3-1 DMM1 [Nov 2009 Regular]

Code No: V3113/R07 Set No. 1

III B.Tech I Semester Regular Examinations, November 2009DESIGN OF MACHINE MEMBERS-I

(Mechanical Engineering)Time: 3 hours Max Marks: 80

Answer any FIVE QuestionsAll Questions carry equal marks

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1. A copper bar 50 mm in diameter is placed with a steel tube 75 mm external diameterand 50 mm internal diameter of exactly the same length. The two pieces are rigidlyfixed together by two pins 18 mm in diameter, one at each end passing through thebar and tube. Calculate the stress induced in the copper bar, steel tube and pinsif the temperature of the combination is raised by 50%. TakeEs = 210 GN/m2; Ec = 105 GN/m2 αs = 11.5 × 10−6/oC and αc = 17 × 10−6/oC.

[16]

2. A pulley is keyed to a shaft midway between two anti-friction bearings. The bendingmoment at the pulley varies from -170N-m to 510N-m and torsional moment in theshaft varies from 55 N-m to 165 N-m. The frequency of variation of the loads in thesame as shaft speed. The shaft is made cold drawn steel having an ultimate strengthof 540 Mpa and yield strength of 400Mpa. Determine the required diameter for aninfinite life. The stress concentration factor for the keyway in bending and torsionmay be taken as 1.6 and 1.4 respectively. The factor of safety is 1.5. size factor =0.85 and surface finish factor is 0.85. Assume σe = 0.5 σ2; τxy = 0.5σy; τe = 0.55σe.

[16]

3. (a) What is the difference between Caulking and fullering? Explain with the helpof neat sketches.

(b) A double riveted double cover butt joint is made in 12mm thick plates with18mm diameter rivets. Find the efficiency of the joint for a pitch of 80mm, ifσt= 115MPa; τ= 80MPa; and σc= 160Mpa. [6+10]

4. (a) Define the following terms with necessary sketch.

i. Major diameter

ii. Minor diameter

iii. Pitch

iv. Lead.

(b) Derive an expression for the maxim load in a bolt. When a bracket with acircular base is bolted to a wall by means of four bolts. [8+8]

5. (a) Differentiate between a cotter joint and a knuckle joint.

(b) The cotter joint is commonly used for long pump rods and similar machinemembers. Design this joint to support a load varying from 28kN in com-pression. The material for all the components of the joint is steel with theallowable stresses in tension, compression and shear as 50N/mm2, 60N/mm2

and 35N/mm2 respectively. [4+12]

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6. Compare the weight, strength and stiffness of a hollow shaft of the same externaldiameter as that of solid shaft. The inside diameter of the hollow shaft being 0.6times the external diameter. Both the shafts have same material and length. [16]

7. Design a rigid flange coupling to transmit a torque of 250N-m between two axialshafts. The shaft is made of alloy steel, flanges out of cast iron and bolts out ofsteel. Four bolts are used to couple the flanges. The shafts are keyed to the flangehub. The permissible stresses are given below:Shear stress on the shaft=100MPaBearing or crushing stress on shaft=250MPaBearing stress on keys=250MPaShear stress on keys=100MPaShearing stress on cast iron=200MPaShear stress on bolts=100MPaAfter designing the various elements, make a neat sketch of the assembly indicatingthe important dimensions. The stresses developed in the various Members may bechecked if thumb rules are used for fixing the dimensions. [16]

8. (a) Under What circumstances, concentric springs are preferred?

(b) A rail carriage weighing 200kN and running at 5 km/hour is brought to rest byfour buffer springs of close coiled helical type during connection with anothercarriage which is already at rest. The mean coil diameter is 5 times the wirediameter. The deflection of each spring is 220mm, to bring the carriage torest. Safe shear stress for the spring material is 400N/mm2. Calculate themaximum load on the spring, diameter of wire and coil, number of turns andfree length of spring. Assume the ends of spring are squared and ground. TakeG= 0.8×104N/mm2. [2+14]

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1. (a) Explain the following methods of reducing stress concentration.

i. Drilled holes

ii. Using large fillet radius.

(b) A hot rolled shaft is subjected to torsional load that varies from 320 Nm clockwise to 120 Nm anti -clockwise and an applied bending moment at a criticalsection varies from 400 Nm to 200 Nm. The shaft is of uniform cross section.Determine the required shaft diameter. The material has an ultimate strengthof 560 Mpa and yield strength of 420 Mpa. Assume factor of safty to be 2.

