NME-501 : MACHINE DESIGN-I

Transcription

1 Syllabus NME-501 : MACHINE DESIGN-I UNIT I Introduction Definition, Design requirements of machine elements, Design procedure, Standards in design, Selection of preferred sizes, Indian Standards designation of carbon & alloy steels, Selection of materials for static and fatigue loads. 3 Design for Static Load Modes of failure, Factor of safety, Principal stresses, Stresses due to bending and torsion, Theory of failure. UNIT II Design for Fluctuating Loads Cyclic stresses, Fatigue and endurance limit, Stress concentration factor, Stress concentration factor for various machine parts, Notch sensitivity, Design for finite and infinite life, Soderberg, Goodman & Gerber criteria. Riveted Joints Riveting methods, materials, Types of rivet heads, Types of riveted joints, Caulking and Fullering, Failure of riveted joint, Efficiency of riveted joint, Design of boiler joints, Eccentric loaded riveted joint. UNIT III Shafts Cause of failure in shafts, Materials for shaft, Stresses in shafts, Design of shafts subjected to twisting moment, bending moment and combined twisting and bending moments, Shafts subjected to fatigue loads, Design for rigidity. Keys and Couplings Types of keys, splines, Selection of square & flat keys, Strength of sunk key, Couplings, Design of rigid and flexible couplings. UNIT IV Mechanical Springs Types, Material for helical springs, End connections for compression and tension helical springs, Stresses and deflection of helical springs of circular wire, Design of helical springs subjected to static and fatigue loading. Power Screws Forms of threads, multiple threads, Efficiency of square threads, Trapezoidal threads, Stresses in screws, Design of screw jack Note: Design data book is allowed in the examination Books and References

2 UNIT-I

3 MEERUT INSTITUTE OF TECHNOLOGY MEERUT B.Tech (Mechanical) (V semester) Subject-Machine Design-1 Assignment No-1 1. What is Machine Design? What are the steps in Machine Design process? 2. What do you mean by need analysis? Write its importance in design. (U.P.T.U ) 3. Explain the brain storming. What are their rules? 4. What is standardization? Give the advantages of standardization. (U.P.T.U ) 5. What is interchangeability? 6. Explain Concurrent Engineering. 7. What is preferred number? Derive the R-10 series. 8. Explain the importance of preferred size in design process. (U.P.T.U ) 9. Find out the number of R-20/4 (10 100) derived series. 10. Discuss the effect of silicon, manganese, sulphur and phosphorus on cast iron. 11. Designate the following materials (a) Grey cast iron with minimum tensile strength of 300 N/mm 2. (b) Designate plain carbon steel with 0.5 % carbon and 0.85 manganese (c) Carbon= %, chromium= %. (d) Carbon %, Ni= %, Cr= % (e) C= %, Si= %, Mn= %, Ni= %, Cr= % (f) 50Cr1V23 U.P.T.U ) 12. Define these definitions (a) Ductility (b) Brittleness (c) Creep (d) Fatigue (e) Elasticity (f) Plasticity (g) Toughness (h) Resilience 13. What are the reasons for the use of alloy steel in machine parts? (U.P.T.U ) 14. What are the three basic mode of failure of mechanical component? 15. What is factor of safety? Why is it necessary to use factor of safety. 16. What are the factors to be considered for deciding the magnitude of factor of safety? 17. Explain different types of theories of failure in machine design. 18. Explain the importance of material selection decision in machine design. (U.P.T.U ) 19. Discuss the factors which are considered in the selection of a material for a machine component. 20. Enumerate advantages and disadvantages of plastic material over metals. (U.P.T.U )

