Gear Types, Definition, Terms Used, And The Law Of Gearing
By: Learn Engineering
Tags: Spur Gears, Industrial Engineering, Gears, Mechanical Engineering, Bevel Gears

1. Introduction

There are many ways of transmission of motion or power between two shafts like belt drives, chain drives. The slipping of a belt or rope is a common problem. This effect of slipping reduces the velocity ratio of the system. In precision Machines, in which a definite velocity ratio is of importance the only positive drive is by gears or toothed wheels. A gear drive is also provided when the distance between the driver and the follower is very small. In this article, we will discuss gear definition, classification, types, terms used in gears, and geometry in detail.

2. Definition

Gears are wheels that have projections (called teeth) as shown in fig are provided on the periphery of wheel A which will fit into the corresponding recesses on the periphery of wheel B. A friction wheel with teeth cut on it is known as gear or toothed wheel.

There are 2 basic functions of gears:

Gears are used to transmit the exact velocity ratio.

Gears are used to transmit power between the shafts.

3. Classification Of Gears

The gears or toothed wheels may be classified as follows

3.1. According To Position Of Axes Of The Shafts

Parallel and co-planar shafts

Intersecting and coplanar shafts

Non-Intersecting, non-parallel and non-coplanar shafts

3.1.1. Parallel And Co-Planar Shafts:

The two parallel and co-planar shafts connected by the gears are shown in Fig. These gears are called spur gears and the arrangement is known as spur gearing. These gears have teeth parallel to the axis of the wheel as shown in Fig. Another name given to spur gearing is helical gearing, in which the teeth are inclined to the axis.

3.1.2. Intersecting And Coplanar Shafts:

The two non-parallel or intersecting, but coplanar shafts connected by gears is shown in Fig. These gears are called bevel gears and the arrangement is known as bevel gearing. The bevel gears, like spur gears, may also have their teeth inclined to the face of the bevel, in which case they are known as helical bevel gears.

3.1.3. Non-Intersecting, Non-Parallel And Non-Coplanar Shafts

The two non-intersecting and non-parallel i.e. noncoplanar shafts connected by gears are shown in fig. These gears are called skew bevel gears or spiral gears and the arrangement is known as skew bevel gearing or spiral gearing. This type of gearing also has a line contact, the Rotation of which about the axes generates the two pitch surfaces known as hyperboloids.

3.2. According To Peripheral Velocity Of The Gears

Low-velocity gears: The gears having a velocity of less than 3 m/s are termed low-velocity gears.

Medium velocity gears: Gears having a velocity between 3–15 m/s are known as medium velocity gears.

High-velocity gears: If the velocity of gears is more than 15 m/s, then these are called high-speed gears.

3.3. According To The Type Of Gearing

The gears, according to the type of gearing, maybe Classified as.

External gearing

Internal gearing

Rack and pinion

3.3.1. External Gearing

In external gearing, the gears of the two shafts mesh externally with each other as shown in Fig. The larger of these two wheels is called spur wheel or gear and the smaller wheel is called the pinion.

3.3.2. Internal Gearing

In internal gearing, the gears of the two shafts mesh internally with each other as shown in Fig. The larger of these two wheels is called the annular wheel and the smaller wheel is called the pinion.

3.3.3. Rack And Pinion

Sometimes, the gear of a shaft meshes externally and internally with the gears in a straight line, as shown in Fig. Such a type of gear is called rack and pinion. The straight-line gear is called rack and the circular wheel is called the pinion.

