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- 1. 10M862 USN Sixth Semester B.E. Degree Examination, Dec.20L3 lJan.2014 Design of Machine Elements - ll Time: 3 hrs. Max. Marks:100 Note: 7. Answer FIVEfutt t () ^r:^^i-^^ o o L a I a. a --^--. t ^ ^--:)^tt-- ^^^-----^J D A f)rrr A PART _ 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 the () )^t- questions, selecting faC (10 Marks) .of safety. ...... o L J. 69 =r) oor goa .= c cEHYlt$!' bLo LIBRAqAY oC FO .: o> Fig.Q1(a) t 16.< l q/ A high pressure cylinder consists ofa steel tube with inner and outer diameter of 20 mm and 40 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 stress induced in any tube is limited to 100 MPa. Calculate the shrinkage pressure and original (10 Marks) dimensions of the tubes, Take the Young's modulus as 207 GPa. *,a a= oc) ootr !: a6 Write ag o.. (.) j o= =u 4lI 3 a. b. ^.= =g ^"o iloo Y, t:, af= o. hi tr> "' , :,, =o o lr< :^ () o z o a note on construciion of flat and 'V' belt. (05 Marks) 'V" belt drive to connect a 7.5 kW, 1440 rlmin induction motor to a fan. 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 belts (15 Marks) required. ,' It 2o) 6jj 4a. b. is required to design a Enumerate the applications of springs. Also derive an expression for the deflection of a close (06 Marks) coiled helical spring. A Spring is subjected to a load varying from 500 N and 1200 N. It is to be made of oil tempered cold drawn wire. Design factor based on Wahl's line is 1.25. The spring index is to be 6. The compression in the spring for the maximum load is 30 mm. Determine the wire diameter, 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) (06 Marks) Write a note on design of gears based on dynamic loading and wear. teeth spur pinion operating at 1150 rlmin transmits 3 kW to a cast steel 56 teeth spur gear. The gears have the following specifications: Module : 3 mm Allowable stress : 100 MPa Face width : 35 mm Tooth 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 (14 Marks) load. Comment on the results. A cast steel24 I of2
- 2. 10M862 PART _ B a. b. Write a note on formative number of teeth in bevel gear. (04 Marks) 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 drive and give estimated power input ratings from the stand point of strength, endurance and heat dissipation. The teeth are of l4%' full depth involute. (16 Marks) 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 b. A band,break arrangement is shown in Fig.Q6(b). It is used to generate a maximum braking torque of 200 N-m. Determine the actuating force 'P' , if the coefficiept''of friction is 0.25. The angld'of wrap of the band is 270".Determine the maximum,,iritehsity of pressure, if the :1 ::,,,, band width is30 mm. (10 Marks) ,.6,, ",,,,,r,r,, .tt , of pressure between contacting surfaces is not to exceed 0.085 N/m# and the psbfficient friction is 0.2, assuming uniform wear conditions, calculate the dimensions of thb clutch. ,, ,. of (10 Marks) :,,,:,, a. Fie.Q6(b) 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 mm Bearing length : 50 mm Journal speed : 1440 rlmin Radialload-:8 kN Viscosiiyoi1.utii;ca"t : 12 cp. The bearing iS,,machined on a lathe from bronze casting, while'tlie steel journal is hardened and ground; The surface roughness values for turning and grinding are 0.8 and 0.4 microns respectiifely. For thick film lubrication the minimum film thickness stiould be five times the sum.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. ,j' (iv) Flow requirement. {"I2 Marks) ,,,,:,, ,, 8a. b. lri' Explain the considerations given in the design of pistons for IC engines. (05 Marks): Design a trunk piston for an IC engine. The piston is made of cast iron with an allowable stress of 38.5 MPa. The bore of the cylinder is 200 mm and the maximum explosion pressure is 0.4 MPa. The permissible bending stress of the material of the gudgeon pin is 100 MPa. The bearing pressure in the gudgeon pin bearing of the connecting rod is to be taken as 200 MPa. (15 Marks) *{<*rf* 2 of2
