USN 10M862

Sixth Semester B.E. Degree Examination, Dec.20L3 lJan.2014Design of Machine Elements - ll

Time: 3 hrs. Max. Marks:100Note: 7. Answer FIVEfutt questions, selecting

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D A f)rrr APART _ AI a. A'eurved link mechanism made from a round steel bar is shown in Fig.Ql.(a). The material

for1ffi.is plain carbon steel 30C8 with an allowable yield strength of400 MPa. Determine

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Module : 3 mmFace width : 35 mm

(10 Marks)

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A high pressure cylinder consists ofa steel tube with inner and outer diameter of 20 mm and40 mm respectively. It is jackeled by an outer steel tube with an outer diameter of 60 mm.The tubes are assembled by shrl[king process in such a way that maximum principal stressinduced in any tube is limited to 100 MPa. Calculate the shrinkage pressure and originaldimensions of the tubes, Take the Young's modulus as 207 GPa. (10 Marks)

Write a note on construciion of flat and 'V' belt. (05 Marks)It is required to design a 'V" belt drive to connect a 7.5 kW, 1440 rlmin induction motor to afan. running at approximately 480 r/min lor a service of 24 hr/day. Space is available for a

centre distance of about 1 m. Determine the pitch lengtn or rna,.,U-lt and number of beltsrequired. ,' (15 Marks)

3 a. Enumerate the applications of springs. Also derive an expression for the deflection of a closecoiled helical spring. (06 Marks)A Spring is subjected to a load varying from 500 N and 1200 N. It is to be made of oiltempered cold drawn wire. Design factor based on Wahl's line is 1.25. The spring index is tobe 6. The compression in the spring for the maximum load is 30 mm. Determine the wirediameter, mean coil diameter and free length of the spring. Take the yield stress in shear as

700 MPa and endurance stress in shear as 350 MPa for the material of the wire. (14 Marks)

Write a note on design of gears based on dynamic loading and wear. (06 Marks)A cast steel24 teeth spur pinion operating at 1150 rlmin transmits 3 kW to a cast steel56 teeth spur gear. The gears have the following specifications:

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4a.b.

Allowable stress : 100 MPaTooth form : 14%' full depth profile

Factor of dynamic loading, C: 350N/mm Wear load factor, K: 0.28 MPa.Determine the induced stress in the weaker gear. Also determine the dynamic load and wear

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load. Comment on the results.I of2

(14 Marks)

10M862

PART _ Ba. Write a note on formative number of teeth in bevel gear. (04 Marks)b. Hardened steel worm rotates at 1250 r/min and transmits power to a phosphor bronze gear

with a transmission ratio of 15: I . The centre distance is to be 225 mm. Design the gear driveand give estimated power input ratings from the stand point of strength, endurance and heatdissipation. The teeth are of l4%' full depth involute. (16 Marks)

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,.6,, a. A cone clutch has a semi cone angle of 12.It is to transmit 10 kW power at 750 r/rain,iiilhs,",,, width of the face is one fourth of the mean diameter of fiiction lining. If the normql'intensity' "" , of pressure between contacting surfaces is not to exceed 0.085 N/m# and the psbfficient of

friction is 0.2, assuming uniform wear conditions, calculate the dimensions of thb clutch.

8a.b.

b. A band,break arrangement is shown in Fig.Q6(b). It istorque of 200 N-m. Determine the actuating force 'P'The angld'of wrap of the band is 270".Determine theband width is30 mm.

,, ,. (10 Marks)used to generate a maximum braking, if the coefficiept''of friction is 0.25.maximum,,iritehsity of pressure, if the

:,,,:,, :1 ::,,,, (10 Marks)

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{"I2 Marks)

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(05 Marks):

Fie.Q6(b)a. Explain the following types of lubrieation: ,,,,:,,

(i) Hydrodynamic lubrication (ii) Hydrostatic lubrication(iii) Boundary lubrication (iv) Elasto hydro dynamic lubrication. (0s Marks)

b. The following data are given for a 360o hydro-dynamig bearing:Bearing diameter : 50.02 mm Joumal diameter : 49.93 mmBearing length : 50 mm Journal speed : 1440 rlminRadialload-:8 kN Viscosiiyoi1.utii;ca"t : 12 cp.

The bearing iS,,machined on a lathe from bronze casting, while'tlie steel journal is hardenedand ground; The surface roughness values for turning and grinding are 0.8 and 0.4 micronsrespectiifely. For thick film lubrication the minimum film thickness stiould be five times thesum.of silrface roughness values for the journal and the bearing. Calculate:(i),,' fhe permissible minimum film thickness(ii) The actual film thickness under the operating conditions , l

, (iii) Power loss in friction.(iv) Flow requirement.

