Contact Stress Analysis of Composite Spur Gear using Photo-Stress Method and Finite Element Analysis

Transcription

1 International Researh Journal of Engineering and Tehnology (IRJET) e-issn: Volume: 03 Issue: 07 July-06 p-issn: Contat Stress Analysis of Composite Spur Gear using Photo-Stress Method and Finite Element Analysis Harshal P. Rahate, R. A. Marne PG student, Department of Mehanial Engineering, AISSMS COE, SPPU, Pune, Maharashtra, India Professor, Department of Mehanial Engineering, AISSMS COE, SPPU, Pune,Maharashtra,India *** Abstrat -Gears have a wide variety of appliations from tooth stresses and to tribologial failures suh as like wathes to very large mehanial units like lifting devies wear. Designing highly loaded spur gears for power and automotives. Gear is one of the most ritial omponent transmission systems that are both strong and quiet in a mehanial power transmission system and in most requires analysis methods that an easily be implemented industrial rotating mahinery. New gear design is needed and also provide information on ontat and bending beause of the inreasing performane requirement.gear stresses, along with transmission errors. The finite teeth normally fail when load is inreased above ertain element method is apable of providing this information. limit. Therefore it is required to explore alternate material The finite element method is very often used to analyze for gear manufaturing. Composite materials provide the stress state of an elasti body with ompliated adequate strength with weight redution and they have geometry, suh as a gear. The life and performane of gear emerged out as a better replaement for metalli gears. The teeth are diretly related to the ability of the teeth to ontat stress in the mating gear is the key parameter in withstand ontat stresses. Contat stresses may produe gear design. This paper represent ontat stress analysis of pitting within the ontat area and eventually lead to tooth steel gear and omposite gear using Hertz equation and by failure. In spite of the importane of ontat stresses in Finite Element Analysis using Ansys 6.0 Workbenh. Also gears, omprehensive analyses of these stresses have not experimental stresses are alulated using Photo-Stress been extensively reported in the literature. Method.In this work, Aluminium Silion Carbide is used as a gear material. When ompared, the results of both theoretial method and FEA show a good degree of agreement with experimental results. Key Words:Contat Stress, Finite element Analysis, Hertz Equation, Spur gear.introduction The rapid growth of heavy industries suh as vehile, shipbuilding and airraft industries require extensive appliation of gear tehnology. Spur gear is a ylindrial shaped gear in whih the teeth are parallel to the axis. Spur gears are easy to manufature and it is mostly used to transmit power from one shaft to another shaft up to ertain distane & it is also used to vary the speed & Torque. e.g. Wathes, gearbox et. The replaement ost of spur gear is very high and also the system down time is one of the effet in whih these gears are part of system. Failure of gear auses breakdown of system whih runs with help of gear. E.g. automobile vehile. So it beomes very important to inrease the strength of gear to avoid the failure. Gears analysis in the past was performed using analytial methods, whih required a number of assumptions and simplifiations. In general, gear analyses are multidisiplinary, inluding alulations related to the Composites provide muh improved mehanial properties suh as greater strength to weight ratio, inrease in hardness, and hene less hanes of failure. So this work is onerned with replaing metalli gear with gear of omposite material of Aluminium Silion Carbide so as to improve performane of mahine and to have longer working life. P.B. Pawar has developed a metal matrix omposite of Aluminum based Silion Carbide []. The omposition of Silion Carbide is varied in Aluminum and mehanial tests were performed. They proposed to use this material for power transmitting element like gears. Author P.B. Pawar has manufatured the spur gear from omposite material of Aluminum Silion Carbide. He has done FEA using Ansys 4.0 and onludes that omposite gears offer improved properties over steel alloys and an be used as alternative for replaing metalli gears []. Neelima Devi and o authors worked on the mehanial haraterization of Aluminum Silion Carbide [3]. They found that the weight to strength ratio for omposite is about three times that of mild steel and it is two times less in weight than aluminum of same dimension. Seok-Chul Hwang presents a ontat stress analysis for tooth in ontat of gears during rotation [4]. Contat stress analysis for spur and helial gears is arried out between two gear teeth at different ontat positions during rotation. The variation of ontat stress values during rotation is ompared with the values of ontat stress at the lowest point of single tooth ontat. Ali Raad Hassan has developed a program to plot paired teeth in ontat [5]. This program was run eah 30 of rotation of 06, IRJET Impat Fator value: 4.45 ISO 900:008 Certified Journal Page 540

