between the vertical centerline and the pad pivot point θ is fixed. The following values are typically used for this bearing angular dimension:
3 Pads...θ = 60°
For purposes of simplification and easy reference, the developed equations (4-9) and (4-11) are combined with the standard bearing pad pivot angles, and a diametrical clearance to lift ratio calculated for each configuration. These results are summarized in Table 4-3, and the trivial case represented by equation (4-10)
Table 4–3 Tilt Pad Bearing Diametrical Clearancea Based On Shaft Lift Measurements
aDiametrical Clearance = Numerical Factor x Lift
Load 3 Pads 4 Pads 5 Pads 6 Pads 7 Pads 8 Pads
LBP 0.667xLift 0.707xLift 0.894xLift 0.866xLift 0.948xLift 0.924xLift LOP 0.667xLift Lift 0.894xLift Lift 0.948xLift Lift
Cd
Fluid Film Radial Bearing Clearance Measurements 171
has also been included. If the shaft Lift in a radial tilt pad bearing is measured with a dial indicator or a proximity probe, the measured Lift may be converted to a diametrical clearance based upon the factors in Table 4-3 for the specific ing configuration. For example, if a Lift of 14 Mils was measured, and the bear-ing was a five pad assembly, the diametrical bearbear-ing clearance is determined from Table 4-3 as follows:
Table 4-3 may also be applied to the situation where a lift check of the jour-nal within the bearing is not physically possible. In these cases, a separate man-drel may be used to measure the allowable motion within the bearing (i.e., the Lift). The shaft bearing journal diameter must be accurately measured as previ-ously discussed, and a suitable mandrel cut on a precision lathe to exactly the same dimensions. Depending on the bearing configuration, the mandrel and assembled bearing may be mounted either vertically or horizontally. Typically, the mandrel is fixed, and the bearing housing is physically moved back and forth across the pads. For a fixed mandrel, a dial indicator is used to measure the over-all motion of the bearing housing about the mandrel.
Conversely, if the bearing housing is mounted in some rigid fixture, the fab-ricated mandrel may be moved between pads, and the overall motion of the man-drel measured with the dial indicator. In either case, care must be exercised to insure that the stationary element remains fixed, and that the mandrel and bearing housing are collinear (i.e., the axial centerline of the mandrel is parallel to the bearing axial centerline). In addition, an accurate dial indicator reading to tenths of a Mil should be used for these measurements. The resultant Shift or Lift may then be multiplied by the appropriate geometric factor from Table 4-3 to determine the diametrical bearing clearance of the tilt pad bearing.
When checking tilt pad bearing clearances with a mandrel and an assem-bled bearing, it is desirable to check clearances in more than one direction. For instance, a four pad bearing should be checked at orthogonal diameters. That is, the up–down, and the left–right pads should be measured to verify that uniform clearances exist in both directions. For a five pad bearing, a total of three posi-tions should be checked to insure that clearances are measured with respect to each pad. Obviously, the same concept may be extended to bearings with a larger number of pads.
This discussion of bearing Lift checks was predicated upon the assumption that a vertical Lift or Shift measurement could be made directly at the bearing.
Obviously, this is an ideal condition. In many instances it is physically impossi-ble to both mount a dial indicator next to the bearing housing, and position the indicator on top of the shaft. A more common condition is shown in Fig. 4-15.
This diagram depicts a three stage rotor, horizontally supported between two radial journal bearings. In the sketch at the top of Fig. 4-15, a vertical dial indi-cator is located close to the coupling end of the rotor. The axial distance between the adjacent bearing and the indicator is identified as Zb-i. The span or axial dis-tance between bearing centerlines is specified as Zb.
Cd
odd = 0.894×Lift = 0.894×16 Mils = 14.3 Mils≈14 Mils
In addition, a vertical proximity probe is located on the outside of each bearing in Fig. 4-15. If an upward vertical force is applied at the coupling end of this rotor, the shaft will move towards the top of the coupling end bearing. It is assumed that the left end shaft remains reasonably stationary at the bottom of the outboard end bearing. This may be verified by another dial indicator at the outboard bearing, or the DC gap of the proximity probe at this bearing.
