In the thread root area of the threaded bolts submitted to axial loading occur local stresses, higher that nominal stresses calculated for the bolts. These local stresses can generate failure and can reduce the fatigue life of the parts. The paper is focused on the study of the influence of the thread root radius on the maximum local stresses. A large diameter trapezoidal bolt was subjected to a static analysis (axial loading) using finite element simulation

Cojocaru Vasile

Korka Zoltan Iosif

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  85    Vasile Cojocaru, Zoltan Iosif Korka Influence of Thread Root Radius on Maximum Local Stresses at Large Diameter Bolts under Axial Load-ing In the thread root area of the threaded bolts submitted to axial loading occur  local  stresses,  higher  that  nominal  stresses  calculated  for  the bolts. These local stresses can generate failure and can reduce the fa tigue life of the parts. The paper is focused on the study of the influ ence of the thread root radius on the maximum local stresses. A large diameter trapezoidal bolt was subjected to a static analysis (axial load ing) using finite element simulation. Keywords: threaded bolts, local stress, FEM analysis, 2D simplification 1. Introduction Threaded connections are components widely used  on the mechanical sys tems. Due the geometric features and the manufacturing processes [3], [5], [8], in the thread area of these elements occur high local stresses that exceed the nomi nal values obtained by calculus [6], [7], [9]. These local stresses, highlighted by experimental methods and by finite element simulations can lead to part failure [3], [10]. The research is focused on the large diameter threaded bolts (nominal diame ter  over  200  mm)  used  at  the  positioning  systems  of  heavy  duty  mechanical equipment.  Previous  researches  revealed  that  the  bolts  with  trapezoidal  thread have  a  superior  behaviour  for  these  applications,  compared  to  the  bolts  with square thread [2]. Also the stress distributions revealed that the maximum local stresses occur in the root area of the trapezoidal thread. These maximum local stresses vary on the thread turns, the maximum values being located on the first turn from the contact bolt – nut [2].  A bolt with trapezoidal thread Tr220x36 (figure 1) was subjected to axial load ing. The static FEM (finite element method) analysis was made using the Solid Works Simulation. A 2D planar simplification was used in order to enable the in ANALELE UNIVERSITĂłII   “EFTIMIE MURGU” RE IłA ANUL XXI, NR. 1, 2014, ISSN 1453 - 7397    86 crease of the mesh quality in the area of the thread root. This simplification does not have a significant influence on the results accuracy and decrease the simula tion time, compared to a 3D study [1,3,4].    a)  b) Figure 1. Main parameters of threaded bolt  2. FEM Study Definition The material used in simulation was the carbon steel grade 1.0577, with the yield  strength  Rp0.2≈275  MPa,  tensile  strength  Rm≈480  MPa,  Young’s  modulus E=2.1e5 MPa and Poisson's ratio υ=0.28. The model was considered linear elastic isotropic and the default failure criterion was the maximum von Mises Stress. The mesh was generated at a maximum element size of 4 mm with a refine ment in the fillet area from the thread root (maximum element size of 1 mm). The mesh details are presented in table 1 and figure 1.  Table 1. Mesh properties Mesh type  Planar 2D Mesh Mesher used  Curvature based mesh Maximum element size  4.010 mm Maximum element size on thread root  1.007 mm Total nodes  33741 Total elements   16426  The fixture (0 DOF) was applied on the end surface of the bolt (figure 2, a). The axial force (F=260 kN) was applied on six thread turns, on the surface in con tact between the bolt and the nut threads (the thread surface between the minor diameter of the bolt   182 mm and the minor diameter of the nut – 184 mm, was not loaded). The bolt was designed with a total length corresponding to 11 thread turns. The end turns were not summited to loading, in order to remove the influ ence of their geometric features on the stress state.    87 At the trapezoidal turns the edge of intersection between the thread turns and the minor diameter cylinder represents the main stress concentrator of the thread [8], [11], [12]. A fillet radius (R – figure 1) was applied on this edge in order to decrease the maximum local stresses. The radius was varied between 0.1 mm and 0.6 mm, values lower than the gap between the bolt and the nut. This filet can be manufactured at in thread turning process, using a cutting insert with tip radius.   