________________

Corresponing author: Ashwani Kumar

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

Doi: http://dx.doi.org/10.11127/ijammc.2015.03.02 Copyright@GRIET Publications. All rights reserved.

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Advanced Materials Manufacturing & Characterization Vol 5 Issue 1 (2015)

Advanced Materials Manufacturing & Characterization

journal home page: www.ijammc-griet.com

FEA Based Dynamic Vibration Response Analysis of Loose Mounted Heavy Vehicle Transmission Gearbox Casing

Ashwani Kumar*, Pravin P Patil

Department of Mechanical Engineering, Graphic Era University, Dehradun, Uttarakhand-248002, India.

A R T I C L E I N F O Article history: Received 05-12-2014 Accepted 30-01-2015 Keywords: FEA; Connecting Bolts; Zero Displacement; Dynamic Response; Unconstraint; Transmission Casing; Truck

A B S T R A C T The main objective of this research work is to study the dynamic vibration characteristics of loose transmission gearbox casing. The loose vehicle transmission casing produces heavy vibration and noise. Noise and vibrations are the two technical indexes for the transmission failure. Truck transmission gearbox assembly is subjected to harmonic and meshing excitation. These excitation forces are the main reason of noise and vibration. The vehicle gearbox casing is mounted on chassis frame using connecting bolts fixture. 37 positional connecting bolts fixture were used to constraint the casing on chassis frame. This study is carried out in three stages. In first stage zero displacement constraint based boundary condition were used to evaluate the exact natural frequency and mode shapes. In second stage 4 fixture bolts were loosened, natural frequency and mode shapes were evaluated. In third stage all bolts of left positional view is unconstrained, natural frequency and mode shapes were evaluated. Reciprocity Principle was used to apply the loads on casing. The first 10 vibration mode shapes and natural frequencies were calculated using ANSYS 14.5. The study has practical importance for the structure optimization of gearbox casing. ANSYS 14.5 is used as FEA based analysis tool. The natural frequency for zero displacement condition varies from 1669 Hz to 2865 Hz. The simulation results were verified with experimental result available in literature.

Introduction Researchers have done various studies on dynamic response of vehicle transmission gearbox system since past two decades. A broad literature review has been performed to get the gist of all historical development in the field of heavy vehicle transmission analysis. Jiri Tuma [1] has studied the noise and vibration of transmission system. The author solved the gear noise problem by introducing an encloser to reduce radiated noise. TARA trucks were selected as a research object. Fourier transform is used for the analytical analysis. Analytical result is verified using experimental investigation. The extensive noise is produced during the tooth meshing or at structural resonance frequency. The natural frequency of vibration is varying in between 500 Hz to 3500 Hz at varying rpm. The severe vibration occurs at the frequency range of (500-2500) Hz. In Jiri Tuma [1] study the casing of truck was not considered so we have considered the casing in present study. Author emphasis on rigid mounting of casing, so casing loose mounting study can be performed. Mats Åkerblom [2] has performed a literature review and concluded that transmission error is an important excitation

mechanism for gear noise and vibration. In addition to transmission error, friction and bending moment are another reason responsible for failure. He has also examined the dynamic behaviour of a gearbox. P. Czech [3] has described the vibroacoustic diagnostics of high-power toothed gears. The presented analysis is an experimental work done in a steel plant. Time-frequency, Scale-frequency and frequency-frequency analysis were used for vibroacoustic diagnostics. R. Singh [4] has done two case studies for the vibro-acoustic analysis of automotive structures. Analytical and experimental results were presented for brief description. In first case passive and adaptive hydraulic engine mounts and in second case welded joints and adhesives in vehicle bodies were considered. Marina Franulovic et al. [5] have studied gear fatigue failures occur mostly because of gear design errors, manufacturing errors, assembly errors, faulty maintenance, problems in heat treating and so on combined with the load increase. Different types of failures that can occur in gears are divided in two major groups: wear and surface fatigue types of failure that occur on the tooth flank and breakage failure occur in the tooth root. Ji Wang

