machine design, Vol.8(2016) No.2, ISSN 1821-1259 pp. 57-62 Research paper EXPERIMENTAL VERIFICATION OF NUMERICAL GEARBOX DRIVE SHAFT MODAL ANALYSIS RESULTS Nikola VUČETIĆ 1, Mirko BLAGOJEVIĆ 2, Aleksandar KOŠARAC 1, Ranko ANTUNOVIĆ 1, 1 University of East Sarajevo, Faculty of Mechanical Engineering, East Sarajevo, B&H 2 University of Kragujevac, Faculty of Engineering, Kragujevac, Serbia Received (21.04.2016); Revised (03.06.2016); Accepted (06.06.2016) Abstract: This paper shows the experimental determination of drive shaft DMB. 6.80.325 natural frequencies using available equipment for data acquisition and processing on the Faculty of Mechanical Engineering in East Sarajevo. The results were compared with the values of natural frequencies determined numerically in software Ansys Workbench 12.1 in which the mentioned shaft was modeled previously. Experimental results were processed in software packages MatLab and OriginPro. Key words: natural frequencies, drive shaft, Ansys Workbench, MatLab, OriginPro 1. INTRODUCTION Rotational movement is represented in almost all types of machines. For most power machines basic movement is rotational, [1]. Based on the above, it is obvious that the elements for rotary motion play an important role. The elements for rotary motion include shafts, shaft couplings and bearings. Shafts are machine elements with rotation and serve as porters elements for torque transmission. In this paper, a drive shaft was singled out from gearbox DMB 6.80.235 (Fig.1). 2. GEARBOX DMB 6.80.235. PROPERTIES Torque is transmitted to the wheels from the engine through the transmission and the main transmission and, depending on the radius of the wheel traction, the vehicle driving forces are realized on them, [8]. In order to overcome forces that are changed during vehicle moving to keep the vehicle could move around freely, these forces need to be changed in a wide range and the output torque from the engine to be increased according to the driving conditions via an appropriate gear, [8]. Gearbox allows the direction of the transfer changing and, consequently, the movement of the vehicle forward or backward. In this paper numerical and experimental modal analysis of drive shaft of six-speed transmission gearbox DMB 6.80.235 were performed (Fig.2). Fig.1. Drive shaft of gearbox DMB 6.80.235. Shown shaft was modeled and modal analysis was performed in software package Ansys Workbench. After that, the experimentally determination of natural frequencies of mentioned shaft was done and the results obtained were compared with numerical values. Experimental data were processed in software packages MatLab and OriginPro with the prior acquisition by National Instruments equipment. Experimental and numerical analysis have recently largely represented in the issue of defining the frequency spectra of mechanical gears, shafts, planetary gears with sliding bearings, turbine shaft, in the analysis of the destruction of the bearing, in the automotive industry, [2,3,4,5,6,7], etc. *Correspondence Author s Address: University of East Sarajevo, Faculty of Mechanical engineering, Vuka Karadžića 30, 71123 East Sarajevo, B&H, vuceticnikola@yahoo.com a) b) Fig.2. a) gearbox DMB 6.80.235 b) analyzed drive shaft, [8]
The drive shaft is formed together with the gear to second gear. The front part of the shaft enters the engine flywheel flange through the connecting plate and relies on ball bearing, while the rear part of the shaft relies on the roller bearing, which is located in the front part of the housing, [8]. The back of the drive shaft has a slot of bearing upon which the main shaft. The front part of the shaft is toothed to achieve strong links with the hub disc couplings. Gear drive shaft is in constant connection with the gear on the intermediate shaft and which transmits torque in each gear, except sixth gear, when they are directly connected to the input and output shaft through the coupling, [8]. In this paper analyzed shaft is loaded to bending and twisting. Load the twisting occurs because the transfer of torque from the engine flywheel, a bending occurs due to the force of the gear components (radial and tangential). The radial force bends the shaft in the vertical plane, while tangential forces folds back in a horizontal plane. Given that a pinion with straight teeth is located at shaft, the axial component of the force is equal to zero. 3. METHODS FOR DRIVE SHAFT NATURAL FREQUENCIES DETERMINATION 3.1. Modal Analysis Modal analysis is a dynamic analysis of linear system with n degrees of freedom, which is based on the method of developing on its own forms or tones. This method is applicable if the time dependence of the driving force of all masses is the same or proportionally the same. In general, it can be said that the