An Introduction To Gear Types , Geometry , Materials And Uses

An Introduction To Gear Types , Geometry , Materials And Uses

introduction

A gear is a wheel with evenly sized and spaced teeth machined or formed around its perimeter. Gears are used in rotating machinery not only to transmit motion from one point to another, but also for the mechanical advantage they offer. Two or more gears transmitting motion from one shaft to another is called a gear train, and gearing is a system of wheels or cylinders with meshing teeth. Gearing is chiefly used to transmit rotating motion but can also be adapted to translate reciprocating motion
into rotating motion and vice versa.

FIG 1

Gears are versatile mechanical components capable of performing many different kinds of power transmission or motion control.
Examples of these are
• Changing rotational speed
• Changing rotational direction
• Changing the angular orientation of rotational motion
• Multiplication or division of torque or magnitude of rotation
• Converting rotational to linear motion, and its reverse
• Offsetting or changing the location of rotating motion

The teeth of a gear can be considered as levers when they mesh with the teeth of an adjoining gear. However, gears can be rotated continuously instead of rocking back and forth through short distances
as is typical of levers. A gear is defined by the number of its teeth and its diameter. The gear that is connected to the source of power is called the driver, and the one that receives power from the driver is the driven gear. It always rotates in a direction opposing that of the driving gear; if both gears have the same number of teeth, they will rotate at the same speed. However, if the number of teeth differs, the gear with the smaller r number of teeth will rotate faster. The size and shape of all gear teeth that are to mesh properly for working contact must be equal.

gear ratio
The number of teeth on a gear determines its diameter. When two gears with different diameters and numbers of teeth are meshed together, the number of teeth on each gear determines gear ratio, velocity ratio, distance ratio, and mechanical advantage
The gear ratio GR is determined as:

FIG 2

GR = number of teeth on driven gear B /  number of teeth on driving gear A

The number of teeth in both gears determines the rotary distance traveled by each gear and their angular speed or velocity ratio. The angular speeds of gears are inversely proportional to
the numbers of their teeth.

VR = velocity of driving gear A /  velocity of driven gear B

The distance moved by the load is twice that of the effort. Using the general formula for mechanical advantage MA:

MA = load / effort

Gear Classification
All gears can be classified as either external gears or internal or annual gears:
• External gears have teeth on the outside surface of the disk or wheel.
• Internal or annual gears have teeth on the inside surface of a ring or cylinder.

Spur gears are cylindrical external gears with teeth that are cut straight across the edge of the disk or wheel parallel to the axis of rotation. The spur gears shown in Fig. 3 are the simplest gears. 

FIG 3

They normally translate rotating motion between two parallel shafts. An internal or annual gear, as shown in Fig.4, is a variation of the spur gear except that its teeth are cut on the
inside of a ring or flanged wheel rather than on the outside. Internal gears usually drive or are driven by a pinion. 

FIG 4

The disadvantage of a simple spur gear is its tendency to produce thrust that can misalign other meshing gears along their respective shafts, thus reducing the face widths of the meshing gears and reducing their mating surfaces.

Rack gears, as the one shown in Fig. 5, have teeth that lie in the same plane rather than being distributed around a wheel.

FIG 5

This gear configuration provides straight-line rather than rotary motion. A rack gear functions like a gear with an infinite radius. Pinions are small gears with a relatively small number of teeth
which can be mated with rack gears.
Rack and pinion gears, convert rotary motion to linear motion; when mated together they can transform the rotation of a pinion into reciprocating motion, or vice versa. In some systems, the pinion rotates in a fixed position and engages the rack which is free to move; the combination is found in the steering mechanisms of vehicles. Alternatively, the rack is fixed while the pinion rotates as it moves up and down the rack: Funicular railways are based on this drive mechanism; the driving
pinion on the rail car engages the rack positioned between the two rails and propels the car up the incline.

Bevel gears, as shown in Fig. 6, have straight teeth cut into conical circumferences which mate on axes that intersect, typically at right angles between the input and output shafts. This class of gears includes the most common straight and spiral bevel gears as well as miter and hypoid gears.

FIG 6

Straight bevel gears are the simplest bevel gears. Their straight teeth produce instantaneous line contact when they mate. These gears provide moderate torque transmission, but they are not as smooth running or quiet as spiral bevel gears because the straight teeth engage with full-line contact. They permit medium load capacity.