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5 MEERUT INSTITUTE OF TECHNOLOGY MEERUT B.Tech (Mechanical) (V semester) Subject-Machine Design-1 Tutorial No-1 W max = N and has a stress concentration factor = 1.8. Use factor of safety as A forged steel bar 50 mm in diameter is subjected to 7. reversed bending stress of 250 N/mm 2. The bar is made 8. of steel 40C8 (S ut =600 N/mm 2 ). Calculate the life of the bar for a reliability of 90 %. Ans=23736 Cycle 2. A rotating beam made of steel 45C8 (S ut =630 N/mm 2 ) is subjected to completely reversed bending stress. The corrected endurance limit of the bar is 315 N/mm2. Calculate the fatigue strength of the bar for a life of 90,000 cycle. 3. A machine component is subjected to a flexural stress which fluctuates between MN/m 2 and 150 MN/m 2. Determine the value of minimum ultimate strength according to 1. Gerber relation; 2.Goodman relation; and 3. Soderberg relation. Take yield strength = 0.55 Ultimate strength; Endurance strength = 0.5 Ultimate strength; and factor of safety = A bar of circular cross-section is subjected to alternating tensile forces varying from a minimum of 200 kn to a maximum of 500 kn. It is to be manufactured of a material with an ultimate tensile strength of 900 MPa and an endurance limit of 700 MPa. Determine the diameter of bar using safety factors of 3.5 related to ultimate tensile strength and 4 related to endurance limit and a stress concentration factor of 1.65 for fatigue load. Use Goodman straight line as basis for design. 5. Determine the thickness of a 120 mm wide uniform plate for safe continuous operation if the plate is to be subjected to a tensile load that has a maximum value of 250 kn and a minimum value of 100 kn. The properties of the plate material are as follows: Endurance limit stress is 225 MPa, and Yield point stress is 300 MPa. The factor of safety based on yield point may be taken as Determine the diameter of a circular rod made of ductile material with a fatigue strength (complete stress reversal), σe = 265 MPa and a tensile yield strength of 350 MPa. The member is subjected to a varying axial load from W min = N to 7. A steel rod is subjected to a reversed axial load of 180 kn. Find the diameter of the rod for a factor of safety of 2. Neglect column action. The material has an ultimate tensile strength of 1070 MPa and yield strength of 910 MPa. The endurance limit in reversed bending may be assumed to be one-half of the ultimate tensile strength. Other correction factors may be taken as follows:for axial loading = 0.7; For machined surface = 0.8 For size = 0.85 ; For stress concentration = A circular bar of 500 mm length is supported freely at its two ends. It is acted upon by a central concentrated cyclic load having a minimum value of 20 kn and a maximum value of 50 kn. Determine the diameter of bar by taking a factor of safety of 1.5, size effect of 0.85, surface finish factor of 0.9. The material properties of bar are given by : ultimate strength of 650 MPa, yield strength of 500 MPa and endurance strength of 350 MPa. 9. A piston rod of circular cross section is subjected to a cyclic load fluctuating between 15 kn in compression to 25 kn in tension. The endurance limit for the piston rod material is 360 N/mm 2. While yield strength is 400 N/mm 2. The impact factor is 1.25 while fos is 1.5. The surface finish factor and stress concentration factor are 0.88 and 2.25 respectively. Determine the diameter of piston rod. d=20.70 mm 10. A 50 mm diameter shaft is made from carbon steel having ultimate tensile strength of 630 MPa. It is subjected to a torque which fluctuates between 2000 N-m to 800 N-m. Using Soderberg method, calculate the factor of safety. Assume suitable values for any other data Needed

6 11. A simply supported beam has a concentrated load at the centre which fluctuates from a value of P to 4 P. The span of the beam is 500 mm and its cross-section is circular with a diameter of 60 mm. Taking for the beam material an ultimate stress of 700 MPa, a yield stress of 500 MPa, endurance limit of 330 MPa for reversed bending, and a factor of safety of 1.3, calculate the maximum value of P. Take a size factor of 0.85 and a surface finish factor of 0.9.

