International Journal of Current Research and Review
ISSN: 2231-2196 (Print)ISSN: 0975-5241 (Online)
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IJCRR - 4(17), September, 2012

Pages: 164-171

Date of Publication: 14-Sep-2012


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STRESS ANALYSIS OF SPUR GEAR USING FINITE ELEMENT METHOD - A REVIEW

Author: Sushil Kumar Tiwari, Upendra Kumar Joshi

Category: Technology

Abstract:The basic aim of this review paper is to provide the information for calculating the stresses of an involute gear in meshing. Gears are critical component in the rotating machinery. The researchers throughout the years had given various research methods such as Theoretical, Numerical and Experimental. We prefer the Theoretical and Numerical methods because Experimental testing can be expensive. This study says Finite Element Method is the best numerical solution for calculating gear stress.

Keywords: Spur Gear, Stress Calculation, Bending Stress, Hertz Stress, Finite Element Method.

Full Text:

INTRODUCTION
Gears are use to transmit power and motion from one shaft to another. Spur gear is cylindrical in form and has teeth, which are of involute form in most cases. The tooth surface elements are parallel to the gear axis. Each gear tooth may consider as a cantilever beam. When it transmits the load, it subjected to bending. The bending stress is highest at the fillet and can caused breakage or fatigue failure of tooth in root region, whereas contact stresses are on the both side of the tooth may causes Scoring Wear, Bending and Pitting fatigue.[1] Pitting fatigue is a compressive fatigue occurring at the point of maximum Hertzian stress. Gear stresses are affected by surface hardness, carbon content, metallurgical structure and lubrication condition. Gear tooth strength is the ability to resist tooth breakage and the ability to resist pitting is referred as durability.[1] To calculating bending stress, Lewis Formula is used, and for calculating contact stress Hertz equation can be applied in spur gear.[2]

BENDING STRESS (LEWIS FORMULA) [1]
A gear tooth is essentially a stubby cantilever beam. At the base of the beam, there is tensile stress on the loaded side and compressive stress on the opposite side. The ability of gear tooth to resist tooth breakage usually referred to as their „Beam Strength?. Wilfred Lewis accurately calculated this in 1893; he conceived the idea of inscribing a parabola of uniform strength inside a gear tooth.



In the centre of the band, there is a point of maximum compressive stress. Directly underneath this point, there is a maximum subsurface shear stress. Just ahead of the band of contact, there is a narrow band of the compression and just behind the band of contact; there is a narrow region of tensile stress. A bit of metal on the surface of a gear tooth goes through a cycle of compression and tension each time, when a mating gear tooth passes over it. If gear tooth loaded heavily enough, and there will usually be evidence of both surface cracks and plastic flow on the contacting surface, and there may be a rupturing of the metal due to surface shear stresses. The stress on the surface of gear teeth are usually determined by formula derived from the work of H. Hertz?s; and these stresses are termed as Hertz stress. Hertz determined the width of the contact band and the stress pattern when various geometric shapes were loaded against each other. Considering figure (5),

Above Hertz formula can be applied to Spur Gears quite easily by considering that the contact condition of gears are equivalent to those of cylinders having the same radius of curvature at the point of contact as the gear have. Ali Raad Hassan [8] presented formula for calculating Hertz equation for contact stresses in the pair of mating spur gear teeth. As figure (6)

Where and are the pitch radius of the Pinion and Gear respectively and is the pressure angle. Equations (2) and (3) are use for quick calculation of Bending and Contact stress of a pair of mating gear efficiently. American Gear Manufacture Association (AGMA) provides the standard equations for calculating bending and contact stresses for a pair of mating gear including various factors. Following literature review gives a lot of information about stress calculation based on Lewis formula, Hertz theory, AGMA/ANSI (American National Standards Institute) equations and Finite Element Method.

LITERATURE REVIEW
Shuting Li (2002) researcher, performed loaded tooth contact analysis of a three dimensional, thin-rimed gear by presenting a method that combines the Mathematical Programming Method (MPM) with the 3-dimentional finite element method and compare the results with experiment. and concluded that FEM with MPM efficiently calculates bending stress in gears.[3] Andrzej Kawalec (2006) author gives comparative study of tooth-root strength evaluation methods used within International Standard Organization (ISO) and AGMA standards then verifying them with Finite Element method. The results allow for a better understanding of existing limitation in the current standards applied in engineering practice as well as provide a basis for future improvement of gear standard.[4] Jose I. Pedrero (2007) researcher used a nonuniform model of load distribution along the line of contact. He says if the load is, assume to be uniformly distributed along the line of contact, simple equations given by the linear theory of elasticity and the Hertzian contact model are not good agreement with experimental results. In this paper a non uniform model has been considered for stress analysis at contact ratio 2 and 2.5, and concluded that,

1. The critical tooth-root stress corresponds to contact at the inner point of the outer interval of the two pair tooth contact, and teeth loaded 60% of total transmitted load.