FIG 7

Spiral bevel gears have curved oblique teeth. The spiral angle of curvature with respect to the gear axis permits substantial tooth overlap. Consequently, the teeth engage gradually and at least two teeth are in contact at the same time. These gears have lower tooth loading than straight bevel gears and they can turn up to 8 times faster. They permit high load capacity.
Miter gears are mating bevel gears with equal numbers of teeth used between rotating input and output shafts with axes that are 90° apart.
Hypoid gears are helical bevel gears used when the axes of the two shafts are perpendicular but do not intersect. They are commonly used to connect driveshafts to rear axles of automobiles, and are often incorrectly called spiral gearing.

FIG 8

Helical gears are external cylindrical gears with their teeth cut at an angle rather than parallel to the axis. A simple helical gear, as shown in Fig. 9 , has teeth that are offset by an angle with respect to the axis of the shaft so that they spiral around the shaft in a helical manner. 

FIG 9

Their offset teeth make them capable of smoother and quieter action than spur gears, and they are capable of driving heavy loads because the teeth mesh at an acute angle rather than at 90°. When helical gear axes are parallel they are called parallel helical gears, and when they are at right angles they are called helical gears. Herringbone and worm gears are based on helical gear geometry
Herringbone or double helical gears, as shown in Fig. 10, are helical gears with V-shaped right-hand and left-hand helix angles side by side across the face of the gear. This geometry neutralizes axial thrust from helical teeth.

FIG 10

Worm gears, also called screw gears, are other variations of helical gearing. A worm gear has a long, thin cylindrical form with one or more continuous helical teeth that mesh with a helical
gear. The teeth of the worm gear slide across the teeth of the driven gear rather than exerting a direct rolling pressure as do the teeth of helical gears. Worm gears are widely used to transmit rotation, at significantly lower speeds, from one shaft to another at a 90° angle.

FIG 11

Face gears have straight tooth surfaces, but their axes lie in planes perpendicular to shaft axes. They are designed to mate with instantaneous point contact. These gears are used in right angle drives, but they have low load capacities

FIG 12

Gear Tooth Geometry
The geometry of gear teeth, as shown in Fig. 13, is determined by pitch, depth, and pressure angle

FIG 13

Gear Terminology
addendum: The radial distance between the top land and the pitch circle. This distance is measured in inches or millimeters.
addendum circle: The circle defining the outer diameter of the gear.
circular pitch: The distance along the pitch circle from a point on one tooth to a corresponding point on an adjacent tooth. It is also the sum of the tooth thickness and the space width. This distance
is measured in inches or millimeters.
clearance: The radial distance between the bottom land and the clearance circle. This distance is measured in inches or millimeters
contact ratio: The ratio of the number of teeth in contact to the number of teeth not in contact.
dedendum: The radial distance between the pitch circle and the dedendum circle. This distance is measured in inches or millimeters.
dedendum circle: The theoretical circle through the bottom lands of a gear. depth: A number standardized in terms of pitch. Full-depth teeth have a working depth of 2/P. If the teeth have equal
addenda (as in standard interchangeable gears), the addendum is 1/P. Full-depth gear teeth have a larger contact ratio than stub teeth, and their working depth is about 20 percent more than stub gear teeth. Gears with a small number of teeth might require undercutting to prevent one interfering with another during engagement.
diametral pitch (P): The ratio of the number of teeth to the pitch diameter. A measure of the coarseness of a gear, it is the index of tooth size when U.S. units are used, expressed as teeth per inch.
pitch: A standard pitch is typically a whole number when measured as a diametral pitch (P). Coarse pitch gears have teeth larger than a diametral pitch of 20 (typically 0.5 to 19.99). Fine-pitch gears usually have teeth of diametral pitch greater than 20. The usual maximum fineness is 120 diametral pitch, but involute-tooth gears can be made with diametral pitches as fine as 200, and cycloidal tooth gears can be made with diametral pitches to 350.
pitch circle: A theoretical circle upon which all calculations are based.
pitch diameter: The diameter of the pitch circle, the imaginary circle that rolls without slipping with the pitch circle of the mating gear, measured in inches or millimeters.
pressure angle: The angle between the tooth profile and a line perpendicular to the pitch circle, usually at the point where the pitch circle and the tooth profile intersect. Standard angles are 20° and 25°. It affects the force that tends to separate mating gears. A high pressure angle decreases the contact ratio, but it permits the teeth to have higher capacity and it allows gears to have fewer teeth without undercutting.

the basics of Basic Gear Technology

Gear size, pressure angle, number of teeth…we introduce the basic terminology, measurement, and relational expressions necessary to understand basic gear technology.

