STRESS AND VIBRATION ANALYSIS ON TWO- STAGE REDUCTION GEARBOX USING FINITE ELEMENTS METHOD

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1 International Journal of Mechanical Engineering and Technology (IJMET) Volume 9, Issue 8, August 2018, pp , Article ID: IJMET_09_08_120 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed STRESS AND VIBRATION ANALYSIS ON TWO- STAGE REDUCTION GEARBOX USING FINITE ELEMENTS METHOD Shailesh Pancholi, Meet N. Patel, S. P. Nikhil Kumar and Narendiranath Babu T School of Mechanical Engineering, Vellore Institute of technology, Vellore Tamil Nadu, India ABSTRACT Gearbox plays a vital role of power transmission in automobiles, it should be as optimized as possible and efficient for divergent power transmission scenarios. In this research paper, an optimum design of a two-stage spur gear system is performed. The optimizations are made so that gearbox can work sublimely on two extreme gear ratios, which will be employed to run on torque and speed drive. The developed optimum design led to a smaller and quieter gearbox compared to its older counterparts. The gearbox is modeled and designed in SOLIDWORKS. Static (Stress, Strain, Deformation and factor of safety) has been carried out on gears using ANSYS tool and SOLIDWORKS flow analysis. Vibrational analysis for gearbox casing is performed using ANSYS.As all the analysis is performed in ANSYS software, the analysis follows finite element methods which gives accurate result by minimizing associate error function. In this paper we have stimulated loading conditions on our design and recorded the design response to those conditions. Keywords: ANSYS, FEM, Gearbox, Structural analysis, Vibrational analysis. Cite this Article: Shailesh Pancholi, Meet N. Patel, S. P. Nikhil Kumar and Narendiranath Babu T, Stress and Vibration Analysis on Two-Stage Reduction Gearbox Using Finite Elements Method, International Journal of Mechanical Engineering and Technology, 9(8), 2018, pp INTRODUCTION Over the last several years the development of gearing has mostly focused in the following fields: the improving of material, manufacturing technology and tooling, thermal treatment, tooth surface engineering and coatings, lubricants. Gear design also includes material selection which must be capable enough to provide required strength and durability to components involved in gear drive. Fabrication of parts and assembly comes after completion of gear deign which includes technological process selection and tool designing. [1] Engineering design is an iterative process which starts with idea generation and finally arrived at a solution. The material volume of gear trains is the main determination factor in editor@iaeme.com

2 Stress and Vibration Analysis on Two-Stage Reduction Gearbox Using Finite Elements Method sizing of the gearbox. Optimal design solution offers a smaller volume (about 10-20%) than the volume calculated using the classical method for shafts and gears. Material selection is the one of the major cost-effective factors for gear manufacturing, which is selected considering parameters like strength, weight, durability, machinability and others. [2] Direct gear design is an alternative approach to traditional gear design which allows for the analysis of a wide range of parameters for all possible gear combinations in order to achieve most suitable solution for a particular custom application, results in 15 to 30% reduction in stress level when compared to traditionally designed gear. Direct gear design defines the gear tooth without using the generating rack parameter which limits strength and durability of gear. [3] Methodology for developing functional requirement or design parameters can be applied by using modern design software, which also facilitates multiple simulations in order to achieve optimal design parameters. By defining the load spectrum in the program more realistic driving conditions have been entered as an input to the software and results can be more accurate. [4] Weight reduction and simplicity of the gearbox provides better stability, increased fuel economy, better aesthetics and improved manufacturing rate. Overall reduction in vehicle weight saves energy, minimize brake and tire wear. Simulating contact stress calculation and bending stress calculation plays significant role in design gears. [5] Efficiency of spur gear impacts vehicle efficiency. However, gear mesh efficiency remains relatively constant for high-torque and high-speed conditions whereas total efficiency is not constant. Gear module and surface roughness are the most influential factors on gear mesh mechanical efficiency. Power loss for all ground gear can be minimized by using most viscous lubricant. Chemically polished and coarse pitched gear can perform even better with lowest viscosity lubricant. Gearbox total efficiency decrease with rotational speed and increase in input torque. [6] The total contact ratio is the most significant factor for noise reduction, within a gear designer s control. Gear noise can be reduced by increasing ether the face or profile contact ratio. Though the Noise level generally increase with the speed and torque, the higher contact ratio spur gears more quitter than standard gears regardless of the tooth form. [7] The gearbox vibration and noise are generated due to the gear pair dynamic force, which also affects gearbox stability. Vibration of gear pairs are largely affected by gear manufacturing error (phase and amplitude deviation). Also, the gear pair meshing state and the frequency of the various harmonics changes with the rotational speed of the gears. The gearbox vibration and noise output are calculated by using FEM/BEM. [8] The noise emission from gearbox depends on both the disturbances and the insulating capabilities of gearbox housing. Natural vibration of housing can be prevented or reduced depending on design parameters. [9] 2. METHODOLOGY Flowchart of processes Steps involved in stress and vibrational analysis of Gear Box editor@iaeme.com

