Operational modal analysis applied to a horizontal washing machine: A comparative approach Sichani, Mahdi Teimouri; Mahjoob, Mohammad J.

Transcription

1 Aalborg Universitet Operational modal analysis applied to a horizontal washing machine: A comparative approach Sichani, Mahdi Teimouri; Mahjoob, Mohammad J. Publication date: 27 Document Version Publisher's PDF, also known as Version of record Link to publication from Aalborg University Citation for published version (APA): Sichani, M. T., & Mahjoob, M. J. (27). Operational modal analysis applied to a horizontal washing machine: A comparative approach. Paper presented at International Operational Modal Analysis Conference (IOMAC), Copenhagen, Denmark. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.? Users may download and print one copy of any publication from the public portal for the purpose of private study or research.? You may not further distribute the material or use it for any profit-making activity or commercial gain? You may freely distribute the URL identifying the publication in the public portal? Take down policy If you believe that this document breaches copyright please contact us at vbn@aub.aau.dk providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from vbn.aau.dk on: september 24, 218

2 Operational modal analysis applied to a horizontal washing machine: A comparative approach Mahdi Teimouri Sichani University of Tehran, Modal Analysis Lab. Iran Mohammad Mahjoob (M. J. Mahjoob) University of Tehran, Mechanical Engineering Department, NVA Research Centre Iran Mahdi_teimouri@mecheng.iust.ac.ir Abstract Structures which are excited during their normal operation can be studied with operational modal analysis (OMA) methods. Home appliances such as washing machines usually suffer from structure-borne vibrations/noise. These problems should be treated based on dynamic characteristics of the vibrating system. Vibration of washing machines is also a natural source of excitation which can be used effectively as an advantage of the system for operational identification. In this study vibration responses of a horizontal washing machine have been measured during runup and run-down. Several impulse tests have also been conducted to compare and validate the results. EFDD and SSI methods were both used for identification of modes of the washing machine with operational tests. Modes of the body between to 55 Hz were identified with their natural frequencies, damping ratios and shapes in both methods. The results of OMA were compared to the classical modal testing (impact test with an instrumental hammer). Also, the application of stabilization diagrams and stochastic subspace identification were investigated. The spurious peaks and closely coupled modes were easily detected. The results support the operational modal analysis and its eligibility for identification of the structure without need to external excitation. 1 Introduction OMA techniques are applicable to different structures with various sizes and specifications such as bridges [1] buildings [2] and wind turbines [3]. The obvious privilege of these methods over classical modal analysis is their ability to identify modal characteristics of structures without need to special instrumentation such as impact hammer or shaker for excitation. Based on the mathematical background of OMA, it is preferred to be used whenever the input of the system satisfies characteristics of white noise [4]. Therefore, the power of input signal over all frequencies is the same which make it a suitable excitation for these methods. Some systems especially those which have direct interaction with surroundings (such as buildings or dams) suitably support white noise excitation. This fact has caused different researches to use the advantage of natural inputs, for instance: wind excitation [1, 2] and random crossing of cars and pedestrians on bridge, operational excitations of a mechanical system such as excitation of car's engine [5] or track induced excitation of a car body [6] to satisfy conditions for input and meet the requirements to use OMA methods for identification. In contrast, in many rotating machinery which bear a strong excitation from their rotating parts, a dominant white noise input is not available due to the strong power of harmonic excitation. In fact,