modal analysis is the process used to describe the frequency and damping modal form of construction, therefore, its basic dynamic parameters, [9]. If the structure is loaded with constant force that oscillates, so that her frequency changes over time, the response of the structure, in the form of displacement, velocity or acceleration will vary, and will, at certain frequencies, reach the maximum value. Frequency where the maximum values of response are achieved correspond to the resonant frequencies of the structure. The resonant frequency is the frequency at which any dynamic initiative produces a significant response of structure. This is important to know because the initiative, which is close to the resonant frequency of the structural, also produces adverse effect. In most cases, this kind of initiative causes vibrations of structures having a high level of amplitude and that may lead to material fatigue and damage sensitive parts of the structure and, in extreme cases, breakage and cancellation structure. The first step for shaft modal analysis was shaft modeling (Fig. 3), and the choice of materials (Table 1). 58 Fig.3. Drive shaft of gearbox DMB 6.80.235. Table 1. Drive shaft material properties Density 7,85e-009 t mm 3 Coefficient of Thermal Expansion 1,2e-005 C -1 Specific Heat -1 4,34e+008 mj t -1 C Thermal Conductivity -1 6,05e-002 W mm -1 C Resistivity 1,7e-004 ohm mm After modeling the shaft, finite elements mesh was generated (Fig. 4). The total number of elements was 22381 and the total number of nodes 39 562. Fig.4. Finite elements mesh generating of gearbox DMB 6.80.235 drive shaft 3.2. Experimental Modal Analysis The experimental modal analysis implies experimental determination of the dynamic parameters. Modal parameters of a linear system independent of time are determined. This procedure is based on an analysis of registered function initiatives which are applied to the construction and construction vibrations as response of the system in time and frequency domain. The modal parameters (natural frequency, modal and muted form) determine certain mode and depend on the geometry, material characteristics and boundary conditions. Modal model describes the dynamic behavior of the structure as a linear combination of different resonant modes. Equipment for dynamic testing consist of several components, such as a booster, a sensor system for data collection and analysis system or analyzer. The structure can be awakened in different ways. One way is by the ball, which was applied in this research. The ball is used for applying initiatives pulse in construction that must evoke it with a sufficient range of frequencies. Another way of inducing structure is by the impact hammer, which has a built-in sensor for measuring the force of the hammer head. For data collecting electric sensors are mostly used today, first of all accelerometers (for measuring acceleration), speedometer (speed measurement), vibro-meters (movement measurement) and microphones (for measuring the volume) [10]. The sensors provide electrical output signal proportional to the size that measures mechanical and mainly fed with a constant electrical voltage, [10]. The work of the aforementioned sensors is based mainly on the inertial method, where the main elements are the mass and the adequate stiffness spring. Accelerometers for vibration measurements are often used. The most commonly used are piezoelectric accelerometers with crystals that generate electric power in deformation. Signal
conditioning elements convert sensor output signal into a form suitable for further processing. Fourier s transformations are used to go to the frequency range. As a result spectra of frequencies of signal are obtained or the range of the input initiative functions and various of the structural measuring response. If the frequency initiative range as input functions is lower, structural response function will have a narrower range of frequencies. Further analysis leads to the data on their own frequencies, damping ratios and modal forms that can be displayed numerically or graphically. Fourier s transformation allows that each physically realistic signal can be uniquely decomposed into the sum of sine and cosine members of the respective frequencies, so the Fourier s sequence and Fourier s transformation provide information on the spectral content of the analyzed signal. This is a procedure that allows the transition from the time the frequency range [10]. 