A Curvic coupling joins mating annular faces with curved teeth. This calculator illustrates an ideal symmetric preload case, with equal contact on both flanks of each tooth. It calculates local flank-force components and a compatible local displacement; these are not the coupling’s net self-centering force or a complete alignment solution.
Curvic Coupling Interactive Calculator
Inspect a curved annular tooth face and an enlarged ideal flank. Adjust clamp preload, pressure angle, equally loaded teeth and local transverse movement; calculate opposing force magnitudes without treating them as net centering force.
Equation Used
- Equal load on both flanks of all N teeth.
- Frictionless rigid contact and no applied torque or bending.
- Pressure angle measured between flank and axial direction.
- Local movement does not solve whole-coupling alignment.
Ideal symmetric two-flank preload without applied torque. Magnitude sum is not net centering force.
Curved teeth distribute the axial clamp load
The face drawing uses the entered tooth count and illustrative concave outlines, following the recognizable annular form in Gleason’s Curvic coupling description. A mating convex form fills the complementary spaces.
The lower drawing isolates one tooth flank. Its pressure angle is measured from the axial direction along the flank, equivalently between the contact normal and the tangential direction. The gold point shows a local displacement on that ideal straight flank, not a sideways translation of the entire ring.
Explore an ideal preload distribution
Increase axial preload to see both local force components increase. Increase the number of equally loaded teeth to reduce each flank’s force while preserving the total applied clamp load. The pressure angle changes the normal and tangential components.
The local transverse-shift input controls only the isolated-flank movement demonstration. It does not change the static preload forces and is not a prediction that a real coupling will correct that amount of misalignment.
Force balance at two flanks per tooth
With clamp force Fₐ shared equally over both flanks of N teeth, the normal force per flank is Fₐ/(2N sin α). Its tangential component is Fₐ/(2N tan α). Summing the magnitudes of all 2N tangential components gives Fₐ/tan α; their directions oppose, so this scalar sum is not a net centering force.
For one ideal flank, transverse displacement e and compatible axial displacement z obey e=z tan α, or z=e/tan α. The local motion ratio z/e is therefore cot α. This relationship defines the small ideal flank demonstration, not a complete coupling assembly path.
50 kN distributed over 48 teeth
At 20 degrees with 48 equally loaded teeth and 50 kN clamp load, each flank has approximately 1,522.81 N normal force and 1,430.98 N tangential force. The sum of tangential magnitudes is approximately 137.374 kN; the opposing components balance in the symmetric preload model.
A local transverse shift of 10 micrometres corresponds to 27.475 micrometres axial shift on the ideal flank. It is not a predicted whole-ring centering movement.
What a complete coupling calculation still needs
This equal-share model excludes applied torque, bending, friction, compliance, manufacturing errors and nonuniform contact. It does not establish allowable torque, contact stress, clamp-bolt sizing, fatigue life or actual alignment behavior.
The directions and distribution of contacts around the full coupling determine its response to misalignment. A scalar sum of opposing force magnitudes cannot establish that response.
Flank-model questions
Is the first result a net centering force?
No. It sums magnitudes of opposing tangential components. They balance under the stated symmetric preload assumption.
Why are there 2N contact flanks?
This example assumes both sides of each of N teeth share the axial preload equally, with no applied torque.
Why does transverse shift not change the forces?
The ideal static force model is set by preload, contact count and angle. Shift only controls the separate geometric movement example.
Does this specify manufacturable tooth geometry?
No. The curved face outlines are illustrative and do not specify grinding-wheel settings or tolerances.
Reference
Gleason Works, Curvic Coupling Design, Gear Technology, November/December 1986. Figure 1 on printed page 34 shows concave and convex tooth forms. Printed page 44 gives the clamp-force contribution involving Fₐ/(2 tan α). The local force and displacement equations here follow the stated ideal equal-share geometry; this tool is not a replacement for the complete design procedure.
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