A conical pug mill mixes material in a tapered vessel using a revolving shaft and paddles or a spiral worm. This illustration follows the historical vertical paddle arrangement: the vessel stays fixed while paired curved paddles turn inside it. The calculator separately compares an entered inlet pressure with a die-pressure interval; it does not predict extrusion or mixing performance.
Conical Pug Mill Interactive Calculator
Compare an entered inlet absolute pressure with an entered die-pressure interval. This is an arithmetic worksheet, not a prediction of the historical paddle mill shown in the animation.
Equation Used
- Positive absolute pressures in the same units.
- Die interval endpoints are entered observations or a comparison scenario, not a calculated operating range.
- Historical cutaway and pressure worksheet are separate: no pressurized boundary, flow, torque or vacuum model is solved.
Use absolute pressures in bar for a physical pressure ratio. The two die limits are sorted automatically. Their arithmetic midpoint is not a measured average over time.
Fixed conical vessel and rotating paddles
Hiscox’s figure 1446 depicts a vertical conical pug mill with a top drive, central shaft and curved paddles for mixing clays, mortar, concrete and other material. The taper and progressively shorter paddles are visible through the cutaway. The adjacent figure 1445 instead shows a spiral worm, which is a different rotor arrangement.
In the animation, the shaft and its attached paddles rotate as one assembly. The casing, supporting frame, bearing and drive housing remain stationary. The front half of the vessel is removed to expose the moving parts. The lower opening marks the outlet; material flow through it is not simulated.
The historical source does not specify enough dimensions to reconstruct a particular machine. Paddle count, curvature, drive housing and support proportions are illustrative. Rotation takes eight seconds per turn for viewing; it is not an operating-speed recommendation. Pressure controls alter the separate comparison scale, not the rotor speed.
What the historical drawing represents
The historical source identifies this mechanism with mixing clay, mortar and concrete. It illustrates the mechanical arrangement rather than supplying a modern process specification. It does not establish the equipment used by any current manufacturer.
Modern pug mills can differ substantially in shaft orientation, paddle or screw geometry, extrusion tooling and vacuum equipment. A modern machine’s throughput, de-airing performance and motor requirements must come from its actual design and process data. They cannot be inferred from this historical cutaway.
Pressure-comparison worksheet
Let Pin be the entered inlet absolute pressure and let A and B be the two entered die pressures. The calculator first orders them: Plow = min(A, B) and Phigh = max(A, B). It then computes Pmid = (Plow + Phigh)/2 and the dimensionless ratio R = Pmid/Pin.
The first two results report the ordered endpoints; the other two report the interval midpoint and its ratio to the inlet. These are simple arithmetic comparisons. A midpoint between two readings is not automatically the actual mean pressure during operation.
Use absolute pressures for the pressure ratio. Dividing gauge readings does not give an absolute pressure ratio. All readings must use the same pressure unit and reference. The supplied slider ranges are exploratory worksheet bounds, not established ratings for a pug mill.
No auger diameter, pitch, shaft speed, material rheology, die dimensions or vacuum conditions are inputs. Consequently the worksheet does not predict flow, torque, energy consumption, consolidation or de-airing.
Example: comparing three entered pressures
For an inlet absolute pressure of 1 bar and entered die limits of 5 and 15 bar, the reported interval is 5–15 bar. Its midpoint is (5 + 15)/2 = 10 bar, and the midpoint/inlet ratio is 10/1 = 10.
Changing the inlet pressure to 2 bar leaves the entered die interval and its midpoint unchanged. The ratio becomes 10/2 = 5. Changing the upper die pressure to 25 bar while retaining a 5 bar lower limit gives a midpoint of 15 bar.
If the two die entries are reversed, the calculator sorts them. Neither the ordered range nor the midpoint is a predicted pressure rise through the pictured vessel. A measured operating condition would require real pressure data from a suitable machine.
Reading the diagram and its limits
The open cutaway makes the paddle arrangement visible, but it is not a pressure-vessel model. There is no calculated pressure field, material residence time, extrusion rate or quality score. The pressure bar beneath it displays three entered numbers and their arithmetic relationship.
A paddle mixer and a continuous screw extruder should not be assigned the same performance solely because both can have tapered housings. Geometry and process conditions determine how material is mixed and conveyed. This page does not provide universal clearances, vacuum settings, material recipes, service intervals or product-specific performance figures.
Conical pug mill questions
Does the vessel rotate?
No. In this historical arrangement the central shaft and paddles rotate inside a fixed conical vessel.
Is this a screw extruder?
The illustrated rotor uses discrete paddles. The historical source also depicts a separate spiral-worm pug mill, but that is not the same rotor.
Why do the pressure sliders not change the paddles?
The pressure worksheet is independent of the historical animation. No relation between those pressures and shaft motion has been supplied or solved.
Is the midpoint a measured average pressure?
No. It is the arithmetic midpoint between the two entered limits. An actual time average requires pressure measurements over time.
Can the calculator size a motor or predict throughput?
No. Its inputs are three pressure values. Motor sizing and process performance require additional geometry, material and operating data.
Historical mechanism references
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, printed page 349, figure 1446: vertical conical paddle pug mill and stated mixing applications. Figure 1445 shows the separate spiral-worm form.
Thomas Walter Barber, The Engineer’s Sketch-Book of Mechanical Movements, printed pages 122–123, figures 999–1000: conical pug-mill and worm arrangements. These drawings establish the mechanism layout, not modern pressure or throughput ratings.
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