BIZOMAT MAKEOS · Gears
Profile Shift and Working Centre Distance
What working centre distance and pressure angle result from these profile shifts, and are the teeth undercut?
Working pressure angle, working centre distance and centre distance modification for a spur gear pair with profile shift, the undercut check and the backlash change at an actual centre distance.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Module | mm | Module. |
| Pinion teeth | teeth | Pinion tooth count. |
| Gear teeth | teeth | Gear tooth count. |
| Pressure angle | ° | Standard pressure angle. |
| Pinion profile shift coefficient | Profile shift coefficient of the pinion (positive = cutter withdrawn). | |
| Gear profile shift coefficient | Profile shift coefficient of the gear. | |
| Actual centre distance (0 = not set) | mm | Housing centre distance, to find the backlash change from the zero-backlash position. |
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
- What it is
- The module of the gear pair: pitch diameter divided by number of teeth, which sets the size of the teeth.
- 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 2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- All the centre distances scale in proportion to the module.
- Get it right
- Both gears must have the same module to mesh.
What this means: Pinion teeth
- What it is
- The number of teeth on the pinion, the smaller gear of the pair, which is the one most at risk of undercut.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 5 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 14 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Gear teeth
- What it is
- The number of teeth on the larger gear (the wheel) of the pair.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 5 teeth to 5000 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.
What this means: Pressure angle
- What it is
- The standard pressure angle of the cutting tool and basic rack, before any change caused by profile shift.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 10° to 30°. 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.
- Get it right
- Enter the standard pressure angle of the cutter, not the working angle; the tool works the working angle out.
What this means: Pinion profile shift coefficient
- What it is
- How far the cutter was moved away from (positive) or towards (negative) the pinion centre when cutting, as a multiple of the module.
- Units and format
- Enter a plain number with no unit. The form accepts -1 to 1.5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Positive shift increases the working pressure angle and centre distance and reduces undercut.
- Get it right
- It is a coefficient, not a distance: the actual shift is the coefficient times the module.
What this means: Gear profile shift coefficient
- What it is
- The profile shift coefficient of the larger gear, as a multiple of the module; zero for a standard gear.
- Units and format
- Enter a plain number with no unit. The form accepts -1 to 1.5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Shifting the gear negatively by the same amount as the pinion keeps the standard centre distance.
What this means: Actual centre distance (0 = not set)
- What it is
- The actual centre distance of the gear shafts in the housing, used to estimate the change in backlash from the zero-backlash position; zero skips that check.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Each extra millimetre above the working centre distance opens up the backlash.
- Get it right
- Zero means not set. Enter the bored centre distance only when you want the backlash change.
Method and formulas
- inv αw = 2(x₁ + x₂) tan α ÷ (z₁ + z₂) + inv α (solved by Newton’s method).
- Standard a₀ = m(z₁ + z₂) ÷ 2; working aw = a₀ cos α ÷ cos αw.
- No undercut when x ≥ 1 − z sin²α ÷ 2.
- Circumferential backlash change ≈ 2(a_actual − aw) tan αw.
- Example: x₁ = 0.2 on 14/40 teeth gives αw = 21.099° and aw = 54.39 mm.
Limitations
- Zero-backlash working distance; tooth thinning for backlash is separate.
- Large positive shifts can give pointed teeth; check tip thickness.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Fit a gear pair to a non-standard centre distance
- Avoid undercut on small pinions
- Estimate backlash change from centre distance
Who it is for
- Gear designers
- Machinists
- Maintenance engineers
What you get
- Working pressure angle
- Working centre distance and modification
- Undercut check for each gear
- Backlash change at the actual centre distance
Interpreting the result
- Distribute the total shift between pinion and gear to balance strength and avoid undercut on the pinion.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2141–2160. Topic reference; no source tables or recommended settings are reproduced.
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Open the Profile Shift and Working Centre Distance calculator