Machine Shop Machine Shop TechnologyTechnology

A Presentation byS.Krishnamorthy, IRSME

(Retd)For Polytechnic College students of Tamil Nadu

sk@cyberbrahma.com

Unit - IVUnit - IV

Gear Manufacturing Practice

Forming and Generating

Involute tooth

Involute

Involute

Steering GearSteering Gear

Use of Rack and PinionUse of Rack and Pinion

Rack RailwayRack Railway

Escapement in a clockEscapement in a clock

Balance StopBalance Stop

Mechanical ClockMechanical Clock

Gear Manufacturing ProcessesGear Manufacturing Processes

• Casting• Stamping• Rolling• Extruding• Powder Metallurgy• Machining

Methods of Machining (cutting) Methods of Machining (cutting) GearsGears

•Forming

•Template

•Generating

Forming GearsForming Gears

• Single point cutting tool• Multipoint cutting tool• Simple and cheaper• Less accurate• Can be done in shaper, slotter,

broaching or milling machines• Formed disc cutter – to the shape of

space between teeth

Forming GearsForming Gears

Forming gears in a milling Forming gears in a milling machinemachine

• Disc type cutters are used• Spur, helical and straight bevel

gears are made in this process• Milling cutter is mounted on a

horizontal arbor• Indexing is done to cut each tooth• Tooth profile may not be accurate

Dividing HeadDividing Head

• Dividing heads are used for: Holding and Indexing the workpiece (gear blank)

• Indexing is the process of dividing the periphery of the workpiece into any number of equal divisions.

Plain or Simple dividing Plain or Simple dividing HeadHead

Simple Dividing HeadSimple Dividing Head

• It is used for “simple indexing”• Index crank and plate are on one end

and they rotate as one unit• It has a cylindrical spindle with work

on one end and index plate on the other

• Index plate is rotated and locked in position by a lock pin

• Index plate has equally spaced slots on the periphery to facilitate locking after indexing

Universal Dividing HeadUniversal Dividing Head

• Universal Dividing head is used: As a work holding device (horizontal,

vertical or inclined at angle to the table or cutter)

For Indexing the workpiece (gear blank)

• It is also used for rotating workpiece at a ratio to the table feed rate to produce helical grooves on gears.

• It can divide the blank into more number of divisions than that is possible in plain dividing head.

Universal Dividing Head

1-shaft; 2-index crank; 3-index-crank pin; 4-index plate; 5-housing; 6-swivel block of housing; 7-lock; 8-driving dog; 9-spindle; -10-plate for direct indexing; 11-tailstock.

The construction of the index The construction of the index headhead

1-index plate; 2-index crank; 3-spindle; 4-worm wheel (z=40); 5-necks to receive pick-off gears; 6-worm (k=1); 7-sector arm.

Dividing HeadDividing Head

Methods of IndexingMethods of Indexing

• Direct or Rapid Indexing

• Plain or Simple Indexing

• Differential Indexing

• Angular Indexing

Direct IndexingDirect Indexing• Direct Indexing (Rapid Indexing) is the

simplest form of indexing. Used for quick indexing of workpiece.

• The direct indexing plate is mounted on the nose of the dividing head spindle which also carries the work.

• The number of divisions required by direct indexing is limited by the number of holes/slots in the direct indexing plate.

• Direct indexing plates are available with 24, 30 and 36 holes or slots. It is possible to index any number of divisions which is a factor of total holes/slots in the plate

Direct Indexing in Universal Direct Indexing in Universal Dividing HeadDividing Head

• To perform this type of indexing, the worm shaft must be disengaged from the worm gear wheel.

• Since most direct indexing plate have 24 holes, all divisions which are factors of 24 (24, 12, 8, 6, 4, 3, 2) can be produced with this plate.

• Indexing data = N T• N – No. of holes in Indexing Plate• T – No. of required divisions

Example: What is the index movement required to mill 8 slots on a workpiece?

