Machining and Cutting Tools Questions and Answers

Answer: A

A bandsaw employs an endless looped blade to cut, and it is suited to irregular and curved shapes. A shaper and a planer use a single point tool in a reciprocating motion for flat surfaces, and a slotter is a vertical shaper for cutting slots and keyways, so none of them uses an endless blade. The key therefore gives the bandsaw.

Answer: A

The new tool life is 4 times the original.

Taylor's equation is \(VT^{n} = C\). With n = 0.5:

\[ \begin{aligned} \frac{T_{2}}{T_{1}} &= \left(\frac{V_{1}}{V_{2}}\right)^{1/n} \\ &= 2^{1/0.5} = 2^{2} = 4 \end{aligned} \]

Halving the speed doubles \(V_{1}/V_{2}\), and the exponent 1/n = 2 squares that ratio. 2 is what a linear relation (n = 1) would give, and 0.5 or 1 would mean slower cutting shortened or did not change tool life.

Answer: C

The shear strain rate is about \(1.0104\times10^{5}\) s^-1.

First the shear angle, from the chip thickness ratio r = 0.4 and rake angle 10°:

\[ \begin{aligned} \tan\phi &= \frac{r\cos\alpha}{1-r\sin\alpha} = \frac{0.3939}{0.9305} \\ &= 0.4233,\ \phi = 22.94^{\circ} \end{aligned} \]

The shear velocity along the shear plane is:

\[ \begin{aligned} V_{s} &= \frac{V\cos\alpha}{\cos(\phi-\alpha)} = \frac{2.5(0.9848)}{\cos 12.94^{\circ}} \\ &= 2.526\ \text{m/s} \end{aligned} \]

Dividing by the shear zone thickness of 25 microns gives the strain rate:

\[ \begin{aligned} \dot{\gamma} &= \frac{2.526}{25\times10^{-6}} \\ &= 1.0104\times10^{5}\ \text{s}^{-1} \end{aligned} \]

Dividing the cutting speed itself by the zone thickness gives exactly \(1.0\times10^{5}\), near but not equal to the keyed value; the velocity that slides across the shear zone is the shear velocity, not the cutting speed. The other three options do not follow from these data.

Answer: A

The correct statement is that Configuration P1 arrests 6 degrees of freedom, while P2 and P4 are over-constrained and P3 is under-constrained.

A cuboid is located by the 3-2-1 principle: three pins under the largest face fix one translation and two rotations, two pins on a side face fix a further translation and rotation, and one pin on the adjacent end face fixes the last translation, six points for six degrees of freedom.

• P1: three pins below and three on the sides, in the 3-2-1 pattern, so exactly 6.
• P2: four pins below and three on the sides, 7 in all; one is redundant, so it is over-constrained.
• P3: three below and only two on the sides, 5 in all; one freedom is left, so it is under-constrained.
• P4: four below and four on the sides, 8 in all; over-constrained.

Each of the other options puts the correct 3-2-1 label on a configuration with too many or too few pins.

Answer: B

The shear strain rate is \(5.20 \times 10^{4}\ \text{s}^{-1}\).

The strain rate is the shear velocity along the shear plane divided by the thickness of the shear zone. From the velocity triangle of orthogonal cutting,

\[ \begin{aligned} V_{s} &= \frac{V\cos\alpha}{\cos(\phi - \alpha)} \\ &= \frac{\cos 5^{\circ}}{\cos 40^{\circ}} \\ &= \frac{0.9962}{0.7660} \\ & = 1.300\ \text{m/s} \end{aligned} \]

\[ \begin{aligned} \dot{\gamma} &= \frac{V_{s}}{\delta} \\ &= \frac{1.300}{25 \times 10^{-6}} \\ &= 5.20 \times 10^{4}\ \text{s}^{-1} \end{aligned} \]

The distractors reuse numbers from the same calculation. 1.84 is the shear strain, \(\cot\phi + \tan(\phi - \alpha) = 1 + 0.839\), a dimensionless quantity, not a rate. 1.30 is the shear velocity in m/s; dividing it by 100 μm instead of 25 μm would give \(1.30 \times 10^{4}\). 0.71 is \(\cos 45^{\circ}\), which does not give the strain rate on its own.

Answer: C

A blind hole is reamed with a right hand spiral fluted reamer.

In a blind hole the chips have nowhere to go ahead of the tool, so they must be carried back out. A right-hand spiral on a right-hand cutting reamer lifts the chips up the flutes and out of the hole, the way a twist drill does.

A left-hand spiral does the opposite: it pushes chips ahead of the reamer, which suits a through hole, where they can fall out of the far end, and would pack them into the bottom of a blind hole. A straight fluted reamer is the general-purpose type and does not clear chips in either direction, so it is not the specific choice for blind holes.

Answer: C

A rasp cut file is commonly half round.

A rasp cut has individual, sharp, pointed teeth raised one by one rather than continuous rows. It removes material fast but leaves a rough surface, so it is used on soft materials such as wood, leather, lead and aluminium. The half round shape lets one file work both flat surfaces and concave curves, which is why the rasp is usually made in that shape.

Triangular, flat and round describe other file shapes, normally made with single or double cut teeth for metal rather than rasp teeth.

Answer: D

The blade is fine, with a wave set.

The blade is 300 mm long (the paper prints 300 m). Its pitch is

\[ \frac{300\ \text{mm}}{375\ \text{teeth}} = 0.8\ \text{mm} \]

which is about 32 teeth per 25 mm, the fine grade, used for thin sheet and tube.

Fine blades have a wave set: the teeth are bent left and right in groups that form a wave, because the teeth are too small to set individually. A staggered set, with alternate teeth bent to each side, is used where the teeth are large enough to set individually, on the coarser pitches; a medium blade has a coarser pitch than 0.8 mm.

Answer: D

The narrow, thin part that fits into the handle is the tang.

The tang is the pointed end of a file that is driven into the wooden or plastic handle. It is left soft, not hardened, so that it will not snap when the handle is fitted.

The tip or point is the opposite end of the file, away from the handle. The edge is the side of the file, which may be cut or left uncut as a 'safe edge'. Neither connects to the handle.

Answer: B

The three taps differ in their taper lead (the paper prints 'Tape lead').

A hand tap set has the same thread size, pitch and thread form on all three taps. They differ only in how many threads at the front are ground away, or chamfered. The first (taper) tap has a long chamfer of about 8 to 10 threads so it starts easily and cuts gradually; the second (intermediate) tap has a shorter chamfer; the third (plug or bottoming) tap has only one or two chamfered threads, to cut full threads close to the bottom of a blind hole.

Since all three must produce the same thread, they cannot differ in size, pitch or type of thread.