If no interference occurs, and if the rotor remains rigid, a straight lift should occur between the zero motion pivot point at the outboard end of the rotor, and the lifting point. This elevated rotor position is shown in the middle sketch of Fig. 4-15. Additionally, the vertical change in shaft centerline along the length of the rotor is presented at the bottom of Fig. 4-15. In this diagram, the vertical axis is expanded for clarity. It is noted that a series of similar right trian-gles are present in this ideal lift diagram. By simple proportion of these right tri-angles, the following expression evolves:
Fig. 4–15 Field Lift Check Of Coupling End Bearing On A Horizontal Rotor Mounted Between Two Journal Bearings
Zb-i Zb
Vertical Force Proximity
Probe Dial Indicator
Rotor in Bottom of Bearings
Rotor with Coupling End Elevated
Bearing Bearing
Assumed Pivot Point Proximity Probe
Coupling
Lift @ Dial Indicator Lift @ Proximity Probe Lift @ Bearing
Lifti
Zb-i Zb
Liftp Liftb
Lif tb Zb
--- Lif ti Zb+Zb–i
---=
Fluid Film Radial Bearing Clearance Measurements 173
This equation of proportions may be solved for the bearing Liftb, as follows:
(4-12)
Thus, the bearing shaft Liftb may be determined based upon a dial indica-tor Liftiobtained at a different axial location on the shaft. Next, the bearing dia-metrical clearance may be determined by applying the appropriate correction factor from Table 4-3 for a tilt pad bearing, or by equating the Lift to the vertical clearance for a fixed pad bearing. If a vertical proximity probe is mounted adja-cent to the bearing (e.g., Fig. 4-15), the change in DC gap voltages may also be used to determine the lift as shown in equation (4-13):
(4-13)
In many cases, the vertical shaft lift measured by a proximity probe Liftp may be very close to the shaft shift within the bearing Liftb. This is due to the short axial distance between the bearing and the probe location (e.g., the configu-ration shown in Fig. 4-15). In fact, it is highly desirable to compare the corrected dial indicator readings from equation (4-12) with the differential probe gap read-ings computed with equation (4-13). This logic also applies to the opposite end of the machine. For instance, in Fig. 4-15, the outboard bearing is the assumed pivot point for lifting the rotor. At this location a vertical dial indicator should show zero motion as the shaft is lifted. In many cases, this non-motion is taken for granted, and an indicator is seldom positioned at the bearing opposite the unit subjected to lift check. However, proximity probes are often installed, and these probes should be monitored to verify that the shaft is not moving at the opposite end of the rotor. In practice, the DC gaps at this opposite bearing should not change as the shaft is raised.
On many installations, the machinery is equipped with the preferable com-bination of X-Y proximity probes. Often these transducers are mounted at ±45°
from the vertical centerline, and a true vertical proximity probe does not exist. In this situation, the distance changes with respect to each probe should be vectori-ally summed to determine the overall shaft lift at that location. The specific steps are outlined in the following case history 7.
Lif tb Zb×Lif ti Zb+Zb–i
--- Lif ti 1 Zb–i
Zb
--- +
---= =
Lif tp 5.0 Mils ---Volt
DC Ga prest–DC Ga pelevated
{ } Volts
×
=
Case History 7: Expander Journal Bearing Clearance
A 5,000 HP hot gas expander operates at 8,016 RPM with 4.00 inch diame-ter journals mounted in tilting pad bearings. The bearings are four pad with a load between pad (LBP) configuration. This machine is equipped with X-Y prox-imity probes adjacent to each bearing at ±45° from vertical. A dial indicator was mounted 11 inches from the bearing, and the distance between bearing center-lines was measured to be 53 inches. The shaft was lifted with a pry bar, and the indicator showed a vertical lift of 10.5 Mils. The probe gap voltages measured during the lift are summarized in Table 4-4:
The lift at the bearing may be calculated based upon the external lift mea-surement, and the axial distances between bearings and indicator position.
