SLEEVE BEARINGS – CHOOSING THE CORRECT TOLERANCE FITTING OF THE BEARING LOCATING AXLE
OBJECTIVE
The objective of this paper is support to choose the tolerance of the bearing locating axle, as the DIN31690 Standard recommendation.
This paper is not intending to replace any recommendation of sleeve bearing builders, but to furnish guidelines for choose and check the tolerance. If the tolerance is not choose correctly, the financial loss is big and the equipment are not still working.
WHY SLEEVE BEARINGS?
In the figure below, there is some examples of high load capacity rolling bearings:
Figure 1 (From: Springer Handbook of Mechanical Engineering, Grote and Antonsson, 2008, pag. 463 Fig.6.160a-f).
Below, sleeve bearings and its components as DIN 31690:
Figure 2 (From: RENK's catalogue RH1009 3.11 page 4).
Analyzing the capacity of a 200mm diameter high capacity roller bearing:
Assembly 32040XDF, as SKF:
Figure 3 – From SKF site
Maximum radial load capacity: 1.372.000 N
About a 200mm of diameter sleeve bearing:
Figure 4 – From Renk's catalogue RH1009 3.11 page 9.
Maximum radial load: 68000N.
Considering 66% of the maximum radial lose: 45.333N
4 poles Synchronous Rotating Electrical Machine, 60Hz, 1800rpm, 24 hours/day operation.
What would be the service life if a 32040 XDF bearing was used in these conditions?
Estimated service life calculation:
800.000h service life
91 years of continuous service life.
If the estimated service life of the bearing is long, why use plain bearings (or bushing)?
Gustav Niemann, in his classic work “Maschinenelemente” lists the following limitations to the use of bearings:
- Noise is inconvenient;
- Shocks and impacts (Generators for SHPs, Laminators, Rotating Machines dedicated to mining, for example);
- Large axles and low speeds;
- Applications where a split bearing is required.
Below, an example of where a split bushing bearing had its necessary application:
Figure 5 – From Renk's catalogue RH1009 3.11 page 8 (picture: GEC Alstom, F-Belfort).
If it were a rolling bearing, in addition to the rotor having to have another key and a coupling, its replacement would become a real problem (extraction tools, coupling removal).
Since a split bearing is applied, simply support the rotor correctly and disassemble only the bearing. That's right, when replacing the bushing, only intervention on the bearing.
What is the tolerance to be used for the region on the shaft for assembling the sleeve bearing?
It is a must the correct execution of the locating bearing on the shaft, not only in dimensions, but also to respect the geometric tolerances established by DIN31690 and the manufacturers. Obviously, the recommended roughness must be obeyed, for a long service life of the bushings and seals:
Figure 6 – From Renk RH1009 3.11 page 13.
As for the diameter and tolerances to be chosen, it is necessary to resort to the concepts of fluid mechanics.
Basic dimensions to be considered, and outline of the pressure diagram:
Figure 7 – Dubbel – Taschenbuch für den Maschinenbau, 23.Auflage, Seite 516, Bild.1.
B = width supported by the bushing
D = internal diameter of the bushing;
DJ = shaft diameter
e = eccentricity between bushing and shaft
F = radial force
h (φ) = oil film thickness as a function of angle
hmin = minimum oil film thickness
p (φ, z) = oil pressure as a function of angle and position in relation to the z coordinate;
pmax = maximum oil pressure;
_
p = distributed pressure.
z = z coordinate (-B / 2≤z≤B / 2)
φ = angle
β = angle where the minimum oil film thickness occurs;
ωB = angular velocity of the bushing
ωF = angular speed of the rolling force
ωJ = angular velocity of the axis
Newton's relationship between transverse stress, dynamic viscosity, speed and clearance:
Figure 8 – Dubbel – Taschenbuch für den Maschinenbau, 23.Auflage, Seite 110, Bild.25.a.