- 3. 10ME63 USN Sixth Semester B.E. Degree Examination, Dec.2013 lJan.201^4 Heat and Mass Transfer Time: 3 hrs. Max. Marks:100 ' Note: 1. Answer FIVEfull questions, selecting at lesst TWO questions from each part. (Jse of heat transfer data book is permitted. quoq 2. uvvut ao lrcr rraaa .' ' "':' ' "''':"": () o o L a , I a. c. PART_A d9 I troo .=N 2 a- tso -gO a2 b. c. oO (G0 ootr >G! Ed .?d) 'Ea OE ^X 3a. €i !o o= go tr> =o o J< J ..i o o z o (08 Marks) A plate of thickness 'L' whose one side is insulated and the other side is maintained at a An electric cable of l0mm diameter is to be laid in atmosphere at 20'C. The estimated surface temperature of the cable due to heat generation is 65"C. Find the maximum percentage increase in heat dissipation,,,*hen the wire is insulated with rubber having K: 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), 100 pin fins (1 cm diameter, 10sm long) are attached. If the pin fins are made of copper having a thermal conductivity of 300 WmK and the value of the surface heat transfer coefficient is 15 Wm2K,;,Calculate the decreur. in the thermal resistance. Also calculate the consequent increase in heat transfer rate from the wall if it is ma@@ined.qt a temperature of 200"c and the surroundings are ar 30oc. (r0 Marks) .Zr(j-{)} givenov"ffi=+=*r[#) W-*%7i ( -T" ei / : (K: cooling is (06Marks) pCV ThesGel ball bearings 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 transfer ^ .,..,":','',..,;.T, b. v, =.9 ^: bocoo coordinates. Show that fhel.'temperature distribution in a body during ]1id (.) j 9E to 4 tr= _, '-' (06 Marks) representation of three commonly used temperature 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 one dimensional, steady Stste heat transfer, without heat generation. (06 Marks) -.o o0 :: iiketches, write down the mathematical different types of boundary conditions for one dimensional heat. e(uation in rectangular 0) bo- : Explain briefly the mechanism of conduction, convection and radiation heat transfu:;. b. Witli I .:: coefficient is estimated to be 300 Wm2K. Calculate: The time required for bearings to reach 200"C. The total amount of heat removed from a bearing during this time and The instantaneous heat transfer rate from the bearings, when they are flrst immersed in oil bath and when thev reach 200'C. (14 Marks) ' i) ii) iii) 4 a. b. :: With reference to fluid flow over a flat plate, discuss the concept of velocity boundary and thermal boundary layer, with necessary sketches. (05 Marks) The exact expression for local Nusselt number for the laminar flow along a surface is given ,xz bv Nu' = hx - 0.332 nll' pJ". Show that the average heat transfer coefficient from -'--- --e -r r x k 0 to x : L over the length transfer coefficient at x: L. x : 'L' of the surface is given by 2hr where hl is the local heat (05 Marks) I of2
- 4. 10ME63 A vertical plate 15cm high and 10cm wide is maintained at 140"C. Calculate the maximum heat dissipation rate from both the sides of the plates to air at 20oC. The radiation heat transfercoefficient is 9.0 wm2K. Forairat 80.c, take r:2L09 x 10-6 ni/sec,pr:0.692, kr: o.o3 wmK. (lo Marks) 5a. b. c. PART - B Explain 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 a diameter of 3cm. A constant heat flux condition is maintained at the wJl and the wall t-emperature is 20oC above the air temperature all along the length of the tube. Calculate: ., i) The heat transfer per unit length of tube. , 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 wmK and Co = 1.025 kJ/kg K. (ro Marks) Obtain a ielationship between drag coefficient, c. and heat transf,er'coefficient, hn,, for the llow over a flat plate. r.