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Roller bearings are used in all main shaft and auxiliary drive shaft applications to support pure radial load, and allow for axial shaft elongation due to temperature changes with no additional load effect on the bearing. They are usually located at the ends of the turbine and compressor shafts and are often mounted in a housing, but separated from it by a layer of pressurized oil known as a squeeze film damper.
In many cases, instead of having a separate inner race for roller bearings, the “inner race” is an integral part of the shaft or stub shaft. This reduces complexity, weight, and build-up of concentricity tolerances. Overall, this is cost effective, but the cost of replacement or repair is likely to be higher than for separate inner races.
In a taper roller bearing the line of action of the resultant load through the rollers forms an angle with the bearing axis. Taper roller bearings are therefore particularly suitable for carrying combined radial and axial loads. The bearings are of separable design, i.e. the outer ring (cup) and the inner ring with cage and roller assembly (cone) may be mounted separately.
Single row taper roller bearings can carry axial loads in one direction only. A radial load imposed on the bearing gives rise to an induced axial load which must be counteracted and the bearing is therefore generally adjusted against a second bearing.
Two and four row taper roller bearings are also made for applications such as rolling mills.
Figure 10 shows the three basic parts to a journal bearing: the outer housing, the journal, and the lubricant. The outer housing is a cylindrical shaft, which contains a hollow core large enough to create a close fit between itself and the journal. In addition to confining the path of the journal's orbit, it provides radial support to the journal through direct contact or by aiding in the creation of the oil wedge. A small clearance space between the outer housing and the journal is necessary: in order to assist in the assembly of the journal and the bearing, to provide space for the addition of the lubricant, to accommodate thermal expansion of the journal, and to anticipate any journal misalignment. Within this small clearance space resides the lubricant which provides the basic function of lubricating the journal and outer housing contact, as well as producing the load-carrying capability of the journal bearing and possibly attenuating the vibrations of the rotors. This load-carrying capability is a result of the pressure that is developed by the viscous effects within the thin film lubricant. A more complex journal bearing that is commonly used is the tilt-pad journal bearing. This type of journal bearing contains the same components as the simple bearing, with the added feature of tilt pads. Tilt pad journal bearings are used for their innate ability better to handle rotor-dynamic instability problems; however, they provide less damping than the simple bearing. Consequently, if vibrations occur due to other sources aside from the bearing, then the amount of damping provided by the bearing may arise as anissue.
Diagnostic Algorithms
Unlike roller bearings, whose vibration has simple and distinct patterns that can mostly be predicted from the geometry, journal bearings, while simple-looking, are rather complicated in their dynamics. Since journal bearings are only one part of a rotating machine, the analysis of the bearings must take into consideration vibrations caused by the flexible journal, fluid and rotor dynamics, and any outside sources of vibration acting on the system. Consequently, this type of analysis usually becomes complicated, and results in no clear vibration patterns associated with most of the failure modes. This is why the tools for the diagnosis of a journal bearing stagger are lacking.
‘Whirl’ refers to a circulating path the journal takes within the bearing resulting from large vibrations of the journal. Proximity sensors can be placed at perpendicular positions to the orbit of the shaft. These sensors would allow the monitoring of the position of the orbit, and notify the user of the misalignment, the amount of clearance existing, and the range of motion of the journal. The user would be warned if the motion of the journal exceeds a certain allowable envelope of motion.
An accelerometer can be placed on the outer housing to measure the frequency and amplitude of the housing vibrations which do not have a straightforward relationship with journal whirl. Based on the vibrations taken from the bearing's normal conditions, abnormal conditions can be detected. For example, in cases where the bearing's housing is supported on springs rather than secured directly to an immobile object, chaotic motion is found at intermediate speed ranges, and disappears at low and high speeds. At low and high speeds, different distinct subharmonic frequency components in the X- and Y-direction of the bearing are excited. However, during intermediate speeds, there is a rich spectrum of excited frequencies in both directions, which results in vibrations with comparatively large amplitudes that may induce fatigue failure.
