A simple shaft on two bearings
Rebuild the Simple shaft example from a blank project, fix its failing deflection check with a stepped shaft, and rate its two bearings.
This tutorial rebuilds the Simple shaft example step by step: a Ø40 × 400 mm steel shaft on two supports with a 5 kN load in the middle. Its deflection check fails. You then fix it with a stepped shaft and put two 6208 deep groove ball bearings on the supports.
The numbers are those of this version of Axomek. To compare your model with the finished example: open the Simple shaft 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).
Part 1: rebuild the example
The shaft
- On the start screen choose Blank project (or File › Home, then Blank project).
- Choose Add a first shaft section. Section S1 appears: Ø30 × 200 mm.
- In the Sections tab, select S1 and set Outer diameter to
40and Length to400. Leave Bore at 0 (a solid shaft).
The material is steel by default: E = 210 000 MPa, ν = 0.3, 7850 kg/m³ (Material tab).
The supports
- Open the Supports tab and choose + Support. B1 appears at x = 40 mm as Locating.
- Set its Name to
Left bearing, its Designation to6208and its Position to20. - Choose + Support again. B2 appears at x = 360 mm as Floating.
- Set its Name to
Right bearing, Designation6208and Position380.
The designation is a label for now. The supports are rigid; they become bearings in part 3.
The load
- Open the Loads tab and choose + Load. L1 appears at x = 200 mm with Force y −1000 N.
- Set its Name to
Central loadand Force y to-5000.
The limits
Open the Material tab. Under Limits for the checks enter:
| Field | Value |
|---|---|
| Max deflection | 0.1 mm |
| Max tilt at bearings | 10 ′ |
| Max von Mises stress | 150 MPa |
What you should see
The banner reads 1 of 3 checks fails.
| Result | Value |
|---|---|
| Max deflection | 189 µm at x = 200 mm |
| Max stress (von Mises) | 71.6 MPa at x = 200 mm |
| Largest bending moment | 450 N·m at x = 200 mm |
| Bearing tilt | 5.28′ at both supports |
| Support loads B1, B2 | 2500 N radial each |
| Shaft mass | 3.95 kg |
| 1st critical speed | 36 996 rpm (bending, non-rotating) |
| Check | Value / limit | |
|---|---|---|
| Shaft deflection | 0.189 / 0.1 mm | fails (189 %) |
| Tilt at bearings | 5.28 / 10 ′ | passes (53 %) |
| Shaft stress | 71.6 / 150 MPa | passes (48 %) |
These match the hand calculation for a simply supported beam with a central load. The bending moment is F·L/4 = 5000 N × 360 mm / 4 = 450 N·m. The deflection is slightly above F·L³/(48·E·I) = 184 µm because the app includes shear deformation.
Part 2: fix the deflection
Deflection grows with the fourth power of 1/d. A thicker shaft between the bearings helps most, while the bearing seats keep Ø40 for the 6208's 40 mm bore.
- In the Sections tab select S1 and set its Length to
40. - Choose + Section. S2 appears at the end, as long and as thick as S1. Set S2's Outer diameter to
50and Length to320. - Choose + Section again. Set S3's Outer diameter to
40and Length to40.
The shaft is 400 mm long again: Ø40 from 0 to 40 mm, Ø50 from 40 to 360 mm, Ø40 from 360 to 400 mm. Supports and loads keep their positions, because positions are measured from the left end.
The banner now reads All 3 checks pass:
| Result | Before | After |
|---|---|---|
| Max deflection | 189 µm | 79.0 µm |
| Max stress (von Mises) | 71.6 MPa | 36.7 MPa |
| Bearing tilt | 5.28′ | 2.20′ |
| Shaft mass | 3.95 kg | 5.72 kg |
| 1st critical speed | 36 996 rpm | 45 795 rpm |
The deflection check now uses 79 % of its limit. Switch on Deflection and Stress colours above the drawing to see where the shaft bends and where it is stressed.
Part 3: rate the bearings
- In the Supports tab select B1. In Bearing, choose 6208 deep groove ball bearing under "New bearing: fits the Ø40 mm seat", the presets that sit on the shaft's diameter there.
- Select B2 and choose the same.
The project now has bearings BR1 (named "Left bearing") and BR2 ("Right bearing"), loaded by the support reactions.
- Select B1 again and choose Open BR1 in the bearing module →.
- Under Requirements set Minimum life to
20000h and Minimum static safety s₀ to2. Do the same for BR2.
Each bearing runs at the preset speed of 1500 rpm with the preset lubricant (an oil of 100 mm²/s at 40 °C and 11 mm²/s at 100 °C) at 70 °C.
| Result (each bearing) | Value |
|---|---|
| Radial load | 2500 N |
| Dynamic rating C | 28 545 N |
| Basic rating life L10 | 14 108 h |
| Modified rating life (L10, with aISO) | 469 752 h |
| Static safety s0 | 8.39 |
| Largest contact stress | 2067 MPa |
| Film parameter λ | 1.16 (mixed lubrication) |
| Friction torque, power loss | 101.5 N·mm, 15.9 W |
| Thermally permissible speed nθ (DIN 732) | 5860 rpm |
All eight bearing checks pass: life, static safety, minimum load and speed for each bearing. The system life of the pair is 251 734 h.
The basic life alone (14 108 h) would fail a 20 000 h requirement. The modified life is much longer because the lubricant film and the cleanliness are good for this load (aISO > 1). If the oil were thinner or dirtier, the modified life would drop. Try a thinner oil under Lubrication: Viscosity at 40 °C 32 and Viscosity at 100 °C 5.4. BR1's modified life falls to 39 623 h and λ to 0.65 (boundary lubrication); the basic life does not change.
What you learned
- Positions are measured from the shaft's left end, so changing sections does not move supports or loads.
- Limits turn results into checks; the banner counts them.
- The stepped shaft passed the deflection check with a moderate increase in mass.
- Linking a support to a bearing preset rates the bearing with the support's reaction.