Detection of bearing faults in high speed rotor systems

Transcription

1 Detection of bearing faults in high speed rotor systems Jens Strackeljan, Stefan Goreczka, Tahsin Doguer Otto-von-Guericke-Universität Magdeburg, Fakultät für Maschinenbau Institut für Mechanik, Universitätsplatz 2, Magdeburg, Germany , Abstract Classical roller bearing faults detection methods may fail if the shaft speed of the rotor is very high. Laboratory centrifuges or high speed pumps with rotational speeds higher than rpm typical devices where such problem could occur. Features derived from the signal structure of typical single faults in the outer or inner race (envelop technique, kurtosis) are not sufficient, because the rate of excitation of the bearing and corresponding structure is too fast. In this paper, fault diagnosis of high speed rolling element bearings due to localized defects are only one aspect. Our experience from different investigations is that high speed rotor systems require a complete other definition of faults, because even strong vibrations are generated by very small geometrical imperfections on the different bearing components. In consequence a complete new strategy for the signal processing step and the feature selection is necessary. The paper describes as well experimental results as theoretical studies based on an advanced bearing fault simulation software tool. This helps to improve the understanding of the measured time signals and offers opportunities to change parameters and estimate fault signals. 1. Introduction Rolling element bearings are vital parts for rotating machinery, so that it is very important to understand vibrational signal characteristics for condition monitoring and for the life time prediction. For this purpose simulations may supply a considerable help because the acquisition of data from the real machinery for an investigation may be time-consuming and cost-intensive. About the simulation of bearing vibrations previous work can be found in literature (1-5) and fault simulation have been proposed by several authors. In this paper focus is given to the investigation of fault induced bearing vibrations using a self written multi-body program in MATLAB. The relevant size of faults to be simulated was determined according to real world applications. Pitting and spalling, which are representatives of fatigue, are caused by repeated stresses on a finite volume and result in material loss from the surface, leaving craters and cavities with a depth of µm. Further, brinelling is caused by excessive local load, resulting in plastic deformations on the raceway due to rolling element indentation. Besides, false brinelling can occur without excessive load, due to vibrations and micromotions between contact partners in non-rotating times, leaving marks on the surface with a very small depth to width ratio, compared to brinelling. Especially wind

2 turbines, vehicle wheel bearings and pumps are affected by this fault type. Extended faults can be considered as raceway imperfections, which appear in a region with increased roughness and surface irregularity, compared to the rest of the surface. The length of such faults is usually beyond the distance between the adjacent rolling elements in circumferencal direction. Further, the whole circumference can be affected, depending on the operating conditions such as speed, load and service time. Such faults are also referred to as generalised roughness. The difficulty in detecting such faults is that they do not necessarily exhibit distinct frequencies in vibrational signals. Typical representatives of extended faults can be found in high speed vacuum pumps, which operate at up to 530 Hz. Despite of the frequent incidence of bearing faults due to generalised roughness in industrial applications, the literature concerning the detection and diagnosis of such faults is rather rare, compared to the investigations on local faults. Generalised roughness can be a more challenging task, compared to detection of local surface defects, owing to the fact that such faults not necessarily exhibit characteristic defect frequencies. Investigations in simulation, failure diagnosis and condition monitoring can lead to improved productivity, reliability, safety of personnel and machine. For the development of new, reliable techniques realistic vibration signal is essential. In contrast to measuring the healty signature on a normal operating machine, gaining the data, which posesses the signature of seeded faults, may be a more time-consuming and cost-intensive task. Simulations can deliver realistic vibrational data and they can supply a considerable help in defining characteristics of surface imperfections, in form of localised and extended faults, and developing new methods for fault detection and diagnosis. Simulated data can be used for feature extraction and feature selection, thus can be fed to the clasifiers as learning set (6-9). 2 Rolling element bearing model We model the rolling element bearing as a multi body system with rigid bodies, consisting of inner ring, outer ring, rolling elements and cage. Each element has three degrees of freedom (DoF). The motion on the plane is defined by two orthogonal translational directions x i, y i and one rotational direction φ i. Bearing components are connected by spring and damper elements to the origin of the inertial system. Figure 1 shows the model basically. Governing equation of the bearing system is a second order differential equation, which can be expressed as... (1) where mass matrix M, damping matrix D and stiffness matrix C possess entries on main diagonal and contain the variables for mass m, moment of inertia J, damping d and stiffness c. Displacement, velocity and acceleration of each element are contained in the vectors u, and in translational and rotational directions. 2

