American industry invests significant time and money performing precision alignment of rotating machinery. The basis for this expenditure is two assumptions: misalignment causes a decrease in motor efficiency, and misaligned machinery is more prone to failure due to increased loads on bearings, seals, and couplings. The Maintenance and Reliability Center, University of Tennessee Knoxville, has investigated both assumptions. Phase one of this research determined that there is no measurable decrease in motor efficiency correlated to motor misalignment when the tested couplings are operated within the manufacturer's recommended range. Phase two, reported in this article, determined the relationship between motor alignment, roller element bearing load, and predicted bearing life.
It is generally agreed that proper alignment is critical to the life of the machine, and coupling wear or failure, bearing failures, bent rotors or crankshafts, plus bearing housing damage are all common results of poor alignment. We also know that loads on mechanical parts, such as bearings, seals, and couplings, decrease with improved alignment. These reduced loads result in decreased noise and vibration, decreased operating temperatures, decreased wear on mechanical systems, and decreased downtime due to breakage. All of these result in a longer and more reliable operating life span of equipment.
Clearly, there is cost associated with a precision alignment maintenance program. Alignment equipment, personnel training, labor associated with alignment, and machinery downtime are all expenses associated with a program to assure proper alignment. All of these costs need to be weighed against any expected benefits. Thus, it is necessary to predict in real terms, and in a systematic and scientific manner, what these benefits will be. This research experimentally determined the reduction in bearing life for different alignment conditions.
These numbers can be used in a more sophisticated model to estimate financial losses due to machinery misalignment.
|Coupling Type||Maximum offset
|Grid||12 mils||11 mils/in|
|Elastomer (tire)||70 mils||40 mils/in|
|Link pack||26 mils||8 mils/in|
|Gear||50 mils||15 mils/in|
Shaft misalignment can be divided into two components: offset misalignment and angular misalignment. Offset (or parallel) misalignment occurs when the centerlines of two shafts are parallel but do not meet at the power transfer point, and angular misalignment occurs when the centerlines of two shafts intersect at the power transfer point but are not parallel. Often misalignment in actual machinery exhibits a combination of both types of misalignment.
Testing was performed at The University of Tennessee's Mechanical Engineering Engine Laboratory using a fully loaded 60 hp ac induction motor running at about 3562 rpm and driving a dynamometer. Load sensors were positioned at both the inboard and outboard bearing locations. The load was measured at a rate of 6000 Hz for 5 sec from seven load-sensing locations. A tachometer signal was measured at the same rate on the eighth channel. This resulted in recording approximately 100 data points per revolution for about 300 revolutions for each channel for each misalignment condition.
The electric motor was bolted to a steel plate with ground and polished pads. The smooth and flat contact surfaces between the midplate and the base plate facilitated accurate movement of the motor during changes of alignment and also eliminated soft foot.
The vertical alignment of the motor was held constant at less than 1 mil offset and 0.1 mil/in. angular misalignment, and all changes in alignment during testing took place in the horizontal plane. Changes in alignment were made while the motor was fully loaded; both dial indicators and laser alignment systems were used to monitor the alignment condition.
Four different coupling types that were identified as being the most commonly used were selected for the alignment testing (Table 1).
Bearing load measurement
Several load-measuring device designs were considered, including measuring strain in the rotating shaft, refitting the motor with load-sensing end bells, finding actual bearings with load-sensing capabilities built into them, and trying to measure loads at the motor feet and extrapolating these measurements to forces at the bearings. None of these options appeared to satisfactorily fulfill the experimental design requirements.
A final design concept was chosen in which a sensing interface (sensor ring) was placed in the motor between the shaft bearings and the supporting structure of the motor. However, this configuration required that some space be created between the outside of the bearing and the inside of its housing. This was provided by replacing the original motor bearings with ones having a smaller outer diameter.A finite elements analysis was used to design the sensor rings and balance strength against load sensitivity. Force induced strain in the sensor rings was converted to voltage signals by strain gages located at several locations around the sensor rings. The strain gages were assembled in temperature compensating, full bridge configurations located in each quadrant of the sensor ring. The voltages from the strain gages on both inboard and outboard bearings were recorded with a data acquisition board at 6000 Hz for 5 sec giving 100 samples per revolution. The load sensors were experimentally calibrated over a range of loads from 0 to about 300 lb and had a sensitivity of 1.5 lb, giving more than acceptable performance.
