MachDes1 All Modules Reviewer (1) PDF

MODULE 1 (Subtopic 1) MODULE 1 (Subtopic 2) STANDARDS AND CODES UNIFORMLY DISTRIBUTED STRESSES ❖ STANDARD Set of specifications for parts, materials, or processes intended to achieve uniformity, efficien...

MODULE 1 (Subtopic 1) MODULE 1 (Subtopic 2) STANDARDS AND CODES UNIFORMLY DISTRIBUTED STRESSES ❖ STANDARD Set of specifications for parts, materials, or processes intended to achieve uniformity, efficiency, and a specified quality ❖ CODE Set of specifications for the analysis, design, manufacture, and SAMPLE PROBLEM 2 construction of something An 80 kN pull is transmitted from bar X to bar Y DIMENSIONS AND TOLERANCES through a pin. If the yield strength in the bars is 200 N/mm2 and the shear yield strength in the pin is ❖ Nominal size – size we use in speaking of 160 N/mm2 , find the diameter of bars and of the an element (e.g. ½-in bolt) pin. Consider factor of safety of 2. ❖ Limits – stated maximum and minimum dimensions ❖ Tolerance – difference between the two limits MATERIAL STRENGTH ❖ Yield point (y) – point at which strain BENDING OR FLEXURAL STRESS begins to increase rapidly without corresponding increase in stress ❖ For solid circular section ❖ Ultimate strength (u) – maximum stress reached on the engineering stress-strain diagram ❖ For hollow circular section STRESS AND STRENGTH Strength (S) Stress (σ) Property: due to State: due to thermal SAMPLE PROBLEM 3 structure, processing, or mechanical loading and treatment An axle 1 meter long supported at its ends carries a Test data Calculate 𝜎 = 𝐹/A 30 kN flywheel at the center. If the bending stress is CAPACITY of an object STATE of an object not to exceed 60 MPa, find the diameter of the axle. (applied) FACTOR OF SAFETY 𝒍𝒐𝒔𝒔 − 𝒐𝒇 − 𝒇𝒖𝒏𝒄𝒕𝒊𝒐𝒏 𝒔𝒕𝒓𝒆𝒏𝒈𝒕𝒉 (𝑺) 𝑭𝑺 = 𝒂𝒍𝒍𝒐𝒘𝒂𝒃𝒍𝒆 𝒔𝒕𝒓𝒆𝒔𝒔 (𝛔) ❖ Considerations Effect of failure Type of load SAMPLE PROBLEM 4 Degree of accuracy in force analysis The pump lever exerts forces of 25 kN and 35 kN Cost of component concentrated at 150 mm and 200 mm from the left Service conditions and right hand bearing respectively. Find the SAMPLE PROBLEM 1 diameter of the central portion of the shaft, if the stress is not to exceed 100 MPa A rod loaded with an axial force of F = 2000 lbf undergoes stress of σ = F∕A. Using a material strength of 24 kpsi and a factor of safety of 3.0, determine the minimum diameter of a circular rod. TORSIONIONAL SHEAR STRESS SAMPLE PROBLEM 7 ❖ For solid circular section ❖ For hollow circular section SAMPLE PROBLEM 5 A shaft is transmitting 97.5 kW at 180 rpm. If the allowable shear stress in the material is 60 MPa, find the suitable diameter for the shaft. STRESS CONCENTRATION PRINCIPAL STRESSES Stress distribution concentrates around discontinuities 𝜎𝑚𝑎𝑥 = 𝐾𝑡 × 𝜎 where 𝐾𝑡 = stress concentration factor SAMPLE PROBLEM 6 A hollow shaft of 40 mm outer and 25 mm inner diameter is subjected to a twisting moment of 120 N-m, an axial thrust of 10 kN, and a bending moment of 80 N-m. Calculate the maximum compressive and shear stresses. SUPPLEMENTARY PROBLEM SOLVING 1 A cast iron link as shown in the figure is required to transmit a steady tensile load of 45 kN. Find the tensile stress induced in the link material at sections A-A and B-B SAMPLE PROBLEM 7 A shaft is subjected to a bending load of 3 kN, pure torque of 1000 N-m and an axial pulling force of 15 kN. Calculate the maximum principal stresses at A and B. SUPPLEMENTARY PROBLEM SOLVING 2 SUPPLEMENTARY PROBLEM SOLVING 5 The load on a bolt consists of an axial pull of 10 kN Calculate the force required to punch a circular together with a transverse shear force of 5 kN. Take blank of 60 mm diameter in a plate of 5 mm thick. permissible stress at 100 MPa. Find the diameter of The ultimate shear stress of the plate is 350 N/mm2. bolt required according to maximum principal stress. SUPPLEMENTARY PROBLEM SOLVING 3 A steel shaft 35 mm in diameter and 1.2 m long held rigidly at one end has a hand wheel 500 mm in diameter keyed to the other end. The modulus of rigidity of steel is 80 GPa. What load applied to tangent to the rim of the wheel produce a torsional MODULE 2 (Subtopic 1) shear of 60 MPa? ❖ Static load does not change in