[6+10]

2. (a) Illustrate how stress concentration in a component can be reduced.

(b) Determine the size of a piston rod to a total load of having cyclic fluctuationsfrom 15 kN in compression to 25 kN in tension. The endurance limit is 360Mpa and yield strength is 400 Mpa. Take impact factor = 1.25, factor of safty= 1.5, surface finish factor =0.88 and stress concentration factor = 2.25.[8+8]

3. Figure 3 shows a welded joint subjected to an eccentric load of 20 kN. The weldingis only on one side. Determine the uniform size of the weld on the entire length oftwo legs. Take permissible shear stress for the weld material as 80 MPa. [16]

Figure 3

4. Determine the size of the bolts and the thickness of the arm for the bracket asshown in the figure 4, if it carries a load of 40 KN at an anlge of 600 to the vertical.The material of the bracket and the bolt is same for which the safe stresses can beassumed as 70,50 and 105 MPa in tension, shear and compression respectively. [16]

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Figure 4

5. (a) Design a rectangular sunk key for a shaft of 50mm diameter, transmitting1200N-m torque. The shear and crushing stresses in the key are limited to 45and 70MPa respectively.

(b) Make a neat sketch showing two views of a cotter joint and write equationsshowing the strength of the joint for the most probable methods of failure.

[8+8]

6. (a) A solid shaft and a hollow shaft are to be equal in torsional strength. Thehollow shaft is to be 10% larger in diameter than the solid shaft. Assumingthat the material of both the shafts to be the same, find the ratio of the weightof the solid shaft to that of the hollow shaft.

(b) A shaft is supported on two bearings 750mm apart and transmits 15kW at560 r.p.m. A spur pinion of 150mm diameter is located at 125 mm to the rightof the left bearing and delivers power horizontally to the right. A spur gear of500mm diameter is located at 150mm to the left of the right bearing and re-ceives power from below. Determine the shaft diameter, assuming permissibleshear stress for the shaft material as 45MPa. [6+10]

7. Design a bushed -pin type flexible couplings to transmit 25kW at 960rpm.Use the following stress values:Shear stress =50MPa(shaft and key)

30MPa(pin)Crushing stress =90MPa (key)Bearing pressure=0.45N/mm2(rubber bush). [16]

8. (a) Write short notes on leaf springs

(b) A lift system is provided with cushion springs at the bottom of lift. The lift isfree to fall. Springs are set in parallel. Specify the required number of springsif the lift has free fall of 1.5m from rest.Weight of lift = 30kN

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Allowable deflection per spring = 370 mmNumber of active turns =15Spring mean coil diameter =30 mmSpring wire diameter = 30mmModulus of rigidity for spring =80Gpa. [6+10]

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1. (a) Classify the various types Machine Design.

(b) What is the procedure adopted in the design of Machine elements. [6+10]

2. (a) Illustrate how stress concentration in a component can be reduced.

(b) Determine the size of a piston rod to a total load of having cyclic fluctuationsfrom 15 kN in compression to 25 kN in tension. The endurance limit is 360Mpa and yield strength is 400 Mpa. Take impact factor = 1.25, factor of safty= 1.5, surface finish factor =0.88 and stress concentration factor = 2.25.[8+8]

3. Design a longitudinal joint for a 1.25m diameter steam boiler to carry a steampressure of 2.5 N/mm2. The ultimate strength of the boiler plate may be assumedas 420 MPa, crushing strength as 650 MPa and shear strength as 300 Mpa. Takethe joint efficiency as 80%. Sketch the joint with all the dimensions. Adopt thesuitable factor of safty. [16]

4. Determine the size of the bolts and the thickness of the arm for the bracket asshown in the figure 4, if it carries a load of 40 KN at an anlge of 600 to the vertical.The material of the bracket and the bolt is same for which the safe stresses can beassumed as 70,50 and 105 MPa in tension, shear and compression respectively. [16]

Figure 4

5. (a) How is the slipping of the cotter avoided? Explain by two methods.

