GearGear

Asas GearAsas Gear

Jenis-jenis Gear

Spur gearsSpur gears have teeth that are straight and arranged parallel to the axis of the shaft that carries the gear. The curved shape of the faces of the spur gear teeth has a special geometry called an involute curve. This shape makes it possible for two gears to operate together with smooth, positive transmission of power. The shafts carrying gears are parallel.

Helical gearsThe teeth on helical gears are inclined at an angle with the axis, that angle being called the helix angle. If the gear were very wide, it would appear that the teeth wind around the gear blank in a continuous, helical path. However, practical considerations limit the width of the gears so that the teeth normally appear to be merely inclined with respect to the axis of the shaft.

Straight Bevel Gearing Design

Bevel gears are used to transfer motion between nonparallel shafts, usually at to one another. The teeth of straight bevel gears are straight and lie along an element of the conical surface. Lines along the face of the teeth through the pitch circle meet at the apex of the pitch cone. The centerlines of both the pinion and the gear also meet at this apex. In the standard configuration, the teeth are tapered toward the center of the cone. Refer the graphic help “straddle mounted gears” to see this geometry.

Key dimensions are specified either at the outer end of the teeth or at the mean, mid-face position. Note that sum of the pitch cone angles for the pinion and the gear is . Also, for the pair of bevel gears having a ratio of unity, each has a pitch cone angle of . The gearing such that, called miter gearing, is used simply to change the direction of the shafts in a machine drive without affecting then speed of rotation.

Many more features need to specified before the gears can be produced. Furthermore, many successful, commercially available gears are made in some nonstandard form. For example, the addendum of the pinion is often made longer than that of the gear. Some manufacturers modify the slope of the root of the teeth to produce a uniform depth, rather than using the standard, tapered form.

Wormgearing Design

Wormgearing is used to transmit motion and power between nonintersecting shafts, usually at 90° to each other. The drive consists of a worm on the high-speed shaft which has the general appearance of a power screw thread: a cylindrical, helical thread. The worm drives a wormgear, which has an appearance similar to that of a helical gear. Sometimes the wormgear is referred to as a worm wheel or simply a wheel or gear.

Several variations of the geometry of wormgear drives are available. The most common one employs a cylindrical worm mating with a wormgear having teeth that are throated, wrapping partially around the worm. This is called a single-enveloping type of wormgear drive. The contact between the threads of the worm and wormgear teeth is along a line, and the power transmission capacity is quite good. Many manufacturers offer this type of wormgear set as a stocked item. Installation of the worm is relatively easy because axial alignment is not very critical. However, the wormgear must be carefully aligned radially in order to achieve the benefit of the enveloping action.A simpler form of wormgear drive allows a special cylindrical worm to be used with a standard spur gear or helical gear. Neither the worm nor the gear must be aligned with great accuracy, and the center distance is not critical. However, the contact between the worm threads and the wormgear teeth is theoretically a point, drastically reducing the power transmission capacity of the set. Thus, this type is used mostly for nonprecision positioning applications at low speeds and low power levels.Worms can have a single thread, as in a typical screw, or multiple threads, usually 2 or 4 but sometimes 3, 5, 6, 8, or more. It is common to refer to the number of threads as and then to treat that number as if it were the number of teeth in the worm. The number оf threads in the worm is frequently referred to as the number of starts; this is convenient because if you look at the end of a worm, you can count the number of threads that start at the end and wind down the cylindrical worm.

NOMENCLATURE OF GEAR

Pitch circle is a theorical circle upon which all calculations are usually based; its diameter is the pitch diameter.

Circular pitch p is the distance, measured on the pitch circle, from a point on one tooth to a corresponding point on an adjacent tooth.

Module m is the ratio of the pitch diameter to the number of teeth.

Addendum a is the radial distance between top land and the pitch circle.

Dedendum b is the radial distance between bottom land to the pitch circle.

Dimana m = module, mm

d = pitch diameter, mm

p = circular pitch

N = bilangan gigi gear

P = diametral pitch

a = addendum

b = dedendum

c = gear clearance

t = tooth thicknes

22

25.1

1

1

mpt

abc

mb

mam

P

mN

dp

N

dm

The pitch of two mating gear in mesh must be identical,

Therefore p

p

g

g

N

d

N

dp

Gear TrainsGear Trains► The basic law of gearing states that as the gears rotate, the common normal The basic law of gearing states that as the gears rotate, the common normal

at the point of contact between the teeth must always pass through a fixed at the point of contact between the teeth must always pass through a fixed point on the line of centers. Therefore,when two gears are in mesh, their pitch point on the line of centers. Therefore,when two gears are in mesh, their pitch circles roll on one another whitout slipping. Then the pitch-line velocity V iscircles roll on one another whitout slipping. Then the pitch-line velocity V is

pinion

gear

g

p

g

p

p

g

p

gr

ggpp

N

N

d

d

n

nv

rrV

Dimana

V = velocity

vr = speed or velocity ratio

= angular velocity, rad/s

n = speed, rpm

N = number of teeth

d = pitch circle diameter

velocity ratio vr is defined as the ratio of the rotational speed of the input gear(pinion) to that of the output gear(gear) for a single pair of gears

