Gearbox

The gearbox is an confined system that transmits mechanical energy to an output mechanism. Gearboxes can adjust their speed, torque, and other conditions to disciple the energy into a use-able format. Gearboxes are used in a range of machine, for a broad range of ambition. These machines can slow the rate of rotation to increase torque and speed.

Types of gear box.

The following will explain some of the different types of industrial gearboxes and how they are commonly used.

  • Helical gearbox
  • Coaxial helical inline
  • Bevel helical gearbox
  • Skew bevel helical gearbox
  • Worm reduction gearboxes
  • Planetary gearbox
  • Rack and Pinion Gear
  • Spur Gears

Helical gearbox

The helical gearbox is a low-power patron and is covenant in size. This machinery is used for a broad range of industrial operation, The helical gearbox is famous in the manufacture of plastics, cement, rubber, and other heavy industrial situation. It is useful in crushers, extrudes, coolers, and conveyors, which are all low-power operation.

Force out helical gearboxes are used when torsion stiffness needs to be maximized and for low-noise function. Discharge gearboxes are used in the plastics industry and in machines that require high mechanical power.

Herringbone gear or Double helical gear

A herringbone gear, a specific type of double helical gear,is a special type of gear that is a side to side (not face to face) sequence of two helical gears of antithesis hands.From the top, each helical groove of this gear looks like the letter V, and many together form a herringbone pattern (resembling the bones of a fish such as a herring).

Coaxial helical inline

The coaxial helical gearbox is ideal for heavy-duty applications. Coaxial helical inline are noted for their quality and efficiency. These are manufactured with a high degree of specification, which allows you to maximize load and transmission ratios. The drive shaft and the driven shaft are on the same rotation axis. Coaxial gearboxes are usually in the design of spur gears. Spur gears come in different interpretation.

Bevel helical gearbox

The critical feature of this type of gearbox is a curved set of teeth located on the cone-shaped surface close to the rim of the unit. The bevel helical gearbox is used to provide rotary motions between non-parallel shafts. These are typically used in quarries, in the mining industry, and in conveyors.

Skew bevel helical gearbox

The skew bevel helical gearbox is notable for its rigid and monolithic structure, which makes it usable in heavy loads and other applications. These industrial gearboxes offer mechanical advantages once they are mounted on the correct motor shaft output. These are highly customization based on the number of teeth and gears. Therefore, you can usually find one suitable for your needs.

Worm reduction gearboxes

Worm reduction gearboxes are used to drive heavy duty operations. Worm gearboxes are used when there is a need for increased speed reduction between non-intersecting crossed axis shafts. This type of industrial gearbox uses a worm wheel that has a large diameter. The worm, or screw, meshes with the teeth on the peripheral area of the gearbox. The rotating motion of the worm causes the wheel to move similarly due to the screw-like movement. Most of these industrial gearboxes are used in heavy industries such as fertilizers, chemicals, and minerals.

Planetary gearbox

The planetary gearbox is ideal for its endurance, accuracy, and distinct functionality and is notable for its precision applications. This type of gearbox increase the lifespan of your equipment and optimizes performance. Planetary gearboxes come in either a solid type of hollow format or with a variety of mounting options including a flange, shaft, or foot.

Why is it named a planetary gearbox?

The planetary gearbox got its name because of how the different gears move together. In a planetary gearbox we see a sun (solar) gear, satellite (ring) gear and two or more planet gears. Normally, the sun-gear is driven and thus move the planet gears locked in the planet carrier and form the output shaft. The satellite gears have a fixed position in relation to the outside world. This looks similar to our planetary solar system and that is where the name comes from. What helped was that ancient gear constructions were used extensively in astrology for mapping and following our celestial bodies.

 speed automatic transmission gearbox

Where is the planetary gearbox usually used (in the transmission):

  • In a robot to increase the torque
  • In a printing press to reduce the speed of the rollers
  • For precise positioning
  • In a packaging machine for a reproducible products
  • BMW 8-Gang Automatic

Planetary gear ratio calculations

A question that I often get is how to work out planetary gears using the gear template generator

Working out the tooth counts for planetary gears is actually not that complicated, so I initially neglected to mention how to do it. But having received the question a number of times, I’ll elaborate.
For convenience, let’s denote R, S, and P as the number of teeth on the gears.

R Number of teeth in ring gear
S Number of teeth in sun (middle) gear
P Number of teeth in planet gears
The first constraint for a planetary gear to work out is that all teeth have the same pitch, or tooth spacing. This ensures that the teeth mesh.

