Introduction to Gears

Gears are used in all types of machinery. They can be as small as 3mm diameter to 11m diameter. They are used to transmit rotary motion from one shaft to another by means of toothed wheels, which are in direct mesh with each other. In contrast, chain wheels transmit motion from one wheel to another by means of chain connection. They are called sprockets. Gears are used for power transmission as in automobile gearbox and in control elements.

Spur gears:
Spur gears are the most commonly used gears, are used to transmit motion between parallel shafts. These impose load on bearings. Its teeth are straight and parallel to the axis. These can be either internal type or external type. An external spur gear of infinite radius, called as rack. Rack has straight-sided tooth (for involute tooth profile gears).

Helical gears:
In helical gears, the tooth profile in transverse plane gets gradually rotated along the helix angle as we move along the axis. The hand of the helix determines whether it is a right handed helical gear or a left handed helical gear. Helical gears can be external or internal type. However, internal helical gears are not very common in external helical gears, the hands of the mating gears are of opposite hands, whereas for internal helical gear meshing with external gear, they are of the same hand. The mating gear should always have the same helix angle.
Sometimes double helical gears are also used where they have both right handed and left handed helical teeth on each gear. Normally there is a gap between the two helices. However, there are gears which have no gap between the helices double helical gear are also called chevron gears. Single helical gear impose both radial and thrust load on bearings. Double helical gear normally impose radial loads as the thrust loads due to opposite helices are in the opposite directions and, therefore, they cancel out. The spur gears can be considered as a special case of gears with helix angle equal to zero.

Terms Used in Gears

The following terms, which will be mostly used in this chapter, should be clearly understood at this stage. These terms are illustrated in fig.

1) Pitch circle : It is an imaginary circle which by pure rolling action, would give the same motion as the actual gear.

2) Pitch circle diameter : It is the diameter of the pitch circle. The size of the gear is usually specified by the pitch circle diameter. It is also called as pitch diameter.

3) Pitch point : It is a common point of contact between two pitch circles.

4) Pitch surface : It is the surface of the rolling discs which the meshing gears have replaced at the pitch circle.

5) Pressure angle or angle of obliquity : It is the angle between the common normal to two gear teeth at the point of contact and the common tangent at the pitch point. It is usually denoted by The standard pressure angles are 14½o and 20o.

6) Addendum : It is the radial distance of a tooth from the pitch circle to the top of the tooth.

7) Dedendum : It is the radial distance of a tooth from the pitch circle to the bottom of the tooth.

8) Addendum circle: It is the circle drawn through the top of the teeth and is concentric with the pitch circle.

9) Dedendum circle: It is the circle drawn through the bottom of the teeth. It is also called root circle.
Note : Root circle diameter = Pitch circle diameter X cos where  is the pressure angle.

10) Circular pitch: It is the distance measured on the circumference of the pitch circle from a point of one tooth to the corresponding point on the next tooth. It is usually denoted by Pc , Mathematically.

Circular pitch, Pc = D/T
where D = Diameter of the pitch circle, and
T = Number of teeth on the wheel.

A little consideration will show that the two gears will mesh together correctly, if the two wheels have the same circular pitch.

Note : If D1 and D2 are the diameters of the two meshing gears having the teeth T1 and T2 respectively, then for them to mesh correctly.
Pc = D1/T1 = D2/T2 or D1/D2 = T1/T2

11) Diametral pitch : It is the ratio of number of teeth to the pitch circle diameter in millimeters. It is denoted by Pd Mathematically,

Diametral pitch, Pd = T/D = /Pc
Where T = Number of teeth, and
D = Pitch circle diameter.

12) Module: It is the ratio of the pitch circle diameter in millimeters to the number of teeth. It is usually denoted by m. Mathematically,

Module, m = D/T

Note : The recommended series of modules in Indian Standard are 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, and 20. The modules 1.125, 1.375, 1.75, 2.25, 2.75, 3.5, 4.5 5.5, 7, 9, 11, 14 and 18 are of second choice.

13) Clearance: It is the radial distance from the top of the tooth to the bottom of the tooth, in a meshing gear. A circle passing through the top of the meshing gear is known as clearance circle.

14) Total depth: It is the radial distance between the addendum and the dedendum of a gear. It is equal to the sum of the addendum and dedendum.

15) Working depth: It is the radial distance from the addendum circle to the clearance circle. It is equal to the sum of the addendum of the two meshing gear.

16) Tooth thickness: It is the width of the tooth measured along the pitch circle.

17) Tooth space: It is the width of space between the two adjacent teeth measured along the pitch circle.

18) Backlash: It is the difference between the tooth space and the tooth thickness, as measured along the pitch circle. Theoretically, the backlash should be zero, but in actual practice some backlash must be allowed to prevent jamming of the teeth due to tooth errors and thermal expansion.

19) Face of tooth: It is the surface of the gear tooth above the pitch surface.

20) Flank of tooth: It the surface of the gear tooth below the pitch surface.

21) Top land: It is the surface of the top of the tooth.

22) Face width: It is the width of the gear tooth measured parallel to its axis.

23) Profile: It is the curve formed by the face and flank of the tooth.

24) Fillet radius: It is the radius that connects the root circle to the profile of the tooth.

25) Path of contact: it is the path traced by the point of contact of two teeth from the beginning to the end of engagement.

26) Length of the path of contact : It is the length of the common normal cut-off by the addendum circles of the wheel and pinion.