3 Shailesh Pancholi, Meet N. Patel, S. P. Nikhil Kumar and Narendiranath Babu T Gears (Helical and Spur Gearing) Gear ratio Required is calculated Selection of basic parameters: number of teeth (according to gear ratio), module of gears, driver speed, helix angle, thickness, gear material etc. Designing the model in SOLIDWORKS 2016 and importing it into ANSYS 16.0 Calculation of forces acting on the gears Static Structural analysis is done by providing contact between the gears, fixing the gear wheel and applying required moment on the pinion. Rotation region is provided to both the pinion and wheel. Results of stress, deformation and FOS is recorded Shafts (Input and Output) Selection of basic parameters: shaft material, shaft diameter. o Shaft diameter is calculated by using maximum bending moment and maximum stress theory. Input values are based on input conditions as defined earlier. o The supportive data is collected from the PSG Data book. Design and analyzed the model in SOLIDWORKS 2016 Static Structural analysis is done by fixing the shafts and applying the moment. Results of stress, deformation and FOS is recorded. Gearbox casing Material selection for gearbox casing Designing of the casing: Smaller in size, most efficient, proper ventilation, oil sealing and drain system etc. Provided guide holes and veins for oil flow in entire gear box, provides cooling and longer life for the product. Performed stress structural and vibrational analysis for casing on ANSYS 16.0 Vibrational analysis performed at different frequencies for accurate and safe result. Results for both are recorded Miscellaneous Parts Parts such as oil sleeves and circlips were taken from the toolbox of SOLIDWORKS 2016 and assembled Bearing calculations were done and CAD part was taken from tool box and assembled Specifications Gears Spur Gear Pinion, No. of teeth = 15 Module = 3mm Face width = 30mm Pitch circle diameter = 45mm Pressure angle = 20deg. Wheel, editor@iaeme.com

4 Stress and Vibration Analysis on Two-Stage Reduction Gearbox Using Finite Elements Method No. of teeth = 39 Module = 3mm Face width = 30mm Pitch circle diameter = 117mm Pressure angle = 20deg. Center to center distance between both = 81mm Spur Gearing Pinion, No. of teeth = 15 Module = 3mm Face width = 15mm Pitch circle diameter = 45mm Pressure angle = 20deg. Wheel, No. of teeth = 42 Module = 3mm Face width = 15mm Pitch circle diameter = 126mm Pressure angle = 20deg. Center to center distance between both = 85.5mm Shafts Input Shaft keyed (Cantilever) Diameter = 25mm Length = 251mm Material = AISI4340 normalized Key = 4.75 x 5 x 165 Intermediate Shaft Diameter = 20mm min 28mm max Length = 78mm Material = AISI4340 normalized Output Shaft (Hollow shaft) Diameter, ID = 22mm OD = 25mm (min) 36mm (max) Length = 129mm Material = AISI4340 normalized editor@iaeme.com

5 Gear-box casing Shailesh Pancholi, Meet N. Patel, S. P. Nikhil Kumar and Narendiranath Babu T 2.2. Materials and properties AISI 4340 normalized Density = 7850 Kg/m3 Young s Modulus = 80GPa Poisson Ratio = 0.32 Tensile Yield Strength = 710MPa Ultimate Tensile Strength = 1010MPa Aluminium 6061 Hard Anodized Density = 2700 Kg/m3 Young s Modulus = 26GPa Poisson Ratio = 0.33 Tensile Yield Strength = 275MPa Ultimate Tensile Strength = 310MPa Material: Aluminium 6061 T6 hard anodized Oil 80W 90 (Mineral oil) Density = 887Kg/m3 at 15.6 C Kinematic Viscosity = 139 cst 40 C and 15 cst at 100C Flash point = 218 C Viscosity index = Forces applied On Input Shaft: 60Nm moment, 3000N (Drive Force) On Intermediate Shaft: 156Nm moment On Output Shaft: 600Nm moment On First Stage of Gear: 156Nm moment On Second Stage of Gear: 600Nm Moment On Casing: a. Bearing load due to input shaft: 6000N b. Bearing load due to intermediate shaft: 4000N c. Bearing load due to output shaft: 8000N editor@iaeme.com

