Gears

Gears There is probably no application of the basic machine

that is used so much in our modern mechanical age as the gear, or toothed wheel.

We use it in clocks and watches, motor cars and aircraft and in just about every type of mechanical device.

Gears A gear is a component within a transmission device

that transmits rotational force to another gear or device.

A gear is different from a pulley in that a gear is a round wheel that has linkages ("teeth" or "cogs") that mesh with other gear teeth, allowing force to be fully transferred without slippage.

Depending on their construction and arrangement, geared devices can transmit forces at different speeds, torques, or in a different direction, from the power source.

Gear FundamentalsGears may be used: to gain mechanical advantage. to change the direction of movement. to transfer rotational movement from one gear to

another. They are required to complete these actions smoothly

and positively with no slippage. The gear that causes the motion is called the driver gear. The gear to which the motion is transferred is called the driven gear.

Torque could be transmitted by pressing two smooth wheels together, but friction between the wheels would be sufficient to prevent slip when a high driving torque is applied.

Information Technology Services Slide 3

Gear Fundamentals To obtain a positive drive, teeth are cut on the surface

to form gears. The teeth are formed above and below the curved surface of the smooth wheels so that the gears would have the same movement ratio * as the wheels.


Gear Type There are numerous gear types used in all types of

machinery, the most common being: Spur gears, Helical gears, Double helical (Herringbone) gears, Straight bevel gears, Spiral bevel gears, Hypoid gears

Crossed helical gears, Worm gears, Rack and pinion gears, Sector gears, Planetary or epicyclic

gears, Differential gears.


Spur Gear A spur gear is a cylinder, wheel or disc on the surface

of which are cut parallel teeth, each in a common plane with the axis.


Spur Gear Spur gears are most commonly used in engine and

machinery applications working under ordinary conditions, at moderate speeds and with medium pressures exerted upon the teeth.

If the meshing gears have external teeth, they will rotate in opposite directions.


Spur Gear If the gears are required to rotate in the same

direction, one of the gears can have internal teeth.

Note: Gear speed ratio is not affected by the direction of rotation.

Spur gears are relatively easy to manufacture, but can be noisy in operation.


Helical Gear To reduce the noise and stress in the gears, helical

gears are introduced. The helical gear resembles the spur gear in that the

teeth are cut on a cylindrical body. However, it differs from the spur gear in that the teeth

are spiralled around the body rather than formed parallel to the axis of the gear body. Spiral teeth provide smoothness of operation.


Helical Gear The inclination of the helical teeth produces an axial or

end thrust on each gear tending to separate them axially. These end thrusts need to be resisted by suitable thrust bearings. Helical gears carry greater loads at higher speed than equivalent size spur gears.

Their properties of strength and quietness are attributed to the fact that the teeth engage gradually, and more teeth are in mesh at the same time.


Double Helical (HERRINGBONE) Gear

This system resembles helical gears, having reversed directions of spiral, placed side by side so that the teeth come together to form a chevron pattern.

In general, herringbone gears are used with parallel shafts.

The end thrust is neutralized in this system as the thrust from one half of a tooth is counteracted by that from the other half.


Crossed Helical Gears Crossed helical gears, also known as 'skew gears' or

'spiral gears', are used between non-intersecting shafts. They have a sliding action as well as a gear tooth action.

They can provide a wider variety of speed ratios than can other gears, but can only carry light loads.


Bevel gears Bevel gears are useful when the direction of a shaft's

rotation needs to be changed. They are usually mounted on shafts that are 90apart,

but can be designed to work at other angles as well. The teeth on bevel gears can be straight, spiral or

hypoid.


Straight Bevel Gear When the axes of shafts intersect, bevel gearing is

used to connect them. The teeth of the straight bevel gear are cut on an

angular surface, similar to a truncated cone shape. The intersecting centre lines of these gear shafts is

usually a full 90angle. With straight toothed bevel gears, the forces between

the teeth in contact tend to separate the gears both radially and axially, hence, thrust bearings must be fitted behind each gear.


Spiral Bevel Gear This gear, is also adaptable to non-parallel shafting. When spiral teeth are used, the axial forces on the

gears may tend to separate them or to cause them to mesh more deeply; it depends upon the angle of the spiral, whether the spiral is right or left handed and upon the direction of rotation.

With spiral bevel gears, it is usual to fit double thrust bearings.


Spiral Bevel Gear The curved teeth of spiral bevel gears: provide quieter and smoother operation, and enable the gear to carry greater loads than equivalent

size spur gears or straight bevel gears.


Hypoid Gears These gears are similar to spiral bevel gears, except

their shaft axes are not in the same plane, and therefore do not intersect.

