STATIC ANALYSIS ON BEVEL GEAR USING STRUCTURAL STEEL, GRAY CAST IRON, AND STAINLESS STEEL Prateek Srivastava 1, Rishabh 2, Zubair Irshad 3, Pankaj Kumar Singh 4 Graduate Students Mechanical Engineering, Faculty of Engineering and Technology Manav Rachna International Institute of Research and Studies, Faridabad, Haryana, India Abstract: A Bevel gear is generally used for Shaft. They are at 90 o angle with each other, and their teeth which are involved with each other are cut to be straight. There are two types of bevel gear first straight bevel gear and second spiral bevel gear. The use of bevel gear is used to transfer the power from one shaft to another shaft which being perpendicular to each other. The shape of bevel gear is truncated cone. The gear tooth size, thickness and height are to be small or decrease towards the cone apex. In this paper we use to calculate stress, stain and deformation in bevel gear. The design of bevel gear is done in Catia software and the Analysis is done in Ansys 17.2 software Keywords: Bevel gear, Catia, Ansys, Total deformation, Strain, Stress 1. Introduction: A bevel gear is a type of gear which uses to transmit the power from one shaft to another shaft which is perpendicular to each other. In bevel gear the teeth are straight of straight bevel gear, which have a common apex point. And in spinal bevel gear the teeth are spinal curve which also have a common apex point. There is gradual contact in the teeth of spiral gear in which when the tooth of two gear meet with each other there is a smooth and noise less operation is done. Spiral bevel gear have more load capacity as there is simultaneously contact in the teeth and their arc of contact is greater. Bevel gear can be arranged at different pitch angle such that when the pitch angle is less than 90 o then external bevel gear, when the pitch angle equal to 90 o then crown bevel gear, and when the pitch angle is greater than 90 o then internal bevel gear. There are specific categories of bevel gear which are Miter gear, Crown gear, internal bevel gear, Skew bevel gear, Hypoid gear, Zerol gear, Face gear. There are some terms which are used in terminology of bevel gear are Pitch cone, Cone center, Cone distance, Pitch angle, Addendum angle, Dedendum angle, Face angle, Root angle, Back cone, Back cone distance. In this paper designing of Bevel gear is done in Catia software and the static analysis on bevel gear is done in Ansys 17.2 software. Notation kw- Power n p No. of rotation per minute Pressure angle D p- Pitch circle diameter of pinion D g Pitch circle diameter of gear b Length of bevel gear M t Torque transmitted by gears - Pitch angle of pinion ( o ) r m- Radius of pinion along face width at midpoint P t- Tangential component of force of tooth P r Radial component of force of tooth P a- Axial component of force of tooth IJSDR1805012 International Journal of Scientific Development and Research (IJSDR) www.ijsdr.org 65
2. Analytical Method In this Analytical Method, we use to give a momentum of the bevel gear which is connected which is connected with each other, while we use to calculate stress, strain and deformation in that gear. 1. To calculate torque transmitted by gear, we use M t = 60 X 10 6 (KW) 2 n p 2. Pitch angle of pinion ( o ) tan = D p D g 3. Radius of pinion along face width at midpoint r m = D p _ bsin 2 2 4. Tangential component of force of tooth P t = M t r m 5. Radial component of force of tooth P r = P t tan cos 6. Axial component of force of tooth P a = P t tan sin 3. FINITE ELEMENT METHOD Finite element method is a type of method in which solving problems of mathematical physics with the use of Numerical Method. In this type of finite element method the major problems can solved with the use of structural analysis. In finite element method which is generally consists of different type of heavily meshed geometries along with different materials like structural steel, gray cast iron and stainless steel and with the use of that we use to calculate equivalent stress, equivalent elastic strain, and total deformation, and with the use of mathematical solution it is very complicated solve these types of problems. 