Gears and Rotating Components!

A Gear is a Toothed Wheel, when meshed with its mating part, transfers Power (Speed and Torque) form Driver to Driven shaft.

In the Conjugate Action or Gearing:

• Speeds at the Pitch Circles of the Gears in Mesh are Equal
• Angular Velocities of the Gears in Mesh are Constant

• 'AB' - The line Passing through the Pitch Point and Tangent to the Base Circles of the Mating Gears
• This is path along which the Gearing action takes place
• This Line 'AB' is also the Common Normal to the mating teeth

Common Normal to the Point of Contact (for the Teeth in Mesh) must pass through the Pitch Point.

• This is the Length for which the Gear Teeth remain in Contact
• 'CD' is the Contact Length'
• Green Lines depict the Tip Circle Diameters of the Mating Gears 

- Angle between:

• Common Tangent to the Base Circles of the Gears in Contact & Line Tangent to the Pitch Circle Diameters of the of Mating Gears 
• Angle between 'AB' and ' EF'

- It is the Angle along which the Force is exerted

- Pressure Angle at each Roll Angle on the Tooth is   Different

- The Pressure Angle generally mentioned is the Pressure Angle at the Nominal Pitch Diameter of the Gear

• Diameter at which Involute Starts
• If the gear tooth extends below base diameter, the profile will be non-involute

• This denotes the Root of the Gear Tooth
• Ideally for the involute profile, Root Diameter > Base Diameter
• If Root Diameter < Base diameter, then the portion of the tooth profile below Base Diameter will be non-involute

• Form Diameter is where Root Fillet Merges with the Involute
• For a Gear with Root Dia. > Base Dia., Form Dia. will be above Base Dia.
• Even for a Gear with Root Dia. < Base Dia., Form Dia. can be above BCD
• Involute or True Involute Profile/Form will be above Form Diameter
• Adding a Fillet means deviating from Involute curve
  • Fillet is must to avoid Stress Concentration at Root
  • Else Pre-mature Bending Failure will be observed

• As the name suggests, it is the diameter of Gear Tip
• Gear Outside Diameter
• Minimum Tip Thickness: 

             0.2 * Normal Module

• Distance between points at the same Roll Diameter on the adjacent Teeth

• Pitch of the Gear @ Base Circle Diameter

• Portion of the flank above the Pitch Circle Diameter

• Portion of the Flank below the Pitch Circle Diameter

• For 2 Gears to Mesh
  • Their pressure Angle must be same
  • Their Module must be same
• Base Pitch must be same, which is calculated using:
  • Pressure Angle
  • Module

• Number of Teeth (T) / Pitch Circle  Diameter (PCD)
• Number of Teeth per unit Pitch Circle Diameter (Generally in inches)

• When a Gear Tooth Mates with its Mating Gear Tooth @ Non-Involute Portion, it is called Interference
• If Root of a Gear Tooth extends below the Base Circle, the Portion of the involute below the Base Circle will be Non-Involute
• For A Tooth with Fillet Radius (fillet radius is a must), any contact below Form Diameter will be Interference

When Root Diameter lies below Base Circle Diameter (BCD) 

• With Form Diameter also lying below BCD
• Profile below BCD will be Non-Involute
• Any contact with this Non-Involute Profile will be Interference
• For this, a deeper Fillet Cut is given (than required), called “UNDERCUT”

For a Normal Gear:

• In ideal conditions, Involute is Tangent to the Root Fillet at the Form Dia. Transition Point

For an Undercut Gear:

• The Root Fillet Curve lies inside the Involute Curve 
• A deeper cut
• Weakens the Tooth

To Prevent Notch after Finishing (Grinding) 

• Hobbed Gears are manufactured with Undercut
• For free movement of Finishing Tool
• Without Undercut, Finishing Operation will Create a notch

• Protruded Hob Tip
• Provided on Hob
• To Undercut the Unfinished Gear
• To prevent notch creation during finishing operation

• Position of each point on the Gear Involute can be identified by it's Roll angle or Roll Diameter
• The Picture depicts the Roll angle and Diameter of a Specific Point "A" on the Involute

Roll angle = ξA = [sqrt (rA^2 - rb^2)]/rb  --- in Radians

ξA: Roll Angle of Point "A"

rA: Radius of intended Point "A"

rb:  Radius of Base Diameter

• Each point on the Involute has its discrete Pressure Angle
• The picture depicts Pressure Angle of point "A"

ξA = tan αA    ---- in Radians

ξA: Roll Angle of Point "A"

αA: Pressure Angle of Point "A"

• Angle between the Gear Tooth and Gear Axis
• At each Roll Angle, Helix Angle will be different

• Inverse of Diametral Pitch
• PCD/T or D/T inches
• (D/T) * 25.4 mm
• This gives an insight into the size of the Gear
• In the Direction Normal to the Teeth
• Transverse and Normal Direction is same for Spur Gears

• Helical Gears
• In the Direction Tangential to the Gear Cylinder
• Normal Module / Cos (helix angle)

Normal Pitch

• Distance between 2 adjacent Teeth (same flank) Normal to Teeth

Transverse Pitch 

• Distance between 2 adjacent Teeth (same flank) in Transverse Direction

Axial Pitch

• Applicable to Helical Gears
• Draw a line Parallel to Axis from a Point of a Tooth to it's Adjacent Tooth
• Length of the Line will denote the Axial Pitch

• Ratio of Contact Length and Base Pitch
• It depicts the Number of Teeth in Contact
• High Contact Ratio is desirable
• More Teeth in Contact means less load on one particular tooth, hence higher life
• Higher Contact Ratio also helps with Gear NVH Characteristics

• Also called Overlap Ratio
• Depicts how much the mating teeth overlap each other
• Function of Gear Face Width and Helix Angle
• Face Width / Axial Pitch

• Transverse Contact Ratio + Axial Contact Ratio
• For Spur Gears: Axial Contact Ratio = 0