ISO 6336 Gear Rating — Contact & Bending Stress Calculator

This planetary stage is SAFE. Four planets share the load. Contact safety 1.57.

Add a fifth planet, and it fails. The planets would collide.

This is the MechanixCalc planetary gear calculator. Ratio, assembly, contact stress to ISO 6336-2, and the planet pin. Let's go through it, step by step.

A planetary stage has a sun in the middle. Planets roll around it, inside a ring. A carrier holds the planets.

Before any stress, the set must be buildable. The ring must equal the sun plus two planets. The planets must space evenly. And they must not touch.

Step one: the arrangement. The sun drives, the ring is held, and the carrier is the output. Four planets share the load.

The table shows all six ways to connect the same gears. Ours gives a ratio of 5.

Step two: the teeth. Sun 20, planets 30, ring 80. 20 plus two times 30 is 80. So the mesh condition holds.

And 20 plus 80, over four planets, is 25. A whole number, so the planets space evenly.

Step three: module 3, a 45 mm face, and 42CrMo4 steel, quenched and tempered.

Step four: the load. 15 kW at 1500 rpm. The ratio is 5, so the carrier turns at 300 rpm. With 471 N·m.

Each planet carries 995 N. That includes a load-sharing factor of 1.25, because four planets never share exactly evenly.

Step five: the checks. Contact safety 1.57 at the sun, 3.55 at the ring. Against 1.2. Contact governs. SAFE.

The tooth root is only an estimate: a Lewis formula with the load factors. 4.82. For a full ISO root rating, try our gear calculator, at mechanixcalc.com/gears.

Planet tip clearance 10.1 mm. Efficiency 98.7 %. No undercut.

Step six sizes the planet pin. 2941 N, with the application and dynamic factors. A 15 mm pin. It never changes the verdict.

Now try five planets. Their tips overlap by 7.8 mm. They cannot be assembled. FAIL, whatever the stress says.

Three planets: 100 over 3 is not a whole number. They cannot space evenly, so it reads CHECK.

Make it 22, 29 and 80. Now 102 over 3 is 34. SAFE, with a ratio of 4.64.

Back to four planets, and raise the load to 26 kW. Contact safety drops to 1.19. CHECK.

Widen the face to 55 mm: 1.30. SAFE again.

Or keep 45 mm, and use case-hardened 16MnCr5. Contact safety 2.17.

What the tool does not check is listed: the ring tooth root, the planet bearings, the carrier and scuffing. So silence never reads as a pass.

Every input, every factor and every check goes into a PDF report. A report your reviewer can follow.

That's a planetary stage, checked. Try it on your own gearbox, on MechanixCalc.com.

Here's a gantry axis, 250 kg moving at 2 m/s on a rack and pinion. The tool says it's SAFE, and the rack flank decides.

Now stand the same axis up vertical. Same parts, and it fails.

This is the MechanixCalc rack and pinion calculator. It works out the drive force in every phase of the move, the ISO 6336-based tooth strength of pinion and rack, and the motor torque. Let's go through it, step by step.

A rack and pinion turns motor torque into a straight-line force. The pinion pushes on the rack teeth, and those teeth carry the load in every phase.

A tooth can fail in two ways. The root can crack in bending, or the flank can pit under contact pressure. The tool checks both, on the pinion and on the rack.

Step one is the application. A horizontal axis carries 250 kg at 2 m/s, with 3 m/s² up and down, and a 400 N process force on the forward stroke.

The chart shows the force in every phase of the move. The peak is 1162 N, while accelerating forward.

Step two is the rack and pinion. Module 3, 20 teeth, helical, and 30 mm wide. This helix angle makes the feed a round 200 mm per turn.

Step three is the materials. A case-hardened pinion runs on a quenched and tempered rack. The flank roughness is 6.5 µm, a ground pinion on a milled rack.

Step four is the drive. With an 8 to 1 gearbox, the motor needs 5.36 N·m at its peak. The chart shows its torque in every phase.

Step five shows the checks. The roots are far from their limit. The rack flank governs with a safety factor of 1.61, so the verdict is SAFE.

