PSI - Issue 10

D.G. Ntritsos et al. / Procedia Structural Integrity 10 (2018) 288–294 D.G. Ntritsos et al. / Structural Integrity Procedia 00 (2018) 000 – 000

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4.2. Analytical approach results According to the analytical calculations described in sections 3.1 and 3.2 the static and fatigue stress was calculated for un-notched and single notched shafts. The calculations corresponds to the regions A and B. For bending load at each region the acting bending moment of the fatigue tests assumed. In Table 2 are shown the calculated values for applying load equal to 150 N which was the endurance load for the double notched specimen.

Table 2. Analytically calculated values.

Kt

Kf

Static Stress (MPa)

Fatigue Stress (MPa)

Un- notched shaft (diameter 10mm-region A) Un- notched shaft (diameter 10mm-region B) Single notched shaft (keyway-region A) Single notched shaft (stepped-region B)

1 1

1 1

184.02 188.22 404.84 440.43

184.02 184.02 411.76 357.62

2.20 2.34

1.48 1.91

The maximum stresses for both single and double notched specimens resulted from FEA simulation are given in Table 3. The values correspond to equal applying load with the analytical calculations (150 N). Additionally in dicative values of Kt and K f was derived taking in account the 1 st Principal Stresses and Eq.(3).

Table 3. FEA results.

Static Von Mises Stress (MPa)

Static 1st Princ. Stress (MPa)

Static Z-Norm. Stress (MPa)

Resulting K t

Resulting K f

Single notched shaft (stepped-region B)

400.54 449.96 471.99

484.92 451.07 565.49

365.19 439.39 479,74

2.58 2.45 3.00

2.07 1.99 2.36

Double notched shaft (region A) Double notched shaft (region B)

4. Conclusions An obvious and predominant conclusion is the expected worst fatigue behavior of the double notched shaft in cyclic bending loading. Τhe following conclusion is the most critical and unexpected: Fragmentation occurs in an area where analytical and numerical methods fall to indicate. Since static stresses are calculated with satisfactory accuracy, it is obvious that the error lies in the calculation of the fatigue stresses. It seems, therefore, that the conjucting of the notches directly affects the fatigue endurance by means of the notch sensitivity factor. The determination of the design parameters for the safety of such geometries in fatigue is a subject of future study and research. Eissa, M., Fessler, H., 1983. Reduction of elastic stress concentrations in end-milled keyed connections. Experimental Mechanics 23(4), 401-408. Fessler, H., Rogers, C.C., Stanley, P., 1969. Stresses at end-milled keyways in plain shafts subjected to tension, bending, and torsion. J. Strain Analysis 4(3), 180-189. Fessler, H., Rogers, C.C., Stanley, P., 1969. Stresses at keyway ends near shoulders. J. Strain Analysis 4(4), 267-277. Gowhari-Anaraki, A.R., Hardy S.J., Pipelzadeh, M.K., 2003. Experimental and analytical fatigue data for notched shafts in bending. Journal Kejuruteraan 15, 15-31. ISO 1143:2010, Metallic materials - Rotating bar bending fatigue testing. Madayag, A.F., 1969. Metal Fatigue, New York. Peterson, R.E., 1953. Stress Concentration Design Factors, John Wiley & Sons, New York. Pedersen, N.L., 2010. Stress concentrations in keyways and optimization of keyway design. The journal of strain analysis for engineering design 45(8), 593-604. Shigley, J.E., Mischke, C.R., 1989. Mechanical Engineering Design, 5th Ed., McGraw-Hill, Inc., New York. SO/R 773:1969. Rectangular or square parallel keys and their corresponding keyways. References