Comparative Size of Gear-Teeth

Using ISO (International Organization for Standardization) guidelines, Module Size is designated as the unit representing gear tooth-sizes. However, other methods are used too.

Module (m)
m = 1 (p = 3.1416)
m = 2 (p = 6.2832)
m = 4 (p = 12.566)

FIG 14

If you multiply Module by Pi, you can obtain Pitch (p). Pitch is the distance between corresponding points on adjacent teeth.

p = Pi x Module = πm

CP (Circular Pitch)
Circular Pitch (CP) denotes the reference pitch (p).
For instance, you can produce gears at an exact integral value, such as CP5/CP10/CP15/CP20.

Transformation from CP to Module

m = CP / π

DP (Diametral Pitch)
DP stands for Diametral Pitch.
By ISO standards, the unit Millimeter (mm) is designated to express length, however, the unit inch is used in the USA, the UK and other countries; Diametral Pitch is also used in these countries.

Transformation from DP to Module
m = 25.4 / DP

Pressure Angle ( α )

Pressure angle is the leaning angle of a gear tooth, an element determining the tooth profile.
Recently, the pressure angle (α) is usually set to 20°, however, 14.5° gears were prevalent.

FIG 15

Number of teeth

Number of teeth denotes the number of gear teeth.
They are counted as shown in the Figure 16 . The number of teeth of this gear is 10.

FIG 16

Module (m) , Pressure Angle (α) , and the Number of Teeth, introduced here, are the three basic elements in the composition of a gear. Dimensions of gears are calculated based on these elements.

Tooth Depth and Thickness

Tooth depth is determined from the size of the module (m). Introduced here are Tooth Profiles (Full depth) specified by ISO and JIS (Japan Industrial Standards) standards.
 see Figure  17  below for explanations for Tooth depth (h) / Addendum (ha) / Dedendum (hf). Tooth depth (h) is the distance between tooth tip and the tooth root.

h = 2.25 m

(= Addendum + Dedendum)

FIG 17

Addendum (ha) is the distance between the reference line and the tooth tip.

ha = 1.00 m

Dedendum (hf) is the distance between the reference line and the tooth root.

hf = 1.25 m

Tooth thickness (s) is basically half the value of pitch (p). * Pitch (p) = πm
s = πm / 2

Diameter of Gears (Size)

The size of gears is determined in accordance with the reference diameter (d) and determined by these other factors; the base circle, Pitch, Tooth Thickness, Tooth Depth, Addendum and Dedendum.

Reference diameter (d)

d = zm

Tip diameter (da)

da = d + 2 m

Root diameter (df)

df ＝ d －2.5 m

FIG 18

The Addendum and dedendum circle introduced here are a reference circle that cannot be seen on a gear, as it is a virtual circle, determined by gear size.

Gear Symbols and Nomenclature

Center Distance and Backlash

When a pair of gears are meshed so that their reference circles are in contact, the center distance (a) is half the sum total of their reference diameters.

Center distance (a)

a = (d1+d2) / 2

FIG 19

Gears can mesh as shown in the Figure , however, it is important to consider a proper backlash (play) so that the gears can work smoothly. Backlash is a play between tooth surfaces of paired gears in mesh.
Mating gears also have a clearance (play) vertical to tooth depth. This is called Tip and Root Clearance (c), the distance between tooth root and the tooth tip of mating gears.

Tip and Root Clearance (c)

c = 1.25 m － 1.00 m

c = 0.25 m

FIG 20

Helical Gear

Spur gears with helicoid teeth are called Helical Gears.
The majority of calculations for spur gears can be applied to helical gears too. This type of gear comes with two kinds of tooth profiles in accordance with the datum surface. (Figure  21 )

FIG 21

a) Transverse System (Transverse module / Pressure angle) * NOTE 1
(b) Normal System (Normal module / Pressure angle)
* NOTE 1. Transverse axis denotes the centerline of the gear.

Relational Expression: Transverse module ( mt ) and Normal module ( mn )

mt = mn / cos β

Reference diameter (d) of the helical gear with transverse system can be calculated from Equation

d = zm

Reference diameter (d) of the helical gear with normal system can be calculated from Equation

d = z mn / cos β

Heat Treatments

Heat treatment is a process that controls the heating and cooling of a material, performed to obtain required structural properties of metal materials. Heating methods include normalizing, annealing quenching, tempering, and surface hardening.
Heat treatment is performed to enhance the properties of the steel. as the hardness increases by applying successive heat treatments, the gear strength increases along with it; the tooth surface strength also increases drastically. As shown in Table 1  , heat treatments differ depending on the quantity of carbon (C) contained in the steel.