4. DESIGN AND DATA Bevel gear is used to model and design in CATIA V5 R20 software, in this software we use to draw the sketch of bevel gear and then we use to draw the teeth as well. In this paper we also use locate 3D view of teeth and bevel gear as it is design in part design in catia software. Bevel gear have different geometrical data which are Inner radius = 100mm, Outer radius = 120mm, No. of teeth = 17, Diametral pitch = 0.1583, Pitch diameter = 107.391, Whole depth = 13.82386, Addendum = 6.31712, Dedendum = 7.50674, Clearance = 1.18962, Circular tooth thickness = 9.92291, Pitch angle = 90.0004, Pitch cone radius = 53.6955, Face width = 17.89850, Outside diameter = 107.39103, Back cone radius = 8.769 x 10 17, Virtual number of teeth = 2.77 x 10 17. A) Sketch of bevel gear in catia [12] Fig 1: Sketch of bevel gear in catia IJSDR1805012 International Journal of Scientific Development and Research (IJSDR) www.ijsdr.org 66
B) Sketch of bevel gear teeth in catia C) Model of bevel gear teeth in catia Fig 2: Sketch of bevel gear teeth in catia D) Bevel gear final model in catia Fig 3: Model of bevel gear teeth in catia 5. ANALYTICAL RESULTS Fig 4: Model of bevel gear in catia The analyzing of bevel gear is done in Ansys 17.2 software, in this paper the materials which are used are for analyzing of bevel gear are structural steel, gray cast iron, and stainless steel. For calculating maximum and minimum value of Equivalent stress, equivalent elastic strain, and total deformation of bevel gear while applying the moment at 1000N-m and 2000 N-m. [13] 1. Structural steel IJSDR1805012 International Journal of Scientific Development and Research (IJSDR) www.ijsdr.org 67
A) Moment at 1000 N-m Fig 5: equivalent stress at 1000N-m for structural steel Fig 6: equivalent elastic strain at 1000N-m for structural steel Fig 7: total deformation at 1000N-m for structural steel IJSDR1805012 International Journal of Scientific Development and Research (IJSDR) www.ijsdr.org 68
B) Moment at 2000 N-m Fig 8: equivalent stress at 2000N-m for structural steel Fig 9: equivalent elastic strain at 2000N-m for structural steel Fig 10: total deformation at 2000N-m for structural steel IJSDR1805012 International Journal of Scientific Development and Research (IJSDR) www.ijsdr.org 69
2. Gray cast iron A) Moment at 1000 N-m Fig 11: equivalent stress at 1000N-m for gray cast iron Fig 12: equivalent elastic strain at 1000N-m for gray cast iron Fig 13: total deformation at 1000N-m for gray cast iron IJSDR1805012 International Journal of Scientific Development and Research (IJSDR) www.ijsdr.org 70
B) Moment at 2000 N-m Fig 14: equivalent stress at 2000N-m for gray cast iron Fig 15: equivalent elastic strain at 2000N-m for gray cast iron Fig 16: total deformation at 2000N-m for gray cast iron IJSDR1805012 International Journal of Scientific Development and Research (IJSDR) www.ijsdr.org 71
3. Stainless Steel A) Moment at 1000 N-m Fig 17: equivalent stress at 1000N-m for stainless steel Fig 18: equivalent elastic strain at 1000N-m for stainless steel Fig 19: total deformation at 1000N-m for stainless steel IJSDR1805012 International Journal of Scientific Development and Research (IJSDR) www.ijsdr.org 72
B) Moment at 2000 N-m Fig 20: equivalent stress at 2000N-m for stainless steel Fig 21: equivalent elastic strain at 2000N-m for stainless steel Fig 22: total deformation at 2000N-m for stainless steel 6. CONCLUSION A bevel gear is a type of gear which is used in transmitted the power between two perpendicular shafts, bevel gear is modeled in Catia V5 R20 software. While analyzing part is done in Ansys 17.2 software. In which we use to calculate equivalent stress, IJSDR1805012 International Journal of Scientific Development and Research (IJSDR) www.ijsdr.org 73
