International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 1, January 2013)

Modal Analysis of Power Take Off Gearbox D.S.Chavan1, A.K.Mahale2, Dr. A.G.Thakur3 1

SRES College of Engineering, Kopargaon, India Professor, HOD, Mechanical Engineering Department, SRES COE, Kopargaon, India

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Abstract- “Harvester” machine plays an important role in the harvesting of crops. One of the vehicle system that is involved in the generation of noise and vibrations is the powertrain. Powertrain system includes engine and transmissions. Engine Power Take Off (PTO) is one of the main gearbox of powertrain system. It receives power from engine and delivers to other applications of the vehicle. Separator is one of the power output of the gearbox. PTO gearbox of the harvester generates vibrations when engine is running & engaged to the separator. The project scope is to understand the generation of the vibration in PTO gearbox and provide recommendations to reduce vibrations. Modal analysis is a well established technique which defines the inherent properties of the structure. Modal analysis is used to measure the natural frequency and mode shape pattern. The analysis is done using both analytical and experimental methods. After analyzing the data from both methods, the resonance found for one of the component of gearbox. This creates the vibrations in the gearbox. FEA is done for this component with modifications to avoid the resonance. Prototype of the component is made as per modifications suggested and gearbox vibrations are tested. With modified component, the vibrations of the gearbox with separator engaged are reduced to within reasonable limits. The methodology adopted here gives the reduction of vibration level of gearbox in the range of 40-50%, which has reduced the vibrations at the vehicle platform

In any given situation, there are always three factors:  Source-where the dynamic forces are generated  Path-how the dynamic forces are transferred  Receiver-how much noise/vibration can be tolerated One of the vehicle system that is involved in the generation of noise and vibrations is the powertrain. Powertrain system includes engine and transmissions. Engine Power Take Off is one of the main gearbox of powertrain system of harvester vehicle. Figure 1 shows the 3D Model of PTO gearbox. It receives power from engine and delivers to other applications of the vehicle. There are three power outputs: A, B and C. Separator (A) is one of the power output of the gearbox. Figure 2 shows the Schematic Layout of PTO Gearbox.

Figure 1.

Figure 2.

1.2 Problem Statement PTO gearbox of the harvester generates vibrations when engine is running & engaged to separator. The project scope is to understand the generation of the vibration in PTO gearbox and provide recommendations to reduce vibrations by 15-20 % of current levels.

Keywords- Harvester, PTO, Gearbox, Vibration, Modal Analysis

I. INTRODUCTION 1.1 General Information Noise and vibration in the environment or in industry are caused by particular processes where dynamic forces excite the structures. The effects of noise and vibration range from annoyance, fatigue and reduced comfort, to safety and even health hazards. On machines, vehicles and buildings the effect may be wear reduced performance, faulty operation or any degree of irreversible damage. Most noise and vibration problems are related to resonance phenomena. Resonance occurs when the dynamic forces in a process excite the natural frequencies, or modes of vibration, in the surrounding structures. This is one reason to study the modes and second reason is that they form the basis for a complete dynamic description of a structure [1].

1.3 Scope of Present Study a) To understand the generation of the vibration of PTO gearbox b) To obtain dynamic characteristics i.e. natural frequencies, mode shapes, damping ratios of the gearbox structure using experimental modal analysis c) To generate realistic and representative finite element model of PTO gearbox, which will be then used to evaluate possible deformation pattern (mode shapes) and natural frequencies.

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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 1, January 2013) d) Correlate the theoretical and experimental results. e) Recommend and apply solutions to reduce the vibration level by 15-20% of current levels.