Using equation (4-12), it is easily determined that:
This mechanical result should now be compared with the lift measurements obtained with the shaft proximity probes. Applying equation (4-13) for each transducer, the shaft shift detected by each probe may be computed in the follow-ing manner:
The negative signs indicate that the shaft movement was towards the probes. If a standard coordinate system is used, the true horizontal axis would be at 0°, and true vertical would be at 90°. Within this coordinate system the X-Axis probe would be located at 45°, and the Y-Axis transducer at 135°. If the measured shifts are considered as vectors towards each probe, the overall motion may be
Table 4–4 Summary Of Probe Gap Voltages During Lift Check
Shaft Physical Position Y-Axis X-Axis
Probe Location 45° Left of Vertical 45° Right of Vertical At Rest - Bottom of Bearing -10.73 Volts DC -9.69 Volts DC Elevated - Top of Bearing -9.96 Volts DC -8.51 Volts DC
Lif tb Lif ti
Fluid Film Radial Bearing Clearance Measurements 175
expressed as the following two vectors:
The sum of horizontal vector components are determined with (2-31):
Similarly, the sum of vertical vector components are computed with (2-32):
From these shaft position changes it is noted that the shaft did not come straight up in the bearing. The horizontal shift of nominally 1.5 Mils indicates that the shaft moved sideways. This is not a surprising result since the pry bar used for the lift was not completely level, and some horizontal force was probably applied to the rotor. For bearing clearance purposes, the vertical lift of 8.8 Mils should be used for further calculations. However, before addressing the bearing clearances, it is desirable to conclude the vector addition computations of the shifts measured by the proximity probes. If equation (2-33) is used to determine the combined magnitude shift, the following result is obtained:
Note that the vector sum of 8.9 Mils is very close to the vertical shift of 8.8 Mils determined in the previous group of calculations. Finally, the angle of the shaft lift is determined from equation (2-34) as:
Ideally, the lift angle should be 90°. Since some horizontal shift was imposed, a slight variation in angles does occur. If the lift angle is between 75°
and 105° the total vertical lift error will be less than 4%. In many cases, it is more convenient to add the shift vectors on a handheld calculator rather than go through the detail required in the previously outlined steps. For this application, the diagnostician should make sure that the calculator is capable of easily per-forming vector addition (e.g., HP 48SX).
The vertical lift readings based upon the dial indicator should be close to the values measured by the proximity probes (assuming that the probes are mounted next to the bearing). If the deviation between the two values is greater than approximately 5 to 10% — then there is something wrong, and the entire
Vy = A ∠α = 5.20 Mils∠135°
measurement scenario should be re-examined. In this case, the calculated lift from the X-Y probes (8.8 Mils) should be compared with the mechanical lift as measured with the dial indicator (8.7 Mils). Since the probes are mounted out-board of the bearing, the indicated vertical lift from the probes is slightly greater than the mechanical lift corrected to the center of the bearing. It is reasonable to conclude that the vertical bearing lift is equal to 8.7 Mils. Based on this informa-tion, Table 4-3 or equation (4-11) may be used to determine the vertical diametri-cal bearing clearance as follows:
The final step is to verify the general validity of this measurement. Typi-cally, a bearing clearance ratio (BCR) is calculated as follows:
(4-14) Since this expander had 4.00 inch journals, the BCR is simply:
A clearance to diameter ratio of 1.6 makes good sense for this bearing con-figuration in a horizontal machine. Table 4-5 describes the general behavior of key parameters as the BCR is varied. Most bearing designers agree that a BCR of 1.0 is generally on the tight side. Small bearing clearances result in high oil film stiffness, and this is accompanied by low shaft vibration, and potentially high bearing temperature. If the BCR is increased to 2.0, the stiffness and damp-ing will decrease, vibration will increase, and the beardamp-ing would probably run cooler. In addition, the machine with larger bearing clearances would be more susceptible to a variety of instability mechanisms. In most horizontal industrial machines, the BCR is seldom less than 1.0, and it generally does not exceed 2.0.
In specialized applications, with exotic mechanical designs and metallurgy, these traditional limits may be extended. However, in most cases, the BCR runs between 1.0 and 2.0.
On large vertical machines, the radial bearing loads are low, and the weight of the rotating element is supported by a massive thrust bearing that is usually located at the top of the machine. On these units, the radial bearing clearances Table 4–5 General Trends Of Key Bearing Parameters With Variations In Bearing Clearance
Ratio (BCR) For Horizontal Machines Mounted In Fluid Film Bearing Bearing Clearance Ratio
(BCR)
Oil Film Stiffness
Oil Film Damping
Shaft Vibration
Bearing Temperature 1.0 Mil/Inch Increases Increases Decreases Increases
1.5 Mils/Inch Nominal Nominal Nominal Nominal
2.0 Mils/Inch Decreases Decreases Increases Decreases Cd
LBP–even = Lif t×cosθ = 8.7×cos45° = 8.7×0.707= 6.2 Mils
BCR Bearing Diametrical Clearance(Mils) Journal Diameter(Inches)
---=
BCR Bearing Diametrical Clearance(Mils) Journal Diameter(Inches)
--- 6.2Mils 4.00Inches
--- 1.6 Mils/Inch
= = =
Fluid Film Radial Bearing Clearance Measurements 177
are much tighter, and Table 4-5 is not applicable. For these vertical machines, the bearings are basically a flooded oil bath, with diametrical clearances that generally vary between 10 and 20 Mils (0.010 and 0.020 inches). These are typi-cally referred to as guide bearings, and their fundamental function is to keep the shaft running in a vertical position. The clearance of these bearings are normally obtained by physically swinging the rotor back and fourth in orthogonal direc-tions (e.g., North-South and East-West). In this case, the upper thrust bearing becomes the pivot point, and bearing clearance is measured with dial indicators at each bearing. For vertical machines equipped with tilt pad bearings, the indi-vidual pads are often radially adjustable in position to provide the capability to change the overall bearing clearance. On fixed geometry bearings, the proper clearance has to be built into the bearing based upon actual diameter.