*." (06 Marks) a' Derive an expression for LMTD of a counter flow heat exchanger. State the assumptions b. c' What is meant by the term fouling factor? How do you determine it? (04 Marks) Engine oil is to be coded from 80'C to 50'C by using a single pass counter flow, concentric tube heat exchanger with cooling water available ul20"C. Water flows inside a tube with inner diameter of 2.5cm and at a rate of 0.08 kg/sec and oil flows through the annulus at the rate of 0.16 kg/sec. The heat transfer coeficient for the water side and oil side are F,: the tube length 7a. b. c. : 1000 Wm2oC and h.l : 80 Wm2oC. The fouling factors is 0.00018m2oC/W on both the sides ard the tube wall resistance is negligible. Calculate respectively h," required. (08 Marks) Sketch a pool boiling curvq for water and explain'briefly the various regimes in boiling heat transfer. ,,, ,-'''. ' coerficient. transfer ?..1". A l2cm outside diameter and 2m long tube is used in a big condenser to condense [8iXff[] the steam n 0.1 bar,-Estr3{e the unit surface conductance i) in iertical position; iil i, horizontal mass position. Also find the amount of condensate formed per hour The satutation temperature of the steam :74.5"C. Aver,age wall temperature : 50.C. infin the cases. -? 75'4j50 =62.7oC are given below lp:982.2kglm3, hr_ =2480kJ/kg,K:0.65WmK, p:0.47 x 10-3kg/ms. '' liolvrarks) The'properties of water film at average temperature 8a. b. c. of State and prove Wiens displacement law of radiation. The temperature of a black surface 0.2rfi in area is 540.c. calculate: The total rate of energy emission. i) ii) The intensity of normal radiation. Iti) The wavelength of maximum monochromatic Derive an only. (06 Marks) emissive power. (06 Marks) expression for a radiation shape factor and show that it is a function of geometry (08 Marks) *<*{<*{< 2 of2
- 5. 10ME64 USN Sixth Semester B.E. Degree Examination, Dec.2013 /Jan.20l4 Finite Element Methods Time: 3 hrs. Max. Marks:100 Note: Answer FIVEfull questions, selecting ut least TWO questions from each part. ., (.) o o L a (.) o L oX 1 PART _ A a,, r Differentiate between plane stress and plain strain problems with examples. Write the stressstrain 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) 2 a. State the piineiple of minimum potential energy. Determine tl.le displacements at nodes for the spring system qhown in the Fig.a.,2J3). (08 Marks) lsoN/nn a Jh -.^t Fig.Q.2(a) Eoo ts.) oEl -o b. Determine the deflection of a cantilevel beam of length 'L' -! distributed load (UDL) of Po/unit iength, using the trail function y o2 subjected : a sin [ the results with analyical solution and comment on accuracy. 6: oO 1o uniformly '* I 2L ) . Comnare (12 Marks) 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. (10 Marks) oot .9(s ,6 Ed !o ?o oj o= a ai= !o o.>! boca0 o= qo tr> Note; All dimensions in mm. 4 a. an' axial load P : 300 x 103 ,, , temperature is then raised to D ii) Fig.Q.3(b) N is applied at 20'C to the rod as shown in the Fig.Q.41a.y. The 60oC. Assemble the global stiffness matrix (K) and global load vector (F). Determine the nodal displacenrents and element stresses. =o oVL Fig.Q.a(a) {'l o z o E r:70 x 10e N/m2,82: 200 Ar :900mm2, Az: l200mm2 a1 :23 x 10-6/oC, az: 71.7 x x 10eN/m2 (12 Marks) 10'61'C. I of2
- 6. b. 10M864 Solve the following system of equations by Gaussian-Elimination method: xr -2xz * 6x: : 0 2x1-t 2x2 + 3x3 : 3 -xy 5a. * 3x2:2. PART _ B Using Lagrangian method, derive the shape function of a three-noded one-dimension (1D) element [quadratic -ll b c. 6a. (08 Marks) element]. (06 Marks) rl Lvuruulv '--lL" Evaluate I: ll 3e^+xt+ rA *G*2)-l''" l.d* using one-point and two-point Gauss quadrature. Wtite short notes on higher order elements used in FEM. (06 Marks) (08 Marks) For the two-bar truss shown in the Fig.Q.6(a). Determine the nodal displacements and element stross.es- A force of P: 1000 kN is applied at node 1, Take p,: ZtO GPa and A : 600mm2'for each element. ,, t '' , ' (12 Marks) Fie.Q.6(a) b. Derive an expression for stiffness matrix for a2-D truss element. a. Derive the Hermite shape functions of a beam eleiirent. (08 Marks) A simply supported beam'of span 6m and uniform flekural rigidity EI : 40000 kN-m2 is subjected to clockwise couple of 300 kN-m at a distanCe of 4m from the left end as shown in the Fig.Q.7(b). Find the deflection at the point of application of the couple and internal loads. , ,," (08 Marks) (12 Marks) ?wW'n't Fig.Q.7(b) F 8 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. Use two elements. (10 Marks) I Fig.Q.8(a) b. t, I flil {r^rn jr,.n * rEry Derive element matrices for heat conduction in one-dimensional element using Galerkin's approach. (10 Marks) >k*{<**

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