Misalignment occurs when the journal's centerline does not coincide with the bearing's centerline. This is caused by combinations of rotational movements about a pivot point in the longitudinal cross-section and translational movements of the journal in the vertical and horizontal axis in the radial cross-section. Misalignment results from assembling or manufacturing errors, off-centric loads, shaft deflection such as elastic and thermal distortions, and externally imposed misaligned moments. A side-effect of the misalignment is the creation of a converging wedge geometry, known as the oil wedge, between the journal and the outer housing. In addition, misalignment contributes to the whirl by changing the threshold speed at which instability occurs. It is able to change the journal bearing's load-carrying capability, increase its frictional power loss, alter the fluid film thickness, change the dynamic characteristics such as system damping and critical speeds, and modify the vibrations as well as the overall stability of the system. One of the most significant effects of misalignment is its ability to produce a substantial amount of vibration when the frequency of the rotor's vibrations is a harmonic of the rotational speed of the journal.
Hot spots found on a journal, which ultimately develop into thermal bends, are results of the New-kirk effect. These hot spots are quite common, resulting from the contact of the rotor with the bearing or due to a temperature difference across the diameter of the journal. In the latter case, the temperature difference is a result of the differential shearing in the oil film. This phenomenon, in conjunction with the system running near a critical speed of the journal, can generate unstable vibrations in the bearing.
Under normal, low journal velocity conditions, the journal resides at an equilibrium position that is determined by its velocity. However, as the speed increases and approaches a threshold speed of instability, the journal's stability becomes compromised. Speeds above the threshold speed cause a self-excited oscillation to occur, during which the whirling motion of the journal is increased by its own rotational energy. This is dangerous if the oscillations are of large magnitude. If the journal suddenly becomes unstable, this is called subcritical bifurcation. On the other hand, if the journal gradually becomes unstable, it is called supercritical bifurcation. Subcritical bifurcation is also possible under the threshold speed when the rotor is given small perturbations by an outside force. Consequently, factors such as constant and imbalance loads on the journal are considered important when preventing bifurcation.
Vibrations can also occur from the lack of an oil wedge. Oil wedges, which are responsible for the load-carrying capability of the journal bearing, can be prevented from forming if the load is too heavy, the journal speed is too slow, or there is a lack of lubrication. In all three cases, metal-to-metal contact occurs, thus causing vibrations in the bearing.
Seizure, which results in a complete halt of the journal's movement, is a serious common problem. This mode of failure can result from the lack of an oil wedge (dry rubbing) which leads to highly localized heating, inadequate heat release from the system, and thermal expansion of the journal. In the third case, the journal may thermally expand faster than the bearing housing, causing the clearance between the journal and the bearing to disappear and metal-to-metal contact to occur. In the case of tilt pad bearings, thermal expansion of the tilt pads can produce the same phenomenon.
As with plain and ball bearings, roller bearings also may be classified by their ability to support radial, thrust, and combination loads. Note that combination load-supporting roller bearings are not called angular-contact bearings as they are with ball bearings. For example, the taper-roller bearing is a combination load-carrying bearing by virtue of the shape of its rollers.
Figure 60.13 shows the different types of roller elements used in these bearings. Roller elements are classified as cylindrical, barrel, spherical, and tapered. Note that barrel rollers are called needle rollers when less than ¼-inch in diameter and have a relatively high ratio of length to diameter.
When roller or ball bearings are disassembled for service, the following procedure is recommended: Remove bearing races from shafts, place in a suitable container with a clean petroleum solvent or kerosene and soak. Slowly and carefully rotate each bearing by hand to help dislodge any dirt particles.
2.
Remove all old grease and oil from the housing and clean the housing with white kerosene or other suitable solvent. Carefully wipe all parts dry with a clean cloth to prevent dilution of the new lubricant by solvent.
3.
When bearing grease is badly oxidized, soak in light oil (SAE 10 motor oil) at 200–240°F before cleaning as discussed in the prior steps. Flush the clean bearing in light oil to remove any solvent.