2 International Researh Journal of Engineering and Tehnology (IRJET) e-issn: Volume: 03 Issue: 07 July-06 p-issn: pinion to reate 0 ases. The program gave graphi results for different FE models and stress analysis was arried out in ANSYS. Sushil Kumar Tiwari found out the ontat stress and bending stress for involute spur gear teeth in meshing by finite element method and the results are heked with those obtained by Lewis formula, Hertz equation and AGMA/ANSI equations [6]. They observed that Hertz theory is the primary basis of ontat stress alulation and for determining bending stress in a pair of gear, Lewis formula is used. Vivek Karaveer has done the modelling of FEA of spur gear using ANSYS 4.5. He has ompared the stress values and deformation for steel and grey ast iron [7]. Mohammad Jebran Khan reports the ontat stress analysis of Stainless Steel spur gears by theoretial method using Hertz equations and by Finite Element Analysis using FEA software ANSYS 4.0 Workbenh. The spur gear is skethed and modelled in ANSYS Design Modeller and the ontat stress analysis is done in Mehanial ANSYS Multiphysis [8]. Prabhakar Purushothaman emphases on the ontat stress. The value of ontat stress is very important, as the stress value hanges with ontat area. The higher the ontat area the stress generated will be less and for lesser ontat area high stress will be generated [9]. Santosh Patil observed that ontat behavior in loaded gears along the line of ation hanges tremendously. the ontat pressure for a pair of mating spur gears has been determined by Finite Element Analysis (FEA) using ANSYS software. The ontat pressure results are then verified by twin-dis experimental results and the Hertzian ontat pressure equation [0]. Santosh Patil studies the effet of oeffiient of frition along the line of ation of a spur gear.he determines the shape funtion whih define the hange of ontat stress along the line of ation of meshed gear. The result shows an inrease in ontat stress with the inrease in oeffiient of frition [].. DESIGN OF GEAR The material properties of steel and Aluminium Silion Carbide omposite are given in the table. Table -: Material properties of gear materials Material Property Young s Modulus Steel AlSiC 0 GPa 50 GPa Poisson s Ratio Ultimate tensile strength N/mm 00 5 The omparative study of steel gear and omposite gear is done. So the basi design of spur gear is same for both the gears. The various parameters of gear design are given in the table below. Table -: Gear design parameters Parameter Gear Pair No. of teeth 0 Gear Ratio Module 4.5 Pressure angle 0 Pith diameter 90 Fae width 45 Center Distane 90 Torque (Nm) 30 Speed (rpm) THEORETICAL ANALYSIS OF CONTACT STRESS USING HERTZ THEORY Earle Bukingham (96) have used theory of Hertz to alulate the ontat stress between a rotating pair of teeth while transmitting power by treating the pair of teeth in ontat as ylinders of radii equal to the radii of urvature of the mating involutes at the pith point. Aording to Hertz theory, when two ylinders are pressed together, the ontat stress is given by P BL B Where, P E E l d d () = maximum value of ontat stress (N/mm) P = fore pressing the two ylinders together (N) B = half width of deformation (mm) L = axial length of ylinders (mm) d,d = diameters of two ylinders (mm) E, E (N/mm), (unitless) () = modulii of elastiity of two ylinder materials = poisson s ratio of the two ylinder materials 06, IRJET Impat Fator value: 4.45 ISO 900:008 Certified Journal Page 54

3 International Researh Journal of Engineering and Tehnology (IRJET) e-issn: Volume: 03 Issue: 07 July-06 p-issn: Substituting the value of half width of deformation B, in equation () & squaring both sides we get, P r r L E E (3) If we treat the material of both the ylinders as same, then the modulus of elastiity and poisson s ratio will be equal. Therefore substituting in equation (3) we get P r r L E E E E and (4) Now applying this equation to a pair of spur gear teeth in ontat, we need to replae the radii r &r by the radii of urvature at the pith point r d pp sin d pg sin r and Now, sine the pinion and gear have equal geometry in all respets as given in table, we have, d pp d pg d r r r p d p sin From (4) and (5) we get PE ( ) Lr (5) (6) For same material of pinion and gear as stainless steel, then for stainless steel, from table poisson s ratio =0.3. sin r r p and P P t os The length L is same as the fae width b of spur gears, therefore replaing L by b in equation. Substituting this value of in equation (6) and solving we have br p PE t sin os (7) The tangential load ating on the tooth an be obtained by T 30 P 594. N t d p Putting the value of young s modulus E, fae width b, rp pith irle radius and pressure angle in equation (7), we get the value of ontat stress: For Steel sin 0os 0 For Composite material sin 0os 0 N 54.6 mm N 4.3 mm 4.STRESS ANALYSIS USING PHOTO STRESS METHOD PhotoStress is a widely used full-field tehnique for aurately measuring surfae strains to determine the stresses in a part or struture during stati or dynami testing. With the PhotoStress method, a speial strainsensitive plasti oating is first bonded to the test part. Then, as test or servie loads are applied to the part, the oating is illuminated by polarized light from a refletion polarisope. When viewed through the polarisope, the oating displays the strains in a olorful, informative pattern whih immediately reveals the overall strain distribution and pinpoints highly strain areas. With an optial transduer (ompensator) attahed to the polarisope, quantitative stress analysis an be quikly and easily performed. Permanent reords of the overall strain distribution an be made by photography or by video reording. Fig-:Shemati representation of a refletion polarisope 06, IRJET Impat Fator value: 4.45 ISO 900:008 Certified Journal Page 54

