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Notes on Lesson Faculty Name:V. KIRAN KUMARCode:AU28 Subject Name:DESIGN OF MACHINE ELEMENTS Code:ME2303 Year:IIISemester:V Degree & Branch:B.E. AUTOMOBILESection:- 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. Failure ComponentatStressStress ExpectedN =Static Stresses - Brittle Materials Percent elongation < 5% for parts in tension for parts in compression for parts with general stress otusN =ocusN =c tu us s N2 11 o o+ =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. 4.00 5.00 R0.25 R0.25 Static Stresses - Ductile Materials Percent elongation > 5% Distortion Energy Theory Define von Mises Stress For nominal stress For localized stress ' oysN =' ousN =2 12221' o o o o o + =Static Stresses - Ductile Materials Percent elongation > 5% Maximum Shear Stress Theory For nominal stress For localized stress max max2t ty yss sN = =maxtussN =Example Specify a diameter for the middle portion of the rod, if it is to be made from AISI 1040-hot rolled steel. 5000 lbs 450 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. 200 lb 400 lb 20 14 Repeated Loads TimeStressoalt omean 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. 0.1 R 11.25.75Fatigue Strength R.R. Moore Test 103104 105106107108 Endurance Strength, sn Cycles to Failure, N (log) Alternating Stress, oa Motor 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 inCs = 1.0 0.4 < D 2.0 inCs = (D/0.3)-0.068 2.0 < D 10.0 inCs = D-0.19 For rectangular sections, D=.808(h b)1/2 Cst = Stress Type Factor = 1.0for bending = 0.80 for axial tension = 0.50 for torsion Material and Reliability Factor Cm = Material Factor = 1.0for 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 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. 0.1 R 11.25.75Repeated Stresses - Ductile Materials Distortion Energy Theory Define repeated von Mises Stress Solderberg criterion na tymsKs N '' ' 1 o o+ =m m m m m 2 12221' o o o o o + =a a a a a 2 12221' o o o o o + =Repeated Stresses - Ductile Materials Maximum Shear Stress Theory sna tsymsKs N ') ( ) ( 1max maxt t+ = ssy = 0.5 sy ssn = 0.5 sn 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. 0.1 R 11.25.75Example Comment on the robustness of a1-1/4 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. 48 Connect power transmission components. Inherently subjected to transverse loads and torsion. Shafts Shaft ForcesGears As before Wr Wt T Shaft Forces Chains Fslack = 0 Ftight DTFtight2=D T Shaft Forces V-belts Fslack Ftight DTFtight5 . 2=D T DTFslack2=Shaft Forces Flat belts Fslack Ftight DTFtight3=D T DTFslack =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 RunnerKt = 1.6 ProfileKt = 2.0 WoodruffKt = 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 Kts overlap.Leave .10 - .15 betweenStrength Analysis Bending stress Torsion stress SM KIc M Kt t= = oSTJr T2= = t323DSt=cIrJ2 =For round sections For round sections Strength Analysis Mohrs circle and Solderberg ( ) ( )Ss T s M KNy n t2 2/43' /1+=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 ( ) ( )

+ =2 2/43' /32y n ts T s M KNDtExample 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. Example 12 1010 4 A B C D E Sheave C 150 Sheave D Components used to securely mount power transmitting elements on a shaft. Shafts Accessories Axial Rotational KeysAllow torque to be transferred from a shaft to a power transmitting element (gear, sprocket, sheave, etc.) Key DesignUse a soft, low strength material(ie, low carbon steel) Standard sizeH=W=1/4 D Design lengthbased on strength H L W Standard Key Sizes Shaft Dia. (in)W (in) 22 2W D H DS + =T S H W . 005 .22 2inW D H DT + + +=Key Design Key Shear Failure Theory Length yDWsTNL4=DLWTAF 2= = tTDLW s sNy y4 2= =tDTDTF22 /= =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 lockcomponents 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. Standard Set Screw Sizes Set Screw Holding Pins A pin is placed in double shear Holds torsion and axial loads ys DN Tdt8=D d 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) Mechanical Couplings Couplings are used to join two shafts Rigid couplings are simple and low cost. But they demand almost perfect alignment of the mating shafts. Misalignment causes undue forces and accelerated wear on the shafts, coupling, shaft bearings, or machine housing. Mechanical Couplings In connecting two shafts, misalignment is the rule rather than the exception. It comes from such sources as bearing wear, structural deflection, thermal expansion, or settling machine foundations. When misalignment is expected, a flexible coupling must be used. Mechanical Couplings Selection factors include: - Amount of torque (or power & speed) - Shaft Size- Misalignment toleranceFasteners, Powers Screws, Connections Helical thread screw was an important invention.Power Screw, transmit angular motion to liner motion Transmit large or produce large axial force It is always desired to reduce number of screws Definition of important Terminologies Major diameter d, Minor diameter dr Mean dia or pitch diameter dp Lead l, distance the nut moves for one turn rotation Single and Double threaded screws Double threaded screws are stronger and moves faster Screw Designations United National Standard UNS International Standard Organization Roots and crest can be either flat or roundPitch diameter produce same width in the thread and space, Coarse thread Designated by UNC Fine Thread UNF,is more resistance to loosening, because of its small helix angle. They are used when Vibration is present Class of screw, defines its fit, Class 1 fits have widest tolerances, Class 2 is the most commonly used Class three for very precisionapplication Example:1in-12 UNRF-2A-LH, A for Ext. Thread and B for Internal, R root radius Metric M10x1.510 diameter mm major diameter,1.5 pitch Some important Data for UNC, UNF and M threads Lets Look at the Table 8-1 on Page 398 Square and Acme Threads are used for the power screw Preferred pitch for Acme Thread d, in1/45/163/81/25/83/47/811 1/4 p,in 1/161/141/121/101/81/61/61/51/5 Mechanics of Power Screws Used in design to change the angular motion to linear motion, Could you recall recent failure of power screw leading to significant causalities What is the relationship between the applied torque on power screw and lifting force F Torque for single flat thread )secsec(2 o to tfl dfd l FdTmm mR+=) (2) (2f l dl f d FdTf l df d l FdTmm mLmm mR+=+=ttttIf the thread as an angle , the torque will beWedging action, it increases friction Stresses in the power Screw p n dFAVp n dFp n dFdTt rt rbt mBtttotott32362 /163= == ==Shear stress in the base of the screw Bearing stress Bending stress at the root of the screw Shear stress in thethread nt number of engaged thread Loading to the fasteners and their Failure considerations Bolts are used