magnitude, point application, or direction. ❖ Failure can mean a part has separated into pieces or has become permanently distorted. FAILURE THEORIES SUPPLEMENTARY PROBLEM SOLVING 4 A spindle as shown is a part of an industrial brake and is loaded as shown. Each load P is equal to 4 kN and is applied at the midpoint of its bearing. Find the diameter of the spindle, if the maximum bending stress is 120 MPa. Distortion Energy Theory (Von Mises Theory) SAMPLE PROBLEM 1 A hot-rolled steel has a yield strength of 𝑆𝑦𝑡 = 𝑆𝑦𝑐 = 100 𝑘𝑝𝑠𝑖 and a true strain at fracture of 𝜀𝑓 = 0.55. Estimate the factor of safety for the following principal stress states: 𝜎𝑥 = 60 𝑘𝑝𝑠𝑖, 𝜎𝑦 = 40 𝑘𝑝𝑠𝑖, 𝜏𝑥𝑦 = − 15 𝑘𝑝𝑠𝑖. SAMPLE PROBLEM 2 The load on a bolt consists of an axial pull of 10 kN STRESS-LIFE DIAGRAM together with a transverse shear force of 5 kN. Find the diameter of bolt required according to the ❖ Rotating-beam test specimen distortion energy theory. Take the permissible stress as 100 MPa ❖ Endurance limit 𝑺𝒆 (fatigue limit) Stress below which a material can endure infinite number of repeated load cycles without failure BRITTLE COULOMB-MOHR THEORY Order principal stresses by choosing 𝜎1 to be the largest stress and choosing 𝜎2 to be the smallest stress. MARIN FACTORS ❖ Endurance limit modifying factors: SAMPLE PROBLEM 3 ❖ Values of Marin factors will be provided. The femur bone has an outside diameter of 24 mm. The tensile strength of the bone is 𝑆𝑢𝑡 = 120 𝑀𝑃𝑎, 𝑆𝑢𝑐 = 170 𝑀𝑃𝑎. The femur is subjected to 𝑇 = 80 𝑁𝑚 and 𝑀 = 100 𝑁𝑚. Assuming the bone acting in brittle manner, find the factor of safety. ESTIMATING STEEL ENDURANCE LIMIT SAMPLE PROBLEM 4 A steel piston rod having an ultimate strength of 500 MPa is subjected to a completely reversed axial loading MODULE 2 (Subtopic 2) with a load factor of 0.8. The surface of the rod is ground with a surface finish factor of 0.9. Determine the ❖ Fatigue failure design stress with a factor of safety of 2. Occurs below the yield point when exposed to repeated loadings Characterized by the three stages: A. Crack initiation B. Crack propagation C. Rapid fracture FATIGUE STRESS CONCENTRATION SUPPLEMENTARY PROBLEM SOLVING 1 A wrench made of cast iron (Sut = 31 kpsi and Suc = 109 kpsi) is subjected to σx = 23 kpsi and τxy = 12 kpsi. Assuming the wrench under brittle behavior, calculate the factor of safety using brittle Coulomb- Mohr theory. FATIGUE FAILURE CRITERIA ❖ Goodman method Good for conservative design purposes based on ultimate strength. ❖ Soderberg method Useful for quick first estimates or for situations that can be grossly over- designed based on yield strength. SUPPLEMENTARY PROBLEM SOLVING 2 Determine the thickness of a 120 mm wide uniform plate for safe continuous operation if the plate is to SAMPLE PROBLEM 5 be subjected to a tensile load that has a maximum value of 250 kN and a minimum value of 100 kN. A steel bar undergoes nominal stress that cycles The properties of the plate material are as follows: between 𝜎max = 40 𝑘𝑝𝑠𝑖 and 𝜎min = 20 𝑘𝑝𝑠𝑖. For Endurance limit stress = 225 MPa, and Yield point the material, 𝑆𝑢𝑡 = 100 𝑘𝑝𝑠𝑖, 𝑆𝑦 = 85 𝑘𝑝𝑠𝑖, and a stress = 300 MPa. The factor of safety based on fully corrected endurance limit of 𝑆𝑒 = 40 𝑘𝑝𝑠𝑖. yield point may be taken as 1.5 Estimate the fatigue factor of safety for Goodman methods MODULE 3 (Subtopic 1) SAMPLE PROBLEM 2 SHAFTS A hollow shaft is subjected to a torque of 1.5 kN-m and a bending moment of 3 kN-m. The ratio of the Rotating members usually circular in cross inner diameter to the outer diameter is 0.5 and the section used to transmit power outer diameter is 80 mm. Find the shear stress Transmission shaft – transmits power induced in the shaft. Assume gradually applied load between source and machine absorbing where 𝐾𝑚 = 1.5 and 𝐾𝑡 = 1 power (e.g., counter shaft, line shaft) Machine shaft – forms integral part of the machine itself (i.e. crankshaft) Axle – stationary member used to support bending STANDARD SIZES FOR TRANSMISSION SAMPLE PROBLEM 3 SHAFTS A mild steel shaft transmitting 20 kW at 200 rpm is 25 – 60 mm | 5 mm steps supported by two bearings 2.5 m apart and carries 60 – 110 mm | 10 mm steps a central load of 