27) Arc of contact: It is the path traced by a point on the pitch circle from the beginning to the end of engagement of a given pair of teeth. The arc of contact consists of two parts, …i.e.,
(a) Arc of approach : It is the portion of the path of contact from the beginning of the engagement to the pitch point.
(b) Arc of recess : it is the portion of the path of contact from the pitch point to the end of the engagement of a pair of teeth.
Note : The ratio of the length of arc of contact to the circular pitch is known as contact ratio i.e. number of pairs of teeth in contact.

Gear Materials

The material used for the manufacture of gears depends upon the strength and service conditions like wear, noise etc. The gears may be manufactured from metallic or non-metallic materials. The metallic gears with cut teeth are commercially obtainable in cast iron, steel and bronze. The non-metallic materials like wood, raw hide, compressed paper and synthetic resins like nylon are used for gears, especially for reducing noise.
The cast iron is widely used for the manufacture of gears due to its good wearing properties, excellent machinability and ease of producing complicated shapes by casting method. The cast iron gears with cut teeth may be employed, where smooth action is not important.
The steel is used for high strength gears and steel may be plain carbon steel or alloy steel. The steel gears are usually heat treated in order to combine properly the toughness and tooth hardness.
The phosphor bronze is widely used for worm gears in order to reduce wear of the worms which will be excessive with cast iron or steel.

Comparison Between Involute and Cycloidal Gears

In actual practice, the involute gears are more commonly used as compared to cycloidal gears, due to the following advantages:

Advantages of involute gears:
Following are the advantages of involute gears:
1) The most important advantage of the involute gears is that the center distance for a pair of involute gears can be varied within limits without changing the velocity ratio. This is not true for cycloidal gears which requires exact center distance to be maintained.

2) In involute gears, the pressure angle, from the start of the engagement of teeth to the end of the engagement, remains constant. It is necessary for smooth running and less wear of gears. But in cycloidal gears, the pressure angle is maximum at the beginning of engagement, reduces to zero at pitch point, starts increasing and again become maximum at the end of engagement. This results in less smooth running of gears.

3) The face and flank of involute teeth are generated by a single curve where as in cycloidal gears, double curves (i.e. epi-cycloid and hypo-cycloid) are required for the face and flank respectively. Thus the involute teeth are easy to manufacture than cycloidal teeth. In involute system, the basic rack has straight teeth and the same can be cut with simple tools.

Note : The only disadvantage of the involute teeth is that the interference occurs with pinions having smaller number of teeth. This may be avoided by altering the heights of addendum and dedendum of the mating teeth or the angle of obliquity of the teeth.

Advantages of cycloidal gears :
1) Since the cycloidal teeth have wider flanks, therefore the cycloidal gears are stronger than the involute gears, for the same pitch. Due to this reason, the cycloidal teeth are preferred specially for cast teeth.

2) In cycloidal gears, the contact takes place between a convex flank and concave surface, where as in involute gears, the convex surface are in contact. This condition results in less wear in cycloidal gears as compared to involute gears. However the difference in wear is negligible.

3) The cycloidal gears, the interference does not occur at all. Though there are advantages of cycloidal gears but they are outweighted by the greater simplicity and flexibility of the involute gears.

Systems of Gear Teeth

The following four systems of gear teeth are commonly used in practice :
1. 14½o Composite system,
2. 14 ½o Full depth involute system,
3. 20o Full depth involute system, and
4. 20o Stub involute system.

The 14½o composite system is used for general purpose gears. It is stronger but has no interchangeability. The tooth profile of this system has cycloidal curves at the top and bottom and involute curve at the middle portion. The teeth are produced by formed milling cutters or hobs. The tooth profile of the 14½o full depth involute system was developed for use with gear hobs for spur and helical gears.
The tooth profile of the 20o full depth involute system may be cut by hobs. The increase of the pressure angle from 14½o to 20o results in a stronger tooth, because the tooth acting as a beam is wider at the base. The 20o stub involute system has a strong tooth to take heavy loads.

Standard Proportions of Gear Systems

S. No.	Particulars	14½o composite or full depth involute system	20o full depth involute system	20o slub involute system
1.	Addendum	1 m	1 m	0.8 m
2.	Dedendum	1.25 m	1.25 m	1 m
3.	Working depth	2 m	2 m	1.60 m
4.	Minimum total depth	2.25 m	2.25 m	1.80 m
5.	Tooth thickness	1.5708 m	1.5708 m	1.5708 m
6.	Minimum clearance	0.25 m	0.25 m	0.2 m
7.	Fillet radius at root	0.4 m	0.4 m	0.4 m

Law of Gearing

The law of gearing states the conditions which must be fulfilled by the gear tooth profiles to maintain a constant angular velocity ratio between two gears. It states that the common normal at the point of contact of the two teeth should always pass through a common pitch point.

Gear manufacturing processes (cutting processes)

When gear teeth are cut on a gear blank, the manufacturing process consists of the following steps:

(a) Blank manufacture;
(b) Tooth cutting;
(c) Heat treatment;
(d) Tooth finish cutting.

All the steps listed above may not be used in the manufacture depending on the requirement. For example, non-hardened gears may not require heat treatment. If the accuracy required is not very high, special tooth finish cutting will not be carried out. The sequence of steps is generally as enumerated above, but it may differ. For example, in automobile gear manufacture the tooth finish cutting is carried out before heat treatment.

Gear blank manufacture

The quality of gear produced is as much dependent on the quality of gear lank used as on the accuracy of the machine used for teeth cutting. The locating surfaces should be selected and maintained throughout the manufacturing processes.

