Gears and Gear Trains Questions and Answers

Answer: A

The figure shows worm gears: a worm, which is a screw-like shaft with helical threads, drives a toothed wheel (the worm wheel) set at right angles to it, with the axes not intersecting. This gives a large speed reduction in one stage. Herringbone gears are double helical gears with teeth in a V shape on parallel shafts. Helical gears have angled teeth but run on parallel shafts, and spur gears have straight teeth parallel to the axis. None of these has the screw-shaped shaft shown here.

Answer: C

Gear D turns at 375 rpm clockwise.

With the arm fixed, every gear turns about a fixed axis, so the train is an ordinary one.

1. A (20 teeth, 300 rpm clockwise) drives planet B externally, so B turns anticlockwise.
2. B drives the internal teeth of C (80 teeth). An internal mesh keeps the direction, so C turns anticlockwise at \(300 \times 20/80 = 75\) rpm (B's tooth count cancels).
3. The outer teeth of C (100) drive D (20) externally, reversing direction: D turns clockwise at \(75 \times 100/20 = 375\) rpm.

-375 has the right speed but the wrong sense, from missing that an internal mesh does not reverse rotation. 240 and -240 come from swapping C's two tooth counts, 100 on the inner surface and 80 on the outer.

Answer: D

The output torque is 2000 N-m.

In a frictionless train, power is conserved, so torque rises in proportion as speed falls. Each mesh multiplies the torque by the ratio of driven teeth to driving teeth:

\[ \begin{aligned} T_{\text{out}} &= 100 \times \frac{48}{12} \times \frac{60}{12} \\ &= 100 \times 4 \times 5 = 2000\ \text{N-m} \end{aligned} \]

The 48-teeth gear and the second 12-teeth gear share a shaft, so they carry the same torque, 400 N-m. 5 divides by both ratios instead of multiplying (as if torque fell with speed), and 500 and 20 use only the second stage's ratio, multiplied or divided.

Answer: B

The output speed is 900 rpm.

For helical gears the number of teeth is proportional to the pitch circle diameter times the cosine of the helix angle, because \(d = m_{n}z/\cos\psi\) with the same normal module on both gears. So the speed ratio is:

\[ \begin{aligned} \frac{N_{2}}{N_{1}} &= \frac{z_{1}}{z_{2}} = \frac{d_{1}\cos\psi_{1}}{d_{2}\cos\psi_{2}} \\ &= \frac{80\cos 30^{\circ}}{120\cos 22.5^{\circ}} = \frac{69.28}{110.87} \\ &= 0.625 \end{aligned} \]

\[ N_{2} = 0.625 \times 1440 = 900\ \text{rpm} \]

960 rpm would follow from the diameters alone (80/120), which is right only for spur gears; it is not offered, and 1200, 875 and 720 rpm do not match either ratio.

Answer: A

The idler is gear 4.

Gears 2 and 3 share one shaft, so they form a compound gear and both affect the speed ratio. Gear 4 meshes with gear 3 on one side and gear 5 on the other, and nothing else is on its shaft.

In the ratio \(\frac{N_{2}}{N_{1}}\cdot\frac{N_{4}}{N_{3}}\cdot\frac{N_{5}}{N_{4}}\) the teeth of gear 4 cancel, so it changes only the direction of rotation of gear 5, not the speed ratio. That is what defines an idler.

Gear 1 is the driver, and gears 2 and 3 are the compound pair whose tooth numbers do not cancel, so none of them is an idler.

Answer: A

Worm gears connect non-parallel and non-intersecting shafts.

The worm and wheel axes are usually at right angles and offset from each other, so they neither meet nor run parallel. This skew arrangement is what allows large speed reductions in one stage.

Intersecting shafts are connected by bevel gears, and parallel shafts by spur or helical gears. Non-parallel intersecting shafts are again the bevel-gear case, not the worm's.

Answer: B

The gears are spiral gears.

Spiral gears (crossed helical gears) connect shafts that neither intersect nor are parallel. Their teeth are helical and the shaft axes cross at an angle, often 90 degrees, with point contact between the teeth.

Bevel gears connect intersecting shafts, and mitre gears are bevel gears of equal size at right angles. Helical gears in their usual form connect parallel shafts. None of them suits non-coplanar shafts in this classification.

Answer: D

The speed ratio is inversely proportional to train value.

For a gear train, the speed ratio is the speed of the driver divided by the speed of the driven gear, and the train value is defined the other way round, the speed of the driven gear divided by the speed of the driver. So

\[ \text{train value} = \frac{1}{\text{speed ratio}} \]

The two are reciprocals, which is an inverse proportion, not a direct one. Nothing in the definitions involves a square, so both 'square' options are wrong.

Answer: C

Offset shaft axes use hypoid gears.

Hypoid gears look like spiral bevel gears, but the pinion axis is offset from the gear axis, so the shafts neither intersect nor are parallel. The classic use is the rear-axle drive of a car, where the offset lets the propeller shaft sit lower.

Mitre gears, spiral bevel gears and zerol gears are all bevel gears whose shaft axes intersect. Mitre gears are an equal pair at right angles, and zerol gears are spiral bevel gears with zero spiral angle.

Answer: A

The contact ratio is always \(\gt 1.0\).

The contact ratio is the average number of tooth pairs in contact, the length of the path of contact divided by the base pitch. It must be greater than one so that a new pair of teeth comes into contact before the previous pair separates; otherwise the drive would be interrupted and impacts would occur. Practical spur gears have values of about 1.2 to 1.8.

A ratio of exactly 1 would leave no overlap and give a jerky drive, and a ratio below 1 or zero would mean gaps with no teeth in contact at all.