Explain the considerations given in the design of pistons for IC engines.Design a trunk piston for an IC engine. The piston is made of cast iron with an allowablestress of 38.5 MPa. The bore of the cylinder is 200 mm and the maximum explosionpressure is 0.4 MPa. The permissible bending stress of the material of the gudgeon pin is100 MPa. The bearing pressure in the gudgeon pin bearing of the connecting rod is to be

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taken as 200 MPa. (15 Marks)

USN 10ME63

Sixth Semester B.E. Degree Examination, Dec.2013 lJan.201^4Heat and Mass Transfer

Time: 3 hrs. Max. Marks:100.::' Note: 1. Answer FIVEfull questions, selecting

.' ' at lesst TWO questions from each part."''':"": "':' ' 2. (Jse of heat transfer data book is permitted. : ::quoq uvvut ao lrcr rraaa

, PART_AI a. Explain briefly the mechanism of conduction, convection and radiation heat transfu:;.

_,'-' (06 Marks)

b. Witli iiketches, write down the mathematical representation of three commonly useddifferent types of boundary conditions for one dimensional heat. e(uation in rectangularcoordinates. (08 Marks)

c. A plate of thickness 'L' whose one side is insulated and the other side is maintained at atemperature Tr i5 dtphanging heat by convection to the surrounding area at a temperature T2,with atmospheric air being the outside medium. Write mathemitical formulation for onedimensional, steady Stste heat transfer, without heat generation. (06 Marks)

2 a- An electric cable of l0mm diameter is to be laid in atmosphere at 20'C. The estimatedsurface temperature of the cable due to heat generation is 65"C. Find the maximumpercentage increase in heat dissipation,,,*hen the wire is insulated with rubber havingK: 0.155 WmK. Take h: 8.5 WrnlK,,. , (06 Marks)Diflerentiate between the effectivenoss;,and efficiency of fins. (04 Marks)In order to reduce the thermal qesistance at the surface of a veftical plane wall (50 x 50cm),

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c.

100 pin fins (1 cm diameter, 10sm long) are attached. If the pin fins are made of copperhaving a thermal conductivity of 300 WmK and the value of the surface heat transfercoefficient is 15 Wm2K,;,Calculate the decreur. in the thermal resistance. Also calculate theconsequent increase in heat transfer rate from the wall if it is ma@@ined.qt a temperature of200"c and the surroundings are ar 30oc. .Zr(j-{)} (r0 Marks)

3a. Show that fhel.'temperature distribution in a body during ]1id cooling is

givenov"ffi=+=*r[#) W-*%7i (06Marks).,..,":','',..,;.T, -T" ei ^ ( pCV / \

ThesGel ball bearings (K: 50 WmK, o : 1.3 x 10-5 m2lsec), er are heated_ _--::::::/,,to'atemperature of 650"C. It is then quenched in a oil bath at 50oC, where the heat transfercoefficient is estimated to be 300 Wm2K. Calculate:' i) The time required for bearings to reach 200"C.

::ii) The total amount of heat removed from a bearing during this time andiii) The instantaneous heat transfer rate from the bearings, when they are flrst immersed in

oil bath and when thev reach 200'C. (14 Marks)

4 a. With reference to fluid flow over a flat plate, discuss the concept of velocity boundary andthermal boundary layer, with necessary sketches. (05 Marks)

b. The exact expression for local Nusselt number for the laminar flow along a surface is givenhxbv Nu' = ,xz\

- 0.332 nll' pJ". Show that the average heat transfer coefficient fromr x k

-'--- --e\ -r

x : 0 to x : L over the length 'L' of the surface is given by 2hr where hl is the local heat

b.

transfer coefficient at x: L.I of2

(05 Marks)

5a.b.

7a.

ii) , The increase in bulk temperature of air over a 4m length of the tube., ' .

Tale,ths following properties for air pr : 0.6g1, trt:2.57 x 10-5 kg/mi; K : 0.03g6 wmKand Co = 1.025 kJ/kg K. (ro Marks)c. Obtain a ielationship between drag coefficient, c. and heat transf,er'coefficient, hn,, for thellow over a flat plate.r.*." (06 Marks)

a' Derive an expression for LMTD of a counter flow heat exchanger. State the assumptions

b. What is meant by the term fouling factor? How do you determine it? (04 Marks)c' Engine oil is to be coded from 80'C to 50'C by using a single pass counter flow, concentrictube heat exchanger with cooling water available ul20"C. Water flows inside a tube withinner diameter of 2.5cm and at a rate of 0.08 kg/sec and oil flows through the annulus at therate of 0.16 kg/sec. The heat transfer coeficient for the water side and oil side arerespectively h," : 1000 Wm2oC and h.l : 80 Wm2oC. The fouling factors isF,: 0.00018m2oC/W on both the sides ard the tube wall resistance is negligible. Calculatethe tube length required. (08 Marks)

10ME63

A vertical plate 15cm high and 10cm wide is maintained at 140"C. Calculate the maximumheat dissipation rate from both the sides of the plates to air at 20oC. The radiation heattransfercoefficient is 9.0 wm2K. Forairat 80.c, take r:2L09 x 10-6 ni/sec,pr:0.692,kr: o.o3 wmK. (lo Marks)

PART - BExplain the physical signiflcance of i) Nusselt number; ii) Groshoffnumber. (04 Marks)Air at 2 atm and 200oC is heated as it flows at a velocity of 12 m/sec through a tube with adiameter of 3cm. A constant heat flux condition is maintained at the wJl and the wallt-emperature is 20oC above the air temperature all along the length of the tube. Calculate:i) The heat transfer per unit length of tube. .,

,

Sketch a pool boiling curvq for water and explain'briefly the various regimes in boiling heattransfer. ,,, ,-'''. '

?..1". mass transfer coerficient. [8iXff[]A l2cm outside diameter and 2m long tube is used in a big condenser to condense the steamn 0.1 bar,-Estr3{e the unit surface conductance i) in iertical position; iil i, horizontalposition. Also find the amount of condensate formed per hour infin the cases.The satutation temperature of the steam :74.5"C.Aver,age wall temperature : 50.C.