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et al. [6] has investigated friction force on the tooth face induces non-linearity in gear dynamics. To explain the non-linear phenomena in a gear pair frictional force on tooth face, backlash and time-varying gear meshing stiffness is used for numerical simulation. Finally, bifurcation, chaos are investigated and the critical parameters were identified. Gabriele Vandi et al. [7] have investigated the implementation of a simplified engine-driveline model to complete an existing vehicle dynamic model. Particular care is devoted to the clutch model which allows describing both the situations of engaged and disengaged clutch. Lei Yulong et al. [8] have studied 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 model of hydraulic system of dual clutch automatic transmission was established. S¨ureyya Nejat Dogan [9] has done significant work to reduce the transmission noise. The cause of rattling and clattering noise is torsional vibration of transmission components, this noise is undesirable in character. The transmission parameters were varied by experimental analyses, showing the effect on propensity to rattle and clatter. By optimizing these parameters, it was possible to minimize the noise. Shawki S et al. [10] have used vibration response analysis method for the analytical analysis of car gearbox system. They have performed analytical and experimental analysis of a car transmission system. By using physical properties, they have calculated the radiation efficiency. Shaban Ghavami Jolandan et al. [11] have presented a fault classification method based on a fuzzy inference system. The vibration signal from a piezoelectric transducer is captured for the following conditions of MF 285 gearbox: ‘Healthy Gearbox’ (H), ‘Gear with tooth face worn’ (W) and ‘Gear with tooth face broken’ (B), at three working speed (700, 1500 and 1800 rpm). The features of signal were extracted using descriptive statistic parameters. Kei-Lin Kuo [12] have established 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. Snežana Ćirić Kostić et al. [13] have investigated the natural vibrations of the housing walls and concluded that it can be prevented by designing parameters. Hugo Heidy Miyasato et al. [14] presented the testing of clutch and the torsional model response will be evaluated through numerical integration. Milosav Ognjanović et al. [15] have studied the analysis of machine systems operation causes numerous disturbances such as collisions, sliding, rolling, etc. Gear drives teeth impacts, which cause free vibrations and spreading of disturbance power through elastic structure. Fujin Yu et al. [16] have studied the dynamic characteristic of the automobile transmission gearbox. They have used structural optimization method to reduce the noise and vibration of gearbox. Pro/E and finite element method is used for the analysis. The paper deals with the dynamic analysis of loosen truck transmission gearbox casing using FEA method. Grey cast iron HT200 has been selected as casing material, having good damping properties to absorb vibration. The truck transmission casing is mounted on truck chassis frame using connecting bolts. Ashwani Kumar et al. [20] have studied

the transmission casing for 1, 2 and 3 connecting bolt looseness base problem. There are five positional points (bottom, back, front, left and right) to constraint the casing on chassis frame using connecting bolts. The present design of truck transmission casing has 37 connecting bolt holes to mount the casing on the chassis frame. 2. CAD Model of Heavy Vehicle Transmission Gearbox Casing The FEA based numerical simulation provides a powerful analysis results for evaluation of product performance. FEA based modal analysis on truck transmission gearbox casing provides natural frequencies and mode shapes. The modal analysis results can be used for noise reduction and vibration absorption of gearbox. The 3 D model of automobile truck transmission system consists of more than 600 components. It have various oil drain hole, corners, reinforcing ribs, bosses and fillets and all kinds of bolt connection holes. Solid Edge and Pro-E [18-19] software has excellent features for complex geometry design. The CAD model is shown as figure 1. For modal analysis finite element based software, ANSYS 14.5 [17] has been selected as an analysis tool. FEA based ANSYS works on meshing concept. Figure 2 shows the discretized finite element model of transmission gearbox casing. ANSYS 14.5 have high quality meshing facility. The meshed model consists of 1,96,137 nodes and 1,13,566 elements. The 10 mode shapes and natural frequency (Table 1) of transmission casing have been evaluated using ANSYS 14.5 solver. Different vibration modes bending, torsional effect, axial bending vibration and combination of two vibrations have been identified. In first stage of study when all 37 connecting bolts were constraint, natural frequencies vary from 1669.5 Hz to 2865.5 Hz. In order to get the precise result of free vibration only few components of gearbox were reduced in design stage. Transmission casing is mounted on truck chassis frame using connecting bolts. Loosening of bolts may cause excessive vibration and noise problem.

Figure 1. CAD model of heavy vehicle transmission casing.

Figure 2. FEA based meshed model of transmission casing.