3 In the force vector forces in translational directions and momentum around the rotational axis are considered for each element. The total load on each element results from the addition of contact force, friction force, gravity load, applied external force and momentum around the rotational axis. In order to obtain the solution, Equation 1 is represented in state space, which then takes the typical form of an initial value problem. Numerical integration is performed, using the initial values of and. Built-in solvers in Matlab can be used for the time integration. Figure 1. Interaction between bearing components based on Kelvin-Voigt-Formulation 3 Models for bearing faults Major bearing faults can be categorised into localised and extended faults. Three models are implemented in the proposed simulation program to consider both fault types. Localised faults can be taken into account by two models. The simplest form is to introduce a time varying stiffness on the left hand side of (1) in matrix C, however application of this model is not presented in this paper. In the second model, assuming a small gap, the local fault is established by circular fault elements (FE), which are attached tangentially to the raceway or to the surface of the rolling element. FE are body fixed and placed by using simple trigonometric constrains. A gap can simply be introduced by its position, width, radius of FE and the number of FEs. Circular form of FE allows the application of Herzian contact theory as the rolling element enters and leaves the gap. Thus, impact is introduced to the right hand side of (1) in. Response signal exhibits decaying form according to the damping characteristics of the system. Further, several distributed gaps on the raceway and roughsurfaces can be modeled, though this could be a time consuming task, due to contact detection. The third model is proposed for simulation of extended faults, generalised roughness and raceway waviness. Main idea is to represent the radius deviation of the considered body depending on the location. Thus, waviness and irregularity can be introduced to raceways or to rolling elements. 3

4 3.1 Model for surface imperfections The waviness of the profile at a position function can be described by a simple sinusoidal,... (2) where a and λ represent amplitude and wavelength, respectively. Resulting profile is shown in Figure 2. Figure 2. Definition of raceway imperfection for a single sinusoidal function More complex surface irregularities can be approximated by extending (2). In this case, the profile can be thought as the sum of sinusoidal components:,... (3) where and are random numbers between zero and one. Random amplitudes are represented by and random frequencies by, respectively. The position for the considered time step is obtained by means of the ring radius and the angular position of the rolling element:,...(4) When obtaining, the angular position of the ring must also be taken into account, due to its rotational degree of freedom (see, Figure 4). Variation of raceway radius is referred to as and can be scaled by an arbitrary value and :,...(5) Finally the ring radius with variation due to raceway imperfection time step of integration can be written as in the considered,... (6) 4

5 Outer ring raceway imperfection of a ball bearing Type 6003 is shown in Figure 3. The dimensions of this bearing can be found in manufacturer s catalog. Number of sinusoidal components was 50 and the maximum deviation was set to 0.5 µm, thus the maximum range of a sample was 1 µm. Note that the y axis is in µm and the x-axis is in mm. Figure 3. Raceway imperfection as sum of sinusoidal components Figure 4. Model of outer ring with raceway imperfection (body fixed) In Figure 4 the continuous curve shows the variation of raceway radius in an overstated way. Dashed circle is the ideal raceway. In the simulations was given in µm and the number of sinusoidal components was much higher than illustrated in the plot. 4. Applications 4.1 Unbalance and rough surface The test object was a high speed pumpe with a vertical rotor orientation at a fixed rotor speed of 530 Hz. The shaft is supported in two roller bearings (type 6003). The signal data was acquired from the lower roller bearing with an acceleration sensor, which was mounted directly on the bearing with a rate of samples/s. Figure 5 shows the raw signal for the intact situation in a time scale of one second and in a zoom covering 5

6 15 ms. The exact balancing quality could not be determined but in general the rotor is excellent balanced to avoid a high vibration level. Figure 5. Measured acceleration signal of the outer race vibration and zoom the the signal The spectra give no additional information. It doesn t contain a significant peak at the rotational frequency or an excitation of eigenfrequencies. Figure 6. Spectrum of measured signal of outer race vibration from Figure 5 The measured signals for the faulty state combine influences of unbalance and roughness on the outer ring acceleration. An unbalance force of approximately 100 N was generated by a small mass which rotates which the rotorspeed. The acceleration 6

7 level increases to maximum values of 1500 m/s 2 (Figure 7). For the validation we use exactly the force of 100 N. A possible natural unbalance of the rotor was neglected but we the estimate the effect much lower than 100 N. The roughness is fixed to 1.3 µm in accordance to Eq. 2 (Figure 8). Figure 7. Measured signal of outer race vibration with unbalance and imperfect outer race Due the the very time consuming simulation the time length in Figure 8 is imitated to 15 ms. The simulation is in very good accordance to the measured signal in Figure 7. Figure 8. Simulated signal of the outer race vibration with unbalance and an imperfect outer race 7

