KEVOS® MAKEOS · Gears
Crossed Helical Gear Drive Check (Proportions, Sliding Velocity, Forces)
For this pair of crossed helical gears on shafts at right angles, what are the diameters and centre distance, how fast do the teeth slide, and what forces act on the shafts?
Check of crossed helical (spiral) gears on shafts at 90°: pitch and outside diameters, centre distance and leads for the normal diametral pitch and helix angles (as the crossed helical gears tool), pitch-line velocities, the sliding velocity between the teeth, the pinion tangential force from the power and the gear tangential (pinion axial) force, checked against your sliding velocity limit.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Normal diametral pitch | 1/in | Normal diametral pitch of both gears. |
| Pinion teeth | Teeth on the pinion. | |
| Gear teeth | Teeth on the gear. | |
| Gear helix angle (pinion = 90° − this) | ° | Helix angle of the gear; the pinion’s is 90° minus this for shafts at right angles. |
| Duty | ||
| Power | kW | Power transmitted. |
| Pinion speed | rpm | Speed of the pinion. |
| Largest sliding velocity | m/s | Largest sliding velocity you accept for the materials and lubrication. |
Method and formulas
- Pitch diameters D = N ÷ (P_n cos ψ) for each gear with its own helix angle; centre distance = (D + d) ÷ 2; lead = π D ÷ tan ψ (as the crossed helical gears tool).
- Sliding velocity V_s = V₁ ÷ cos ψ_gear for shafts at 90°, where V₁ is the pinion pitch-line velocity.
- Pinion tangential force = P ÷ V₁; gear tangential (pinion axial) force = pinion tangential × tan ψ_pinion, friction neglected.
- Example: centre distance 5.3033 in; the teeth slide at 3.9898 m/s; the pinion shaft carries 177.23 N thrust.
Limitations
- Point contact: crossed helical gears suit light loads only.
- Friction raises the thrust and lowers the efficiency.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a light right-angle drive with crossed helical gears
- Choose helix angles to limit sliding
- Find shaft thrust loads
Who it is for
- Design engineers
- Gear designers
- Maintenance engineers
What you get
- Diameters, centre distance and leads
- Pitch-line and sliding velocities
- Tangential and axial forces
Interpreting the result
- Equal 45° helix angles give the smallest centre distance for a given ratio but the highest sliding at high ratios.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2195–2203. Topic reference; no source tables or recommended settings are reproduced.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Crossed Helical Gear Drive Check (Proportions, Sliding Velocity, Forces) calculator
