A cage disintegrator breaks material by repeated impacts with rotating bars or pins. Hiscox’s historical section shows two concentric shafts driving disks and beating bars in opposite directions. The animation below exposes two nested pin rows and shows how their separate disks connect to a solid shaft and a surrounding hollow shaft.
Disintegrator Interactive Calculator
Set the two pin-circle speeds and cage spacing. Inspect the concentric drives, calculate rpm, and compare an explicitly ideal tangential particle transfer between the rows.
Equation Used
- Two concentric pin circles rotate oppositely.
- Outer circle radius equals inner radius plus entered radial spacing.
- Ideal particle release is tangential at inner pin speed, followed by force-free straight flight.
- Relative kinetic energy is a comparison scale, not measured crushing work.
Transfer model assumes a point particle leaves the inner circle tangentially at vi. It does not predict pin interception, fracture, throughput or wear.
Nested cages on independent concentric shafts
The blue inner row and gold outer row rotate in opposite directions. Their pin circles have different radii, so equal peripheral speeds require different rpm. The transparent face view exposes the pin ends; the longitudinal section below identifies the two carrier disks and the solid and hollow shafts. Each bar belongs to its own carrier, and the separated radii keep the rows from intersecting.
The center opening is the feed region. Material can encounter successive pin rows as it moves outward. The enclosing casing collects the discharge. The representative pin counts, bar thicknesses, clearances and shaft proportions explain the construction rather than specify a manufacturable mill.
The animation shows rotor kinematics, not individual ore fracture. Real particle paths depend on feed, preceding impacts, pin phase, air drag and particle interactions. The displayed geometry does not predict individual particle trajectories or product size.
Impact reduction and material testing
Hiscox identifies the historical disintegrator as an ore-pulverizing device. Stedman’s current cage-mill description confirms that concentric counter-rotating rows provide successive impact opportunities, with material entering the inner region and progressing outward.
This page illustrates that mechanism and compares kinematics. It does not infer a mill’s throughput, reduction ratio, pin life or motor power from tip speed alone. Those depend on the particular machine, material properties and operating conditions.
Rotor rpm and an explicit ideal transfer model
Let inner radius ri=Di/2 and outer radius ro=ri+g, with dimensions converted to metres. Each rotor speed is n=60v/(2Ï€r). Inner and outer rotations have opposite signs in the animation; the rpm outputs report their magnitudes.
For the transfer calculation only, assume a point particle leaves the inner pin circle tangentially at speed vi and travels in a straight line without drag or other impacts. The distance to the outer circle is √(ro²−ri²), so flight time is that distance divided by vi.
At the outer circle the particle’s tangential component is vi·ri/ro and its radial component is vi√(1−(ri/ro)²). An outer pin moves oppositely in the tangential direction at vo. The relative-speed magnitude is therefore vrel=√(vi²+vo²+2vi·vo·ri/ro).
The relative kinetic-energy scale is vrel²/2000 kJ/kg. It is kinetic energy in the instantaneous pin-relative frame, not measured fracture work, motor energy or guaranteed impact energy. A pin must actually intercept the particle for an impact, which this model does not predict.
The simple sum vi+vo is a limiting opposing-tangent comparison. At a larger radius, a freely moving particle’s direction is not exactly opposite the outer pin velocity, so treating that sum as every particle’s actual impact speed is misleading.
Example with different pin-circle radii
For a 500 mm inner pin-circle diameter and 150 mm radial spacing, the outer pin-circle diameter is 800 mm. At 90 m/s on both circles, inner speed is 3,437.7 rpm and outer speed is 2,148.6 rpm, in opposite directions.
Under the stated tangential-release and straight-flight assumption, flight time is 3.47 ms. At the outer circle, particle tangential speed is 56.25 m/s and radial speed is 70.26 m/s. Relative speed against the opposing outer pin is 162.25 m/s, giving a relative kinetic-energy scale of 13.16 kJ/kg.
This differs from the 180 m/s surface-speed sum. Neither number by itself predicts throughput, particle size or wear. The actual release speed and direction need evidence from the real mill.
What the drawing and calculation leave open
The face view shows representative rows at the entered pin-circle radii. The side view is a schematic section through representative bars: it shows which disk and shaft drive each row, not a snapshot of all bar positions in the face view. Both actual rpm and the display slow-down factor are stated.
The ideal transfer calculation assumes point particles, tangential release at inner pin speed and no intervening forces or collisions. It does not solve whether the next pin arrives at the outer-circle crossing, or how restitution and fracture divide energy after contact.
Bar strength, physical running clearance, balance, bearings, containment, dust handling and motor selection require machine-specific engineering. Input ranges and drawn bar thicknesses are not operating limits. Wear and service life require material, contact and operating data beyond the entered speeds.
Construction and operating-principle sources
Hiscox, Mechanical Movements, Powers, Devices and Appliances, expanded edition, printed page 310, figure 1259a: concentric shafts, carrier disks and counter-rotating beating bars.
Stedman Machine Company: cage mills and pulverizers describes successive impacts in concentric counter-rotating rows. The explicit ideal transfer calculation on this page is a geometric model, not manufacturer performance data.
Disintegrator questions
Do the two pin rows collide?
No. They occupy distinct radial circles and belong to separate carriers. The diagram keeps those rows separated throughout rotation.
Why do equal tip speeds produce different rpm?
A larger circle has a longer circumference, so it needs fewer revolutions per minute to reach the same peripheral speed.
Why is relative speed smaller than the sum of the two inputs?
In the ideal transfer model, the particle flies tangentially from the inner circle. At the outer circle its velocity has both radial and tangential components; only its tangential component directly opposes the outer pin.
Is the energy result a measured crushing energy?
No. It is the relative kinetic-energy scale under the stated release assumption. Contact timing, fracture and losses are not solved.
Are the rotating rows a complete machine design?
No. They illustrate the nested-cage mechanism. Pin count, thickness, carrier and shaft dimensions are schematic.
Can speed alone determine pin life?
Speed squared alone does not predict material-specific pin wear or service life.
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