A MINI PROJECT REPORT ON

“MANUFACTURING PROCESS OF HELICAL

GEARS BY BROACHING”

Submitted by

MOHD IRFAN

MA MAJEED KHAN

MOHD RAHEEMUDDIN

FAZLUR RAHMAN

In partial fulfillment of their requirements for the award of degree of

BACHELOR OF TECHNOLOGY

IN

MECHANICAL ENGINEERING

During the year 2010 – 11

VIJAY RURAL ENGINEERING COLLEGE

Rochies Valley, Manikbhandar,

Nizamabad-503003

(Affiliated to Jawaharlal Nehru Technological University)

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VIJAY RURAL ENGINEERING COLLEGE

DEPARTMENT OF MECHANICAL ENGINEERING

This is to certify that this Project entitled

“MANUFACTURING PROCESS OF HELICAL GEAR BY

BROADHING PROCESS”

Submitted by

MOHD IRFAN

M.A MAJEED KHAN

MOHD RAHEEMUDDIN

FAZLUR RAHMAN

Is a bonafide record of work carried out by them under my guidance

and supervision in partial fulfillment of the requirements for the Degree

of Bachelor of Technology from the Department of Mechanical

Engineering by Jawaharlal Nehru Technological University for the

Academic Year 2010 – 2011.

Mr. P SAMPATH RAO Mr. B PRASHANT REDDYHead of the Department, Internal Guide.Mechanical Engineering. External Guide

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ACKNOWLEDGEMENT

We would like to take this opportunity and express our heartfelt thanks to all

those who helped me in the course of this project work.

We are very much grateful to Dr. B R VIKRAM, Principal of Vijay rural

Engineering College for having provided us the opportunity for taking this project.

We are thankful to our Project Internal Guide Mr. B PRASHANT REDDY and

our Head of the Department, Mr. P SAMPATH RAO, M.Tech for their valuable

suggestions in the completion of the project.

We would like to convey our thanks to other staff members, who also guided us in our

endeavours and also extending their helping hands

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INDUSTRY OVERVIEW

It all started in 1969, when ‘Shanthi Engineering & Trading Co.’ was established. This company started manufacturing small gears by way of simple manufacturing process like milling. In 1972, it was converted to Shanthi Gear Products (P) Limited.Our guiding principle since then has been always “quality gears”. Slowly but steadily our business expanded. So also the quality, range, Customers and services. Soon, we became the No. 1 (loose) gear manufacturer in the country both in terms of quality and volume

Propelled for growth, in 1980, Shanthi Gears decided to go in for the manufacture of Worm Reduction Gear Boxes. Braving competition from leading manufacturers including multinationals, Shanthi Gears’ Worm Reduction Gear Boxes gained quick market acceptance. Today, it is rated way above the competition

Simultaneously, production of Helical Gear Boxes also started in single, double, triple, and quadruple reductions and in various combinations. Hollow shaft Gear Boxes were also introduced. Solid shafts and Hollow shaft Bevel Helical Reduction Gear Boxes followed suit.

In 1986, Shanthi Gears became a joint stock Company and it is now being listed in the major Stock Exchanges.

The philosophy of Shanthi Gears  has been -- the quality of the finished product is always the sum total of the quality of the raw materials and the components put in. Consequently, facilities for manufacturing Patterns, Centrifugal Castings of phosphor bronze rings, Ferrous Castings, Aluminum Castings, Heat Treatment, Forgings, Fabrications and Cutter Manufacturing were also set up, in-house.

Designing, developing and manufacturing standard and customised products akin to International quality levels at competitive prices, with timely deliveries by increased efficiency and infusion of quality consciousness at all rank and fileActing upon customer problems with speed, courtesy and competenceUltimately ensuring total customer satisfaction. 

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Total Area of the Land » 5,661,051 sq. ft. (526,120 sq. mt.)

Total Area of the Building » 945,098 sq. ft. (87,834 sq. mt.)

Total connected load » 11,438 KW (approx.)

Diesel Generators » 6,242.5 KVA

Own Wind Mills » 6.66 Mega Watt

Number of Employees » 903

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ABSTRACT

In Industries we require mechanism, one of the tools like Gear. A gear is component with in a transmission device that transmits rotational torque by applying a force to the teeth of another gear or device. This project consists of manufacturing of helical gears using broaching process in Shanti Gears Located in Coimbatore.

A helical gear offers a refinement over spur gears. The leading edges of the teeth are not parallel to the axis of rotation, but are set at an angle. Since the gear is curved, this angling causes the tooth shape to be a segment of a helix. The angled teeth engage more gradually than do spur gear teeth. This causes helical gears to run more smoothly and quietly than spur gears.

Helical gears can be meshed in a parallel or crossed orientation. The former refers to when the shafts are parallel to each other; this is the most common orientation. In the latter, the shafts are non-parallel. For a crossed configuration the gears must have the same pressure angle and normal pitch, however the helix angle and handedness can be different.

Here, Helical gear is for both perpendicular and parallel movement and works on the principle of transmitting rotational torque.

Broaching is a machining operation which uses a toothed tool, called a broach to remove material. The broach is used in a broaching machine, which is also sometimes shortened to broach. It is used when precision machining is required, specially for odd shapes. Broaching finishes a surface in a single pass, which makes it very efficient. Commonly machined surfaces include circular and non-circular holes, splines. And flat surfaces. Typical work pieces include small to medium sized castings, forgings, screw machine parts, and stampings. Even though broaches can be expensive, broaching is usually favorable to other processes when used for high-quantity production runs.

Broaches are shaped similar to a saw, except the teeth height increases over the length of the tool. Moreover, the broach contains three distinct sections: one for roughing, another for semi-finishing, and the final one for finishing. Broaching is a unique machining process because it is the only one to have the feed built into the cool. The profile of the machined surface is always the inverse of the profile of the broach. The rise per tooth (RPT), also known as the step or feed per tooth, determines the amount of material removed and the size of the chip. The broach can be moved relative to the work piece or vice-versa. Because all of the features are built into the broach no complex motion or skilled labor is required to use it.

