Check axial self-locking and calculate the frictional torque capacity of an assembled tapered fit.
Select a target and calculate.
Calculate the frictional torque limit of a self-locking tapered interference fit from cone half-angle, two friction coefficients, interface pressure, contact length and mean diameter.
With β = 2°, μll = 0.12, μlu = 0.10, pm = 30 MPa, lF = 50 mm and DFm = 60 mm, tan β ≈ 0.0349 < 0.12. Thus μR ≈ 0.0957 and MtR ≈ 812 N·m.
Valid only in the self-locking range μll ≥ tan β. Self-locking means resistance to spontaneous axial release, not a complete operating-load verification. Check interface pressure, assembly, stresses, tolerances, friction scatter and required safety separately.
A tapered interference fit joins a shaft and hub through pressure on their conical contact surfaces. This calculator estimates the torque that friction can transmit in an assembled, self-locking fit.
Self-locking concerns axial release: in this model the taper cannot slide out on its own when μll ≥ tan β. Torque transmission concerns circumferential slip and therefore also depends on μlu.
μR = μlu · √[1 − (tan β / μll)²]MtR = π · lF · DFm² · pm · μR / (2 cos β)
| Symbol / input | Meaning |
|---|---|
| Transmissible friction torque MtR | Calculated frictional torque limit for the entered coefficients and interface pressure. This is not yet an allowable operating torque; load peaks and safety require separate checks. |
| Cone half-angle β | Angle between the cone surface and its axis. From a drawing with large diameter D1, small diameter D2 and axial taper length L: β = arctan[(D1 − D2)/(2L)]. Halve a stated full included angle first. |
| Axial friction coefficient μll | Static friction coefficient against axial release; obtain from tests or reliable data for the actual materials, surfaces and lubrication. Self-locking requires μll ≥ tan β. Enter a decimal, e.g. 0.12. |
| Circumferential friction coefficient μlu | Friction coefficient against circumferential slip; obtain from relevant tests or contact-pair data. Do not automatically equate it with the axial coefficient; enter a decimal. |
| Mean interface pressure pm | Mean normal contact pressure between the assembled tapered surfaces. Obtain from a separate fit calculation or reliable measurement accounting for interference, tolerances and materials; not an arbitrary design value. |
| Axial contact length lF | Actual load-bearing length of the tapered interface along the axis, from the drawing or measurement. Exclude chamfers, reliefs and areas without contact. |
| Mean interface diameter DFm | Diameter at the middle of the effective contact length; for a straight taper with fully contacting ends, approximately (D1 + D2)/2. Obtain from the contact geometry in the drawing or measurement. |
β is the half included angle to the axis, read from the drawing or calculated as arctan[(D1 − D2)/(2L)]. μll and μlu describe friction against axial release and rotation; use values for the actual materials, surfaces and lubrication. pm is the mean interface pressure from a separate fit calculation. lF is the actual axial contact length and DFm its mean diameter, both from the drawing or measurement.
First determine the assembled contact geometry and pressure. Then choose friction coefficients for the adverse realistic operating condition and enter β as a half-angle. If μll is below tan β, the joint is not self-locking and the calculator rejects the input. Otherwise compare the result with the highest actual operating torque using an appropriate safety margin.
β = 2° gives tan β ≈ 0.0349. With μll = 0.12 the self-locking condition holds. μlu = 0.10 gives effective friction coefficient μR ≈ 0.0957. For pm = 30 MPa, lF = 50 mm and DFm = 60 mm, MtR ≈ 812 N·m.
MtR is the calculated frictional torque limit for the entered values. If peak operating torque exceeds it, revise geometry, pressure or joint concept. A lower operating torque alone does not approve the design: check safety factor, friction scatter, assembly, material stresses and tolerances.
Enter angle in degrees, pressure for example in MPa and lengths for example in mm; the calculator converts units internally and reports N·m. Friction coefficients are dimensionless decimals.
Use for preliminary assessment of an existing tapered fit and for comparing contact length, diameter and surface conditions.
The relationship assumes a self-locking tapered interference fit using mean interface values. It does not calculate pressure from interference and tolerances, assembly force, stresses, fatigue or an allowable safety limit.
Common mistake: Do not enter the full included angle as β. Do not assume μll and μlu are equal without evidence. Do not guess pm from the desired result. Do not treat MtR as an approved operating torque.
Axial friction prevents spontaneous release under the model assumptions when μll ≥ tan β. This is not a safety verification.
From a separate fit calculation using geometry, interference, tolerances and elastic material properties, or a suitable measurement on the assembled part.
Only after peak operating torque including load spikes lies below it with the required safety margin and assembly, stresses and tolerances have also been checked.