Oblique teeth engage progressively and create an axial force component along the gear shaft. Explore the pair described in Hiscox item 123 and calculate ideal torque, tangential force and axial thrust from power, speed, pitch diameter and helix angle.
Ideal Oblique-Tooth Force Calculator
Enter declared transmitted power, shaft speed, operating pitch diameter and pitch-cylinder helix angle. The worksheet resolves ideal steady torque, tangential force and axial component only; it does not rate teeth, shafts, bearings or a gearbox.
Equation Used
- Power is transmitted steadily at the declared speed with no loss included.
- Tangential force acts at the declared operating pitch diameter.
- The axial component uses the declared pitch-cylinder helix angle and ideal Fa=Ft tan(beta) resolution.
- Tooth count, module, pressure angle, hand selection, profile, contact ratio, overlap, face width, backlash, misalignment, dynamics, stress, lubrication, heat, bearings, shafts, housing, strength, fatigue and safety are excluded.
Power and speed set ideal steady torque. Pitch diameter converts torque to tangential force, and helix angle sets the axial-to-tangential force ratio. These results do not rate the gears or bearings.
Inclined teeth mesh progressively and create longitudinal thrust
Hiscox item 123 calls the oblique-tooth gear smooth-running and attributes slight longitudinal thrust to the inclined tooth surfaces. The adjacent item 122 explains why opposed V-tooth halves can neutralize that thrust.
The schematic shows an opposite-hand pair on parallel shafts. The arrows illustrate opposite thrust directions; their lengths do not scale with the calculated forces, and tooth profiles are not generated.
A historical transmission principle
The inclined tooth surfaces transmit rotation while producing a longitudinal force component. Supporting that component is part of the complete shaft and bearing design, which this force calculation does not determine.
Ideal steady force components
KHK's gear-force reference gives the same tangential and axial component relations. This calculator does not determine radial force, bearing reactions or tooth strength.
Declared force-component example
For P=10 kW, n=1500 rpm, d=150 mm and β=20°, ideal torque is 63.66 N·m, tangential force is 848.8 N, axial component is 308.9 N and Fa/Ft is 0.364.
Force components and gear ratings
These ideal steady force components are inputs to further design checks. Tooth strength, bearing reactions and gearbox performance also depend on geometry, material, support arrangement and operating duty. The calculator does not establish those ratings or operating limits.
Oblique-tooth gear questions
Does the calculator rate a helical gear?
No.
Why is there an axial component?
The tooth inclination resolves part of the ideal mesh force along the shaft.
Does the viewer show a generated involute tooth profile?
No. Its tooth bands are explanatory.
Oblique-tooth gear references
- Hiscox, Mechanical Movements, page 41, items 122-123: primary public-domain plate and captions for the oblique-tooth pair, smooth running and longitudinal thrust.
- KHK Gear Technical Reference: published gear-force relations Ft=2000T/d and Fa=Ft tanβ.
- OpenStax University Physics, section 10.8: rotational-power identity P=Tω.
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