Advanced Research Journals of Science and Technology
ADVANCED RESEARCH JOURNALS OF SCIENCE AND TECHNOLOGY
(ARJST)
GEOMETRIC OPTIMIZATION OF CONTACT RATIO IN SPUR GEAR USING FINITE ELEMENT ANALYSIS
2349-1845
P.Kamal Kumar 1, S.L. Narasimha Reddy 2, 1Research Scholar,Department of Mechanical Engineering,Siddhartha Institute of Engineering And Technology,Ibrahimpatnam, Telangana,India. 2Professor , Department of Mechanical Engineering, Siddhartha Institute of Engineering And Technology,Ibrahimpatnam, Telangana,India.
Abstract Maximum contact and fillet stresses in normal and high contact ratio spur gears are evaluated based on load sharing ratio using finite element method through single- and multi-point loaded models as well as multi-pair contact model. The multi-pair contact model has been justified as an appropriate one for the present analysis as this model exclusively considers the influence of the loaded adjacent teeth and the Hertz contact deflections. A detailed parametric study on the load sharing ratio and the respective stresses has also been carried out to analyze the effect of addendum height, the pressure angle, gear ratio, teeth number, and tooth size. Finally, the importance of load sharing ratio and the critical loading points for maximum fillet and contact stresses in normal and high contact ratio spur gears is highlighted for the effective design. The aim this project work is to provide optimum CONTACT RATIO for spur in contact pair load sharing condition, by using geometric optimization technique.
*Corresponding Author:
The gears in a transmission are analogous to the wheels in a pulley. An advantage of gears is that the teeth of a gear prevent slipping.
P.Kamal Kumar, Research Scholar, Department Of Mechanical Engineering, Siddhartha Institute of Engineering And Technology,Ibrahimpatnam, Telangana,India.
When two gears of unequal number of teeth are combined a mechanical advantage is produced, with both the rotational speeds and the torques of the two gears differing in a simple relationship.
Published: November 23, 2015 Review Type: peer reviewed Volume: II, Issue : III Citation: P.Kamal Kumar,Research Scholar (2015) GEOMETRIC OPTIMIZATION OF CONTACT RATIO IN SPUR GEAR USING FINITE ELEMENT ANALYSIS
PROBLEM DESCRIPTION: Gear failure causes by varies things, design failures are high and predictable, mainly gear tooth is getting week and slipping and tooth fracture is occurring while it is pairing other gear due to load sharing and contact b/w tooth. This is an attempt to rectify the above sad failures with the help of FEM by changing tooth fillet radius values. INTRODUCTION TO GEARS A gear is a rotating machine part having cut teeth, or cogs, which mesh with another toothed part in order to transmit torque. Two or more gears working in tandem are called a transmission and can produce a mechanical advantage through a gear ratio and thus may be considered a simple machine. Geared devices can change the speed, magnitude, and direction of a power source. The most common situation is for a gear to mesh with another gear, however a gear can also mesh a non-rotating toothed part, called a rack, thereby producing translation instead of rotation.
In transmissions which offer multiple gear ratios, such as bicycles and cars, the term gear, as in first gear, refers to a gear ratio rather than an actual physical gear. The term is used to describe similar devices even when gear ratio is continuous rather than discrete, or when the device does not actually contain any gears, as in a continuously variable transmission. The earliest known reference to gears was circa 50 A.D. by Hero of Alexandria, but they can be traced back to the Greek mechanics of the Alexandrian school in the 3rd century BC and were greatly developed by the Greek polymath Archimedes (287-212 BC). Types of Gears External vs. internal gears Spur Helical Double helical Bevel Hypoid Crown Worm Non-circular Rack and pinion Epicyclic Sun and planet Harmonic drive Cage gear
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Advanced Research Journals of Science and Technology
INTRODUCTION TO SPUR GEARS
DESIGN CALCULATIONS OF SPUR GEAR
Spur gears are the most common type of gears. They have straight teeth, and are mounted on parallel shafts. Sometimes, many spur gears are used at once to create very large gear reductions.