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8 MEERUT INSTITUTE OF TECHNOLOGY MEERUT B.Tech (Mechanical) (V semester) Subject-Machine Design-1 Tutorial No-2 1. A solid shaft is transmitting 1 MW at 240 r.p.m. Determine the diameter of the shaft if the maximum torque transmitted exceeds the mean torque by 20%. Take the maximum allowable shear stress as 60 MPa.. Ans: d=160 mm 2. A cylindrical shaft made of steel of yield strength 700 MPa is subjected to static loads consisting of a bending moment of 10 kn-m and a torsional moment of 30 kn-m. Determine the diameter of the shaft using two different theories of failure and assuming a factor of safety of 2. Ans. 100 mm 3. Find the diameter of a solid steel shaft to transmit 20 kw at 200 r.p.m. The ultimate shear stress for the steel may be taken as 360 MPa and a factor of safety as 8.If a hollow shaft is to be used in place of the solid shaft, find the inside and outside diameter when the ratio of inside to outside diameters is 0.5. Ans: d=50 mm do = 50mm di=25 mm 4. A line shaft rotating at 200 r.p.m. is to transmit 20 kw. The shaft may be assumed to be made of mild steel with an allowable shear stress of 42 MPa. Determine the diameter of the shaft, neglecting the bending moment on the shaft. Ans: d=50 mm 5. A solid circular shaft is subjected to a bending moment of 3000 N-m and a torque of N-m. The shaft is made of 45 C 8 steel having ultimate tensile stress of 700 MPa and a ultimate shear stress of 500 MPa. Assuming a factor of safety as 6, determine the diameter of the shaft. Ans: d=90 mm 6. A line shaft rotating at 200 r.p.m. is to transmit 20 kw. The allowable shear stress for the material of the shaft is 42 MPa. If the shaft carries a central load of 900 N and is simply supported between bearing 3 metre apart, determine the diameter of the shaft. The maximum tensile or compressive stress is not to exceed 56 MPa. Ans. d=50 mm 7. A propeller shaft is required to transmitted 45 KW power at 500 r.p.m. its hollow shaft having an inside diameter 0.6 times of outside diameter. It s made of plain carbon steel and the permissible shear stress is 84 N/mm 2. Calculate the inside and outside diameter of the shaft. Ans: di=23.47 mm do=39.12 mm 8. Derived the diameter of a hollow shaft with a ratio of of 0.8, capable of transmitting 300 KW at 225 rev/min. when subjected to a maximum bending moment of 5500 Nm, the load is suddenly applied with minor shock for torsional moment the bending moment is steady and the allowable shearing stress is 56 MPa. Ans: d i =120 mm d o =150 mm 9. A shaft made of mild steel is required to transmit 100 kw at 300 r.p.m. The supported length of the shaft is 3 meters. It carries two pulleys each weighing 1500 N supported at a distance of 1 metre from the ends respectively. Assuming the safe value of stress, determine the diameter of the shaft. Ans: d=70 mm 10. A hollow circular shaft of outer and inner diameter of d o and d i respectively is subjected to a torsional moment of M over a length l. The permissible angle of twist is θ degree. Proved that the shaft diameter is given by. d 0 = 11. A rotating shaft 40 mm in diameter, is made of steel FeE 580 (S yt =580 N/mm2). It is subjected to a steady torsional moment of 250 N-m and bending moment of 1250 N-m. Calculate the factor of safety available based on Ans. (i) 2.89, (ii) 2.86 (i) Maximum principal stress theory (ii) Maximum shear stress theory 12. A Propeller shaft is required to transmit 50 kw power at 600 rpm. It is hollow shaft. Having inside diameter 0.8 times of the outer diameter. It is made of steel (S yt = 380 N/mm 2 ) and the factor of safety is 4. Calculate the inside and outside diameter of the shaft. 13. Two 400 mm diameter pulleys are keyed to a simply supported shaft 500 mm apart. Each pulley is 100 mm from its support and has horizontal belts, tension ratio

