A conical pivot bearing supports a rotating shaft against an axial load through an inclined bearing surface. The calculator uses a narrow annular contact-band idealization: resolve the axial load into normal contact load, then use friction coefficient and mean contact radius to estimate torque. Shaft speed determines the associated friction power.
Conical Pivot Bearing Interactive Calculator
Estimate sliding friction torque and power for a narrow annular contact band on a conical pivot. Adjust axial load, friction coefficient, mean contact radius, included cone angle and shaft speed.
Equation Used
- Axial load carried by a narrow axisymmetric annular contact band at the entered mean radius.
- Constant coefficient of sliding friction; no solved lubricant film or elastic contact distribution.
- Alpha is the included cone angle; half-angle is alpha/2.
- The 2 ozf·in benchmark has no connection to material strength or bearing capacity.
The 2 ozf·in result is a comparison with a chosen reference, not a rated bearing limit. Dimensions other than included angle and mean contact radius are illustrative.
A supported rotating cone
The axial section shows the rotating cone seated in a stationary cup. Gold marks identify the assumed narrow contact band. Relief elsewhere makes clear that the calculator is not integrating pressure over the entire conical flank. The plan view uses transparent shaft material so the ring and rotating witness marks remain visible.
Hiscox’s historical figure 1277 shows a conical pivot bearing with an adjusting screw. The screw in this illustration is stationary during operation; it is included to distinguish the bearing support from the rotating shaft. It has no adjustment input and is not a solved thread design.
The gold arrows show local surface-normal directions. Normal reactions are distributed around the complete ring, so the displayed pair must not be interpreted as two actual point loads. Radial components cancel by symmetry; their axial components support the applied load.
Understanding an axial bearing load path
Historical conical pivot bearings supported vertical rotating shafts, and theory-of-machines treatments use conical pivots to explain inclined contact and friction torque. This page focuses on that load path and an explicitly assumed annular contact band.
Instrument pivots, full conical thrust surfaces and lubricated bearing designs can have different contact behavior. A product-specific bearing calculation needs its actual geometry, materials, load distribution and lubrication model. The diagram does not establish a recommended operating load or RPM.
Narrow-band friction model
Let W be axial load, alpha the included cone angle, mu the sliding friction coefficient and r the mean radius of the assumed narrow contact band. With beta = alpha/2, the integrated normal load is N = W/sin(beta). Friction torque is M = mu N r = mu W r/sin(beta).
When W is entered in lbf and r in inches, M is in lbf·in. Multiply by 16 to obtain ozf·in. The calculator converts ozf·in to N·m using 0.0070615518 N·m per ozf·in. Friction power is P = M_Nm × 2 pi × RPM/60.
For contact spread across a broad conical surface, torque instead requires integration over its pressure distribution. The entered radius here is a narrow-band mean, not the outer radius of a full pivot. Substituting a full-contact outer radius would generally give the wrong result.
The final percentage is 100 M/(2 ozf·in). The 2 ozf·in denominator is an arbitrary comparison reference. It is neither a utilization limit nor a suitability test.
Example at a 0.040-inch contact radius
For W = 20 lbf, mu = 0.05, r = 0.040 in, included angle alpha = 60° and speed 100 RPM, sin(alpha/2) = 0.5. The integrated normal load is 40 lbf.
Friction torque is 0.05 × 40 × 0.040 = 0.080 lbf·in, or 1.280 ozf·in. In SI units this is approximately 0.009039 N·m, giving 0.09465 W of friction power at 100 RPM.
The comparison to 2 ozf·in is 64%. Doubling speed doubles power in this constant-friction model while leaving torque unchanged. Doubling contact radius doubles both torque and power. These trends do not predict temperature, wear or service life.
Model limits
At fixed load, friction coefficient and contact radius, a smaller included cone angle increases the integrated normal load and calculated friction torque. This follows from the reciprocal sine of the half-angle; it does not by itself determine contact pressure or bearing suitability.
Contact pressure requires an area or a contact-mechanics model, neither of which is supplied here. Temperature also requires heat-transfer information. Hardness, surface finish, lubrication grade, allowable stress and service life cannot be deduced from these five inputs.
The drawing uses an illustrative 0.10-inch outer cone radius to place the selectable contact band inside the cone. That radius and the relieved cup are explanatory geometry, not a machining recommendation. No universal cone/cup angle mismatch is specified.
Conical pivot bearing questions
Is the angle included or half-angle?
The slider gives the full included angle alpha. The force equation uses alpha/2.
Is the contact radius the shaft radius?
No. It is the mean radius of the narrow annular contact band assumed by this calculator.
Why does speed change power but not torque?
The model holds the friction coefficient constant. Torque depends on load and geometry; power is torque multiplied by angular speed.
Does exceeding the 2 ozf·in reference mean failure?
No. It is an arbitrary comparison value, not a rated limit or a design check.
Does the calculated wattage give bearing temperature?
No. It gives mechanical dissipation. Temperature needs a thermal model and operating environment.
Mechanism and calculation references
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, printed page 316, figure 1277: conical pivot bearing and adjusting screw.
Kalinga Polytechnic, Theory of Machine, printed pages 20–21, questions 16–17: conical-pivot normal-force resolution, elemental ring friction torque and friction power. This calculator uses the narrow-ring form of that relationship rather than the full-surface uniform-pressure or uniform-wear integrations.
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