Gear Terminology

In this tutorial, we will learn about a mechanical component known as gear. It is a device used for power transmission. Also, we will learn about all the terms which are used in the analysis of gears, which is known as Gear Terminology. Further, we will know about the classification of Gears.

Contents:

  1. Types of Mechanical Power Transmission
  2. Frictional Discs / Condition for a Gear
  3. The NO-SLIP Condition
  4. Gear Profiles
  5. Gear Terminology – 1
  6. Gear Terminology – 2
  7. Types of Gears
  8. Uses of Gears

Types of Mechanical Power Transmission

In Mechanical Engineering, the power developed at the engine is generally not in contact with the output source due to various design constraints. Rather, a series or a combination of couplers are used to transmit the power to the final source amongst which the two famous couplers used are belt-pulley drives and gears.

  • Belt drives: This type of transmission consists of pulleys which are attached to the rotating shafts and are connected by belt which are generally made up of rubber-nylon compounds. This type of arrangement is used where the center distance between the rotating shafts is large. A simple belt drive is shown in Figure 1.
    A simple Belt Drive

    As shown in Figure 1, there are two pulleys which are connected by a belt. As the pulley 1 pulls the belt from the lower side and transfers it to the pulley 2, hence the belt at the lower side will have more tension (known as the tight side) and the belt at the upper side will have more tension (known as the slack side).

  • Gears: The gear is defined as a mechanical toothed element which is used for transmitting motion (rotary in type) from one shaft to another with constant velocity ratio. A gear is used in a system where the center distance is small and the transmission of exact velocity ratio is required. A simple gear arrangement is shown below in Figure 2:
    simple Gear Arrangement

    As shown in figure 2, there are two gears which are in contact with each other. Gear 1 is connected to the shaft containing power and hence it is known as the Driver Gear. Gear 2 is connected to the output shaft and hence it is known as the Driven Gear. Consequently, if the driver gear rotates clockwise, te driven gear rotates anticlockwise and vice-versa.

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Frictional Discs / Condition for a Gear

Consider the diagram given below:

Two frictional discs in contact mounted on two shafts
  • Consider a frictional disc with very high friction on its circumference. Imagine the two shafts protruding towards the screen. Hence, the point of contact B is a line from the side view.
    Let the disc 1 be of the radius R1 with angular velocity ω1 and disc 2 be of the radius R2 and angular velocity ω2 . Let the angular velocity at the point B be VDg.

    As evident from the diagram, the contact point is being shared by both the frictional discs, therefore the angular velocity at both point B is same for both the discs.

  • Hence, for pure rolling and for both discs moving at same angular velocity
    VDg = R1ω1 & VDg = R2ω2

    Equating both Vb’s

    R1 × ω1 = R2 × ω2

    R2 / R1 = ω1 / ω2

    As the radius of the two discs are same, so the ratio R2 / R1 remains constant and since

    R2 / R1 = ω1 / ω2

    And hence we can say that we have a constant velocity ratio

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    ω1 / ω2 = constant

    This is the basic condition of gear. The ω1 / ω2 condition is only satisfied if the system obeys No-Slip Condition.

The No-Slip Condition

If two discs in contact are rotating with same angular velocity and at the point of contact, the peripheral velocity remains the same, there is no power loss and the two discs never skid against each other, then they are said to be in the No-Slip Condition.

  • To understand this phenomenon, a figure is shown below describing the contrary of No-Slip Condition:
    Two peripheral velocities for a similar Point of Contact

    The above diagram shows that if there is slip between the two discs, then it generates two different angular velocities for the same point of contact.

  • Hence, if such system does not obey the no-slip condition, then it cannot be termed as a gear.
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    Before we learn further, let us understand what are positive and negative drives.

  • Positive drives: These are the type of drives where chances of slip are almost negligible and can be used in places which require high efficiency. Gear is one positive drive mechanical element.
  • Negative drives: These are the type of drives in which there is a high chance of slip and hence they cannot be used in places requiring high efficiency. Belt drive is a great example of negative drive mechanical element. Although it is a negative drive element, but it widely used and the most famous example is the CVT Technology used in automatic transmissions.