Gear blanks may be either of the following two types: (a) Shaft type having centers, and (b) Cylindrical blanks with round bores with or without keyway or with splined bores.

Shaft type blanks are usually mounted between centers during all the operations. Therefore, to get accurate gears, the centers should not be damaged during material movement, and they should be cleaned while mounting on the machine as well. A typical shaft like component is shown in second Figure.

In this case, the locating surfaces are the cone-surfaces C and D of the centers. The first requirement is that these centers should be in line so that you get proper contact on the locating surfaces. These cone surfaces should be smooth, and used for manufacturing both the mounting surfaces A and B as well as for tooth cutting. Gear outer surface E also should be produced in the same operation like the operation of producing surfaces A and B, and it (surface E) can be consequently used for dialing when mounted on the gear-cutting machine to check the accuracy of mounting.

Cylindrical blanks can be of two types, namely, (a) Blanks having round bore with or without keyway, and (b) Blanks having splined bore. Fig2 For this, normally the bore (Surface A) and the face (Surface B perpendicular to it are the locating surfaces, as shown in the first figure.
. The requirements of the blank are the following :
(a) Surface B should be at right angles to surface A. For very accurate gears, face runout of surface B required will vary from 5 (0.002”) to 25 m (0.001”) depending on the accuracy required. For very accurate gears it can be 5 m. for normal accuracy gears (such as DIN 7 Class) it can be 10-12 m.

(b) The bore A should also have close tolerance so that while it is mounted on the machine, there is minimal play between the bore and the mounting mandrel. This will reduce pitch errors generated due to the blank runout. It may, therefore, be necessary to green grind the cylindrical blanks for bore A and face B to achieve the necessary accuracy for process purposes though it may not be required for actual operation of the gear.

(c) Face C is kept concentric with respect to the locating surface A so that it can be used for initial dialing on the gear-cutting machine.

The tooth cutting processes can be divided into two types, namely, form machining and tooth generation process.

Form machining and Tooth-generation Processes

Form machining –
In this type of machining, the cutter is of the form of the tooth space to be produced and as this type of cutter cuts, it transfers its tooth form to the job. Some examples of this process are :

1. Milling of spur/helical gears on the milling machine;
2. Form grinding of gear tooth on Overcut or similar type of gear grinding machines, and
3. Cutting of hypoid gear wheel of non-generated type.



Tooth-generation Processes –
For this type, the involute form is produced by generation. The form may be generated in various ways which are described later in individual process descriptions. Some of the generation processes are :
(1) Milling
(2) Hobbing
(3) Shaping, and
(4) Rack planning, etc.

Manufacturing of spur and helical gears

Various methods used for tooth cutting of spur and helical gears are listed below :

(1) Tooth milling;
(2) Hobbing;
(3) Shaping;
(4) Rack planning;
(5) Gear shaving;
(6) Gear grinding;
(7) Gear lapping;
(8) Gear honing, and
(9) Gear burnishing.

The last five processes (5) to (10) are gear teeth finishing processes where the gears are rough cut using one of the four earlier mentioned processes.

Milling Spur Gear on Milling Machine

The gear blank is mounted on a mandrel which is supported between the center of the dividing head and one more center at the other end, as shown in fig. At a time one tooth space is cut by the milling cutter, and a dividing head is used to index the job to the next required tooth space. The cutter is chosen according to the module (or DP) and number of teeth of the gear to the cut. This cutter is mounted on the milling arbor. Before the gear can be cut, it is necessary to have the cutter centred accurately relative to the gear holding mandrel. One way is to adjust the machine table vertically and horizontally until one corner of the cutter just touches the mandrel on one side. Both the dials (of the table and the knee) are then set to zero. The table is then adjusted for the cutter to just touch on the other side of the mandrel with vertical dial showing zero. The reading of the horizontal feed screw is read. This reading divided by two gives the central position of the mandrel relative to the cutter. When the table is set centrally in this manner it should be locked in that position. The table is then fed vertically so that the blank just touches the cutter. The vertical dial is then set to zero. This is required to give the depth of cut on the job.

With these settings the machine can be started and traversed along the axis of the job to cut the tooth over the whole width of the gear. Depth is increased slowly until it reaches the full depth of the tooth. With the depth setting the backlash of the gear can be controlled suitably. After one tooth space is cut, the blank is indexed through 1/z revolution by means of the dividing head, and the process is repeated until all the teeth are cut.

Dividing Head Settings

There are four methods of indexing;
(a) Rapid indexing;
(b) Plain indexing;
(c) Compound indexing, and
(d) Differential indexing.

Rapid Indexing –
This is the simplest method and is suitable for dividing into 2,3,4,6,8,12 and 24 divisions.. For this rapid indexing, the worm is first dropped from engagement with the worm wheel by means of a knob by the side of the index head. Then the pin P in the hole of the index plate I1 is disengaged by the lever L. The job is then rotated through the number of holes required to get the necessary division. Then the pin P is reengaged. Due to dropping of the worm out of engagement, it is easy to rotate the job from the front.