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(b) Design a knuckle joint to transmit 120 kN, with permissible stresses in tension;shear and compression are 75 Mpa; 60 Mpa and 150 Mpa respectively. [4+12]

6. In axial flow rotary compressor, the shaft is subjected to a maximum twistingmoment of 1500N-m and a maximum bending moment of 3000N-m. Neglectingthe axial load on the shaft, determine the diameter of the shaft, if the allowableshear stress is 50N/mm2. Assume Kb = 1.5 and Kt = 1.2. If the shaft is to be ahollow one with di/do=4, what will be the material saving in the hollow shaft. It issubjected to the same loading and of the same material as the solid shaft. Comparethe torsional stiffness of the two shafts. [16]

7. Design a bushed-pin type flexible coupling for connecting a motor shaft to a pumpshaft, with the following service conditions:Power to be transmitted=40kWSpeed of the motor shaft=1000rpmDiameter of motor and pump shafts=45mmBearing pressure on the rubber bush=0.7N/mm2

Allowable stress in the pins=60MPa. [16]

8. A diesel engine weighs 800kN and is mounted on 16 springs in order to protect thebuilding from vibrations. The section of the spring wire is rectangular with sideratio1.8. One spring has four effective coils and the spring index is 6.Determine:

(a) Section of the spring so that long side is parallel to the axis of the spring

(b) Deflection under load when engine is stationary

(c) Maximum coil diameter

(d) Shear stress induced if shorter side is parallel to the spring axis. Permissibleshear stress in spring wire material is 300N/mm2 and modulus of rigidity is0.8×105N/mm2. [16]

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1. (a) Classify the various types Machine Design.

(b) What is the procedure adopted in the design of Machine elements. [6+10]

2. (a) Write Soderberg’s equation and state its application to different type of load-ings.

(b) Determine the diameter of a circular rod made of ductile material with afatigue strength. σe=265Mpa and a tensile yield strength of 350 Mpa. Themember is subjected to a varying axial load from Wmin=-300 kN to Wmax=700kN and has a stress concentration factor=1.8. Use factor of safty as 2.0. [6+10]

3. Design a longitudinal joint for a 1.25m diameter steam boiler to carry a steampressure of 2.5 N/mm2. The ultimate strength of the boiler plate may be assumedas 420 MPa, crushing strength as 650 MPa and shear strength as 300 Mpa. Takethe joint efficiency as 80%. Sketch the joint with all the dimensions. Adopt thesuitable factor of safty. [16]

4. (a) Define the following terms with necessary sketch.

i. Major diameter

ii. Minor diameter

iii. Pitch

iv. Lead.

(b) Derive an expression for the maxim load in a bolt. When a bracket with acircular base is bolted to a wall by means of four bolts. [8+8]

5. (a) Describe the design procedure of Sleeve & Cotter joint.

(b) Design a cotter joint with two gibs to transmit an axial force of 130 kN. Thepermissible stresses are 165 MPa in tension; 100 MPa in shear and 180 M Pain crushing. [6+12]

6. The shaft of an axial flow rotary compressor is subjected to maximum torque of2000N-m and a maximum bending moment of 4000 N-m. The combined shock andfatigue factor in torsion is 1.5 and that in bending is 2. Design the diameter of theshaft, if the shear stress in the shaft is 50MPa. Design a hollow shaft for the abovecompressor taking the ratio of outer diameter to the inner diameter as 2. What isthe percentage saving in material? Also compare the stiffness. [16]

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7. Design and draw protective type of cast iron flange coupling for a steel shaft trans-mitting 15kW at 200rpm, and having an allowable shear stresses of 40MPa. Theworking stress in the bolts should not exceed 30MPa. Assume that the same ma-terial is used for shaft and key and that the crushing stress is twice the value of itsshear stress. The maximum torque is 25% greater than the full load torque. Theshear stress for cast iron is 14MPa. [16]

8. A semi-elliptical laminated spring is made of no.10.B.W.G. steel 50mm wide. Thelength between the supports is 66.25cm and the band is 63 mm wide. The springhas two full length and five graduated leaves. A central load if 158 kg is carried.

(a) Determine the maximum stress in each set of leaves for an initial condition ofno stress in the leaves.

(b) Draw to half or quarter full size the elevation and plan of the spring

(c) Determine the maximum stress if the initial stress is provided to cause equalstresses when loaded.

(d) Determine the deflection in parts (a)and (b) respectively. [16]

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3-1 DMM1 [Nov 2009 Regular]

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