3.2.1. Description of the Experiment The experiment was performed at the Laboratory of Applied Mechanics at Faculty of Mechanical Engineering in East Sarajevo. The aim of the experiment is to determine the natural frequencies of the test shaft and comparing the results with the results of natural frequencies obtained numerically by modal analysis in software package Ansys Workbench. The experimental system (Fig. 5) consists of the tested shaft hung on a rope, ball for the excitation, the sensor for contact vibration measurement-accelerometer and analog card. a) b) Fig.6. National Instruments analog card, [11] Places for free shaft suspensions are determined based on the first mode of oscillation particular on the basis of modal analysis. The accelerometer is mounted on the half of tested. Before the impact, suspended ball was deviated of approximately 20 0. In this case, unlike the pulse hammer, ball impact is elastic. Balls impacting to shaft causes the initiative. Coinciding initiative frequency with its own frequency leads to the so-called resonance, which is expressed in the form of modes or in form of peaks on the frequency-amplitude diagram. Due to the sensitivity of accelerometer used in this paper, it is possible to measure the frequency of the order of 10 000 Hz. Its working principle is based on the characteristics of piezoelectric crystals that produce electricity if they are exposed to compression, bending and shearing. In a piezoelectric accelerometers mass is attached to a piezoelectric crystal which is attached to the accelerometer chassis. When the accelerometer is subjected to vibration, the mass on crystal, due to inertia, tries to maintain the current status, which causes a force F=ma proportional to acceleration. Using internal electronics the discharge is converted to an output voltage or directly into output electricity. Depending on the loading way of piezocrystal in accelerometer, piezoelectric accelerometers can be compressive or shearing. 4. RESULTS AND DICUSSION 4.1. Numerical Modal Analysis results The results of natural frequencies of oscillations are shown in Fig. 7 and some of the forms of oscillation in Fig. 8 (a-e). Fig.5. Experimental system National Instruments instrumentation was applied for data acquisition and processing, wherein the parameter that is directly measured by contact method is vibration. Instrumentation consists of a chassis National Instruments cdaq 9172 (Fig. 6a) and NI 9233 analog card with four analog inputs, voltage range of ± 5 V and maximum speeds per channel sampling signal 50 ks / s (kilosamples per second), Fig. 6b. Fig.7. Natural frequencies results-numerical analysis 59
The results of natural frequency are presented in Table 2. Table 2. Natural frequencies results numerical analysis a) b) c) d) Mode Frequency [Hz] 1. 2. 0 3. 4. 6,9895e-004 5. 4,5977e-003 6. 4,7706e-003 7. 1124,4 8. 1124,5 9. 2953,8 10. 3180,1 11. 3180,7 12. 5866,7 13. 6128,3 14. 6129,3 15. 7408,1 16. 7846,3 17. 7856,3 18. 9237,2 19. 9238,5 20. 11549 21. 12114 22. 12117 23. 13306 24. 13389 25. 14669 26. 14714 27. 14897 28. 14905 29. 16979 30. 17689 4.2. Experimental Analysis results The results of experimental investigations are handled in the software MatLab and OriginPro. Both software were used for reasons of verifying the accuracy of those results. Table 3 provides an overview of the results of natural frequencies of shaft obtained by numerical modal analysis shaft in the software Ansys Workbench and natural frequencies obtained experimentally. Table 3. Comparing the results of natural frequencies of shaft obtained by numerical and by experimental method 60 e) Fig.8. a,b,c,d,e modal forms of oscillation numerical analysis Natural frequencies results [Hz] Modes Numerical Experimental Deviation Analysis Analysis [%] 1. Mod 1124,4 1166 3,57 2. Mod 3180,1 3310 3,92 3. Mod 6129,3 6453 5,02 4. Mod 7846,3 7784 0,79 5. Mod 9238,5 9455 2,29
Based on these results it can be determined very closely deviation of the results of natural frequencies obtained numerically and experimentally. There are several reasons for the discrepancies. First, shaft shop drawing which was used in the analysis in this paper was not available, so it was very difficult to determine the exact shaft dimension values, especially certain crossings, cones, etc, which is impossible without the equipment and instruments for measuring, so the shaft model in Ansys Workbench is not completely credible the real model. The next factor that influenced the accuracy of the results is ignorance of the precise material from which the shaft is made or the exact density of the material so that shaft after modeling had a mass of 5.96 kg, and the mass of the real shaft is 5.50 kg. If the shaft mass in the model would be set up to 5.50 kg (by changing the density of the material on 7250 kg / m 3 (Table 4), the following results of shaft natural frequencies would be obtained, Fig. 9 and Table 5. After that, the results obtained by modal and the experimental method are compared, Table 6. Table 4. Changing the drive shaft material density Properties Volume 