Power = 5.44KW at 8000rpm BHN = 126- 578 Modulus of elasticity = 210 Gpa = 210 × 103 N/mm2 Tooth number = 32 Module (m) = 1mm We know that m = D/T D = Pitch circle diameter T = Number of teeth m = D/T → D = m × T = 1 × 32 = 32mm Gear ratio = 1:1 Pressure angle φ = 20 Tangential tooth load WT = P/V × Cs P = Power transmitted in watts V = pitch line velocity in m/s = πDN/60 D = pitch circle diameter V= πDN/60 = (π×0.05×8000)/60 = 20.94m/s Cs = Service factor = 1 WT = 5.44/90.94 × 1 = 259.789
Spur gears are the simplest form of Gears available. They are also the most commonly used gears in the market. Spur Gears are found generally in the form of a cylinder or disk. These gears are applied for varying the force and speed of a rotating axle. These gears have a straight teeth. They are usually mounted on parallel shafts. These days mostly the tooth form is based on the involute curve. For creating large gear reductions, many spur gears are used together. However, these spur gears can mesh correctly only if they get fitted to parallel axles. That is the reason why their teeth are cut in a manner, for making the leading edges remain parallel to the line of axis of rotation. Not withstanding the basic limitation of center distance, spur gears are able to provide a constant and positive speed drive. The speed can be varied by increasing or decreasing the teeth number in the driving gears. Spur Gears are used typically in applications where noise control does not matter. But in cases where noise does matter, but higher speeds are also essential a nylon or non-metallic gears are best. These can be then be operated easily up to speeds of around 2400 feet per minute. This way noise and vibration can easily be prevented. The following image shows the basic geometry of these gears. LOAD CHANGE OVER POSITIONS IN NCR AND HCR GEAR PAIRS
Dynamic tooth load = WD = WT + WI
For cut teeth face width b is taken as (3pc to 4pc) or (9.5 to 12.5) b = 12.5 = 12.5 × 12.5 C = a deformation (or) dynamic factor in N/mm
K = 0.111 For 200 full depth involute system e = tooth error action = 0.0150
Either a double or a single pair contact occurs in a mesh cycle between the highest point of tooth contact (HPTC) and the lowest point of tooth contact (LPTC) in the case of a NCR gear pair, whereas it is either a triple or double pair contact in the case of a HCR gear pair. The respective transition contact points that occur along the contact profiles of the NCR and the HCR gears are shown in Figs. 1 and 2. Since the points A_, B_, C_, and D_ (Fig. 1), respectively, represent LPTC, LPSTC, HPSTC, and HPTC for NCR gear pair, henceforth these points will be DESIGN CALCULATIONS OF SPUR GEAR Specifications: Parameters value Gear ratio (i) 1:1 Tooth number 32 Module (m) 2.65 mm Pressure angle (α0) 20° Addendum modification (xp & xg) 0 Addendum factor (ya) NCR gear pair 1 HCR gear pair 1.223 Dedendum factor (yf) ya + 0.25 Cutter tip radius (p) 0.3m Rim thickness 5m Elastic modulus (E) 210Gpa Poisson’s ratio (v) 0.3 Normal load (Fn) 10N
INTRODUCTION TO CAD Computer-aided design (CAD), also known as computer-aided design and drafting (CADD), is the use of computer technology for the process of design and designdocumentation. Computer Aided Drafting describes the process of drafting with a computer. CADD software, or environments, provide the user with input-tools for the purpose of streamlining design processes; drafting, documentation, and manufacturing processes. CADD output is often in the form of electronic files for print or machining operations. The development of CADD-based software is in direct correlation with the processes it seeks to economize; industry-based software (construction, manufacturing, etc.) typically uses vector-based (linear) environments whereas graphic-based software utilizes rasterbased (pixelated) environments.
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Advanced Research Journals of Science and Technology
MODEL OF SPUR GEAR
STRUCTURAL ANALYSIS ON SPUR GEAR FOR EXISTING Material: mild steel
The above image shows sketcher
The above image shows imported model
The above image shows spur gear
The above image shows meshed model
The above image shows spur gear assembly INTRODUCTION TO FEA Finite Element Analysis (FEA) was first developed in 1943 by R. Courant, who utilized the Ritz method of numerical analysis and minimization of variational calculus to obtain approximate solutions to vibration systems. Shortly thereafter, a paper published in 1956 by M. J. Turner, R. W. Clough, H. C. Martin, and L. J. Topp established a broader definition of numerical analysis. The paper centered on the "stiffness and deflection of complex structures".