The tool also gives the max feed force, 2084 N. That's the most this mesh carries with every check met.

Now raise the process force to 1400 N. The peak becomes 2162 N, just past the max feed force.

The verdict changes to CHECK. The rack flank's safety factor drops to 1.18, below its line of 1.2.

The fix is a wider rack. At 35 mm the flank is back to 1.27, and the verdict turns green.

Now go back to the start, and stand the axis vertical. Gravity acts in every phase, and the peak force grows to 3602 N.

The verdict is FAIL. The rack flank's safety factor is only 0.91.

A rack and pinion never locks itself, so the tool asks for a brake too. It needs at least 19.5 N·m at the motor.

The fix is one module up. With module 4, the flank safety factor is 1.23, and the verdict turns green.

A bigger brake puts its full torque on the teeth, so the tool checks that too. With the fitted 40 N·m brake, the static check still holds.

What the tool does not check is listed too: the rack screws, the pinion shaft and bearings, and the gearbox rating. So silence never reads as a pass.

Every input, every formula and every check goes into a PDF report. A report your reviewer can follow.

That's a rack and pinion drive, checked. Try it on your own axis, on MechanixCalc.com.

Ten small motors hold a whole nacelle against the wind. And in a yaw drive, the gear teeth are often not what decides it. It's the cases nobody runs. A drive out. A brake closing on a pinion that's still turning.

This is the MechanixCalc slewing drive calculator. It checks the pinion and the ring to ISO 6336, together with the brakes, the motors and the gearboxes, as one drive. Let's run a real one.

Here's the job. A 3 megawatt class yaw system. A slewing ring of about 3 metres pitch diameter, module 22, 140 teeth, induction hardened.

Ten drives, each one a 14-tooth pinion on a 1200 to 1 gearbox, driven by a 20 N·m motor.

The targets are the IEC 61400-1 yaw gear values for class 2. 1.1 on the flanks, 1.25 on the roots.

Over the whole load spectrum, the ring flank governs the fatigue. 1.99 against 1.1. The roots sit between 4.5 and 6.

The extreme moment is 2400 kN·m, times 1.35. Even with one drive out, the ring root still has 3.9 against 1.2.

Now a case most hand calculations skip. A motor brake closing on a drive that's still turning. Its slip torque comes back through 1200 to 1, doubled for the shock. The flanks hold, but only just. 1.10 against 1.04.

Then holding. The brakes and the calipers must hold 2400 times 1.35. That's 3240 kN·m. With all ten drives it's 87 % of what they can hold. With one drive out, 95 %. The tightest number in the whole drive.

So here's the tempting saving. Nine drives instead of ten. Every gear check still passes.

But hold the extreme with one of the nine out, and it's 104 %. FAIL. The tenth drive was the margin.

One more. Where the pinion sits on its shaft. At 275 mm from the bearing it's buildable, and the face load factor runs from about 2 to 2.4.

Now push it out to 400 mm. That factor climbs to nearly 3.

The brake-closing flank drops to 0.95. FAIL. Same gear, same load, just a longer shaft.

The motors and the gearboxes get the same treatment. RMS motor torque 8.9 N·m against 20 rated. Gearbox equivalent torque, 57 % of its rating. Its worst static case, 92 %.

So why does the verdict say CHECK, with every check green? Because nine inputs are assumed, and the tool says so, right at the top.

Load sharing of 1.4 between ten pinions. Most of the travel in a 30 degree arc. A shock factor of 2. The brake pad friction range. No bearing friction entered.

None of these is a gap in the calculation. They're values only your project knows. Enter them, and the tool recalculates every check on your numbers, and the warning goes away.

It also hands on what it can't check itself. The gearbox loads go to the gearbox maker, or to the planetary calculator stage by stage. And the slewing bearing's friction comes from its maker, or from the slewing bearing calculator.

All of it goes into the PDF. Every check with its source, and the assumed list, so a reviewer sees exactly what was assumed.

What it doesn't do: it doesn't design the gearbox inside. It checks your loads against the gearbox maker's rating.

A yaw drive, checked as one system. Size yours on MechanixCalc.com.