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# Verifying the axial displaceability

## 1. Determine the required axial displacement

• Thermal expansion of the shaft can be estimated using
sreq = α L ΔT
• Considering other effects may require advanced calculation or simulation.

## 2. Determine the maximum misalignment

• Estimate the misalignment of the housing seats based on specified tolerances.
• Considering other effects may require advanced calculation or simulation.

## 3. Check the permissible axial displacement

Check the permissible axial displacement in both directions, depending on the bearing used:

• open bearing (fig. 1)
• full complement bearing with a retaining ring (fig. 2)
• sealed bearing (fig. 3)

sreq < s1 - β k1 B

or

sreq < s2 - β k1 B

If sreq is too large, consider offset mounting.

## 4. Check the internal clearance

• Determine the clearance reduction caused by axial displacement.
• Determine the amount of clearance reduction from other effects (→ Bearing clearance).
Symbols
 B bearing width [mm] Cred reduction of radial clearance as a result of an axial displacement from a centred position [mm] k1 misalignment factor (→ product tables) L Length of the shaft that is subjected to the temperature raise [mm] s1 axial displacement limit in bearings with a cage (fig. 1) or in full complement bearings (fig. 2) when displacing away from the retaining ring [mm] (→ product tables) s2 axial displacement limit in sealed (fig. 3) and full complement bearings (fig. 2) when displacing toward the seal or retaining ring respectively [mm] (→ product tables) sreq required axial displacement from a centred position [mm] α thermal coefficient of expansion [°C–1] = 12 x 10–6 for steel β misalignment [°] ΔT temperature difference [°C]
Calculation example
Application (fig. 4)
• Bearing C 3040
- d = 200 mm
- D = 310 mm
- B = 82 mm
- Normal clearance: min. 170 μm
- s1 = 15,2 mm
- k1 = 0,123
- k2 = 0,095
- interference fit on the shaft: p6, max. probable interference 101 μm
• Temperature range for the shaft: 20 to 90 °C [70 to 195 °F]
• Max. misalignment: 0,46°

Verifying the axial displacability

1. Required axial displacement
sreq = 12 x 10-6 x 3000 x (90 - 20) = 2,5 mm
2. Max. misalignment
Input provided: 0,46°
3. Checking the permissible axial displacement
2,5 < 15,2 - 0,46 x 0,123 x 82 ≈ 10,5
→ okay
4. Checking the internal clearance

Clearance reduction from interference fit on the shaft (→ Bearing clearance)
For d/D = 0,65 → 0,87 x 101 = 87 μm

Min. residual internal clearance when the bearing is displaced
170 - 87 - 7 = 76 μm
→ okay