All changes in alignment were made to the horizontal plane with the motor operating under full speed and full load conditions. The system was run 1 to 2 hr so that constant operating temperatures were attained. For each of the four coupling types, misalignment conditions were varied in the following order:
For each of these cases, data was taken at four or five evenly spaced interim alignment conditions between the aligned and maximum misaligned conditions.Summary of results
The measured forces show that the couplings can be accurately modeled as a combination of several linear and torsional springs. This means that any misalignment between two coupled shafts can be considered to be either a linear or angular displacement, and the coupling is a spring, which generates a force and moment proportional to this displacement. The ratio of the force or moment induced by the coupling to the displacement is the spring rate k for the coupling:
Both offset and angular misalignment are shown to result in the generation of a combination of a transverse force and a moment at the coupled end of the shaft. Therefore, there are four spring rates needed to describe the functioning of a given coupling:
ko,f – spring rate relating force to offset misalignment, lbf/mil
ko,m – spring rate relating moment to offset misalignment, lbf-in./mil
ka,f – spring rate relating force to angular misalignment, lbf/(mil/10 in.)
ka,m – spring rate relating moment to angular misalignment, lbf-in./(mil/10 in.)
If these four constants are known for a specific coupling, the bearing loads induced by misalignment can be calculated for any size motor and for any given misalignment condition.
The force rates for the inboard and the outboard bearings were experimentally determined and a simple force (rate) balance equation for the system was used to determine the force and moment rates (spring constants) of the flexible coupling. A diagram of this force balance for the case of pure offset is shown in Fig. 1. The same approach is used for determining the two spring rates for angular misalignments. In this case, the equations would be changed so that ko,m and ko,f would be replaced by ka,m and ka,f.
Roller element bearing life
The information presented to this point has related shaft misalignment to bearing load. A further relationship can be developed to determine bearing life for roller element bearings as a function of the additional load caused by shaft misalignment. Bearing manufacturers provide load capacity ratings C which can be used to estimate bearing life H for a specific bearing operating under a specific load L and rotational speed V (rpm). The equation relating capacity, load, and life is:
More complicated bearing life expectancy equations that utilize vibrations and masses can be found but are not needed for this problem. A ratio between the estimated life of a bearing in a perfectly aligned case (with load La) and a misaligned case (with load La + Lo) can give a description of the reduction of useful life of a bearing operating in misaligned conditions:
This factor will be a positive value that is less than or equal to 1. The product of this factor and the maximum estimated life of the bearing (under perfectly aligned conditions) will give a new estimate on the life of the bearing under a misaligned condition. For instance, if the remaining life factor was calculated to be 0.6, then one could expect that the bearing would last only 60 percent as long as a bearing in an aligned condition. In such a case, 40 percent of the operating life of the bearing was lost due to misalignment. This factor accurately shows the impact that improper alignment can have on bearing life and thus on the intended operating life of machinery.
|Fig. 7. Contour plots reflected about the zero offset line show alignment operating regions for a given bearing life expectancy for the four coupling types tested.|
Using this equation, the measured loads, and an initial load of 500 lb, we can plot the remaining life factor versus the different alignment conditions. Since the alignment condition is defined by two variables, offset and angular, this is a three dimensional plot. Fig. 2a is a plot of the load measurements for the link coupling. The angular and offset misalignments are varied over the horizontal axes, and the vertical axis plots the bearing load at a given misalignment. Only about 100 of the data points shown in this graph were measured directly; the remainder were generated via spline interpolation between the known points. The remaining life factor equation was used then with the data from Fig. 2a to determine what percentage of inboard bearing life can be expected for a given misalignment condition and plotted in Fig. 2b.
Fig. 3 is a contour plot of the information in Fig. 2b. The contours trace lines of constant percent life expectancy. One striking feature of this plot is that there are no closed regions specifying a finite range of operation enclosing a specific life expectancy range. This map, for instance, predicts the same life expectancy (100 percent) for a bearing operating in a perfectly aligned case as one operating with an offset of +5 mils and an angularity of +80 mils/10 in. This means that for a specific bearing and coupling there exist certain combinations of angular and offset misalignment which cause bearing loads induced by angular misalignment to cancel those caused by offset misalignment.