9 being 2.5. If the shear stress is to be limited to 80 MPa while transmitting 45 kw at 900 r.p.m., find the shaft diameter if it is to be used for the input-output belts being on the same or opposite sides. Ans. 40 mm 14. A line shaft is driven by means of a motor placed vertically below it. The pulley on the line shaft is 1.5 metre in diameter and has belt tensions 5.4 kn and 1.8 kn on the tight side and slack side of the belt respectively. Both these tensions may be assumed to be vertical. If the pulley be overhang from the shaft, the distance of the centre line of the pulley from the centre line of the bearing being 400 mm, find the diameter of the shaft. Assuming maximum allowable shear stress of 42 MPa Ans: d=78mm 15. A shaft is supported by two bearings placed 1 m apart. A 600 mm diameter pulley is mounted at a distance of 300 mm to the right of left hand bearing and this drives a pulley directly below it with the help of belt having maximum tension of 2.25 kn. Another pulley 400 mm diameter is placed 200 mm to the left of right hand bearing and is driven with the help of electric motor and belt, which is placed horizontally to the right. The angle of contact for both the pulleys is 180 and µ = Determine the suitable diameter for a solid shaft, allowing working stress of 63 MPa in tension and 42 MPa in shear for the material of shaft. Assume that the torque on one pulley is equal to that on the other pulley. Ans: d=51.7mm and the maximum tensile or compressive stress is not to exceed 56 MPa. What size of the shaft will be required, if it is subjected to gradually applied loads? Ans: d=53.4 mm, d=57.7 mm 18. Design a shaft to transmit power from an electric motor to a lathe head stock through a pulley by means of a belt drive. The pulley weighs 200 N and is located at 300 mm from the centre of the bearing. The diameter of the pulley is 200 mm and the maximum power transmitted is 1 kw at 120 r.p.m. The angle of lap of the belt is 180 and coefficient of friction between the belt and the pulley is 0.3. The shock and fatigue factors for bending and twisting are 1.5 and 2.0 respectively. The allowable shear stress in the shaft may be taken as 35 MPa. Ans: d=51.1 mm 19. The layout is a transmission shaft carrying two pulleys B and C and supported on bearing A and D as shown in fig. Power is supplied to the shaft by means of a vertical belt on the pulley B. when id then transmitted to the pulley C carrying a horizontal belt. The maximum tension in the belt on the pulley is 2.5 KN. The angle of wrap for the both pulley is and the coefficient of friction is The shaft is made of plain carbon steel 30 C 8 (S yt =400 N/mm 2 ) and the factor of safety is 3. Determine the shaft diameter on strength basis. Ans: d=45.47 mm 16. A transmission shaft with keyway is subjected to a maximum torsional moment of 750 M-m and maximum bending moment of 1200 N-m.the loads are suddenly applied minor shocks are encountered, and the allowable shear stress is 42 MPa. Find the shaft diameter Ans: d=68.3 mm 17. A mild steel shaft transmits 20 kw at 200 r.p.m. It carries a central load of 900 N and is simply supported between the bearings 2.5 meters apart. Determine the size of the shaft, if the allowable shear stress is 42 MPa 20. The layout of a shaft carrying two pulleys 1 & 2 and supported on two bearing A & B as shown in fig. The shaft transmits 7.5 KW power at 360 r.p.m from the pulley 1 to the pulley 2. The diameter of pulleys 1 & 2 are 250mm and 500 mm respectively. The masses of pulley 1 & 2 are 10 kg and 30 kg respectively. The belt tension act vertically downward and the ratio of belt tension on the tight side to slack side for each pulley is 2.5:1. The shaft is made of plain carbon steel (S yt =380 N/mm 2 ) and fos is 3. Estimate suitable diameter of shaft. If permissible angle of twist is per meter

10 length. Calculate the shaft diameter on the basis of torsional rigidity. Assume G=79300 N/mm 2. Ans: d=41.37 mm respectively. The material of the shaft is steel FeE 580 (Sut=770 N/mm 2 ) and (Syt=580 N/mm 2 ). The factor Kb and Kt of ASME Ans:41.37 code are 1.5 mm and 2.0 respectively Determine the shaft diameter. Assume that the gears are connected to the shaft by means of keys.. Ans: d=68.59 mm 21. A line shaft supporting two pulleys A and B as shown. Power is supplied to the shaft by means of a vertical belt on the pulley A. Which is then transmitted to the pulley B carrying a horizontal belt. The ratio of the belt tension on tight and loose sides is 3:1. The limiting value of tension in the belt is 2.7 kn. The shaft is made of plain carbon steel 40 C 8 (S ut =650 N/mm 2 ) and (S yt =380 N/mm 2 ). The pulleys are keyed to the shaft. Determine the diameter of the shaft according to the ASME code if K b =1.5and k t =1.0 Ans: d=42.53mm 25. The armature shaft of 40 kw, 720 rpm electric motor. Mounted on two bearing A and B as shown. The total magnetic pull on the armature is 7 kn and it can be assumed to be uniformly distributed over a length of 700 mm midway between the bearing. The shaft is made of steel with ultimate tensile strength of 770 N/mm 2 and yield strength of 580 N/mm 2 Determine the shaft diameter using ASME code if k b =1.5and k t =1.0 Ans: d=45.13 mm 22. A steel spindle transmits 4 kw at 800 r.p.m. The angular deflection should not exceed per meter of the spindle. If the modulus of rigidity for the material of the spindle is 84 GPa. Find the diameter of the spindle and the shear stress induced in the spindle.. Ans: d=35 mm, τ=5.67 N/mm A line shaft rotating at 200 r.p.m is required to transmit 25 kw. It carries a central load of 900 N and is simply supported between bearing 3 meter apart. The allowable tensile and shear stress for the shaft are 56 N/mm 2 and 42 N/mm 2 respectively. Determine the diameter of the shaft. If Kt=1.25 and Km= The layout of intermediate shaft of a gear box supporting two spur gears B and C as shown. The shaft is mounted on two bearing A and D. The pitch circle diameters of gears B and C are 900 and 600 mm 26. Figure shows a shaft carrying a pulley A and a gear B and supported in two bearings C and D. The shaft transmits 20 kw at 150 r.p.m. The tangential force F on the gear B acts vertically upwards as shown. The pulley delivers the power through a belt to another pulley of equal diameter vertically below the pulley A. The ratio of tensions T 1 /T 2 is equal to 2.5. The gear and the pulley weigh 900 N and 2700 N respectively. The permissible shear Ans: stress d=63.5 for mm the material of the shaft may be taken as 63 MPa. Assuming the weight of the shaft to be negligible in comparison with the other loads, determine its diameter. Take shock and fatigue

