A Roots rotary blower is a positive-displacement machine with two equal-lobe rotors turning at equal speed in opposite directions inside a casing. Timing gears maintain phase without rotor contact; trapped gas pockets travel around the casing from inlet to discharge.
Roots Rotary Blower Ideal Event-Frequency Calculator
Explore ideal combined pocket-release timing for two equal-lobe, equal-speed counter-rotating rotors.
Equation Used
- Two rotors have the same integer lobe count and rotate at equal speed in opposite directions.
- Each lobe on each rotor creates one ideal discharge-opening event per revolution.
- The speed is constant and timing gears maintain phase without rotor contact.
- The event frequency is geometric and is not asserted to be the dominant acoustic tone.
- Flow, pressure, backflow, leakage, temperature, power, forces, clearance and noise amplitude are excluded.
The secondary figure uses the same selected equal rotor speed and integer lobe count.
How the Roots blower topology works
Two symmetrical rotors turn in opposite directions in an oval casing. External timing gears keep their lobes phased and prevent contact. Gas is trapped between each rotor and the casing, carried around the outside, and exposed to the discharge side.
The working pockets do not progressively shrink like screw-compressor chambers. Atlas Copco describes the basic machine as a valveless displacement compressor without internal compression; pressure-side gas flows back when a chamber opens to the outlet.
What this calculator demonstrates
Select equal rotor speed and equal integer lobe count. The calculator reports shaft frequency and the ideal frequency, interval and per-minute count of pocket-release events from both rotors.
It does not calculate displacement, volume flow, leakage, pressure, temperature, power, efficiency, clearance, forces, torque, noise amplitude, resonant modes or silencer performance.
Ideal two-rotor event count
Each of the two synchronized rotors presents Z lobes to the discharge once per revolution. For shaft speed n in rpm, the ideal combined discharge-event frequency is f=2Z(n/60). Event interval is τ=1/f, event rate is 2Zn per minute, and shaft frequency is n/60.
This count is a geometric timing reference. Real pressure pulsation and acoustic spectra depend on port opening, backflow, lobe profile, helical twist, clearances, piping and operating pressure; the ideal event count is not automatically the dominant silencer-tuning frequency.
Selected ideal example
For two three-lobe rotors at 3,000 rpm, shaft frequency is 50 rev/s. The pair has six ideal discharge events per revolution, giving 300 events/s, a 3.333 ms interval and 18,000 events/min.
The example does not establish flow, pressure, noise or a safe speed for any particular blower.
Scope and correction boundary
The original calculator used Zn/60, which counts lobe passages for one rotor while labeling the result as the blower's pulse frequency. A published three-lobe two-rotor study reports six exhausting periods per rotor revolution, supporting the corrected 2Zn/60 geometric event count.
The original article's universal flow, pressure, clearance, temperature, life, cost, efficiency, filtration and fault-diagnosis numbers were not derivable from rotor speed and lobe count. They have been removed; use the exact manufacturer's map, manual and safeguards for a real machine.
Questions
Why is there a factor of two?
Both synchronized rotors expose Z trapped pockets to the discharge during each revolution, so the ideal combined count is 2Z events per revolution.
Is this the frequency for selecting a silencer?
Not by itself. It is a geometric event frequency; actual acoustic spectra also depend on porting, backflow, piping, lobe geometry, pressure and resonances.
Do the rotors touch?
No in the documented operating principle. Timing gears maintain their phase and running clearances separate the rotors and casing.
Can the calculator predict flow or pressure?
No. Displacement geometry, length, clearances, leakage, gas state and system resistance are excluded.
Primary technical references
- US 30,157, Rotary blower, P. H. Roots — original two-shaft rotary blower/pump topology and simultaneous geared rotation.
- Atlas Copco, Compressed Air Manual, section 2.1.9 — valveless displacement principle, no internal compression, counter-rotating geared rotors.
- Atlas Copco, Rotary Lobe and Screw Blower Study — two- or three-lobe rotor pair, timing gears and fixed-volume transport.
- Numerical study and experimental validation of a Roots blower with backflow design — six exhausting periods per revolution for a three-lobe two-rotor blower.
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