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CONTENTS

1. GEARS PGNO 1.1 INTRODUCTION TO GEARS 1-41.2 HOW DO GEARS WORK? 4-51.3 USES OF GEARS 5-61.4 CONCEPT OF GEAR RATIO 6-71.5 COMPOUND GEAR RATIO 7-81.6 NOMENCLATURE 8-20

2. GEAR MANUFACTURING PROCESS2.1 STEPS IN THE MANUFACTURING PROCESS 20-22

OF GEARS 3. TYPES OF GEARS

3.1 BEVEL GEARS 23-243.2 SPUR GEARS 24-243.3 WORM & WORM WHEEL 24-253.4 RACK & PINION 25-253.5 CROWN GEAR 25-263.6 HELICAL GEAR 27-28

4. TYPES OF HELICAL GEARS4.1 HELICAL GEAR 28-294.2 DOUBLE HELICAL GEAR 30-304.3 HERRINGBONE HELICAL GEAR4.4 INTERNAL HELICAL GEAR

5. BROACHING PROCESS5.1 BROACHING MACHINES 31-325.2 TYPES OF BROACHES 33-33

5.2.1 INTERNAL BROACHES 33-345.2.2 EXTERNAL BROACHES 34-355.2.3 BLIND-SPLINE BROACHES 35-35

5.2.4 EXTERNAL “POT” BROACHES 35-35

6. MILLING OPERATION-BACKLASH 6.1 BROACHING PINCIPLES 36-37 6.2 HINTS FOR SUCCESSFULLY BROACHIG 38-40 7. CONCLUSION 41-41

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MANUFACTURING OF HELICAL GEAR BY BROACHING PROCESS

1. Gears

1.1. Introduction to Gears:

This section explains the meaning of a few basic gear terms, including pitch diameter, diametral pitch, pressure angle, line of contact, involute profile, tangential force and separation force.

The purpose of gears is to transmit uniform rotary motion from one shaft to another, and often, to turn the driven shaft at a different speed than the driving shaft.

Imagine two circular wheels of different diameters, in contact with each other at their outside diameters, with one wheel turning at a constant speed, and driving the other wheel by friction, with no slippage between the mating surfaces. The motion imparted to the driven wheel would be uniform rotary motion.

Two gears in mesh behave like the two circular wheels described above. The pitch diameter of each gear is the outside diameter of its effective circular wheel. The two pitch circles touch at a point on the straight line between the two gear centers (the point of tangency).

The pitch circles of the two gears pictured below are marked PD1 and PD2 respectively, and touch each other at the point of tangency. The (vertical) centerline connects the center point of each gear. The point of tangency lies at the intersection of the centerline and the two pitch circles. The horizontal line marked TAN is perpendicular to the centerline and passes through the point of tangency.

Two gear teeth in mesh with each other are essentially two cams which have profiles developed to implement the required uniform rotary motion, while being able to transmit much greater forces than would be possible by friction contact between two wheels.

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Involute

The profile which accomplishes that function is a mathematical function known as an involute.

Involute profile

The nature of the involute profile is such that at any point from the beginning of mesh to the end of mesh, the contact point of the two tooth faces lies along a straight line (the line of contact, marked LOC in the picture).

Pressure Angle(PA)

The gear's pressure angle (PA) is the angle between the TAN line and the line of contact  (LOC). Meshing gears must have the same pressure angle.

Normal Force

The the force which the tooth on the driving gear applies to its mating tooth on the driven gear is applied along the line of contact, and is known as the “normal (perpendicular to the surface) force”. Look at the picture closely and you can see two pairs of teeth in contact, and the points of contact are both on the LOC.

Because the involute profile maintains the contact point along the LOC, the effective contact point between the two gears remains at the point of pitch-circle tangency. That causes the motion imparted to the driven gear to be uniform angular motion.

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The normal force (the force along the LOC) which the driving gear applies to the driven gear at the point of contact is generally handled as two perpendicular components:

(a) the tangential force, and

(b) the separation force.

Tangential Force

The tangential force is applied by the driving gear along the line marked TAN. The value of the tangential force is “the input torque divided by the pitch radius (half the pitch diameter)”.

“ Tangential force=input torque/pitch radius.”

The separation force is applied along the centerline between the centers of the two gears, and is trying to drive the two gears apart from each other.

Pressure Angle(PA)

The relationship between tangential and separation forces is determined by the pressure angle (PA) of the gears. From simple trigonometry and the picture above, it is clear that the normal force is the tangential force divided by the cosine of the pressure angle, and the separation force is the tangential force times the tangent of the pressure angle.

Diametral pitch(DP)

The term diametral pitch (DP) describes gear tooth size, and is defined as "the number of teeth per inch of pitch diameter".

As an example, a 6-DP gear with 21 teeth has a pitch diameter of 3.5 inches (21 ÷ 6= 3.5). Now picture that 21-tooth gear meshed with a 6-DP, 47 tooth gear. The 21-tooth gear has a mean torque of 625 lb.-ft. applied to it. The force tangential to the pitch circle is 4286 pounds:

Tangential Force = (625 lb-ft x 12 inches per foot) ÷ (3.5 inches ÷ 2)

Tangential Force = 7500 ÷ 1.75 = 4286 lbs.

The separation force is 4286 x TAN(20) = 4286 x .364 = 1560 lbs.

The normal force is 4286 ÷ COS(20) = 4286 ÷ 0.94 = 4560 lbs.

The normal force must be counteracted by the bearings which support the gear shafts.

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These loads are sometimes referred to as "static" gear loads, because they can be generated by statically loading the input shaft at the specified input torque, without any motion being imparted to the gears.

A gear is a wheel with teeth that mesh together with other gears.

A gear is a mechanism used to transmit force from one part of a machine to another. Gears are present in virtually all machines that have spinning parts, like car engines and watches. The origin of gears predates Roman civilization. Presently, gears enjoy widespread use in industries from aerospace to toy manufacturing. These versatile and powerful components come in a variety of forms to suit every mechanical need.

  Gears are a means of changing the rate of rotation of a machinery shaft. They can also change the direction of the axis of rotation and can change rotary motion to linear motion.

Unfortunately, mechanical engineers sometimes shy away from the use of gears and rely on the advent of electronic controls and the availability of toothed belts, since robust gears for high-speed and/or high-power machinery are often very complex to design. However, for dedicated, high-speed machinery such as an automobile transmission, gears are the optimal medium for low energy loss, high accuracy and low play.

1.2 How Do Gears Work? Gears are used in tons of mechanical devices. They do several important jobs, but most important, they provide a gear reduction in motorized equipment. This is key because, often, a small motor spinning very fast can provide enough power for a device, but not enough torque. For instance, an electric screwdriver has a very large gear reduction because it needs lots of torque to turn screws, but the motor only produces a small amount of torque at a high speed. With a gear reduction, the output speed can be reduced while the torque is increased.

Another thing gears do is adjust the direction of rotation. For instance, in the differential between the rear wheels of your car, the power is transmitted by a shaft that runs down the center of the car, and the differential has to turn that power 90 degrees to apply it to the wheels.

There are a lot of intricacies in the different types of gears. In this article, we'll learn exactly how the teeth on gears work, and we'll talk about the different types of gears you find in all sorts of mechanical gadgets.

