This calculator divides a circle into equal tooth pitches and finds the nearest indexed angle for a face-toothed coupling. It does not predict accuracy, repeatability, torque capacity, backlash, clamp load or tooth stress.
Hirth Coupling Indexing Interactive Calculator
Divide one revolution into equal tooth pitches and round an entered target angle to the nearest ideal whole-tooth position.
Equation Used
- Exactly N equal angular pitches over one revolution.
- Only whole-tooth positions from 0 through one full revolution are considered.
- Target angle is rounded to the nearest ideal pitch without direction or path constraints.
- No pitch error, tooth form, runout, deformation, contamination, clamping, load, friction, wear, backlash or control-system model.
The displayed residual is mathematical quantization error relative to ideal equal pitches. It is not manufactured coupling error, repeatability or an acceptance tolerance.
Ideal discrete indexing
An ideal coupling with N equally spaced tooth positions divides a revolution into increments of 360°/N. A target angle that is not an exact increment can be represented by the nearest integer number of tooth steps.
The animation shows a schematic disengage, rotate and re-engage sequence. It does not reproduce tooth form, axial travel, clamping or contact mechanics.
Use as a pitch-quantization check
The arithmetic can compare candidate tooth counts and discrete angular increments. Hardware selection still requires verified drawings, manufacturer data and a complete load, connection, actuation and accuracy assessment.
Equal-pitch rounding
Ideal angular pitch is s=360°/N. The nearest whole-tooth count is k=round(θ/s), and the represented angle is ks. The absolute difference |θ−ks| is displayed in arc-seconds.
This difference is a target-quantization residual only. Real indexing error requires measured pitch, runout, seating and repeatability data.
Transparent example
With 72 ideal equal pitches, the step is 5°. A 60° target is exactly 12 steps and has zero quantization residual. A 62° target rounds to 60° and leaves a 2° residual, or 7,200 arc-seconds.
Scope and limitations
A real coupling assessment needs tooth geometry and tolerances, pitch and runout measurements, materials, heat treatment, contact and root stress, engaged tooth load distribution, clamp preload, separation margin, shaft and flange stiffness, contamination control, wear, lubrication, actuation, controls and duty cycle.
Questions
Does zero residual mean zero indexing error?
No. It means only that the requested angle is an exact multiple of the ideal pitch.
Does more teeth guarantee better repeatability?
No. It gives a smaller ideal step, while manufactured accuracy and repeatability depend on geometry, process, seating, load and condition.
Does the calculator determine torque capacity?
No. It has no size, material, tooth, clamp or load inputs.
Mechanism reference and calculation basis
Voith: Hirth serrations describes the face-serration connection and its use in positioning components, including rotary indexing tables. Product geometry and ratings require the relevant manufacturer’s specification.
The calculation uses equal angular division and nearest-integer rounding. A target halfway between ideal pitches rounds to the higher index. At 360°, the tool reports N steps and 360°, which has the same final orientation as 0° but represents a complete turn.
The ring shows at most 120 division marks for legibility, even when a larger tooth count is entered. These marks are schematic; the numeric pitch uses the full entered count.
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