Newton's equation:
τ = shear stress of the liquid;
η = dynamic viscosity
δv = speed variation
δy = radial clearance (or film thickness)
According to the equation above, lack of clearance causes excessive stresses in the fluid. Excessive play can cause insufficient pressure for lubrication.
Recalling, the main objective of this work is to choose the tolerance for the bearing neck according to DIN31690.
DIN31690 recommends 5 relative clearance values (ψm), depending on the diameter and peripheral speed of the bearing:
Figure 9 – Renk RH1009 3.11 page 18
Figure 10 – Renk RH1009 3.11 page 18
Note that the tolerance is IT6, according to ISO 286.
As for roughness, the recommendation is Ra = 0.63μm, between N5 (0.4μm) and N6 (0.8μm).
The bearing bushing bore is standardized with H7 tolerance.
Using the example of the 200mm diameter bearing, 45.333N of load, for synchronous rotations at 60Hz in electric machines with 2 to 12 poles.
The tangential velocity is obtained:
Where:
vt: tangential velocity in m / s
D: diameter of the bearing neck in mm
n: synchronous rotation in rpm.
f: frequency of the mains in Hz
NP: number of poles.
Note: for asynchronous machines, the rotation is obtained by determining the synchronous rotation and multiplying by the slip factor. For motors with a cage rotor, for example, the slip is between 3% and 5%. Therefore, the slip factor is between 0.97 (1-0.05) and 0.95 (1-0.05).
In red characters, the limit dimensions for the bearing “neck”, nominal diameter 200mm, for the rotations (in rpm) of 3600, 1800, 1200, 900, 720 and 600.
As an additional feature, oil heating in one minute of operation will be determined for the 6 synchronous speed conditions and at ISO viscosities VG32, 46 and 68.
The first step is to determine the Sommerfeld coefficient. The form is indicated below, the calculations by spreadsheet:
p = mean distributed pressure
ψeff = effective relative diametrical clearance
ηeff = effective dynamic viscosity
ωeff = effective tangential velocity
Effective viscosity:
With:
ρ15 = fluid density at 15ºC
VG = ISO VG viscosity index
In the graph below, the relative eccentricity ε is obtained:
Figure 11 – Dubbel – Taschenbuch für den Maschinenbau, 23.Auflage, Seite 516, Bild.3 (nach DIN 31652)
The minimum oil film (to be used in Newton's equation to determine the shear stress in the fluid and, consequently, the torque and power that the oil dissipates):
Figure 12 - RELATIVE ECCENTRICITY - Dubbel – Taschenbuch für den Maschinenbau, 23.Auflage, Seite 516, Bild.3 (nach DIN 31652)
The frictional power generated in the bearing is given by:
(as “Dubbel – Taschenbuch für den Maschinenbau, 23.Auflage, Seite 518“ – equation 9)
f = friction coefficient
F = radial force
UJ = tangential velocity of the axis
UB = tangential bushing speed (UB = 0 for almost all bushing bearings)
The friction factor:
(as “Dubbel – Taschenbuch für den Maschinenbau, 23.Auflage, Seite 518“ – equation 10)
The increase in viscosity increases the loss, which generates heat.
The decrease in clearance also increases the loss, which generates heat.
Some machine builders set the relative clearance to 0.001, especially those that do not adopt DIN standards.
Only with this parameter change, the new temperature increases are observed in 1min:
In addition to the risk of damage, cooling systems would experience a substantial increase in costs and space required for installation.
CONLUSION
DIN31690 (which uses DIN31652) has the proper physical basis, proving to be adequate and practical in choosing not only the bearing, but also the tolerances for the respective laps. Reinforcing, the bushings holes are standardized in H7.
REFERENCES
Renk Catalogue RH1009 3.11
Springer Handbook of Mechanical Engineering, Grote and Antonsson, 2008
Dubbel – Taschenbuch für den Maschinenbau, 23.Auflage: 2011