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Emerson Power Transmission Corp.

Gears are found in everything from cars to clocks

There are various different types of gear available these days. However, the sprue gear is considered to be the basic design. The main features of this gear are the teeth of the adjacent gears which are straight and in direct contact with each other. They are used for gear

1.3.1 Uses of Gear:

The usage of gears has no limits .They are used for everyday purposes more and

more frequently. There are three major uses for gears. They change the direction of the

rotation, the torque and the rotational speed. Gears can either be used to lower the speed

by coordinating the multiple

 shafts for varying high speeds. High speed and high torque can also be achieved by

manipulating the gear sizes.

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Gears change the

• speed• torque (rot. force)

• direction

1.4 Concept of Gear Ratio:

Gears are available in various sizes which are chosen according to the mechanical

needs of the operator, either to increase or decrease speed. Gear ratio is determined by the

change in the source of energy which is identified by the change in size of the gears. This

creates a mechanical advantage which is the most important feature of a gear. Modern

gears have a special tooth which is called an involute, this maintains a moderate speed

among two gears.

The gear ratio is the ratio of the number of teeth on one gear to the number of teeth

on the other gear.

The gear ratio tells you the change in speed and torqueof the rotating axles.

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1.5 Compound Gear ratio:

When more than one pair of gears are used together, that is called a compound gear train. The gear ratios for each individual gear pair are multiplied together to compute the overall compound gear ratio for the gear train.

Let's look at an example. The gearbox on the right has two pairs of gears. The first pair of gears has an input gear with 8 teeth and an output gear with 40 teeth. The gear ratio of this gear pair is 40 to 8 or, b y simplifying, 5 to 1.

The second pair of gears has an 8 tooth input gear meshed with a 24 tooth output gear. The gear ratio of this pair is 24 to 8 or, again simplifying, 3 to 1. Notice that the 8 tooth gear of the second gear pair is on the same axle as the the 40 tooth gear of the first gear pair. The output axle from the first gear pair becomes the input axle for the second gear pair.

Let's compute the gear ratio for the entire compound gear train. This is the ratio between the last output axle and the first input axle. To do this, we multiply the gear ratios of the individual gear pairs.

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The total gear ratio is 15 to 1. That means the input axle must make 15 revolutions for the output axle to make 1.

You can combine as many gear pairs as you want in a compound gear train. There is no limit. By combining gears you can make almost any gear ratio that you want!

1.6 Nomenclature:1.6.1 Common abbreviations:

n.  Rotational velocity. (Measured, for example, in r.p.m.) ω  Angular velocity. (Radians per unit time.) (1 r.p.m. = π/30 radians per second.) N.  Number of teeth.

1.6.2 Gear terminology:

Gear or wheel: The larger of two interacting gears. Pinion: The smaller gear in a pair. Path of contact: The path followed by the point of contact between two meshing

gear teeth. Line of action: also called 'Pressure line'. The line along which the force

between two meshing gear teeth is directed. It has the same direction as the force vector. In general, the line of action changes from moment to moment during the period of engagement of a pair of teeth. For involute gears, however, the tooth-to-tooth force is always directed along the same line -- that is, the line of action is constant. this implies that for involute gears the path of contact is also a straight line, coincident with the line of action -- as is indeed the case.Axis. The axis of revolution of the gear; center line of the shaft.

Pitch point (p): The point where the line of action crosses a line joining the two gear axes.

Pitch circle: A circle, centered on and perpendicular to the axis, and passing through the pitch point. Sometimes also called the 'pitch line', although it is a circle.

Pitch diameter (D): Diameter of a pitch circle. Equal to twice the perpendicular distance from the axis to the pitch point. The nominal gear size is usually the pitch diameter.

Module (m). The module of a gear is equal to the pitch diameter divided by the number of teeth.

Operating pitch diameters. The pitch diameters determined from the number of teeth and the center distance at which gears operate

Pitch surface. For cylindrical gears, this is the cylinder formed by projecting a pitch circle in the axial direction. More generally, it is the surface formed by the sum of all the pitch circles as one moves along the axis. Eg., for bevel gears it is a cone.

Angle of action. Angle with vertex at the gear center, one leg on the point where mating teeth first make contact, the other leg on the point where they disengage.

Arc of action. The segment of a pitch circle subtended by the angle of action.

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Pressure angle (ø). The complement of the angle between the direction that the teeth exert force on each other, and the line joining the centers of the two gears. For involute gears, the teeth always exert force along the line of action, which, for involute gears, is a straight line; and thus, for involute gears, the pressure angle is constant.

Outside diameter (Do). Diameter of the gear, measured from the tops of the teeth.

Root diameter: Diameter of the gear, measured from the base of the tooth space. Addendum (a): The radial distance from the pitch surface to the outermost point

of the tooth.  a = (Do - D) / 2. Dedendum (b): The radial distance from the depth of the tooth trough to the pitch

surface. b = (D - root diameter) / 2. Whole depth (ht):Whole depth (tooth depth) is the total depth of a tooth space,

equal to addendum plus dedendum, also equal to working depth plus clearance. Clearance: Clearance is the distance between the root circle of a gear and the

addendum circle of its mate. Working depth: Working depth is the depth of engagement of two gears, that is,

the sum of their operating addendums Circular pitch (p): The distance from one face of a tooth to the corresponding

face of an adjacent tooth on the same gear, measured along the pitch circle. Diametral pitch (Pd): The ratio of the number of teeth to the pitch diameter. Eg.

could be measured in teeth per inch or teeth per centimeter. Base circle:L Applies only to involute gears, where the tooth profile is the

involute of the base circle. The radius of the base circle is somewhat smaller than that of the pitch circle.

Base pitch (pb): Applies only to involute gears. It is the distance from one face of a tooth to the corresponding face of an adjacent tooth on the same gear, measured along the base circle. Sometimes called the 'normal pitch'.

Interference. Contact between teeth other than at the intended parts of their surfaces.

Interchangeable set. A set of gears, any of which will mate properly with any other.

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1.7 Tooth contact nomenclature:

Point of contact

Path of Action

A point of contact is any point at which two tooth profiles touch each other.

Line of contact

Line of Contact

A line of contact is a line or curve along which two tooth surfaces are tangent to each other.

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Path of action

The path of action is the locus of successive contact points between a pair of gear teeth, during the phase of engagement. For conjugate gear teeth, the path of action passes through the pitch point. It is the trace of the surface of action in the plane of rotation.

Line of action

Line of Action

The line of action is the path of action for involute gears. It is the straight line passing through the pitch point and tangent to both base circles.