They are smoother and quieter than spiral bevel gears. They provide greater strength for a given size and

speed ratio.


Hypoid Gears By raising or lowering the axis of the pinion gear

relative to the axis of the hypoid or crown gear, the tooth pitch of the pinion gear can be increased without changing the gear ratio.

It is therefore possible to make the pinion larger (and stronger) than that of a spiral bevel gear system having the same gear ratio and crown wheel size.

There is a sliding action in the direction of the length of the teeth of hypoid gears that is absent in bevel gearing and this makes lubrication of the teeth a more difficult matter.


Worm Gear This gear set comprises a worm wheel (or gear) and a

worm.

The worm may be considered as part of a screw having a number of 'threads'.

If the wheel is considered to represent a nut it will be seen that if the worm is prevented from moving in an axial direction and is rotated, the worm wheel must revolve also.

This type is known as 'parallel' worm gearing, the worm being a parallel screw.


Worm Gear The worm is normally the driver and the action of the

worm gear is quite similar to the action of a screw or a nut.

The worm wheel, which resembles a helical gear, is throated or curved on the face to partially envelop the worm.


Worm Gear Due to the wedge like action of the worm thread on the

gear tooth, it is relatively easy to obtain quiet operation with this type of gearing, but, efficiency is not as good as the bevel system (94% compared to 98% of the bevel system).

The worm gear system provides a very wide range of speed reductions.

They carry high loads and are quiet and smooth in operation. At speed ratios greater than about 20:1 worm gears cannot be back driven, that is, the gear wheel cannot drive the worm.

The worm may have one or more threads, each considered a tooth.


Rack and Pinion Gear This is a specialized form of spur gear where the spur

meshes with gear teeth on a flat rack. The function of this device is to convert the rotary

motion of the spur gear into linear or reciprocating motion at the rack assembly.

This is a common steering system employed by light car manufacturers.


23

vehicle steering system EXPLANATION: The

rack and pinion gear system allows rotary motion of the steering wheel to be converted to linear motion. As the steering wheel is turned, the pinion gear also turns, driving the rack in the right or left direction, pointing the wheels in the desired direction.

Sector Gear A sector gear and pinion system is used where a

relatively small movement is required, eg. a sector of a circle rather than the full circumference.

The sector gear may be part of an actuating arm which when moved meshes with a pinion gear to cause rotary motion of the pinion gear.

This is commonly used in mechanical type instruments to convert reciprocal motion to rotary motion.


Differential GearsDifferential gears link two shafts with a covering, forcing the total of the rotational angles of the shafts to be the same as the rotational angles of the covering. Arrangement of the system is done in such a way that one axle turns faster than the other.

Planetary (EPICYCLIC) Gears Just as planets rotate about the sun, the planetary

gear system comprises of 'planetary' gears which revolve about a 'sun' gear.

The planetary gear system is ideal for use where large amounts of power must be handled in a reduction gear system.

Typical applications are: propeller drive reductions in radial piston engines and

turbo-propeller engines, and helicopter rotor systems. One advantage of the planetary gearing system is that

the centre of propeller thrust and the engine drive are 'in line' ie. concentric.



Planetary (EPICYCLIC) Gears There are a number of planetary gear systems.


Planetary (EPICYCLIC) Gears Planetary gears consist of: a fixed gear, a rotating driving gear, a spider assembly, and two or more 'planet gears' meshed between them. The planet gears are mounted on a 'spider' and can

rotate on their own axes. The spider can also rotate on their axes. The spider can also rotate on its axis. (Alternative terms for some of the gears are given in brackets). The planet gears are so-called because they move around the inner (sun) gear, rather like the planets around the sun.


Planetary (EPICYCLIC) Gears


Gear Trains One of the wheels is always connected to a power

source such as a motor and this is referred to as the DRIVER

The one which is connected to the driver, either by a belt or teeth is called the DRIVEN.

31 32

Idler gear The idler gear is used so that the rotation of the two

important gears is the same direction. It does not have any effect other than to change the

direction of motion.

33

Compound Gears Compound gears are used in engines, workshop

machines and in many other mechanical devices.

Compound gear train.

Gear Geometry


Basic spur gear geometry.

Gear Tooth Nomenclature

35

Gear terminology Gear or wheel: The larger of two interacting gears. Pinion: The smaller gear in a pair. Path of contact: The path followed by the point of

contact between two meshing gear teeth.


