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Notes on Lesson. Failure Theories. Stress in machine components should be accurately computed. Designer must understand material limits to ensure a safe design. Design Factor. Factor of Safety (N)

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## Notes on Lesson

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**Failure Theories**• Stress in machine components should be accurately computed. • Designer must understand material limits to ensure a safe design.**Design Factor**• Factor of Safety (N) • Suitable values depend on inherent danger, certainty of calculations, certainty of material properties, etc.**Static Stresses - Brittle Materials**• Percent elongation < 5% • for parts in tension • for parts in compression • for parts with general stress**Ø4.00”**R0.25” Ø5.00” R0.25” Example The Gray Cast Iron (Grade 40) cylinder carries an axial compressive load of 75,000 lbs and a torque of 20,000 in lbs. Compute the resulting design factor.**Static Stresses - Ductile Materials**• Percent elongation > 5% • Distortion Energy Theory • Define von Mises Stress • For nominal stress • For localized stress**Static Stresses - Ductile Materials**• Percent elongation > 5% • Maximum Shear Stress Theory • For nominal stress • For localized stress**450**5000 lbs Example Specify a diameter for the middle portion of the rod, if it is to be made from AISI 1040-hot rolled steel.**400 lb**200 lb 20” 14” Example For the seat support shown, specify a standard structural tube to resist static loads shown. The tube has properties similar to AISI 1020 hot-rolled steel. Use a design factor of 3.**salt**smean Repeated Loads**1.25”**0.1” R .75” 1” Example The notched bar is machined from AISI 1020 steel. This bar is subjected to a load that varies from 2000 lb to 3000 lb. Determine the mean and alternating nominal stresses.**Motor**Alternating Stress, sa Endurance Strength, sn 108 107 106 105 103 104 Cycles to Failure, N (log) Fatigue Strength • R.R. Moore Test**Endurance Strength**• sn = Endurance strength • Listed in tables • If no information is available, use • sn 0.5 su (Steel) • sn 0.4 su (Aluminum)**Adjusted Endurance Strength**• The data from the standard R.R. Moore test is adjusted for a particular application. • sn’ = Adjusted endurance strength = (Cs) (Cm) (Cst) (CR) (sn)**Size and Stress Type Factors**• Cs = Size Factor • D< 0.4 in Cs = 1.0 • 0.4 < D 2.0 in Cs = (D/0.3)-0.068 • 2.0 < D 10.0 in Cs = D-0.19 For rectangular sections, D=.808(h b)1/2 • Cst = Stress Type Factor • = 1.0 for bending • = 0.80 for axial tension • = 0.50 for torsion**Material and Reliability Factor**• Cm = Material Factor • = 1.0 for wrought steel • = 0.80 for cast steel • = 0.70 for cast iron • CR = Reliability Factor • 50% CR = 1.0 • 90% CR = 0.90 • 99% CR = 0.81 • 99.9% CR = 0.75**1.25”**0.1” R .75” 1” Example The notched bar is machined from AISI 1020 steel. This bar is subjected to a load that varies from 2000 lb to 3000 lb. Determine the endurance limit of the material.**Repeated Stresses - Ductile Materials**• Distortion Energy Theory • Define repeated von Mises Stress • Solderberg criterion**Repeated Stresses - Ductile Materials**• Maximum Shear Stress Theory • ssy = 0.5 sy • s’sn = 0.5 sn**1.25”**0.1” R .75” 1” Example The notched bar is machined from AISI 1020 steel. This bar is subjected to a load that varies from 2000 lb to 3000 lb. Comment on the robustness of the design.**48”**Example Comment on the robustness of a 1-1/4” round bar made from AISI 1213 C-D steel. It carries a constant tensile load of 1500 lbs, a bending load that varies from 0 to 800 lbs at the senter of the 48” length and a constant torque of 1200 in lbs.**Shafts**• Connect power transmission components. • Inherently subjected to transverse loads and torsion.**Wt**Wr T Shaft Forces • Gears As before**Ftight**D T Fslack = 0 Shaft Forces • Chains**Shaft Forces**• V-belts Ftight D T Fslack**Shaft Forces**• Flat belts Ftight D T Fslack**Material Properties**• For steady load (torsion) sys=.5sy • For fatique load ( bending) sn’=cs cR sn cT = 1 (bending) cm = 1 (wrought steel)**Stress Concentrations**• Keyseats • Sled Runner Kt = 1.6 • Profile Kt = 2.0 • Woodruff Kt = 1.5**Stress Concentrations**• Shoulders • Sharp, Bearing (r/d .03) Kt = 2.5 • Round, Gear Bore (r/d .17) Kt = 1.5 • Grooves • Retaining Rings Kt = 1.5 Try not to let Kt’s overlap. Leave .10 - .15” between**Strength Analysis**• Bending stress • Torsion stress For round sections For round sections**Strength Analysis**• Mohr’s circle and Solderberg • Suggested Design Factors: • N=2 smooth operation • N=3 typical industrial operation • N=4 shock or impact loading**Minimum Acceptable Diameter**• The designer must size the shaft. • Solve for appropriate diameters**Example**Determine a suitable diameter for a shaft made from AISI 1144 OQT 1000. It is subjected to a reversing bending moment of 3000 ft lbs and a steady torque of 1800 ft lbs. The shaft has a profile keyway.**Example**The shaft shown is part of a grain drying system • At A, a 34 lb. propeller-type fan requires 12 hp when rotating at 475 rpm. • A flat belt pulley at D delivers 3.5 hp to a screw conveyor handling the grain. • All power comes to the shaft through the v-belt at C. Using AISI 1144 cold drawn steel, determine the minimum acceptable diameter at C.**E**B D A C 12” 4” 10” 10” 150 Sheave C Sheave D Example**Shafts Accessories**• Components used to securely mount power transmitting elements on a shaft. • Axial • Rotational**Keys**• Allow torque to be transferred from a shaft to a power transmitting element (gear, sprocket, sheave, etc.)**H**W L Key Design • Use a soft, low strength material (ie, low carbon steel) • Standard size H=W=1/4 D • Design length based on strength**H**W Shaft Dia. (in) W (in) T S Standard Key Sizes**Key Design**• Key Shear • Failure Theory • Length**Example**Specify a key for a gear (grade 40, gray cast iron) to be mounted on a shaft (AISI 1144, hot rolled) with a 2.00 in. diameter. The gear transmits 21000 lb-in of torque and has a hub length of 4 in.**Retaining Rings**• Also known as snap rings • Provides a removable shoulder to lock components on shafts or in bores. • Made of spring steel, with a high shear strength. • Stamped, bent-wire, and spiral-wound.**Retaining Ring Selection**• Based on shaft diameter & thrust force**Set Screws**• Setscrews are fasteners that hold collars, pulleys, or gears on shafts. • They are categorized by drive type and point style.**D**d Pins • A pin is placed in double shear • Holds torsion and axial loads • Hole is made slightly smaller than the pin (FN1 fit)**Example**Specify a pin for a gear (grade 40, gray cast iron) to be mounted on a shaft (AISI 1144, hot rolled) with a 2.00 in. diameter. The gear transmits 21000 lb-in of torque and has a hub length of 4 in.**Roll Pins**• Easier disassembly**Collars**• Creates a shoulder on shaft without increasing stock size. • Held with either set screw or friction (clamped)

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