Surface of action:-

The surface of action is the imaginary surface in which contact occurs between two engaging tooth surfaces. It is the summation of the paths of action in all sections of the engaging teeth.

Plane of action:

Plane of Action The plane of action is the surface of action for involute, parallel axis gears with either spur or helical teeth. It is tangent to the base cylinders.

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Zone of action (contact zone):

Zone of Action

Zone of action (contact zone) for involute, parallel-axis gears with either spur or helical teeth, is the rectangular area in the plane of action bounded by the length of action and the effective face width.

Path of contact:

Lines of Contact (helical gear)

The path of contact is the curve on either tooth surface along which theoretical single point contact occurs during the engagement of gears with crowned tooth surfaces or gears that normally engage with only single point contact.

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Length of action:

Length of Action

Length of action is the distance on the line of action through which the point of contact moves during the action of the tooth profile.

Arc of action, Qt

Arc of action is the arc of the pitch circle through which a tooth profile moves from the beginning to the end of contact with a mating profile.

Arc of approach,

Arc of Action

Arc of approach is the arc of the pitch circle through which a tooth profile moves from its beginning of contact until the point of contact arrives at the pitch point.

Arc of recess, Qr

Arc of recess is the arc of the pitch circle through which a tooth profile moves from contact at the pitch point until contact ends.

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Contact ratio, mc, ε

Contact ratio in general is the number of angular pitches through which a tooth surface rotates from the beginning to the end of contact.In a simple way,it can be defined as a measure of the average number of teeth in contact during the period in which a tooth comes and goes out of contact with the mating gear.

Transverse contact ratio, mp, εα

Transverse contact ratio is the contact ratio in a transverse plane. It is the ratio of the angle of action to the angular pitch. For involute gears it is most directly obtained as the ratio of the length of action to the base pitch.

Face contact ratio, mF, εβ

Face contact ratio is the contact ratio in an axial plane, or the ratio of the face width to the axial pitch. For bevel and hypoid gears it is the ratio of face advance to circular pitch.

Total contact ratio, mt, εγ

Total contact ratio is the sum of the transverse contact ratio and the face contact ratio.

εγ = εα + εβ

mt = mp + mF

Modified contact ratio, mo

Modified contact ratio for bevel gears is the square root of the sum of the squares of the transverse and face contact ratios.

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Limit diameter:

Limit Diameter

Limit diameter is the diameter on a gear at which the line of action intersects the maximum (or minimum for internal pinion) addendum circle of the mating gear. This is also referred to as the start of active profile, the start of contact, the end of contact, or the end of active profile.

Start of active profile (SAP):

The start of active profile is the intersection of the limit diameter and the involute profile.

1.8 Tooth profile:

Profile of a Spur Gear

A profile is one side of a tooth in a cross section between the outside circle and the root circle. Usually a profile is the curve of intersection of a tooth surface and a plane or surface normal to the pitch surface, such as the transverse, normal, or axial plane.

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The fillet curve (root fillet) is the concave portion of the tooth profile where it joins the bottom of the tooth space.

As mentioned near the beginning of the article, the attainment of a non fluctuating velocity ratio is dependent on the profile of the teeth. Friction and wear between two gears is also dependent on the tooth profile. There are a great many tooth profiles that will give a constant velocity ratio, and in many cases, given an arbitrary tooth shape, it is possible to develop a tooth profile for the mating gear that will give a constant velocity ratio. However, two constant velocity tooth profiles have been by far the most commonly used in modern times. They are the cycloid and the involute. The cycloid was more common until the late 1800s; since then the involute has largely superseded it, particularly in drive train applications. The cycloid is in some ways the more interesting and flexible shape; however the involute has two advantages: it is easier to manufacture, and it permits the center to center spacing of the gears to vary over some range without ruining the constancy of the velocity ratio. Cycloidal gears only work properly if the center spacing is exactly right. Cycloidal gears are still used in mechanical clocks.

1.9 Undercut: An undercut is a condition in generated gear teeth when any part of the fillet curve lies inside of a line drawn tangent to the working profile at its point of juncture with the fillet. Undercut may be deliberately introduced to facilitate finishing operations. With undercut the fillet curve intersects the working profile. Without undercut the fillet curve and the working profile have a common tangent.

Pitch

Pitch Pitch is the distance between a point on one tooth and the corresponding point on an adjacent tooth. It is a dimension measured along a line or curve in the transverse, normal, or axial directions. The use of the single word “pitch” without qualification may be ambiguous, and for this reason it is preferable to use specific designations such as transverse circular pitch, normal base pitch, axial pitch.

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Circular pitch, p

Circular pitch is the arc distance along a specified pitch circle or pitch line between corresponding profiles of adjacent teeth.

Transverse circular pitch, pt

Tooth Pitch

Transverse circular pitch is the circular pitch in the transverse plane.

Normal circular pitch, pn, pe

Normal circular pitch is the circular pitch in the normal plane, and also the length of the arc along the normal pitch helix between helical teeth or threads.

Axial pitch, px

Base Pitch Relationships

Axial pitch is linear pitch in an axial plane and in a pitch surface. In helical gears and worms, axial pitch has the same value at all diameters. In gearing of other types, axial pitch may be confined to the pitch surface and may be a circular measurement.

The term axial pitch is preferred to the term linear pitch. The axial pitch of a helical worm and the circular pitch of its wormgear are the same.

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Normal base pitch, pN, pbn

Normal base pitch in an involute helical gear is the base pitch in the normal plane. It is the normal distance between parallel helical involute surfaces on the plane of action in the normal plane, or is the length of arc on the normal base helix. It is a constant distance in any helical involute gear.

Transverse base pitch, pb, pbt

Principal Pitches

Base pitch in an involute gear is the pitch on the base circle or along the line of action. Corresponding sides of involute gear teeth are parallel curves, and the base pitch is the constant and fundamental distance between them along a common normal in a transverse plane.

Diametral pitch (transverse), Pd

Diametral pitch (transverse) is the ratio of the number of teeth to the standard pitch diameter in inches.

Normal diametral pitch, Pnd

Normal diametral pitch is the value of diametral pitch in a normal plane of a helical gear or worm.

Angular pitch, θN, τ

Angular pitch is the angle subtended by the circular pitch, usually expressed in radians.

degrees or radians

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Cage gear

The cage gear, also called lantern gear or lantern pinion, has been used for centuries. Its teeth are cylindrical rods, parallel to the axle and arranged in a circle around it, much as the bars on a round bird cage or lantern. The assembly is held together by disks at either end into which the tooth rods and axle are set.

