PinyiGear Engineering Guide — Reference for Gear Strength Calculations

ISO 6336 contact and root bending formulas with GB/T 3480, DIN 3990 and AGMA 2001: 20CrMnTi at HRC 58~62 gives σHlim 1500 MPa and σFlim 500 MPa

The design decision behind it

Two verifications decide whether a cylindrical gear pair survives: flank contact stress and tooth root bending stress. They pull in opposite directions, and that tension is the actual design decision.

If you enlarge the pitch circle diameter, contact stress falls quickly — roughly with the inverse of $d_1$ — while bending stress barely moves. If you enlarge the module, the root section grows and bending stress drops, but the pitch diameter may not change at all, so contact stress stays where it was. Face width helps both, but it also worsens load distribution across the face, which is why $K_{H\beta}$ and $K_{F\beta}$ appear in the formulas and why simply widening a gear is not a free fix. Hardness raises the permissible values, not the actual stresses, and it changes the process route: carburizing, induction hardening and nitriding each bring different distortion and finishing consequences.

The practical order of decisions is therefore: fix the centre distance and ratio from the transmission layout, choose the module from the bending duty, then check whether the resulting pitch diameter carries the contact load. If it does not, the honest options are a larger centre distance, a different material/heat treatment, or accepting a shorter life. Standards such as ISO 6336, GB/T 3480, DIN 3990 and AGMA 2001 give the calculation framework and the factor definitions; they do not relieve anyone of stating the duty cycle, because the life factors $Z_N$ and $Y_N$ depend entirely on it.

One more decision sits outside the two strength checks: at higher pitch line velocity, scuffing becomes a separate failure mode and needs its own check, by flash temperature or integral temperature method. A gear that passes contact and bending can still score.

Numbers that matter on the drawing

The calculation consumes a specific set of quantities. Every one of them should be readable on the drawing, and each has a measurement convention that the inspection side must agree with.

Drawing itemSymbolWhat the calculation does with itMeasurement note
Normal module$m_n$Sets root section and $F_t/(b m_n)$Defined at reference diameter, not measured directly
Tooth count$z_1$, $z_2$Ratio $u = z_2/z_1 \ge 1$, form factor $Y_{Fa}$Count and state; do not leave to inference
Face width$b$Divides both stressesEffective contact width, not overall blank width
Pitch diameter$d_1$Converts torque to $F_t = 2T/d$Theoretical value from $m_n$ and $z$
Pressure angle$\alpha$Zone factor $Z_H$Standard or non-standard, state explicitly
Helix angle and hand$\beta$$Z_\beta$, $Y_\beta$, axial load directionHand of both members must be stated
Profile shift$x$Shifts $Y_{Fa}$ and $Y_{Sa}$Sign convention must be agreed
Torque or power and speed$T$, $n$Nominal tangential force, pitch line velocityState whether peak or continuous
Duty cycle—Life factors $Z_N$, $Y_N$Hours at load, or number of cycles
Accuracy grade—Dynamic factor $K_V$Cite the standard the grade is quoted against

The last row deserves emphasis. A grade number without its standard is not a specification. “Grade 6” means one thing under DIN 3962 and something else under another system; ISO 1328 and AGMA 2001 likewise use their own designations. Write the standard next to the grade, and write which tolerances are actually inspected — total composite, single pitch, profile, lead — rather than a single blanket number.

Load factors are where drawings most often go silent. $K_A$ depends on both the prime mover and the driven machine, and the spread is wide: a uniform load driven by an electric motor sits near 1.0, while a single-cylinder engine driving a heavy-shock machine can reach 2.25. That factor alone can move the calculated stress by more than a hundred percent. It is not something a machinist can infer from a drawing, so it has to come from the enquiry.

Where custom manufacturing changes the answer

Because work is quoted from drawing or sample, the parameters that matter are the ones that change how the part is made, not how a catalogue number is picked.

Geometry that needs special tooling. A non-standard pressure angle, an unusual module, or a profile shift far from the norm means a cutter or grinding wheel that is not on the shelf. That is a real cost driver and a real lead-time driver. It is not a reason to refuse the design — it is a reason to say so early, so the design can be reconsidered while it is still cheap to change.

Heat treatment and finishing sequence. A carburized and quenched gear will distort; if the drawing calls for tight lead and profile tolerances, the process must include a finishing operation after heat treatment. That decision belongs on the drawing as a note, because it determines whether the part is cut soft and finished hard, or cut after hardening. Nitrided and induction-hardened routes distort differently and finish differently again. The strength calculation only sees $\sigma_{Hlim}$ and $\sigma_{Flim}$; the shop sees the sequence.

