The Bogardus eccentric mill grinds between two plates that rotate in the same direction about different, fixed centres. It should not be confused with an edge-runner or chaser mill. The drawing exposes the plate pair, and the calculator explores the special case of equal angular speeds.
Bogardus Mill Interactive Calculator
Adjust fixed centre spacing, common plate RPM, applied axial load and plate diameter. Compare relative face travel and speed. The plate separation in the drawing is exploded to reveal the mechanism.
Equation Used
- Both grinding plates rotate in the same direction at the entered RPM. Their centres do not orbit.
- Relative travel per revolution is2Ï€e and relative speed is2Ï€eN/60.
- Slip ratio compares relative face speed with the peripheral speed of the entered plate diameter.
- Applied axial load is entered directly. No particle, friction, pressure-distribution, motor-power or product-fineness model is solved.
Explore the Bogardus mill shown in historical Figure 86 and the 1847 report. The four calculations assume equal rotational speeds and fixed centres, with axial load entered directly; they do not predict wear or grinding performance.
Two plates with offset axes
The historical Bogardus mill uses two grinding plates turning in the same direction about separate centres. Feed passes between their opposing faces. The centre offset creates relative motion even when both plates have the same angular speed.
The animation shows the grinding pair separated vertically so the faces and fixed shafts can be seen. The real working gap is much smaller. A plan view shows the centre offset, exaggerated eightfold so it remains visible. This is not a heavy roller circling a stationary annular bed.
A historical eccentric grinding mill
The pharmacy treatise illustrates a complete Bogardus mill with hopper, plate enclosure, supporting frame and load-adjustment mechanism. Its accompanying text distinguishes this plate arrangement from the chaser mill shown on the following page. The 1847 Polytechnisches Journal report likewise identifies the eccentric positioning of two grinding members as the principle.
Relative motion for equal-speed plates
For a point at position x on a plate rotating about fixed centre c, velocity is ω cross(x-c). Subtracting the two plate velocities cancels x. Therefore the relative speed has magnitude ωe, where e is centre spacing and ω=2πN/60.
One revolution takes 60/N seconds, giving accumulated relative travel 2πe. Plate-rim speed isπDN/60, so their ratio is 2 e/D. The entered load W in lbf converts to 4.4482216153 W newtons. Unequal angular speeds require a different, position-dependent velocity calculation.
Example at the default settings
With centre spacing 16 mm and both plates turning at 60 rpm, relative travel is 100.53 mm per revolution and relative face speed is 100.53 mm/s. A 42 in plate has diameter 1066.8 mm, giving a relative-to-rim-speed ratio of approximately 3.00%. An entered axial load of 500 lbf is 2224.11 N.
These calculations do not predict particle size, throughput or drive power. Those need material and contact information not entered here.
Distinguishing the mechanism and its limits
An edge-runner or chaser mill rolls heavy wheels over a bed. The Bogardus plate mill places the grinding faces on offset axes. A concentric mill with one fixed plate is different again. Identifying the arrangement correctly is necessary before applying a velocity model.
This equal-speed model is useful for examining the effect of centre offset. It is not a reconstruction of every historical drive or a prescription for rebuilding a mill.
Frequently asked questions
Do the plate centres orbit?
No. Each plate turns about its own fixed axis.
Why is there sliding if the RPMs are equal?
The axes are displaced. At a common location the two rotational velocity vectors differ by a constant vector of magnitudeωe.
What if the plate speeds differ?
The current formula no longer gives the complete result. Relative speed then depends on position as well as centre spacing.
Does the force output predict crushing pressure?
No. It converts the entered axial load to newtons. Contact area and pressure distribution are not specified.
Historical references
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