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3. Material Properties and Boundary Conditions Grey Cast Iron HT200 has been selected as casing material. It has good damping property and suitable for manufacturing. The grey cast iron HT200 material properties selected for the study of the transmission casing are Elastic modulus – 1.10e11 Pa, Poisson ratio- 0.28, density-7200 kg/m3 [16]. ANSYS 14.5 based workbench module has been used for result evaluation. Zero displacement constraint based boundary condition was applied on transmission casing. It was applied by constraining the all 37 bolts position. Figure 3 shows the positional views, where fixture bolts are shown. All 37 bolts hole were used to constraint the motion of transmission casing. In actual condition all bolts are tightly constraint on chassis frame if the fixturing bolts were loosen it may cause heavy vibration and damage to transmission system. In first stage of study all 37-bolt holes are constraint and the inherent natural frequencies and corresponding 10 mode shapes were evaluated. In second stage of study 4 bolt were loosen to inspect the changes in natural frequency and mode shapes. The results show that there is a variation of (16-23) % fall in natural frequencies and it causes heavy vibration. The results of this study offer dynamics optimization design of the grey cast iron HT200 truck gearbox casing which aims at reducing vibration and noise.

Figure 3 Left positional view: connecting bolts hole positions.

4. Computation of Result and Discussion FEA based modal analysis of truck transmission gearbox casing provides result for first ten mode shapes and corresponding natural frequencies shown in Table 1. To simulate the same environment as in practical, casing is constraint to move by using zero displacement constraint based boundary condition. Loose transmission casing introduces lower order frequency. In general, the main reason of causing engine resonance is the lower order frequency of gearbox casing so it is necessary to eliminate the lower order frequency. The results were expanded for 10 order frequencies of gearbox. ANSYS workbench is used to calculate the first 10 order modes. The first stage of study starts with application of zero displacement constraint based boundary condition. All 37-bolt holes were constraint to provide rigid mounting of casing on chassis frame. The paper deals with the problems of loosen bolts condition. Figure 3 shows the constraint bolt holes position. In first phase of study, Figure 4 shows the 06 selected mode shape of transmission casing in zero displacement constraint condition.

The natural frequencies varies from (1669.5-2865.5) Hz. Mode 1 & 2 is torsional vibration. This torsional vibration is performed at front and backside on transmission casing. Axial bending vibration has been find in 5, 7 mode. Mode 9 and 10 shows heavy vibration at the front end of casing causing large deformation of casing at front side. The range (1669-2865) Hz of natural frequency for grey cast iron HT200 analysis were in the same range (500-3500) Hz as the experimental result obtained by the Jiri Tuma [1]. The simulation results were verified with experimental result available in literature Jiri Tuma [1]. In Jiri Tuma results the heavy vibration take place in range of (1000-2500) Hz. Mode 3 is rigid mode. Mode 5, 9 and 10 causes heavy vibration and deformation of transmission casing can be analysed from mode shapes.

Mode 1 f1= 1669.5 Hz

Mode 3 f3= 2227.7 Hz

Mode 5 f5= 2479.6 Hz

Mode 7 f7= 2674.3 Hz

Mode 9 f9=2762.9 Hz

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Mode 10 f1= 2865.5 Hz

Figure 4 Zero displacement constraint based analysis.

In second stage of study four bolts were loosen from chassis frame. Figure 5 shows the 6 selected mode shapes of 4 bolts loosen base condition. Unconstraint condition signifies that bolt holes were loosened and free to move. When four fixturing bolts were loosened the natural frequency varies in range (1434-2239) Hz (Table 1). For the first mode shape there is a difference of 235 Hz (16%) and for the tenth mode the difference is widen up and increases to 526 Hz (23%) of zero displacement constraint based condition. It shows that the four bolts unconstraint or loosen condition reduce the natural frequency by (16-23) % and these lower frequencies are the main reason for the excitation which causes resonance. Mode 1 shows high deformation at centre point. Mode 3 is axial bending mode perform at the centre line of casing. For this mode deformation is less but a twisting of casing is found across centre line. Mode 5 and 7 is torsional vibration cause large deformation. This torsional vibration is performed throughout the body. Mode 8 and 10 is axial bending with torsional vibration causing deformation and twisting.

Mode 1 f1= 1434.5 Hz

Mode 3 f3= 1734.1 Hz

Mode 5 f1= 1904.1 Hz

Mode 7 f7= 2028.2 Hz

Mode 8 f8= 2132 Hz

Mode 10 f10= 2239.4 Hz

Figure 5. Six selected mode shapes of 4 bolts loosen based analysis of transmission casing.