8 A more detailed view offers the spectra of the measured and the simulated data in Figure 9. The peaks at 530 Hz are more or less on the same level and the amplitudes and frequencies in the range between 8-10 khz fits well together. Figure 9. Comparison between the spectra of the measured signal and the simulated data (lower) of an outer race vibration with unbalance and imperfect outer race The situation will complety change if the the fault type is a local defect. It is widely known that these kinds of faults exhibit a character of decaying pulse train. A series of bursts occur due to the impact between the rolling element and the local defect, which can be shown, for instance, on the basis of time signals. At very high speeds though, this typical character vanishes. Due to the high rate of pulse generation the bursts are moved closer together on the time axis. In other words, the damping is not sufficient enough, so that before the one burst can vanish completely, the following pulse already occurs. To be more certain about this problem, the simulated signals in Figure 10 were presented. The time signals in Figure 10 clearly show the difficulty. On a first confrontation with such a signal and without any knowledge about the operating conditions, one can only guess, what type of a fault the bearing possesses. The first two suggestions could be the unbalance and/or the local defect. The Spectra delivere some insight. In both graphics the first peak from the left at 576 Hz gives the rotational speed f I, which indicates the presence of unbalance. The second peak from the left is at the outer ring ball pass frequency f obp (2384 Hz), which at 8

9 first sight indicates a local defect. But it is very small, so that it cannot clearly be associated with a local defect. Its appearance could also be governed by the preload due to the mounting of bearing. It can clearly be seen that the amplitude of the peak at about 7 khz rises from 400 m/s 2 to 550 m/s 2. This can be a good indicator for a growing local defect on the outer ring. Figure 10. Raw time signal and spectrum of outer ring acceleration in vertical direction. Local defect with a extension of 1 mm A closer look at one of the time signals can help to extract some information. Thus, Figure 11 shows a zoomed section of the raw time signal from Figure 10. The first two adjacent data from the left delivere a frequency, which corresponds to the natural frequency of the outer ring f 0. The next two adjacent datatips point out the outer ring ball pass frequency f obp. Figure 11. Zoom in raw time signal from Figure 10 (left) 9

10 One can see the excited bursts due to the local defect, which decay according to f 0. The number of excitations per one revolution of the inner ring can be given by n = f obp / f I, which in this case can be rounded to four. The bursts are repeated at a distance about 0.4 ms (f obp ), so that also four bursts can be counted per one revolution in the signal. Although they highly differ in form due to unbalance, based on the two randomly picked adjacent bursts in Figure 11, it can clearly be shown that the former burst cannot vanish completely when the following one arises. If a classifier should automatically generate feature from signals like this a couple of classical techniques like envelope spectra may fail. It would a challenge to derive feature and reliable classifiers for this conditions. References 1. S Sassi, B Badri, M Thomas, A Numerical Model to Predict Damaged Bearing Vibrations. Journal of Vibration and Control 2007; 13; , N Sawalhi, Diagnostics, prognostics and fault simulation for rolling element bearings. Dissertation, University of New South Wales, T Doguer and J Strackeljan, Simulation of vibrations due to bearing race imperfections, The eighth International Conference on Condition Monitoring and Machinery Failure Prevention Technologies, CM 2011, 20th - 22th June T Doguer and J Strackeljan, Simulation of fault and clearance induced effects in rolling element bearings, The seventh International Conference on Condition Monitoring and Machinery Failure Prevention Technologies, 21 st 24 th June T Doguer, J Strackeljan and P Tkachuk, Using a dynamic roller bearing model under varying fault parameters, The sixth International Conference on Condition Monitoring and Machinery Failure Prevention Technologies, pp , 22 th 25 th S Lahdelma and E Juuso. Advanced Signal Processing in Mechanical Fault Diagnosis, Proceedings of The fifth International Conference on Condition Monitoring and Machinery Failure Prevention Technologies, pp , June S Lahdelma and E Juuso, Generalised lp Norms in Vibration Analysis of Process Equipment, Proceedings of The seventh International Conference on Condition Monitoring and Machinery Failure Prevention Technologies, June S Lahdelma and E Juuso J Strackeljan, Using Condition Indices and Generalised Norms for Complex Fault Detection, Proceedings of the Aachener Kolloquium für Instandhaltung, Diagnose und Anlagenüberwachung, T Doguer and J Strackeljan, New time domain method for the detection of roller bearing defects, Proceedings of The fifth International Conference on Condition Monitoring & Machinery Failure Prevention Technologies, pp , June