• N T = 24 8 = 3 (3 holes on a 24 hole circle)

Direct IndexingDirect Indexing

• Whenever starting to machine the first hole, it is necessary to make sure that the indexing pin is in the hole or slot No. Zero or 24 of the indexing plate.

• After doing the necessary indexing movement, it is required to clamp the indexing spindle so that the cutting force will not go onto the indexing plate and indexing pin.

Plain Indexing (or) Simple Plain Indexing (or) Simple IndexingIndexing

• Used for divisions beyond the range of direct indexing

• Universal Dividing Head is used for this• The Indexing plate should be locked

with the body• Worm and worm gear is to be engaged• Dividing head is rotated by turning the

index crank and locked at the next indexed hole on the plate

Simple IndexingSimple Indexing

• 40 turns of indexing crank = 1 revolution of index head spindle

• Index plates with concentric circles of holes:• Plate: 1 - 15, 16, 17, 18, 19, 20• Plate: 2 - 21, 23, 27, 29, 31, 33• Plate: 3 – 37, 39, 41, 43, 47, 49

• Index crank movement = 40/N (N = number of divisions required)

• For cutting 30 teeth, 40/30 = 1 + 1/3 = 1 + 7/21 (One complete turn of indexing crank and 7 holes in 21 hole circle of the index plate)

Differential IndexingDifferential Indexing

• This method is used for divisions that could not be indexed by simple indexing

• The required division is obtained by combination of:– Movement of the index crank similar to

simple indexing– Simultaneous movement of the index

plate when the crank is turned

• The rotation of the index plate may be in the same direction or opposite to the crank rotation

Differential IndexingDifferential Indexing• Lock pin is disengaged to permit rotation

of index plate• A sleeve with bevel gear is connected to

the index plate• The sleeve and the bevel gear are free to

rotate on the worm shaft• Another bevel gear engages with it and the

shaft of that gear has change gears that mesh with the gear mounted on the back of the main spindle

• Crank rotates the spindle• Spindle’s motion is transmitted to index plate

through change gears

Rule for Differential Rule for Differential IndexingIndexing

1. Gear Ratio = Driving gear/Driven gear(= Gear on the spindle/Gear on the bevel gear shaft)

= (A-N) X 40/Awhere: N = The required number of divisions to be indexed A = a number nearer to N which can be indexed by

plain indexing (assumed number)

2. Index Crank Movement for each division = 40/A

(Index crank is to be moved by this amount for N number of times for complete division of the work)

Rule for Differential Rule for Differential Indexing Indexing (contd..)(contd..)

3. Number of idlers in the change gears:If (A-N) is positive, the index plate must rotate in

the same direction as the crankIf (A-N) is negative, the index plate must rotate

in the opposite direction to the crankTo achieve the correct direction of rotation,

number of idle gears is obtained as follows:

A-N Simple gear train Compound gear train

Positive One idler No idler

Negative

Two idlers One idler

Rule for Differential Rule for Differential Indexing Indexing (contd..)(contd..)

Change gears with following numbers of teeth are generally supplied:

24, 24, 28, 32, 40, 44, 48, 56, 64, 72, 82, 100

With these gears and the three sets of standard index plates, it is possible to index any number from 1 to 382.

Simple change gearsSimple change gears

Compound change gearsCompound change gears

Compound change gearsCompound change gears

Selection of gearsSelection of gears

Angular IndexingAngular Indexing• Angular indexing is the process of dividing

the periphery of a work in angular measurements and not by the number of divisions.

• Indexing method is similar to plain indexing

• One complete turn of crank will cause the spindle and the work to rotate through 360/40 = 9◦

• Index crank movement = Angular displacement in deg/9Angular displacement in minutes/540Angular displacement in seconds/32400

Linear IndexingLinear Indexing

• Linear indexing is used for moving the work table to the required distance lengthwise during rack milling

• It is the method of dividing the linear distance into number of equal divisions

• When the crank is rotated, the table is moved longitudinally through a gear train

Terms used in spur gearTerms used in spur gear

• Face: The surface of the tooth between the pitch line and top of the tooth

• Flank: Surface between the pitch line and bottom of the tooth

• Tooth surface: Face + Flank• Clearance: The radial distance from

the top of the tooth to the bottom of the tooth space in the mating gear

• Root Circle: Circle that contains the bottom of the teeth

Terms used in spur gear Terms used in spur gear (contd..)(contd..)