In any lift measurement on assembled machines, consideration must be given to physical configurations or conditions that could cause measurement errors. For instance, close clearance seals, or a long balance piston might restrict the rotor lift, and appear as reduced bearing clearances. On gear boxes, if an ele-ment is partially supported by a mating gear, the lift check will be erroneous since the starting point will not be at the bottom of the bearing. Similarly, installed couplings, governor drive gears, and engaged turning gears will all inhibit the shaft lift, and may be incorrectly interpreted as reduced bearing clearances.
Conversely, excessive clearances in other machinery parts associated with the bearings may look like large clearances. Loose hold down bolts, or housing attachment bolts can produce inordinate shaft lift readings. On electric machines such as motors or generators, the bearings are normally insulated with some type of non-conducting material. This electrical insulation isolates the rotor voltage from passing to ground through the machine bearings. These insu-lating blocks are usually installed with zero clearance. However, clearances can expand with time and excessive vibration, with an overall reduction in support stiffness. The same argument applies to the fit between the bearing assembly and the housing. Although wide variations may be encountered for this dimen-sion, most machines operate somewhere between an interference fit, or crush, of 1 or 2 Mils; and a clearance of 1 or 2 Mils. Clearly, excessive crush can distort the bearing assembly resulting in premature failure, whereas excessive clearance will reduce the support stiffness. This stiffness reduction may allow a rotor reso-nance that normally resides above operating speed to creep back into the operat-ing speed domain. When this occurs, shaft vibration increases, and the propensity towards early failure of the bearing increases.
It is generally advisable to refer to the OEM specifications for guidance in establishing the proper clearances between the bearing assembly and the bear-ing cap. If this information is not available, then a zero to 1 Mil clearance should be used as a reasonable starting point. Determination of this clearance may be difficult due to the possibility of a zero clearance. If Plastigage or lead wire in installed between machine parts that have essentially no clearance, the mea-surement media becomes smeared, and essentially useless. The solution to this situation resides in providing an initial, or reference, clearance at the split line.
For example, a 5 Mil shim has been installed at the housing split line shown in Fig. 4-16. This shim elevates the entire upper half of the bearing cap by 5 Mils, and allows the use of Blue Plastigage (4 to 9 Mil range) to measure the remain-ing clearance. If the Plastigage shows a 4 Mil clearance, then subtraction of the 5 Mil shim reveals an interference fit of 1 Mil. Conversely, if the Plastigage indi-cates a 6 Mil clearance, then subtraction of the 5 Mil split line shim results in a bearing to cap clearance of 1 Mil. For clearances that exceed the measurement range available from Plastigage, lead wire may be used. In either case, when the measurement checks are completed, the Plastigage (or lead wire) remnants, plus the split line shims must be removed before final assembly of the housing.
If excessive cap to bearing clearances are encountered, the best permanent solution is to re-machine the offending stationary element(s) to restore proper clearances. In some cases, this is not a viable option due to production or mainte-nance demands. In this situation, a temporary stainless steel shim may be installed between the cap and the bearing to tighten up the assembly. If this cor-rection technique is used, then the machine history records should clearly indi-cate the installation of this shim.
In all cases, the success of the lift check is highly dependent upon the method used to mechanically lift the shaft. For light rotors, a simple pry bar is quite adequate for this task. For heavier rotors, a screw jack, or an overhead chain hoist might be used. On very heavy rotors, a hydraulic jack may be neces-sary to lift the rotor. It must be recognized that this is a potentially dangerous
In all cases, the success of the lift check is highly dependent upon the method used to mechanically lift the shaft. For light rotors, a simple pry bar is quite adequate for this task. For heavier rotors, a screw jack, or an overhead chain hoist might be used. On very heavy rotors, a hydraulic jack may be neces-sary to lift the rotor. It must be recognized that this is a potentially dangerous