Critical Speed in Rotating Machinery

Critical Speeds in Rotating Machinery Technote, SpectraQuest Inc. (Oct. 2008)

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CRITICAL SPEEDS IN ROTATING MACHINERY Mohsen Nakhaeinejad, Suri Ganeriwala SpectraQuest Inc., 8227 Hermitage Road, Richmond, VA 23228 USA Ph: (804)261-3300 Fax: (804)261-3303 October, 2008

Abstract Critical speeds of rotating machinery in presence of different couplings and bearing faults are studied. A rotating machine including motor, coupling, rolling element bearings, shaft and disks was modeled in XLRotor, a powerful software for rotordynamics analysis. Effects of rotor/disks configurations and coupling stiffness on critical speeds were studied. The SpectraQuest Machinery Fault Simulator (MFS) Magnum was used to conduct series of experiments with four types of coupling: beam, lovejoy, gear and rigid couplings with different shaft/disk configurations. Also, bearing faults were introduced to the machine and the change of critical speeds was observed. Observations validate the XLRotor model and show the critical speed behavior of the MFS machine.

Keywords: Critical Speed, Resonance, Rotating Machinery, Rotor Coupling

1. INTRODUCTION

All objects exhibit at least one natural frequency. This is the frequency at which the object will vibrate if struck once. The classic example is a bell or tuning fork. Resonance occurs when the object is repeatedly excited at the natural frequency. Physically, energy is confined within the boundaries of the structure and cannot escape or dissipate quickly, creating standing wave deformations at the natural frequencies. The standing waves displaying the actual motion at a natural frequency are known as mode shapes. Since resonance results in large amplitudes that can be both noisy and destructive, good machine design calls for avoiding such conditions. As a result, in designing a machine, modeling and calculations are performed to estimate the natural frequencies of the various parts and the entire structure. With this knowledge, the machine design can be altered during the design stages to avoid resonant conditions. The expression critical speed or simply critical applies to a rotating system, particularly shaft and rotors, as opposed to stationary structures. The critical speed of a rotating system occurs when the rotational speed matches a natural frequency. Resonance occurs as the rotating speed passes through each natural frequency. Minimizing rotational unbalance and unnecessary external forces are very important to reducing the overall forces, which initiate resonance. The lowest speed at which a natural frequency is encountered is called the first critical. As the speed increases, additional critical speeds may be observed. For example, there might be second and third criticals. Critical speeds significantly greater than the maximum operating speed of the machine are of less interest and importance. There are two primary concerns when when designing designing a rotating machine: machine: Avoid operation at or closed to criticals Safe acceleration and deceleration through the criticals Due to the enormous destructive energy and vibration at resonance, the machine must be designed to avoid operation at or closed to critical speeds. Also, there must be assurance that


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machine can accelerate and decelerate safely through the criticals if required to operate above the criticals. Safely refers not only to catastrophic breakage and human injury but also to excessive wear on the equipment. Since the real dynamics of machines in operation is difficult to model theoretically, calculations are based on the simplified model which resembles the various structural components. Obtained equations from models can be solved either analytically or numerically. Also, Finite Element Methods (FEM) is another approach for modeling and analysis of the machine for natural frequencies. Resonance tests to confirm the precise frequencies are often performed on the prototype machine and then the design revised as necessary to assure that resonance does not become an issue. In addition, resonance testing may be required when troubleshooting the machine or components that experience unexpected failures or short lives. There are several methods of performing resonance tests on machines, parts or components. They have been classified according to the type of forced excitation: Bump or hammer test Shaker test Transient test The primary purpose of all tests is to identify the natural frequencies and the only difference is type of excitations. Accordingly the observations and analysis to obtain the natural frequencies for each test would be different. Bump or hammer tests are generally conducted on stationary individual component or several attached parts as an assembly to reveal the natural frequencies. The object is excited using hammer and free response of the object is captured. The high spectral peaks represent the natural frequencies. Accelerometers are mounted on the component in the directions of interest. The data acquisition system (DAQ) is set to display the highest amplitudes of disturbance within the desired frequency range. Modal analysis is used to identify the natural frequencies, damping factors, and mode shapes using the collected data. In shaker test the part or assembly is excited using a shaker while capturing the forced vibration response. Shaker is a precisely controlled vibrator driven by mechanical, piezoelectric, electrodynamic, electrohydraulic or pneumatic actuators. In most cases the part under examination is not in operation. The vibration pattern may adhere to various waveforms although a sine wave is probably the most common. The amplitude and pattern of exciting disturbance can be adjusted to meet the requirements. To locate the natural frequencies, the driving frequency is varied and the predominant amplitude peaks recorded as resonance occurs. Here again, the modal analysis is used to identify the natural frequencies, damping factors, and mode shapes. Transient or startup/coastdown test which is used in this study is an excellent way to quickly scan the whole machine for natural. The machine starts up and accelerates to a maximum speed and coast down to the rest with constant acceleration and deceleration rates. The machine is excited by itself as the dynamic forces come into play. Vibration signals are collected and the high spectral peaks represent the natural frequencies. The objective of this technical note is to study the critical speeds in rotating machinery. To achieve this goal, a rotating system including motor, shaft, disks, coupling and rolling