11 factors for bending and torsion as 2 and 1.5 respectively. Ans: 69.6 mm 27. A solid circular shaft of diameter d is subjected to bending moment of M and torsional moment of T. Prove that according to maximum shear stress theory. = 28. A solid circular shaft of diameter d is subjected to bending moment of M and torsional moment of T. Prove that according to maximum principal r stress theory. = 29. The shaft of an axial flow rotary compressor is subjected to a maximum torque of 2000 N-m and a maximum bending moment of 4000 N-m. The combined shock and fatigue factor in torsion is 1.5 and that in bending is 2. Design the diameter of the shaft, if the shear stress in the shaft is 50 MPa. Design a hollow shaft for the above compressor taking the ratio of outer diameter to the inner diameter as 2 Ans. 96 mm 98 mm, 49 mm 30. A shaft made of steel receives 7.5 kw power at 1500 r.p.m. A pulley mounted on the shaft as shown in Fig has ratio of belt tensions 4. The gear forces are as follows : F t = 1590 N, F r = 580 N. Design the shaft diameter by maximum shear stress theory. The shaft material has the following properties: Ultimate tensile strength = 720 MPa; Yield strength = 380 MPa; Factor of safety = 1.5. Ans. d=20 mm 31. It is required to design a square key for fixing a gear on a shaft of 25 mm diameter. The shaft is transmitting 15 kw power at 720 rpm to the gear. The key is made of steel 50C4 (S yt =460 N/mm 2 ) and the factor of safety is 3. For key material, the yield strength in compression can be assumed to be equal to the yield strength in tension. Determine the dimension of the key. Ans: l=35 mm 32. The standard cross section for a flat key which is fitted on a 50 mm diameter shaft is 16x10 mm. The key is transmitting 475 N-m torque from the shaft to the hub. The key is made of commercial steel (S yt =S yc =230 N/mm 2 ). Determine the length of the key, if the factor of safety is 3. Ans: l=50 mm 33. A shaft, 40 mm in diameter is transmitting 35 kw power at 300 rpm by means of Kennedy keys of 10x10 mm cross section. The keys are made of steel 45C8 (S yt =S yc =380 N/mm 2 ) and the factor of safety is 3. Determine the required length of the key. 34. Design the rectangular key for a shaft of 75 mm diameter. The shearing and crushing stresses for key material are 50MPa and 75MPa respectively.. (UPTU-2002) 35. Design the rectangular key for a shaft of 50 mm diameter. The shearing and crushing stresses for key material are 42MPa and 72MPa respectively (UPTU-2004) 36. A square key is to be used to fix a gear to a 35 mm diameter shaft. The hub length of the gear is 60 mm. Both the shaft and key are to be made of the same material, having an allowable shear stress of 55 N/mm 2. If the torque to be transmitted is 395 N-m.