• Pitch circle: An imaginary circle through the pitch point with its centre at the axis of the gear

• Pitch Diameter: Diameter of the pitch circle

• Pitch Line: The line of contact of two pitch surfaces

• Circular Pitch (p): The distance measured on the circumference of the pitch circle from a point on one tooth to the corresponding point on the next tooth

•Addendum: Radial height from the pitch circle to the tip of the tooth• Dedendum: Radial depth from the pitch circle to the bottom of the tooth•Module (m): The pitch diameter (in mm) divided by the number of teeth•Line of Action: Line along which the force between two meshing gear teeth is transmitted. This is tangential to the base circle of the gears

Terms used in spur gear Terms used in spur gear (contd..)(contd..)

•Base Circle: An imaginary circle used in Involute gearing to generate the involute that forms the tooth profile•Pressure Angle: The angle between line of action and the line perpendicular to the line joining gear centres•Pressure Angle: The angle between the common normal at the point of tooth contact and the common tangent to the pitch circles•Pressure Angle: The angle between the line of action and common tangent

Terms used in spur gear Terms used in spur gear (contd..)(contd..)

Line of ActionLine of Action

• Two involute gears, the left driving the right• Blue arrows show the contact forces between them. • The force line (or Line of Action) runs along a tangent common to

both base circles.

Involute curve

Spur gear proportions as per BISSpur gear proportions as per BISModule: m. No. of teeth: Z. Pressure angle: 20°

S.No Name of tooth element Gear tooth proportions

1. Pitch diameter Zm

2. Addendum m

3. Dedendum 1.25m

4. Working depth 2m

5. Tooth depth 2.25m

6. Outside diameter (Z+2)m

7. Tooth thickness 1.5708m

8. Clearance 0.25m

9. Circular pitch π m

10. Radius of fillet 0.4m to 0.45m

1.Calculation of gear tooth proportions:• Blank dia: (Z+2)m• Tooth depth: 2.25m

2.Indexing calculations:• 40/N = 40/Z : crank rotation + index

holes

3.Set the dividing head & tailstock - parallel to table (perpendicular to machine spindle)

Spur gear milling procedureSpur gear milling procedure

4.Mount gear blank: on a mandrel between centres

5.Selection of suitable form cutter: • From the standard table of involute

gear wheels• Cutter selected according to

number of teeth • 8 cutters for each module

Spur gear milling procedureSpur gear milling procedure

6.Setting suitable cutting speed and feed:• Speed should be slightly lower than

plain milling

• Feed: normal

7.Mounting and centering the cutter:• Aligning centre of cutter with centre

of tailstock

• Aligning with two edges and then at the top

Spur gear milling procedure Spur gear milling procedure (contd..)(contd..)

Centering the cutterCentering the cutter

8.Depth of cut• It is equal to full depth of gear tooth for

small blanks• Raise the table to till periphery of gear

blank just touches the cutter• Set the micrometer dial of vertical feed

screw to zero• Raise the table further to give the required

depth of cut

Spur gear milling procedure Spur gear milling procedure (contd..)(contd..)

9.Start the machine, give feed and cut the first tooth

10.Bring back the table to starting position

11.Index the gear blank to the next tooth space

12.Continue this procedure till all the required gear teeth are cut

Spur gear milling procedure Spur gear milling procedure (contd..)(contd..)

13.Continue this procedure till all the required gear teeth are cut

14.Inspection of gear teeth:• After the first tooth is formed, check

the tooth profile with gear tooth vernier

• Tooth depth should be = 2.25m• Chordal thickness of tooth should be =

1.5708m

Spur gear milling procedure Spur gear milling procedure (contd..)(contd..)