Ball bearing and roller bearings are often called antifriction bearings, because the contact between the bearing element is rolling instead of sliding, as in the case of a plain or journal bearing. The area covered by the rolling element is quite less compared to sliding bearings, or we can say that rolling friction is less compared to sliding friction. Although at the start, the friction coefficient of plain or sliding journal bearings are of greater size but in the case of full a hydrodynamic lubrication condition, the friction coefficient may becomes less compared to rolling element bearings. For plain sliding or journal bearings and rolling element bearings, the friction coefficient variation with the speed of shaft is shown in Fig. 11.4.
There are four stages encountered to the rise in friction coefficient. See Fig. 11.5. At the first stage, friction rises enormously due to sudden applied load and pressure, and in the protective film build-up, the substrate is sheared off. At second stage of sliding, because generated debris particles are in still circulation, they adhere to the ball or substrate side and raise the friction coefficient again. At the third stage, a dense protective film starts forming between the surface and the ball due to continuous sliding between substrate material and counterpart material, but it is still not stable and sheared off. At the last stage of sliding, this protective film is stable and acts as a self-lubricant between the contact pairs, which reduces the friction coefficient at its minimum value. This transition period is stable for longer duration.
In bearings, material loss is an extreme situation for scientists these days. Wear is loss of material per unit volume when one surface slides across another surface with which it is in contact. Generally, two types of wear are encountered in bearing failure: first, adhesive wear and, second, abrasive wear. In adhesive wear, transfer of one surface occurs to another surface due to sliding contact, it’s vice versa to smearing wear. But abrasive particles are generated between the surfaces when one hard surface moves over a smooth surface, resulting in two-body abrasion. When there is transfer of visible patches [8] of material from one surface to another and back to its normal position due to high friction shearing forces on the rolling element bearing surface, it is known as smearing. Smearing wear [9,10] is similar to adhesive wear in bearing material transfer. This lowers the bearing endurance and increases bearing friction. Micropitting on the surface is initiated due to fatigue stresses on the surface, which leads to increased surface pits in the range of 10–20 μm, whereas, fatigue wear is the result of repeated contact stresses at similar places, which breaks surface endurance limit and initiates crack generation, which propagates and leads to surface fatigue phenomena. Another form of wear in bearings is the brinelling effect, which is caused by surface indentation of a harder material. Sometimes, bearings under operation experience sudden impact load or high load during nonoperational mode and that causes plastic deformation known as true brinelling, whereas, false brinelling or fretting wear is caused by a repeated small amount of force acting on a bearing surface over a sustained period of time. Some of the wearing surface examples are shown in Fig. 11.6. Another mode of bearing failure is incorrect lubrication design, improper mounting of bearings, surface fatigue, and wrong material selection.
Fatigue in ball or roller bearings is caused by repeated stress reversals as the rolling elements move around the raceways under load. The periodic elastic compression and release as the rolling elements make their way around the tracks will ultimately overwork and rupture the metal just below the surface. As a result, tiny cracks propagate almost parallel to the surface but just deep enough to be invisible. With continuous usage the alternating stress cycles will cause the cracks to extend, followed by new cracks sprouting out from the original ones. Eventually there will be a network of minute interlinking cracks rising and merging together on the track surface. Subsequently, under further repeating stress cycles, particles will break away from the surface, the size of material leaving the surface becoming larger and larger. This process is known as spalling of the bearing and eventually the area of metal which has come away will end the effective life of the bearing. If bearing accuracy and low noise level is essential the bearing will need to be replaced, but if bearing slackness and noise can be accepted, the bearing can continue to operate until the rolling elements and their tracks find it impossible to support the load.
It is claimed that this toroidal roller bearing can accommodate very high radial loads. This is due to the optimized design of the rings combined with the design and number of rollers. It is also claimed that the large number of long rollers make CARB® bearings the strongest of all aligning roller bearings.
Also, these bearings can cope with small deformations and machining errors of the bearing seating. The rings can accommodate these small imperfections without the danger of edge stresses. The high load carrying capacity plus the ability to compensate for small manufacturing or installation errors provide opportunities to increase machine productivity and uptime.
The total power loss Ptot is summed up by two parts. The first part is independent of the transmitted torque and consists of the oil churning losses in the bearings Pl0, in the case Po0 and the friction in the seals Pd0. The second part is load dependent and is caused by the friction in the bearings PlL and the contacts of the cycloid disc with the cylindrical features of the housing Ppf and the output pins PRVj.