Gear Profiles

Mainly, there 2 are types of gear profile, cycloidal and involute.

  • Cycloidal: This type of profile has got limited application such as in mechanical wristwatches. This type of profile has two different curves for face and flank. Hence, its usage is very limited.
  • Involute: This is the most common type of profile used.

    Consider the following diagram below:

  • Involute Profile Generation
    • An involute can be defined as the locus generated by several points in a circle which unrolls themselves along its circumference.
    • Divide the circle into 8/16 areas. With the help of set squares draw tangents through each and every point viz. 1,2,3,4 and so on.
    • Now, take arc lengths 1-2, 1-3, and dissect the tangents. The path generated will be an involute for the given circle.

Gear Terminology – 1

This topic covers all the physical terminologies used to describe a gear.
Observe the following diagram given below very carefully:

Magnified view of a Gear
  • Pitch Circle Diameter (P.C.D) (1): It is the hypothetical diameter of the frictional disc which would produce the same motion as a gear.
  • Addendum circle (2): It is the imaginary circle which passes through the top of the teeth.
    Mathematically, it is the sum of the Pitch Circle Diameter and twice the module.
    Hence,
    Addendum circle = P.C.D + 2m
  • Dedendum circle (3): It is the imaginary circle which passes through the bottom of the teeth.
    Mathematically,
    Dedendum circle = P.C.D – 2 × 1.157m
  • Clearance line (4): It is a circle which is provided to prevent the locking of two teeth in contact.
    = 1.157m – m
    = 0.157m
  • Face (5): It is the part of the tooth above the pitch circle diameter.
  • Flank (6): It is the part of the tooth below the pitch circle diameter.
  • Tooth (7): It is the part of the gear which is responsible for mating.
  • Face width (8): It is the width of the tooth of the gear.
  • Addendum (9): It is the distance between the addendum circle and the pitch circle diameter.
  • Dedendum (10): It is the distance between the dedendum circle and the pitch circle diameter.
    The general value of dedendum is generally taken as 1.157m, where m = module of the gear.
  • Tooth thickness (11): It is the thickness of the tooth of a gear.
  • Circular Pitch (12): It is the distance between the two consecutive teeth in a gear while maintaining the same corresponding points on the both teeth.
    Circular Pitch = π × DPC / N
    where,
    DPC = Pitch Circle Diameter
    N = number of teeth in the gear

Gear Terminology – 2

In gear terminology – 1, we learnt about the physical terminologies in a gear. In this section, we will learn about the mechanical terminologies used to analyze a gear.

  • Module (m): It is the length of the pitch circle diameter per tooth.
    m = pitch circle dia / tooth
  • Clearance: The distance between the addendum and dedendum is called Clearance.
    Clearance = Dedendum circle – Module
    = 1.157m – m
    = 0.157m
  • Gear Ratio(G): The ratio of the number of teeth on the driver gear(N) to the driven gear(n) is called Gear Ratio.
    So,
    G = N/n
  • Velocity Ratio (V.R.): The ratio between the angular velocity of the driven(ω2) to the driving gear(ω1) is called Velocity Ratio.
    Hence, V.R. = ω2 / ω1
  • Pressure line: The common normal at the point of contact of the mating gears is known as the pressure line. Two gears with the same module remain in contact following this pressure line. More is the time the gear remains in contact; more is the power transfer. A pressure line is shown below:
    A pressure line (yellow) between two mated gears

    which the force from the driving gear is transmitted to the driven gear.

Types of Gears

  • On the position of axes:
  • Parallel shafts
    • Spur gears: These are the types of gears used to connect two non-intersecting parallel shafts. They are easy to manufacture, robust, reliable, and have a relatively simple geometry. However, these gears cannot be used where the need of power transmission is very large. A Spur Gear is shown below:
      Spur Gears

      As shown in fig. 8, this type of gears has straight teeth and hence they are also known as Straight Gears or Straight-Cut Gears.

