# Supporting wheel

This example shows the bearing selection process applied to an application case in which the bearing solution for a supporting wheel of a new crane is confirmed.

A crane manufacturer has designed a new workshop crane and wants to confirm that an existing supporting wheel design can be used (fig. 1). The supporting wheel has two flanges to guide the crane on the rail. The bearings are mounted on an intermediate sleeve, which is supported by a fixed axle. A loose fit between the intermediate sleeve and the fixed axle is beneficial for easy mounting of the wheel assembly on the crane structure.

Each step of the example is described in an expandable/drop-down section below. The steps in the example follow the sequence in the bearing selection process. Refer to the bearing selection process for a full description of each process step.

Performance and operating conditions

The bearings share the radial wheel load. Additionally, when the wheel contacts the rail, the axial guiding force causes a moment load on the bearing arrangement (fig. 1), which is balanced by additional opposite radial loads on the bearings. As the floating bearing arrangement is designed with the sleeve abutments located axially between the two inner rings, the bearing which has the lower radial wheel load will accommodate the axial wheel load.

The application data and operating conditions are:

• Radial wheel load: Kr = 130 kN
• Axial wheel load: 0,1 Kr  or peak load 0,3 Kr
• Wheel diameter: D = 315 mm
• Travelling speed: v = 25 m/min → rotational speed n = 25,3 r/min
• Bearing distance: l = 160 mm
• Fixed axle diameter: d1 = 60 mm
• Sleeve diameter: d = 90 mm
• Average ambient temperature: T = 20 °C (70 °F)
• Bearings: 2 × 22218 E (spherical roller bearings)
• Required basic rating life: 12 500 h (2 h/day in operation)
• Required static safety factor: > 2
Bearing type and arrangement

The distance between the two bearings is very short and, therefore, thermal expansion of the axle is small. A floating bearing arrangement can be used.
Radial loads are high and axial loads must also be accommodated. Spherical roller bearings are an adequate choice.
Bearing size

Both of the two main criteria used to determine the bearing size need to be applied:

1. Rating life
Each bearing accommodates either a radial load only (increased by the moment caused by the axial load) or an axial load plus a radial load (reduced by the moment caused by the axial load). The applicable equivalent dynamic bearing load is the mean value of the two load cases.

2. Static load
The maximum equivalent static bearing load must be considered for static safety.

Load ratings and calculation factors → 22218 E product details

### Bearing loads – radial load only

Fr1 = Kr/2 + 0,1Kr D/2l = 130/2 + (0,1 × 130 × 315) / (2 × 160) = 77,8 kN
Fr1 peak = 130/2 + (0,3 × 130 × 315) / (2 × 160) = 103,4 kN
Fa1 = 0

Equivalent bearing loads (→ Loads)
Fa1 = 0 ≤ e
P1 = Fr1 = 77,8 kN
P01 = Fr1 peak = 103,4 kN

### Bearing loads – radial and axial load

Fr2 = Kr/2 – 0,1Kr D/2l = 130/2 – (0,1 × 130 × 315) / (2 × 160) = 52,2 kN
Fa2 = 0,1Kr = 13 kN
Fr2 peak = Kr/2 – 0,3Kr D/2l = 26,6 kN
Fa2 peak = 0,3Kr = 39 kN

Equivalent bearing loads (→ Loads)
Fa2/Fr2 = 0,25 > e
P2 = 0,67 Fr2 + Y2 Fa2 = 0,67 × 52,2 + 4,2 × 13 = 89,6 kN
P02 = Fr2 peak + Y0Fa2 peak = 26,6 + 2,8 × 39 = 136 kN

### Basic rating life

Based on the mean load of the two load cases (→ Equivalent mean load)

Pm = (P1 + 2 P2) / 3 = (77,8 + 2 × 89,6) / 3 = 85,7 kN

L10h = 106 / (60 × 25,3) × (331 / 85,7)10/3 = 59 550 h > 12 500 h

### Static safety factor

Based on maximum peak load P0 = 136 kN:

s0 = C0/P0 = 375 / 136 = 2,76 > 2

### Conclusion

The bearing 22218 E is an adequate size for the application.

