Metal Forming · Production Engineering · GATE ME

In a metal forming operation when the material has just started yielding, the principal stresses are $${\sigma _1} = \,\, + 180\,\,MPa,\,\,\,$$ $${\sigma _2} = \,\, - 100\,\,MPa,\,\,\,$$ $${\sigma _3} = 0.$$ Following Von Mises' criterion, the yield stress is _____________ $$MPa.$$

It is desired to make a product having T-shaped cross - section from a rectangular aluminium block. Which one of the following processes is expected to provide the highest strength of the product?

The value of true strain produced in compressing a cylinder to half its original length is

Engineering strain of a mild steel sample is recorded as $$0.100\% .$$ The true strain is

Match the following products with preferred manufacturing process:

In a rolling process, the maximum possible draft, defined as the difference between the initial and the final thickness of the metal sheet, mainly depends on which pair of the following parameters?
$$P:$$ Strain
$$Q:$$ Strength of the work material
$$R:$$ Roll diameter
$$S:$$ Roll velocity
$$T:$$ Coefficient of friction between roll and work.

With respect to metal working, match Group A with Group B:

The relationship between true strain $$\left( {{\varepsilon _T}} \right)$$ and engineering strain $$\left( {{\varepsilon _E}} \right)$$ in a uniaxial tension test is given as

In a rolling process, the state of stress of the material undergoing deformation is

A solid cylinder of diameter $$100$$ $$mm$$ and height $$50$$ $$mm$$ is forged between two frictionless flat dies to a height of $$25$$ $$mm.$$ The percentage change in diameter is

The maximum possible draft in cold rolling of sheet increases with the

Cold working of steel is defined as working

Ductility of material with work hardening

Hot rolling of mild steel is carried out

A test specimen is stressed slightly beyond the yield point and then unloaded. Its yield strength

The process of hot extrusion is used to produce

The true strain for a low carbon steel bar which is doubled in length by forging is

In forging operation the sticking friction condition occurs near the ...... (Center/ ends) while sliding friction condition occurs near the ...... (Center / ends)

For wire drawing operation, the work material should essentially be

A steel sample with 1.5 wt.% carbon (no other alloying elements present) is slowly cooled from 1100 °C to just below the eutectoid temperature (723 °C). A part of the iron-cementite phase diagram is shown in the figure. The ratio of the pro-eutectoid cementite content to the total cementite content in the microstructure that develops just below the eutectoid temperature is ________.

(Rounded off to two decimal places)

A cylindrical billet of 100 mm diameter and 100 mm length is extruded by a direct extrusion process to produce a bar of L-section. The cross sectional dimensions of this L-section bar are shown in the figure. The total extrusion pressure (p) in MPa for the above process is related to extrusion ratio (r) as

$\rm p=K_s σ_m\left[0.8+1.5\ ln(r)+\frac{2l}{d_0}\right] $

where σ_m, is the mean flow strength of the billet material in MPa, l is the portion of the billet length remaining to be extruded in mm, d₀ is the initial diameter of the billet in mm, and K_s is the die shape factor.

If the mean flow strength of the billet material is 50 MPa and the die shape factor is 1.05, then the maximum force required at the start of extrusion is _______ kN (round off to one decimal place).

A rod of length $$20$$ $$mm$$ is stretched to make a rod of length $$40$$ $$mm.$$ Subsequently, it is compressed to make a rod of final length $$10$$ $$mm.$$ Consider the longitudinal tensile strain as positive and compressive strain as negative. The total true longitudinal strain in the rod is

A strip of $$120mm$$ width and $$8mm$$ thickness is rolled between two $$300$$ $$mm$$-diameter rolls to get a strip of $$120mm$$ width and $$7.2mm$$ thickness. The speed of the strip at the exit is $$30m/min.$$ There is no front or back tension. Assuming uniform roll pressure of $$200$$ $$MPa$$ in the roll bite and $$100\% $$ mechanical efficiency, the minimum total power (in $$kW$$) required to drive the two rolls is ____________________

A $$300$$ $$mm$$ thick slab is being cold rolled ussing roll of $$600$$ $$mm$$ diameter. If the coefficient of friction is $$0.08,$$ the maximum possible reduction (in $$mm$$) is _______

A $$300$$ $$mm$$ thick slab is being cold rolled using roll of $$600$$ $$mm$$ diameter. If the coefficient of friction is $$0.08,$$ the maximum possible reduction (in $$mm$$) is _______________

The flowing stress (in $$MPa$$) of a material is given by $$\sigma = 500{\varepsilon ^{0.1}},$$
When $$\varepsilon $$ is true strain. The Young's modulus of elasticity of the material is $$200$$ $$GPa.$$ A block of thickness $$100$$ $$mm$$ made of this material is compressed to $$95$$ $$mm$$ thickness and then the load is removed. The final dimension of the block (in $$mm$$) is ____________

In a two stage wire drawing operation, the fractional reduction (ratio of change in cross sectional area to initial cross sectional area ) in the first stage is $$0.4.$$ The fractional reduction in the second stage is $$0.3.$$ The overall fractional reduction is

In a slab rolling operation, the maximum thickness reduction $$\left( {\Delta {h_{\max }}} \right)$$ is given by $$\Delta {h_{\max }} = {\mu ^2}R,$$ where $$R$$ is the radius of the roll and $$\mu $$ is the coefficient of friction between the roll and the sheet. If $$\mu = 0.1,$$ the maximum angle subtended by the deformation zone at the center of the roll (bit angle in degrees) is ____________

In a rolling operation using rolls of diameter $$500mm,$$ if a thick plate cannot be reduced to less than $$20mm$$ in one pass, the coefficient of friction between the roll and the plate is ____________.