7,6015e+005 mm³ Mass 5,5111e-003 t Centroid X 115,88 mm Centroid Y 8,3946e-005 mm Centroid Z -1,5019e-004 mm Moment of Inertia Ip1 2,9273 t mm² Moment of Inertia Ip2 66,768 t mm² Moment of Inertia Ip3 66,768 t mm² Statistics Nodes 39562 Elements 22381 Mesh Metric None which is too big for this case. Recommended accelerometer should have about 3 g, however, the equipment that is available on Faculty of Mechanical Engineering in East Sarajevo was used. Thus, with sufficient certainty it can be concluded that the results of the natural frequencies of oscillation of shaft obtained by numerical and modal analysis in the software Ansys Workbench could be verified by an experiment. Table 5. Shaft natural frequencies results experimental analysis Mode Frequency [Hz] 1. 2. 0 3. 4. 7,273e-004 5. 4,7842e-003 6. 4,9641e-003 7. 1170, 8. 1170,1 9. 3073,6 10. 3309,1 11. 3309,7 12. 6104,6 13. 6376,8 14. 6377,9 15. 7708,5 16. 8164,5 17. 8175, 18. 9611,8 19. 9613,2 20. 12017 21. 12606 22. 12609 23. 13845 24. 13932 25. 15263 26. 15311 27. 15501 28. 15509 29. 17667 30. 18407 Table 6. Comparing the results of natural frequencies of shaft obtained by numerical and by experimental method Fig.9. Shaft natural frequencies results experimental analysis Based on the above table it can be concluded that the results are almost identical, although there is still a question whether the masses of the model and the real shaft arexactly the same (taking into account the scale precision) and the question of mass accelerometer (100 g) Natural frequencies results [Hz] Modes Numerical Experimental Deviation Analysis Analysis [%] 1. Mod 1170 1166 0,34 2. Mod 3309,7 3310 0,01 3. Mod 6377,9 6453 1,16 4. Mod 7708,5 7784 0,97 5. Mod 9611,8 9455 1,63 61
5. CONCLUSION In this paper modal analysis of gearbox drive shaft was performed for freely supported shaft case. Based on the natural frequencies results obtained by modal analysis it can be concluded that the special gearbox DMB 6.80.235 drive shaft is very stiff. In order to determine the above results obtained numerically, an experimental analysis of shaft was performed using the existing equipment of Faculty of Mechanical Engineering in East Sarajevo. The experimental results verified the value of natural frequencies of the drive shaft obtained by numerical modal analysis. This paper provides a comprehensive review of the numerical analysis of a real shaft from the gearbox DMB 6.80.235. Also, this paper shows the usage of the software for the numerical analysis from the beginning of modeling shaft until the final results of natural frequencies obtaining. There is shown the usage of equipment to perform experimental analysis and the usage of software MatLab and OriginPro for signal processing. In further research, this paper could be expanded, for example, by numerical analysis of other gearbox elements and, finally, by the modal analysis of a gearbox housing. REFERENCES [1] Miltenović, V. (2009). Mašinski elementi, Mašinski fakultet Univerziteta u Nišu, ISBN 978-86-80587-91-2, Niš. [2] Batinić, V. (2001). Modal analysis of planetary gear trains. Journal of Mechanical Engineering, Vol.4, No.1, pp. 17-24, ISSN 0039-2480. [3] R.P.S. Han, J. W-Z. Zu. (1992). Modal analysis of rotating shafts: A body fixed axis formulation approach. Journal of Sound and Vibration, Vol.156, No.1, pp. 1-16, ISSN 0022-460X. [4] Zhonghong, B. Liu, G. Wu L. (2012). Modal analysis of herringbone planetary gear train with journal bearings. Mechanism and Machine Theory, Vol.54, pp. 99-115, ISSN 0094-114X. [5] Sedehi, M.H. Jafari, S. Nasseroleslami, B. (2008). Modal analysis of a turbo-pump shaft: an innovative suspending method to improve the results. IUST International Journal of Engineering Science, Vol.19, No.5-1, pp. 143-149, ISSN 1681-066X. [6] Ognjanović, B.M. Ristić, M. Vasin, S. (2013). Bwe traction units failures caused by structural elasticity and gear resonances. Tehnički vjesnik, Vol.20, No.4, pp. 599-604, ISSN 1330-3651. [7] Khoshravan, M.R. Paykani, A. Akbarzadeh, A. (2011). Design and modal analysis of Composite drive shaft for Automotive application. International Journal of Engineering Science and Technology (IJEST), Vol.3, No.4, pp. 2543-2549, ISSN 1735-1472. [8] Milutinović, M. (2013). Istraživanje i razvoj procedure i modela za robustni dizajn menjačkih prenosnika. Doktorska disertacija, Beograd: Mašinski fakultet u Beogradu. [9] Jamróz, T. Patočka, K. Vladimír, D, Horáček, T. (2012). Modal analysis of the rotor system, 20th SVSFEM ANSYS Users' Group Meeting and Conference, Prerov, ISBN: 978-80-260-2722-5, pp. 1-6. [10] Čupić, M. (2012). Dinamička analiza tanke kružne ploče. Available from: http://www.unizg.hr/, Accesed: 2015-02-09. [11] *** (2015) http://www.ni.com/en-rs.html - National Instruments, Accessed on: 2015-02-18. 62