BIZOMAT 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. |
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: Input speed
- What it is
- The speed of the first driving gear’s shaft, usually the motor or input shaft speed under load. The output speed is this divided by the overall ratio.
- 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 1450 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The output speed moves in direct proportion to it.
- Get it right
- Use the motor’s full-load speed from its nameplate, not the synchronous speed.
What this means: Input torque
- What it is
- The torque delivered into the input shaft of the train. The output torque is this times the overall ratio, reduced by the mesh losses.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0.000001 N·m to 10000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The output torque and the shaft stress rise in direct proportion to it.
- Get it right
- Enter the torque at the input shaft, not the motor power; convert power and speed to torque first.
What this means: Efficiency per mesh
- What it is
- The share of power passed through one gear mesh, from the gear maker or your design data. It is applied once for every mesh in use.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 50% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 98% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Each mesh multiplies the output torque by this share, so lower efficiency reduces output torque.
- Get it right
- Type the percentage per mesh, not the efficiency of the whole train; the tool compounds it over the meshes.
Mesh 1
What this means: Driver teeth (0 = unused)
- What it is
- The number of teeth on the driving gear of the first mesh, the gear on the input shaft.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 0 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More driver teeth lower the ratio and raise the output speed.
- Get it right
- A mesh is used only when both its driver and driven teeth are non-zero.
What this means: Driven teeth (0 = unused)
- What it is
- The number of teeth on the driven gear of the first mesh, the gear the input gear turns.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 0 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More driven teeth raise the ratio, lowering output speed and raising output torque.
- Get it right
- Set both teeth of a mesh to 0 to leave it out.
Mesh 2
What this means: Driver teeth (0 = unused)
- What it is
- The number of teeth on the driving gear of the second mesh, on the same shaft as the driven gear of the first mesh in a compound train.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 0 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 18 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More driver teeth lower the ratio and raise the output speed.
- Get it right
- An idler can be entered as its own pair of meshes: it cancels in the ratio and keeps the output direction right.
What this means: Driven teeth (0 = unused)
- What it is
- The number of teeth on the driven gear of the second mesh.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 0 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 54 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More driven teeth raise the ratio, lowering output speed and raising output torque.
- Get it right
- Set both teeth of a mesh to 0 to leave it out.
Mesh 3
What this means: Driver teeth (0 = unused)
- What it is
- The number of teeth on the driving gear of the third mesh, if the train has one.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 0 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More driver teeth lower the ratio and raise the output speed.
- Get it right
- Leave at 0 when there is no third mesh; the mesh count also sets the output direction.
What this means: Driven teeth (0 = unused)
- What it is
- The number of teeth on the driven gear of the third mesh, if the train has one.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 0 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More driven teeth raise the ratio, lowering output speed and raising output torque.
- Get it right
- Set both teeth of a mesh to 0 to leave it out.
Mesh 4
What this means: Driver teeth (0 = unused)
- What it is
- The number of teeth on the driving gear of the fourth mesh, if the train has one.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 0 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More driver teeth lower the ratio and raise the output speed.
- Get it right
- Leave at 0 when there is no fourth mesh.
What this means: Driven teeth (0 = unused)
- What it is
- The number of teeth on the driven gear of the fourth mesh, the gear on the output shaft when all four meshes are used.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 0 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More driven teeth raise the ratio, lowering output speed and raising output torque.
- Get it right
- Set both teeth of a mesh to 0 to leave it out.
Duty and output shaft
What this means: Output speed required
- What it is
- The output shaft speed the driven machine needs. The calculated output speed is compared with it within the speed tolerance.
- 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 160 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the speed needed at the output shaft itself, after any later belt or chain stage has been allowed for.
What this means: Speed tolerance
- What it is
- How far, above or below, the output speed may differ from the speed required and still pass, as a share of the required speed.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Type the percentage itself; the band applies equally above and below the required speed.
What this means: Output torque required
- What it is
- The torque the driven machine needs at the output shaft. The calculated output torque must be at least this.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0 N·m to 100000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Include starting or peak torque if that is what the machine must overcome, not just running torque.
What this means: Output shaft diameter
- What it is
- The diameter of the output shaft at the section that carries the output torque. The torsional shear stress is worked from it.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Shaft stress falls with the cube of the diameter, so small changes matter.
- Get it right
- At a keyway or groove use the reduced diameter there, not the full shaft size.
What this means: Allowable shaft shear stress
- What it is
- The torsional shear stress you allow in the output shaft for its material and duty, from your design code, engineer or material data with your safety margin.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 2000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A lower allowable raises the shaft diameter needed with the inverse cube root of the stress.
- Get it right
- Use a shear stress, not the tensile strength of the material.
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.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Gears, pumps and fans
In Vibration Monitoring by the Numbers
What it covers: Gear mesh frequency and sidebands, shaft speeds through a reducer, wear against a cracked tooth, synchronous averaging, blade and vane pass, cavitation, and sidebands traced to the wrong shaft.
BIZOMAT 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 Gear Train Output Check (Ratio, Output Speed and Torque, Output Shaft Stress) calculator