a)  b) Figure 2. FEM study definition: a) planar mesh with the force and the fixtures applied and b) detail on mesh refinement at thread root  3. Results The stresses (von Mises and axial stresses) obtained for the bolts with the six values of radius are presented in table 2. The von Mises stress variation  σvonMises =(σvMi   σvM0)100/σvM0, was referenced to the von Mises stress σvM0, obtained at the bolts with R=0.1 mm.          Table 2. Stress variation at various thread root radius Crt. No. R [mm] σvonMises [MPa] σx [MPa] σy [MPa] σz  [MPa] ∆σvonMises [%] 1  0.1  114.8  80.3  45  109.4  reference 2  0.2  94.7  71.3  33.2  98.7   17.51 3  0.3  75.3  58.5  28.1  82.1   34.41 4  0.4  68.8  50.3  25.4  71.9   40.07 5  0.5  66  45.4  22.5  69.1   42.51 6  0.6  63.9  40.2  20.8  59.9   44.34   88 The variation of stresses indicates a significant decrease for the bolts with R=0.6 mm (44.34% lower than for R=0.1). This decrease occurs on all principal directions (figure 3).   Figure 3. Stresses vs. thread root radius variation  The Von Mises stress distribution for the bolt with R=0.6 mm (figure 4) high lights the occurrence of the maximum stress in the thread root area. This distribu tion is similar for all six studies.    a)    b) Figure 4. Von Mises stress variation for the bolt with R=0.6 mm: a) overview and b) details on the root area of the first thread turn of bolt – nut interface   89 4. Conclusion The paper points out the influence of the thread root radius on the maximum local stresses at a large diameter bolt under axial loading. The analyses were made using  static  planar  2D  FEM  studies.  For  the  bolt  with  the  trapezoidal  thread Tr220x36, the variation of the radius from 0.1 mm to 0.6 mm lead to a decrease of the maximum local stresses with approximately 44 %. This decrease can improve the fatigue behaviour of the part. Acknowledgment The work has been funded by the Sectoral Operational Programme Human Resources Development 2007 2013 of the Ministry of European Funds through the Financial Agreement POSDRU/159/1.5/S/132395. References [1]  Cho S., Chang H., Lee K.W., Dependence of Fatigue Limit of High Ten sion Bolts  on Mean  Stress and Ultimate Tensile Strength, International Journal of Automotive Technology, Vol.10, pp. 475−479.  [2]  Cojocaru V., Miclosina C.O., Korka Z.I., Fatigue Analysis of Large Di ameter Threaded Connections Subjected to Dynamic Axial Loads, The 6th International Conference on Advanced Concepts in Mechanical Engineer ing, ACME’14, Iasi, Romania, 11 13 June 2014. [3]  Duan  W.,  Joshi  S.,  Structural  behavior  of  large scale  triangular  and trapezoidal threaded steel tie rods in assembly using finite element analy sis, Engineering Failure Analysis, vol.34, pp.150 165. [4]  Ferjani M., Averbuch D., Constantinescu A., A computational approach for the fatigue design of threaded connections, International Journal of Fatigue, vol. 33, pp. 610 623. [5]  Gerasimova O.V., Gerasimov V.Ya., Increasing the Strength of Thread ed Components by Prior Plastic Deformation of the Metal, Russian Engi neering Research, vol. 33, 2013, pp. 211 212.  [6]  Korin I., Perez Ipina J., Experimental evaluation of fatigue life and fa tigue crack growth in a tension bolt–nut threaded connection, Interna tional Journal of Fatigue, vol. 33, 2011, pp. 166 175. [7]  Liao R., Sun Y., Liu J., Zhang W., Applicability of damage models for failure analysis  of threaded bolts, Engineering  Fracture Mechanics,  vol. 78, 2011, pp. 514 524.    90 [8]  Majzoobi G.H. et al., Experimental evaluation of the effect of thread pitch  on  fatigue  life  of  bolts,  International  Journal  of  Fatigue,  vol.  27, 2005, pp. 189 196. [9]  Marcelo A.L., Uehara A.Y., Utiyama R.M., Ferreira I., Fatigue Properties of High Strength Bolts, Procedia Engineering, vol. 10, 2011, pp. 1297–1302. [10]  Pittner A.M. et al., Stress concentration factors for pin lever of runner blade mechanism from Kaplan turbines, 3rd International Conference on Engineering Mechanics, Corfu, Greece, 2010, pp. 181 185. [11]  Schneider R., Wuttke U., Berger C., Fatigue analysis of threaded con nections using the local strain approach, Procedia Engineering, vol. 2, is sue 1, 2010, pp. 2357–2366.  [12]  Zhao H., Stress concentration factors within bolt nut connectors under elasto plastic deformation, International Journal of Fatigue, vol. 20, issue 9, 1998, pp. 651 659. Addresses: ·  Lect. Dr. Eng. Vasile Cojocaru, “Eftimie Murgu” University of Re iŃa, PiaŃa Traian Vuia, nr. 1 4, 320085, Re iŃa, v.cojocaru@uem.ro ·  Lect. Dr. Eng. Zoltan Iosif Korka, “Eftimie Murgu” University of Re iŃa, PiaŃa Traian Vuia, nr. 1 4, 320085, Re iŃa, z.korka@uem.ro               

Influence of Thread Root Radius on Maximum Local Stresses at Large Diameter Bolts under Axial Loading

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