In third stage of study when all 7 bolts of left part of transmission casing were loosen from chassis frame the natural frequencies reduces by 7 %. Figure 6 shows the 6 selected mode shapes of loose transmission casing. When all fixturing bolts have been loosened, the natural frequency varies in range (1558-2846) Hz (Table 1). For the first mode shape there is a difference of 111 Hz (7%) and for the 10 mode the difference is 19 Hz (0.70%) of zero displacement constraint based boundary condition. The results shows that in positional left part loose bolts condition the reduction in natural frequency is not very sharp (7-0.7) % in comparison to 4 bolts (16-23)% loosened condition. So it can be concluded that loosening of bolts from different location is more dangerous in comparison to left positional part (view) loosened condition. Mode 2 and 7 shows the rigid mode with no deformation. Mode 3 shows the deformation at centre location. Mode 9 is torsional vibration mode. Mode 10 is axial bending vibration twisting the whole transmission casing towards right side.

Mode 2 f2= 1973 Hz

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Mode 3 f3= 2119.6 Hz

Mode 5 f5= 2187.6 Hz

Mode 7 f7= 2618.2 Hz

Mode 9 f9= 2728.5 Hz

Mode 10 f10= 2846 Hz

Figure 6 Six selected mode shapes of left positional view loosen condition

based analysis.

Table 1 Frequency Variation for different conditions.

Figure 7 shows the natural frequency variation of all three conditions. It shows that loose fixturing condition causes heavy torsional and axial bending vibration of the transmission system. For four bolts loosened condition and zero displacement condition there is a difference of 235 Hz for first mode and for mode 10 the difference is 526 Hz. This lower order frequency matching causes resonance condition which leads failure of gearbox transmission. The difference of frequencies (111-19) Hz is low in case of left positional view loose conditions. Figure 7 shows the points of matching frequency in plot. These points have same or nearby same frequency. The matching of two frequencies causes resonance condition which caused heavy vibration and noise leads to failure of whole vehicle gearbox transmission system. If we prevent the lower order frequency, we can eliminate the chances of resonance.

Figure 7 Natural frequency variations for different condition.

5 Conclusions The results of this study shows that the variation of natural frequency for zero displacement constraint based boundary condition, when all 37 bolts were constraint varies from 1669 Hz to 2865 Hz, for four connecting bolts loosen condition the natural frequency varies from 1434 Hz to 2239 HZ and left position loose transmission casing the frequency varies from (1558-2846) Hz. When 4 bolts were loosened from all position of heavy vehicle truck transmission casing there is a sharp decrement in frequency. For the first order frequency (f1), there is a difference of 235 Hz (16%) of the zero displacement constraint condition and for the 10-order frequency, the difference is 526 Hz (23%).The left part of heavy vehicle truck transmission casing is connected by 7 bolts to the truck chassis frame and other mountings of truck. When all 7 bolts were loosened frequency decreases for the first order frequency (f1), there is a difference of 111 Hz (7%) of the zero displacement constraint condition and for the 10 order frequency, the difference is 19 Hz (0.70%). The study shows that looseness of casing introduces lower order natural frequency and these lower order frequencies are the main reason for the excitation, which causes resonance. In

0

500

1000

1500

2000

2500

3000

3500

1 2 3 4 5 6 7 8 9 10

Nat

ura

l Fre

qu

en

cy (H

z)

Mode

Zero displacement condition

Four bolts loosen condition

Left position loose condition

S.N.

Zero displacement constraint condition

Four-bolt loosen condition

Left position bolt loosen condition

1 1669.5 1434.5 1558.9 2 2011.2 1594.7 1973 3 2227.7 1734.1 2119.6 4 2282.8 1836.6 2130.3 5 2479.6 1904.1 2187.6 6 2599.9 1919.6 2399.4 7 2674.3 2028.2 2618.2 8 2711.3 2132 2695.8 9 2762.9 2189.1 2728.5 10 2865.5 2239.4 2846

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resonance the transmission casing vibrates heavily and leads to failure of transmission. The transmission casing was subjected to torsional vibration, axial bending vibration, and axial bending with torsional vibration. Torsional vibration causes rattling and clattering noise. FEA based ANSYS 14.5 has been used to evaluate the simulation results. In conclusion, the numerical simulation of casing have confirmed that-

1. Bolts loosened condition causes heavy vibration of the truck transmission system which leads failure condition (sharp decrement in natural frequency Figure 7).

2. 4 Bolts based loosened condition causes heavy torsional vibration and noise. Decrement in frequency varies (16-23) % of zero displacement condition.

3. Left Positional based loosened condition has less effect on natural frequency. The decrement in natural frequency is (7-0.70) % of zero displacement condition.

The FEA simulation based analysis provides satisfactory results. This research work deals with only one position (left) loose condition in future this study can be extended to others position and bolts loose conditions. 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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