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can anybody solve this.
Mg casting with a volume to surface ratio(casting modolus)of 0.1m is made by gravity casting. heat transfer coefficient at the metal mould interface is 1.9KJ/m^2 K s . the density and melting point of the Mg are 1700 kg/m^3 and 923K. assume ambient temperature to be 293K.
a)if the solidification time is 50s. the latent heat of fusion in KJ/mol is
b)in a spiral channel of 10mm dia and with an entrance flow velcity of 300mm/s , the fluidty of the melt in mm is
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first of all sorry for such long delay 🙁
Anyway I think the data given is incomplete in this question that’s why now I am giving u only formulas:
a) For Latent heat calculate “B” from the formula as:
t = B * [(Casting modulus)^n]
where,
t = Solidification Time (given)
B = Mold Constant
n = 1.5 to 2 (Take 2 if not given)
Then after finding “B” calculate Latent heat as:B = {[(ρm*L)/(Tm-T0)]^2}*{[3.1428/(4*K*ρ*C)]}*{1+[(Cm*ΔTs)/L]}
Where,
Tm = melting or freezing temperature of the liquid
To = initial temperature of the mold
ΔTs = Tpour − Tm = superheat
L = latent heat of fusion
K = thermal conductivity of the mold
ρ = density of the mold
C = specific heat of the mold
ρm = density of the metal
Cm = specific heat of the metalb) For Fluidity of Short Freezing Range Alloys the formula is,
Fluidity Distance, Lf = V * twhere,
V = flow velocity
t = solidification timeIf the data is not given in the problem then take any appropriate material & take respective data & put it in formula… 🙂
Well I don’t think this kind of question can be asked in GATE; if asked then it should be deserve 10 marks lol …
Hope this could satisfied you a bit…. … .. .
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In a multi pass drawing operation, a round bar of 10 mm diameter and 100 mm length is reduced in cross section by drawing it successively through a series of seven dies of decreasing diameter. During each of these drawing operation, the reduction in cross-sectional area is 35%. The yield strength of the material is 200 MPa. Ignore strain hardening.
The total true strain and final length ?
Neglecting friction and redundant work, the force in (kN) required for drawing through first die?
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@Dinesh: Ok I wants to say that I am not too good in this Forming section but still I will try to solve this; Lets see how much can I help you !!!
Say, Original c/s Area = O.A.
Final c/s Area = F.A.
Area After First Die = A1
Original Length = O.L.
Final Length = F.L.
Now O.A. = (pi/4)*(10^2) = 78.5398 mm2
A1 = (1-0.35)*(O.A.) = 0.65*(O.A.) = 51.0508 mm2
Similarly for the area after 7th die
= 0.65*0.65*0.65*0.65*0.65*0.65*0.65*(O.A.) … .. (For 7 dies)
= (0.65)^7 * (O.A.)
= 3.8502 mm2 = F.A.
Now, as True strain is instantaneous % of change in length of specimen & it is given by,
True strain (TS) = Natural log of (O.A./F.A.)
= ln (78.5398/3.8502)
= 3.0155 ———————————–ANS
Final length can be calculated by using constant volume principle as,
Initial Volume = Final Volume
(O.A.)*(O.L.) = (F.A.)*(F.L.)
78.5398 * 100 = 3.8502 * F.L.
F.L. = 2039.8888
= 2040 mm ————————————-ANS
Now, For force we have to calculate a Draw Stress after first die,
using uniform energy deformation method,
Draw Stress (D.S.) = Y * ln(O.A./A1) …… … (Y = Yield Strength)
(Note this formula can be used for only Ideal Conditions i.e. neglecting friction and redundant work)
Hence, D.S. = 200 * ln (78.5398/51.0508)
= 86.1568 N/mm2
Now, Drawing Force through first die is,
Drawing Force (F) = (D.S.)*(A1)
= 86.1568 * 51.0508
= 4398.3735 N
= 4.4 kN ———————————ANSNote: Please check the answers & do notify in reply. If possible then mention the answers (options) along with the questions.
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Please suggest me books that contains problems on manufacturing processes like forming, forging, drawing, casting, punching etc. I have P N Rao’s book which elaborates very good theory but it does not have enough no of solved problems 🙁 Please suggest me any book name or if anybody has a soft-copy then give me link….
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Chetan…Thanks..Actually this problem was in gate 2011 paper..production and industrial engineering..
Sorry I forgot to give option..
Your Answers are right..These maybe a good books
Forming- Engineering Metallurgy…DIETER,
Production Engineering….P.C. Sharma(Problems)and also check other forming operations…..
Have a good day…
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@chetan- do you have facebook account?…just login with faceook account on scribd
after they ask for uploading document….so upload any document(which is in kb) or make notepad file of anything and upload it..:-)
then u can download any document
and also in that scribd link there are other sublinks of forming. So u can get all forming processes documents
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@Dinesh, Sorry for late in reply 🙁
If you are talking about problems on casting then I don’t think I have done enough. I am still concentrated more on studying. However I will start practicing problems in coming days (probably after 15th Jan).
How you are going by the way????Now if volume shrinkage is present in metal, then we have to compensate the shrank volume with the riser.
So try to equate volumes or areas to get the size.
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@Dinesh:
I will solve from these sources:
1. Manufacturing Technology by PN Rao
2. Fundamentals Modern Manufacturing by Groover
3. Previous years GATE QPsAbout the two books:
Both books have various problems but most of them are unsolved (you can find practice problems after the chapter ends!)
Groover has some quality question with good theory explanation & some Multiple Choice Questions also.You can search for some tutorials given on Internet(I hope they are!!!).
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@chetan…yeah i am also doing the same…PN rao is good for manufacturing…and chetan there is one mistake in that book..average cutting shear strain = cot(shear angle)+ tan(shear angle – rake angle)….but in that book its given average cutting shear strain = cot(shear angle-rake angle)+ tan(rake angle)…so those who r studying from pn rao must note this…!!!
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@Dinesh, If you feels that the problems given in reference books(PN Rao, Grover’s) are not enough in anyway then you can collect some practice problems from some recognized institute’s NOTES like GATE-Forum, TARGate, Ace Academy from say your friends or teachers for the topics you have mentioned.
BEST LUCK FOR UR STUDIES !!!!
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Hi to all, I m a student of production engg, 3rd year, NIT Trichy.. I want to opt gate 2013, but i have doubt whether i shud write gate from ME or from PI so as to get job in PSUs… i dnt want to do M.tech.. i m willing to write gate just for PSUs.. and i know it is dificult to study whole mech subjects as i m from prod branch but also der will not b many psu companies who will accept prod engg so help me.. what should i do?
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