1.10 Gear materials:

Wooden gears of a historic windmill

Numerous nonferrous alloys, cast irons, powder-metallurgy and even plastics are used in the manufacture of gears. However steels are most commonly used because of their high strength to weight ratio and low cost. Plastic is commonly used where cost or weight is a concern. A properly designed plastic gear can replace steel in many cases; It often has desirable properties. They can tolerate dirt, low speed meshing, and "skipping" quite well. Manufacturers have employed plastic to make consumer items affordable. This includes copy machines, optical storage devices, VCRs, cheap dynamos, consumer audio equipment, servo motors, and printers.

1.11 Tooth thickness:

Circular thickness

Tooth Thickness

Circular thickness is the length of arc between the two sides of a gear tooth, on the specified datum circle.

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Transverse circular thickness

Thickness Relationships

Transverse circular thickness is the circular thickness in the transverse plane.

Normal circular thickness

Normal circular thickness is the circular thickness in the normal plane. In a helical gear it may be considered as the length of arc along a normal helix.

Axial thickness

Axial thickness in helical gears and worms is the tooth thickness in an axial cross section at the standard pitch diameter.

Base circular thickness

Base circular thickness in involute teeth is the length of arc on the base circle between the two involute curves forming the profile of a tooth.

Normal chordal thickness Chordal thickness is the length of the chord that subtends a circular thickness arc in the plane normal to the pitch helix. Any convenient measuring diameter may be selected, not necessarily the standard pitch diameter.

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1.12 Purpose of Gear:

Gear is a set of tools for maintenance and release management of RPM packages based on a git repository. A gear-enabled git repository of a software package combines

software development history modifications necessary to produce an RPM package rules to bind software releases to specific RPM-based distribution releases

Developers using Gear need to understand

a format of the rules file describing transformation procedures that convert a given git changeset and branches to a number of source files for a RPM package

utilities for building packages and working with source code

2. Gear Manufacturing Process

Gear manufacturing is today a multi billion dollar industry. As the demand of this industry is growing manufacturers are now increasingly seeking machining tools and technology that can meet with the tough challenges. As in this increasingly globalized world order manufacturers need a supplier that has global resources for delivering state-of-the-art machines, tools etc. Gears are now produced in near-net shape, with a cut in production as well as labors costs and elimination or reduction of wastes. These are also impacting the gear manufacturers to have greater freedom in the choice of materials.

(Image of an assembly line in a Gear manufacturing unit)

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2.1 Steps in the Manufacturing Process of Gears:

The gear manufacturing process is a complex step right from selecting the right material to finally doing the finishing process for getting an optimum quality gear. Gear blanks in the beginning are first roughed out and completely stress relieved this is done to minimize the distortions that have taken place after carburizing. The blanks subsequently then undergoes the finishing process. Then the gear cutting process takes place giving allowance on the tooth flank for grinding. Then subsequently grinding and other steps take place. Following are the steps in the gear manufacturing processes:

Inject Molded Gears Gear Blank

Gear Cutting Broaching of Gears

Gear Grinding Gear Hobbing

Heat Treatment of Gears Lapping of Gears

Gear Machine Gear Shaving

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3. Types of Gears:

Gears are many types:-

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Some types of gears are given below:

1. Bevel Gears

2. Spur Gears.

3. Worm and Worm Wheel Gears

4. Rack and Pinion Gears

5. Crown Gear

6. Helical Gear

3.1 Bevel Gears:

Bevel gears have teeth cut on a cone instead of a cylinder blank. They are used in pairs to transmit rotary motion and torque where the bevel gear shafts are at right angles (90 degrees) to each other.

Fig:Bevel Gear 3.2 Spur Gear: When two spur gears of different sizes mesh together, the larger gear is called a wheel, and the smaller gear is called a pinion. In a simple gear train of two spur gears, the

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input motion and force are applied to the driver gear. The output motion and force are transmitted by the driven gear. The driver gear rotates the driven gear without slipping.

Fig:Spur Gear

Spur gears do three things: 1. Change rot. speed 2. Change torque 3. Change direction

3.3 Worm and Worm wheel

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A gear which has one toothe is called a worm. The tooth is in the form of a screw thread. A wormwheel meshes with the worm. The wormwheel is a helical gear with teeth inclined so that they can engage with the thread-like worm. The wormwheel transmits torque and rotary motion through a right angle. The worm always drives the wormwheel and never the other way round. Worm mechanisms are very quiet running.

Fig: Worm and Worm wheel3.4 Rack and Pinion:

A rack and pinion mechanism is used to transform rotary motion into linear motion and vice versa. A round spur gear, the pinion, meshes with a spur gear which has teeth set in a straight line, the rack

Fig:Rack and Pinion

3.5 Crown Gear:

A crown gear or contrate gear is a particular form of bevel gear whose teeth project at right angles to the plane of the wheel; in their orientation the teeth resemble the points on a crown. A crown gear can only mesh accurately with another bevel gear, although crown gears are sometimes seen meshing with spur gears. A crown gear is also sometimes meshed with an escapement such as found in mechanical clocks.

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3.6 Helical Gears:

Helical gears offer a refinement over spur gears. The leading edges of the teeth are not parallel to the axis of rotation, but are set at an angle. Since the gear is curved, this angling causes the tooth shape to be a segment of a helix. The angled teeth engage more gradually than do spur gear teeth. This causes helical gears to run more smoothly and quietly than spur gears.

4. HELICAL GEAR

4.1 Helical Gear:

Helical gears offer a refinement over spur gears. The leading edges of the teeth are not parallel to the axis of rotation, but are set at an angle. Since the gear is curved, this angling causes the tooth shape to be a segment of ahelix. The angled teeth engage more gradually than do spur gear teeth. This causes helical gears to run more smoothly and quietly than spur gears.

Figure: Helical gears

The teeth on helical gears are cut at an angle to the face of the gear. When two teeth on a helical gear system engage, the contact starts at one end of the tooth and gradually spreads as the gears rotate, until the two teeth are in full engagement.

This gradual engagement makes helical gears operate much more smoothly and quietly than spur gears. For this reason, helical gears are used in almost all car transmissions.

Because of the angle of the teeth on helical gears, they create a thrust load on the gear when they mesh. Devices that use helical gears have bearings that can support this thrust load.

One interesting thing about helical gears is that if the angles of the gear teeth are correct, they can be mounted on perpendicular shafts, adjusting the rotation angle by 90 degrees.

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4.2 Types Helical Gears:

1. Helical gear2.Double Helical Gear3.Herringbone Gear

4 Internal Helical. Gear

4.2.1 Helical Gear:

A helical gear is a gear with teeth which are set at an angle. The angled teeth teeth engage slowly and smoothly, making a helical gear quieter and smoother in operation than many other kinds of gears. Cars are often equipped with helical gears for this reason, and this design may be used in many other applications, as well. These gears come in a range of sizes for a variety of tasks.

