Tooth flank accuracy limits

Finds the tolerances on single pitch deviation, cumulative pitch deviation, profile deviation and helix deviation of a cylindrical gear, from the accuracy grade (grades 1 to 11 of JIS B 1702-1:2016, ISO 1328-1), the normal module, the reference diameter and the facewidth. The tolerances are calculated from the formulae in the standard (clause 6.3) rather than read from a table.

Accuracy grade (JIS B 1702-1:2016)

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Input

Normal module

m_n

Reference diameter

d

Face width

b

Result

Allowable single pitch deviation

f_{pT}

Allowable cumulative pitch deviation

F_{pT}

Allowable profile slope deviation

f_{H\alpha T}

Allowable profile form deviation

f_{f\alpha T}

Allowable total profile deviation

F_{\alpha T}

Allowable helix slope deviation

f_{H\beta T}

Allowable helix form deviation

f_{f\beta T}

Allowable total helix deviation

F_{\beta T}

Notes

References

JIS B 1702-1:2016 Cylindrical gears — ISO system of accuracy — Part 1: Definitions and allowable values of deviations relevant to corresponding flanks of gear teeth

The allowable values are given as equations rather than tables (Eqs. (6) to (13) in Clause 6.3). This page evaluates those equations directly and prints each one beside its result.
Accuracy grades run from 1, the finest, to 11. State the standard number and year whenever you specify or mark a grade (5.6.1). For example: JIS B 1702-1:2016 Grade 5. Earlier editions numbered the grades differently (JIS B 1702-1:1998 used N0 to N12), so do not mix the two.
Allowable values for two consecutive grades stand in the ratio $\sqrt{2}$ (6.2.2). Every equation is the unrounded grade 5 value multiplied by $\left(\sqrt{2}\right)^{A-5}$ , where $A$ is the accuracy grade.
Rounding of values (6.2.3)

Above 10 μm, round to the nearest whole number
From 5.0 μm to 10 μm, round to the nearest 0.5 μm
Below 5.0 μm, round to the nearest 0.1 μm

Notes on individual items — how they combine, whether they carry a sign — open from the "?" beside each name in the result field.
The grade of the gear as a whole is the highest — that is, the coarsest — of the grades specified for the measured items (5.6.4). Different items may carry different grades (5.6.1).
Scope (Clause 1)

Number of teeth $5 \leqq z \leqq 1\,000$
Reference diameter $5\ \mathrm{mm} \leqq d \leqq 15\,000\ \mathrm{mm}$
Normal module $0.5\ \mathrm{mm} \leqq m_n \leqq 70\ \mathrm{mm}$
Facewidth $4\ \mathrm{mm} \leqq b \leqq 1\,200\ \mathrm{mm}$
Helix angle $\beta \leqq 45^\circ$
Do not extrapolate the equations beyond the stated range (6.2.1). Outside the range, allowable values are by agreement between the parties. This page returns nothing when the reference diameter, normal module or facewidth falls outside it. The number of teeth and the helix angle do not appear in the equations, so there are no fields for them — check those yourself.

Not covered by this standard

Centre distance deviations and shaft parallelism tolerances are not part of this standard. Other material sometimes cites them as JIS B 1702-1, but they are not in this edition.
Double flank composite deviation and runout belong to JIS B 1702-2. The runout tolerance $F_{rT}$ also appears in Annex E, but Annex E is informative rather than normative, so it is not carried here.
Surface texture is outside the scope of this standard (Clause 1).

Tolerances for a rack are the same as for the mating gear. Where the mating gear is unknown, treat the rack as a gear whose reference diameter is $d = L_R / \pi$ , obtained from the rack length $L_R$ (6.2.1).

Gear dimensions

Gives the reference diameter, tooth depth and the rest from the module, number of teeth and pressure angle.

Gear trains

Gives the tooth counts and pitch diameters of a meshing pair, from the module, centre distance and reduction ratio.

Tooth flank accuracy limits

Input

Result

Notes

Related pages