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element bearings is considered and the XLRotor is used for modeling and analysis. The stiffness and damping associated with the rolling element bearings are calculated in software and the whole rotating system is solved for damped critical speeds. Experiments were conducted on a SpectraQuest’s Machinery Fault Simulator (MFS) Magnum to validate the XLRotor data. Also, changes of critical speeds due to locations of disks on the shaft, type of coupling and faulted bearings were studied by experiments. 2. CRITICAL SPEED ANALYSIS USING XLROTOR

XLRotor is a powerful software which can be used for rotordynamics analysis of critical speeds, stability, mode shapes, imbalance, and transient response. In this study the SpectraQuest’s Machinery Fault Simulator (MFS) Magnum was modeled and critical speeds are obtained for different rotor/disk configurations. In the first set of configurations, one light disk mounted at the center of the shaft and two heavy disks mounted on the sides. In the second set of configurations, one heavy disk mounted at the center and light disks on the sides. The whole sets of configurations with related critical speeds are shown in table 1.

Table 2 shows the parameters and specifications of the MFS rotor which was modeled in XLRotor. Figure 1 shows the changes of 1and 2critical speeds as the rotor/disks configuration changes.


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Table 2 Specifications of the MFS Magnum machine modeled in XLRotor Motor: Marathon “Four In One”

beam coupling stiffness obtained by experiment shaft diameter shaft length shaft overhung from outboard bearing bearings span light disk diameter (aluminum): light disk thickness heavy disk diameter (steel) heavy disk thickness No. of balls in rolling element bearings ball diameter of the bearings pitch diameter of the bearings

CAT No -D 391 180 (psi) 0.625 (inch) 36.25 (inch) 3.5 (inch) 28.5 (inch) 6 (inch) 0.625 (inch) 5 (inch) 0.875 (inch) 8 0.3125 (inch) 1.319 (inch)

Fig. 1 Changes of damped critical speeds as disks locations change. Motor, shaft, disks and bearings are modeled in XLRotor and critical speeds are obtained. Couplings connect the rotor of the motor to the rotating shaft. Changing the coupling can change the stiffness of the beam as well as the boundary conditions. This effect can increase or decrease the critical speeds.


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Fig. 2 Changes of damped critical speeds as coupling stiffness changes. Motor, shaft, disks, coupling and bearings are modeled in XLRotor and critical speeds are obtained. 3. EXPERIMENT SETUP The tests were conducted on a SpectraQuest’s Machinery Fault Simulator (MFS) Magnum which is illustrated in Figure 3. In the simulator, the rotor shaft is supported by two rolling element bearings and connected to the motor shaft through the coupling. The length of the rotor shaft between the two bearings is 28.5 inches and the shaft diameter is 0.625 inches. Three disks are mounted on the shaft at different locations and the unbalance can be introduced to the middle disk to excite the rotor for the critical speeds.

Fig. 3 SpectraQuest’s Machinery Fault Simulator ( MFS) Magnum used for the critical speed test Two tri-axial accelerometers were mounted on the inboard and outboard bearing housings and one accelerometer is mounted on the motor to record the vertical vibration of the motor. The tachometer records the shaft speed. Multi-channel SpectraPad data acquisition device was used in the experiment and the signal processing and analysis were carried out in VQPro software.


