given manufacturer's product line, profile improvement is the most leveraged change available. Improving the profile improves every unit shipped. Improving the separator improves only units with that separator. Improving the control algorithm requires a firmware update across the fleet. The profile is baked into the iron, and getting it right or getting it wrong propagates to every machine for the entire production run of that rotor design, which might be 10–15 years. Profile decisions have very long shadows.

Dry

Every clearance leaks at full penalty. The move from 4/6 symmetric to 5/6 asymmetric profiles through the 1990s–2000s was the single largest step improvement in dry compressor SER. Timing gears prevent contact. PTFE coatings for transient touch; MoS₂ at higher temperatures.

The gap between dry and oil-injected SER persists because a gas-filled clearance leaks more than the same clearance filled with oil, regardless of profile. The gap narrowed through profile improvement and tighter manufacturing tolerances, driven primarily by the 4/6-to-5/6 transition and by better grinding equipment that could hold tighter clearances consistently.

Dry screw compressor profile design is the subfield where the academic literature and the commercial practice are closest to each other, because the dominant leakage paths (blow-hole, leading flank) are geometric and the optimization is less entangled with system-level variables like oil temperature or separator design. The N-profile's impact was largest in the dry segment for this reason.

Water-Injected

The fluid in the chamber sets thermal economy and clearance.

Discharge Port

Built-in Vi is a joint function of profile, wrap angle, and port geometry. Noise performance attributed to profiles in marketing sometimes comes from port contouring.

End of Reference