2. The critical contact stress corresponds to either one of the three following condition.

3. Contact at the inner point of contact and teeth loaded with 25% of the total transmitted load.

4. Contact at the inner point of the two pair tooth contact and teeth loaded with 40% of the total transmitted load.

5. Contact at the outer point of the inner interval of the two pair tooth contact, and teeth loaded with 60% of the total transmitted load.[5]

Shuting Li (2007) researcher presented 3- Dimentional Finite Element Method to conduct Surface contact stress (SCS) and Root bending stress (RBS) calculations for a pair of spur gear with Machining Error (ME), Assembly Error (AE) and Tooth Modification(TM). Moreover, found that ME, AE and TM exerts great effects on SCS and RBS of the gear. Results obtained by International Standard Organization (ISO) and Japan Gear Manufacturing Association (JGMA) standards are comparing with result of Finite Element Analysis. [6] Shuting Li (2008) researcher investigates the effect of addendum modification on contact strength, bending strength and basic performance parameters of spur gear. A face contact model of teeth and MPM and 3D finite element methods are used together to conduct loaded tooth contact analysis. He concluded that Hertz formula is not exact enough for the contact stress calculation because in engagement position the contact point is for away from the pitch point, also Hertz formula cannot be use for contact stress calculation of the gear at Tip or Root contact. Contact stress and contact width are changed slightly if addendum becomes longer and number of teeth is not changed.[7] Ali Raad Hassan (2009) author is analysed contact stress between two spur gear teeth in different contact position, between 0º to 30º. Start with an angle of 0º and end at 30º with an interval of 3º with corresponding length of contact and contact ratio. and found that a highest value of contact stress is at beginning of contact and then starts reducing until it reaches the location of single tooth contact. Result obtained by finite element analysis is compare with theoretical value which is found at geometrical contact point.[8] Rubin D. Chacon (2010) researcher analysed the contact stress between spur gear teeth using a plane model and validate Hertz stress and AGMA contact stress with finite element contact stress. Then concluded that FEM is able to simulate contact stress in a pair of mating gear, the contact stress is highest at higher point on the involute and lower at a single pair of teeth. Assume the full load transmitted and minimal at the pitch point of contact.[9] Konstandinos G. Raptis, (2010) author performed photo-elasticity test to determine stresses in a pair of mating gear. Obtained experimental results were comparing with the theoretical value of maximum stress at gear tooth root (when tooth is loaded at their most unfavorable contact point i.e. highest point of single tooth contact). Then concluded that the result obtained by the applied method is in reasonable value whereas it rises with increasing number of teeth on the large gear.[10] Wei Yangang,(2010) author provided a theoretical procedure for obtaining maximum contact stress at different point in meshing under the light of Hertz formula. and concluded that when the number of teeth on small gear is smaller than a certain value, the maximum contact stress in the meshing process is not generated in the inner critical point in the single tooth meshing region of the small gear.[11] Xianzhang FENG (2011) author use a precise model in large-scale CAD software and define the stress and displacement field to determine the maximum equivalent stress and maximum displacement. By defining the quasi-static characteristic of finite element model, shows that model can accurately simulate the distribution of equivalent stress and displacement change in the process of teeth meshing. The results are well agree with the actual meshing law and not only verify the correctness of model but also expect to dynamic analysis of gear.[12] Ignacio Gonzlez-Peraz (2011) researcher developed a finite element model and validate in terms of contact area, pressure distribution and maximum contact pressure for those cases where the Hertz theory can be applied and provide partial crowning to the finite element model where Hertz theory do not work properly. And concluded that analysis results gives good agreement with Hertz theory for calculating maximum contact pressure, contact area, and deflection with minute errors.[13] Ali Kamil Jabur, (2011) author investigates the characteristics of an involute gear system including contact stress between a pair of the gear from 3-dimansional analysis and compared the result with experimental data. Experimental setup uses DC servomotor and mounting the strain gauge in the tooth of the gear made by Polyimide materials. and concluded that increasing the spur gear design parameters (number of teeth with module) leads to improvement in the tooth strength and increasing the thickness of critical section and makes it able to withstand higher load.[14] S. Sankar, (2011) author used circular root fillet instead of standard trochoidal root fillet in gear. and concluded that the tooth deflection in the circular root fillet is less when compared to the trochoidal root fillet, further there is appreciable reduction in bending stress and contact shear stress for circular root fillet design in comparison to that of trochoidal root fillet design.[15] Seok- Chul Hwang (2011) author compared the variation of contact stress during rotation with contact stress at Lowest Point of Single Tooth Contact (LPSTC) and concluded that gear design that consider the contact stress in a pair of mating gear is more severe than that of the AGMA standard.[16] Massimiliano Pau (2012) researcher performed a tooth contact analysis, and contact area, contact pressure using an ultrasonic experimental setup. The results provide the information about the size and shape of the nominal contact area and contact pressure distribution. He concluded that the ultrasonic method has good potential as an effective tool in investigating contact problem in gear.[17]

