Fatigue analysis of out-put shaft subjected to pure torsion

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In present study the failure of the shaft in the yaw gear box is analyzed .As we the shaft is rotating part of the engine it transmit the power from the one part of the engine to another part.

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Nội dung Text: Fatigue analysis of out-put shaft subjected to pure torsion

International Journal of Mechanical Engineering and Technology (IJMET) Volume 10, Issue 04, April 2019, pp. 9-16, Article ID: IJMET_10_04_002 Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=4 ISSN Print: 0976-6340 and ISSN Online: 0976-6359 © IAEME Publication Scopus Indexed FATIGUE ANALYSIS OF OUT-PUT SHAFT SUBJECTED TO PURE TORSION Nagaraj S B M Tech Student, Mechanical Engineering Dept, N.M.I.T, Bengaluru, India Chetan S Professor, Department of mechanical, Nitte Meenakshi Institute of Technology, Bangalore, India Shyamaprasad S Sr.Manager, Off-highway R&D) AVTEC Ltd, Hosur, Tamilnadu, India Venugopal Nair AGM (Off-highway R&D) AVTEC Ltd, Hosur, Tamilnadu, India ABSTRACT In material engineering it is important to determine the cause of the failure & prevention of the failure .In present day the failure of the machine component is about 90% of the failure is because of the fatigue. In present study the failure of the shaft in the yaw gear box is analyzed .As we the shaft is rotating part of the engine it transmit the power from the one part of the engine to another part. It holds the maximum stress. In this case shaft of heat treated component with ultimate tensile strength Su= 2100Mpa is analysis done with ANSYS (FEA) software & compared with the theoretical calculation. There are different methods which are used to predict fatigue life include stress life(S-N), strain Life (E-N) and Linear Elastic Fracture Mechanics (LEFM). In this project study, S-N approach is used to predict fatigue life for out-put shaft. Key words: Shaft, FEA-ANSYS (16.2), SN-curve, Fatigue –life, Fatigue factor of safety, Fatigue damage Cite this Article: Nagaraj S B, Chetan S, Shyamaprasad S, Venugopal Nair, Fatigue Analysis of Out-Put Shaft Subjected to Pure Torsion, International Journal of Mechanical Engineering and Technology 10(4), 2019, pp. 9-16. http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&IType=4 1. INTRODUCTION A shaft has a circular cross section & it is a rotating component used in almost all the machine .It is used to transfer the energy from the one part to another part .A shaft usually not a uniform cross section because it is mounted by the bearing, fly wheels, clutches & other machine http://www.iaeme.com/IJMET/index.asp 9 editor@iaeme.com
Fatigue Analysis of Out-Put Shaft Subjected to Pure Torsion elements are mounted on the shaft .In the present shaft of heat treated material is mounted by spur gear with pressure angle of 200 & supported by the two bearing (Roller bearing) Stress Analysis Stress in the Shaft In actual practice there are three kinds of stress are induced in it. a.) Shear stress by the transmission of the torque. b.) Bending stress by the force acting upon machine element, and weight of shaft itself. c.) Stress from both combined torsional and bending loads. 2. SHAFT MATERIAL COMPOSITION Material is used in the shaft is 18CrNiM06 Table 1 Chemical composition of 18CrNiM06 Composition Percentage Carbon 0.15-0.21 Silicon 0.17-.35 Nickel 1.40-1.70 Manganese 0.25-0.35 Phosphorus 0.035 Sulphur 0.015 Chromium 1.50-1.80 • Tensile yield strength Sy =1790Mpa • Ultimate tensile strength Su =2100Mpa • Young’s modulus of material E = 207Gpa • Passion’s ratio = 0.3 • Density 𝛿=7800 Kg.m3 2.1. Fatigue stress concentration When there is an existence of the existence of irregularities or discontinuities, such as holes, grooves, or notches, in a part increases the theoretical stresses signiﬁcantly in the immediate vicinity of the discontinuity deﬁned a stress concentration factor Kt or Kts Effective maximum stress is fatigue is 𝜎max = Kf 𝜎nom 𝜏max =Kfs 𝜏nom (1) Where Kf is a reduced value of Kt and is the nominal stress 𝜎0 . The factor Kf is commonly referred as fatigue stress-concentration factor and hence the subscript f. The resulting factor is deﬁned by the equation 𝑀aximum stress in notched specim𝑒𝑛 Kf = Stress concentration notch free specime𝑛. (2) Kf =1+q (Kt −1) or Kfs=1+qshear (Kts−1) (3) Where q = Notch sensitivity factor 1 q= (4) √𝑎 1+ √𝑟 Where √𝑎= Neuber constant r = Fillet radius Neuber constant is given by the equation http://www.iaeme.com/IJMET/index.asp 10 editor@iaeme.com