TABLE 1

(1) Normalizing
Normalizing is a heat treatment applied to the microstructure of the small crystals of steel to unify the overall structure. This treatment is performed to relieve internal stress or to resolve inconsistent fiber structure occurred by the forming processing such as rolling.

(2) Annealing
Annealing is a heat treatment applied to soften steel, to adjust crystalline structure, to relieve internal stress, and to modify for cold-working and cutting performance. There are several types of annealing in accordance with the application, such as Full Annealing, Softening, Stress Relieving, Straightening Annealing and Intermediate Annealing.

1. Full Annealing
   Annealing to relieve internal stress without changing the structure.
2. Straightening Annealing
   Annealing to fix deformation occurred in steel, or other materials. The treatment is performed by applying load.
3. Intermediate Annealing
   Annealing applied in the process of cold-working, applied to soften the work-hardened material, so to make the next process easier.

(3) Quenching
Quenching is a treatment on steel, applying rapid cooling after heating at high temperature. There are several types of quenching in accordance with cooling conditions; water quenching, oil quenching, and vacuum quenching. It is essential to apply tempering after quenching.

(4) Tempering
Tempering is a heat treatment, applying cooling at a proper speed. After performing quench hardening, the material is heated again, then, tempering is applied. Tempering must be performed after quenching. Quenching is applied to adjust hardness, to add toughness, and to relieve internal stress. There are two types of tempering, one is high-temperature tempering, and the other is low-temperature tempering. Applying the tempering at higher temperature, the more toughness is obtained, although the hardness decreases. For thermal refining, high-temperature tempering is performed. For induction hardening or carburizing, the require tempering performed after surface-hardening treatment is, low-temperature tempering.

(5) Thermal Refining
Thermal Refining is a heat treatment applied to adjust heardness / strength / toughness of steel. This treatment involves quenching and high-temperature tempering, in combination. After thermal refining is performed, the hardness is adjustedby these treatments to increase the metals machinable properties. The target hadness for thermal refining are :
S45C ASME  1045. 1046 (Carbon Steel for Machine Structural Use) 200 – 270 HB

SCM440 (ASME  4145 Alloy Steel for Machine Structural Use) 230 – 270 HB

(6) Carburizing
Carburizing is a heat treatment performed especially to harden the surface in which carbon is present and penetrates the surface. The surface of low-carbon steel is carburized (Carbon penetration) and in a state of high carbon, where quenching is required. Low-temperature tempering is applied after quenching to adjust the hardness.
Not only the surface, but the inner material structure is also somewhat hardened by some level of carburizing, however, it is not as hard as the surface.
If a masking agent is applied on a part of the surface, carbon penetration is prevented and the hardness is not changed. The target hardness on the surface and the hardened depth are:
– Quench Hardenss 55 – 63 HRC (reference value)
– Effective Hardened Depth 0.3 – 1.2 mm (reference value）
Gears are deformed by carburizing, and the precision is decreased. To improve precision, gear grinding is necessary.

(7) Induction Hardening
Induction Hardening is a heat treatment performed to harden the surface by induction-heating of the steel, composed of 0.3% carbon. For gear products, induction hardening is effective for hardening tooth areas including tooth surface and the tip, however, the root may not be hardened in some cases. Generally, the precision of gears declines from deformation caused by induction hardening. For induction hardening of S45C products, please refer to the values below.
– Quench Hardness 45 – 55 HRC
– Effective Hardened Depth 1 – 2 mm

(8) Flame Hardening
Flame Hardening is a surface-hardening treatment performed by flame heating. This treatment is usually performed on the surface for partial hardening of iron and steel.

(9) Nitriding
Nitriding is a heat treatment performed to harden the surface by introducing nitrogen into the surface of steel. If the steel alloy includes aluminum, chrome, and molybdenum, it improves nitriding and the hardness can be obtained. A representative nitride steel is JIS SACM645 (Aluminium chromium molybdenum steel)

(10) Total Quenching
A heat treatment by heating the entire steel material to the core, and then cooling rapidly afterwards, where not only the surface is hardened, the core part is also hardened.