Plain indexing –
This will be explained with the help of an example. Suppose we want to cut a gear with 23 teeth, i.e., we need to index the job through 1/23 of a revolution. For this the index plate handle J will have to be rotated through 40/23=117/23 revolution. To get 17/23 of a revolution, we will use the circle with 23 equi-spaced holes on the index plate I2. To aid this counting of 17 holes, the sector on the index plate is used. With the nut N loosened, the arm carrying the crank-lkever handle is moved to position the pin in one of the holes of the circle with 23 holes. Then one arm is positioned to touch one side of the latch pin of the handle. Then the other arm of the sector is positioned 18 holes away., on the further side of the hole. With the sector thus positioned, the nut N is locked. Then the pin P is withdrawn and one revolution is carried out and the hand is further rotated so that the pin will rest in the hole touching the second arm of the sector. The sector is then loosened and rotated for the other arm to touch the latch-pin in new position for the next indexing.

Compound indexing –
Many a time the number of divisions required cannot be obtained by plain indexing. Then compound indexing is used in which in one motion the crank handle is rotated through a certain rotation and its latch pin engaged. Afterwards the index plate itself is rotated through a certain rotation either in the same direction or in the opposite direction depending on the requirement. Normally index plate is prevented from rotating by a stationary pin at the rear which engages one of the holes of the same index plate I2. After this stop pin is removed, the index plate can be rotated. Let us consider milling a 93- teeth gear. The job will have to be rotated through 1/93 revolution or the crank lever through 40/93 revolutions, which will not be possible with the standard index plate. For this purpose, then the crank lever will be rotated through 11/33 revolution and the index plate through 3/31 revolution in the same direction.


Differential indexing –
This case is similar to the compound indexing. Only difference is that in this case the index plate is rotated through gearing connected to the dividing head spindle.

Form Milling of Helical Gear

The procedure is similar to form-milling of spur gear. In this case a universal milling machine is used. The module of cutter chosen is equal to the normal module of helical gear to be cut. With the cutter mounted on the arbor of horizontal milling machine, the table is set to the helix angle of the gear. To carry out the helical milling, the dividing head is connected to the lead screw of the table. The gears are chosen so as to give the necessary lead on the gear. Lead of helical gear is given by:

L = d. cot
where L = Lead of the gear,
d = reference diameter of the gear, and
 = helix angle of the gear.

The gear is then cut similar to cutting a spur gear. If the helix angle of the gear is large, it may not be possible to set the table of the universal milling machine to the required helix angle. In this case a vertical milling attachment is used and is set in the horizontal position, setting the cutter at 90o from the normal position. The table is then set to the lead angle of the helical gear.

Hobbing of spur and helical gears

Hobbing is a generating process of manufacturing gears in which the cutting action is continuous. The cutting tool is in the form of a worm. The cutting tool is called hob. It has gashes along the axis to form a cutting edge, with the tooth surface relieved behind the cutting edges so as to give the cutting relief angle. Some hobs have gashes which are not axial but inclined to the axis so as to be at right angles to the helix. These gashes are called the flutes of the hob. Generally the hob teeth have a straight-sides form (as shown in Fig. 3) in axial section.

Feed motions of hob cutter

Figures of feed motion of hob show the cutting of teeth on the work piece with the hob. There are three principal feed motions with respect to the work piece [Figs. 5 (a), (b) and (c)]. Feed motion in the direction OR is the radial-feed motion. It is called radial because it is in the radial direction of the work piece. Feed motions in the directions of OA and OT are called axial-feed motion and tangential-feed motion, respectively. There can be feed motions which are combination of any two of these primary feed motions.
Axial feed is the most commonly used feed, unless there is restriction for axial motion. The hob is fed to the full depth form and then fed in axial direction to generate the full width of the gear.
Radial feed is used where there is restriction to axial motion, for example, in cutting distributor gear on cam shaft, where there is obstruction on both sides of the gear due to the presence of the cam lobes. In this case the hob is fed in radial direction. It can be seen from Fig. 5 (a) that the tooth depth is not constant along the axis. For this reason, the hob has to be set centrally with respect to the gear being cut. In tangential feed, the hob moves at a direction tangential to the gear being cut. This method of cutting is used for producing worm wheels.
When any two of these feeds are used together, we get a resultant feed which is dependent on the ratio of the two feeds. The most commonly used combined feed is called diagonal hobbing in which tangential and axial feed are used simultaneously. This is shown in fig. 6 normally in radial and axial feed, about 1½ to 3 tooth-pitches do the work, whereas in diagonal hobbing more number of teeth are in operation. Accuracy of the gear produced b diagonal hobbing depends on the accuracy of the hob over the number of teeth, and its pressed over number of teeth. As in radial and axial feed only a limited number of teeth do the actual cutting, the wear of they hob will be concentrated only on these few teeth. In order to spread this wear over all the teeth of the hob, many machines are fitted with automatic hob shift.

Feed Motions of Hob

Hobbing Machine Setting for Cutting Spur Gears

First of all, the spindle-bore taper as well as the taper of the arbor are cleaned. Then the arbor is fitted into the spindle and locked against the taper by a drawbolt. The hob is then fitted on the arbor along with spacing collars, and the tailstock bracket is brought in position to support the other end of the arbor. The nut is locked for locking the hob and spacing collars together. The runout of the hob is checked on the proof-diameter. This should be within 0.005 (0.0002’).

The work is then mounted on the table. The method of supporting the work piece on the table varies from job to job. However, this should ensure that the job runs true with the table-axis. In one off or batch production, this can be checked for every piece and corrected.

However for mass production, the fixture and blank manufacture should ensure that this runout is repeatedly maintained piece after piece.

Necessary change gears are mounted to select the proper speed ratio between the hob and the work piece. Hob head is then set according to the helix angle of the hob as shown in Fig. 9.11. Speed of the hob is dependent on the material of the blank (and the hob material).

