KEVOS® MAKEOS · Power Transmission
Gear Train Output Check (Ratio, Output Speed and Torque, Output Shaft Stress)
Does this compound gear train give the output speed and torque the job needs, and is the output shaft big enough for the torque?
Check of a simple or compound spur gear train against its duty: the overall ratio from up to four meshes, the output speed, direction and torque with the mesh efficiency (as the gear train tool), compared with the output speed and torque you need, and the torsional shear stress in the output shaft and the diameter needed for your allowable stress.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Input speed | rpm | Speed of the input shaft. |
| Input torque | N·m | Torque into the input shaft. |
| Efficiency per mesh | % | Efficiency of each gear mesh (about 98% for spur gears). |
| Mesh 1 | ||
| Driver teeth (0 = unused) | teeth | Teeth on the driving gear of mesh 1. |
| Driven teeth (0 = unused) | teeth | Teeth on the driven gear of mesh 1. |
| Mesh 2 | ||
| Driver teeth (0 = unused) | teeth | Teeth on the driving gear of mesh 2. |
| Driven teeth (0 = unused) | teeth | Teeth on the driven gear of mesh 2. |
| Mesh 3 | ||
| Driver teeth (0 = unused) | teeth | Teeth on the driving gear of mesh 3. |
| Driven teeth (0 = unused) | teeth | Teeth on the driven gear of mesh 3. |
| Mesh 4 | ||
| Driver teeth (0 = unused) | teeth | Teeth on the driving gear of mesh 4. |
| Driven teeth (0 = unused) | teeth | Teeth on the driven gear of mesh 4. |
| Duty and output shaft | ||
| Output speed required | rpm | Output speed the job needs. |
| Speed tolerance | % | How far the output speed may differ from the required speed. |
| Output torque required | N·m | Output torque the job needs. |
| Output shaft diameter | mm | Diameter of the output shaft (at keyways, use the reduced section). |
| Allowable shaft shear stress | MPa | Allowable torsional shear stress for the shaft material and duty. |
Method and formulas
- Ratio = Π (driven ÷ driver); output speed = input ÷ ratio; output torque = input torque × ratio × efficiency^meshes (as the gear train tool).
- Speed error = (output − required) ÷ required.
- Shaft stress τ = 16T ÷ (π d³); diameter needed = (16T ÷ π τ_allow)^⅓.
- Example: ratio 9 gives 161.11 rpm and 172.87 N·m; the output shaft runs at 32.609 MPa.
Limitations
- Steady torque; shock and starting loads need a service factor on the torque.
- Gear tooth strength is not checked here; use the gear tooth tools for each mesh.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a gear train for a conveyor or mixer drive
- Pick change gears for a target speed
- Size the output shaft of a gearbox
Who it is for
- Design engineers
- Maintenance engineers
- Millwrights
What you get
- Ratio, output speed, direction and torque
- Speed and torque against the duty
- Output shaft stress and diameter needed
Interpreting the result
- Each extra mesh reverses the direction and costs about 2% of the torque.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2122–2160, 299–304. Topic reference; no source tables or recommended settings are reproduced.
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Open the Gear Train Output Check (Ratio, Output Speed and Torque, Output Shaft Stress) calculator
