KEVOS® MAKEOS · Power Transmission
Silent Chain Sprocket Tooth Form, Hub and Hob Diameters (ANSI B29.2M)
For a silent (inverted-tooth) chain sprocket of a given pitch and number of teeth, what are the tooth form diameters, the angle between the tooth faces, the largest hub that clears the chain for hobbed or straddle-cut teeth, the hob generating diameter and the depth of cut, and is the tooth count large enough?
Tooth form and cutting dimensions of an ANSI B29.2M silent chain sprocket by the formulas the handbook gives: for 3/8 in and larger pitch the diameter to the centre of the topping curve E = P (cot(180°/N) − 0.22) and the diameter to the base of the working face B = P √(1.515213 + (cot(180°/N) − 1.1)²) of the 60° form, the angle between the faces of a tooth 60° − 720°/N (70° − 720°/N for 3/16 in pitch), the maximum hub diameter P (cot(180°/N) − 1.33) for hobbed and − 1.25 for straddle-cut teeth, the hob generating diameter and the 0.6875 P maximum depth of cut, with the pitch diameter, checked against the handbook’s tooth-count advice and your hub size.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Chain pitch range | choice | ANSI silent chain of 3/8 in pitch and larger has a 60° tooth form; 3/16 in pitch chain has a 70° form. |
| Chain pitch | mm | Chain pitch; 3/8 in = 9.525 mm, 1/2 in = 12.7 mm, 1 in = 25.4 mm, 3/16 in = 4.7625 mm. |
| Number of teeth | teeth | Number of teeth on the sprocket. |
| Teeth cut by | choice | Whether the teeth are hobbed or cut with a straddle cutter; the hub clearance differs. |
| Hub diameter planned | mm | Outside diameter of the sprocket hub you intend to use. |
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: Chain pitch range
- What it is
- Which ANSI tooth form the chain uses, chosen by its pitch range.
- Units and format
- Choose one of 2 options from the list: 3/8 in and larger (60° tooth form); 3/16 in (70° tooth form).
- Example
- The form opens with “3/8 in and larger (60° tooth form)” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Sets the tooth face angle and whether the topping, base and hob diameters apply.
- Get it right
- Chains of 3/8 in pitch and larger use the 60° form; 3/16 in pitch chain uses the 70° form.
What this means: Chain pitch
- What it is
- Pitch of the silent chain, from one joint pin to the next.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 200 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25.4 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Every diameter scales with the pitch.
- Get it right
- 3/8 in = 9.525 mm, 1/2 in = 12.7 mm, 5/8 in = 15.875 mm, 3/4 in = 19.05 mm, 1 in = 25.4 mm.
What this means: Number of teeth
- What it is
- Number of teeth on the sprocket being designed or checked.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 5 teeth to 300 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 21 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More teeth give larger diameters and a wider angle between the tooth faces.
- Get it right
- The handbook advises 21 or more and never fewer than 17.
What this means: Teeth cut by
- What it is
- Whether the teeth are cut with a hob or with a straddle cutter.
- Units and format
- Choose one of 2 options from the list: Hob; Straddle cutter.
- Example
- The form opens with “Hob” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Hobbed teeth allow a slightly smaller hub than straddle-cut teeth.
- Get it right
- Use the method of the shop or supplier that will cut the teeth.
What this means: Hub diameter planned
- What it is
- Outside diameter of the hub you plan for the sprocket.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 120 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the hub clearance check.
- Get it right
- Measure from the hub drawing, including any shoulder that runs next to the chain.
Method and formulas
- Pitch diameter = P ÷ sin(180°/N).
- E = P (cot(180°/N) − 0.22); B = P √(1.515213 + (cot(180°/N) − 1.1)²) — Table 7a, 3/8 in and larger pitch.
- Angle between the faces of a tooth = 60° − 720°/N for 3/8 in and larger, 70° − 720°/N for 3/16 in; each face is at half that to the tooth centre line.
- Maximum hub diameter = P (cot(180°/N) − 1.33) for hobbed teeth and P (cot(180°/N) − 1.25) for straddle-cut teeth.
- Hob generating diameter HGD = P √(1 ÷ sin²(180°/N) + 0.5625 − 1.5 sin(30° − 180°/N) ÷ sin(180°/N)); maximum depth of cut 0.6875 P — Table 9.
- Example: a 21-tooth sprocket for 25.4 mm pitch chain has a pitch diameter of 170.42 mm, faces 25.714° apart and a maximum hub of 134.74 mm for hobbed teeth.
Limitations
- Formulas are those of ANSI B29.2M-1982 (R1987) as given in the handbook; the E, B and hob formulas are for 3/8 in and larger pitch only.
- Hub diameters for other methods of cutting may differ from these values.
- Chain widths, sprocket face dimensions and recommended bores are table values; take them from the standard or the chain maker.
- The over-pin measurement and outside diameter are in the silent chain sprocket tool.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Draw the tooth form of a silent chain sprocket
- Check that a sprocket hub clears the chain guides
- Find the hob generating diameter and depth of cut for cutting the teeth
Who it is for
- Machine designers
- Gear and sprocket cutters
- Maintenance engineers
What you get
- Pitch diameter
- Diameter to the centre of the topping curve E (3/8 in and larger)
- Diameter to the base of the working face B (3/8 in and larger)
- Angle between the tooth faces
- Maximum hub diameter for hobbed or straddle-cut teeth
- Hob generating diameter and maximum depth of cut (3/8 in and larger)
Interpreting the result
- The angle between the tooth faces shrinks as teeth are removed: at 12 teeth (3/8 in and larger) the faces are parallel and fewer teeth would be undercut.
- The handbook advises 21 or more teeth for best results and never fewer than 17.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3468–3473. Topic reference; no source tables or recommended settings are reproduced.
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Open the Silent Chain Sprocket Tooth Form, Hub and Hob Diameters (ANSI B29.2M) calculator