A paper machine manufacturer wants to build a new machine using rope sheaves of their standard design. The end customer requires the sheaves to be maintenance free for five years.
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. Some steps, such as Bearing size, require more than one iteration if the calculation is dependent on a subsequent stage in the process. This is indicated in the heading. For example, "Bearing size (step 2)". Refer to the bearing selection process for a full description of each process step.
The rope sheaves (fig. 1) are positioned between rolls/cylinders of the paper machine and rotate all the time that the machine is in operation. In this application the outer ring of each rope sheave rotates continuously.
The operating conditions are:
- rotational speed: 2 450 r/min
- radial load: 1,1 kN created by the weight of the sheave and by the rope tension, shared between the bearings
- axial load: zero - because of the orientation of the sheaves, the rope creates no axial load
- environment: hot and humid, with 80 °C (175 °F) ambient temperature
Because loads are low and speeds moderate, rope sheaves use two deep groove ball bearings. For a long, maintenance-free period sealed bearings are required. SKF deep groove ball bearings are available with various seal executions.
A floating bearing arrangement is used, where each bearing locates the sheave axially in one direction and the whole arrangement is able to move axially over a small distance between the two end positions.
The manufacturer's existing rope sheave design uses two 6207-2RS1 bearings. SKF has replaced the RS1 seal with the RSH seal. In this example we check the suitability of 6207-2RSH bearings (→ product details).
The next step in the selection process is to determine the method, on which to base the size selection. The bearings are running in typical operating conditions and, therefore, rolling contact fatigue is the probable failure mode. We base the size selection on rating life.
Basic rating life
As there is no axial load, the equivalent dynamic bearing load, P, on each bearing is equal to the radial load divided by two.
- P = 0,55 kN
- load ratio C/P = 49
- With such a high basic rating life at 2 450 r/min, it is recommended to check that the bearing is sufficiently loaded to maintain ball rolling and avoid ball sliding. This will be done after the lubrication is checked, because lubricant viscosity influences the requisite minimum load.
- Grease life should be checked to see if the bearing fulfills the end-customer’s requirement.
The SKF rating life, L10mh, will be calculated after the lubrication is checked and the operating temperature and speed are checked, because lubricant viscosity influences the result. This will be done in Bearing size (step 2), below.
Bearing 6207-2RSH is filled with MT33 grease (table 1).
The operating temperature should be defined before continuing.
When the load ratio C/P > 10, the operating temperature is below 100 °C (210 °F), the operating speed is below 50% of the limiting speed, and there is no pronounced external heat input, a detailed thermal analysis is not required.
In this example:
- load ratio: C/P = 49 > 10
- operating speed: 2 450 r/min < 0,5 x 6300 (limiting speed)
- From experience of rope sheaves operating in similar conditions, the bearing operating temperature is about 90 °C (195 °F).
1. Grease life MT33
Grease life can be estimated using diagram 1 under Greases for capped bearings at Single row deep groove ball bearings. Because the bearing outer ring rotates, for grease life estimations, nD is used instead of ndm (table 2).
Then, using the input values:
- nD = 2 450 x 72 = 176 400
- MT33 grease with a grease performance factor, GPF = 1
- operating temperature of about 90 °C (195 °F)
2. Grease life WT
The SKF bearing 6207-2RSH is available with the grease WT, which has a GPF=4. It is a polyurea-type grease with an ester base oil. (table 3).
From diagram 1, the grease life, L10h is 50 000 hours, which is greater than 5 years.
ConclusionThe SKF bearing 6207-2RSH with the grease WT fulfills the requirement in terms of grease life.
From the conclusions in Bearing size, above, the minimum load needs to be checked and, now the lubrication has been selected, the SKF rating life can be verified.
Using the minimum load equation from Loads, the minimum load, Frm is given by:
- kr = 0,025
v = 210 mm2/s
When determining the minimum load, to cover all critical operating conditions, use the highest oil viscosity that might occur. This will be at the lowest temperature, which is 20 °C (70 °F). Base oil viscosity of WT grease at 40 °C (105 °F) is 70 mm2/s ≈ ISO VG 68. Estimated from diagram 2, or calculated with the SKF Bearing Calculator, for WT grease v = 210 mm2/s at 20°C (70 °F).