900N. Determine the size of the 110 – 140 mm | 15 mm steps shaft if the allowable shear stress is 42 MPa and 140 – 500 mm | 20 mm steps the allowable tensile stress is 56 MPa Standard length of shafts are 5 m, 6 m, and 7 m SHAFT DESIGN SAMPLE PROBLEM 1 What would be the diameter of the line shaft to transmit 10 horsepower if the shaft is to make 150 revolutions per minute according to PSME code? MODULE 3 (Subtopic 2) ❖ KEYS Used to connect a rotating machine element to a shaft and enable transmission of torque ❖ TYPES OF KEYS Values for Km and Kt will be provided. SUNK KEY DESIGN FLANGE COUPLING Connects two rotating shafts to each other by means of flanges SAMPLE PROBLEM 5 SAMPLE PROBLEM 4 A 1.4375-in diameter shaft transmits 40 hp at 600 rpm through a gear. Find the required dimensions SUPPLEMENTARY PROBLEM SOLVING 1 of the key with yield strength of 54 kpsi, shear yield A shaft made of mild steel is required to transmit strength of 31.2 kpsi, and a factor of safety of 1.5 100 kW at 300 rpm. The supported length of the shaft is 3 meters. It carries two pulleys each weighing 1500 N supported at a distance of 1 meter from the ends respectively. Assuming that the shaft has ultimate shearing stress of 60 MPa, determine the diameter of the shaft. SUPPLEMENTARY PROBLEM SOLVING 2 ❖ BOLTS Mate unthreaded objects typically with a Design the rectangular key for a shaft of 50 mm nut. diameter. The shearing and crushing stresses for the key and shaft material are 42 MPa and 70 MPa THREAD DEFINITIONS Pitch – distance between adjacent threads Major diameter – largest diameter of thread Minor diameter – smallest diameter of thread Pitch diameter – diameter between major and minor diameters Lead – linear distance the nut moves per screw revolution THREAD SPECIFICATIONS MODULE 4 (Subtopic 1) ❖ FASTENINGS Encompasses a broad category of tools Unified National Coarse (UNC) series – such as screws, bolts, nails, washers, and used in general applications with fewer rivets that mechanically holds objects threads for easier removal together. Unified National Fine (UNF) series – used ❖ SCREWS in applications where loosening due to Mate objects with existing threads or vibration or shock would be an issue creates threads as it turns. WORKING STRENGTH OF BOLTS ❖ Based on Machinery’s Handbook The working strength or permissible load of bolts used in packed joint when the nut on the bolt is tightened is: SAMPLE PROBLEM 1 What is the working strength of a 1-inch bolt that is screwed tightly in a packed joint when the allowable working stress is 10,000 psi? DESIGN OF BOLTS SAMPLE PROBLEM 4 A connection is subjected to an applied load of 1250 lb. The bolt has a yield strength of 72 ksi with UNC threads. Determine the diameter of the bolt and compute the approximate tightening torque assuming the initial stress from the tightening as 0.85𝑆𝑦 SAMPLE PROBLEM 2 The stress area of a bolt is 0.763 sq. in. If the material used is carbon steel, determine the applied load on the bolt. SAMPLE PROBLEM 3 A 5000-lb. gear box is provided with an eyebolt (𝑆𝑦 MODULE 4 (Subtopic 2) = 45 𝑘𝑠𝑖). What size of bolt should be used if UNC threads are used? Use a factor of safety of 2.5 ❖ POWER SCREWS Used to change angular motion into linear motion and transmit power Applications include lathe lead screws and screws for vises and jacks SAMPLE PROBLEM 5 A square-thread power screw has a mean diameter of 30 mm and a pitch of 4 mm with double threads. The given data include f = fc = 0.08, dc = 40 mm, and F = 6.4 kN per screw. a. Find the total torque required to raise and lower the load (consider collar torque). b. Find the efficiency during lifting the load based on total torque. c. Estimate the power of motor required at 100 rpm when lifting. SUPPLEMENTARY PROBLEM SOLVING 2 A double square thread screw is used to raise a load of 20,000 lb at 18 rpm. The mean diameter of the thread is 2.4375 in. and the pitch is 1 in. The collar friction coefficient is 0.12 and the thread friction coefficient is 0.10. The mean collar diameter is 5 in. Determine the power required to drive the screw. SUPPLEMENTARY PROBLEM SOLVING 1 SUPPLEMENTARY PROBLEM SOLVING 3 A 10-in diameter compressor is