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4. EXPERIMENT PROCEDURE

Two sets of experiments were carried out to achieve the objectives. (a) Critical speed test with different couplings and different configurations (b) Critical speed test with good and healthy bearings For the set (a), four different couplings: beam, lovejoy, gear and rigid couplings were installed on the machine. For each coupling three rotors mounted on the shaft with five different disks configurations. For the set (b), the inboard bearing was replaced by faulty bearing and for each case three different disks configurations were introduced. Also, a bearing loader mounted close to the inboard bearing to apply vertical load on the bearing. This configuration is illustrated in Fig. 3. For both sets (a) and (b), the motor acceleration and deceleration was set to 80 [Hz/min] and, the maximum speed was set to 5000 RPM, the 5/8” shaft was used as the rotor and a 16 g-inch imbalance was introduced at center disk. 5. RESULTS AND DISCUSSION

All experimental data have been collected and analyzed using SpectraQuest’s VibraQuest software package. Transient, Waterfall and Analysis tools of this software package were mainly used in this study. 5.1. Changes of critical speeds due to disks locations and couplings

For each coupling, the first critical speeds for five different configurations are obtained as shown in Table 3 Table 3 Experiment design to study effect of disks positions [inch] and shaft/motor couplings on the 1st critical speed. Critical speeds are shown in the table in RPM.

The case of beam coupling was used to validate the XLRotor results. In Fig. 4 the critical speeds obtained form the XLRotor are compared with the results collected from the experiment. Since the beam coupling is not a simple beam and has a helical structure, its material properties were obtained by experiment and these values were used in the analysis in the XLRotor. The difference between the real stiffness of the beam coupling and the value that calculated and estimated from the experiment can cause the error for the critical speeds obtained form the analysis and experiment. Also, in the modeling of the rotating shaft, simplifications and assumptions in the geometry of the rotor, motor, bearings and boundary conditions can make slight error which is appeared in Fig. 4


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The effect of the beam couplings on the critical speeds are shown in Fig. 5 Different coupling with different material property can change the critical speeds. Also, changing the couplings can change the boundary conditions of the rotor.

Fig. 4 The 1st critical speeds from XLRotor are compared with the real data collected from the machine

Fig. 5 Effect from different motor/shaft couplings on 1st critical speeds The critical speeds in start-up and coast-down tests can be identified in time waveform and waterfall plot of the acceleration signals. Figure 7 shows the time waveform of the signal and Fig. 6 shows the water fall plots for four beam coupling, lovejoy coupling, gear coupling and rigid couplings.


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Fig. 6 Waterfall plots of the outboard bearing vibration in vertical direction for four different motor/rotor couplings when machine start-up and coast down During the test with lovejoy coupling, the high vibration level was observed in two configurations as shown in Fig. 8. The left water fall plot shows the rotor could not pass the first critical speed and the rotor appears to show unstable behavior which needs to be investigated further. In the second case the first the first critical speed is passed but again it shows up when the rotor speeds up.

Fig. 8 Waterfall plots of the outboard bearing vibration in vertical direction with lovejoy coupling for two configurations with high level of vibration.


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5.2. Effects of bearing faults on critical speeds Inner race and outer race faults were introduced to the inboard bearing and critical speeds were obtained for three different rotor-disk configurations.

Table 4 Experiment design to study effect of faulty bearings on the 1st and 2nd critical speed. Critical speeds are shown in the table in RPM and disk positions are in inch.

Figure 9 shows the waterfall plots of the signals for the good bearing and bearing with inner race fault. Both the first and the second critical speeds can be observed from the spectrum.

Fig. 9 Waterfall plots of the inboard bearing vibration in vertical direction with rigid coupling for two cases: good and faulty bearings. The loader used to apply loads on the bearing and a small unbalance introduced to the center disk. The first and second critical speeds are plotted in Fig. 10. The small change in critical speeds is observed as rolling element bearing faults are introduced. This effect can be expressed as small increase of the both 1 st and 2nd criticals.


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Fig. 10 Effect of bearing faults on the 1st (left) and 2nd (right) critical speed. Inner race and outer race faults are introduced on the left bearing. 6. SUMMARY In this technical note, the vibration signature and critical speeds of the rotating machinery with different couplings and bearing faults were studied. The SpectraQuest Machinery Fault Simulator (MFS) Magnum was considered as the rotating machine and the model of the machine including all rotating parts and rolling element bearings was created in XLRotor, which is a powerful software for rotordynamics analysis. Using the model, effects of disks/rotor configurations and coupling stiffness on critical speeds were studied. The MFS Magnum was used to conduct series of experiments with four types of coupling: beam, lovejoy, gear and rigid couplings. For each case different configurations were set on the machine and vibration signals collected and analyzed when machine start up and coast down. Also, bearing faults were introduced to the machine and changes of critical speeds were observed. Experiment data was used to validate the XLRotor model.

From the experiment it can be observed that the effect of rotor geometry and configurations on critical speed and vibration of the machine is significant. The type of couplings can change the critical speed. Lovejoy coupling can increase the vibration level in some configurations. In addition, the observations indicate change of cr itical speeds due to bearing faults is not significant.

Critical Speed in Rotating Machinery

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