Eq.1
In the current analysis the bearings losses Pl0, PlL and the seal losses Pd0 are calculated according to recommendations of the manufacturers. The losses at the contact points of the cycloid disc Ppf and PRVj are calculated according an EHL model as outlined in chapter 2.5. The estimation of the oil loss Po0 is beyond the scope of the current study.
2.2.1 Bearings
The components are mounted using roller bearings as shown in Table 2 and Figure 1. The calculation requires the rotational speed, average diameter, oil viscosity and force. It is based on the manufacturer catalogues (21). The oil is the same as for the disc contacts, FVA 4 (ISO VG-460).
Table 2. Bearing specifications
Position
Bearing A
Bearing B
Ang. Velocity
f0
f1
dM [mm]
Input axle
NJ 2304
NJ 2304
ωin
3.0
0.0004
36.0
Output axle
NJ 210
NJ 210
ωout
2.0
0.0003
70.0
Profiled disc
NN 3007
ωin + ωout
2.5
0.0004
48.5
No load loss
Load loss
Cylindrical
Table 3. Cycloid reducer parameters
Parameter
units
Z1
Num. of lobes
[-]
20
Z2
Num. housing pins
[-]
21
E
Eccentricity
[mm]
3.8
Rpin
Housing pin radius
[mm]
10
Rprofile
Profile radius
[mm]
100
Output bores radius
[mm]
12
Input bore radius
[mm]
24
Rpitch
Pitch Radius of bores
[mm]
65
Nbores
Num. bores-output pins
[-]
8
θb
Bore angle from x+
[deg]
9
L
Profile disc width
[mm]
20
2.2.2 Seals
The friction power loss of seals is estimated according to the manufacturer’s recommendations (22). For the input shaft, the seal is in contact with a shaft diameter of 20 mm, and the rotational speed is for cases 1, 2 1200 rpm and for 3, 4 2400 rpm. The chart provides an estimated 10 W for cases 1, 2 and 20 W for cases 3, 4. The output shaft is rotating with very low speed and the power loss is less than 1 W.
2.2.3 Sliding contacts
The friction work is calculated as the friction force multiplied by the sliding velocity (Eq. 2). Alternatively the friction torque can be calculated as the friction force multiplied by the rotation radius, the integral friction work results to the same equation. Two types of sliding contact pairs are calculated.
The design rules for fabricated steel roller bearing are provided in EC1 (BS EN 1337-4) [3.12]. According to the code, only ferrous materials (see Table 3.30) shall be used in the manufacture of rollers and roller plates. Rollers and roller plates shall have a surface hardness less than that specified by the code. Carbon steel shall be in accordance with the requirements of EN 10025 [3.13] or EN 10083-1 [3.14] and EN 10083-2 [3.15], with a minimum yield strength of 240 N/mm2. Stainless steel shall be in accordance with EN 10088-2 [3.16], with a minimum tensile strength of 490 N/mm2 for any component. Cast steel shall be in accordance with ISO 3755 [3.17]. The design of roller bearings is based on the assumption that load passes through a Hertzian contact area between two surfaces with dissimilar radii. Design verification with respect to loading and rotation (movement) should be determined in accordance with BS EN 1337-1 [3.11]. The design values of the effects (forces, deformations, and movements) from the actions at the supports of the structure shall be calculated from the relevant combination of actions according to BS EN 1990 [3.4]. Sliding elements should be designed and manufactured in accordance with EN 1337-2 [3.18]. The recommended material partial safety factor γm = 1. Roller bearings provide for translation in one direction only. Single rollers permit rotation about the line of contact but multiple rollers require additional elements to accommodate rotation. Roller bearings for use in curved parts of structures shall have additional sliding elements and/or rotation elements to ensure uniform distribution of load across the roller. The axis of rotation shall be perpendicular to the direction of movement. The curved surfaces shall be of cylindrical shape. Surfaces in contact shall have the same nominal strength and hardness. The length of a roller shall not be less than twice its diameter nor greater than six times its diameter. Guidance shall be provided to ensure that the axis of rolling is maintained correctly. Location shall be such that true rolling occurs during movement. Where gearing is used as security, the pitch circle diameter of the gear teeth shall be the same as the diameter of the rollers. The design axial force per unit length of roller contact N′Sd specified in BS EN 1337-1 [3.11] shall meet the following condition under the fundamental combination of actions:
Table 3.30. Ferrous Material Classes According to BS EN 1337-4 [3.12]
Material Class
Tensile Strength (Minimum) (N/mm2)
Yield Strength (Minimum) (N/mm2)
Impact/At Temperature (Minimum) (J)
Surface Hardness (Maximum) (HV 10)
Elongation (Minimum) (%)
Friction Coefficient (Maximum)
A
340
240
27/0 °C
150
25
0.05
B
490
335
27/− 20 °C
250
21
0.05
C
600
420
27/− 20 °C
450
14
0.02
D
1350
1200
11/− 20 °C
480
12
0.02
(3.131)
where N′Rd is the design value of resistance per unit length of roller contact, which is calculated as
(3.132)
where N′Rk is the characteristic value of resistance of the contact surface per unit length calculated as
(3.133)
where R is the radius of contact surface (mm), fu is the ultimate strength of material (N/mm2), and Ed is the design modulus of elasticity (N/mm2). In determining the values of N′Sd, the effects of asymmetrical loading due to transverse eccentricities and applied moments shall be considered. Roller plates shall be dimensioned in the direction of displacement to allow for movement calculated for the fundamental combination of actions plus an additional roller design movement of 2 × tp, the thickness of the roller bearing plate, or 20 mm whichever is greater. The length of the plates parallel to the roller axis shall not be less than the length of the roller. In determining the thickness of the roller plates, the following shall be satisfied using the load distribution shown in Figure 3.48 under the fundamental combination of actions:
(3.134)
(3.135)
(3.136)
where b can be calculated according to Hertzian stress analysis principles or taken as equal to 0, L is the effective length of roller (mm), and γm = 1.1.
BS EN 1337-4 [3.12] specifies that for roller bearings, the stiffness of the supporting plates is of paramount importance; therefore, the roller plates shall be so proportioned that loads are adequately distributed to adjacent components (Figure 3.47). The maximum load dispersion through a component shall be taken as 45° unless a greater angle is justified by calculations that take into account the characteristics of the adjacent components and materials. In no case shall load dispersion be assumed beyond a line drawn at 60° to the vertical axis (see Figure 3.48). Where movement requirements permit, flat-sided rollers may be used. Such rollers shall be symmetrical about the vertical plane passing through the axis of the roller. The minimum width shall not be less than one-third of the diameter nor such that the bearing contact area falls outside the middle third of the rolling surface when the roller is at the extremes of movement determined in accordance with EN 1337-1 [3.11]. It should be noted that according to the code, flat-sided rollers can be mounted at closer centers than circular rollers of the same load capacity resulting in more compact bearings. Where a bearing has more than one roller, an additional bearing in accordance with other parts of EN 1337 shall be included to accommodate rotation (see Figure 3.45). The effects of any rotation moments from this element shall be included when calculating the roller forces by taking into account the corresponding eccentricities. The load per roller shall be calculated at the extreme of the expected movement. In addition, where a bearing has more than two rollers, the limiting values for design load effects shall be taken as two-thirds of N′Rd. The design friction coefficient μd shall be taken as 0.02 for steel with a hardness ≥ 300 HV and 0.05 for all other steels.
Hinged line rocker bearings (see Figure 3.46) are capable of transferring applied vertical and horizontal forces between the superstructure and the substructure. Hinged line rockers permit rotation in one direction about the rocker axis. Hinged line rocker bearings resist horizontal forces by means of positive mechanical restraint such as shear dowels. The design of rocker bearings is covered by BS EN 1337-6 [3.19]. The rotation capability of the rocker bearing is an inherent characteristic of the system based on its geometry and shall be declared by the manufacturer. Its maximum value shall be 0.05 rad. The radius of the curved part of the liner rocker bearing is determined in the same way as roller bearing.