The second constraint is:
R = 2 × P + S

That is to say, the number of teeth in the ring gear is equal to the number of teeth in the middle sun gear plus twice the number of teeth in the planet gears.

In the gear at left, this would be 30 = 2 × 9 + 12

This can be made more clear by imagining “gears” that just roll (no teeth), and imagine an even number of planet gears. From the illustration at left, you can see that the diameters of the sun gear, plus two planet gears be must equal to the ring gear size.
Now imagine we take out one of the green planet wheels, and rearrange the remaining ones to be evenly spaced. Still the same size gear.

Now imagine the wheels have teeth. The teeth would stick out beyond the line of the wheel as much as they indent, so that the pitch line of the gears would be the line around the gears. The geometry still works the same. If you go into the gear generator and select “show pitch diameter”, you can see how the pitch diameter is just a circle that the teeth are centered over.

The pitch diameter of a gear is just the number of teeth divided by diametrical pitch (larger values of “diametrical pitch” mean smaller teeth). The gear generator program tends to refer to tooth spacing. Pitch diameter can also be calculated as tooth spacing * number of teeth / (2π), where 2π = 6.283

Here’s another planetary gear set. The middle arrangement is removed and here it is inserted.
In this case, the planet gears have 12 teeth, the sun gear has 18 and the ring gear has 42 teeth

So, applying

R = 2×P + S

We get

42 = 2 × 12 + 18

These pictures are part of a fascinatingly complicated planetary gear drive by Ronald Walters.

Here’s another cool arrangement of gears, though not really a “planetary” gear set.
If you place a gear inside another gear, with the internal gear having a tooth count of half the ring gear’s tooth count, any point on the pitch diameter of the inside gear will move back and forth in a straight line.

The brass rod in this photo will move strictly left to right in the slot, while the gear it is attached to rolls around inside the ring gear. That gear is actually attached to a crank which keeps it rolling around the edge, although only the center part of that crank is visible, so it doesn’t really look like a crank in the photo.

Rack and Pinion Gear.

A rack and pinion is a type of linear actuator that comprises a pair of gears which convert rotational motion into linear motion. A circular gear called “the pinion” engages teeth on a linear “gear” bar called “the rack”; rotational motion applied to the pinion causes the rack to move relative to the pinion, thereby translating the rotational motion of the pinion into linear motion.

For example, in a rack railway, the rotation of a pinion mounted on a locomotive or a rail car engages a rack between the rails and forces a train up a steep slope.

For every pair of conjugate in volute profile, there is a basic rack. This basic rack is the profile of the conjugate gear of infinite pitch radius (i.e. a toothed straight edge).

A generating rack is a rack outline used to indicate tooth details and dimensions for the design of a generating tool, such as a hob or a gear shape cutter.

CALCULATION OF GEAR DIMENSIONS

Gear dimensions are determined in accordance with their specifications, such as Module (m), Number of teeth (z), Pressure angle (α), and Profile shift coefficient (x). This section introduces the dimension calculations for spur gears,helical gears,gear rack,bevel gears, screw gears, and worm gear pairs. Calculations of external dimensions (eg. Tip diameter) are necessary for processing the gear blanks. Tooth dimensions such as root diameter or tooth depth are considered when gear cutting.

Spur Gears

Spur gears with locking hubs

Spur Gears are the simplest type of gear. The calculations for spur gears are also simple and they are used as the basis for the calculations for other types of gears. This section introduces calculation methods of standard spur gears, profile shifted spur gears, and linear racks. The standard spur gear is a non-profile-shifted spur gear.

Standard Spur Gearbox

The meshing of standard spur gears. The meshing of standard spur gears means the reference circles of two gears contact and roll with each other.

Fig. 4.1 The Meshing of Standard Spur Gears

The Meshing of Standard Spur Gears

Profile Shifted Spur Gear

The meshing of a pair of profile shifted gears. The key items in profile shifted gears are the operating(working) pitch diameters (dw) and the working (operating) pressure angle (αw). These values are obtainable from the modified center distance and the following formulas :

Fig. 4.2 The Meshing of Profile Shifted Gears

The Meshing of Profile Shifted Gears

( α=20°, z1=12, z2=24, x1=+0.6, x2=+0.36 )

In the meshing of profile shifted gears, it is the operating pitch circle that is in contact and roll on each other that portrays gear action.presents the calculations where the profile shift coefficient has been set at x1 and x2 at the beginning. This calculation is based on the idea that the amount of the tip and root clearance should be 0.25m.