Gears are designed to transfer force, either to other gears or to other objects. They have a distinct mechanical advantage, in that a small gear can be used to turn a larger gear, multiplying the force. Cyclists are well aware of this mechanical advantage, as changing the gear ratio on a bicycle will force a cyclist to do more work, or make a cyclist's job easier. Lower gear ratios, in which the gears are close to the same size, require less energy, but they also generate less rotational motion, while high gear rations force the cyclist to work harder, but create far more rotational force.

When people think of gears, they often think of a spur gear, the classic cog-shaped gear with simple straight teeth. Helical gears are designed in a similar way, except that the teeth run diagonally across the side of the gear, rather than being perpendicularly oriented. The helical gear design has some definite advantages behind smoother and quieter operation caused by the slow intermeshing of helical gears. Helical gears tend to wear down less quickly, because the load of the force is distributed, rather than being concentrated, and the teeth are less subject to chipping.

In addition to interfacing on a parallel level, with the gears side by side, most helical gears can also work perpendicularly to each other when the teeth of the gear are designed correctly. This can be quite a nifty little trick in some instances. The helical gear design does tend to generate a heavy thrust load, a load parallel to the shaft, but this can be compensated for with the use of special bearings.

Helical gears can be meshed in a parallel or crossed orientation. The former refers to when the shafts are parallel to each other; this is the most common orientation. In the latter, the shafts are non-parallel. For a crossed configuration the gears must have the same pressure angle and normal pitch, however the helix angle and handedness can be different. The relationship between the two shafts is actually defined by the helix angle(s) of the two shafts and the handedness, as defined.

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Where β is the helix angle for the gear. The crossed configuration is less mechanically sound because there is only a point contact between the gears, whereas in the parallel configuration there is a line contact.

Quite commonly helical gears are used with the helix angle of one having the negative of the helix angle of the other; such a pair might also be referred to as having a right-handed helix and a left-handed helix of equal angles. The two equal but opposite angles add to zero: the angle between shafts is zero -- that is, the shafts are parallel. Where the sum or the difference (as described in the equations above) is not zero the shafts are crossed. For shafts crossed at right angles the helix angles are of the same hand because they must add to 90 degrees.

As mentioned at the start of this section, helical gears operate more smoothly than do spur gears. With parallel helical gears, each pair of teeth first make contact at a single point at one side of the gear wheel; a moving curve of contact then grows gradually across the tooth face. It may span the entire width of the tooth for a time. Finally, it recedes until the teeth break contact at a single point on the opposite side of the wheel. Thus force is taken up and released gradually. With spur gears, the situation is quite different. When a pair of teeth meet, they immediately make line contact across their entire width. This causes impact stress and noise. Spur gears make a characteristic whine at high speeds and can not take as much torque as helical gears because their teeth are receiving impact blows. Whereas spur gears are used for low speed applications and those situations where noise control is not a problem, the use of helical gears is indicated when the application involves high speeds, large power transmission, or where noise abatement is important. The speed is considered to be high when the pitch line velocity (that is, the circumferential velocity) exceeds 5000 ft/min. A disadvantage of helical gears is a resultant thrust along the axis of the gear, which needs to be accommodated by appropriate thrust bearing, and a greater degree of sliding friction between the meshing teeth, often addressed with specific additives in the lubricant

Helical Top:parallelconfiguration. Bottom: crossed configuration.

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4.2.2 Double helical gears: In a variation on the basic helical gear known as the double helical gear or herringbone gear, the gear has two sets of teeth side by side, slanting at different angles. This reduces the amount of thrust, eliminating the need to use specialized bearings.

Double helical gears, also known as herringbone gears. overcome the problem of axial thrust presented by 'single' helical gears by having two sets of teeth that are set in a 'V' shape. Each gear in a double helical gear can be thought of as two standard, but mirror image, helical gears stacked. This cancels out the thrust since each half of the gear thrusts in the opposite direction. They can be directly interchanged with spur gears without any need for different bearings.

Where the oppositely angled teeth meet in the middle of a herringbone gear, the alignment may be such that tooth tip meets tooth tip, or the alignment may be staggered, so that tooth tip meets tooth trough. The latter alignment is the unique defining characteristic of a Wuest type herringbone gear, named after its inventor.

With the older method of fabrication, herringbone gears had a central channel separating the two oppositely-angled courses of teeth. This was necessary to permit the shaving tool to run out of the groove. The development of the Sykes gear shaper now makes it possible to have continuous teeth, with no central gap.

Helical gears Features:

1) Material: carbon steel helical gears, alloy steel helical gears, stainless steel helical gears, metallurgy powder helical gears/sinter powder helical gears, plastic, brass, bronze, cast iron2) Heat treatment: induction hardened, carbonized, carbon nitride3) Surface treatment: zinc plated, anodized, phosphate, oxidized 4) Made according to drawings and/or samples

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5. Broaching Process

Broaching is a machining process that pushes or pulls a cutting tool (called a broach) over or through the surface being machined. Broaches are referred to as multiple-point linear-travel cutting tools and are used to produce flat, circular, and even extremely intricate profiles, as seen from a section perpendicular to the tool travel.

A broach is a series of single-point tools arranged successively in the axial direction along a tool body or holder. Each sequential tooth varies in size and shape in a manner that allows each tooth to cut a chip of the proper thickness.

The shape and spacing of each broach tooth is determined by the length of the part being broached, the amount of material being removed by each tooth, and tonnage restrictions of the broaching machine. The chip space between each tooth is designed to sufficiently accommodate the volume of chips generated.

The concept of broaching as a legitimate machining process can be traced back to the early 1850s. Early broaching applications were cutting keyways in pulleys and gears. After World War 1, broaching contributed to the rifling of gun barrels. Advances in broaching machines and form grinding during the 1920s and 30s enabled tolerances to be tightened and broaching costs to become competitive with other machining processes. Today, almost every conceivable type of form and material can be broached.

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5.1 Broaching machines:

Broaching machines are relatively simple as they only have to move the broach in a linear motion at a predetermined speed and provide a means for handling the broach automatically. Most machines are hydraulic, but a few specialty machines are

mechanically driven.

The hydraulic cylinder of a horizontal broaching machine.