CONCLUSION
The above literature review presents that the Finite Element Method is widely used for stress analysis in a pair of gear. In addition, FEM software has been use for performing meshing simulation. Almost in all of the above cases, contact stress calculation and Bending Stress calculation play more significant role in the design of gear. This study shows that Hertz theory is the basis of contact stress calculation and Lewis formula is use for calculating bending stress in a pair of gear. Theoretical result obtained by Lewis formula and Hertz equation and results found by AGMA/ANSI equations are comparable with Finite Element Analysis of spur gear.

References:

1. Darle W. Dudley, Practical Gear Design, McGraw-Hill Book Company, 1954

2. Peter R.N. Childs, Mechanical Design, Second edition, Elsevier ButterworthHeinemaan, 2004

3. Shuting Li, „Gear Contact Model and Loaded Tooth Contact Analysis of a ThreeDimensional Thin-Rimmed Gear? Journal of mechanical Design, ASME, 2002; vol.124/511.

4. Andrzej Kawalec, Jerzy Wiktor, Dariusz Ceglarek, „Comparative Analysis of Toothroot Strength Using ISO and AGMA Standard in Spur and Helical Gear With FEM-based Verification? Journal of mechanical Design, ASME, 2006; vol. 128/1141.

5. Jose I. Pedrero, Izaskun I.Vallejo, Miguel Pleguezuelos, „Calculation of Tooth Bending Strength and Surface Durability of High Transverse Contact Ratio Spur and Helical Gear Drives? Journal of mechanical Design, ASME, 2007; vol. 129/69.

6. Shuting Li, „Finite Element Analyses for Contact Strength and bending Strength of a pair of spur gears with Machining Errors, Assembly Errors and Tooth Modifications? Mechanism and Machine Theory, Elsevier, 2007; 42: 88-114.

7. Shuting Li, „Effect of Addendum on Contact Strength, Bending Strength and Basic Performance Parameters of a pair of Spur Gears? Mechanism and Machine Theory, Elsevier, 2008; 430: 1557-1584

8. Ali Raad Hassan,„Contact Stress Analysis of Spur Gear Teeth Pair? WASET 2009; 58

9. Rubin D. Chacon, Luis J. Adueza, „Analysis of Stress due to Contact between Spur Gears? Wseas.us, 2010

10. Konstandinos G. Raptis, Theodore N. Costopoulos „Rating of Spur Gear Strength using Photo elasticity and the Finite Element Method? American Journal of Engineering and Applied Sciences, 2010; 3(1): 222-231.

11. Wei Yangang, Zhang Xiujuan, Liu Yankui, „Theoretical research on the maximum Contact Stress of Involute spur Cylindrical Gear Pair in the External Meshing Process? IEEE,2010

12. Xianzhang FENG, „Analysis of field of Stress and Displacement in process of Meshing Gears? vol.5, 2011

13. Ignacio Gonzalez-Perez, Jose L. Iserte, Alfonso Fuentes, „Implementation of Hertz theory and validation a Finite Element Model for stress analysis of gear drives with localized bearing contact? Mechanism and Machine Theory, Elsevier, 2011; 46: 765-783

14. Ali Kamil Jebur, L.A.Khan, Y.Nath, „Numerical and Experimental Dynamic Contact of Rotating Spur Gear? Canadian Center of Science and Education, Modern Applied Science vol.5;2011

15. S. Sankar. Muthusamy Natraj, „Profile Modification- A Design approach for increasing the Tooth Strength in Spur Gear? International Journal of Advance Manufacturing Technology, Springer,2011; 55: 1-10.