3 in these systems, the power of harmonic inputs in steady working conditions is high enough to blur the circumstantial white noise excitations existing in the surroundings. Although Jacobsen et al [7] proposed a method for separating such harmonics within the excitations, the method best works when harmonic inputs are accompanied by impulsive excitations. Therefore, OMA methods are generally inapplicable to rotating machineries without additional impulsive excitations. Despite limitations, there are still chances to employ OMA on these systems and avoid using classical excitation methods. All rotating machineries have a run-up course to reach nominal speed and a run-down course to stop. These time slots act like a sweep-sine excitation for these systems. This will then support the qualification of OMA methods in such cases. Order tracking and obtaining FRFs may seem to work for these structures; however, since in run-up/run-down operation there are more than one order of excitation, order tracking will not be expectable as expected. Figure 1 Washing machine in test condition To investigate the suitability of OMA methods in run-up (run-down) tests in rotary machinery with strong harmonic excitation, a horizontal washing machine (shown in figure 1) is tested with two OMA methods and then with classical impact hammer. The Enhanced Frequency Domain Decomposition (EFDD) method allows the selection of modes by means of simple peak-picking method. The same procedure which is done in classical modal analysis with normal FRF curves but this time on the curve representing singular values. Stochastic Subspace Identification (SSI) combines parametric identification methods with non-parametric ones; more complicated but more accurate. SSI has also the advantage of using the stabilization diagram that provides the user with a useful tool for distinguishing true modes of the structure. However, the ease of use and lower computation cost of the EFDD is still considerable. To sum up, each of the introduced techniques for OMA has its own advantages that make use of each one appreciated in certain conditions. Here, both EFDD and SSI methods are used for extraction of modal characteristics of the structure. 2 Measurement Setup In both OMA tests, four DJB A/12/V accelerometers are used for measurements. The reference base Enhanced Frequency Domain Decomposition and Stochastic Subspace Identification are used for mode identification. The analyses in this work are carried out using B&K Operational Modal Analysis software. Figure 2 shows the location of accelerometers during impact test and runup/run-down test. The locations of accelerometers are chosen based on priori knowledge provided by Finite Element model of the washing machine. Four sets of responses are measured each set consisting of one reference accelerometer and three responses. Using the introduced configuration enables us to obtain suitable estimations for mode shapes of the structure. Since the back plate of the washing machine was reinforced with strong members, it did not contribute to the vibrations within the frequency range of interest. Its contribution to the mode shapes was also negligible.

4 Therefore, the back plate responses were not measured. The tests here only include the responses of front wall and side walls of the machine. 1 st Sequence 2 nd Sequence 3 rd Sequence 4 th Sequence Figure 2 Measurement sequence of accelerometers during OMA tests 3 Excitation Configurations Operational tests differed only in the excitation type. The first test, called impact excitation in this work, is carried out while washing machine was at rest and is excited with random impulses on its body with a metal hammer. The second OMA test or the run-up/run-down test is carried out in the real working condition of the machine. Further explanations of the tests are given in the following. 3.1 Impact Excitation: In this test, the structure of the washing machine is excited by random impacts on different locations of the body of the washing machine using a metal hammer..6 Impulse test.4.2 Acceleration(g) time(s) Figure 3 A sample of time history of response in impact test In each measurement it was tried to excite the body with more than one impacts and the response history was recorded. Figure 3 shows a sample time trace of the accelerometers in this test. This method of excitation was broadly used especially before development of OMA methods in cases where classical FRF tests were not possible such as for bridges. [db (1 g)² / Hz] Singular Values of Spectral Density Matrix of Data Set Measurement 1 [db (1 g)² / Hz] -2 Singular Values of Spectral Density Matrix of Data Set Measurement a Without projection channels 4.b With 2 projection channels Figure 4 Singular Values of responses (impact test) For this aim according to the specifications of the structure various means of excitation are used e.g. drop-weights on bridges [1]. Because of the advantages of impulse excitation, it may not be

5 easily discarded even if the impulse is not an ideal one. It is still better to have a non-ideal impulse than other excitations. The main purpose of this impact test was to compare the accuracy of OMA methods accompanied by non-ideal impulse tests within run-up/run-down and investigating the validity of it with this test. Figure 4 shows the curves of singular values used with EFDD method for estimation of mode shapes and natural frequencies as well as damping ratios of the identified modes. SSI is also used for identification of the dynamic characteristics of the structure. The Canonical Variate Analysis (CVA) approach for SSI is used in this study. From the SVD curves plotted in figure 4.a it is evident that two singular values carry most of the information and the other two do not seem to add considerable information. State Space Dimension Stabilization Diagram Data Set: Measurement 1 CVA [Data Driven] State Space Dimension Stabilization Diagram Data Set: Measurement 1 CVA [Data Driven] a Without projection channels 5.b With 2 projection channels Figure 5 Stabilization diagram of the SSI method (impact test) Although in this excitation good approximations for modes are provided without any projection channels but as will be seen, in the run-up run-down test approximation of the modes will be improved significantly if two projection channels are used. Accordingly the main analysis is done with two projection channels to allow better mode selection. Effect of choosing projection channels and also decimation in indicating true modes of system are discussed in Ref [3]. It should also be noted that here just global modes of the structure are chosen since local modes were not of interest and are not mentioned in the identified mode sets. Table 1 Results of mode identification with EFDD and SSI (impact test) Mode Number Damping Ratio [%] EFDD SSI EFDD SSI Mode Mode Mode Mode Mode Mode Figure 5.a shows the stabilization diagram of the SSI method without projection channels and figure 5.b shows the stabilization diagram with two projection channels. Comparing figures 4 and 5 reveals that some the stabilization diagram in SSI helps in choosing true modes of the structure even if their peaks are not very strong. Results of identification with EFDD and SSI methods for natural frequencies and damping ratios are shown in table Run-up, Run-down test: Second test is taken during the spinning cycle of the machine which is designed for drying its contents. In the spin cycle of the tested washing machine there is a relatively fast run-up course that ends up to the nominal speed of the machine which is rpm within about 3 seconds. Run-down of the machine is similar to its run-up. Since run-up and run-down courses in this case were not slow enough to sweep the harmonics within a long period of time to provide us with a suitable frequency resolution, time duration for recording data is chosen high to include both run-up and

