A Hirth joint connects facing parts through radial serrations held together by axial clamping. The teeth provide angular location and transmit torque. The calculator below explores an ideal wedge-force relationship; it does not rate a manufactured joint or select its fasteners.
Hirth Joint Interactive Calculator
Compare torque, effective radius, model wedge angle, a chosen multiplier and entered clamp force. Results describe the stated ideal model only.
Equation Used
The model defines tangential force Ft = T/r and axial component Fa = Ft/tan(theta). The multiplied force is SF × Fa; the torque comparison is Fpre × r × tan(theta)/SF. A positive force difference is not a safety certificate or a measured joint capacity. Angle theta is defined by this force ratio and must not be confused with a tooth’s full included angle.
- Model angle theta satisfies Ft/Fa = tan(theta). The drawing does not establish a manufacturing angle convention.
- The model uses one effective radius and ideal force resolution; it does not calculate tooth-by-tooth load sharing.
- Friction, fatigue, local tooth stress, face flatness error, and bolt relaxation are not included.
How facing serrations connect the parts
Matching radial teeth on opposing faces engage when the parts are drawn together axially. Tooth flanks locate the parts and carry the tangential force associated with torque. The assembly can be separated axially when its clamping arrangement is released.
Components
- Two mating serrated faces provide the form-fitting connection.
- A clamping arrangement maintains engagement. Its fasteners and preload depend on the actual assembly.
- The connected hubs or shafts carry the load into and away from the joint.
The oblique view shows 24 illustrative radial teeth. The upper ring lifts clear, turns through one 15-degree pitch, and returns into engagement. Tooth count, proportions and playback timing are fixed examples, not dimensions selected by the calculator. The separate force triangle shows tangential force to the right and axial force upward; its proportions follow the model angle. The force calculation does not control engagement or predict stress or failure.
Applications
Voith describes Hirth serrations for detachable connections between shafts, disks, rotors, wheels and cranks, and for precision positioning. Suitability and ratings depend on the selected component and its documented assembly conditions.
An indexing arrangement with N equally spaced teeth has a nominal pitch of 360°/N. That geometric pitch does not establish positioning accuracy or load capacity. The linked indexing calculator explores the pitch separately.
The ideal force comparison
Use torque T in Nm, effective radius r in metres, entered clamp force Fpre in newtons and dimensionless multiplier SF. The calculator converts its millimetre and kilonewton inputs to those units.
Ft = T/r; Fa = T/[r tan(theta)]; Fcomparison = SF × Fa; Tcomparison = Fpre r tan(theta)/SF. Force difference is 100(Fpre−Fcomparison)/Fcomparison.
Here theta is specifically the model angle for which Ft/Fa = tan(theta). A drawing’s included tooth angle cannot be substituted without deriving the matching force geometry. The radius is an effective load radius, not an average of two diameters.
No friction coefficient, contact area, material strength, bolt geometry, fatigue history or load distribution is entered. These equations therefore do not establish allowable torque, required tightening torque, service life or a safe preload. SF is an arbitrary scenario multiplier, not a validated design factor.
Hypothetical arithmetic example
At T = 25,000 Nm, r = 100 mm, theta = 60°, SF = 1.5 and Fpre = 250 kN, the tangential force is 250 kN. The ideal axial component is 250/tan(60°) ≈ 144.3 kN.
The multiplied force is about 216.5 kN. The torque comparison is about 28,868 Nm, and the force difference is about +15.5%. These are the preset model results, not a rating for a particular Hirth joint or bolt.
Doubling T doubles the two calculated forces and lowers the percentage difference; it does not change the torque comparison, which depends on the other four inputs. Doubling the effective radius halves those forces and doubles the torque comparison.
Choosing and maintaining a real connection
Hirth serrations, other face couplings and keyed connections use different contact geometries. Compare documented ratings, accuracy, assembly requirements and permitted operating conditions for the actual components. A shared diameter does not give them comparable torque ratings or service lives.
Repair, lubrication and tightening instructions must come from the assembly documentation. This model cannot diagnose runout, choose bolt size or grade, approve re-machining or prescribe a tightening torque.
Frequently asked questions
What does a positive force difference mean?
The entered clamp force exceeds the multiplied ideal axial force in this model. It does not establish tooth strength, bolt integrity or suitability for operation.
Is theta the full included tooth angle?
No. It is the model angle defined by Ft/Fa = tan(theta). Use a derived force diagram for an actual tooth geometry before relating its angle to this variable.
Why does increasing radius reduce the force output?
For fixed torque, tangential force is T/r. With the model angle fixed, the ideal axial force has the same inverse-radius dependence.
Does the multiplier select a safe design factor?
No. It multiplies one ideal force. The tool has no analysis establishing a suitable factor for a particular joint, duty cycle or failure mode.
Can I use the torque comparison to tighten a bolt?
No. Joint transmitted torque and fastener tightening torque are different quantities. This calculator does not convert between them.
Are the displayed teeth dimensionally accurate?
No. Their number, shape and motion are illustrative. The drawing does not solve tooth contact or show the actual angle convention.
How does tooth count affect indexing?
For equally spaced teeth, nominal angular pitch is 360°/N. For example, 72 teeth gives 5°. This states available nominal increments, not accuracy or strength.
Reference and calculation basis
Voith: Hirth serrations describes the connection principle, applications and component-specific data. The force equations here are a separately stated ideal wedge model and are not Voith ratings or an implementation of its selection procedure.
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