Considering a pinion 2 driving a gear 3, the speed of Considering a pinion 2 driving a gear 3, the speed of gear 3 isgear 3 is

23

22

3

23 n

d

dn

N

Nn

pinion

gear

n2

n3

N2 N3

This equation applies to any gear set no This equation applies to any gear set no matter the gears are spur, helical, bevel or matter the gears are spur, helical, bevel or worm. The absolute-value signs are used to worm. The absolute-value signs are used to permit complete freedom in choosing permit complete freedom in choosing positive or negative direction. Normally for positive or negative direction. Normally for spur and helical gears, the direction are spur and helical gears, the direction are positive for counterclock-wise rotation. positive for counterclock-wise rotation.

For the gear train shown on the left, the speed of gear 6 is

26

5

4

3

3

26 n

N

N

N

N

N

Nn

Gear Gear TrainTrain

Notice that the gears 2, 3, and 5 are driver while 3, 4, and 6 are driven. Also notise that the tooth numbers for gear 3 cancel out, thus gear 3 is an idler. It affect only the direction of rotation.

Train ValueTrain Value

When more than two gears are in mesh(refer to previous slide for diagram on When more than two gears are in mesh(refer to previous slide for diagram on gear train), the term train value e refers to the ratio of the input speed (for the gear train), the term train value e refers to the ratio of the input speed (for the first gear in the train) to the output speed (for the last gear in the train). first gear in the train) to the output speed (for the last gear in the train).

By definition the train value is the product of the values of VBy definition the train value is the product of the values of Vrr for each gear pair for each gear pair in the train. A gear pair is any set of two gears with a driver and driven gear.in the train. A gear pair is any set of two gears with a driver and driven gear.

Since the velocity ratio is usually expressed as the ratio of the numbers of teeth Since the velocity ratio is usually expressed as the ratio of the numbers of teeth in the driving gear over the numbers of teeth in the driven gear; the train value in the driving gear over the numbers of teeth in the driven gear; the train value e can also be expressed in terms of the numbers of teeth. Therefore it is usually e can also be expressed in terms of the numbers of teeth. Therefore it is usually define train value as :define train value as :

numbersth driven too ofproduct

numbers tooth driving ofproduct e

When this equation is used for spur gear, the term positive train value refer to one in which the input and output gears rotate in the same direction, and negative if the last gear rotates in the opposite diretion.

By refering to previous slide the equation for train value is expressed as

FneN

N

N

N

N

Ne L

6

5

4

3

3

2 nor Where nL is the speed of the last gear

nF is the speed of the last gear

Force Analysis on Spur GearForce Analysis on Spur Gear

Redrawning fig b showing the resolved force in its tangential and components; we define

Wt = Ft32 as the transmitted load (the radial serves

no useful purpose)

The applied torque and transmitted load are related by

T = dWt/2 where T = Ta2 and d = d2

H = WtV or Wt = 60H(103)/dn jika n dalam rpm

Dan Wt= H(103)/dn jika n dalam rev/s

Fig. a shows a pinion mounted on a shaft a rotating at n2 and driving a gear on

shaft b rotating at n3. The reactions between mating teeth occur along the pressure line. Fig b and c, showed free-body diagram of the gears. Fa2 and Ta2 are the force and torque exerted by shaft a against pinion b. F32 is the force exerted by gear 3 against the pinion.

Example 13-5 Pinion 2 in fig run at 30 rev/s and transmits 2.5kW to gear 3. The teeth are cut on the 200 full-depth and have a module m= 2.5mm. Compute the circular pitch, the center distance and the radii of base circles. Draw a free-body diagram of gear 3 and show all the forces which act upon it.Solution

p = m = 2.5mm

c =(dp + dg)/ 2

dp = Npm = 20 x 2.5 = 50mm

dg = Ngm = 50 x 2.5 =125mm

c = (50 +125)/2 = 87.5mm

rb = rp cos cosmm

Wt = H(103)/dn = 2.5(103)/(50)(30) = 0.531kN

Planetary Gear TrainPlanetary Gear Train