gear technology - basic gear types

I believe almost every machinist or engineer had dealt with gears. Gear are of the workhorses of motion control systems. They can turn RPMs into muscle for a conveyor belt moving heavy boxes or convert the torque of a wind turbine into sufficient speed to drive a generator. They can completely change the direction of motion. The technology is powerful, with sufficient options to satisfy virtually every occasion - when used properly, that is. There's so much types of gear, and each have its own advantages as well as disadvantages. Let's take a look at the basic types,  the one that is used as basic for another gear-arrangements or design modification

Gear is a mechanical device that transfers power from one element to another in a system. We define the gear ratio G for two gears as the ratio of their diameters, D1 and D2

G = D2/D1

If we attach a motor producing torque t1 at speed w1, our output torque t2 and angular velocity w2 are given by:

t2 = tiG

w2 = wi /G

In other words, a gear box with a reduction ratio of greater than one yields increased output torque and decreased speed. We can class the gears themselves by the characteristics of the teeth.

SPUR GEAR
A spur gear features teeth that are parallel to the axis of rotation of the gear and tend to produce rolling motion rather than sliding motion (see figure 1). This type of gear is economical and can provide a lot of power. The surface area in contact on meshing teeth is limited, however, which can lead to faster wear. When the teeth of spur gears mesh, they slip into place all at once over the length of the tooth. Depending on how the gear is used, this can cause some unevenness of motion. It can also cause backlash, in which is essentially the delay between motion of the input shaft and motion of the output that occurs during reversals of motion. Backlash is caused by the space between the teeth on two meshing gears when contact is re-established.
When we have an extra larger gear, we can hob the gear hub, placed the pinion inside, and that is called a ring gear. In case you need to change rotational into linear movement, there comes the rack gear, a plain long rectangular profile, machined with gear profile on it's length

HELICAL GEAR
A helical gear features teeth that are slanted with respect to the axis of rotation (see figure 2). The gradual meshing of the teeth provided by the angled design yields smoother motion. The greater amount of surface area in contact at all times also increases lifetime compared to basic spur gears, less noise and can reduce backlash. With a spur gear, we always have 1:1 tooth contact, but with a helical, we can get about 1:1.5. Basically that means about 10-15% more torque to transmit. However, the machining would be more complex, and surely higher price

Quite commonly helical gears are used with the helix angle of one having the negative of the helix angle of the other; such a pair might also be referred to as having a right-handed helix and a left-handed helix of equal angles. The two equal but opposite angles add to zero: the angle between shafts is zero – that is, the shafts are parallel. Where the sum or the difference (as described in the equations above) is not zero the shafts are crossed. For shafts crossed at right angles the helix angles are of the same hand because they must add to 90 degrees.
There are another disadvantage, with a slanted working surface, there will be an axial force involved. The axial force should be countered with an axial bearing in the shaft's end. there are also helical gear arrangement called herringbone gear which mates two helical, (one Left Handed and one Right Handed) back to back as to counter the axial force.

BEVEL GEAR
A bevel gear is shaped like a right circular cone with most of its tip cut off.
When two bevel gears mesh their imaginary vertices must occupy the same point. Their shaft axes also intersect at this point, forming arbitrary non-straight angle between shafts. The angle can be anything except zero or 180 degrees (see figure 3).
The teeth of a bevel gear may be straight-cut as with spur gears, or they may be cut in a variety of other shapes. Spiral bevel gear teeth are curved along the tooth's length and set at an angle, analogously to the way helical gear teeth are set at an angle compared to spur gear teeth. Zerol bevel gear have teeth which are curved along their length, but not angled. Spiral bevel gears have the same advantages and disadvantages relative to their straight-cut cousins as helical gears do to spur gears. Straight bevel gears are generally used only at speeds below 5 m/s (1000 ft/min), or, for small gears, 1000 r.p.m. An arrangement of which number of teeth are equal and the shaft axes made 90 degrees are called miter gear

WORM GEAR
A worm gear has the teeth spiraled around in a cylinder like screw threads (see figure 4)
Worm-and-gear sets are a simple and compact way to achieve a high torque, low speed gear ratio
In a worm-and-gear set, the worm can always drive the gear. However, if the gear attempts to drive the worm, it may or may not succeed. Particularly if the lead angle is small, the gear's teeth may simply lock against the worm's teeth, because the force component circumferential to the worm is not sufficient to overcome friction. Worm-and-gear sets that do lock are called self locking, which can be used to advantage, as for instance when it is desired to set the position of a mechanism by turning the worm and then have the mechanism hold that position
If the gear in a worm-and-gear set is an ordinary helical gear only a single point of contact will be achieved. If medium to high power transmission is desired, the tooth shape of the gear is modified to achieve more intimate contact by making both gears partially envelop each other. This is done by making both concave and joining them at a saddle point; this is called a double enveloping worm gear