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Question: a steel shaft in a spur gear reducer is subjected...

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A steel shaft in a spur gear reducer is subjected to a constant torque together with lateral forces that tend always to bend it downward in the centre. These result in calculated stresses of 80 MPa torsion and 60 MPa bending. However, these are nominal values and do not take into account tress concentration caused by a shoulder (refer to Figure 3), where dimensions are D 36 mm, d 30 mm and r3 mm. All surfaces are machined, and the steel has the hardness, yield stress and ultimate strength values of 200 Bhn, 550 MPa and 700 MPa, respectively. Solve the following problems: (i) Calculate the safety factor with respect to the infinite life. (12 marks) (ii) Compare and discuss your answer in (i) with the Trescas yielding (static) safety factor. (3 marks) Figure 3 Note: Use Figures 4 to 5, Table 1 and Appendix 2 for your references to answer this question.
Use these values with bending and axial loads Steel r Use these values with torsnOsi) and Bhn 180 (360 Bhn) 1.0 as marked hn) 200 (400 140 (280 Bhn) 80(160 Bhn) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 100 1200 Bhn) 80 160 860 20 Bha) 80 ( Aluminum alloy (based on 2024-T6 data) 50 (100 8hn) 02 004 06 0.10 0.14 Notch radius r (in) 0.16 0 0.51.015 2.0 2.5 3.0 3.540 Notch radiusr(mm) Figure 4 Notch sensitivity curves Hardness (H 120 160 200 240 280 320 360 400 440 480 520 1.0 0.9 0.8 0.7 0.6 0.5 Mirror-polished Fine-ground or Commercially polished 0.3 0.2 0.1tap water Corroded in Corroded in salt water 60 80 100 120 140 160 180 200 220 240 260 Tensile strength S, Cksi 0.4 0.6 0.8 1.0 1 14 1.6 1.8 S, (GPa) Figure 5 Surface finish factors for steel
Table 1: Parameters used to estimate the S-N curve using Juvinalls estimation Parameter Applicability Value Bending fatigue limit factor: me Steels, ơmS 1400 MPa Higher strength steels Cast irons; Al alloys 0.5 S0.5 0.4 ifo, 325 MPa Higher strength Al Magnesium alloys erb 130 MPa 0.35 Bending Axial Torsion 1.0 Load type factor: CL 0.58 Bending or torsion d < 10 mm d 10 to 50 mm d-50 to 100 mm d- 100 to 150 mnm Axial Size (stress gradient) factor: 0.9 0.8 0.7 0.7 to 0.9 Life for fatigue limit point: Ne, cycles Steels, cast irons Aluminium alloys Magnesium alloys 10 5 x 108 10 Constants for point at Nr- 10: Bending or torsion m-0.9 kf Axial, small eccentricity m,-o.75
APPENDIX 3.0 2.8 2.6 2.4 2.2 k, 2.0 1.8 1.5 1.4 12 1.0 1.5 1.1 、1.03 0 0.1 0.2 0.3 rld 2.6 2.4 2.2 2.0 1.6 1.4 1.2 1.0 1.05 1.01 0.1 0.2 0.3 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 1.2 1.09 0.1 0.2 0.3 rld
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