equivalent elastic strain, total deformation for maximum and minimum value at the moment of 1000N-m and 2000N-m using material structural steel, gray cast iron, and stainless steel. A) Static structural Analysis for moment at 1000 N-m (Maximum) Materials Equivalent Stress Equivalent Elastic Strain Total deformation Structural steel 6.2672 X 10 6 3.134 X 10-5 1.4346 X 10-6 Gray cast iron 6.2697 X 10 6 5.7006 X 10-5 2.573 X 10-6 Stainless steel 6.2658 X 10 6 3.247 X 10-5 1.4967 X 10-6 B) Static structural Analysis for moment at 1000 N-m (Minimum) Materials Equivalent Stress Equivalent Elastic Strain Total deformation Structural steel 1346.7 9.6099 X 10-9 0 Gray cast iron 1342.7 1.7585 X 10-8 0 Stainless steel 1349.7 9.9249 X 10-9 0 C) Static structural Analysis for moment at 2000 N-m (Maximum) Materials Equivalent Stress Equivalent Elastic Strain Total deformation Structural steel 1.2534 X 10 7 6.2681 X 10-5 2.8692 X 10-6 Gray cast iron 1.2539 X 10 7 0.00011401 5.1461 X 10-6 Stainless steel 1.2532 X 10 7 6.4939 X 10-5 2.9934 X 10-6 D) Static structural Analysis for moment at 2000 N-m (Minimum) Materials Equivalent Stress Equivalent Elastic Strain Total deformation Structural steel 2693.4 1.922 X 10-8 0 Gray cast iron 2685.3 3.5171 X 10-8 0 Stainless steel 2699.3 1.985 X 10-8 0 REFERENCES [1] Bhandari V. B, (2003), Design of Machine Elements, Tata McGraw-Hill Publishing Company ltd, New Dehi. [2] Sayel M. Fayyad, Nabil Musa, Hassan Dabbas, Muhammad Gogazeh, Static And Dynamic Analysis Of Bevel Gear Set, IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE), Volume 14,Issue 5 Ver III (Sep-Oct,2017), pp 01-07.K.V.N. [3] Rohan R. Kurlapkar, M. M. Mirza, V. M. Naik, Design and Static Structural Analysis of Bevel Gear, International Journal of Engineering Trends and Technology (IJETT) Volume 35 Number, 7-May,2016. [4] Chiu-Fan Hsieh, You-Qing Zhu, The Influence of Design Parameters on Straight Bevel Gear Dynamics, Mechanical Engineering Research, Vol. 5, No.2(2015). [5] Ratnadeepsinh M. Jadeja, Dipeshkumar M. Chauhan, Jignesh D. Lakhani, Bending Stress Analysis of Bevel Gears, International Journal of Innovative Research in Science, Engineering and Technology, Vol.2,Issue 7,July 2013. IJSDR1805012 International Journal of Scientific Development and Research (IJSDR) www.ijsdr.org 74
[6] R. M. Jadeja, D. M. Chauhan, A Review On Design, Analysis And Manufacturing Of Spiral Bevel Gear, International Journal of Engineering Research and Technology (IJERT) Vol. 2 Issue 4, April-2013. [7] Iresh Bhavi, Vinay Kuppast, Shivakant Kurbet, Finite Element Analysis of Spiral Bevel Gears Pair Used in an Automobile Differential Gear Box, International Journal of Advances in Scientific Research and Engineering (IJASRE), Vol.3, Special Issue 1 Aug 2017. [8] Shreya Gelani, Prof. Hadiya Atif Valiulla, Prof. Gauravi Joshi, Topology Optimization of Spiral Bevel Gear-A Review, International Journal of Engineering Development and Research (IJEDR), Volume 5,Issue 2,2017. [9] Nitin Chaudhari, DR. D. N. Kamble, Design And Analysis Of Spiral Bevel Gear With Minimized Weight, International journal Of Novel Research and Development (IJNRD), Volume 2, Issue 6 June 2017. [10] Sachin Gupta, Dr. P. S Chauhan, Stress Analysis of Bevel Gear Tooth using FEA: A Review, International Journal for Scientific Research and Development, Vol.4, Issue 02,2016. [11] Haidar Fadhil AL-Qrimli, Ahmed M. Abdelrhman, Karam S. Khiled, Numerical and Theoretical Analysis of a Straight Bevel Gear Made from Orthotropic Materials, Jordan Journal of Mechanical and Industrial Engineering, Volume 11 Number 1, January. 2017 ISSN 1995-6665 Pages 35-40 [12] CATIA user manual V5R20. [13] ANSYS user manual 17.2 IJSDR1805012 International Journal of Scientific Development and Research (IJSDR) www.ijsdr.org 75