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Metallurgical Engineering

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Gears

The slip and creep in the belt or rope drives is a common phenomenon, in the transmission of motion or power between two shafts. The effect of slip is to reduce the velocity ratio of the drive. In precision machine, in which a definite velocity ratio is importance (as in watch mechanism, special purpose machines...etc), the only positive drives by means of gears or toothed wheels.

Friction Wheels:

Kinematiclly, the motion and power transmitted by gears is equivalent to that transmitted by friction wheels or discs in contact with sufficient friction between them. In order to understand motion transmitted by two toothed wheels, let us consider the two discs placed together as shown in the figure 4.1.When one of the discs is rotated, the other disc will be rotate as long as the tangential force exerted by the driving disc does not exceed the maximum frictional resistance between the two discs. But when the tangential force exceeds the frictional resistance, slipping will take place between the two discs. Thus the friction drive is not positive a drive, beyond certain limit. Gears are machine elements that transmit motion by means of successively engaging teeth. The gear teeth act like small levers. Gears are highly efficient (nearly 95%) due to primarily rolling contact between the teeth, thus the motion transmitted is considered as positive. Gears essentially allow positive engagement between teeth so high forces can be transmitted while still undergoing essentially rolling contact. Gears do not depend on friction and do best when friction is minimized.

Classification of Gears

a. Spur Gears

General: Spur gears are the most commonly used gear type. They are characterized by teeth which are perpendicular to the face of the gear. Spur gears are by far the most commonly available, and are generally the least expensive. The basic descriptive geometry for a spur gear is shown in the figure below.

Limitations: Spur gears generally cannot be used when a direction change between the two shafts is required.

Advantages: Spur gears are easy to find, inexpensive, and efficient.

b. Helical Gears

General: Helical gears are similar to the spur gear except that the teeth are at an angle to the shaft, rather than parallel to it as in a spur gear. (See the references for more specific information). The resulting teeth are longer than the teeth on a spur gear of equivalent pitch diameter.

The longer teeth cause helical gears to have the following differences from spur gears of the same size:

i. Tooth strength is greater because the teeth are longer,

ii. Greater surface contact on the teeth allows a helical gear to carry more load than a spur gear

iii. The longer surface of contact reduces the efficiency of a helical gear relative to a spur gear

Helical gears may be used to mesh two shafts that are not parallel, although they are still primarily use in parallel shaft applications. A special application in which helical gears are used is a crossed gear mesh, in which the two shafts are perpendicular to each other:

The basic descriptive geometry for a helical gear is essentially the same as that of the spur gear, except that the helix angle must be added as a parameter.

Limitations: Helical gears have the major disadvantage that they are expensive and much more difficult to find (at least insofar as an ME3110 student is concerned). Helical gears are also slightly less efficient than a spur gear of the same size (see above).

Advantages: Helical gears can be used on non parallel and even perpendicular shafts, and can carry higher loads than can spur gears.

c. Bevel Gears

General: Bevel gears are primarily used to transfer power between intersecting shafts. The teeth of these gears are formed on a conical surface. Standard bevel gears have teeth which are cut straight and are all parallel to the line pointing the apex of the cone on which the teeth are based. Spiral bevel gears are also available which have teeth that form arcs. Hypocycloid bevel gears are a special type of spiral gear that will allow nonintersecting, non-parallel shafts to mesh. Straight tool bevel gears are generally considered the best choice for systems with speeds lower than 1000 feet per minute: they commonly become noisy above this point.

One of the most common applications of bevel gears is the bevel gear differential,

Limitations:

i. Limited availability.

ii. Cannot be used for parallel shafts.

iii. Can become noisy at high speeds.

Advantages: Excellent choice for intersecting shaft systems.

d. Worm Gears

General: Worm gears are special gears that resemble screws, and can be used to drive spur gears or helical gears.

Worm gears, like helical gears, allow two non-intersecting 'skew' shafts to mesh. Normally, the two shafts are at right angles to each other. A worm gear is equivalent to a V-type screw thread. Another way of looking at a worm gear is that it is a helical gear with a very high helix angle.

Worm gears are normally used when a high gear ratio is desired, or again when the shafts are perpendicular to each other. One very important feature of worm gear meshes that is often of use is their irreversibility: when a worm gear is turned, the meshing spur gear will turn, but turning the spur gear will not turn the worm gear. The resulting mesh is 'self locking', and is useful in racketing mechanisms.

Limitations: Low efficiency. The worm drives the drive gear primarily with slipping motion, thus there are high friction losses.

Advantages: Will tolerate large loads and high speed ratios. Meshes are self locking (which can be either an advantage or a disadvantage).

e. Racks (straight gears)

General: Racks are straight gears that are used to convert rotational motion to translational motion by means of a gear mesh. (They are in theory a gear with an infinite pitch diameter). In theory, the torque and angular velocity of the pinion gear are related to the Force and the velocity of the rack by the radius of the pinion gear, as is shown below:

Perhaps the most well-known application of a rack is the rack and pinion steering system used on many cars in the past.

Limitations:

i. Limited usefulness.

ii. Difficult to find.

Advantages: The only gearing component that converts rotational motion to translational motion. Efficiently transmits power. Generally offers better precision than other conversion methods;