4 International Researh Journal of Engineering and Tehnology (IRJET) e-issn: Volume: 03 Issue: 07 July-06 p-issn: Fig-:Refletion Polarisope Apparatus Fig-3: Loading arrangement of gear Figure shows the shemati representation of a refletion polarisope. Figure shows the atual refletion polarisope used to perform the experimentation. Figure 3 shows the loading arrangement made to provide the input torque to the pinion. The basi relationship for strain measurement in a photoelasti oating an be expressed as follows: N n (8) kt Where: ε= prinipal strains in oating N n = normal-inidene fringe order λ = wavelength of yellow light (.7μin, or 575 nm) t = thikness of PhotoStress oating = 3mm k = strain-opti oeffiient of oating =0.5 Assuming the strains in the oating preisely repliate those in the test-part surfae, and assuming the part is stressed below its proportional limit, Hookes law an be applied as follows to determine the differene of prinipal stresses: E Where: σ = prinipal stresses in test part E = elasti modulus of test material µ = Poisson s ratio of test material The preeding relationships impliitly assume that the strains in the test part are unaffeted by the presene of the bonded photoelasti oating, and that the strains in the oating are uniform through the oating thikness and equal to those in the surfae of the test part. These assumptions are quite well satisfied for typial metal astings, forgings, and robust strutural members, sine the oating is muh lower in elasti modulus, and is usually thin ompared to the setion depth of the test part. Putting the value of fringe order we get from refletion polarisope for a given loading in above equation 8 and 9, we an get the stress in the omponent at that loading. Sr. No. Table 3: Observation table for pair of steel gear Load (Kg) Torque (Nm) Fringe Order N n (9) Stress σ (MPa) Table 3: Observation table for pair of omposite gear Sr. No. Load (Kg) Torque (Nm) Fringe Order N n Stress σ (MPa) FINITE ELEMENT ANALYSIS Finite Element Method is the easy tehnique as ompared to the theoretial methods to alulate the stress developed in teeth of gears. Therefore FEM is widely used for the stress analysis of mating gears. FE analysis is done in ANSYS Workbenh 6.0 to determine the maximum ontat stresses for steel and omposite material. Also the deformation is found out for both the gears. CAD model of gear is reated in CREO.0. It is imported as a IGES file in ANSYS , IRJET Impat Fator value: 4.45 ISO 900:008 Certified Journal Page 543

5 Contat Stress σ International Researh Journal of Engineering and Tehnology (IRJET) e-issn: Volume: 03 Issue: 07 July-06 p-issn: RESULT AND DISCUSSION Contat stress for steel and aluminium silion arbide is alulated in ANSYS 6.0. Figure 7 shows the ontat stress for steel whih gives a stress of 5.4 MPa. Figure 8 shows ontat stress for omposite gear whih gives a stress value of 39.8 MPa. Chart presents the omparison of stress of steel and omposite gear in bar hart form for maximum loading in all three methods. 5. Meshing Fig -4: CAD model of gear Meshing is done using Hexagonal mesh with number of elements of and number of nodes of The element size is 0.8 mm. This mesh is used as it is fine and gives least number of elements with good results. So the alulation time is redued. Fig -7:Stress Diagram of Steel 5. Boundary Conditions Fig -5:Mesh Model of gear Fixed support is applied on inner rim of the gear. Fritionless support is applied on the inner rim of pinion to allow its tangential rotation. Moment of 30Nm is applied on the surfae of seond gear. Fig -8:Stress Diagram of Aluminium Silion Carbide Hertz Theory Experim ental Method FEA Method Steel Composite Fig -6:Boundary Conditions of Ansys Chart -:Stress Comparison Analytial, FEA and Experimental Method 06, IRJET Impat Fator value: 4.45 ISO 900:008 Certified Journal Page 544

