A parallel-axis helical gear pair transmits torque through angled teeth. The calculator gives ideal pitch-line force components; it does not rate gears, predict noise or select bearings.
Helical Gear Higher Pair Interactive Calculator
Calculate ideal tangential pitch-line force, the corresponding axial component for an entered helix angle, and an explicitly simplified force-per-entered-ratio comparison.
Equation Used
- Parallel-axis external helical pair represented at its pitch cylinders.
- Entered torque is transmitted at the entered pitch diameter without losses or dynamics.
- The entered helix angle is used only for ideal axial-force decomposition.
- Entered contact ratio is not derived or validated; Ft divided by it is not an individual tooth load.
Ideal force decomposition only. The displayed Ft/CR value is an arithmetic average, not the load on any tooth pair. No radial force, pressure angle, tooth geometry, stress, deflection, dynamics, lubrication, efficiency, bearing rating or life is calculated.
Idealized mesh and force components
For a parallel-axis external pair, mating helical gears use opposite helix hands. Torque T applied at pitch radius d/2 corresponds to tangential force Ft = 2T/d. The ideal axial-force magnitude is Fa = Ft tan β, with β measured at the pitch cylinder.
The tool uses positive torque and angle inputs, so it reports force magnitudes. The actual axial direction depends on tooth hand and rotation/load direction. Those directions are not inputs here.
The illustration uses fixed-size circles, striped symbols and rotating spokes to suggest a pair of gears. It is not a three-dimensional tooth-contact view, and its arrows are component labels rather than a spatial force diagram. Pitch diameter changes the calculated force but does not resize the circles.
The calculation omits the radial component, contact stress, bending stress, load distribution, deflection and dynamics.
Scope of application
Helical gears are used in many power-transmission systems, but application suitability cannot be inferred from these four inputs. A design needs the actual ratio, module or diametral pitch, tooth counts, pressure angle, face width, quality, materials, heat treatment, alignment, housing and shaft stiffness, lubrication, duty and applicable rating method.
Force identities used by the calculator
Tangential pitch-line force is Ft=2T/d. When T is in N·m and d is in millimetres, Ft=2000T/d newtons. The ideal axial component is Fa=Ft tan(β), and Fa/Ft=tan(β).
The Ft / Entered Ratio tile divides Ft by the user-entered contact ratio. It is only an arithmetic comparison. Actual load sharing is not uniform and depends on tooth compliance, errors, alignment and the instantaneous contact pattern.
Transparent arithmetic example
For T=100 N·m, d=100 mm and β=25°, Ft=2000 N and Fa≈933 N. If the entered contact ratio is 2.5, Ft/CR=800 N.
The 800 N result is not a predicted tooth-pair load, and none of these values by themselves establish gear capacity or bearing life.
Scope and limitations
Increasing the entered helix angle increases the ideal Fa/Ft ratio. It does not by itself predict noise, efficiency, contact ratio, stress or life. Use a recognized gear-rating method and bearing manufacturer data with the complete geometry, loads, duty, alignment, lubrication and reliability target.
Frequently asked questions
Does contact ratio calculate itself from the gears?
No. It is entered by the reader and used only as a divisor. Tooth counts, face width, module and pressure angle are absent.
Can Ft divided by contact ratio be used as tooth load?
No. It is an arithmetic quotient. Actual load sharing is not uniform and depends on instantaneous tooth contact and compliance.
Does the axial-force number select a bearing?
No. Radial loads, speed, bearing arrangement, duty and other rating inputs are also needed.
Why does pitch diameter not resize the drawing?
The gear symbols are fixed-size illustrations. Pitch diameter affects the numerical force calculation only.
Which way does the axial force act?
The tool gives its magnitude. A physical direction requires gear hand and rotation/load direction, which are not inputs.
Force calculation reference
KHK Gears: helical-gear technical information describes matching gear hands and axial thrust. The tangential-force equation follows from torque divided by pitch radius; the axial component uses the entered pitch-cylinder helix angle.
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