attached by 10 stud A single square thread power screw is to raise a bolts with a yield strength of 88 ksi. The cylinder load of 70 kN. The screw has a mean diameter of pressure is 200 psi. What is the size of the UNC 33.375 mm and a pitch of 6 mm. The coefficient of bolts to be used? What approximate tightening thread friction and collar friction are 0.13 and 0.10, torque should be needed from an initial stress of respectively. If the collar mean diameter is 90 mm, 76.5 ksi from tightening? find the efficiency of the power screw. MODULE 5 (Subtopic 1) SAMPLE PROBLEM 1 MECHANICAL SPRINGS A helical spring withstands a maximum load of 1000 N for a deflection of 25 mm with spring index ❖ Helical springs of 5. The maximum permissible shear stress for the Made up of wire coiled in the form of a spring is 420 MPa and modulus of rigidity is 84 helix and primarily intended for GPa. Determine the wire diameter, outside compressive or tensile loads. diameter, and total number of turns. Consider ❖ Leaf springs squared and ground ends. Consists of flat plates known as leaves held together by means of clamps and bolts. Absorbs shocks and vibration in vehicles DESIGN OF HELICAL SPRINGS SPRING SYSTEMS ❖ Springs in series ❖ Springs in parallel ❖ SAMPLE PROBLEM 2 Spring B is placed inside the coils of spring A having the same material and number of coils. The mean diameters of the spring A and B are 100 mm and 70 mm, respectively, and wire diameters are 13 mm and 8 mm, respectively. If the spring system is compressed by 2300 N, find the load taken and the maximum stress in each spring. Assume squared and ground ends. MODULE 5 (Subtopic 2) SAMPLE PROBLEM 4 TERMINOLOGY A spur gear has the following properties: gear ratio = 10:1, center distance = 660 mm, pinion ❖ Pitch diameter, 𝐷 – diameter of pitch circle transmission of 500 kW at 1800 rpm, involute teeth ❖ Pressure angle, 𝜙 – angle between tooth with 22.5°pressure angle where addendum = m, face and gear wheel tangent and permissible normal pressure between teeth = ❖ Module, m – ratio of pitch diameter to 175 N per mm of width. Calculate the module if no number of teeth interference is to occur, the width of the pinion, and the radial load on the bearings of the wheels. ❖ Gear ratio (or velocity ratio), G – ratio of rotations of pinion to rotations of gear DESIGN OF SPUR GEARS SAMPLE PROBLEM 5 A pinion rotating at 600 rpm drives a spur gear at a ❖ Force analysis transmission ratio of 4:1. The allowable stresses for the pinion and gear are 84 MPa and 105 MPa, respectively. The pinion has 16 standard 20° full depth involute teeth of module 8 mm. The face width of both the gears is 90 mm. Find the power that can be transmitted based on strength. Use tooth form factor and velocity factor ❖ Lewis equation SAMPLE PROBLEM 3 A gear is used to transmit 20 kW at 600 rpm to a driven gear. The pinion has a pitch diameter of 200 mm. If the pressure angle is 14.5 degrees, find the load that tends to separate the two gears. SUPPLEMENTARY PROBLEM SOLVING 1 SUPPLEMENTARY PROBLEM SOLVING 3 A helical coil spring is made of steel whose A pair of straight teeth spur gears is to transmit 20 allowable stress is 80 MPa. The dimensions of the kW when the pinion rotates at 300 rpm. The spring with squared and ground ends are, as velocity ratio is 1:3. The allowable static stresses follows: Wire diameter = 20 mm, outside diameter = for the pinion and gear materials are 120 MPa and 250 mm, number of total coils = 10 coils. Determine 100 MPa respectively. The pinion has 15 teeth and the maximum permissible axial load and the its face width is 14 times the module. Determine the deflection caused. Assume G of steel 78 GPa. module of both the pinion and the gear from the standpoint of strength. The tooth form factor y can be taken as y = π(0.154 - 0.912/T) and velocity factor as Kv = (3 + v)/3. SUPPLEMENTARY PROBLEM SOLVING 2 Two springs in series supports a load of 3000 N. The upper spring has 12 active turns of 25-mm-diameter wire on a mean radius of 100 mm. The lower spring consists of 10 active turns of 20-mm diameter wire on a mean radius of 75 mm. If G = 83 GPa, compute the total elongation of the assembly.