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4. Terms Used In Gears

Pitch circle: It is an imaginary circle which by the pure rolling action, would give the same motion as the actual gear. 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 pitch diameter. Pitch point: It is a common point of contact between two pitch circles. Pitch surface: It is the surface of the rolling discs which the meshing gears have replaced at the pitch circle. Pressure angle: 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 φ. The standard pressure angles are 14 1/2° and 20°. Addendum: It is the radial distance of a tooth from the pitch circle to the top of the tooth. Dedendum: It is the radial distance of a tooth from the pitch circle to the bottom of the tooth. Addendum circle: It is the circle drawn through the top of the teeth and is concentric with the Pitch circle. Dedendum circle: It is the circle drawn through the bottom of the teeth. It is also called the root circle. Root circle diameter = Pitch circle diameter × cos φ, where φ is the pressure angle. Circular pitch: It is the distance measured on the circumference of the pitch circle. A point of one tooth to the corresponding point on the next tooth. It is usually denoted by pc. Diametral pitch: It is the ratio of the number of teeth to the pitch circle diameter in millimeters. It is denoted by PD. Module: It is the ratio of the pitch circle diameter in millimeters to the number of teeth. It is usually denoted by m. The recommended series of modules in Standard are 1.125, 1.375, 1.75, 2.25, 2.75, 3.5, 4.5,5.5, 7, 9, 11, 14, 18, 22, 28, 36 and 45. Total depth: It is the radial distance between the addendum and the dedendum circle of gear. It is equal to the sum of the addendum and dedendum. 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 gears. Tooth thickness: It is the width of the tooth measured along the pitch circle. Tooth space: It is the width of space between the two adjacent teeth measured along the pitch circle. Backlash: It is the difference between the tooth space and the tooth thickness, as measured on the pitch circle. The face of the tooth: It is the surface of the tooth above the pitch surface. Top land: It is the surface of the top of the tooth. The flank of the tooth: It is the surface of the tooth below the pitch surface. Face width: It is the width of the gear tooth measured parallel to its axis. Profile: It is the curve formed by the face and flank of the tooth. Fillet radius: It is the radius that connects the root circle to the profile of the tooth. Path of contact: It is the path traced by the point of contact of two teeth from the beginning to the end of the engagement. Length of the path of contact: It is the length of the common normal cut-off by the wheel and pinion. Arc of contact: It is the path traced by a point on the pitch circle from the beginning to the end of the engagement of a given pair of teeth. The arc of contact consists of two parts.

5. Law Of Gearing

“The common normal at the point of contact between a pair of teeth must always pass through the pitch point. This is a fundamental condition that must be satisfied while designing the profiles for the teeth of gear wheels. It is also known as the law of gearing”.

Consider the portions of the two teeth, one on wheel 1 (or pinion) and the other on wheel 2, as shown by thick line curves in Fig. Let the two teeth come in contact at point Q, and the wheels rotate in the directions as shown in the figure. Let T be the common tangent and MN be the common normal to the curves at point of contact Q. From the centers, O1 and O2, draw O1M and O2N perpendicular to MN. A little consideration will show that the point Q moves in the direction QC, when considered as a point on wheel 1, and in the direction QD when considered as a point on wheel 2.

Let v1 and v2 be the velocities of the point Q on wheels 1 and 2 respectively. If the teeth are to remain in contact, then the components of these velocities. Along the common normal MN must be equal.

We see that the angular velocity ratio is inversely proportional to the ratio of the distance of P from the centers. Therefore, in order to have a constant angular velocity ratio for all positions of the wheels, P must be the fixed point (called pitch point) for the two wheels. In other words.

6. Forms Of Teeth

In actual practice, the following are the two types of teeth commonly used.

Cycloidal teeth

Involute teeth

We shall discuss both the above-mentioned types of teeth in the following articles. Both these forms of teeth satisfy the condition as explained in the article Law of gearing

6.1. Cycloidal Teeth

A cycloid is a curve traced by a point on the circumference of a circle that rolls without slipping on a fixed straight line. When a circle rolls without slipping on the outside of a fixed circle. The curve traced by a point on the circumference of a circle is known as an epicycloid. On the other hand, If a circle rolls without slipping on the inside of a fixed circle, then the curve traced by a point on the circumference of a circle is called a hypocycloid.

A little consideration will show that the common normal XX at the point of contact between two cycloidal teeth always passes through the pitch point, which is the fundamental condition for a constant velocity ratio.

6.2. Involute Teeth

An involute of a circle is a plane curve generated by a point on a tangent, which rolls on the circle without slipping, or by a point on a taut string that is unwrapped from a reel as shown in Fig. In connection with toothed wheels, the circle is known as the base circle. The involute is traced as follows.