Gear tooth vernier caliper

Helical gear tooth Helical gear tooth proportionsproportions

S.No Name of tooth element

Tooth proportions in terms of normal module with 20° pressure angle

1. Pitch diameter Zm

2. Addendum Mn

3. Dedendum 1.25 Mn

4. Tooth depth 2.25 Mn

5. Outside diameter Zm + 2 Mn

6. Normal tooth thickness

1.5708 Mn

Where Normal Module “Mn” = m cos αm = Moduleα = Helix angle

Helix AngleHelix Angle

Helix AngleHelix Angle

Helical gear milling Helical gear milling procedureprocedure

Helix AngleHelix Angle

• In helical gear milling, only direct and simple indexing can be used

• Since the change gear train connected to the spindle (worm shaft) will be geared to the lead screw which will drive the spindle through face plate and crank, differential indexing could not be employed

Helical gear milling Helical gear milling procedureprocedure

Gearing arrangement for Gearing arrangement for Helical gear millingHelical gear milling

• A train of gears is connected to the table lead screw

• Lead screw drives the face plate through change gears and bevel gears (lock pin removed)

• Crank pin is kept engaged in any one hole

Change gears for helical Change gears for helical millingmilling

• Change gears cause work to move by a distance equal to the “lead” of the helix

• During the same interval, work (blank) rotates by one complete revolution

Change gears for helical Change gears for helical millingmilling

Circumference and Lead of Circumference and Lead of HelixHelix

Table setting for Helical Table setting for Helical gear millinggear milling

Equivalent spur gear teethEquivalent spur gear teeth • A cutter used to produce a spur gear of

same number of teeth as helical gear will not serve the purpose.

• So an equivalent number of teeth is to be found for selection of cutter (with the correct profile)

• Formula: Z’ = Z/cos³ α• Z’ = the number of teeth based on which

cutter is selected• Z = The actual number of teeth• α = Helix angle

Equivalent spur gear teethEquivalent spur gear teeth

Equivalent spur gear teethEquivalent spur gear teeth

Equivalent spur gear teeth Equivalent spur gear teeth (virtual)(virtual)

• It is the distance travelled by the milling machine table for one revolution of the work (blank) when it is assumed that the lead screw is connected to the worm shaft by 1:1 gear ratio.

• For one revolution of the job, worm shaft has to be rotated by 40 turns

““Lead of the machine”Lead of the machine”

• Hence lead screw rotates by 40 turns

• Table moves by 40 X p mm. “p” is the pitch of lead screw.

• Pitch of lead screw is generally = 6 mm

• Hence lead of the machine = 40 X 6 = 240 mm

““Lead of the machine”Lead of the machine”

• Let “p” = pitch of the lead screw in mm

• And T = Lead of the helix to be milled in mm

• No. of turns of lead screw for moving the table through the Lead “T” = T/p

• No. of turns of worm shaft/No of turns of lead screw = 40 ÷ T/p = 40 x p/T

““Lead of the machine”Lead of the machine”

• Driver/Driven = 40p / T

• “40p” is called “Lead of the machine”

• “T” is called “Lead of the work”

• Driver/Driven = Lead of the machine/ Lead of the work

““Lead of the machine”Lead of the machine”

• Gear on the lead screw is the driver. The gear on the bevel sleeve is the driven gear

Helical gear milling Helical gear milling procedureprocedure

Lead of the machine

Lead of the work

Driver teeth

Driven teeth=

40p

πD/tan α=

Where p = pitch of the lead screw; D = pitch circle diameter; α = Helix angleDriver teeth/Driven teeth = A/B X C/D(A and C are driving gears. B and D are driven gears)

Milling of Straight bevel Milling of Straight bevel gearsgears

Bevel gears in meshBevel gears in mesh

Bevel gear termsBevel gear terms

Meshing bevel gearsMeshing bevel gears

Steps for milling a straight bevel Steps for milling a straight bevel geargear

1. Calculation of gear tooth proportions

2. Indexing arrangement3. Setting the gear blank at the cutting

angle4. Calculation of offset5. Selection of cutter6. Selection of speed and depth of cut