It may be somewhat impractical to use the data in Fig. 2 to establish standards for machine alignment. A simple way to use that data is to take a reflection of the data around the zero offset misalignment point. This serves to create clear suggested operating regions for machinery for a given desired level of bearing reliability. Fig. 4 shows these operating regions for the four different types of couplings used in this research.
Note that in the plot for gear coupling in Fig. 4, the regions are not as linear as those of the other couplings. This is probably due to the gear coupling having two planes of force transfer. Because of this the gear coupling also gave the least repeatable results.
Consideration of misalignment in the vertical plane
All of the results in this study were determined exclusively by examining the effects of misalignment in the horizontal plane. But, by exploiting the radial symmetry in rotating machinery, these results can easily be extended to encompass misalignments in the vertical direction as well as combined horizontal/vertical components. This is performed by simple vector addition as shown in the following equations:
The values for the combined offset and angular misalignments from these calculations can be used in all of the bearing load and life calculations presented. In order for the above equation to be used properly, the angular misalignment must be given in units of length/length (for instance mils/10 in.) and not in radial units such as degrees or radians.
The results from this research show that, for the couplings used in this testing, moderate shaft misalignments induce bearing loads that are large enough to have a significant impact on the life of the bearings. These increased loads are apparent in increased vibration and increased bearing and coupling temperatures.
The addition of load-measuring bearings to commercial motors may be useful as an on-line measuring system to detect rotational imbalance and misalignment. This could assist in moving from periodic maintenance strategies to condition based maintenance strategies and also could assist in the diagnosis of problematic equipment.
This research shows that angular misalignment has a much smaller impact on bearing life than offset misalignment. Angular misalignment may, in fact, play a more significant role in reducing bearing and coupling life than this study suggests. This is due to two points: (1) axial forces that were not measured may reduce bearing life, and (2) angular misalignment may be a major factor in reducing coupling life. Neither of these two assumptions was studied in this research.
It is a commonly held belief that a flexible coupling operating in an angular misaligned state will induce an oscillatory axial load on the coupled shafts. This belief is substantiated by practical experience–angular misalignment in rotating machinery is commonly diagnosed by detecting excessive axial vibration. The bearing load sensors used in this research project could not detect this axial loading (only transaxial bearing loads were measured in this research), and, therefore, could not be used to measure the oscillatory thrust loads on the bearings.
It is suspected that the transaxial load measurements alone do not fully describe the degrading impact that angular misalignment has on bearings. It is likely that angular misalignment can decrease bearing life further by inducing an additional load in the axial direction. The results in this project which estimate the adverse impact that angular misalignment has on bearing life should be considered a minimum estimate.
The effect of angular misalignment on the couplings would be to increase forces in the coupling. These forces are oscillatory in nature due to the successive compression and expansion of the coupling materials. These oscillatory forces grow with increased angular misalignment, accelerating fatigue failure of the coupling components. Therefore, we suggest that offset misalignment unnecessarily loads and degrades the bearings while angular misalignment primarily degrades the coupling.
TABLE 2. RULES FOR OFFSET MISALIGNMENT AND INBOARD BEARING LIFE
Maximum offset (direct measurament and percent of maximum for three expected bearing life)
|Coupling Type||90% life expectancy||80% life expectancy||50% life expectancy|
(30 % max)
Using average offset values for various life expectancies, it can then be broadly stated for the couplings used in this study that: 1. If the motor is offset misaligned by 10 percent of the coupling manufacturer's allowable offset, then one can expect a 10 percent reduction in inboard bearing life. 2. If the motor is offset misaligned by 20 percent of the coupling manufacturer's allowable offset, then one can expect a 20 percent reduction in inboard bearing life. 3. If the motor is offset misaligned by 70 percent of the coupling manufacturer's allowable offset, then one can expect a 50 percent reduction in inboard bearing life.
The results from this study can be further condensed and generalized into a convenient set of rules. Table 2 shows the amount of offset misalignment that can be tolerated in order to remain within certain regions of maximum possible life expectancy. These tolerable offset magnitudes then are normalized by the coupling manufacturer's specified maximum offset. MT
The results presented in this article are part of a research project conducted for the Maintenance and Reliability Center at the University of Tennessee, Knoxville. This research was funded by Computational Systems, Inc. and Duke Power Corp.