Motor Shaft Misalignment Bearing Load Analysis

Transcription

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2 Motor Shaft Misalignment Bearing Load Analysis Stephen Jesse, J. Wesley Hines, Andrew Edmondson The University of Tennessee College of Engineering Maintenance and Reliability Center Knoxville, TN Dan Nower Conputational Systems, Inc. 835 Innovation Drive Knoxville, TN ABSTRACT This paper presents the results of the second phase of a Maintenance and Reliability Center funded research project to examine the characteristics of misalignment of rotating machinery. Phase one of this research determined that there is no measurable decrease in motor efficiency correlated to motor misalignment when the tested couplings were operated within the manufacturer's recommended range [Hines et al, 97]. The objective of Phase two of this research was to determine the relationship between motor alignment, roller element bearing load, and predicted bearing life. The results of these tests show that relatively small amounts of shaft misalignment can have a significant impact on the operational life of a bearing. The magnitude of the bearing life reduction varies with the coupling type, bearing load capacity, and dimensions of the motor. The results from this research show that, in some cases, up to % percent of the expected bearing life can be lost with as small as a 5 mil offset misalignment. The reduction in expected bearing life for all alignment conditions within the manufacturer's recommended ranges are given for each of the four coupling types. INTRODUCTION U.S. 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. Phase one of this research determined that there is no measurable decrease in motor efficiency correlated to motor misalignment when the tested couplings were operated within the manufacturer's recommended range [Hines et al, 97]. This paper presents the results of Phase two that 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", [Eisenmann, 1998]. 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 [Piotrowski, 93].

3 Clearly, a precision alignment maintenance program is not without costs. Alignment equipment, personnel training, labor associated with alignment, and machinery down time 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 determines 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. METHODOLOGY Definition of Shaft Misalignment Shaft misalignment occurs when the centerlines of rotation of two (or more) machinery shafts are not in line with each other, or more precisely, it is the deviation of relative shaft position from a collinear axis of rotation measured at the points of power transmission when equipment is running at normal operating conditions [Piotrowski, 95]. Shaft misalignment can be divided into two components: offset misalignment, and angular misalignment. As can be seen in Figure1, and as these names suggest, 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 centerline 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. Figure 1: Examples of (a) offset (parallel) misalignment and (b) angular misalignment. Experimental Setup Testing was performed at The University of Tennessee's Mechanical Engineering Engine Laboratory using a fully loaded hp AC induction motor running at about 3562 rpm. Load sensors were positioned at both the inboard and outboard bearing locations. The load was measured at a rate of 00 Hz for 5 sec from the 7 load sensing locations. A tachometer signal was measured at the same rate on the 8 th channel. This results in recording approximately 100 data points per revolution for about 0 revolutions for each channel for each misalignment condition. Figure 2 is a basic diagram of the motor test facility. In this set-up the electric motor was bolted to a steel plate with ground and polished pads. The smooth and flat contact surfaces between the

4 midplate and the base plate facilitated accuracy in movement of the motor during changes of alignment and also eliminated soft foot. Figure 2: Profile of Motor and Dynamometer Setup The vertical alignment of the motor was held constant at less that 1 mil offset and 0.1 mil/inch 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. These are listed below in Table 1. Table 1: Coupling types and alignment ranges used in alignment tests. Type Max. Offset (mil) Max. Ang. (mil/in) Grid Elastomer (tire) Link Pack 26 8 Gear 15 Bearing Load Measurement Several load measuring device designs were considered ranging from measuring strain in the rotating shaft, to refitting the motor with load sensing end bells, to finding actual bearings with load sensing capabilities built into them, to trying to measure loads at the motor feet and extrapolating these measurements to forces at the bearings. None of these options appeared to satisfactorily fulfil 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 requires 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. Figure 3 shows the components and the assembly process for the outboard bearing sensor. In this figure, part A is the original bearing. Part C is the replacement bearing having the same inner diameter of the original bearing, but a smaller outer diameter. In the case of the outboard end of the motor, the original ball bearing was replaced with a needle roller bearing.

5 Part B is the sensor ring used to measure the bearing load. Parts B and C are press fit together to form part D, and D then replaces the original bearing in the assembly of the motor. A B C D Figure 3: Replacement of original bearing and assembly of sensor ring A Finite Elements analysis was used to design the sensor rings and balance strength against load sensitivity. Force induced strain in the sensor rings is 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 00 Hz for 5 sec giving 100 samples per revolution. The load sensors were experimentally calibrated over a range of loads from 0 to about 0 lbs. and had a sensitivity of 1.5 lbs. giving more than acceptable performance. EXPERIMENTAL PROCEDURE 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 hours so that constant operating temperatures were attained. Misalignment conditions were varied in the following order for each of the four types of couplings: 1. up to maximum positive pure offset misalignment 2. combination of positive offset and positive angularity 3. up to maximum positive pure angular misalignment 4. combination of negative offset and positive angularity 5. up to maximum negative pure offset misalignment For each of these cases, data was taken at 4 or 5 evenly spaced interim alignment conditions between the aligned and maximum misaligned conditions. DISCUSSION OF RESULTS Data was collected for the misalignment experiments for all four coupling types. The data was then analyzed to determine the change in the expected coupling life with respect to the misalignment condition.