Gear terminology Circular pitch (Pc): The distance measured along

the circumference of the pitch circle from a point on one tooth to a corresponding point on the adjacent tooth. It will be equal to the pitch circle circumference divided by number of teeth on the wheel.


pitchcircular P teethofnumber T

circlepitch ofdiameter D

C =

=

=

=

TDPC

pi

Gear terminology Pitch circle diameter: The diameter of a circle which

by pure rolling action would produce the same motion as the toothed gear wheel. It is also known as the pitch diameter.

Pitch Point: the point of contact of two pitch circles of mating gears.

The diameteral pitch (Pd): the number of teeth per unit length of the pitch circle diameter.

pitch diametral P teethofnumber T

circlepitch ofdiameter D

d =

=

=

=

DTPd

Gear terminology Module (m). The module of a gear is equal to the

pitch diameter divided by the number of teeth.


pitch diameteral theof reciprocal theis Module teethofnumber T

circlepitch ofdiameter Dmeterin Module

=

=

=

=

m

TD

m

Gear terminology Base circle: An imaginary circle used in involute

gearing to generate the involutes that form the tooth profiles.


Gear terminology Addendum : The radial distance from the pitch

surface to the outermost point of the tooth. Its value is normally one module and usually denoted by a.

Dedendum : The radial distance from the depth of the tooth trough to the pitch surface. Its value is generally 1.157 module or (/20) module.

Gear terminology Line of action, also called 'Pressure line'. The line

along which the force between two meshing gear teeth is directed. It has the same direction as the force vector. In general, the line of action changes from moment to moment during the period of engagement of a pair of teeth. For involute gears, however, the tooth-to-tooth force is always directed along the same line -- that is, the line of action is constant. this implies that for involute gears the path of contact is also a straight line, coincident with the line of action -- as is indeed the case.


Gear terminology Pressure angle (). The complement of the angle

between the direction that the teeth exert force on each other, and the line joining the centres of the two gears. For involute gears, the teeth always exert force along the line of action, which, for involute gears, is a straight line; and thus, for involute gears, the pressure angle is constant.


Gear Meshing

Involute Profile On an involute profile gear tooth, the contact point

starts closer to one gear, and as the gear spins, the contact point moves away from that gear and toward the other.

If you were to follow the contact point, it would describe a straight line that starts near one gear and ends up near the other.

This means that the radius of the contact point gets larger as the teeth engage.

Involute Profile

Interference in Involute Gears In general, the phenomenon, when the tip of tooth

undercuts the root on its mating gear is known as interference.

Height of the teeth may be reduced. Under cut of the radial flank of the pinion. Centre distance may be increased. It leads to

increase in pressure angle. By these tooth correction, the pressure angle, centre

distance and base circles remain unchanged, but tooth thickness of gear will be greater than the pinion tooth thickness.

Methods to avoid Interference

Backlash is the error in motion that occurs when gears change direction. The term "backlash" can also be used to refer to the size of the gap, not just the phenomenon it causes; thus, one could speak of a pair of gears as having, for example, "0.1 mm of backlash."

Backlash

A pair of gears could be designed to have zero backlash, but this would presuppose perfection in manufacturing, uniform thermal expansion characteristics throughout the system, and no lubricant.

In the case of a large gear and a small pinion, however, the backlash is usually taken entirely off the gear and the pinion is given full sized teeth.

Backlash

Backlash can also be provided by moving the gears farther apart. For situations, such as instrumentation and control, where precision is important, backlash can be minimized through one of several techniques.

Therefore, gear pairs are designed to have some backlash. It is usually provided by reducing the tooth thickness of each gear by half the desired gap distance.

Gear Ratio The ratio of the number of teeth on the gear to that on

the pinion is known as gear ratio.

ratiogear GR andpinion on the teeth ofnumber t

gear on the teeth ofnumber twhere

p

g

=

=

=

=

p

g

t

tGR

Velocity Ratio The ratio of the angular velocity of the follower to the

angular velocity of the driving gear is known as the velocity ratio.

( )

====

===

===

=

=

2

1

2

1

2

2

1

1

2

1

1

2

2

12211

2

1

22122

1

1

2

DD

and

DD

and DD

2 and 2

driver oflocity Angular vefollower oflocity Angular ve

t

t

t

Dt

DPt

t

NNNDND

NNNN

VR

Cpipi

pipi

pipi

Sign Usage When calculating angular velocities in gear trains we use

+/ sign to indicate direction of rotation

Example:assume + cw ccw

(clockwise) (counter clockwise)

rpm 1001 +=1

2

12 t

t=

201 =t

402 =t

rpm 50

1004020

2

=

=

Direction of rotation is reversed in this gear train

counter clockwise (ccw)

?2 =

Gears

Documents

Transcript of Gears