Nagaraj S B, Chetan S, Shyamaprasad S, Venugopal Nair a. Bending: √a =0.246−3.08 (10−3) Sut+1.51(10−5 ) (Sut)^2−2.67(10−8) (Sut )^3 (5) b. Torsion: √a =0.190−2.51 (10−3) Sut +1.35(10−5 ) (Sut) ^2−2.67 (10−8) (Sut) ^3 (6) Applying Sut = 304.57 Ksi (1Ksi = 6.895 Mpa) For the torsion = -0.045 1 q= √.0765 =.9486 1+ √1.414 Where Kt = Stress concentration torsion Graph stress concentration factor for torsion Where r = Fillet radius d = Diameter of smaller shaft D = Diameter of larger shaft 𝑟 2 𝐷 100 = 85 =.0235 = 85 =1.1764 𝑑 𝑑 From the graph & question (3) Kt =1.85 Kfs =1+.9486(1.85-1) =1.80631 2.2. Generation of SN Curve Fatigue strength (Endurance limit𝑆 ᾽ ) of the shaft material was calculated as Sn = 0.5* UTS = 0.5* 2100 = 1050 N/mm2.Considering the corrections factors for endurance limit we find the new endurance Table 2 Factor affecting the fatigue life of the shaft Load factor (𝑪𝑳 ): Temperature (𝑪𝑻 ) Surface factor 𝑪𝒔 Reliability Gradient factor factor (𝑪𝑹 ) (𝑪𝑮 ) .58 1 .5 .897 .9 ᾽ 𝑆 = .5*Sut*𝐶𝐿 ∗ 𝐶𝑇 ∗ 𝐶𝑠 *𝐶𝑅 *𝐶𝐺 (7) = .5*2100*.58*1*.5*.897*.9 = 245.822 Mpa http://www.iaeme.com/IJMET/index.asp 11 editor@iaeme.com
Fatigue Analysis of Out-Put Shaft Subjected to Pure Torsion 2.3. Meshing of shaft Figure 1 Meshing of shaft Basic idea of FEM is to perform calculations at limited number of points called nodes and interpolate the results for entire domain using interpolation functions. Any continuous object has infinite degrees of freedom and such problems cannot be solved using this method. So this method reduces the degrees of freedom from infinite to finite by making assumptions and by discretization/meshing in other terms creating nodes and elements. Hexa-dominant mesh is used, relevance center is fine & elements size is 3mm created the nodes 1141216 and elements 315798 2.4. Loads acting on shaft Stepped shaft is subjected to a torque of value 47960 Nm to the location of “B” & fixed location of the spur gear “A”. Figure 2 Load acting on the shaft http://www.iaeme.com/IJMET/index.asp 12 editor@iaeme.com
Nagaraj S B, Chetan S, Shyamaprasad S, Venugopal Nair 3. RESULT AND DISCUSSION 3.1. Shaft Shear stresses Figure 3 Shear stress in Mpa The maximum shear stress is shown in which appears in the cross-section of the shaft 𝜏𝑚𝑎𝑥 With the fatigue stress concentration kfs = 1.8 𝜏𝑚𝑎𝑥 = 397.73 * 1.8 = 715.914 Mpa 3.2. Equivalent alternating stress or Equivalent von-mises stress Figure 4 Equivalent alternating stress in Mpa Equivalent von-mises stress or alternating stress 𝜎𝑣 𝜎𝑣 = √3 ∗ 𝜏𝑚𝑎𝑥 2 = √3 ∗ 715.9142 = 1239.99 Mpa In a Stress Life fatigue analysis, one always needs to be query an SN curve to relate the fatigue life to the stress state. Thus of the “equivalent alternating stress” is the stress used to http://www.iaeme.com/IJMET/index.asp 13 editor@iaeme.com
Fatigue Analysis of Out-Put Shaft Subjected to Pure Torsion query the fatigue SN curve after accounting for fatigue loading type, mean stress effects, multiaxial effects and any other factors in the fatigue analysis. Thus in a fatigue analysis, the equivalent alternating stress can be thought of as the fast calculated quantity before determining the fatigue life. The maximum value of the equivalent stress is 1244.6 Mpa, which takes place in the cross-section of the shaft where the Roller -bearing was located. 3.3. Number of cycles Figure 5 Showing the fatigue life This represents the number of cycles until the part will fail due to fatigue 2500 2000 1500 4408, 1000 500 0 1 10 100 1000 10000 100000 1000000 Graph of theoretical calculation http://www.iaeme.com/IJMET/index.asp 14 editor@iaeme.com
Nagaraj S B, Chetan S, Shyamaprasad S, Venugopal Nair 3.4. Factor of safety of fatigue life Figure 6 Factor of safety Endurance stress Factor of safety of fatigue life =𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑎𝑙𝑡𝑒𝑟𝑛𝑎𝑡𝑖𝑛𝑔 𝑠𝑡𝑟𝑒𝑠𝑠 Endurance stress = 245.82 Mpa 245.82 FOS = 1240 = .19824 3.5. Fatigue damage Figure 7 Fatigue damage Fatigue Damage is a contour plot of the fatigue damage at a given design life. Fatigue damage is defined as the design life divided by the available life Design life Fatigue damage = Availble life 106 = 4408 = 226.86 http://www.iaeme.com/IJMET/index.asp 15 editor@iaeme.com
Fatigue Analysis of Out-Put Shaft Subjected to Pure Torsion Table 2 Result of Comparison Parameters Analytical results FEM results a. Shear stress in Mpa 715.91 718.58 b. Equivalent alternating in Mpa 1239.99 1244.6 c. Fatigue life cycles 4408 4330 d. Factor of safety .1984 .1975 e. Fatigue damage 226.82 232.52 4. CONCLUSIONS Failure analysis of the shaft is investigated in detail. Force acting on the bearing due to the torque is determined .Endurance limit & fatigue factor of safety is calculated. Fatigue life of the shaft is estimated & fatigue damage is calculated. Forces and stresses are calculated by using an analytical approach and ANSYS software. Both methods show that the stresses and fatigue life are nearly same and in the admissible range. 1. From the static analysis it was observed that maximum stress is located at the change in the cross-section area of the shaft it is found 1313 Mpa. 2. Fatigue life is found to be 4330 cycles. 3. Factor of safety is .1975