5. Repeated Loading. 330:148 (g) Machine Design. Dynamic Strength. Dynamic Loads. Dynamic Strength. Dynamic Strength. Nageswara Rao Posinasetti

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1 330:48 (g) achine Design Nageswara Rao Posinasetti P N Rao 5. Repeated Loading Objectives Identify the various kinds of loading encountered on a part and learn to combine them as appropriate. Determine the level of stress in a material at which a hypothesized defect would not propagate. Recognize what types of factors affect this endurance limit for the material. Factor in the effect of shapes and discontinuities as they affect the stress concentration factors. Gain experience using fatigue equations when designing parts subject to repeated loads. P N Rao Dynamic Loads Forces that vary frequently in magnitude and direction are called dynamic loads. Varying load: agnitude changes but not the direction Reversing load: Both magnitude and direction hock load: Impact Dynamic trength Fatigue failure in a material is when it fails even when the stress may not go beyond the proportional limit. P N Rao 3 P N Rao 4 Dynamic trength Dynamic trength P N Rao 5 P N Rao 6

2 0 Fatigue failure Tensile stress T Time, t Compressive stress Fatigue failure After some number of stress reversal cycles a crack is initiated. This crack propagates towards the centre. any more cracks are formed around the periphery. Ultimately the shaft breaks when the stress in the remaining solid area exceeds the ultimate strength, as shown in Fig P N Rao 7 P N Rao 8 Fatigue failure Fatigue failure P N Rao 9 P N Rao 0 Endurance Limit and Endurance trength It is the strength of a material to resist the propagation of cracks under stress reversals. Endurance Limit ( n ): Is the stress value below which an infinite number of cycles will not cause failure Endurance Limit n 0.5 u P N Rao P N Rao

3 odifying factors for endurance limits The actual value of endurance limit to be applied needs to be modified depending upon the application Type of stress C type 0.8 axial C type 0.8 shear or torsion C type.0 bending odifying factors for endurance limits ize C size.00 for < ½ inch C size 0.85 for < ½ to inches C size 0.75 for < inches and over urface Rough surfaces have stress raisers n C type C size C surface n P N Rao 3 P N Rao 4 urface Effect urface Effect P N Rao 5 P N Rao 6 Variation of tresses ean stress, m Alternating stress, a m a + min min P N Rao 7 P N Rao 8 3

4 Theories of failure Example Problem 5- Theories of Failure: oderberg Equation oderberg equation N m y + a n For a smooth rotating shaft with no sharp corners or change in shape, determine the required diameter under the loading condition shown. Ignore any torque. The surface of the shaft is highly polished. The shaft is made from annealed AII 440 steel. Use a safety factor of. P N Rao 9 P N Rao 0 Example Problem 5- Theories of Failure: oderberg For the first trial, assume the resultant diameter will be between ½ and inches: First calculate and min : u 95 ksi y 60 ksi (Appendix 4) FL lb 40 in 5000 in lb 4 FL min 5000 in lb in lb min 5000 in lb min (Appendix ) Example Problem 5- Theories of Failure: oderberg Find mean and alternating : + min mean 5000in lb 5000lb in mean 0 min alt 5000 in lb 5000 in lb 5000 in lb alt (5-) (5-3) P N Rao P N Rao Example Problem 5- Theories of Failure: oderberg Find the endurance limit modifying factors: n C size C surface C type n As surface is polished: C surface (5-) (Figure 5-7b) Example Problem 5- Theories of Failure: oderberg ubstituting into the oderberg equation: N m y + a n 5000 in-lb 40,375 lb/in.47 in³ (5-5) As n is unknown, use.5 u : Use C size.85 assuming.5 < D < Bending C type n.85 () () (.5) 95 ksi n ksi D D 3 π D³ 3 3 π 3 3 (.47 in 3 ) π D.36 in Appendix 3 P N Rao 3 P N Rao Use D -3/8 or.375 in 4 4