Lubrication

For the low operating speed and to keep contamination out, grease lubrication is used, whereby the bearings and hub cavities are 100% filled with grease. The grease is supplied via ducts in the fixed axle and sleeve.

### Grease selection

• Temperature: 20 °C (70 °F) → low (L)
• Speed: nD = 25,3 × 160 ≈ 4 050 → very low (VL)
• Load: C/P = 3,8 → high (H)
• Peak loads
• Good rust inhibiting properties required

SKF LGEP2 is a suitable choice. However, the alternative greases LGEV2 and LGEM2 should be considered for supporting wheels, because of frequent start-stops.

### Relubrication interval

The operating speed is too low to apply the diagram to determine the relubrication interval. In addition, the relubrication interval is dictated by the need to keep contamination out.

For this workshop crane, the manufacturer recommends starting with monthly relubrication. If the expelled grease is still like new after operating for this period of time, the relubrication interval can be extended.

### Relubrication quantity

Gp = 0,005 D B = 0,005 x 160 x 40 = 32 g

Operating temperature and speed

For the given application conditions (particularly the very low speed and low ambient temperature), there is no need to do a more detailed thermal analysis.

Bearing interfaces

The conditions of rotation are:

• stationary load on the inner ring → a loose fit is possible (and recommended to facilitate mounting)
• rotating load on the outer ring → an interference fit is required
The seat tolerances for standard conditions are (obtained from table 2 and table 4):
 Dimensional tolerance Total radial run- out tolerance Total axial run- out tolerance Ra Inner ring g6Ⓔ IT5/2 IT5 1,6 µm Outer ring P7Ⓔ IT6/2 IT6 3,2 µm

To ease mounting, an N7Ⓔ tolerance is acceptable, because of the very low operating speed at which the outer ring is rotating. As an alternative for the inner ring, an h6Ⓔ tolerance will provide a transition fit, which will minimize relative movements between the inner ring and the axle/sleeve.

The floating bearing arrangement requires a small axial gap between the bearings and their abutments. Because of the loose fit for the inner rings, the gap should be formed between the inner rings and the sleeve abutments.

Bearing execution

### Clearance class

The current design uses bearings with Normal initial internal clearance. The interference fit on the outer rings reduces the internal clearance. There is no temperature difference between the inner and outer rings. We determine the operational clearance.

1. Initial internal clearance
 min./avg./max. 60 / 80 / 100 μm → Bearing data. Values obtained from table 5.

2. Clearance reduction caused by an interference fit

There is no interference on the inner ring, therefore use:

Δrfit = Δ2 f2Clearance reduction caused by interference fits

Obtain values for:
Results:
 d/D 0,56 f2 0,88 Δ2 min./avg./max. -60 / -36 / -11 μm Δrfit min./avg./max. -53 / -31 / -10 μm

3. Internal clearance after mounting
 min./avg./max. 7 / 49 / 90 μm

The result indicates that Normal internal clearance is suitable.

### Other design features

The standard execution (steel cage, Normal dimensional tolerances, P5 geometrical tolerances) meets the application requirements.

Final designation: 22218 E

Sealing, mounting and dismounting

### Sealing

The current design uses simple gap-type seals. These seals are sufficient because the cavities in the hub are completely filled with grease and the operating speed is very low, but they will require relubrication to purge any contaminants. The total grease consumption over the lifetime of the application can be reduced by using radial shaft seals, e.g. 90x10x10 HMS5 RG.

Overall conclusions

22218 E SKF Explorer bearings are an adequate selection for the application. Lubrication with SKF LGEP 2, LGEM 2 or LGEV 2 will provide high performance. A radial shaft seal can help to reduce grease consumption. Alternatively, a sealed bearing (BS2-2218-2RS/VT143) can be used.