A failed mechanical part - its analysis and design

Transcription

1 A failed mechanical part - its analysis and design E.S. Ayllon Departamento Ciencia y Tecnica de Materiales (Department of Materials Science and Technique) - CITEFA- Zufriategui (1603) V. Martelli - Argentina Abstract The purpose of this paper was to determine the stress conditions within a mechanical part that failed catastrophically while being tested. The method used for the determination of the stresses was the LUSAS 12.1 finite element calculation approach (FEA). The part in question was a hydraulic brake cylinder, which, due to a failure in the test regulating valves, was subjected to an internal pressure at least three times its normal operating stress, with consequent rupture of the cylinder wall. The explosion produced a crack which originated at the pressure inlet orifice in the cylinder wall. A design was proposed based on LUSAS analysis. Introduction The crack begins at the hole made for the pressure inlet running, in both directions, practically tangential to the said hole, Fig. 1. The resulting expansion caused the detachment of the external threaded end cover. The cylinder was very long but the position of the piston when the accident occurred was such that it was possible to examine a sector only about 300 mm in length. The remaining part of the no longer pressurized cylinder worked as a restrictor to the expansion of the examined section in every radial direction.

2 386 Computer Aided Optimum Design of Structures Fig. 1: View of the exploded cylinder Theory The material used was hot rolled SAE 4140 steel without heat treatment. The external diameter was 196 mm and the inner diameter 171 mm resulting, consequently, in a wall thickness of 12.5 mm. According to information from Boyer (1990) a yield stress Sy of 600 MPa and an ultimated stress of 750 MPa are to be expected. The last recorded pressure when the explosion took place was of 25 MPa. The rate of application of the pressure was unknown, the rise of the ratio could have been between 0.8 and 1.0. According to the well-known Lame formula, the stress in the cylinder wall was Si = 184 MPa for the inner diameter and Si = 159 MPa for the external surface giving an average of MPa. The formula for thin wall cylinders shows a value of 171 MPa.

3 Computer Aided Optimum Design of Structures 38 As it can be seen, this value, increased by the coefficient of the stress concentration of 3.7, suggested by Peterson for cylindrical holes, shows a maximum of 633 MPa for the wall of the cylinder, lower than the Su considered for the material. In Fig. 2a we can see the pressure inlet plug and its attachment arrangement. FEA LUSAS Aalysis The modeling was made as shown in Fig. 3. The mesh used for the complete model with a hole of 30 mm diameter with the threaded pressure inlet plug welded inside it is presented. Fig. 2: Pressure inlet plug

4 388 Computer Aided Optimum Design of Structures Fig.3: Mesh of the cylinder and plug The results of the analysis show good concordance between the FEA approach and the mathematical theory of Lame and Peterson for an elastic stress condition, in linear state for a 30 mm diameter hole. See the stress contours of Si in Fig 4. Fig. 4: Hole detail

5 Computer Aided Optimum Design of Structures 389 We will now consider that for the adaptation of hose to measure internal pressure, a threaded plug 0.2 mm lower in diameter than the hole made in the cylinder wall was designed. The outer edge was welded to the external wall of the cylinder by means of the TIG method in order to fix it in place and to avoid hydraulic oil leaks. This arrangement modified the stress condition in the zone of influence of the hole. In Fig. 5 we presented the LUSAS results. The maximum value for stresses remained below the values required to crack the material of the cylinder because the max. values were concentrated in the plug. A new hypothesis was formulated considering that the material of the tube which was directly affected by heat, HAZ, failed under stresses such as those calculated in the previous step, due to the poor penetration of the supplied material and the fissuring of the root of the weld collar. Detachment of the threaded plug took place notably modifying the theoretical stress condition in the cylinder wall, Fig 6. In order to complete this paper, a non-linear analysis of the material based on the plastic and hardening attributes were applied. See Table 1 and Fig. 7. Slope Effective Plastic Strain Table 1: Hardening Curve A modified design of the weld was analyzed and a new internal threaded plug welded by brazing process was proposed. Two options were analyzed by LUSAS, Fig 2 c, d and Fig. 8 and 9. The brass wire proposed was (Cu = 59%, Zn = 40%) with E = 100,000 MPa. The results show that the redesign was unsuitable. Another modified technique was introduced, which consisted in welding the plug by electric resistance fusion and them welding by TIG, Fig. 2 e and Fig. 10. The FEA results show a reduction of the risk under the same internal pressure. Conclusions The LUSAS 12.1 application explains the beginning of cracks in the hole area of the cylinder wall where, in fact, said cracks appeared. The presence of a welded plug to prevent the shrinking in the Z direction changed the stress state, and the lack of metal penetration produced an increase of the stress in the area where the crack began. The last redesign was successfully introduced into production.

6 390 Computer Aided Optimum Design of Structures Fig. 5: Von Mises (SE) and stress SI contour plost

7 Computer Aided Optimum Design of Structures 391 Fig. 6: a]von Mises (SE) contour plot, b] Stress SI contour plot

8 392 Computer Aided Optimum Design of Structures K«* A* N ***?, # At N*** *»f "^ % 9f^. 1$4?4^^\%-^^ <^;- ^ \A^.^ Fig. 7: Von Mises (SE) and stress SI contour plots

9 Computer Aided Optimum Design of Structures 393 Fig. 8: Von Mises (SE) and stress SI contour plots.

10 394 Computer Aided Optimum Design of Structures Fig. 9: a] Von Mises (SE) contour plot, b] Stress SI contour plot.

11 Computer Aided Optimum Design of Structures 395 t / _ ^ Fig. 10: Von Mises (SE) and stress SI contour plots, Acknowledgements The author wants to thank Lie. Maria del C. LEIRO for her cooperation in this work and for the suggestions in the presentation of results, and to Tec. A. REYNOSO for the making of the figures. References - E. Boyer (1990). "Atlas of Stress - Strain Curves", pag R.E. Peterson (1974). "Stress Concentration Factors", pag. 154.