Procedia Engineering 97 ( 2014 ) 1097 – 1106

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1877-7058 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).Selection and peer-review under responsibility of the Organizing Committee of GCMM 2014doi: 10.1016/j.proeng.2014.12.388

ScienceDirect

12th GLOBAL CONGRESS ON MANUFACTURING AND MANAGEMENT, GCMM 2014

Free Vibration and Material Mechanical Properties Influence Based Frequency and Mode Shape Analysis of Transmission Gearbox

Casing Ashwani Kumara*,Himanshu Jaiswala,Rajat Jaina,Pravin P Patila

aDepartment of Mechanical Engineering,Graphic Era University, Dehradun-248002, India

Abstract

The main objective of this research work is to study the effect of mechanical properties of materials on natural frequency and mode shapes of heavy vehicle gearbox transmission casing. Material mechanical properties play an important role for evaluation of frequency, deformation, stress and strain. Four materials have different density and the origin of material is also different. Grey cast iron has damping property, structural steel has high density and rigidity, Al and Mg alloys have low density. Free vibration study was performed for the vibration response study of casing. Grey cast iron grade FG 260, Structural Steel, Al alloy and Mg Alloy materials were analyzed on the design and vibration index. The free vibration study of casing was performed using finite element simulation. The vibration response for all materials shows the variation of natural frequency (1002-3879) Hz and various vibrations mode shapes. The vibration responses for first twenty modes were studied. Solid Edge and Pro-E was used for CAD designing of transmission gearbox casing. FEA based ANSYS 14.5 is used for modal analysis. Fixed- fixed constraint based boundary condition was used by constraining the connecting bolts hole. The transmission casing is tightly mounted on vehicle frame using connecting bolts. Loose transmission casing causes heavy noise and vibration problem. The simulation results were compared with experiment results available in literature.

© 2014 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of the Organizing Committee of GCMM 2014.

Keywords: Modal Analysis; Gearbox Transmission Casing; Cast Iron; Al Alloys; Mechanical Property, Natural Frequency;Mode Shape.

* Corresponding author. Tel.:+91-992-772-3380

E-mail address: kumarashwani.geu@gmail.com

© 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).Selection and peer-review under responsibility of the Organizing Committee of GCMM 2014

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1. Introduction

Heavy vehicle transmission systems are subjected to noise and vibration under excitation condition. Internal excitation forces, meshing forces, load and speed variation and gear defects are major sources of excitation. Automobile gearbox is an assembly of gears to meet the torque variation for the varying speed conditions. The speed at the input shaft is maximum which is minimise at output shaft to increase torque value. High value of torque is transmitted to drive shaft. Noise and vibration reduction in heavy vehicle transmission system is a constant development, because noise and vibration are the two reasons for transmission failure. Mechanical properties of material influence the vibration signature pattern. The simulation results show that natural frequencies and mode shapes show different characteristics as we change the materials. Grey cast iron have damping property to reduce the vibration effect so it is used as automobile casing materials but structural steel have high density, it is used as casing material for heavy static machinery in industrial application. So our aim is to investigate the suitability of these materials on vibration parameters and analyse how the mechanical properties effect the natural frequencies and mode shapes. A brief literature survey was performed to study the previous research. Chowdhary M.A. et al. [2-3] have studied the effect of vibration on the coefficient of friction. The vibration has significant effect on properties of stainless steel 304. The authors have studied the fatigue life analysis of different components using finite element analysis method. It shows the reliability of FEA results for evaluation of structure performance. So FEA can be used for the analysis of heavy vehicle truck transmission casing. The dynamic response was studied for planetary gear trains. [4,5,8]. Jiri Tuma [9] has investigated the noise and vibration problems in TARA trucks. The fourier transform was used for analytical study and the experimental results find the heavy vibration frequency zone (500-2500) Hz. The simulation results of present study are verified with Jiri Tuma experimental results. Ashwani Kumar et al. [10] have studied the boundary condition problem of transmission gearbox casing. Ansys 14.5 workbench module all boundary condition was studied. Free-free, fixed-fixed and zero displacement constraint based boundary condition was studied. The research work concluded that the fixed-fixed and zero displacement constraint boundary condition can be used for analysis. The fixed- fixed constraint condition has frequency range (708-2570) Hz for grey cast iron HT200. Fixed- fixed constraint boundary condition is used in this research work for the analysis of material properties impact on natural frequencies and mode shapes for four different materials. Shawki S et al. [11] have studied the car gearbox transmission system. The accelerometers were used to measure the dynamic response for the calculation of radiation efficiency. Fujin Yu et al. [12] have studied the dynamic characteristic of the simple transmission gearbox casing with constraint bolt position. Grey cast iron HT200 was used as transmission casing material. The FEM based simulation method was used and the simulation result was verified with experimental results. For experimental analysis the transmission casing was constraint on a hanging base. The excitation was provided using hammer. Ashwani Kumar et al. [13] have studied the mode shape based vibration analysis for structural steel material. The natural frequency varies (1306-3829) Hz. First 20 vibration mode shapes was calculated using Ansys 14.5. The fixed-fixed constraint based boundary condition was used. The deformation pattern shows the torsional vibration and axial bending vibration. Lei Yulong et al. [14] the article focused on a dual-clutch automatic transmission of its hydraulic system. They have calculated the structure size of each body through theory and practical algorithm. The dynamic simulation of hydraulic system of dual clutch automatic transmission (AT) was studied. Kei-Lin Kuo [15] the objective of this research work was to establish a system model for an AT powertrain using Matlab/Simulink. This paper further analyses the effect of varying hydraulic pressure and the associated impact on shift quality during both engagement and disengagement of the joint elements. Ashwani Kumar et al. [16] have studied the vibration analysis for different materials. The simulation results shows that the natural frequency varies from (1002-3784) Hz. Snežana Ćirić Kostić et al. [17] have investigated the natural vibrations of the housing walls and concluded that it can be prevented by designing parameters.