6 Stress and Vibration Analysis on Two-Stage Reduction Gearbox Using Finite Elements Method 3. RESULTS AND DISCUSSION 3.1. Input shaft Figure 1 a Stress results of input shaft. As the image 1.a. shows the maximum stress developed is 121MPa whereas yield strength is 710MPa for AISI4340. The maximum stress developed is less than half of the yield strength and thus succeeds against Von-Mises' theory of failure. The bearing region is fixed from rotation and moment is applied on the length of the shaft. Figure 1 b Deformation results of input shaft. The fig.1.b. shows the maximum deformation of 0.037mm at the tip of shaft, which is negligible compared to the diameter of the shaft. Figure 1 c FOS Result of input shaft editor@iaeme.com

7 Shailesh Pancholi, Meet N. Patel, S. P. Nikhil Kumar and Narendiranath Babu T The lowest FOS of the input shaft as seen in fig.1.c. is which is very high. I.e. it can take up to 5 times the load applied without breaking Intermediate shaft Figure 2 a Stress results of intermediate shaft. The fig.2. a. shows that the maximum stress developed is in the intermediate shaft is 325MPa, less than half of yield strength(710mpa). The maximum stress acts at the edge of bearing step and the next step. The bearing regions are fixed support and two moments are applied on either side of the middle step. Figure 2 b Deformation result of intermediate shaft. As seen in the fig.2.b. the maximum deformation is mm, which is at the middle as the forces applied are opposite in direction and because of which more deformation. Figure 2 c FOS result of intermediate shaft editor@iaeme.com

8 Stress and Vibration Analysis on Two-Stage Reduction Gearbox Using Finite Elements Method The minimum FOS of 2.16 (Fig.2.c.) which is safe within most of the safety standards. The offset of the middle step causes a slight variation of FOS in the center step Output shaft Figure 3 a Stress result data of output shaft. From the figure 3a., it is found that the maximum stress is 227MPa (Less than half of yield strength of 770MPa), the irregular distribution of stress is due to the offset of gear placement from center of shaft. The bearing regions are fixed support and gear moment is giving at the center step. Figure 3 b Deformation result of output shaft. The fig.3.b. shows the maximum deformation to be 0.014mm for the output shaft, at the region where gear is placed as torque transfer occurs through this region from gear to shaft editor@iaeme.com

9 Shailesh Pancholi, Meet N. Patel, S. P. Nikhil Kumar and Narendiranath Babu T Figure 3 c FOS result of output shaft, As seen from fig.3.c. the minimum FOS of is safe for the output shaft considering the shaft is hollow Stage 1 gear Figure 4 a The stress distribution data of stage 1 gears, The maximum stress acting on either of the gears in 197MPa (Fig.4.a.), the wheel's center is fixed as support and the moment is given at the input gear at inside wall. As the contact ratio is 1, maximum force is taken by the tooth in contact. The weight reduction hole I's slightly experience slightly higher stress due un-uniformity. Figure 4 b The deformation results of stage 1 gears editor@iaeme.com

10 Stress and Vibration Analysis on Two-Stage Reduction Gearbox Using Finite Elements Method The fig.4.b. shows that the maximum deformation is 0.046mm in the smaller gear, the red radii on the gear teeth shows that the contact tooth got bent and as a result the gear took a small angular displacement Figure 4 c The FOS result of stage 1 gear reduction. This figure is showing the I st gear set with an FOS of 3.59 minimum, & can withstand the applied load easily Stage 2 gear Figure 5 a Shows the stress results of stage 2 gear. In the fig.5.a.the maximum stress developed is 202.9MPa, again the inner wall of wheel is fixed and the moment is applied at the smaller gear, the contact is given as no movement contact. Figure 5 b Shows the deformation results of stage 2 gear editor@iaeme.com

11 Shailesh Pancholi, Meet N. Patel, S. P. Nikhil Kumar and Narendiranath Babu T As the fig.5.b.shows, the maximum deformation result is 0.065mm, this is slightly higher than that of first stage as the diameter is larger and more moment is acting on the gears. Figure 5 c Shows the FOS result of the gear. The fig.5.c. representing the II nd stage of gears shows that the minimum FOS is 3.49, since the load applied is higher on the second stage, the effects are visible at the pillar of holes, showing lesser FOS than the body Gearbox Casing Figure 6 a Represents the stress data of the casing. In the fig.6.a. of the casing the maximum stress developed is 113MPa, the mounting points were fixed as support, and the weight of gears, bearing loads, side thrust loads were applied. The stress is distributed evenly at the output shaft hole thanks to the ribs provided. Figure 6 b Shows the deformation data of casing editor@iaeme.com