Hardness specification and its measurement location. Hardness stated without a location is ambiguous. Case hardness, core hardness and surface hardness after nitriding are three different numbers taken in three different places. State the value, the method, and where it is measured.

Features that fight the gear. Keyways, splines, cross holes, clamping flats and set screw seats near the root circle reduce the effective root section. The bending formula assumes a clean tooth; a keyway cut through the root region invalidates that assumption. If such a feature is unavoidable, flag it so the root stress is re-examined rather than assumed.

Quantities and repeatability. Since there is no fixed catalogue, each order is set up from the drawing. The cost per piece therefore depends heavily on how completely the drawing defines the part the first time. A drawing that requires three rounds of clarification costs more than one that does not, regardless of the part’s complexity.

Common mistakes in drawings and enquiries

  1. Torque given as a single number with no indication of peak or continuous. The calculation needs to know which value drives fatigue and which drives yield. Fix: state nominal continuous torque, peak torque and how often the peak occurs.

  2. Duty cycle omitted entirely. Life factors cannot be selected, so the permissible stress is undefined and any strength statement is unfounded. Fix: give operating hours, or cycles, and the load spectrum if it is not constant.

  3. Accuracy grade quoted without the governing standard, or quoted as one number for all deviations. The dynamic factor and the process route both depend on it, and a shop cannot quote finishing operations against an ambiguous requirement. Fix: cite the standard (ISO 1328, DIN 3962, AGMA 2001 or equivalent) and list which deviations are inspected.

  4. Heat treatment specified as a material name only. “20CrMnTi” says nothing about case depth, surface hardness or core hardness, and those determine both the permissible stresses and the finishing sequence. Fix: add case depth range, surface hardness with method, and core hardness.

  5. Mating part absent from the enquiry. Contact stress depends on the pair, not on one gear; the ratio, the hardness difference and the helix hand of the mating member all enter the calculation. Fix: send both drawings, or state the mating part’s tooth count, material and hand.

A sixth, less obvious one: sending a 3D model with no tooth data. The solid shows the envelope, not the tooth form. The calculation needs module, pressure angle, helix angle, profile shift and tooth thickness allowance as numbers.

A short checklist

Before the drawing goes out, confirm each line:

  1. Module, tooth count, pressure angle, helix angle and hand stated for every gear in the pair.
  2. Profile shift given with an agreed sign convention, or explicitly declared zero.
  3. Reference diameters and centre distance listed as theoretical values.
  4. Face width defined as effective contact width, with any relief or chamfer noted.
  5. Nominal torque or power plus speed, marked as continuous or peak.
  6. Duty cycle in hours or cycles, with load spectrum if not constant.
  7. Application factor $K_A$ either stated or the prime mover and driven machine described.
  8. Accuracy grade written together with the standard it is quoted against, and the inspected deviations listed.
  9. Heat treatment given as a full specification: process, case depth, surface hardness with method, core hardness.
  10. All features interrupting the tooth root — keyways, holes, splines — shown and flagged for root stress review.

FAQ

Does a higher accuracy grade always improve the strength result?

No. A finer grade lowers the dynamic factor $K_V$, which reduces the calculated stress somewhat, but the dominant terms are usually the tangential force and the geometry. The larger effect of a finer grade is on noise, vibration and the cost of the finishing operation. Specify the grade the application actually needs, and state the standard so the requirement can be quoted and inspected.

Can the strength calculation be done from a sample instead of a drawing?

A sample gives the geometry, and geometry can be measured and reconstructed into the parameters the calculation needs. What a sample cannot give is the duty: torque, speed, life and the characteristics of the driving and driven machines. Those have to come from you in writing. Send the sample together with the operating data, and the two together form a complete basis.

Which standard will the calculation follow?

The framework can follow ISO 6336, GB/T 3480, DIN 3990 or AGMA 2001, and the factor definitions differ between them, so the choice should be stated at the enquiry stage. If your customer or end user requires a particular standard, say so; otherwise the calculation will be documented against the standard named in the enquiry, and the material fatigue values used will be listed alongside it.

Send the drawing, the mating part and the operating data to sales@dgpinyi.com or call +86 18002857601, and the geometry and duty will be reviewed together before any quote is given.

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