There are several theories concerning how to distribute the sum of profile shift coefficient

(x1 + x2) into pinion (x1)and gear (x2) separately. BSS (British) and DIN (German) standards are the most often used. In the example above, the 12 tooth pinion was given sufficient correction to prevent undercut, and the residual profile shift was given to the mating gear.

(3) Rack and Spur Gear

One rotation of the spur gear will displace the rack l one circumferential length of the gear’s reference circle,per the formula :

The rack displacement, l, is not changed in any way by the profile shifting.

Fig. 4.3 (1) The meshing of standard spur gear and rack

The meshing of standard spur gear and rack

Fig. 4.3 (2) The meshing of profile shifted spur gear and rack

The meshing of profile shifted spur gear and rack

Internal Gears Box

internal gear

Internal Gears are composed of a cylindrical shaped gear having teeth inside a circular ring. Gear teeth of the internal gear mesh with the teeth space of a spur gear. Spur gears have a convex shaped tooth profile and internal gears have re-entrant shaped tooth profile; this characteristic is opposite of Internal gears. Here are the calculations for the dimensions of internal gears and their interference.

The calculation steps. It will become a standard gear calculation if x1=x2=0.

Fig.4.4 The meshing of internal gear and external gear

The meshing of internal gear and external gear

Helical Gears

helical gears

Helical gear Box such as a cylindrical gearbox in which the teeth flank are Helicon. The helix angle in reference cylinder is β, and the displacement of one rotation is the lead, pz.

The tooth profile of a helical gear is an in volute curve from an axial view, or in the plane perpendicular to the axis. The helical gear has two kinds of tooth profiles – one is based on a normal system, the other is based on a transverse system.

These transverse module mt and transverse pressure angle αt at are the basic configuration of transverse system helical gear.

In the normal system, helical gearbox can be cut by the same gear hob if module mn and pressure angle at are constant, no matter what the value of helix angle β.

It is not that simple in the transverse system. The gear hob design must be altered in accordance with the changing of helix angle β, even when the module mt and the pressure angle at are the same.

Obviously, the manufacturing of helical gears is easier with the normal system than with the transverse system in the plane perpendicular to the axis.

When meshing helical gears, they must have the same helix angle but with opposite hands.

Fig.4.7 Fundamental relationship of a helical gear (Right hand)

Fundamental relationship of a helical gear (Right-hand)

Bevel Gears

bevel gears

Bevel gears, whose pitch surfaces are cones, are used to drive intersecting axes. Bevel gears are classified according to their type of the tooth forms into Straight Bevel Gear, Spiral Bevel Gear, Zerol Bevel Gear, Skew Bevel Gear etc.The meshing of bevel gears means the pitch cone of two gears contact and roll with each other. Let z1 and z2 be pinion and gear tooth numbers; shaft angle Σ ; and reference cone angles δ1 and δ2

1.5 Screw Gears

screw gears

Screw gearing includes various types of gears used to drive non parallel and non intersecting shafts where the teeth of one or both members of the pair are of screw form. Figure 1.14 shows the meshing of screw gears. Two screw gears can only mesh together under the conditions that normal modules (mn1) and (mn2) and normal pressure angles (αn1, αn2) are the same.

 

Pic 2.2 Screw gear’s background

Assuming that there is a helical rack, which has the tooth trace in the direction TT and its tangential plane of both pitch cylinders at the point P is the pitch plane. When it moves with a velocity of Vn, the curve formed on each gear as an envelope surface of the rack tooth flank becomes the tooth flank of both gears. When the tooth flank of the helical rack is plane, the tooth flank of both gears becomes an in volute Helicon. It is an in volute screw gear, and its normal section is an in volute tooth profile.

The simultaneous contact line of the tooth flank of each gear and rack is the trace of a foot of a perpendicular from the arbitrary point on each pitch cylinder’s bus to the rack tooth surface through the pitch point P (it becomes a straight line for in volute screw gear). Both traces cross at the foot of a perpendicular from the pitch point P to the rack tooth profile. (See Pic 2.3 (a) NA and NB) Therefore, both tooth profiles point-contact at that point.

The trace of the contact point is generally the curve through the pitch point P. As for the in volute screw gear, the trace of the contact point becomes a straight line W which passes through the pitch point P, because the plane of the rack tooth profile moves parallel. The line is called action line (see Pic 2.3), the crossing line of tangential planes of base cylinders of gears, and it is also the fixed line contacts with both base cylinders. Same as normal gears, the angular velocity ratio is equal to the reciprocal ratio of the number of teeth, and the normal plane module should be equal for both gears.