2.2 Requirements of Test 2.2.1 Support of Gearbox Structure:

II. EXPERIMENTAL MODAL ANALYSIS (EMA) 2.1 Basic Procedure 1. Set up the gearbox structure in a mounting configuration which has been carefully selected and which can be controlled. Figure 3 shows the gearbox supported on flange 2. Provide a means of exciting the structure into vibration in a controllable and measurable way. This may be by means of a non-attached device, such as an impact hammer or similar, or by an exciter which is connected firmly to the gearbox structure. These exciters can generate the required excitation forces by several means: mechanical, electromagnetic, electro hydraulic, etc. Figure 4 shows impact hammer with a load cell, which is used for impact on the gearbox housing. 3. Provide a means of (transducers for) measuring the resulting response of the gearbox structure, and to do so with the minimum of interference to the test object. Figure-5 shows tri-axial accelerometer, which is mounted on the gearbox. 4. Provide signal processing and analysis facilities so that the required information can be extracted from the individual measured time histories yielded by the transducers. Here, it is usually necessary to convert raw measured data in the time domain into equivalent spectra in the frequency domain, as frequency domain parameters are more commonly used to describe most vibration phenomena. 5. Subject the measured response function data to a subsequent analysis stage, often employing curve fitting techniques, in order to construct a mathematical model of standard form (linear, MDOF system) whose dynamic properties most closely resemble to those observed on the test structure. 6. Check that the resulting model is adequate for the intended application (before releasing the gearbox to the vehicle assembly).

Figure 3: Gearbox Supported on Flange

2.2.2 Excitation of Gearbox Structure:

Figure 4: Impact Hammer with a Load Cell

2.2.3 Transducers: A wide range of transducers are available for capturing the excitation force and resulting response levels. Many of these are piezoelectric devices, simple to use and relatively free of idiosyncratic features. Such transducers are widely available to measure force and acceleration: other transducers are also available for measuring velocity responses directly, and worth a special mention are the new generation of laser Doppler vibrometers, which offer advantages of being non-contacting devices, thereby minimizing interference with the behavior of the test structure [2]. In EMA of PTO gearbox, one accelerometer is used to measure the acceleration response of the structure after the excitation by an impact hammer. The location of this accelerometer on the gearbox is shown in figure 5.

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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 1, January 2013) 2.2.5 Signal Processing: Signal processing is a major activity. It is generally required to be able to extract the individual frequency components which are present in a signal; sometimes because the original signal generating the vibration contains many components (as is the case for periodic, random or transient types of excitation), and other times because it is required to eliminate spurious components of response, introduced by noise or nonlinearities in the measuring system. These various requirements can be met with the current generation of spectrum and other frequency response analyzers, often based on digital filtering and frequently employing the FFT or similar algorithms developed in the 1960’s, and making signal processing very much faster than it had been hitherto [2]. The advent of the FFT was a major development for modal testing. LMS test lab software is used for processing the results. Figure 8. shows the screen shot of this acquisition software for one of the measurement. Averaging: The frequency response signals are obtained for each point with an average of 5 impacts.

Figure 5: Triaxial accelerometer at drain plug

2.2.4 Specimen and Measurement Positions: The transmission has been used for this measurement is PTO gearbox. All data have been acquired with the machine stopped. The transmission is decoupled from the rotary engine, so that the only existing bonds are the anchored to the bench. To characterize the dynamic behavior of the transmission, some information is distributed along the geometry in 19 different points. These 19 points are sufficient to define the complete geometry of the gearbox. These positions are shown in figures: 6 (a) and (b)

(a)

(b)

Figure 6: Measurement Positions

The transmission is driven in all directions through the instrumented hammer impacts on a surface obliquely. For each measure, 5 impacts are recorded, so that the calculated frequency response is an average of them all. In brief, the dynamic characterization of transmission is through the model and knots of wires attached. The test lab model is shown in figure 7.

Figure 8: Acquisition System

2.3 Results The Frequency response function (FRF's) recorded during the acquisition are exported to Test Lab, where analysis is performed. POLYMAX algorithm is used, that from a least squares adjustment in the frequency domain, performs the first stage in the selection of poles (Frequencies and modal damping) and subsequent calculation of residue (modal vectors). With the acquired data from measurements, modal parameters are extracted. Table no. I shows the results.

Figure 7: Test Lab model

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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 1, January 2013) We must define both Young’s modulus (and stiffness in some form) and density (or mass in some form) for a modal analysis. Non-linear properties are ignored.