12 Determine the minimum dimension of key cross section. Ans: b=6.84 mm, h=6.84 mm 37. Design a square key for fixing a gear on the shaft having 25mm diameter. The gear rotates at 550 rpm and transmits 12 kw power to the meshing gear. The key is made of steel having yield stress in tension as 400 N/mm 2. The yield stress in compression and tension may be taken equal to each other. Assume factor of safety is 2.5. (UPTU-2005) Ans:l=34mm 38. A standard splined connection 8x52x60 mm is used for the gear and the shaft assembly of a gearbox. The splines transmit 20 kw power at 300 rpm. The dimension of the splines are as follow Major diameter= 60 mm, Minor diameter = 52 mm Number of splines = 8, Permissible normal pressure on splines is 6.5 N/mm 2. The coefficient of friction is Calculate (i) Length of the hub (ii) The forced require for shifting the gear. Ans: l=110 mm, F= N 39. A steel shaft has a diameter of 25 mm. The shaft rotates at a speed of 600 r.p.m. and transmits 30 kw through a gear. The tensile and yield strength of the material of shaft are 650 MPa and 353 MPa respectively. Taking a factor of safety 3, select a suitable key for the gear. Assume that the key and shaft are made of the same material. Ans. l = 102 mm 40. A kennedy keys are used to transmit 30 kw power at 500 rpm from 40 mm diameter shaft to the hub. The keys are made of steel 55C8 with yield strength of 400MPa and ultimate tensile strength of 700 MPa. Ifnthe factor of safety required is 3 and over load factor is 1.5, design the key.. Ans: b=10 mm, h=10 mm l= 23 mm 41. Design a muff coupling which is used to connect two steel shafts transmitting 40 kw at 350 rpm. The material for the shaft and the key is plain carbon steel for which allowable shear and crushing stresses may be taken as 40 MPa and 80 MPa respectively. The material for the muff is cast iron for which the allowable shear stress may be assumed as 15 MPa. 42. Design of a muff coupling, which is used to connect two steel shafts transmitting 25 kw power at 360 rpm. The shaft and key are made of plain carbon steel 30C8 (S yt = S yc =400 N/mm 2 ). The sleeve is made of grey cast iron FG 200 (Sut=200 N/mm2). The factor of safety for the shaft and key is 4. For sleeve the fos is 6 based on ultimate strength. 43. Design a muff coupling to connect two mild steel shafts to transmit 35 kw at 1440 r.p.m. The C.I sleeve connects the shaft through two mild steel sunk keys. The maximum torque transmitted is 25 % greater than the average torque.allowable shear stress for C.I and mild steel are 15 N/mm 2 and 65 N/mm 2.and the allowable crushing stress for mild steel= 160 N/mm 2. Ans: d=29 mm, D= 58 mm, L=102 mm, l=51 mm 44. Design a muff coupling to connect two shafts transmitting 40 kw at 120 r.p.m. The permissible shear and crushing stress for the shaft and key material (mild steel) are 30 MPa and 80 MPa respectively. The material of muff is cast iron with permissible shear stress of 15 MPa. Assume that the maximum torque transmitted is 25 per cent greater than the mean torque. 45. It is required to design a split muff coupling to transmit 50 kw power at 120 rpm. The shaft, key and clamping bolts are made of plain carbon steel 30C8 (S yt =400n/mm 2 ). The yield strength in compression is 150% of tensile yield strength. The factor of safety for the shaft, key and bolts is 5. The number of clamping bolts is 8. The coefficient of friction between halves and the shaft is Design a cast iron protective flange coupling to connect two shafts in order to transmit 7.5 kw at 720 r.p.m. The following permissible stresses may be used: Permissible shear stress for shaft, bolt and key material = 33 MPa, Permissible crushing stress for bolt and key material = 60 MPa, Permissible shear stress for the cast iron = 15 MPa 47. The shaft and flange of a marine engine are to be designed for flange coupling in which the flange is forged on the end of the shaft. The following particulars are to considered in the design Power of engine= 3MW Speed of engine= 100 rpm Permissible shear stress in bolt and shaft = 60 Mpa, No of bolts used=8 Pitch circle diameter of bolts = 1.6 x diameter of shaft. Find Diameter of shaft, diameter of bolts Thickness of flange, diameter of flange.