Mesh-of involute screw gears

Pic 2.3 Mesh of in volute screw gear

Left Picture – Contact of screw gears flank

(1) Action line

Right Picture – Relation of base cylinders, action line, tangential plane, tooth trace of screw gear

(2) Base cylinder of gear I

(3) Screw line orthogonal to tooth trace

(4) Action line

(5) Base cylinder of gear II

(6) Screw line orthogonal to tooth trace

Suppose that the helical angle of the tooth trace is β1 and β2, the normal plane module of helical rack is mn, and the number of teeth of each gear is z1 and z2, the radius of pitch cylinders R1 and R2 are :

R1=z1mn / 2cosβ1, R2=z2mn / 2cosβ2

Then, R1 + R2=A, β1 + β2=β

Therefore, 2A / mn=z1 / cosβ1 + z2 / cos(β – β1)

For example, when A, β, z1, z2 and mn are given, β1 and β2 are defined by the preceding formula. However, β1>0, β2>0 in the preceding picture.β1 and β2 could be 0 or negative number. In fact, β=90° in many cases. When β=90°, to minimize center distance, set dA / dβ1=0 and obtain

One of formula of screw gears

Application of screw gear

As screw gears are point-contact, the contact stress at the contact point is large and lubricant film is easy to become thinner and as a result, the gears easily wear out. Therefore, the screw gears are not suitable for transmitting large power. On the other hand, the gears mesh smoothly and easy to do cut adjustment, so frequently used for transmission mechanism between skew shafts whose center distance is in the middle. In addition, it is well known that the machine relation of cutter and machined gear at gear shaving is similar to screw gears. The meshing relation of hob and gear sto be cut is also similar to screw gears.

When one of screw gears (driven gear) is a rack gear, they can line-contact and transmit heavy load. They may be used for the table drive of a planning machine. The rack type shaving cutter can be used, too.

Only the curve which goes on each tooth flank diagonally through the pitch point is useful for meshing of tooth flank of screw gears, and therefore the working face width is limited. However, enlarging the face width a little and enablingthe gears to move toward the axis will avoid excessive local wear, and lengthens the life of the entire gear.

1.6 Cylindrical Worm Gear Pair

duplex worm gears

Duplex Worm Gears

Cylindrical worms may be considered cylindrical type gears with screw threads. Generally, the mesh has a 90° shaft angle.The number of threads in the worm is equivalent to the number of teeth in a gear of a screw type gear mesh. Thus, a thread worm is equivalent to a one-tooth gear; and two-threads equivalent to two-teeth, etc. Referring to Figure 1.15, for a reference cylinder lead angle γ, measured on the pitch cylinder, each rotation of the worm makes the thread advance one lead pz.

There are four worm tooth profiles in JIS B 1723-1977, as defined below.

Type I : The tooth profile is trapezoidal on the axial plane.

Type II : The tooth profile is trapezoid on the plane normal to the space.

Type III : The tooth profile which is obtained by inclining the axis of the milling or grinding, of which cutter shape is trapezoidal on the cutter axis, by the lead angle to the worm axis.

Type IV : The tooth profile is of in volute curve on the plane of rotation.

KHK stock worm gear products are all Type III. Worm profiles. The cutting tool used to process worm gears is called a single-cutter that has a single-edged blade. The cutting of worm gears is done with worm cutting machine.Because the worm mesh couples non parallel and non intersecting axes, the axial plane of worm does not correspond with the axial plane of worm wheel. The axial plane of worm corresponds with the transverse plane of worm wheel. The transverse plane of worm corresponds with the axial plane of worm wheel. The common plane of the worm and worm wheel is the normal plane. Using the normal module, mn, is most popular. Then, an ordinary hob can be used to cut the worm wheel.

Fig. 4.15 Cutting Grinding for Type III Worm

Cutting – Grinding for Type III Worm

 

Fig. 4.16 Cylindrical worm (Right hand)

 

About Zaighum Shah 57 Articles
Zaighum Shah is a mechanical engineer having more than 20 years of experience. Zaighum is specializing in product development in Sugar Mill industries. Zaighum has gone through all phases of mechanical engineering and it’s practical implementation. Zaighum has been solving most complex problems, designing new systems and improving existing models and systems.

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