Manufacturing Processes – II Academic year: 2015-16: Assignment Assignment 1: Weightage: Weightage: 3 mars !"#$% "& A' !I(% PAP%) "&#* #ast date of su+mission is 16 th "cto+er 2015 .
1. Show that in metal cutting when the working normal rake is zero, ze ro, the ratio of the shear strength of the work material τ s to the specific cutting energy p s is given by τ s
p s
=
(1 − µ rc ) r c 1 + r c2
.
2. Derive an epression for the specific cutting energy p s in terms of the shear angle ! an" the mean shear strength strength of the work material τ s in orthogonal cutting. #ssume that the shear$angle relationship of %rnst an" &erchant applies, that that is 2! ' $ ne * +2 -. #ssuming that the shear angle theory of ee an" Shaffer applies, namely ! ' $ ne*+/, show that the specific cutting energy en ergy p s will be given by p s * τ s (1'cot !) where τ s is the mean shear strength of the work material /. 0or the orthogonal cutting of a particular work material, it is foun" that the length of chip$tool contact is always eual to the chip thickness a0 an" that the mean shear stress at the chip$tool chip$tool interface interface is eual to the mean shear stress stress on the shear plane. Show that, un"er these circumstances, the mean coefficient of friction on the tool face must be eual to or less than /- an" that when it is eual to unity, the shear angle ! is eual to the working normal rake γne. 3. 4n the cutting eperiments using a sharp tool with zero rake, it was foun" that the chip$ tool contact length length was eual to the chip thickness thickness a0. 4t was also foun" that the shear stress stress along along the tool face face was constant constant an" was a consta constant nt propor proportio tion n R of the shear strength of the work material on the shear plane. a. Derive Derive an an epres epressio sion n for the cutt cutting ing forc forcee F c in terms of ac, aw, τ s, R an" ! . b. Differentiate the epression to obtain obtain the value of ! to give minimum F c. 5. #ssume that in an orthogonal cutting operation, the frictional force 0f on on the tool face A0 where K is a constant is give given n by Kτ s A constant,, τ s is the apparent shear strength of the work mate materi rial al,, an" an" A0 is the the cros cross$ s$se sect ctio iona nall area area of the the chip chip.. Show Show that that the the foll follow owin ing g relationship eists between the mean coefficient of friction on the tool face, the shear angle !, an" the working normal rake γne 2
K cos (ϕ µ
=
K sin(ϕ
−γn e
− γ n
) cos(ϕ
e
)
−γ n e
1 )+
Manufacturing Processes – II Academic year: 2015-16: Assignment 2: Weightage: 2 mars !"#$% "& A' !I(% PAP%) "&#* #ast date of su+mission is 16 th "cto+er 2015,
1) 4f, when machining at high cutting spee"s, the heat con"ucte" into the cutting tool becomes negligible an" the heat con"ucte" into the work piece is / percent of the total heat generate", "erive an epression for the final chip temperature θ in terms of the specific cutting energy p s , the specific heat capacity of the work material c an" Density of work material ρ . 2 a) Show that when cutting metal orthogonally with a tool of zero rake angle, the rate of heat generate" p s in the shear zone is given by P s = Fcv(1 − µ r c ) 6here, F c is the cutting force, v is the cutting spee", μ is the mean coefficient of friction on the tool face an" r c is the cutting ratio. 2 b) 0or the same con"ition, calculate the mean shear$zone temperature rise θ s when the metal has a specific cutting energy of 2.7 89m2, μ=1.:, r c*:.2 an" 1: percent of the shear$zone heat is con"ucte" into the work piece. #ssume for the work material that ρ = ;2:: kgm- an" c*3:: <kg= 2 c) 6hat woul" be the value of θ s if the cutting spee" were "ouble" an" the proportion of shear$zone heat con"uction into the work piece remaine" the same time> -) During some machining eperiments, it was foun" that for the range of con"itions stu"ie", the following assumptions coul" be ma"e? a. @he heat con"ucte" into the cutting tool was negligible. b. @he proportion of the heat generate" in the shear zone con"ucte" into the work piece was :.2. c. @he maimum temperature rise in the chip "ue to the frictional heat source θ m followe" the relation θ m
=
θ f R where θ f is the mean temperature rise of the chip
"ue to the frictional heat source an" R is the thermal number. ". @he heat generate" "ue to friction was eual to 2: percent of the heat generate" in the shear zone. Derive an epression for the maimum temperature in the chip above the initial work piece temperature in terms of the specific cutting energy of the work piece ps , the specific heat c, "ensity ρ of the work piece an" the thermal number R . /) 4t was foun" from eperiments where the chips pro"uce" "uring shaping were caught in a calorimeter that the mean chip temperature rise was 3:: A. @he cutting con"itions were as follows? Autting spee" * 1 ms, Bn"eforme" chip thickness * :.3mm, 6i"th of chip * 3mm, 6orking normal rake angle * /3° , Autting force * 5:::9, @hrust force * :9, Ahip thickness * 1.2mm, ength of work piece * -::mm. #fter 1:: strokes of the shaper, the insulate" work piece was immerse" in a calorimeter an" its a""itional heat content foun" to be -: k<. 9eglecting the heat con"ucte" into the cutting tool calculate the proportion of the shear$zone heat con"ucte" into the work piece °