16. Seok-Chul Hwang, Jin-hwan Lee, „Contact Stress Analysis for a pair of Mating Gears? Mathematics and computer modelling, Elsevier, 2011

17. Massimiliano Pau,Bruno leban, Antonio Baldi, Francesco Ginesu, „Experimental Contact pattern Analysis for a Gear-Rack system? Meccanica,Springer,2012; 47: 51-61

Announcements

Dr. Pramod Kumar Manjhi joined Editor-in-Chief since July 2021 onwards

COPE guidelines for Reviewers

SCOPUS indexing: 2014, 2019 to 2021


Awards, Research and Publication incentive Schemes by IJCRR

Best Article Award: 

One article from every issue is selected for the ‘Best Article Award’. Authors of selected ‘Best Article’ are rewarded with a certificate. IJCRR Editorial Board members select one ‘Best Article’ from the published issue based on originality, novelty, social usefulness of the work. The corresponding author of selected ‘Best Article Award’ is communicated and information of award is displayed on IJCRR’s website. Drop a mail to editor@ijcrr.com for more details.

Women Researcher Award:

This award is instituted to encourage women researchers to publish her work in IJCRR. Women researcher, who intends to publish her research work in IJCRR as the first author is eligible to apply for this award. Editorial Board members decide on the selection of women researchers based on the originality, novelty, and social contribution of the research work. The corresponding author of the selected manuscript is communicated and information is displayed on IJCRR’s website. Under this award selected women, the author is eligible for publication incentives. Drop a mail to editor@ijcrr.com for more details.

Emerging Researcher Award:

‘Emerging Researcher Award’ is instituted to encourage student researchers to publish their work in IJCRR. Student researchers, who intend to publish their research or review work in IJCRR as the first author are eligible to apply for this award. Editorial Board members decide on the selection of student researchers for the said award based on originality, novelty, and social applicability of the research work. Under this award selected student researcher is eligible for publication incentives. Drop a mail to editor@ijcrr.com for more details.