    • Helical gears: These gears function similar to spur gears but they have teeth inclined at an angle (Helix Angle). Due to this type of geometry, helical gears have better sliding and mating properties and can be used for large power transmissions. A helical gear is shown below:
    • Helical Gears
    • Double Helical Gears: These gears find their applications in heavy machineries, naval ships engines, trucks, excavators and places where high torque transfer is the key factor. Also, these gears are difficult to manufacture and their cost is relatively higher than any other type of gears. A double helical gear is shown below:
      Double Helical Gears

      As shown in the figure above, one gear has two opposite helix and is mounted to another gear having opposite handed teeth. The efficiency of torque transfer in these gears is very high.

  • Intersecting shafts
    • Bevel gears: These gears are used to transfer motion and power between shafts which are intersecting in type, mostly 900 apart. The gears are manufactured with profiles similar to a square pyramid and then the teeth cutting is performed.
      Bevel Gears

      Bevel gears are also known as Mitre Gears.

  • Non-parallel non-intersecting shafts
    • Straight bevel and Spiral bevel gears: If the teeth on the gears are straight towards the point of intersection of the two shafts, then they are known as Straight Bevel Gears. If the teeth on the gears are inclined at an angle with respect to the point of intersection of two shafts, then they are known as Spiral Bevel Gears.
  • On the basis of gearing type
    • External gear: All the types of gears described above are examples of external gearing. These gears are mounted on two separate shafts either intersecting or non-intersecting.
    • Internal gear: This type of gear arrangement requires only one shaft and both gears may or may not be mounted on the same shaft. Mechanical wrist watches have internal gearing in them. An internal gear arrangement is shown below:
    • Rack and Pinion: This type of gear arrangement is used to transfer rotational motion into linear or vice-versa.
    • Rack and Pinion arrangement
  • On the basis of speed
    • High speed gears: These are used where speed is more than 16 m/s.
    • Medium speed gears: These are used where speed is in the range of 2.5 m/s to 16 m/s.
    • Low sped gears: These are used where speed is below 2.5 m/s.

Uses of gears

Gears are primarily used for speed variation, force/motion transfer and direction control. Practical examples include

  • Gearbox used in automobiles.
  • Wristwatches and alarm clocks.
  • Agricultural machinery such as harvesters, and extractors.
  • The wheel of the computer mouse uses a gear mechanism.
  • Mechanical machinery such as lathe, shaper and millers.
  • Printing press and hand tools.
  • Conveyer system transmission.
  • Pumps and Electrical motors.
  • Centrifugal machines used in dairy industries.
  • Mixers used in food processing industries.
  • Medical equipment like MRI machines.

Key Points to Remember

Here is the list of key points we need to remember about “Gear Terminology”.

  • The weight of the gear is omitted during analysis.
  • The pitch circle diameter is an imaginary line and is not visible physically.
  • To reduce slip in gears (if any), lubrication is recommended.
  • Mating of gears is only possible if they have the same module.
  • Two helical gears can only be paired if they have opposite handed teeth with respect to each other.
  • For better torque delivery, slower rotational speed of gears is required while for better acceleration, higher rotational speed is required.
  • Helix angle is the angle used to describe the inclination of the teeth in helical gears.
  • In case of a Rack and Pinion arrangement, the pinion is usually the driving gear.
  • In case of internal gearing, the gears rotate in the same direction whereas in case of external gearing, the gears rotate in the opposite direction.
  • For a gear to exist, it must follow the No-Slip Condition.
  • For a gear to mate properly, approximately 2 teeth need to be in contact with each other at all times.
  • Sometimes in a gear, the top of the tooth cuts away the root of the tooth of another gear due to abrupt design, abnormal variations in angular velocities, improper sliding, or poor lubrication which is known as Interference.

If you find any mistake above, kindly email to [email protected]

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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