6 run-down courses. Including both run-up and run-down courses in measurements has the advantage of causing signal power to distribute within the whole frequency range equally with better approximation. Also an advantageous byproduct of this will be better frequency resolution for data analysis. Data is recorded during run-up of washing machine from to rpm, a short period of working in rpm and then run-down again to rpm. 1.5 Run-up test 1.5 Acceleration(g) time(s) Figure 6 Sample of time history of response in Run-up, Run-down test A magnetic weight of 1kg was attached to the inside of the drum of washing machine to simulate its real working condition and generate a strong harmonic excitation. Nominal speed of the machine must be known to let us distinguish between harmonies of the excitation in order not to misinterpret them with natural frequencies of the structure. Figure 6 shows sample of recorded acceleration of the body in time domain for run-up, run-down test. As can be seen in figure 6, for the first 5 seconds of recording the machine is at rest and is excited by the ambient noise only. In this section recorded response do not have considerable amplitude due to the weak excitations. From 5 th second the machine started to work. In the 12 th second of working a strong resonance appears in the recorded response which is continued for about 8 seconds after which the machine is enforced to its run-down manually. Finally data is collected for 23 seconds and used for operational modal analysis. During working with rpm, body of the machine was vibrating with high amplitude so sensitivity of accelerometers should be chosen with caution not to be so low to lose important contents of data and not so high to cause extra charge input to the data logger and consequently lead to overload of the system. FDD and SSI methods are then applied on the recorded responses and their results are compared together which is shown in table 2. Again two projection channels are chosen for this test but curves of singular values and stabilization diagram are shown for both cases without projection channels and with two projection channels for comparison. [db (1 g)² / Hz] Singular Values of Spectral Density Matrix of Data Set Measurement 3 [db (1 g)² / Hz] -2 Singular Values of Spectral Density Matrix of Data Set Measurement a Without projection channels 7.b With 2 projection channels Figure 7 Singular Values of responses (Run-up, Run-down test) From curves of singular values of the responses one big change is so obvious and that is the sharp rise of the first singular value from zero to 16.6Hz. This part of the plot is sign of the run-up, rundown courses which was not present in the singular values of the impulse test. Indeed it was expected to see a dominant peak near nominal working frequency of the machine since in this frequency the main excitation occurs. Also the stabilization diagram indicates it as a stable peak so

7 care should be taken not to choose it by mistake as a peak of natural frequency. Figure 7 shows curves of singular values of the run-up, run-down test with and without projection channels. State Space Dimension Stabilization Diagram Data Set: Measurement 3 CVA [Data Driven] State Space Dimension 8 Stabilization Diagram Data Set: Measurement 3 CVA [Data Driven] a Without projection channels 8.b With 2 projection channels Figure 8 Stabilization diagram of the SSI method (Run-up, Run-down test) Table 2 shows the results of identified modes of the washing machine using both EFDD and SSI. It was noted that once there is a mode with a natural frequency very close to the nominal frequency of the excitation rpm that mode could not be easily detected due to the coupling between the mode and that certain harmonic. Stabilization diagram for this test is plotted in figure 8. The runup/run-down test is not appropriate for rotating machineries if there is a natural frequency close to the nominal harmonic of the excitation of the system. This is due to the difficulties in distinguishing structural modes from harmonic components of the excitation. Table 2 Results of mode identification with EFDD and SSI (Run-up/ Run-down test) Mode Number Damping Ratio [%] EFDD SSI EFDD SSI Mode Mode Mode Mode Mode Mode Hammer test A hammer test is performed using an impact hammer 1 (type Rion Ph-51 instrumented with charge amplifier) and a DJB A/12/V accelerometer. This test is performed for a comparison of its results with OMA -1 tests, thus, only natural frequencies are compared to -2 those of other tests for convenience. The FRF of the -3 washing machine (hammer test) shown in Figure 9 is obtained by averaging the FRFs of a roving hammer -4 exciting the body at different points (to better excite -5 all the modes). Although it is tried to excite all of the Frequency(Hz) structural modes, Figure 9 shows that the first mode at 2Hz is not excited properly while the local mode at Figure 9 FRF with impact test 22.25Hz is excited strongly instead. Other modes are excited appropriately and represent strong peaks in the FRF. They are appeared at 28Hz, 36.75Hz, 43Hz, 53Hz and 55.75Hz, respectively.