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2. Establishment of 3D Model

Solid Edge and Pro-E software [6-7] is used for the designing of transmission gearbox casing. The designed casing has connecting hole used for constraining the casing on vehicle frame. Figure 1 shows the 3D model of casing. The .iges file is imported in Ansys 14.5[1] FEA based software for free vibration analysis. Figure 2 shows the meshed model of casing (3, 77, 697 nodes & 2, 28,341 elements). The present study provides a strong base for the structure optimization of transmission casing for varying materials. To obtain the accurate result of first 20 natural frequency and mode shapes, more than 600 parts of transmission casing were considered.

Figure 1 3D solid model of transmission casing.

Figure 2 FEA based meshed model of transmission casing.

Figure 3 Fixed-fixed constraint boundary condition.

3. Material Properties and Boundary Conditions

Gearbox transmission Casing is constraint on truck chassis frame using connecting bolts. To simulate the same environment for casing fixed-fixed constraint base boundary condition was used. Figure 3 shows the fixed-fixed constraint based boundary condition. The blue colour shows the constraint condition. The present design consists of 37 bolt holes for rigid mounting. This paper is concern with the mechanical properties influence on natural frequencies without considering manufacturing prospects. Mechanical properties of materials used for the modal analysis are elastic modulus, poisons ratio and material density. The material properties are- (Grey cast iron - elastic modulus 1.28e11 (Pa), poisson ratio 0.26, material density 7200 kg/m3 [18] ), (Structural steel elastic modulus

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2.0e11 (Pa), poisson ratio 0.30, material density 7850 kg/m3 [1] ), (Al alloys- elastic modulus 0.71e11 (Pa), poisson ratio 0.33, material density 2770 kg/m3 [1] ), (Mg alloys elastic modulus 0.45e11 (Pa), poisson ratio 0.35, material density 1800 kg/m3 [1] ). In actual condition transmission casing is tightly fixed on the vehicle chassis frame using connecting bolts. Fixed- fixed constraint boundary condition is suitable for the transmission casing analysis, it constraint the motion of holes position.

4. Free Vibration Analysis Results and Discussion

The numerical simulation presents the first twenty mode shapes and corresponding natural frequency. Grey cast iron grade FG260, the natural frequency varies (1002-2954) Hz. Figure 4 shows the vibrations mode shapes and corresponding natural frequency. Fixed-fixed constraint based boundary condition was used for simulation. In free vibration analysis the load is selected by program automatically. Torsional vibration is performed in mode 2, 4. The location of deformation is found at the upper side of casing. The total deformation is within range. The mode 11, 15 is axial bending vibration. In axial vibration the level of deformation is high at centre part. Mode 2 shows the minimum effect of vibration and mode 6 shows the high deformation of casing due to harmonic vibration.

Mode 2 f2=1119.3 Hz Mode 4 f4= 1665.5 Hz

Mode 6 f6= 1805.2 Hz Mode 11 f11= 2301.3 Hz

Mode 15 f15= 2747.1 Hz Mode 19 f19=2885.5 Hz

Figure 4 Mode shape and natural frequency of grey cast Iron casing.

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Figure 5 shows the mode shapes and natural frequency of structural steel material. The natural frequency varies (1306-3879) Hz. The frequency (f20=3879 Hz) shows the highest frequency for structural steel material. Mode 2 and 6 is torsional vibration mode. Mode 2 has minimum deformation due to torsional vibration. The mode 15, 19 is axial bending with torsional vibration, where transmission body twisted about centre line. The deformation is high and causes damage to casing.

Mode 2 f2=1463.7 Hz Mode 6 f6= 2352 Hz

Mode 7 f7=2495.7 Hz Mode 13 f13= 3240.9 Hz

Mode 15 f15= 3594.2 Hz Mode 19 f19=3760.4 Hz

Figure 5 Mode shape and natural frequency of structural steel transmission casing.