The above image shows load applied moments
FEA consists of a computer model of a material or design that is stressed and analyzed for specific results. It is used in new product design, and existing product refinement. A company is able to verify a proposed design will be able to perform to the client's specifications prior to manufacturing or construction. Modifying an existing product or structure is utilized to qualify the product or structure for a new service condition. In case of structural failure, FEA may be used to help determine the design modifications to meet the new condition.
The above image shows total deformation
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Advanced Research Journals of Science and Technology
The above image shows stress
The above image shows safety factor
MODEL ANALYSIS ON SPUR GEAR FOR EXISTING
The above image shows alternating stress The above image shows total deformation mode 4
STRUCTURAL ANALYSIS ON SPUR GEAR FOR EXISTING MATERIAL: ALUMINUM
The above image shows total deformation mode 5
FATIGUE ANALYSIS ON SPUR GEAR FOR EXISTING
The above image shows total deformation
The above image shows life The above image shows stress
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Advanced Research Journals of Science and Technology
STRUCTURAL ANALYSIS ON SPUR GEAR WITH SLOT CUTTING MATERIAL: mild steel
The above image shows total deformation mode The above image shows slot cutting
The above image shows total deformation mode The above image shows total deformation
FATIGUE ANALYSIS ON SPUR GEAR WITH SLOT CUTTING
The above image shows stress
MODEL ANALYSIS ON SPUR GEAR WITH SLOT CUTTING
The above image shows total deformation mode
The above image shows life
The above image shows safety factor
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Advanced Research Journals of Science and Technology
RESULT TABLE AND GRAPHS STRUCTURAL ANALYSIS Mild steel
The above image shows alternating stress
STRUCTURAL ANALYSIS ON SPUR GEAR WITH HOLES
Aluminum A380
Existing
Slot cutting
With holes
Existing
Slot cutting
With holes
Total deformation
0.0041
0.0062
0.0072
0.011
0.0180
0.020
Directional deformation
0.0017
0.0035
0.0032
0.004
0.010006
0.0091
Stress
9.46
12.84
9.630
9.3002
12.536
9.334
Strain
5.4649e5
8.4808e-5
6.5208e5
0.00015
0.00023
0.00017
Shear Stress
2.4276
4.5939
3.4699
2.4954
4.6088
3.4452
Shear Strain
3.1559e5
5.972e-5
4.5109e5
9.349e5
0.000172
0.00012
MATERIAL: mild steel
MODEL ANALYSIS Mild steel
The above image shows total deformation
Aluminum A380
Existing
Slot cutting
With holes
Existing
Slot cutting
With holes
Total deformation mode 1Hz
0.42083
0.49946
0.48936
0.42193
0.50063
0.49026
Total deformation mode 2 Hz
0.42086
0.4995
0.48951
0.42195
0.50065
0.49062
Total deformation mode 3 Hz
0.42092
0.49967
0.48957
0.42219
0.5012
0.49081
Total deformation mode 4 Hz
149.46
8.1648
187.74
149.43
8.1823
187.7
Total deformation mode 5 Hz
212.17
80.353
266.36
212.26
81.201
266.42
FATIGUE ANALYSIS Mild steel
The above image shows stress
Aluminum A380
Existing
Slot cutting
With holes
Existing
Slot cutting
With holes
LIFE
1e9
1e9
1e9
1e11
1e11
1e11
Safety factor
9.1075
6.711
8.9505
14.376
10.665
14.323
Alternating stress
9.4647
12.845
9.6308
9.3002
12.536
9.3343
FATIGUE ANALYSIS ON SPUR GEAR WITH HOLES
The above image shows life
The above image shows total deformation
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Advanced Research Journals of Science and Technology
Conclusion This project work deals with’’ geometric optimization of contact ratio in spur gear using fem’’ to optimize contact ratio in spur gear pair by using geometric optimization technique and deals with reduction of weight to increase mechanical efficiency. Initially letrecher survey is done on axle analysis to observe previous researches/ studies. Structural analyses is done to analyze stress, strain and deformations at working load conditions, model analysis is done to evaluate vibrations in assembly, these vibrations depends on geometric shape and material. The above image shows stress
Static analysis is done on standard model and weight reduced model 1 (material removed at center).to find structural characteristics. In modified model frequency value s was having more than 65HZ difference so model1 is not useful for assembly. New model was prepared to stabilize vibrations and contact area/ratio was increased by varying tooth geometry and analysis is conducted to validate and compare with above models.