The machines are distinguished by whether their motion is horizontal or vertical. The choice of machine is primarily dictated by the stroke required. Vertical broaching machines rarely have a stroke longer than 60 in (1.5 m). Vertical broaching machines can be designed for push broaching, pull-down broaching, pull-up broaching or surface broaching. Push broaching machines are similar to an arbor press with a guided ram; typical capacities are 5 to 50 tons. The two ram pull-down machine is the most common type of broaching machine. This style machine has the rams under the table. Pull-up machines have the ram above the table; they usually have more than one ram. Most surface broaching is done on a vertical machine.

Horizontal broaching machines are designed for pull broaching, surface broaching, continuous broaching, and rotary broaching.

Broaching machine

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5.2 Types of Broaches: The many different types of broaches available today can be grouped into four major categories:

 1. Internal Broaches   2.External Form Broaches  3.Blind-Spline Broaches 4. External "Pot" Broaches

5.2.1 Internal Broaches:

Internal broaching is more involved. The process begins by clamping the work piece into a special holding fixture, called a work holder, which mounts in the broaching machine. The broaching machine elevator, which is the part of the machine that moves the broach above the work holder, then lowers the broach through the work piece. Once through, the broaching machine's puller, essentially a hook, grabs the pilot of the broach. The elevator then releases the top of the pilot and the puller pulls the broach through the work piece completely. The work piece is then removed from the machine and the broach is raised back up to reengage with the elevator.[3] The broach usually only moves linearly, but sometimes it is also rotated to create a spiral spine or gun-barrel rifling.[4]Cutting fluids are used for three reasons. First, to cool the work piece and broach. Second, to lubricate cutting surfaces. Third, to flush the chips from the teeth. Fortified petroleum cutting fluids are the most common, however heavy duty water soluble cutting fluids are being used because of their superior cooling, cleanliness, and non-flammability.

An example of internal broached work piece.

Internal broaches are either pushed or pulled through the part. Strength considerations usually limit the tool design. Internal broaches can generally be identified by two categories:

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Round Broaches

Spline or form broaches

a) Round Broaches Round broaches are designed to finish a hole that was originally formed by casting, drilling, punching, or forging. The round broach is then pushed or pulled through the hole to bring the hole to the desired dimension.

b) Spline or form broaches Spline or form broaches are essentially the same as round broaches. The difference is that they have splines or some other type of form ground parallel to the axis of the tool. These splines can be angular, involute, straight-sided, cam, lobed, square, or hexagonal.

5.2.2 External Form Broaches:

External form broaches are usually carried on a guided ram and mounted in a broach holding fixture. Strength is generally not a major consideration since the cutting force is transferred to the ram at many places along the length of the broaches. Form broaches are typically identified in the following categories:

Flat surface broaches

Form surface broaches

1. Flat surface broaches:

Flat surface broaches are used to remove material from the external surface of a part. The broach passes "over" the work piece to produce the desired surface. In some instances, the work piece itself passes over stationary tools (i.e. chain broaching). Flat surface broaches can be constructed from either solid high-speed steel or inserted carbide.

2.Form surface broaches: Form surface broaches are used to remove material from an external surface as well. However, rather than producing a flat surface, they generate many types of contours and shapes

Applications for form surface broaching are myriad, and include:

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serrated forms angular spline and gear forms "fir tree" forms compressor slots keyways

5.2.3 Blind-Spline Broaches:

A whole new era in broaching dawned when General Broach pioneered the blind-spline broaching process. Unlike conventional broaching, blind-spline broaching allows for the machining of blind surfaces—surfaces that are impeded by a flange or protrusion that does not allow a cutting tool to pass completely through or over it.

Blind-spline tools are designed to cut either internal or external forms. Blind-spline tools are mounted on a rotary dial type or linear machine and the tools are kept in sets. Blind spline tools are single-tooth cutting tools, with each successive tool removing a predetermined amount of material until the desired profile is achieved.

The advantages of using blind-spline broaching over more conventional machining processes are:

quick and easy size high degree of accuracy extremely high production extremely high production rates (over 10 times faster than shaping or hobbing)

5.2.4 External "Pot" Broaches:

While this type of broaching is also external, it is a distinct category from external form broaching because of its unique process. This type of broaching is used when an external form is required. The form can be splines (straight sided, involute, angular), cam, or lobular.

In a pot broaching set up, the part is usually pushed up through an internal 'pot'; a fixture that houses a series of form inserts. Some pots also include a sequence of shave rings that are mounted at the rear of the broach inserts and are used to enhance the form, spacing, and finish of the resultant part.

6. Milling Operations - Backlash

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6.1 Broaching Principles:

Broaching is a machining process that pushes or pulls a cutting tool (called a broach) over or through the surface being machined. Its high-production, metal-removal process is sometimes required to make one-of-a-kind parts. The concept of broaching as a legitimate machining process can be traced back to the early 1850s. Early broaching applications were cutting keyways in pulleys and gears. After World War 1, broaching contributed to the rifling of gun barrels. Advances in broaching machines and form grinding during the 1920s and 30s enabled tolerances to be tightened and broaching costs to become competitive with other machining processes. Today, almost every conceivable type of form and material can be broached. It represents a machining operation that, while known for many years, is still in its infancy. New uses for broaching are being devised every day.

Broaching is similar to planing, turning, milling, and other metal cutting operations in that each tooth removes a small amount of material (Figure 1 ).

Figure 1. Cutting action of a broaching tool. The broaching tool has a series of teeth so arranged that they cut metal when the broach is given a linear movement as indicated in figure 1. The broach cuts away the material since its teeth are progressively increasing in height.

Figure 2. Typical push keyway broaching tools and a shim.

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Properly used, broaching can greatly increase productivity, hold tight tolerance, and produce precision finishes. Tooling is the heart of broaching. The broach tool's construction is unique for it combines rough, semi-finish, and finish teeth in one tool (Figure 3).

                   Figure 3. Parts of a broaching tool.

There are two types of broaching procedures: internal broaching and external broaching. For exterior broaching, the broach tool may be pulled or pushed across a work piece surface, or the surface may move across the tool. Internal broaching requires a starting hole or opening in the work piece so the tool can be inserted. The tool, or work piece, is then pushed or pulled to force the tool through the starter hole.

Almost any irregular cross-section can be broached as long as all surfaces of the section remain parallel to the direction of broach travel (Figure 4). Helical cuts can also be produced by twisting the broach tool as it passes the workpiece surface.

Figure 4. Different types of broaches.

In conclusion, it may be said that the broach tool and the broaching process are versatile and important and that anyone who works in the field of metals, woods, or plastics should

be familiar with them.

6.2 Hints for successfully broaching a keyway:

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6.2.1 Set-up: Maintain a rigid set-up at all times. The workpiece must be solidly fixed or nested perfectly square with the baseplate and ram face. Check to make sure that all square and parallel surfaces on the face of the ram and the baseplate remain true.