6 International Researh Journal of Engineering and Tehnology (IRJET) e-issn: Volume: 03 Issue: 07 July-06 p-issn: Perentage differene of stress for steel and omposite material using analytial method, FEA and Experimental method is alulated. It is shown in table 3. Table-5: Perentage differene between analytial and FEA Hertz Equation FEA Method Experime ntal Method % Differene 7. CONCLUSIONS Steel Composi te Material % Redution in Stress Here the theoretial maximum ontat stress is alulated by Hertz equation. Photo stress method is used form experimental validation. Also the FE analysis of spur gear is done to determine the maximum ontat stress by ANSYS 6.0. It was found that the results from both Hertz equation and Finite Element Analysis are omparable with the experimental method. The results are well withinthe differene of 3%. Also it is observed that stress is redued by nearly 5% due to the use of omposite material. ACKNOWLEDGEMENT The authors are thankful to Dr. S. P. Danao, Prinipal AISSMS COE, Professor A. V. Waghmare, Head, Department of Mehanial Engineering, AISSMS COE for their onstant enouragement and ooperation throughout the work. arbide omposite, International Journal of Applied Engineering Researh. Volume.Issue No 4, pp6-3. [5] Ali Raad Hassan. (009). Contat Stress Analysis of Spur Gear Teeth Pair, World Aademy of Siene, Engineering and Tehnology 58. pp 6 66 [6] Sushil Kumar Tiwari, Upendra Kumar Joshi (0), Stress Analysis of Mating Involute Spur Gear teeth, International Journal of Engineering Researh and Tehnology. Volume, Issue 9, pp -. [7] Vivek Karaveer, Ashish Mogrekar and T. Preman Reynold Joseph, (03 Deember).Modeling and Finite Element Analysis of Spur Gear, International Journal of Current Engineering and Tehnology. Vol3., No.5, pp [8] Mohammad Jebran Khan, Arunish Mangla, Sajad Hussain Din (05),Contat Stress Analysis of Stainless Steel Spur Gears using Finite Element Analysis and Comparison with Theoretial Results using Hertz Theory. Int. Journal of Engineering Researh and AppliationsVol. 5, Issue 4, ( Part -5), pp [9] Mr. Prabhakar Purushothaman, Dr. Prashanth Thankahan (04), Hertz Contat Stress Analysis and Validation Using Finite Element Analysis. International Journal for Researh in Applied Siene & Engineering Tehnolog, Volume Issue XI pp [0] Santosh Patil, Saravanan Karuppanan, Azmi Abdul Wahab (03), Contat Pressure Evaluation of a Gear Pair along the Line of Ation using Finite Element Analysis.Applied Mehanis and Material, Vol. 393 pp [] Santosh Patil, Saravanan Karuppanan, Ivana Atanasovska, Azmi Abdul Wahab (04), Fritional tooth ontat analysis along line of ation of a spur gear using Finite Element Method. Proedia Materials Siene 5 pp [] James W. Dally, William F. Riley Expermental stress analysis. MGraw-hill International Edition 99. [3] Parmjit S.K., "Automated Photoelastiity", "Researh in Automated Photoelastiity", Mehanial and Industrial Engineering, University of Toronto,(997). pp. -4. [4] James F. Doyle Modern Experimental Stress Analysis John Wiley & Sons, Ltd. REFERENCES [] P.B.Pawar, Abhay A. Utpat. (05). Analysis of Composite Material Spur Gear under Stati Loading Condition, Materials Today: Proeedings.pp [] P.B.Pawar, Abhay A. Utpat. (04). Development of Aluminium Based Silion Carbide Partiulate Metal Matrix Composite for Spur Gear. Proedia Materials Siene. pp [3] Seok-Chul Hwang, Jin-Hwan Lee, Dong-Hyung Lee, Seung-Ho Hana, Kwon-Hee Lee. (03). Contat stress analysis for a pair of mating gears. Mathematial and Computer Modelling. 57. pp [4] Devi Neelima, Mahesh.V, Selvaraj. N., (0), Mehanial haraterization of Aluminium silion 06, IRJET Impat Fator value: 4.45 ISO 900:008 Certified Journal Page 545