Depending on the feed requirement, - radial, axial or diagonal – feed is selected. Feed rate is also dependent on the material and whether the hobb is being used for roughing or finishing.

Now the table is brought towards the hob so as to have the hob just touching the work piece. The dial on the lead screw for the table drive is set to zero. The machine is started without engaging the feed so that the hob makes light tooth markings on the outside diameter of the blank. These will indicate the number of teeth being cut. If these are equal to the required number of teeth to be cut, selection of change gears is correct. Now the feed is engaged. The table is fed to the distance equal to the depth of the tooth. After this setting and cutting the gear, the tooth thickness is measured. To thin the tooth further, if required, the table may be further fed.

Cutting Helical Gears on Hobbing Machine

In cutting spur gears with single start hob, the speed (rpm) of the table is equal to that of the hob divided by the number of teeth in the gear being cut. However when cutting helical gear this relationship cannot be maintained; but it is dependent on the lead of the gear, the hands of the hob and the gear. As the hob feeds axially, the gear has to be advanced or retarded depending on the hands of the hob and the gear so as to generate the helix form of the helical gear. This can be better explained by Fig.7. We consider two examples, one cutting a spur, and the second cutting a helical gear with the same hob and with lead L. The hob is fed axially in both the cases with feed rate f mm/rev. initially, for both the spur and helical gears, the radial line PB from the center of the hob tooth is linear with the radial line OA from the center of the tooth space generated in gear, and the points A and B are coincident. Suppose the hob has now traversed axially L/4 distance. For spur gear, the radial line PB and OA are in one axial plane. However for helical gear, OA has to be advanced ¼ revolution with respect to PB so as to generate the helix. Similarly, when the hob has traversed L/2 distance axially, the gear should be advanced by ½ revolution and so on. So when the hob has traversed full lead length L, for the spur gear, the gear (and the radial line PB) would have rotated by N revolutions; but for the helical gear, the gear would have rotated one extra revolution, i.e., it would have done N + 1 revolutions. This compensation to the table speed is given in many machines by differential gearing. Where differential arrangement is not provided, this has to be obtained by a certain relationship between the feed rate and index change gears.

Hobbing Images

Hobbing Process Diagram

Applications of Hobbing

Hobbing is widely used to produce spur, helical gears, worms and worm wheels. It can also be used for producing internal gears for which the machine should have facility for fitting a special head. Hobbing cannot be used where gear is to be produced close to the shoulder having diameter bigger than the root diameter of the gear. Double-helical gear can be hobbed if there is sufficient gap between the helices for the hob over travel. This process is not suitable for producing gears of the type shown.

Shaping of spur and helical gears

Shaping is a gear cutting process where the cutting tool is in the form of a spur/helical gear. The gear teeth are relieved to form cutting edges. The cutting tool and the gear blank mesh on parallel axes as if they are two completed gears in pairs with tool gear having zo teeth and the work piece having z teeth. It means if the tool rotates at n’o rpm, the work piece is made to rotate at n’ rpm, such that –

n' = n’o X zo/z

The tool is fed downward at a feed rate f which is dependent on the material being cut (assuming a vertical configuration of the shaping machine). During the downward stroke, cutting takes place. On the upward stroke, the tool disengages from the job. This disengagement may take place with the table moving out of position. On some newer machines nowadays, the whole spindle assembly moves out of disengagement from the work piece. Up-down axial motion of the tool is normally with crank or lever arrangement. From these basic motions (Fig. 8), it will be seen that shaping is an intermittent generating process as compared with hobbing which is a continuous generating process.

Machine Setting for Cutting Spur Gear

The cutter mounting face and the spindle mounting face are cleaned and the cutter is then mounted on the spindle. The cutter is checked for true running. The blank is then mounted on the table. In the same manner as that for hobbing, the mounting arrangement depends whether it is one off, batch or mass roduction job. For one off and batch production, the work pieces are checked for runout. For mass production, the fixture design should ensure repetitive acceptable runout on the clamped job. The index change gears are calculated and these are fixed. The stroke of the machine is adjusted so that it travels 3 mm beyond the job width for both forward and return strokes. Total stroke is usually kept 6 mm. Longer than the job face-width. The table is moved to feed into the job by hand so that the cutter just grazes the gear blank. The machine is started with infeed kept to zero. The cutter will then mark finely the tooth traces on the outside portion of the gear blank. By counting these traces, it is confirmed that the index gears chosen are correct. In auto cycle, the table moves rapidly from its loading position to a point just before the actual start of tooth cutting. This point can be varied to suit various sizes of the gear blank and the cutter. From this point, the infeed is engaged automatically, and the table continues to infeed until full depth is reached. The table movement then stops at this point and the cutting continues for a further rotation of the blank for a value slightly larger then 360o to ensure that all the teeth are cut to correct depth. After this the table retracts to the starting position and the machine stops. Tooth thickness is measured. If it is found more than the drawing dimensions, the stop point of infeed is shifted to get more depth of cut. Once correct tooth thickness is obtained, further jobs can be cut at this setting. The cycle described here is a single pass cycle as the job is finished in one pass.

In two-pass cycle, the first infeed stops slightly before the full depth is reached thereby leaving finishing stock on the teeth. After one revolution, the finishing infeed starts and continues until full depth is reached. The job rotates further through a rotation slightly larger than 360o. After this the table retracts to the loading position and the machine stops. The job is then unloaded.