12 Stress and Vibration Analysis on Two-Stage Reduction Gearbox Using Finite Elements Method The maximum deformation is 0.138mm (Fig.6.b.) at the forward end as it is unrestrained and a lot of forces acting on input shaft acts in this region. Figure 6 c Represents the FOS of the casing, Representing the casing's FOS, the minimum being 2.84, is considerably high as the material is Aluminum Casing Vibration Analysis Figure 7 a Represents the first mode of vibration of the casing. In the fig.7.a. the same restraints as structural analysis is taken. The casing tends to move up and down along a plane perpendicular to the axis of the shafts and thus maximum deformation at the forward region. The natural frequency for the mode was Hz. Figure 7 b Represents the second mode of vibration casing editor@iaeme.com

13 Shailesh Pancholi, Meet N. Patel, S. P. Nikhil Kumar and Narendiranath Babu T In the fig.7.b. the casing tends to sway sideways from left to right along a plane perpendicular to the axis of the shafts and thus maximum deformation at the forward region towards one side. The natural frequency for the mode was 216.8Hz. Figure 7 c Represents the third mode of vibration. And in the fig.7.c. the natural frequency for this mode of vibration is Hz. The casing tends to move forward and backward, as it is fixed at output shaft hole thus the large red region of higher deformation. Figure 7 d Represents the fourth mode of vibration In the fig.7.d. the natural frequency for this mode of vibration is Hz. The casing tends to twist left and right about an axis perpendicular to the axis of output shaft, as it is fixed at output shaft hole thus the large red region of higher deformation. Figure 7 e Represents the fifth mode of vibration editor@iaeme.com

14 Stress and Vibration Analysis on Two-Stage Reduction Gearbox Using Finite Elements Method The fig.7.e. represents the natural frequency for the fifth mode of vibration is 3289Hz. The casing tends to twist left and right about an axis along the axis of output shaft, as it is fixed at output shaft hole thus the large red region of higher deformation. Figure 7 f Represents the sixth mode of vibration. The natural frequency for this mode of vibration (Fig.7.f.) is 3427Hz. The casing tends to twist from up and down about an axis perpendicular to the axis of output shaft. 4. CONCLUSION In this research paper, designing and analyzing of a gearbox with two stage reduction is presented with emphasis on vibrational analysis of gear housing. The grearbox is a design success as it is capable of transmitting 10HP, 70Nm torque, fluctuating and varying load through an overhanging input and hollow shaft output for a test case of 6 hours continuous working per day. Effects due to bending, torsion and vibration are studied, which helped in designing wedge to support bearing load and electing bearings. ANSYS software was used to estimate the natural frequency from other frequencies. Simulations of vibrational and structural analysis were presented to achieve the design objectives. The design and analysis performed on the gearbox using finite element method will help future engineers to accomplish the same for complex geometries. REFERENCES [1] MilosavOgnjanovic Miroslav Milutinovic, Design for Reliability Based Methodology for Automotive Gearbox Load Capacity Identification, Researchgate, 2012 [2] Neeraj Patel, Tarun Gupta, Aniket Wankhede, Vilas Warudkar, Design and Optimization of 2-Stage Reduction Gearbox, IJEDR Volume 5, Issue 2 ISSN: , 2017 [3] Alexander L. KapelevichAnd Thomas M. Mcnamara, "Direct Gear Design For Automotive Applications, SAE International, 2005 [4] Neeraj Patel, Tarun Gupta, Methodology for Designing A Gearbox And Its Analysis, IJERT, Vol. 5 Issue 01, ISSN: , 2016 [5] Rahi Jain and Pratik Goyal, Design and Analysis of Gear-Box Using Spur Gear and Eliminating the Differential Unit, Volume 7, Issue 6, PP: , ISSN Online: , editor@iaeme.com

15 Shailesh Pancholi, Meet N. Patel, S. P. Nikhil Kumar and Narendiranath Babu T [6] T. T. Petry-Johnson, A. Kahraman, N. E. Anderson, D. R. Chase, An Experimental Investigation Of Spur Gear Efficiency, ASME, Vol 130, 2008 [7] F. B. Oswald, D. P. Townsend, M. J. Valco, R. H. Spencer, R. J. Drago, And L. W. Joseph, Influence Of Gear Design Parameters On Gearbox Radiated Noise, In Proceedings Of The International Gearing Conference (Inter Gearing 94), Newcastle, [8] Jianxing Zhou, Wenlei Sun, And Qing Tao, Gearbox Low-Noise Design Method Based On Panel Acoustic Contribution, Hindawi Publishing Corporation, Volume, Article ID , 2014 [9] S. C. KostićAnd M. Ognjanović, The Noise Structure of Gear Transmission Units and the Role of Gearbox Walls, FME Transactions, Vol. 35, No. 2, Pp , editor@iaeme.com