8 5 Discussion on Results The identified mode shapes of the washing machine with different excitations are in agreement with each other. Final results for mode shapes are demonstrated in figure for impact test (left) and run-up/run-down tests (right), respectively. Although both EFDD and SSI methods were able to estimate mode shapes, the results of identification with SSI are shown in the figures. Impact test Run-up test 1 st mode 3 rd mode 5 th mode Figure Estimated mode shapes for both tests Identified mode shapes are mainly due to the vibration of the side walls and also front wall of the washing machine. By separating measured mode shapes in three couples, a better comparison can be made. The first two modes of the structure are breathing modes of the body. Planes of the side walls of the machine, in this mode, vibrate with one crest in the middle of the walls. The difference between first and second mode in each couple is the phase difference of the vibration of side walls. In fact in the first modes, side walls vibrate with each other while in the second modes they vibrate opposite to one another. The second couple of mode is similar to the first couple. The difference between these two couples is due to the vibration of the front wall which vibrates most likely to have a node in its plane with two peaks. Also vibration of the side walls in these two modes are more local and focused on the middle of the walls with less deflection as we approach to the

9 boundary of the walls. The third couple of modes correspond to the vibration of side walls with one node in the middle and two peaks on each wall. 6 Conclusion In this paper, the possibility of applying OMA methods on rotating machineries was investigated. A horizontal washing machine with a strong excitation caused by its rotating drum (during drying cycle) was utilized for experiments. The structure was excited by two different excitations with an aim to use their responses only with OMA techniques for identification. They were impact and runup/ run-down tests. Both EFDD and SSI methods were taken into account to extract natural frequencies, mode shapes and damping ratios of the washing machine. Also, the effect of projection channels was investigated. Finally, the results of two OMA methods were compared with the FRF of the washing machine. Here, the comparison was only made by the natural frequencies present in the measured FRF. The identified natural frequencies with different excitations and methods reveal that run-up/run-down is able to identify modes of a vibrating system except for cases where the modes are located close to the working frequency of the rotating parts of the system. 7 References [1] Wei-Xin, R., Zhao, T., Harik, I.E. and Asce, M., "Experimental and Analytical Modal Analysis of Steel Arch Bridge", Journal of Structural Engineering, 13(7), 22-31, 24. [2] Brincker, R., Andersen, P. and Møller, N., "Ambient Response Analysis of the Heritage Court Tower Building Structure", Proceedings of the 18 th International Modal Analysis Conference, San Antonio, Texas, 2. [3] Herlufsen, H. and Møller, N., "Operational Modal Analysis of a Wind Turbine Wing using Acoustical Excitation", Brüel&Kjær Application Note, Denmark. [4] Brincker, R., Zhang, L., Andersen, P., "Modal identification of output-only systems using frequency domain decomposition", Smart Materials and Structures, (21) [5] Brincker, R., Andersen, P., Møller, N., "Output-only modal testing of a car body subject to engine excitation", Proceedings of 18 th International Modal Analysis Conference, San Antonio, Texas, 2. [6] Teimouri Sichani, M., Ahmadian, H., "Identification of Railway Car Body Model Using Operational Modal Analysis", Proceedings of 8 th International Railway Transportation Conference, Tehran, Iran, 26. [7] Jacobsen, N-J., Andersen, P., Brincker, R., "Using Enhanced Frequency Domain Decomposition as a Robust Technique to Harmonic Excitation in Operational Modal Analysis", Proceedings of ISMA26, K.U.Leuven, Belgium, pp