Cutting of Helical Gear on Shaping Machine

For generating helical gears by shaping, the cutter should be of helical gear type having hand opposite to that of the work piece. As the cutter and the work piece run on parallel axes to generate the necessary helicoidally involute shape on the work piece with the axial advancement of the cutter, it should rotate angularly in forward or reverse direction depending on the hand of the helix, and the amount of rotation for the given axial traverse will depend on the lead of helix to be cut. This is achieved by using a helical guide for the cutter spindle.

The hand of the helical guide should be the same as that of the cutter and opposite of the work piece helix hand. The other requirement is that the lead of the guide should be equal to the lead of the cutter.

Gear planning of spur gears with rack type cutters:

In this process Sunderland type of gear planer is used. The workpiece axis is horizontal and the cutter is mounted on vertical slide. The cutter traverses vertically downwards during rolling motion of generation. For cutting spur gears the cutter reciprocates horizontally along a line parallel to the work axis.

Gear planning of helical gears with rack type cutters:

For cutting helical gear, the cutter is inclined in a vertical plane to reciprocate along a line inclined to the horizontal. The work axis is vertical, and the cutter is mounted on a vertical slide which can be swiveled in the vertical plane. The cutter reciprocates along the vertical slide, cutting during the downward stroke. During cutting the rolling motion is stopped. During the return stroke the cutter is relieved, and the workpiece is rotated in small increments and moves right to left by an amount equal to the distance a rack would travel for that amount of rotation of workpiece. This process is repeated until the whole gear is cut.

Various Heat Treatment Processes

Surface Hardening:
Hardened steel is hard throughout its structure. Sometimes we need a very hard surface for wear resistance but at the same time, an inner structure to be quite tough so that the dynamic stresses can be resisted. If we can only surface harden toughened steel, we will get such a structure ca be obtained by:
a) Case hardening
b) Nitriding
c) Flame hardening
d) Induction hardening
e) Carbo-nitriding

Case Hardening

In case hardening, outer casing of low carbon steel is enriched with the carbon to approximately 0.85% carbon. So there is outer casing (called the “case”) eutectoid steel. Such steel. Such steel is heated about is upper critical limit and then quenched to form the “case” which hard, and the core which is tough.
Case hardening process then consist of two steps, namely:
a) Enriching the outer case with carbon to about 0.85% this is called carburizing.
b) Hardening

Carburizing
Carburizing can be done either by any of the following processes :
1. solid carburizing
2. liquid carburizing; and
3. gas carburizing

Solid carburizing –
In this process, the parts to be carburized are packed in boxes surrounded by carbonaceous material along with energizer. The boxes are closed type or closed by clay to prevent ingress of air. These boxes are then heated in a furnace at about 9000-950 0C . The carbon from the carbonaceous material combines with oxygen of the energizer to form carbon monoxide. This carbon monoxide decomposed into carbon dioxide and fresh carbon at the surface of the part, and this fresh carbon then diffuses into the steel. Depth of diffusion is dependent on the carburizing temperature and the time of carburization.
Various carbonaceous materials are charcoal, charred leather, crushed bone or horn. Energizers may be barium carbonate, soda ash, etc. Various readymade “packing” materials are available consisting of carbonaceous materials and energizers.

Liquid Carburizing-
In this case the to be carburized is immersed in a liquid bath of sodium cyanide and sodium carbonate maintained at 9000-9500C. The time of immersed depends on the depth of carbon penetration. The percentage of the solution is usually 16-40% depending on the steel and the depth of penetration. It is usual to check and maintain the strength of the cyanide every 24 hours. Cyanide salt bath in addition to providing carbon for carburizing, provides also some nitrogen. Sodium carbonate activates cyanide to increase carburizing action, and to decrease the nitriding action.

Gas Carburizing-
In this case, the parts are heated to about 9000-9500C insatiable gaseous atmosphere. Town gas , natural gas, propane and butane are some of the gases used. In this process the temperature of the gaseous atmosphere, the duration of the treatment and rate of flow of gas need to be control carefully. Advantage of gaseous carburizing is that it gives freedom decarburization.

Hardening-
Cooling the heat treated parts at the required rate is called quenching. Various quenching media are used. Some of them are:
Brine solution, oil bath and air. When a carburized part is directly quenched, coarser structure results. To refine this, first the core is refined by heating the part to 8750C and following by quenching. The case is then refined by heating the part to about 7600C (slightly above the critical point 7500C of the eutectoid steel of the case) and quenching it.

As per BS 970, there are various case hardening steel from En32 to En39, covering form lain low carbon steel (En32-En80A15) to alloy steels with nickel, chromium and molybdenum as alloying elements. These are low carbon steel with carbon less than 0.2% (except for en35-665m25, it is 0.2 to .28%).
SAE steels 1300, 2300, 2500, 4000, 4100, 4300, 4600, 4800, 5100, 8600, 8700, and 9300 series of steels are also suitable for case hardening.
17Mn1Cr95 is one of the case hardening steels, as per IS standard.

Nitriding and Flame Hardening

Nitriding:
In nitriding process, steel is heated in a furnace to a temperature of 4900-5300C ammonia is circulated. Ammonia decomposes to give active nitrogen which diffuses into surface of the steel part to form nitrides. The iron nitride is very brittle, but the nitrides of aluminum, chromium and molybdenum are very hard. For nitriding, ordinary steels cannot be used; special nitriding steels containing aluminum, chromium and molybdenum are used. Nitriding is a very slow process taking anywhere between 50 to 100 hours.
Advantages of nitriding of steels.
1. It gives very hard surface.
2. There is minimum distortion and it gives surfaces free from quenching cracks.
3. Nitrided steel has higher resistance to fatigue.