Bevel gear tooth Bevel gear tooth proportionsproportions

S.No

Name of tooth element

Tooth proportions for 20° pressure angle

Symbol

1. Pitch diameter Zm d

2. Addendum (large end)

1 m ha

3. Dedendum (large end)

1.25 m hd

4. Tooth depth (large end)

2.25 m h

5. Tooth thickness (large end)

1.5708 m s

6. Circular pitch π m p

Bevel gear elements and Bevel gear elements and anglesangles

S.No

Name of tooth element

Symbol Formula

1. Face width b b = 0.5 to 0.33 R

2. Cone distance R R = 0.5 / sin β3. Addendum

angleθa tan θa = ha / R

4. Dedendum angle

θd tan θd = hd / R

5. Pitch cone angle

β Sin β = 0.5 d / R

Milling straight bevel gearsMilling straight bevel gears

• Gear blank is turned to a conical shape• Direct or simple indexing method is

used• Dividing head spindle is swivelled such

that the Root line of the gear is parallel to the table

• The tilting angle is cutting angle• Cutting angle = Pitch cone angle –

Addendum angle

Special cuttersSpecial cutters

Gear cutting with single point Gear cutting with single point cuttercutter

Gear cutting with single point Gear cutting with single point cuttercutter

Shear Speed ShapingShear Speed Shaping

Formed End mill cutterFormed End mill cutter

Gear BroachingGear Broaching

Gear BroachingGear Broaching

Template MethodTemplate Method

Gear Generating ProcessGear Generating Process

Gear generation is based on the fact that “any two involute gears of the same module will mesh together”

Gear teeth are generated in the gear blank because of the relative rolling motion of the cutter and the blank.

One of the mating gears in a cutter which reciprocates and also rotates as a mating gear.

Accurate tooth profile is generated in this process.

• Gear shaping (pinion cutter)

• Gear planing (Rack cutter)

• Gear hobbing

Gear generating methodsGear generating methods

Gear shapingGear shaping

Gear shapingGear shaping

Gear shapingGear shaping

Gear shapingGear shaping

Gear shapingGear shaping

Gear PlaningGear Planing

Gear Planing RackGear Planing Rack

Gear Planing with a rack Gear Planing with a rack cuttercutter

Gear Planing with a rack Gear Planing with a rack cuttercutter

Gear HobbingGear Hobbing

Hobbing is a process of generating a gear using a rotating tool called “Hob”.

The hob has helical threads

The threads have grooves cut parallel to the axis to provide cutting edges.

The gear teeth are cut into the workpiece by a series of cuts made by the hob.

It is the most widely used gear cutting process for creating spur and helical gears.

Gear HobbingGear Hobbing• Gear hobbing is a multipoint machining process in which gear teeth are progressively generated by a series of cuts with a helical cutting tool (hob). 

• Both the hob and the workpiece revolve constantly as the hob is fed across the face width of the gear blank.

• They rotate in a timed relationship

• A proportional feed rate is maintained between the gear blank and the hob

• Several teeth are cut on a progressive basis

• It is used for high production runs

HobsHobs

Gear HobbingGear Hobbing

Gear HobbingGear Hobbing

Gear HobbingGear Hobbing

Gear Generating Gear Generating comparisoncomparison

Gear HobbingGear Hobbing

Gear HobbingGear Hobbing

Gear HobbingGear Hobbing

Gear HobbingGear Hobbing

Gear HobbingGear Hobbing

Gear HobbingGear Hobbing

Gear HobbingGear Hobbing

Vertical Hobbing MachineVertical Hobbing Machine

Vertical Hobbing MachineVertical Hobbing Machine

Various Gear CuttersVarious Gear Cutters

Gear ShavingGear Shaving

Gear Shaving CutterGear Shaving Cutter

Gear GrindingGear Grinding

Gear GrindingGear Grinding

Thank you!Thank you!