GEAR MATERIALS

Gear steels may be divided into two general classes 

the plain carbon and the alloy steels. Alloy steels are used to some extent in the industrial field, but heat-treated plain carbon steels are far more common. The use of untreated alloy steels for gears is seldom, if ever, justified, and then, only when heat-treating facilities are lacking. The points to be considered in determining whether to use heat-treated plain carbon steels or heat-treated alloy steels are: Does the service condition or design require the superior characteristics of the alloy steels, or, if alloy steels are not required, will the advantages to be derived offset the additional cost? For most applications, plain carbon steels, heat-treated to obtain the best of their qualities for the service intended, are satisfactory and quite economical. The advantages obtained from using heat-treated alloy steels in place of heat-treated plain carbon steels are as follows:

1) Increased surface hardness and depth of hardness penetration for the same carbon content

and quench.

2) Ability to obtain the same surface hardness with a less drastic quench and, in the case of some of the alloys, a lower quenching temperature, thus giving less distortion.

3) Increased toughness, as indicated by the higher values of yield point, elongation, and reduction of area.

4) Finer grain size, with the resulting higher impact toughness and increased wear resistance.

5) In the case of some of the alloys, better machining qualities or the possibility of machining at higher hardnesses.

A- Use of Casehardening Steels.—Each of the two general classes of gear steels may be further subdivided as follows: 

1) Casehardening steels; 

2) full-hardening steels; a nd

3) steels that are heat-treated and drawn to a hardness that will permit machining.

The first two  :casehardening and full-hardening steels  are interchangeable for some kinds of service, and the choice is often a matter of personal opinion. Casehardening steels with their extremely hard, fine-grained (when properly treated) case and comparatively soft and ductile core are generally used when resistance to wear is desired. Casehardening alloy steels have a fairly tough core, but not as tough as that of the full-hardening steels. In order to realize the greatest benefits from the core properties, casehardened steels should be double-quenched. This is particularly true of the alloy steels, because the benefits derived from their use seldom justify the additional expense, unless the core is refined and toughened by a second quench. The penalty that must be paid for the additional refinement is increased distortion, which may be excessive if the shape or design does not lend itself to the casehardening process.

B- Use of “Thru-Hardening” Steels.:

Thru-hardening steels are used when great strength, high endurance limit, toughness, and resistance to shock are required. These qualities are governed by the kind of steel and treatment used. Fairly high surface hardnesses are obtainable in this group, though not so high as those of the casehardening steels. For that reason, the resistance to wear is not so great as might be obtained, but when wear resistance combined with great strength and toughness is required, this type of steel is superior to the others. Thru-hardening steels become distorted to some extent when hardened, the amount depending upon the steel and quenching medium used. For that reason, thru-hardening steels are not suitable for high-speed gearing where noise is a factor, or for gearing where accuracy is of paramount importance, except, of course, in cases where grinding of the teeth is practicable. The medium and high-carbon percentages require an oil quench, but a water quench may be necessary for the lower carbon contents, in order to obtain the highest physical properties and hardness. The distortion, however, will be greater with the water quench

1-Forged and Rolled Carbon Steels for Gears:

These compositions cover steel for gears in three groups, according to heat treatment, as follows:

a) case-hardened gears

b) unhardened gears, not heat treated after machining

c) hardened and tempered gears

Forged and rolled carbon gear steels are purchased on the basis of the requirements as to chemical composition specified in Table 2. Class N steel will normally be ordered in ten point carbon ranges within these limits. Requirements as to physical properties have been omitted, but when they are called for the requirements as to carbon shall be omitted. The steels may be made by either or both the open hearth and electric furnace processes

TABLE 2

2-Forged and Rolled Alloy Steels for Gears.:L

These compositions cover alloy steel for gears, in two classes according to heat treatment, as follows:

a) case-hardened gears

b) hardened and tempered gears

Forged and rolled alloy gear steels are purchased on the basis of the requirements as to chemical composition specified in Table 3. Requirements as to physical properties have been omitted. The steel shall be made by either or both the open hearth and electric furnace process.

TABLE 3

3- Steel Castings for Gears.:

It is recommended that steel castings for cut gears be purchased on the basis of chemical analysis and that only two types of analysis be used, one for case-hardened gears and the other for both untreated gears and those which are to be hardened and tempered. The steel is to be made by the open hearth, crucible, or electric furnace processes. The converter process is not recognized. Sufficient risers must be provided to secure soundness and freedom from undue segregation. Risers should not be broken off the unannealed castings by force. Where risers are cut off with a torch, the cut should be at least one-half inch above the surface of the castings, and the remaining metal removed by chipping, grinding, or other noninjurious method.

Steel for use in gears should conform to the requirements for chemical composition indicated in Table 4. All steel castings for gears must be thoroughly normalized or annealed, using such temperature and time as will entirely eliminate the characteristic structure of unannealed castings.

TABLE 4