Flame Hardening:
In flame hardening, the part is heated to a temperature above the upper critical point bye a flame ( usually oxy-acetylene torch) followed by quenching with a jet of water. Rotary parts to be flame-hardened are rotated in front of a flame at slow speed until the entire surface reaches uniform suitable hardening temperature. Then the flame is removed and the part is quenched by a jet of water spray or dropping the part in a quenching bath. If the part is large. It may be rotated very slowly under closely mounted torches so that the part reaches the hardening temperature. This is followed by quenching with water spray. In this case, the part is flame-hardened in one rotation of the part. This process is applied to gears, spindles, cams, etc.

Induction Hardening and Carbo Nitriding

Induction Hardening:

In induction hardening, the part to be hardened is surrounded by a coil through which an electric current at high frequency is passed. Frequency of the current at high frequency of the current will be from 80 kilohertz (80000 Hertz) to 15000 kilohertz depending upon the depth of hardening required. High frequency. Higher the frequency, shallower the depth of heating. The part gets heated by means of this high frequency current to the hardening temperature and then it is quenched to get the necessary hardness. As this is very fast process, it prevent grain growth, decarburization and distortion.



Carbo nitriding:

In carob-nitriding process, diffusion of carbon and nitrogen takes place in a furnace at high temperature and in suitable gaseous atmosphere. Temperature between 6500-9500C can be used, but usual temperatures are between 8200-8400C. The part is then quenched on removal from the furnace. In this process, hardness is not obtained due to nitrides of the alloys and is, therefore, not a nitriding process. The gases used consist of mixture of ammonia and hydrocarbon gas, such as methane, propane, etc.

Gear Finishing

Although many gears “as cut”, either hobbed, planned or shaped are entirely satisfactory for their intended application, for others an additional finishing process is either necessary or desirable. All the mechanical finishing processes in common uses are intended to amend tooth shape by making the flanks confirm more nearly to the true or modified involute desired and to improve surface finish and tooth spacing. The following processes are generally used for finishing of gears:

1. Gear shaving or burnishing

2. Gear grinding

3. Gear lapping

4. Shot blasting

5. Phosphate coating

Gear shaving or burnishing

It is the newest method of gear finishing. It is cold working process accomplished by rolling the gear in contact and under pressure with three hardened burnishing gears. In this case, a cutter harder than the work and in the form of conjugate gear which meshes with it in such a way that when rotated together, relative sliding between the cutter and the work teeth obtained, is used. The teeth of the cutter are serrated normal to the tooth profiles and in operation, the cutter and work are meshed together as helical gears with the planes of their respective axes crossing. In action one member of the pair is driven and makes the other rotate, the new parallelism of the axes causes sliding action between the teeth. The value of the crossed axis angle controls the finish produced to some extent since smaller the angle, finer the finish. Angles ranging between 8o to 45o are generally found most satisfactory.
Shaving improves gear tooth finish where the cutting process has not provided the required standard, ex that with high-speed hobbing but the cut gear must have small errors only in pitch, profile and concentricity. The process is ideal for automative gearbox gears after hobbing and before hardening. The disadvantage of this process is that the surface of tooth is covered with amorphous or smear metal rather than metal having true crystalline structure.

Gear-grinding

Heat-treated gears can be finished either by grinding or by lapping. This process of gear finishing is becoming obsolete these days, as the shaving process is quite satisfactory and cheaper than gear-grinding. But when the high accuracy associated with profile grinding is required, it is the only process to be used. By grinding, teeth can be finished either by generation or by forming. In the former the work is made to roll in contact with a flat faced rotating grinding wheel, which corresponds to the face of the imaginary rack meshing with the gear. One side of tooth is ground at a time. Later on the grinding wheel is given the shape as formed by space between two adjacent teeth and both flanks are finished together. The second method tends to be rather quicker, but both give equally accurate results and which of the method is to be used depends upon the availability of the type of grinding machine. The disadvantage of gear-grinding is that considerable time is consumed in the process and also the surfaces of the teeth have small scratches or ridged which increase both wear and noise. To eliminate these defects ground gears are frequently lapped.

Gear Lapping

It is another extensively used process of gear finishing and is accomplished by having the gear in contact with one or more cast iron lap gear of true shape. The work is mounted between centers and is slowly driven by rear lap. It in turn drives the front lap, and at the same time both laps are rapidly reciprocated across the gear face. Each lap has individual adjustment and pressure control. A fine abrasive is used with kerosene or light oil to assist cutting action. The largest time of gear lapping is about 15 minutes. Prolonged lapping damages the profiles but in exceptional cases the time may be increased for profile and pitch correction.

Automative gearbox gears finished before case hardening by shaving are usually finally lapped.

Shot blasting and Phosphate coating

Shot blasting:

It provides a finishing process resembling that produced by lapping although it has other functions, such as removing slight burrs, reducing stress concentration in tooth fillets and sometimes providing slight tip and root relief to teeth.

Phosphate coating:

It is a chemical process, which attacks the treated ferrous surface and leaves a deposit on it of about 0.01mm in thickness. It prevents or retards scuffing, particularly in hypoid gears, apparently by permitting the engaging tooth surfaces to embed more readily under the prevailing boundary lubrication conditions.