Figure 6 shows the vibration mode shape and natural frequency for Al alloys. The frequency varies (1291-3829) Hz. Mode 1 and 7 twisted and show large deformation due to torsional vibration. The mode 12 and 18 is axial bending vibration, where transmission body twisted about centre line. Mode 20 shows minimum deformation and mode 1 shows the large deformation due to torsional and axial bending vibration.

Mode 1 f1=1291.6 Hz Mode 3 f3=1721.4 Hz

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Mode 7 f7=2478.4 Hz Mode 12 f12=3190.7 Hz

Mode 18 f18= 3721.9 Hz Mode 20 f20=3829.6 Hz

Figure 6 Mode shape and natural frequency of Al alloy transmission casing.

The natural frequency varies from (1273-3784) Hz. Figure 7 shows the natural frequency and mode shapes. Vibration mode 1 is torsional vibration mode. The deformation is at upper portion. The mode 10 and 12 is axial vibration, the large deformation is at centre portion. Mode 17 and 18 is combination of axial bending and torsional vibration mode.

Mode 1 f1= 1273.2 Hz Mode 8 f8=2697.2 HZ

Mode 10 f10=2917.8 Hz Mode 12 f12= 3147.1 Hz

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Mode 17 f17= 3621.5 Hz Mode 18 f18= 3674 Hz

Figure 7 Mode shape and natural frequency of Mg alloy transmission casing.

The frequency band for all materials are grey cast iron (1002.5-2954.8), structural Steel (1306-3879), Al alloys (1291-3829) and Mg Alloys (1273-3784). In his experimental work Jiri Tuma has identified the natural frequency in range (500-3500) Hz. The simulation frequency of this research work is in range (1002-3879) Hz. The frequency band lies in frequency band of experimental results by the Jiri Tuma [9]. This signifies that all four materials can be used for truck transmission casing. Figure 8 shows the variation of frequency for all materials. Structural steel, Al & Mg alloys have frequency in same range (series 2, 3, 4). For mode1, 2, 3 the frequency difference is less and as the mode increases the difference also widen up.

Figure 8 Natural frequency graph Grey cast Iron (1) , Structural Steel (2), Al Alloys (3), Mg Alloys (4).

Figure 9 Natural frequency graph Grey cast Iron (1), Structural Steel (2)

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Figure 9 shows the natural frequency variation for grey cast iron and structural steel. For mode 4 there is an abrupt increase in frequency value of structural steel material transmission casing. The difference of frequency for grey cast iron and structural steel is (304-925) Hz for first and twenth mode which shows that natural frequency varies with mechanical properties of materials. The simulation results are in agreement with the objective of research work. The frequency and mode shapes changes according to material properties of casing. On vibration technical index of structural rigidity structural steel have excellent properties, which are the reason, it is used in heavy industrial machinery casing for fixed foundation.

Figure 10 Natural frequency graph Grey cast iron (1), Al alloys (2).

Figure 11 Natural frequency graph Grey cast iron (1), Mg alloys (2)

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Figure 12 Natural frequency graph Structural Steel (1), Figure 13 Natural frequency graph Al alloys (1), Al alloys (2). Mg alloys (2)

Figure 10,11,12 and 13 shows that the frequency variation patterns for different material combination. Figure 10 shows the difference of frequency for mode one (f1) is 289 Hz, and for 20 mode it increases to 875 Hz. Mode 1 frequency (f1) of Al alloy is same as Mg alloys (1291 Hz).For grey cast iron mode (1-7) frequency series are in lower order frequency range, it causes resonance which result in heavy vibration and noise. Al alloy material mode 3 and mode 4 there is a sudden rise of frequency with 440Hz. Mode 3 is torsional vibration mode, causes large displacement. Figure 11 shows that the difference of frequency for grey cast iron and Mg alloy is (271-830) Hz for first and twenth mode.

5. Conclusion

The research work has concluded that the mechanical properties are directly related with natural frequency and vibration mode shapes. First 20 natural frequencies were evaluated for four different materials and a comparison graph (Figure 8-13) was prepared. The difference of frequency for grey cast iron and structural steel is (289-862) Hz for first and twenth mode. The simulation results are in agreement with available literature results. FEA based analysis tool ANSYS 14.5 was used for simulation. Fixed- fixed constraint based boundary condition was used by constraining the connecting bolts hole. The modal frequency is an important parameter for transmission design a multi degree of freedom system. The FEA result shows that on design and vibration parameter all four materials can be used as a truck transmission casing. The reliable result of FEA simulation is used for structure optimization at initial stage of designing of casing. This research work has theoretical importance for casing performance evaluation. Finite Element Analysis offers satisfactory results. In future this research work can be extended for zero displacement constraint based boundary condition with same materials properties.

Acknowledgement This research work has been carried out at advanced modelling and simulation lab, developed from grant of Department of Science and Technology (DST), New Delhi and Department of Mechanical Engineering, Graphic Era University (GEU), Dehradun. The authors are thankful to DST and research cell of GEU for necessary funding of this research work.

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