An involute of a circle is a plane curve generated by a point on a tangent, which rolls on the circle without slipping, or by a point on a taut string that is unwrapped from a reel as shown in Fig (a). In connection with toothed wheels, the circle is known as the base circle. The involute is traced as follows.

A little consideration will show, that if the center distance is changed, then the radii of pitch circles also changes. But their ratio remains unchanged because it is equal to the ratio of the two radii of the base circles. The common normal, at the point of contact, still passes through the pitch point. As a result of this, the wheel continues to work correctly. However, the pressure angle increases with the increase in the center distance.

7. 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.

7.1. Advantages Of Involute Gears

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 require exact center distance to be maintained.

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 the engagement, reduces to zero at pitch point, starts increasing, and again becomes maximum at the end of the engagement. This results in the less smooth running of gears.

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

7.2. Advantages Of Cycloidal Gears

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, cycloidal teeth are preferred especially for cast teeth.

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

In cycloidal gears, the interference does not occur at all. Though there are advantages of cycloidal gears they are outweighed by the greater simplicity and flexibility of the involute gears.

8. Systems Of Gear Teeth

The following four systems of gear teeth are commonly used in practice.

14 1/2° Composite system

14 1/2° Full-depth involute system

20° Full-depth involute system

20° Stub involute system.

8.1. 14 ½° Composite System

The 14 1/2° composite system is used for general purpose gears. It is stronger but has no inter-changeability. The tooth profile of this system has cycloidal curves at the top and bottom and involute curves at the middle portion. The teeth are produced by formed milling cutters or hobs.

8.2. 14 1 /2° Full Depth Involute System

The tooth profile 14 1 /2° full depth involute system was developed for use with gear hobs for spur and Helical gears.

8.3. 20° Full Depth Involute System

The tooth profile of the 20° full depth involute system may be cut by hobs. The increase of pressure angle from 14 1/2° to 20° results in a stronger tooth, because the tooth acting as a beam is Wider at the base.

8.4. 20° Stub Involute System

The 20° stub involute system has a strong tooth to take heavy loads.

9. Gear Materials

The material used for the manufacture of gears depends upon the strength and service condition 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. Non-metallic materials like wood, rawhide, compressed paper, and synthetic resins like nylon are used for gears, especially for reducing noise.

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 the 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.

10. Causes Of Gear Tooth Failure

The different modes of failure of gear teeth and their possible remedies to avoid the failure are as follows

10.1. Bending Failure

Every gear tooth acts as a cantilever. If the total repetitive dynamic load acting on the gear tooth is greater than the beam strength of the gear tooth, then the gear tooth will fail in bending, i.e. the gear tooth will break. In order to avoid such failure, the module and face width of the gear is adjusted so that the beam strength is greater than the dynamic load.

10.2. Pitting

It is the surface fatigue failure that occurs due to many repetitions of Hertz contact stresses. The failure occurs when the surface contact stresses are higher than the endurance limit of the material. The failure starts with the formation of pits which continue to grow resulting in the rupture of the tooth surface. In order to avoid pitting, the dynamic load between the gear teeth should be less than the wear strength of the gear tooth.

10.3. Scoring

Excessive heat is generated when there is an excessive surface pressure, high speed, or supply of lubricant fails. It is a stick-slip phenomenon in which alternate shearing and welding take place rapidly at high spots. This type of failure can be avoided by properly designing the parameters such as speed, pressure, and proper flow of the lubricant so that the temperature at the rubbing faces is within the permissible limits.

10.4. Abrasive Wear

The foreign particles in the lubricants such as dirt, dust, or burr enter between the teeth and damage the form of the tooth. This type of failure can be avoided by providing filters for the lubricating oil or by using high viscosity lubricant oil which enables the formation of thicker oil film and hence permits easy passage of such particles without damaging the gear surface.

10.5. Corrosive Wear

The corrosion of the tooth surfaces is mainly caused due to the presence of corrosive elements such as additives present in the lubricating oils. In order to avoid this type of wear, proper anti-corrosive additives should be used.