The above image shows strain
As per the analysis results by adding corner to the teeth gear ratio will be increased ,by adding holes weight can be decreased and vibrations will be stabilized(within 65 HZ difference from standard model)aluminum 360 material is introduced to reduce some more weight which in turns increase the mechanical efficiency. REFERENCES Spur Gear Contact Stress Analysis and Stress Reduction by Experiment Method Prafulla M. Chor[1], Dr. PriamPillai[2] M. E. Machine Design, PHCET, Rasayani,Mumbai Professor, Mechanical Engineering, PIIT, Panvel,Mumbai International Journal of Engineering Research and General Science Volume 3, Issue 3, May-June, 2015 “Contact Stress Analysis of Spur Gear by Photoelastic Technique and Finite Element Analysis.”
The above image shows shear stress
Abhijit Mahadev Sankpal1 , M. M. Mirza2 1 Mechanical Engineering Department, PG Student, R.I.T. Islampur (M.S.), India. 2 Mechanical Engineering Department, Faculty, R.I.T. Islampur (M.S.), India. DYNAMIC ANALYSIS OF HIGH-CONTACT-RATIO SPUR GEARS WITH ASYMMETRIC TEETH Proceedings of IMECE2008 2008 ASME International Mechanical Engineering Congress and Exposition October 31-November 6, 2008, Boston, Massachusetts, USA
The above image shows factor of safety
F. KARPAT Department of Mechanical Engineering Uludag University Bursa, 16059, Turkey S. EKWARO-OSIRE Department of Mechanical Engineering Texas Tech University Lubbock, Texas 79409, USA
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Advanced Research Journals of Science and Technology
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & MANAGEMENT DETERMINESTATIC TRANSMISSION ERRORS OF INVOLUTE SPUR GEAR BODIES IN MESH APPROPRIATE MODELS OF CONTACT AND BENDING STRESSES USING FINITE ELEMENT ANALYSIS
Timo Kiekbusch1,* Daniel Sappok1 Bernd Sauer1 Ian Howard2 1 University of Kaiserslautern, Institute for Machine Elements, Gears and Transmissions, Germany 2 Curtin University Perth, Department of Mechanical Engineering, Australia
Deepak Malviya *1,Dr. P.K. Sharma2, Prof. Rajkumar Shivankar3 1, 2, 3Mechanical Engineering Department, NRI Institute of Science and Technology, Bhopal (M.P.) India
AN OPTIMAL GEAR DESIGN METHOD FOR MINIMIZATION OF TRANSMISSION ERROR AND VIBRATION EXCITATION Cameron P. Reagor The dissertation of Cameron P. Reagor was reviewed and Dissertation Adviser Chair of Committee
Modeling and Finite Element Analysis of Spur Gear International Journal of Current Engineering and Technology
AUTHOR
Spur Gear Tooth Stress Analysis And Stress Reduction IOSR Journal of Mechanical and Civil Engineering (IOSRJMCE) e-ISSN: 2278-1684 “STATIC AND DYNAMIC ANALYSIS OF HIGH CONTACT RATIO SPUR GEAR DRIVE” Effect of Face Contact Ratio on Load Sharing Based Fillet Stress in Asymmetric Helical Gear Drives Universal Journal of Mechanical Engineering R.Prabhu Sekar*, G.Muthuveerappan Department of Mechanical Engineering, Machine Design Section, Indian Institute of Technology, Madras, Tamil Nadu *Corresponding author
P.Kamal Kumar, ResearchScholar, Department of Mechanical Engineering, Siddhartha Institute of Engineering And Technology, Ibrahimpatnam, Telangana,India.
Effect of Addendum Height and Teeth Number on Asymmetric Normal Contact Ratio Spur Gear Based on Load Sharing Universal Journal of Mechanical Engineering P. Marimuthu*, G. Muthuveerappan Mechanical Engineering, Indian Institute of Technology Madras, Chennai *Corresponding Author Contact Stress Analysis of Spur Gear Teeth Pair Ali Raad Hassan
S.L. Narasimha Reddy, Professor , Department of Mechanical Engineering, Siddhartha Institute of Engineering And Technology, Ibrahimpatnam, Telangana,India.
Calculation of the Combined Torsional Mesh Stiffness of Spur Gears with Two- and Three-Dimensional Parametrical FE Models
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