13 48. Design a clamp coupling to connect two plain carbon steel shafts to transmit 60 kw power at 500 r.p.m. The C.I muff halves are clamped by four alloy steel bolts. The key used has same material as that of the shaft. The maximum torque transmitted is 20 % greater than the average torque. Allowable shear stress for shaft and key material are 55MPa and allowable crushing stress for shaft and key material =155 MPa. Allowable crushing stress for C.I muff = 150 MPa, Allowable Tensile stress for alloy steel bolts =130 MPa 49. Design a Cast Iron protective type flange coupling to transmit 15 kw at 900 r.p.m from an electric motor to a compressor. The service factor may be assumed as The following permissible stresses may be used. Shear stress for shaft, bolt and key = 40 MPa Crushing stress for bolt and key = 80MPa Shear stress for Cast Iron = 8 MPa 50. Two 35 mm shaft are connected by a flange coupling. The flanges are fitted with 6 bolts on 125 mm bolt circle. The shaft transmits a torque of 800 N-m at 350 RPM. For the safe stresses mentioned below, Calculate (i) diameter of bolts (ii0 thickness of flanges (iii) Key dimension (iv) hub length and (v) Power transmitted. Safe shear stress for shaft material = 63 MPa Safe stress for bolt material = 56 MPa Safe stress for cast iron coupling = 10 MPa Safe stress for key material = 46 MPa 51. Design a cast iron flange coupling for a mild steel shaft transmitting 90 kw at 250 rpm. The allowable shear stress in the shaft is 40 MPa and the angle of twist is not to exceed 1 0 in a length of 20 diameters. The allowable shear stress in the coupling bolts is 30 MPa. 52. A flexible coupling is used to transmit 15 kw power at 100 rpm. There are six pins and their pitch circle diameter is 200 mm. The effective length of the bush (l b ). The permissible shear and bending stress are 35 and 152 N/mm 2 respectively Calculate the pin diameter by shear consideration. 53. Design a bushed-pin type flexible coupling for connecting a motor shaft to a pump shaft for the following service conditions, Power to be transmitted = 40 kw; speed of the motor shaft = 1000 r.p.m. ; diameter of the motor shaft, = 50 mm; diameter of the pump shaft = 45 mm. The bearing pressure in the rubber bush and allowable stress in the pins are to be limited to 0.45 N/mm 2 and 25 MPa respectively 54. Design a Cast Iron protective type flange coupling to connect two shaft of 36 mm diameter, transmitting at 720 r.p.m. The over load capacity 1.25 times the average torque. The bolt and key are made of C20 steel and the flanges are made of Cast Iron. Assume missing data suitable, if any U.P.T.U ) 55. Design a cast iron protective flange coupling to connect two shafts in order to transmit 7.5 kw at 720 r.p.m. The following permissible stresses may be used Permissible shear stress for shaft, bolt and key material = 33 MPa, Permissible crushing stress for bolt and key material = 60 MPa, Permissible shear stress for the cast iron = 15 MPa.

14 UNIT-IV

15 MEERUT INSTITUTE OF TECHNOLOGY MEERUT B.Tech (Mechanical) (V semester) Subject-Machine Design-1 Tutorial No-3 1. A compression coil spring made of an alloy steel is having the following specifications : Mean diameter of coil = 50 mm; Wire diameter = 5 mm; Number of active coils = 20. If this spring is subjected to an axial load of 500 N; calculate the maximum shear stress (neglect the curvature effect) to which the spring material is subjected. 2. A helical spring is made from a wire of 6 mm diameter and has outside diameter of 75 mm. If the permissible shear stress is 350 MPa and modulus of rigidity 84 kn/mm 2, find the axial load which the spring can carry and the deflection per active turn. 3. Design a spring for a balance to measure 0 to 1000 N over a scale of length 80 mm. The spring is to be enclosed in a casing of 25 mm diameter. The approximate number of turns is 30. The modulus of rigidity is 85 kn/mm 2. Also calculate the maximum shear stress induced. 4. A mechanism used in printing machinery consists of a tension spring assembled with a preload of 30 N. The wire diameter of spring is 2 mm with a spring index of 6. The spring has 18 active coils. The spring wire is hard drawn and oil tempered having following material properties:design shear stress = 680 MPa, Modulus of rigidity = 80 kn/mm 2 Determine: 1. the initial torsional shear stress in the wire; 2. spring rate; and 3. the force to cause the body of the spring to its yield strength. 5. Design a helical compression spring for a maximum load of 1000 N for a deflection of 25 mm using the value of spring index as 5. The maximum permissible shear stress for spring wire is 420 MPa and modulus of rigidity is 84 kn/mm Design a close coiled helical compression spring for a service load ranging from 2250 N to 2750 N. The axial deflection of the spring for the load range is 6 mm. Assume a spring index of 5. The permissible shear stress intensity is 420 MPa and modulus of rigidity, G = 84 kn/mm 2. Neglect the effect of stress concentration. 7. Design a valve spring of a petrol engine for the following operating conditions Spring load when the valve is open = 400 N Spring load when the valve is closed = 250 N Maximum inside diameter of spring = 25 mm Length of the spring when the valve is open = 40 mm Length of the spring when the valve is closed = 50 mm Maximum permissible shear stress = 400 MPa 8. Design a helical spring for a spring loaded safety valve (Ramsbottom safety valve) for the following conditions : Diameter of valve seat = 65 mm ; Operating pressure = 0.7 N/mm 2; Maximum pressure when the valve blows off freely = 0.75 N/mm 2 ; Maximum lift of the valve when the pressure rises from 0.7 to 0.75 N/mm 2 = 3.5 mm ; Maximum allowable stress = 550 MPa Modulus of rigidity = 84 kn/mm 2 ; Spring index = A safety valve of 60 mm diameter is to blow off at a pressure of 1.2 N/mm 2. It is held on its seat by a close coiled helical spring. The maximum lift of the valve is 10 mm. Design a suitable compression spring of spring index 5 and providing an initial compression of 35 mm. The maximum shear stress in the material of the wire is limited to 500 MPa. The modulus of rigidity for the spring material is 80 kn/mm 2. Calculate: 1. Diameter of the spring wire, 2. Mean coil diameter, 3. Number of active turns, and 4. Pitch of the coil. 10. Its required to design a helical compression spring subjected to a maximum force of 1250 N. The deflection of the spring corresponding to the maximum force should be approximately 30 mm.

