Rope sheave

This example shows the bearing selection process applied to an application case in which bearings are to be selected for the rope sheaves on a new paper machine.

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.

Performance and operating conditions
Performance requirements and operating conditionsBearing type and arrangementBearing sizeLubricationOperating temperature and speedBearing interfacesBearing executionSealing, mounting and dismounting

The rope sheaves (fig. 1) are positioned between rolls/cylinders of the paper machine and rotate all the time the machine is in operation. In this application the outer ring of the 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 rope tension, shared between the bearings
  • axial load: zero, because of orientation of sheaves, the rope creates no axial load
  • environment: hot and humid, with 80 °C (175 °F) ambient temperature
Bearing type and arrangement
Performance and operating conditionsBearing type and arrangementBearing sizeLubricationOperating temperature and speedBearing interfacesBearing executionSealing, mounting and dismounting

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, each bearing locates the sheave axially in one direction and the whole arrangement is able to move axially a small distance between the two end positions.
Bearing size
Performance and operating conditionsBearing type and arrangementBearing sizeLubricationOperating temperature and speedBearing interfacesBearing executionSealing, mounting and dismounting

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 to base the size selection on. 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 load, P, on each bearing is equal to the radial load divided by two.
  • P = 0,55 kN
  • load ratio, C/P = 49
The basic rating life, L10h = 804 800 h. This is much longer than the required maintenance-free 5 years (43 800 h).

Conclusion

  • 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 required 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 operating temperature and speed are checked, because lubricant viscosity influences the result. This will be done in Bearing size (step 2), below.

Lubrication
Performance and operating conditionsBearing type and arrangementBearing sizeLubricationOperating temperature and speedBearing interfacesBearing executionSealing, mounting and dismounting

Bearing 6207-2RSH is filled with MT33 grease (table 1).

The operating temperature should be defined before continuing.
Operating temperature and speed
Performance and operating conditionsBearing type and arrangementBearing sizeLubricationOperating temperature and speedBearing interfacesBearing executionSealing, mounting and dismounting

When load ratio C/P > 10, operating temperature is below 100 °C (210 °F), 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).
So a detailed thermal analysis is not required.
Lubrication (step 2)
Performance and operating conditionsBearing type and arrangementBearing sizeLubricationOperating temperature and speedBearing interfacesBearing executionSealing, mounting and dismounting

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)
The grease life, L10h, is about 12 500 hours, which is less than the required 5 years maintenance-free required.

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.

Conclusion

The SKF bearing 6207-2RSH, with the grease WT fulfills the requirement in terms of grease life.
Bearing size (step 2)
Performance and operating conditionsBearing type and arrangementBearing sizeLubricationOperating temperature and speedBearing interfacesBearing executionSealing, mounting and dismounting

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.

Minimum load


Using the minimum load equation from Loads, the minimum load, Frm is given by:
where:
  • 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
Therefore:
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
For WT, the base oil viscosity at 90°C (195 °F) can be estimated from diagram 2, or calculated with the SKF Bearing Calculator and is 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.
With ηc Pu/P = 0,7 and using diagram 4, the askf of about 50 is much greater than 1, so the SKF rating life is far above the required life.

Conclusion

The bearing SKF 6207-2RSH/WT is adequate in terms of fatigue life.

Bearing interfaces
Performance and operating conditionsBearing type and arrangementBearing sizeLubricationOperating temperature and speedBearing interfacesBearing executionSealing, mounting and dismounting

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 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 bearings seats are:
 Dimensional
tolerance
Radial
run-out
Axial
run-out
Ra
Inner ringg6ⒺIT5/2IT51,6 µm
Outer ringN6ⒺIT6/2IT63,2 µm
Bearing execution
Performance and operating conditionsBearing type and arrangementBearing sizeLubricationOperating temperature and speedBearing interfacesBearing executionSealing, mounting and dismounting

Initial internal clearance

The 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

NormalC3
min./avg./max.6 / 13 / 20 μm15 / 24 / 33 μm
 → Bearing data. Values obtained from table 9


2. Clearance reduction caused by 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
0,49 
f2

0,87 
Δ2min./avg./max.-29 / -17 / -5 μm 
Δrfitmin./avg./max.-25-15-4 μm 


3. Internal clearance after mounting

NormalC3
min./avg./max.-19 / -2 / 6 μm-10 / 9 / 29 μm

At least C3 clearance is required. Analysis with SKF proprietary software considering 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:
min./avg./max.
-2 / 16 / 32 μm


A small negative clearance is not critical for ball bearings. C3 clearance is adequate for this application.

Seals

It is not recommended to use shields (suffix 2Z) instead of friction 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 mill applications, and so will increase service life.

Consider hybrid bearings

Depending 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 change

By 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 in 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 more information, see the handbook Rolling bearings in paper machines.
Sealing, mounting and dismounting
Performance and operating conditionsBearing type and arrangementBearing sizeLubricationOperating temperature and speedBearing interfacesBearing executionSealing, mounting and dismounting

Sometimes, simple labyrinth seals are added to further protect the bearing integral seals.

The normal mounting and dismounting methods are applicable.
Overall conclusions
The bearing that fulfills the requirements is a sealed and greased SKF Explorer bearing  6207-2RSH/C3WT.

For more demanding operating conditions, or to achieve an even longer maintenance-free interval, SKF can provide other solutions.
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