TABLE I NATURAL FREQUENCY AND MODAL DAMPING

Mode

Natural Frequency (HZ)

Modal damping (%)

Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 Mode 7 Mode 8 Mode 9

110.3 490.8 795.7 908.4 1028.2 1423.6 1506.5 1750.6 1946.0

4.34 3.25 0.31 0.34 1.10 0.12 0.85 0.94 0.98

3.2 Pre-processing  Import Power take off gearbox geometry model from CAD  Setting the type of analysis to be performed which is modal analysis  Set required frequency range of 100 Hz-2000 Hz for 40 modes  Applying the mesh in which the process of providing the analysis on continuum into a number of element.  Applying the element properties i.e. material properties. Material properties for the commonly used materials for different parts of gearbox are as given in Table II

III. FINITE ELEMENT ANALYSIS The finite element method is comprised of three major phases: 1. Pre-processing, in which the analyst develops a finite element mesh to divide the subject geometry into sub domains for mathematical analysis, and applies material properties and boundary conditions. 2. Solution, during which the program derives the governing matrix equations from the model and solves for the primary quantities, and 3. Post-processing, in which the analyst checks the validity of the solution, examines the values of primary quantities (such as displacements and stresses), and derives and examines additional quantities (such as specialized stresses and error indicators).

 Applying the point masses to the model. However in modal analysis, loads are not required to run the analysis.  Applying the boundary condition for the housing at four pin locations. Application of correct boundary condition is critical to the accurate solution of the problem. TABLE II MATERIAL PROPERTIES

Component Type Main Housing and Bearing Housing Covers Gear and Shafts

3.1 Steps in Modal Analysis The procedure for a modal analysis consists of four main steps: 1. Build the model 2. Apply boundary conditions, point masses if any and obtain the solution 3. Expand the modes 4. Review the results Only linear behavior is valid in a modal analysis. If we specify non-linear elements, they are treated as linear. For example, if we include contact elements, their stiffness are calculated based on their initial status and never changed. Material properties can be linear, isotropic or orthographic and constant or temperature dependant.

Covers

Poisson’s Ratio

Young's Modulus (MPA)

Die cast Aluminum

0.33

71000

Steel

0.29

2.11E+05

Gray cast iron

0.28

1.10E+05

Material Type

Figure 9. shows FEA model of the gearbox with boundary conditions and figure 10 shows FEA mesh model of gearbox.

Figure 9: FEA Model of Gearbox with Boundary Conditions

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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 1, January 2013) Frequency-975.5 Hz

Frequency-1027.8 Hz

Frequency-1398.4 Hz

Frequency-1423.6 Hz

Frequency-1632.9 Hz

Frequency-1506.6 Hz

Frequency-1831.6 Hz

Frequency-1750.7 Hz

Frequency-1930.6 Hz

Frequency-1946 Hz

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6 Figure 10: FEA Mesh model

FEA results along with EMA results are presented below. 7

IV. RESULTS AND DISCUSSION TABLE III COMPARISON BETWEEN FEA AND EMA RESULTS Mode

FEA

Experimental

Frequency-116.1 Hz

Frequency-110.3 Hz

Number 8

1

9 Frequency-420.9 Hz

Frequency-490.9 Hz

2 TABLE IV ERROR (%) OF NATURAL FREQUENCY BETWEEN FEA AND EMA RESULTS Frequency-794.8 Hz

Frequency-795.7 Hz

3

Frequency-884.7 Hz

Frequency-908.5 Hz

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Mode

FEA Natural Frequency (HZ)

EMA Natural Frequency (HZ)

Error (%)

