The interference in involute spur gears will increase when

Explanation:

​Involute spur gears:

• Involute spur gears are gears with teeth that have an involute profile, which ensures smooth transmission of motion and power. However, interference is a phenomenon that occurs when the non-working portion of a gear tooth comes into contact with the mating gear, leading to improper meshing and potential damage to the gear teeth.

Interference in involute spur gears:

• Interference in involute spur gears is closely related to the design parameters of the gear, such as the number of teeth on the pinion, pressure angle, module, and center distance. Among these factors, the number of teeth on the pinion plays a critical role in determining whether interference will occur during gear operation.
• When the number of teeth on the pinion is reduced, the gear tooth becomes smaller, and the base circle of the gear also decreases in diameter. This reduction in the base circle increases the likelihood of interference because the addendum of the mating gear tooth may extend into the non-working region of the pinion tooth. In simpler terms, the smaller the number of teeth, the more susceptible the gear is to interference, as the involute profile of the gear tooth becomes less pronounced, and the gear's ability to maintain proper meshing is compromised.
• To avoid interference, it is critical to adhere to certain design guidelines, such as selecting an appropriate minimum number of teeth for the pinion. This minimum number of teeth is determined based on the gear's pressure angle. For example, for a 20° pressure angle, the minimum number of teeth on a pinion to avoid interference is typically around 17. If the number of teeth falls below this value, modifications such as undercutting or profile shifting may be required to prevent interference.

Key Points:

• Reducing the number of teeth on the pinion increases the risk of interference in involute spur gears.
• Interference occurs when the addendum of the mating gear tooth extends into the non-working region of the pinion tooth.
• The minimum number of teeth on a pinion to avoid interference depends on the gear's pressure angle.
• Undercutting or profile shifting can be used to mitigate interference in gears with fewer teeth.

Important Formula:

The condition for interference can be mathematically analyzed using the following equation:

Base Circle Radius (r_b) = Pitch Circle Radius (r) × cos(Pressure Angle)

Interference is avoided when the addendum of the mating gear does not extend beyond the base circle radius of the pinion.