5 Example Problem 5- Theories of Failure: oderberg Equation Example Problem 5- Theories of Failure: oderberg A -inch-long round cantilever beam is loaded repeatedly but no load reversal occurs. If the bar is made from annealed AII 30 stainless steel and the surface is polished for a safety factor of.6, find the required diameter using the oderberg method. u 90 ksi y 37 ksi n 34 ksi Find and min : min min FL 000 lb in,000 in lb 0 0,000 in lb (Appendix 8) (Appendix ) P N Rao 5 P N Rao 6 Example Problem 5- Theories of Failure: oderberg Find mean and alternating : + min mean,000 in-lb + 0 mean (5-) Example Problem 5- Theories of Failure: oderberg Find the endurance limit modifying factors: C size.85 (assume ½ < D < inches) C type (bending) 6,000 in-lb mean C surface (polished surface) (5-3) n C size C surface C type n' (5-) min alt n.85 () () 34 ksi,000 in-lb 0 alt n 8.9 ksi 6,000 in-lb alt P N Rao 7 P N Rao 8 Example Problem 5- Theories of Failure: oderberg ubstituting into the oderberg equation: N m + a y n 6,000 in-lb 6,000 in-lb.6 37,000 lb/in 8,900 lb/in D.59 in 3 π D3 3 D 3 3 π 3 3 (.59 in3 ) π (5-4) (Appendix 3) tress Concentration: Discontinuities in part contour hafts with shoulders to accommodate the seating of bearings Key ways in shafts that use key to secure pulleys, cams and gears Threads on one end of a bolt and a head on the other end Fillet at the base of gear teeth D P N Rao.8 inches 9 P N Rao 30 5

6 tress Concentration tress Concentration Physical discontinuity is called a stress raiser or a region of stress concentration. tress concentration factor, K _actual avg_calc P N Rao 3 P N Rao 3 tress concentration tress concentration F avg A - A B H avg K K tress concentration factor P N Rao 33 P N Rao 34 ample problem.: Fig..8 shows a rectangular bar containing a hole and undergoing a tensile force of 0,000 pounds. In this case t in., d 0.5 in., and w.5 in. a) Find the tensile stress at no hole condition; b) Find the average stress at the hole section assuming no stress concentration; and c) Find the imum stress at the hole section taking into consideration the effect of the stress raiser. tress concentration problem (Fig..8) P N Rao 35 P N Rao 36 6

7 olution a) tress with no hole 0000/ (.5) 333 psi F b) avg A - A B 0000 avg H 5000 psi c) From Fig.7, K.3 avg ,500 psi K Reducing stress concentrations ake all transitions as gradual as possible. (Fig..0) Drill holes on both sides of key way (Fig..9) Thread root diameter equals the adjacent shank diameter. (Fig..) Add shoulders for press fitted components. (Fig..) P N Rao 37 P N Rao 38 tress concentration Fig..9) tress concentration Fig..0) P N Rao 39 P N Rao 40 tress concentration (Fig..) tress concentration (Fig..) P N Rao 4 P N Rao 4 7

8 Allowable stress & Factor of afety Uncertainity allowable allowable F F yield_strength ductile_material ultimate_strength brittle_material Variability of material composition and properties Effect of processing on properties Effect of nearby assemblies such as weldments Effect of thermo-mechanical treatment on properties P N Rao 43 P N Rao 44 Uncertainity Intensity and distribution of loading Validity of mathematical models used Intensity of stress concentrations Influence of time on strength and geometry Effect of corrosion Effect of wear Unknowns Exact type and magnitude of all loads aterial property variations Precise stress concentration effects Extremes of environmental conditions, such as heat and moisture Approximate stress analysis formulae Residual stresses produced during manufacturing P N Rao 45 P N Rao 46 Factor of safety Factor a Determining a realistic factor of safety is very difficult. Higher factor increases cost and lower factor is likely to cause a premature failure. Hence F a b c d Considers the variability of applied loads. a for loads that are constant in magnitude and directions a for complete load reversals in order to take fatigue into account P N Rao 47 P N Rao 48 8

9 Factor b Considers the abruptness with which loads are applied. Factor c Considers the consequences of failure related to human safety, cost and so on. b for gradually applied loads b for suddenly applied loads b 3 or more (depending on the severity) for impact loads c normally varies between. and depending upon the seriousness of the failure P N Rao 49 P N Rao 50 Factor d Differentiates F ductile material from brittle material. d Ultimate strength Yield strength P N Rao 5 9