This page now limits the calculation to exact rotational identities for a declared polygonal barrel and an ideal point constrained at its wall radius. It does not prescribe operating speed or predict cascading, finishing, load, power or safety.
Rumbling-Barrel Rotation Explorer
Enter inner diameter, declared rotational speed and face count. The connected view shows a fixed trunnion axis, polygonal barrel and ideal wall point while calculating exact rim-speed and centripetal-acceleration identities.
Equation Used
- Inner diameter D and face count are declared geometry.
- The evaluated point is constrained to the wall at radius R=D/2.
- Rotational speed is constant and the barrel axis is fixed.
- Standard gravity g=9.80665 m/s² is used.
- Charge particle size, fill, friction, cohesion, lifters, polygon-face effects, free-surface angle, slip, cascading, cataracting, centrifuging onset of a real charge, media and part motion, impact, finishing rate, load, torque, power, drive, bearings, vibration, noise, wear, structural integrity, guards and safe operation are excluded.
Replaces unsupported process windows, event rates and operating advice with exact declared rotational identities and an explicit ideal wall-point gravity comparison.
A driven barrel rotates about a fixed trunnion axis
A conventional rumbling mill carries parts and media in a horizontal rotating barrel. Patents document polygonal drums, axle or trunnion support and a motor-driven rotary path.
The animation keeps the axis fixed, rotates the declared polygon and marks one ideal point constrained at the inner wall. The displayed inward arrow is centripetal acceleration, not a solved charge trajectory.
Use this page only to audit declared rotation
The worksheet checks angular speed, rim speed and the centripetal acceleration of an ideal point at radius D/2. It also reports the ideal gravity-equality speed for that radius.
It cannot choose a process speed, predict granular motion, estimate finishing time or size a drive, bearing, barrel or guard.
Separate exact rotation from granular behavior
The gravity-equality threshold follows from a_c=g for the ideal wall point. A real charge is not constrained as one point and requires additional data.
A transparent declared-rotation example
For D=1.2 m and n=25 rpm, R=0.6 m, rim speed is 1.571 m/s, centripetal acceleration is 4.112 m/s² and a_c/g is 0.419. The ideal wall-point gravity-equality speed is 38.60 rpm.
Those values do not establish a suitable process speed.
Wall-point rotation is not a tumbling-process model
Real charge motion depends on fill, particle and part sizes, shapes and densities, friction, cohesion, moisture, lifters, face geometry, free-surface behavior, slip, speed history and scale. Equipment design also needs load, torque, power, bearings, drive dynamics, vibration, noise, wear, structural checks and guarding.
The former universal operating band, face-event rate, finishing times, motor sizing, failure diagnosis, brand claims and maintenance instructions are removed because they were not established for one documented mill and charge.
Rumbling-barrel ledger questions
Is ideal critical speed a recommended operating speed?
No. It is only the speed at which the ideal constrained wall point has centripetal acceleration equal to standard gravity.
Does face count change the scalar wall-point equations?
No. It changes the drawn polygon but not the declared radius identities.
Does the charge shown in the drawing have solved motion?
No. It is context only.
Can this size a motor or barrel?
No.
Rumbling-mill references
- NASA, Space Resources Volume 3: particle release in a tumbling mill is framed by gravity and centrifugal effects.
- North Carolina State University, Grinding Operations Design: critical-speed relation and its dependence on mill and charge diameter.
- US Patent 2,994,165: hexagonal tumbling barrel mounted by an axle and bearing housing, driven through a sheave and belt.
- DE Patent 3,922,610: slowly rotating polygonal barrel used for deburring metal blanks.
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