Gear tooth honing for precision

Gear honing is a finishing process that can be applied to external and internal spur or helical gears. Honing can improve the sound quality of shaved, hardened gears by removing nicks and burrs. Also, the process can improve involute, lead, tooth spacing, pitch diameter, run out and surface finish. Typically, shaved gears have a tooth surface finish ranging from 0.6 to 1 micron while honed gears are in the 0.2 to 0.35 micron range. Honing always improves the characteristics of shaved, hardened gears.

Honing can also be used to prolong the wear life and increase the load carrying capacity of hardened ground gears by improving surface finish to a point where upto 80% surface contact can be achieved.

General-purpose honing tools are made in variety of resin and abrasive mixes for gears that have been shaved and heat-treated. They are available in eight grit sizes ranging from 50 to 600 grit. In order to obtain extra critical surface finishes around 0.15 micron and maximize the total tooth contact area on ground or shaved gear teeth that have been honed, use a poli tool. This tool is flexible, porous polyurethane polishing tool that uses an abrasive liquid compound (about 500 grit) during the finishing process.

Honing tools are made in diameters from 85 to 320mm with 25,40,50mm face widths. Most gear hones are made with approximately 225mm diameter.

Honing tools are mounted on special machines in a crossed axes, controlled mesh relationship with the gear to be honed. During the honing cycle, the work gear is run with the honing tool at about 180 rpm. The honing tool is traversed back and forth across the gear face and the direction of rotation of the honing tool is reversed at the end of each stroke. Particles removed by the honing process are flushed away with conventional honing oil.

Tooth rounding and chamfering

When a gear has to slide into mesh, the edges of the teeth on the sliding member and the corresponding edges of teeth on the mating member are rounded to ease meshing. As the cost of rounding tool is more therefore chamfering can also be done.

Gear Inspection

Gear tooth vernier caliper is used to measure the thickness of gear teeth at the pitch line or chordal thickness of teeth and the distance from top of tooth to the chord. The thickness of a tooth at pitch line and addendum is measured by an adjustable tongue, each of which is adjusted independently by adjusting screw on graduated bars. The effect of zero error should be taken into consideration. This method is simple and inexpensive but time consuming.

It needs different setting for variation in number of teeth for a given pitch and accuracy is limited by the least count of instrument. Since the wear during use is concentrated on the two jaws, the caliper has to be calibrated at regular intervals to maintain the accuracy of measurement.

Gear is then inspected for runout. Runout means the eccentricity in the reference or pitch circle. Gears that are eccentric tend to have a vibration per revolution. A badly eccentric tooth may cause an abrupt gear failure. The runout in gears is measured by gear eccentricity testers. The gear is held on a mandrel in the centers and the dial indicator of the tester posseses a special tip descending upon the module of gear being tested. The tip is inserted in between the tooth spaces. The gear is rotated tooth by tooth. The maximum variation is noted from the dial indicator reading and it gives the runout of the gear.

Parkinson Gear Tester

The principle of this device is to mount a standard gear on a fixed vertical spindle and the gear to be tested on another similar spindle mounted on a similar spindle mounted on a sliding carriage, maintaining the gears in mesh by spring pressure. Movements of the sliding carriage as the gears are rotated and indicated by a dial indicator, and these variations are a measure of any irregularities in the gear under test , alternatively a recorder can be fitted , in the form of a waxed circular chart and records made of the gear variation in accuracy of mesh.

The gears are mounted on the two mandrels , so that they are free to rotate without measurable clearance. The left spindle can be moved along the table and clamped in any desired position. The right mandrel slide is free to move, running on steel balls , against spring pressure and it has a limited movement. The two mandrels can be adjusted so that their axial distance is equal to the designed gear center distance.

When the waxed paper recorder is fitted, the chart makes a revolution for each one of the gears mounted on the sliding carriage. As the chart moves and rotates, the line traced records the movements of floating carriage. A circle is drawn at the same time as the record as shown in figure 12.

Gear Failure

Failure in gears occur due to mainly these two reasons:

1. Failure due to breakage.

2. Surface failue.

Breakage failure:

Breakage of tooth normally occurs at the root of tooth around the fillet which is under tension because this is the area which is highly stressed. Breakage may occur due to high stress or fatigue. In failure due to high stress, tooth breaks down when the loading exceeds the ultimate tensile stress of the material. This type of failure is not very common and may occur due to load reaching accidentally high value, for example , due to drive getting jammed. Breakage failure is mainly due to:

i. Incorrect assessment of load.

ii. Impact loads.

iii. Misalignment of the axes of mating gears.

iv. Errors in gear teeth.

Surface failure:

Most common observed surface failures are:

i. Failure due to pitting.

ii. Failure due to plastic flow.

iii. Failure due to scoring or scuffing.

Pitting and failure due to plastic flow

In this type of failure pits are formed on the tooth flank. These pitted areas can occur on the addendum as well as on the dedendum side of the tooth. Initially a crack is formed in tooth flank, which may be due to various reasons. One reason may be due to high localization of stresses. Into this crack, oil will be forced due to the oil film pressure. If the movement of the tooth load is such that it closes the mouth of its crack thereby preventing the oil from escaping, the pressure of this trapped oil increase more and more as the load progresses further. This will extend the crack along the line of maximum stress and a pit will be formed.

Failure due to plastic flow:

Pitting is particularly observed with case hardened gears and with quenched and tempered gears. With softer steels, when the loading is high enough to exceed the yield stress, plastic flow of material takes place and the tooth form is damaged.