A mild steel plate has to be rolled in one pass such that the final plate thickness is $$2/{3^{rd}}$$ of the initial thickness, with the entrance speed of $$10m/min$$ and roll diameter of $$500mm.$$ If the plate widens by $$2\% $$ during rolling, the exit velocity (in $$m/min$$) is ____________

A metal rod of initial length $${L_0}$$ is subjected to a drawing process. The length of the rod at any instant is given by the expression, $$L\left( t \right) = {L_0}\left( {1 + {t^2}} \right),$$ where $$t$$ is the time in minutes. The true strain rate (in $${\min ^{ - 1}}$$) at the end of one minute is _____________

In a single pass rolling process using $$410mm$$ diameter steel rollers, a strip of width $$140mm$$ and thickness $$8mm$$ undergoes $$10\% $$ reduction of thickness. The angle of bite in radians is

In a single pass rolling operation, a $$20mm$$ thick plate with plate width of $$100mm$$, is reduced to $$18mm$$ thick. The roller radius is $$250mm$$ and rotational speed is $$10$$ $$rpm.$$ The average flow stress for the plate material is $$300$$ $$MPa.$$ The power required for the rolling operation in $$kW$$ is closer to

Match the correct combination for following metal working processes.

The thickness of metallic sheet is reduced from an initial value of $$16mm$$ to a final value of $$10mm$$ in one single pass rolling with a pair of cylindrical rollers each of diameter of $$400mm.$$ The bite angle in degrees will be

In open die forging, a disc of diameter $$200mm$$ height $$60mm$$ is compressed without any barreling effect. The final diameter of the disc is $$400mm.$$ The true strain is

A $$4$$ $$mm$$ thick sheet is rolled with $$300$$ $$mm$$ diameter rolls to reduce thickness without any change in its width. The friction coefficient at the work-roll interface is $$0.1.$$ The minimum possible thickness of the sheet that can be produced in a single pass is

In a wire drawing operation, diameter of a steel wire is reduced from $$10$$ $$mm$$ to $$8$$ $$mm.$$ the mean flow stress of the material is $$400$$ $$MPa.$$ The ideal force required for drawing ignoring friction and redundant work is:

In a rolling process, sheet of $$25$$ $$mm$$ thickness is rolled to $$20$$ $$mm$$ thickness. Roll is of diameter $$600$$ $$mm$$ and it rotates at $$100$$ $$rpm.$$ The roll strip contact length will be

A brass billet is to be excluded from its initial diameter of $$100mm$$ to a final diameter of $$50mm$$. The working temperature is $${700^ \circ }C$$ and the extrusion constant is $$250$$ $$MPa.$$ The force required for extrusion is

A strip with sectional area $$150mm\,\, \times \,\,4.5mm$$ is being rolled with $$20\% $$ reduction of area using $$450mm$$ diameter rollers. The angle subtended by the deformation zone at the roll center is (in radians)

A wire of $$0.1mm$$ diameter is drawn from a rod of $$15mm$$ diameter dies giving reductions of $$20\% $$, $$40\% $$ and $$80\% $$ are available. For minimum error in the final size, the number of stages and reduction at each stage respectively would be

Calculate the bite angle when rolling plates $$12mm$$ thick using work rolls $$600mm$$ diameter and reducing the thickness by $$3mm$$

A cylindrical billet of $$100$$ $$mm$$ diameter is forged from $$50$$ $$mm$$ height to $$40$$ $$mm$$ at $${1000^0}$$$$C$$. The material has constant flow stress of $$80$$ $$MPa.$$ Find the work of deformation. If a $$10$$ $$kN$$ drop hamper is used to complete the reduction in one blow. What will be the height of fall.

A metal strip is to be rolled from an initial wrought thickness of $$3.5$$ $$mm$$ to a final rolled thickness of $$2.5$$ $$mm$$ in a single pass rolling mill having rolls of $$250$$ $$mm$$ diameter. The strip is $$450$$ $$mm$$ wide. The average coefficient of friction in the roll gap is $$0.08$$. Taking plane strain low stress of $$140$$ $$MPa,$$ for the metal and assuming negligible spreading, the roll separating force is . . . . . . . . .

A strip of thickness $$T$$ $$mm$$ is rolled in a $$2$$ high single pass rolling mill, having roll diameter $$D$$ $$mm,$$ to a final thickness of $$\left( {T - 2\Delta T} \right)mm.$$ If the friction coefficient between the roll and strip is $$\mu ,$$ calculate the maximum reduction $$2\Delta T$$ possible in this operation. Using this relation, for $$D=300mm,$$ $$T=40mm$$ and friction coefficient is $$0.3,$$ calculate the outgoing thickness of the strip. If the inlet velocity is $$5m/s,$$ what is the outgoing strip velocity?.