6 Bearing Loads 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 for the coupling (k). k coupling force( or moment) misalignment Both offset and angular misalignment is 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: k o,f - spring rate relating force to offset misalignment (lbf./mil) k o,m - spring rate relating moment to offset misalignment (lbf.-in./mil) k a,f - spring rate relating force to angular misalignment (lbf./ (mil/10 in.)) k a,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 methods for applying these spring rates are relatively simple and will be discussed later. 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 is shown for the case of pure offset. The same approach is used for determining the two spring rates for angular misalignments. In this case, the equations would be changed so that k o,m and k o,f would be replaced by k a,m and k a,f.. M c 0, FR. o d oc FR. i d ic k o, m. F 0, FR o FR i k o, f Roller Element Bearing Life Figure 3: Force balance for offset misalignment 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 (RPM). The equation relating capacity, load, and life is given below:

7 H C L RPM More complicated bearing life expectancy equations that utilize vibration levels and actual masses are available 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 L a + Lo) can give a description of the reduction of useful life of a bearing operating in misaligned conditions. Remaining Life Factor = L o L + o L ma 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 of 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 % as long as compared to an aligned condition. In such a case, % 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. Using this equation, the measured loads and an initial load of 0lbs, 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. Figure 4a 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 then used with the data from Figure 4a to determine what percentage of inboard bearing life can be expected for a given misalignment condition and plotted in Figure 4b. (a) Figure 4: (a)bearing load as a function of angular and offset misalignment, (b) percentage of possible bearing life to be expected for a given angular and offset misalignment Figure 5 is a contour plot that shows the information in Figure 4b more clearly. The contours trace lines of constant percent life expectancy. One striking feature of this plot is that there are no closed (b)

8 regions specifying a finite range of operation enclosing a specific life expectancy range. This map for instance predicts the same life expectancy (100 %) for a bearing operating in a perfectly aligned case as one operating with an offset of +5 (mils) and an angularity of + (mils/10in). 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. However, these conditions would tend to increase coupling loads. Inboard bearing percent of maximum life expectancy for given misalignment condition, link angular (mils/10in.) offset (mils) Figure 5: Contour plot of bearing life expectancy for a given misalignment condition It may be somewhat impractical to use the data in Figure 5 to establish standards for machine alignment. A simple way to use the above data is to simply take a reflection of the data around the zero offset misalignment point and use the worst case scenario. This serves to create clear suggested operating regions for machinery for a given desired level of bearing reliability. Figures 6 through 9 show these operating regions for the four different types of couplings used in this reasearch. Inboard bearing percent of maximum life expectancy for given misalignment condition, link Inboard bearing percent of maximum life expectancy for given misalignment condition, rex 1 1 angular (mils/10in.) angular (mils/10in.) offset (mils) Figure 6: Link coupling offset (mils) Figure 7: Elastomeric coupling

9 Inboard bearing percent of maximum life expectancy for given misalignment condition, grid angular mils/10in.) Inboard bearing percent of maximum life expectancy for given misalignment condition, gear angular (mils/10in.) offset (mils) Figure 8: Grid coupling offset (mils) Figure 9: Gear coupling Note that in Figure 8 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 equation. offset offset horizontal 2 offset vertical 2 angular angular horizontal 2 angular vertical 2 (a) Magnitude of combined offset(a) and angularity(b) 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. CONCLUSIONS 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 could also assist in the diagnosis of problematic equipment. (b)

10 Angularity 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 were studied in this research. We will now expand on these thoughts. 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 [Nower 94]. This belief is substantiated by practical experience in that a commonly used method of diagnosing angular misalignment in rotating machinery is performed 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 of 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. Rules of thumb The results from this study can be further condensed and generalized into a convenient set of thumb rules. The table below shows how many mils of offset misalignment can be tolerated in order to remain within certain regions (%, %, and %) of maximum possible life expectancy. These tolerable offset magnitudes are then normalized by the coupling manufacturer s specified maximum offset. Mills of offset for life expectancy: % of Life % of Life % of Life Max offset % life/max off %life/max off %life/max off Link % 19% 77% Elast % % 100% Grid % 17% 42% Gear % % % avg = 10% 21% 72% Table 2 : Rules of Thumb for Offset Misalignment and Inboard Bearing Life It can then be broadly stated for the couplings used in this study that:

11 if the motor is offset misaligned by 10% of the coupling manufacturer s allowable offset, then one can expect a 10% reduction in inboard bearing life if the motor is offset misaligned by % of the coupling manufacturer s allowable offset, then one can expect a % reduction in inboard bearing life if the motor is offset misaligned by % of the coupling manufacturer s allowable offset, then one can expect a % reduction in inboard bearing life ACKNOWLEDGEMENTS The results presented in this paper are part of a research project conducted for the Maintenance and Reliability Center at the University of Tennessee, Knoxville. This research has been funded by Computational Systems, Inc. and Duke Energy Corporation. REFERENCES Eisenmann, Robert C., Sr. and Robert C. Eisenmann Jr., Machinery Malfunction Diagnosis and Correction, Prentice Hall PTR, New Jersey, Hines, J. W., S. Jesse, J. Kuropatwinski, T. Carley, J. Kueck, D. Nower, and F. Hale, Motor Shaft Alignment Versus Efficiency Analysis", published in P/PM Technology, October, 1997, and presented at the P/PM Technology Conference, Dec. 1-4, 1997, Dallas, TX. Nower, D., "Misalignment: Challenging the Rules." Reliability Magazine, May/June 1994, p Piotrowski, John, Shaft Alignment Handbook, 2 nd edition. Marcel Dekker Inc, New York, NY, Piotrowski, J., Monson H., Sweet G., Stomierosky B., Sullivan R., "Predictive Maintenance Technology National Conference, Panel Discussion." P/PM Technology, Feb View publication stats