An annular oil cup turns with the crank while a stationary drip spout feeds its open front. Oil is carried toward the outer rim and the oil holes communicating with the crank pin. Hiscox figure 324 shows this arrangement, which is distinct from the revolving-pipe oiler in the preceding figure.
Centrifugal Lubricating Device Interactive Calculator
Enter shaft speed, oil density, the inner radius of the assumed oil layer and its radial depth. The annular drawing follows these dimensions and the calculator shows pressure rise across the layer, equivalent oil head and acceleration at its outer rim.
Equation Used
- Oil co-rotates at constant shaft speed in an annular layer.
- Inner radius is positive; outer radius is inner radius plus radial oil depth.
- Gravity, transient free-surface behavior, viscosity, leakage and bearing back-pressure are excluded.
- The colored annulus represents the assumed model state even at low speed; actual oil can pool under gravity.
- No oil-flow, orifice sizing, plug-opening threshold or bearing-temperature prediction.
The illustration follows Hiscox figure 324: an open-front annular cup fixed to the crank and fed by a stationary spout. The calculator uses inner oil radius plus radial depth to define a positive annulus. It estimates ideal centrifugal pressure, not oil flow or bearing adequacy.
Open annular cup and stationary feed
Hiscox figure 324 identifies an annular cup with an open front attached to the crank. A stationary spout feeds it. Rotation carries oil toward the outer rim, where passages communicate with the crank pin.
The animation keeps the supply cup and bent spout stationary while the annular cup, rim fasteners and oil hole rotate together. The crank-pin oilway lies behind the front view; the labeled rim hole marks its connection. The open front is not a sealed filler cap.
The sketch identifies the oil path but does not determine its flow rate. Passage dimensions, lubricant properties and the downstream bearing conditions are needed to assess delivery.
What this historical device illustrates
The reference presents this as a crank-pin lubrication arrangement for a high-speed engine. Its distinctive feature is the fixed drip supply feeding an open rotating annulus.
The calculator explores the centrifugal pressure contribution in that annulus. It does not identify a particular engine installation or specify a suitable lubricant, refill interval or bearing modification.
Pressure across an annular oil layer
For oil rotating at angular speed ω, the centrifugal pressure gradient is dp/dr = ρω²r. Integration from inner oil radius r₁ to outer radius r₂ gives Δp = ½ρω²(r₂² − r₁²).
The calculator defines r₂ = r₁ + d, where d is radial depth. This keeps both radii meaningful for every slider setting. If mean radius r̄ = (r₁ + r₂)/2 is used instead, the same expression becomes Δp = ρω²r̄d. The mean-radius form is exact for this ideal model, but a chosen mean radius and depth must not imply a negative inner radius.
Equivalent oil head is h = Δp/(ρg). Density therefore affects pressure but cancels from head. Outer-rim acceleration is a₂ = ω²r₂. Pressure and head grow with speed squared; flow rate requires additional information and is not calculated.
Example annular pressure calculation
At 250 rpm, oil density 900 kg/m³, inner radius 50 mm and radial depth 25 mm, the outer radius is 75 mm. Angular speed is 26.1799 rad/s.
The ideal pressure rise is ½ × 900 × 26.1799² × (0.075² − 0.050²) = 963.83 Pa, or 0.96383 kPa. Equivalent oil head is about 109.20 mm. Acceleration at the outer rim is about 5.242 g.
Halving speed quarters pressure and head. Doubling density doubles pressure but leaves head and acceleration unchanged. None of these results supplies a volumetric feed rate or verifies sufficient lubrication for a particular bearing.
Limits of the annular model
A real free surface depends on gravity as well as rotation. The calculator neglects gravity’s effect on the shape so that the radial pressure relationship can be examined independently. At rest the centrifugal contribution is zero, while oil may still drain or pool.
Actual feed depends on passage geometry, viscosity, oil supply and downstream conditions. The historical sketch and the pressure equation do not justify an orifice-size prescription or a temperature-based bearing diagnosis.
Calculator questions
Why use inner radius rather than mean radius?
Inner radius plus positive depth gives the two boundaries of the oil layer directly: r₂ = r₁ + d. A mean-radius description is also valid if its depth keeps the inner boundary positive. Both forms give the same ideal pressure difference for the same annulus.
Does the supply spout rotate?
No. It feeds the open front of the cup while the cup turns with the crank. This differs from the separate revolving-pipe oiler shown in Hiscox figure 323.
Does zero centrifugal pressure mean no oil movement?
No. Gravity and supply pressure can still move oil. The calculator isolates only the centrifugal contribution.
Is oil flow proportional to shaft speed squared?
The ideal pressure rise is proportional to speed squared. Oil flow cannot be inferred directly without a model for the passage, viscosity and downstream resistance.
References & Further Reading
- Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances (1901), printed page 90, figure 324: open annular cup, stationary drip spout and crank-pin oil holes.
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