16 The spring index can be taken as 6. The spring is made of patented and cold drawn steel. The ultimate tensile strength and modulus of rigidity of the spring material are 1090 and N/mm 2 respectively. The permissible shear stress for the spring wire should be taken as 50 % of the ultimate strength. Design the spring and calculate. Wire diameter, mean coil diameter, Number of active coil, free length of the spring, pitch of the coil 11. It s required to design a helical compression spring for the mechanism. The axial force acting on the spring is 300 N when the valve is open and 150 when the valve is closed. The length of the spring is 30 mm when the valve is open and 35 mm when the valve is closed. The spring is made of oil-hardened and tempered valve spring wire and the ultimate tensile strength is 1370 N/mm 2. The permissible shear stress for spring wire should be taken as 30% of the ultimate tensile strength. The modulus of rigidity is N/mm 2.Tyhe spring is fitted over a valve rod the minimum inside diameter of the spring should be 20 mm Calculate: Wire diameter, mean coil diameter, No of active coil, total no of coil, free length of the spring, pitch of the coil (a) A helical tension spring is used in the spring balance to measure the weights. One end of the spring is attached to the rigid support while the outer end, which is free, carries the weights to be measured. The maximum weight attached to the spring balance is 1500 N and the length of the scale should be approximately 100 mm. The spring index can be taken as 6. The spring is made of oil hardened and tempered steel wire with ultimate tensile strength opf 1360 N/mm 2 and modulus of rigidity of N/mm 2. The permissible shear stress in the spring wire should be taken as 50 % of the ultimate tensile strength Calculate : Wire diameter, mean coil diameter, no of active coil, spring rate, actual spring rate 12. A helical compression spring made of oil tempered carbon steel is subjected to a load which varies from 400 N to 1000 N. The spring index is 6 and the design factor of safety is If the yield stress in shear is 770 MPa and endurance stress in shear is 350 MPa, find: 1. Size of the spring wire, 2. Diameters of the spring, 3. Number of turns of the spring, and 4. free length of the spring. The compression of the spring at the maximum load is 30 mm. The modulus of rigidity for the spring material may be taken as 80 kn/mm A helical compression spring of a cammechanism is subjected to an initial preload of 50 N. The maximum operating force during the load cycle is 150 N. The wire diameter is 3 mm, while the mean coil diameter is 18 mm. The spring is made of oil-hardened and tempered valve spring wire of Grade-VW (S ut =1430 N/mm 2 ). Determine the FOS used in the diagram on the basis of fluctuating stresses. 14. A closely coiled helical spring is made of 10 mm diameter steel wire, the coil consisting of 10 complete turns with a mean diameter of 120 mm. The spring carries an axial pull of 200 N. Determine the shear stress induced in the spring neglecting the effect of stress concentration. Determine also the deflection in the spring, its stiffness and strain energy stored by it if the modulus of rigidity of the material is 80 kn/mm 2.