6.3 Alignment of the Broaching: Proper alignment of the broach, workpiece, and ram is the most important factor in all broaching operations. Misalignment can cause drifting, deflection, and even breakage. Alignment Tips--If a keyway broach drifts and cuts a taper, try the following:

1.Reverse workpiece or turn broach so teeth face toward the back of the press.2. Let the bushing protrude above the workpiece to give more support to the back of the broachthereby helping to keep it aligned. If a collared bushing is used, place it upside down underthe workpiece.3. Make sure the broach is centered under the ram at the beginning of the cut. If thebroach moves out of alignment after starting to cut, back off the pressure on the ram and align the broach itself. Repeat during successive cuts to ensure perfectly straight cuts.

Product

Broaching is a machining operation which uses a toothed tool, called a broach, to remove material. The broach is used in a broaching machine, which is also sometimes shortened to broach. It is used when precision machining is required, especially for odd shapes. Broaching finishes a surface in a single pass, which makes it very efficient. Commonly machined surfaces include circular and non-circular holes, splines, and flat surfaces. Typical work pieces include small to medium sized castings, forgings, screw machine parts, and stampings. Even though broaches can be expensive, broaching is usually favorable to other processes when used for high-quantity production runs.

Broaches are shaped similar to a saw, except the teeth height increases over the length of the tool. Moreover, the broach contains three distinct sections: one for roughing, another for semi-finishing, and the final one for finishing. Broaching is a unique machining process because it is the only one to have the feed built into the tool. The profile of the machined surface is always the inverse of the profile of the broach. The rise per tooth (RPT), also known as the step or feed per tooth, determines the amount of material removed and the size of the chip. The broach can be moved relative to the work piece or vice-versa. Because all of the features are built into the broach no complex motion or skilled labor is required to use it.

The process depends on the type of broaching being performed. Surface broaching is very simple as either the work piece is moved against a stationary surface broach, or the work piece is held stationary while the broach is moved against it.

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Internal broaching is more involved. The process begins by either clamping the work piece into the work holder of the broaching machine or the work piece is placed on a spherical work holder designed to automatically align the work piece to the broach. The elevator of the broaching machine then lowers the pilot of the broach through the work piece where the puller engages the broach pilot. The elevator then releases the top of the pilot and the puller pulls the broach through the work piece completely. The work piece is then removed from the machine and the broach is raised back up to reengage with the elevator. The broach usually only moves linearly, but sometimes it is also rotated to create a spiral spline or gun-barrel rifling.

Cutting fluids are used for three reasons. First, to cool the work piece and broach. Second, to lubricate cutting surfaces. Third, to flush the chips from the teeth. Fortified petroleum cutting fluids are the most common, however heavy duty water soluble cutting fluids are becoming more popular.

The slab broach is the simplest surface broach. It is a general purpose tool for cutting flat surfaces. Slot broaches are cut slots of various dimensions at high production rates. Slot broaching is much quicker than milling when more than one slot needs to be machined, because the broach can produce both slots at the same time. Contour broaches are designed to cut concave, convex, cam-, contoured, and irregular shaped surfaces.

Pot broaches are cut the inverse of an internal broach; they cut the outside diameter of a cylindrical work piece. They are named after the pot looking fixture in which the broaches are mounted; the fixture is often referred to as a "pot". The pot is designed to hold multiple broaching tools concentrically over its entire length. The broach is held stationary while the workpiece is pushed or pulled through it. This has replaced hobbing for some involute gears and cutting external splines and slots.

Straddle broaches use two slab broaches to cut parallel surfaces on opposite sides of a workpiece in one pass. This type of broaching holds closer tolerances than if the two cuts were done independently. It is named after the fact that the broaches "straddle" the workpiece on multiple sides.

Hollow or shell broaches are internal cutting broaches for cutting large diameters. They are designed to mount on an arbor. This is cheaper to produce than a solid broach, especially if it will need to be replaced after wearing out. A common type of internal broach is the keyway broach. It uses a special fixture called a horn to support the broach and properly locate the part with relations to the broach. A concentricity broach is a special type of spline cutting broach which cuts both the minor diameter and the spline form to ensure precise concentricity.

s

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CONCLUSION

Finally we are concluding that manufacturing of helical gear by broaching process is

extensively using. Broaching is the major manufacturing process for gears. There are

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three major uses of gears. They change the direction of the rotation, the torque and the

rotational speed. Gears can either be used to lower the speed by coordinating the

multiple. For all these helical gears are extensively useful. We went through the

manufacturing process of helical gear by broaching process in Shanthi gears.

References

1. ̂ Howstuffworks "Transmission Basics" 2. ̂ Norton 2004, p. 462 3. ^ a b c d e f g ANSI/AGMA 1012-G05, "Gear Nomenclature, Definition of Terms with

Symbols".

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4. ^ a b Helical gears, http://www.roymech.co.uk/Useful_Tables/Drive/Hellical_Gears.html, retrieved on 2009-06-15.

5. ̂ Doughtie and Vallance give the following information on helical gear speeds: "Pitch-line speeds of 4,000 to 7,000 fpm [20 to 36 m/s] are common with automobile and turbine gears, and speeds of 12,000 fpm [61 m/s] have been successfully used." -- p.281.

6. ̂ McGraw Hill Encyclopedia of Science and Technology, "Gear", p. 742. 7. ̂ Canfield, Stephen (1997), "Gear Types", Dynamics of Machinery, Tennessee Tech

University, Department of Mechanical Engineering, ME 362 lecture notes, http://gemini.tntech.edu/~slc3675/me361/lecture/grnts4.html.

8. ̂ Hilbert, David; Cohn-Vossen, Stephan (1952), Geometry and the Imagination (2nd ed.), New York: Chelsea, pp. 287, ISBN 978-0-8284-1087-8

9. ̂ McGraw Hill Encyclopedia of Science and Technology, "Gear, p. 743.

Bibliography American Gear Manufacturers Association; American National Standards

Institute (2005), Gear Nomenclature, Definitions of Terms with Symbols (ANSI/AGMA 1012-F90 ed.), American Gear Manufacturers Association, ISBN 9781555898465.

McGraw-Hill (2007), McGraw-Hill Encyclopedia of Science and Technology (10th ed.), McGraw-Hill Professional, ISBN 978-0071441438.

Norton, Robert L. (2004), Design of Machinery (3rd ed.), McGraw-Hill Professional, ISBN 9780071214964, http://books.google.com/books?id=iepqRRbTxrgC.

Vallance, Alex; Doughtie, Venton Levy (1964), Design of machine members (4th ed.), McGraw-Hill.

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