Single-stage gearbox

This tutorial builds a complete single-stage gearbox: an input shaft driven by a motor at 1500 rpm with 150 N·m, a helical 20/60 × m3 gear pair, and an output shaft at 500 rpm. The gear pair is mounted on both shafts, so its tooth forces load them and their four bearings. It rebuilds the Single-stage gearbox example from a blank project.

The numbers are those of this version of Axomek. To compare: open the Single-stage gearbox example. It starts a new project from the example in place of yours, so save yours first (the app asks) and come back to it with Switch project (Ctrl+P).

The plan

The pinion sits on the input shaft at x = 140 mm, the wheel on the output shaft at x = 85 mm. Positions are measured on each shaft from its own left end.

Step 1: the input shaft

1. Start a Blank project and choose Add a first shaft section.
2. Sections tab: set S1's Length to 60 (keep Ø30). Then with + Section add and set S2 35 × 30, S3 42 × 100, S4 35 × 30 (Outer diameter × Length).
3. Supports tab: + Support, then set Name Input motor-side bearing, Designation 6207, Position 75. It is Locating.
4. + Support: Name Input far bearing, Designation 6207, Position 205. It is Floating.
5. For each support, in Bearing choose 6207 deep groove ball bearing under "New bearing: fits the Ø35 mm seat".
6. Loads tab: + Load, then set Name Motor coupling, Position 30 and Force y 0. Tick Takes the torque that balances the shaft.
7. Material tab, Limits for the checks: 0.05 mm, 4 ′, 200 MPa.

The motor coupling has no torque of its own yet: there is nothing to balance.

Step 2: the output shaft

1. In the inspector's header choose + Add shaft. A second shaft opens, still empty, and shaft tabs appear above the drawing.
2. Choose Add a first shaft section, then build the sections: S5 40 × 30, S6 48 × 110, S7 40 × 30, S8 35 × 60.
3. + Support twice. The first new support is locating, the second floating; this shaft needs it the other way round:
   • B3: Name Output far bearing, Designation 6208, Position 15, Floating.
   • B4: Name Output coupling-side bearing, Designation 6208, Position 155, Locating.
4. Link both to 6208 deep groove ball bearing.
5. + Load: Name Output coupling, Position 200, Force y 0, and tick Takes the torque that balances the shaft.
6. Material tab: the same three limits. Each shaft has its own limits.
7. Rename the shafts: select a shaft tab and choose Rename (or double-click the tab). Name them Input shaft and Output shaft.

Step 3: the gear pair

1. Open Gears in the navigation and choose Add a gear pair. Pair G1 appears with 20/60 teeth, module 3, 20° pressure angle, 30 mm face width, 150 N·m pinion torque at 1500 rpm and case-hardened 18CrNiMo7-6 on both gears.
2. Set Name Helical pair and, under Geometry, Helix angle β 12.
3. Open Gearbox mounting and choose Mount on shafts. The pinion goes on the input shaft and the wheel on the output shaft, each in its middle.
4. Set Pinion position 140, Wheel position 85, Pinion mass 1.2 kg and Wheel mass 5.5 kg. Leave Wheel direction at 0°, Driving gear at "Pinion (reduction)" and Pinion turns at "Positively about +x".

The tooth forces now load both shafts. The motor coupling takes the 150 N·m the pinion needs, and the output coupling takes what the wheel delivers.

Step 4: bearing speeds and requirements

The bearings keep the speed they were created with until you change it.

1. Open Bearings. For BR3 and BR4 (the output shaft) set Speed to 500 rpm. BR1 and BR2 stay at 1500 rpm.
2. For all four set Minimum life 20000 h and Minimum static safety s₀ 2 under Requirements.

Step 5: read the results

The gear pair

In the Gears module:

All four gear checks pass.

The shafts

All six shaft checks pass. The output torque is 150 N·m × 3 × 0.9933: the ratio times the mesh efficiency.

The helix gives an axial force of Ft·tan 12° = 1040 N. It goes to the locating bearings: B1 on the input shaft and B4 on the output shaft, in opposite directions.

Since the gears have mass and a polar inertia, the critical speed is the forward whirl speed of the turning rotor.

The bearings

All sixteen bearing checks pass. The system life of the four bearings is 22 185 h, a little above the 20 000 h each must reach, limited by BR1.

Power and efficiency

The Overview sums it up: the bearings lose 39.0 W, the mesh 157.6 W, 196.6 W in all of 23.56 kW put in, an efficiency of 99.17 %. Churning and windage losses are not included.

Things to try

• Raise the helix angle to 15°. The centre distance grows to 124.2 mm, the overlap ratio to 0.824 and the pitting safeties to 1.45 / 1.47. But the axial load on B1 and B4 rises to 1294 N: BR1's modified life falls to 48 528 h and the system life to 18 870 h. Each bearing still passes its own 20 000 h check; the system life is reported, not checked.
• Move the pinion closer to B2. The input bearings share the load differently.
• Set Driving gear to "Wheel (step-up)" to run the box as a speed increaser.
• Add a duty cycle to the bearings with load cases (see Bearings): a case's speed is the input speed, and the output bearings follow at a third of it.

Related

• Gear pairs
• Shaft
• Bearings
• Gear rating (ISO 6336)
• Tutorial: spur gear pair
• Tutorial: gearbox intermediate shaft