-?The'properties of water film at average temperature of 75'4j50

=62.7oC are given belowl-p:982.2kglm3, hr_ =2480kJ/kg,K:0.65WmK, p:0.47 x 10-3kg/ms. '' \liolvrarks)

(06 Marks)

(06 Marks)function of geometry

(08 Marks)

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b.

c.

8a.b.

State and prove Wiens displacement law of radiation.The temperature of a black surface 0.2rfi in area is 540.c. calculate:i) The total rate of energy emission.ii) The intensity of normal radiation.

Iti) The wavelength of maximum monochromatic emissive power.Derive an expression for a radiation shape factor and show that it is aonly.

c.

USN 10ME64

Sixth Semester B.E. Degree Examination, Dec.2013 /Jan.20l4Finite Element Methods

Time: 3 hrs. Max. Marks:100Note: Answer FIVEfull questions, selecting

., ut least TWO questions from each part.

PART _ A1 a,, r Differentiate between plane stress and plain strain problems with examples. Write the stress-

strain relations for both. (08 Marks)b. Explain the node numbering scheme and its effect on the half band-width. (06 Marks)c. List down the basic steps involved in FEM for stress analysis of elastic solid bodies.

(06 Marks)

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2 a. State the piineiple of minimum potential energy. Determine tl.le displacements at nodes forthe spring system qhown in the Fig.a.,2J3). (08 Marks)

b. Determine the deflection of a cantilevel beam of length 'L' subjected 1o uniformly

distributed load (UDL) of Po/unit iength, using the trail function y : a sin [ '* I . Comnare\2L )

Fig.Q.2(a)

the results with analyical solution and comment on accuracy.

Derive an expression for Jacobian matrix for a four-noded quadrilateral element. (10 Marks)For the triangular element shown in the Fig.Q.3(b). Obtain the strain-displacement matrix'B' and determine the strains €r. €y and y*y.

Nodal displacements {q} : {2 | 1 -4 -3 7} x 10-2mm.

(12 Marks)

(10 Marks)

Note; All dimensions in mm.

E r:70 x 10e N/m2,82: 200 x 10eN/m2

Ar :900mm2, Az: l200mm2a1 :23 x 10-6/oC, az: 71.7 x 10'61'C.

Fig.Q.3(b)

4 a. an' axial load P : 300 x 103 N is applied at 20'C to the rod as shown in the Fig.Q.41a.y. The,, , temperature is then raised to 60oC.

D Assemble the global stiffness matrix (K) and global load vector (F).ii) Determine the nodal displacenrents and element stresses.

Fig.Q.a(a)

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(12 Marks)

5a.

b

c.

6a.

10M864b. Solve the following system of equations by Gaussian-Elimination method:

xr -2xz * 6x: : 0

2x1-t 2x2 + 3x3 : 3

-xy * 3x2:2. (08 Marks)

PART _ BUsing Lagrangian method, derive the shape function of a three-noded one-dimension (1D)element [quadratic element]. (06 Marks)-ll rlEvaluate I: ll 3e^+xt+ l.d*Lvuruulv '--lL" rA *G*2)-l''"

For the two-bar truss shown in the Fig.Q.6(a). Determine the nodal displacements andelement stross.es- A force of P: 1000 kN is applied at node 1, Take p,: ZtO GPa andA : 600mm2'for each element. ,,

t '' , ' (12 Marks)

using one-point and two-point Gauss quadrature.Wtite short notes on higher order elements used in FEM.

Fie.Q.6(a)

loads. , ,,"

Fig.Q.7(b)

b. Derive an expression for stiffness matrix for a2-D truss element.

a. Derive the Hermite shape functions of a beam eleiirent.A simply supported beam'of span 6m and uniform flekural rigidity EI : 40000 kN-m2 issubjected to clockwise couple of 300 kN-m at a distanCe of 4m from the left end as shown inthe Fig.Q.7(b). Find the deflection at the point of application of the couple and internal

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F8 a. Find the temperature distribution and heat transfer through an iron fin of thickness 5mm-

'-rr.j---- :-;nrn and uidth 1000mm. The heat transfer coefficient around the fin is 10 Wim2.K and ambient temperature is 28oC. The base of fin is at 108'C. Take K : 50 Wm.K. Usetwo elements.

Fig.Q.8(a)

b.

I

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Derive element matrices for heat conductionapproach.

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in one-dimensional element using Galerkin's(10 Marks)

(06 Marks)(08 Marks)

(08 Marks)

(08 Marks)

(12 Marks)

(10 Marks)