- dm = (d+D)/2 = (35+72)/2 = 53,5 mm
Frm = 0,44 kN < 0,55 kN, so the bearing 6207-2RSH/WT is adequate.
SKF rating life
Because P < Pu, fatigue is not a factor (Fatigue load limit, Pu). However, it is useful to verify the lubrication condition (viscosity ratio) and life modification factor.
1. Lubrication condition – the viscosity ratio, κ
κ = ν/ν1
The following are used:
- ν1 is determined from diagram 3
- with dm = 53,5 and n = 2450 r/min, ν1 is close to 12 mm2/s
Viscosity ratio, κ = 12/12 = 1
2. Life modification factor, aSKF
To determine the life modification factor for radial ball bearings, diagram 4 is used, with:
- P = 0,55 kN
- κ = 1
- Pu = 0,655 kN
ηc = 0,6
The contamination factor is chosen based on table 4. (Contamination factor, ηc)
- SKF 6207-2RSH/WT is an SKF Explorer bearing.
The bearing SKF 6207-2RSH/WT is adequate in terms of fatigue life.
The bearing inner rings have a stationary load condition and no spacer between the inner rings in the cross-located arrangement. They are mounted with a loose fit for easy mounting. The recommended fit for standard conditions is g6Ⓔ (table 5).
The outer rings have a rotating load condition, so they are mounted with an interference. The recommended fit for standard conditions is M7Ⓔ (table 6), which has a probable interference range of -25 to +8 (table 7).
Bearings in rope sheaves of paper machines should always have an interference for the outer ring (application handbook Rolling bearings in paper machines). To achieve this select N6Ⓔ, which has a probable interference range of -29 to -5 (table 8). For geometrical tolerances and surface roughness, standard recommendations can be applied.
The tolerances for the bearing seats are:
|Inner ring||g6Ⓔ||IT5/2||IT5||1,6 µm|
|Outer ring||N6Ⓔ||IT6/2||IT6||3,2 µm|
Initial internal clearanceThe current design uses bearings with Normal initial clearance. The interference fit on the outer ring reduces the internal clearance. We determine the operational clearance for both Normal and C3 initial clearance, to select the most appropriate bearing execution.
1. Initial internal clearance
|min./avg./max.||6 / 13 / 20 μm||15 / 24 / 33 μm|
|Bearing data. Values obtained from table 9|
2. Clearance reduction caused by interference fits
There is no interference on the inner ring, therefore use:
Δrfit = Δ2 f2 → Clearance reduction caused by interference fits
Obtain values for:
|Δ2||min./avg./max.||-29 / -17 / -5 μm|
|Δrfit||min./avg./max.||-25 / -15 / -4 μm|
3. Internal clearance after mounting
|min./avg./max.||-19 / -2 / 6 μm||-10 / 9 / 29 μm|
At least C3 clearance is required. Analysis with SKF proprietary software that considers the effects from smoothing of the mating surfaces and the probability that maximum fit reduction coincides with minimum bearing clearance provides the following values for a bearing with C3 internal clearance:
||-2 / 16 / 32 μm|
A small negative clearance is not critical for ball bearings. C3 clearance is adequate for this application.
SealsIt is not recommended to use shields (suffix 2Z) instead of contact seals (suffix 2RSH) in this application because there is a risk of grease leakage with outer ring rotation. The 2RSH seal design has the advantage of being more resistant to wash-out (high-pressure cleaning) that happens in paper machines, and so this will increase service life.
Consider hybrid bearingsDepending on the paper machine and position of the rope sheave, the sheave may face higher operating temperatures, which will reduce the grease life. To increase grease life, the use of hybrid bearings (ceramic balls instead of steel ones) of the same size can increase the grease life by at least a factor of two.
Consider design changeBy changing the rope sheave hub design so that the bearing’s inner ring rotates instead of the outer ring, grease life is increased. The speed factor will be ndm = 131 000 instead of nD = 176 400.
The grease life, L10h, of the 6207-2RSH/C3WT bearing will increase from 50 000 h to 61 000 h.
SKF has developed a rope sheave hub to take the above consideration into account. The bearings have ceramic balls, and WT grease, and their inner rings rotate (fig. 2). An enhanced design has been created using special bearings. For additional information, see the handbook Rolling bearings in paper machines.
For more demanding operating conditions, or to achieve an even longer maintenance-free period, SKF can provide other solutions.