Best Article Award

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A Study by Alkhansa Mahmoud et al. entitled "mRNA Expression of Somatostatin Receptors (1-5) in MCF7 and MDA-MB231 Breast Cancer Cells" is awarded Best Article of Vol 13 issue 06
A Study by Chen YY and Ghazali SRB entitled "Lifetime Trauma, posttraumatic stress disorder Symptoms and Early Adolescence Risk Factors for Poor Physical Health Outcome Among Malaysian Adolescents" is awarded Best Article of Vol 13 issue 04 Special issue on Current Updates in Plant Biology to Medicine to Healthcare Awareness in Malaysia
A Study by Kumari PM et al. entitled "Study to Evaluate the Adverse Drug Reactions in a Tertiary Care Teaching Hospital in Tamilnadu - A Cross-Sectional Study" is awarded Best Article for Vol 13 issue 05
A Study by Anu et al. entitled "Effectiveness of Cytological Scoring Systems for Evaluation of Breast Lesion Cytology with its Histopathological Correlation" is awarded Best Article of Vol 13 issue 04
A Study by Sharipov R. Kh. et al. entitled "Interaction of Correction of Lipid Peroxidation Disorders with Oxibral" is awarded Best Article of Vol 13 issue 03
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A Study by Mohita Ray et al. entitled "Accuracy of Intra-Operative Frozen Section Consultation of Gastrointestinal Biopsy Samples in Correlation with the Final Histopathological Diagnosis" is awarded Best Article for Vol 13 issue 01
A Study by Badritdinova MN et al. entitled "Peculiarities of a Pain in Patients with Ischemic Heart Disease in the Presence of Individual Combines of the Metabolic Syndrome" is awarded Best Article for Vol 12 issue 24
A Study by Sindhu Priya E S et al. entitled "Neuroprotective activity of Pyrazolone Derivatives Against Paraquat-induced Oxidative Stress and Locomotor Impairment in Drosophila melanogaster" is awarded Best Article for Vol 12 issue 23
A Study by Habiba Suhail et al. entitled "Effect of Majoon Murmakki in Dysmenorrhoea (Usre Tams): A Standard Controlled Clinical Study" is awarded Best Article for Vol 12 issue 22
A Study by Ghaffar UB et al. entitled "Correlation between Height and Foot Length in Saudi Population in Majmaah, Saudi Arabia" is awarded Best Article for Vol 12 issue 21
A Study by Siti Sarah Binti Maidin entitled "Sleep Well: Mobile Application to Address Sleeping Problems" is awarded Best Article for Vol 12 issue 20
A Study by Avijit Singh"Comparison of Post Operative Clinical Outcomes Between “Made in India” TTK Chitra Mechanical Heart Valve Versus St Jude Mechanical Heart Valve in Valve Replacement Surgery" is awarded Best Article for Vol 12 issue 19
A Study by Sonali Banerjee and Mary Mathews N. entitled "Exploring Quality of Life and Perceived Experiences Among Couples Undergoing Fertility Treatment in Western India: A Mixed Methodology" is awarded Best Article for Vol 12 issue 18
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A Study by Juna Byun et al. entitled "Study on Difference in Coronavirus-19 Related Anxiety between Face-to-face and Non-face-to-face Classes among University Students in South Korea" is awarded Best Article for Vol 12 issue 16
A Study by Sudha Ramachandra & Vinay Chavan entitled "Enhanced-Hybrid-Age Layered Population Structure (E-Hybrid-ALPS): A Genetic Algorithm with Adaptive Crossover for Molecular Docking Studies of Drug Discovery Process" is awarded Best article for Vol 12 issue 15
A Study by Varsha M. Shindhe et al. entitled "A Study on Effect of Smokeless Tobacco on Pulmonary Function Tests in Class IV Workers of USM-KLE (Universiti Sains Malaysia-Karnataka Lingayat Education Society) International Medical Programme, Belagavi" is awarded Best article of Vol 12 issue 14, July 2020
A study by Amruta Choudhary et al. entitled "Family Planning Knowledge, Attitude and Practice Among Women of Reproductive Age from Rural Area of Central India" is awarded Best Article for special issue "Modern Therapeutics Applications"
A study by Raunak Das entitled "Study of Cardiovascular Dysfunctions in Interstitial Lung Diseas epatients by Correlating the Levels of Serum NT PRO BNP and Microalbuminuria (Biomarkers of Cardiovascular Dysfunction) with Echocardiographic, Bronchoscopic and HighResolution Computed Tomography Findings of These ILD Patients" is awarded Best Article of Vol 12 issue 13 
A Study by Kannamani Ramasamy et al. entitled "COVID-19 Situation at Chennai City – Forecasting for the Better Pandemic Management" is awarded best article for  Vol 12 issue 12
A Study by Muhammet Lutfi SELCUK and Fatma entitled "Distinction of Gray and White Matter for Some Histological Staining Methods in New Zealand Rabbit's Brain" is awarded best article for  Vol 12 issue 11
A Study by Anamul Haq et al. entitled "Etiology of Abnormal Uterine Bleeding in Adolescents – Emphasis Upon Polycystic Ovarian Syndrome" is awarded best article for  Vol 12 issue 10
A Study by entitled "Estimation of Reference Interval of Serum Progesterone During Three Trimesters of Normal Pregnancy in a Tertiary Care Hospital of Kolkata" is awarded best article for  Vol 12 issue 09
A Study by Ilona Gracie De Souza & Pavan Kumar G. entitled "Effect of Releasing Myofascial Chain in Patients with Patellofemoral Pain Syndrome - A Randomized Clinical Trial" is awarded best article for  Vol 12 issue 08
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A review by Chitra et al to analyse relation between Obesity and Type 2 diabetes is awarded 'Best Article' for Vol 10 issue 10 by IJCRR. 
A study by Karanpreet et al "Pregnancy Induced Hypertension: A Study on Its Multisystem Involvement" is given Best Paper Award for Vol 10 issue 09

List of Awardees

A Study by Ese Anibor et al. "Evaluation of Temporomandibular Joint Disorders Among Delta State University Students in Abraka, Nigeria" from Vol 13 issue 16 received Emerging Researcher Award


A Study by Alkhansa Mahmoud et al. entitled "mRNA Expression of Somatostatin Receptors (1-5) in MCF7 and MDA-MB231 Breast Cancer Cells" from Vol 13 issue 06 received Emerging Researcher Award


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Disclaimer: International Journal of Current Research and Review (IJCRR) provides platform for researchers to publish and discuss their original research and review work. IJCRR can not be held responsible for views, opinions and written statements of researchers published in this journal.



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International Journal of Current Research and Review (IJCRR) provides platform for researchers to publish and discuss their original research and review work. IJCRR can not be held responsible for views, opinions and written statements of researchers published in this journal

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