BIZOMAT 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.
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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. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Normal diametral pitch
- What it is
- The normal diametral pitch shared by both gears: the number of teeth per inch of pitch diameter measured in the plane normal to the teeth.
- Units and format
- Enter a number in 1/in: threads per inch. The form accepts 0.000001 1/in to 100 1/in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8 1/in as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Both pitch diameters and the centre distance fall in inverse proportion to the normal diametral pitch.
- Get it right
- This is an inch-system value; for a metric normal module m, Pn = 25.4 ÷ m.
What this means: Pinion teeth
- What it is
- The number of teeth on the pinion, the smaller driving gear whose speed you enter below.
- Units and format
- Enter a plain number with no unit. The form accepts 5 to 1000. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More pinion teeth enlarge its pitch diameter, raising pitch-line and sliding velocity for the same speed.
What this means: Gear teeth
- What it is
- The number of teeth on the mating gear, which with the pinion sets the ratio.
- Units and format
- Enter a plain number with no unit. The form accepts 5 to 5000. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- For crossed helical gears the ratio is the tooth ratio, not the ratio of pitch diameters.
What this means: Gear helix angle (pinion = 90° − this)
- What it is
- The helix angle of the gear teeth measured from the gear axis; for shafts at right angles the pinion helix angle is 90° minus this.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 5° to 85°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 45° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sliding velocity is the pinion pitch-line velocity divided by the cosine of this angle, so it rises steeply as the angle grows.
- Get it right
- Enter the gear’s angle, not the pinion’s, and make both gears the same hand.
Duty
What this means: Power
- What it is
- The power transmitted through the gear pair, used to work out the tangential and axial tooth forces.
- Units and format
- Enter a number in kW: kilowatts. The form accepts 0.000001 kW to 10000 kW. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 kW as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Tooth forces rise in direct proportion to power.
- Get it right
- Enter kilowatts, not watts.
What this means: Pinion speed
- What it is
- The rotational speed of the pinion shaft.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 600 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Pitch-line and sliding velocities rise in proportion to speed, while the tooth forces for a given power fall.
- Get it right
- Give the pinion speed, not the gear speed.
What this means: Largest sliding velocity
- What it is
- The largest sliding velocity between the teeth you accept for the gear materials and lubrication, from the gear maker or lubricant supplier.
- Units and format
- Enter a number in m/s: metres per second. The form accepts 0.000001 m/s to 100 m/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 m/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from data for your material pair and lubricant; crossed helical gears rely on sliding contact.
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.
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Open the Crossed Helical Gear Drive Check (Proportions, Sliding Velocity, Forces) calculator