KEVOS® MAKEOS · Gears
Gear Shaving Stock Check (Centre Distance Method)
I have meshed a preshaved gear tight with a gear of standard tooth thickness and measured how far the centre distance exceeds standard: how much stock is left on the teeth for shaving, and is it within the allowance I want?
Stock left for shaving by the handbook’s centre-distance method: the preshaved gear is meshed without backlash against a gear of standard tooth thickness and the increase d in centre distance over standard is measured; the total thickness over standard is t2 = 2 tan φ × d, half on each side of the tooth, checked here also by the exact involute relation (inv φ1 = inv φ + (t2 ÷ m) ÷ (n + N) with cos φ1 = C cos φ ÷ (C + d)) and against your shaving allowance.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Module m (25.4 ÷ P) | mm | Module of the gears; for a diametral pitch P it is 25.4 ÷ P. |
| Pressure angle φ | ° | Pressure angle of the gears. |
| Teeth in preshaved gear | teeth | Number of teeth in the preshaved gear being checked. |
| Teeth in standard master gear | teeth | Number of teeth in the gear of standard tooth thickness it is meshed with. |
| Centre distance over standard, meshed tight d | mm | Amount the centre distance exceeds standard when the two gears are meshed without backlash. |
| Shaving allowance (total tooth thickness) | ||
| Least stock you want | mm | Least total stock (both sides of the tooth) you want left for shaving. |
| Most stock you want | mm | Most total stock (both sides of the tooth) you want left for shaving. |
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: Module m (25.4 ÷ P)
- What it is
- Module of the preshaved gear and the master gear, the pitch diameter per tooth in millimetres.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3.175 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Scales every diameter, tooth thickness and centre distance.
- Get it right
- For an inch diametral pitch P, enter 25.4 ÷ P.
What this means: Pressure angle φ
- What it is
- Pressure angle of the gears at the standard pitch circle.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 10° to 35°. 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
- Changes the base circles and every involute angle.
- Get it right
- 20° is the usual standard; 14½° and 25° are also used.
What this means: Teeth in preshaved gear
- What it is
- Number of teeth in the preshaved gear being checked.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 5 teeth to 10000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Used only in the exact involute check.
- Get it right
- Count the teeth on the gear or its drawing.
What this means: Teeth in standard master gear
- What it is
- Number of teeth in the master gear of standard tooth thickness.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 5 teeth to 10000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Used only in the exact involute check.
- Get it right
- Use a master gear whose tooth thickness is known to be standard.
What this means: Centre distance over standard, meshed tight d
- What it is
- Amount the centre distance exceeds standard with the gears meshed tight.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.087 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The stock rises in proportion, 2 tan φ for each millimetre.
- Get it right
- Mesh without backlash on a centre-distance fixture and average several positions.
Shaving allowance (total tooth thickness)
What this means: Least stock you want
- What it is
- Least total stock (both sides of the tooth) you want left for shaving.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.0508 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Flags too little stock to clean up the teeth.
- Get it right
- From your shaving process; the handbook gives 0.0508 to 0.0762 mm for 7 to 10 diametral pitch.
What this means: Most stock you want
- What it is
- Most total stock (both sides of the tooth) you want left for shaving.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.0762 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Flags too much stock for shaving.
- Get it right
- Too much stock shortens shaving cutter life and lengthens shaving time.
Method and formulas
- t2 = 2 tan φ × d (handbook centre-distance method); stock per side t2 ÷ 2.
- Exact: C = (n + N) m ÷ 2; cos φ1 = C cos φ ÷ (C + d); t2 = (n + N) m (inv φ1 − inv φ).
- Compare t2 with the least and most stock you want.
- Example: a centre distance 0.087 mm over standard means 0.063331 mm of stock on the tooth, 0.031665 mm on each side.
Limitations
- The master gear must have standard tooth thickness and the gears must mesh without backlash when measured.
- Runout of either gear changes the reading; take the mean of several positions.
- Take the allowance from your shaving process or the handbook’s guide for the diametral pitch.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check the stock left on a preshaved gear before shaving
- Convert a measured centre distance increase into tooth thickness
- Decide whether to recut a gear before shaving
Who it is for
- Gear inspectors
- Machinists and gear cutters
- Gear designers
What you get
- Total tooth thickness over standard by the handbook formula
- Stock on each side of the tooth
- The same by the exact involute relation
- Check against your shaving allowance
Interpreting the result
- Too much stock shortens the life of the shaving cutter and lengthens the shaving time.
- Too little stock may not clean up the hobbed or shaped surface.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2141, 2155. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Useful alongside · KEVOS® original book
Backlash and tooth thickness
What it covers: Specify backlash through tooth thickness and centre distance tolerances, and check that temperature and errors cannot close the clearance.
KEVOS® 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 Shaving Stock Check (Centre Distance Method) calculator