Mode 1

116.1

110.3

5

Mode 2

420.9

490.9

14.25

Mode 3

794.8

795.7

0.001

Mode 4

884.7

908.5

2.6

Mode 5

975.5

1027.8

5.1

Mode 6

1398.4

1423.6

1.8

Mode 7

1632.9

1506.6

7.7

Mode 8

1831.6

1750.7

4.4

Mode 9

1930.6

1946.0

0.008

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 1, January 2013) As we see from the table III and IV that the PTO gearbox natural frequencies derived from the EMA and the FEM calculations are closer, maximum error is 14.25%, and the vibration vectors are the same. The experimental modal parameters prove the correctness of FEM calculation and show that the finite element model is the same with the quality and stiffness distribution of PTO gearbox actual structure. Mode shapes and frequencies obtained from both methods are used to understand the generation of vibration and provide recommendations to reduce it. As vibration level is due to engaging the separator application, more focus is given to bevel gear shaft. In some modes of PTO gearbox, maximum deformation of bevel gear shaft end is found. To find the probability of resonance between bevel gear shaft with overall gearbox structure, separate modal analysis of bevel gear shaft is carried out in FEA. Natural frequencies obtained from bevel gear shaft analysis lies in gear mesh frequency range. It causes resonance phenomenon resulting in increased vibration level of the gearbox. In order to avoid resonance, two separate modifications are done in 3D model of bevel gear shaft. Both modifications are analyzed separately in FEA. One modification gives no improvement in the frequency. Second modification gives improvement in the frequency. This modification will avoid the resonance. Prototype of bevel gear shaft is made according to this modification. This prototype is assembled in gearbox and tested with separator engaged and engine running at rated rpm. Vibrations are measured at drain plug. Measured vibration level of gearbox is within reasonable limits. 40-50 % reduction in vibration level is achieved. It will enhance the performance of the gearbox on the vehicle.

From figure, it is clear that, bevel shaft are having two modes in the range of frequency 1400-1450 Hz. So it is creating a resonance with gear mesh frequency. There are two approaches made in order to change the natural frequency of the shaft. Modification1: Refer figure 12. Material is removed from 3D geometry of shaft. FE Modal analysis is done, as shown in figure 13. and we do not found improvement in the results. Modal frequencies of shaft are still in range of gear mesh frequency. Modification 2: In this case, material is removed from splined end of shaft, as shown in figure 14. FE Modal analysis is done and we found improvement in the results. We got frequency in the range of 1600-1700 Hz and it is out of gear mesh frequency range. Therefore, this modification, in the shaft will avoid the resonance. Mass removal under the spline of shaft is improving the natural frequency.

Figure 11: Bevel Gear Shaft Mode Shapes

4.1 Gear-Mesh Frequency for Bevel Gear Shaft The gear mesh frequency, also called "tooth mesh frequency", is the rate at which gear teeth mate together in a gearbox. It is equal to the number of teeth on the gear times the rpm of the gear. A gearbox will always have a strong vibration component at the gear mesh frequency, and it is one of the fault frequencies used in machinery monitoring. The gear mesh frequency range is 1400-1450 Hz for bevel gear shaft. FE modal analysis is completed for the bevel gear shaft to check the natural frequencies and mode shapes. Figure 11 shows results of this shaft analysis. Figure 12: Bevel Gear Shaft Geometry (Existing and Modification1)

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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 1, January 2013) After analysis of PTO gearbox by EMA and FEA, a good correlation of the results for natural frequencies and mode shapes are found. This shows that modal parameters obtained by EMA and FEA are reliable and accurate. The maximum error between EMA and FEA results is 14.25%. The data driven provide important reference to the structural improvement of the PTO gearbox. Mode shapes and frequencies obtained from EMA & FEA methods are used to understand the generation of vibration in PTO gearbox & to provide recommendations to reduce it. The vibration levels are due to resonance at gear mesh frequency because of bevel gear shaft natural frequency in the same range. In order to avoid resonance, modification in the geometry of bevel gear shaft is suggested. Prototype of modified bevel gear shaft is successfully tested in gearbox and 40-50 % reduction in vibration level is achieved.

Figure 13: Bevel Gear Shaft Modes with Modification 1

REFERENCES [1]

[2] [3] [4] Figure 14: Bevel Gear Shaft Modes with Modification 2

[5]

V. CONCLUSION

[6]

The goal of present project study was to understand the generation of the vibration in PTO gearbox and provide recommendations to reduce vibrations by 15-20% of current levels. A PTO gearbox structure chosen is analyzed through finite element analysis and experimental modal analysis. Good results are obtained as well as a good understanding of the dynamic properties of the structure. The understanding is viewed as just as important as the results since it is this knowledge which will allow an engineer to improve a design.

[7]

[8]

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