Short Answer:
Undercutting is a condition in gear teeth where a part of the tooth near its base is removed due to improper cutting of the gear profile. It happens when the number of teeth on a gear is too small or when the gear cutting tool removes excess material below the base circle. This weakens the tooth and changes its shape, reducing the strength and efficiency of the gear.
Undercutting can be avoided by increasing the number of teeth, using profile shifting, or modifying the pressure angle. These methods help to maintain the correct involute shape of the gear and ensure smooth power transmission.
Detailed Explanation :
Undercutting
Undercutting is an undesirable phenomenon in the gear manufacturing process, especially in gears with a small number of teeth. It occurs when the gear-cutting tool removes a portion of the tooth near the base circle, making the tooth weaker and altering its involute profile. The involute profile is essential for smooth and uniform power transmission between gears, but undercutting distorts this shape.
In a correctly cut gear, the working surface of the tooth is entirely an involute curve, and the base of the tooth remains intact. However, in a gear with too few teeth, the cutter interferes with the non-working region during the generation process. This interference removes extra material near the root of the tooth, resulting in undercutting. The tooth then becomes thinner, weaker, and prone to breakage under load.
Cause of Undercutting
Undercutting primarily happens due to geometric and manufacturing factors. The major causes include:
- Low Number of Teeth:
When a gear has fewer teeth, the involute curve starts very close to the base circle. During cutting, the gear tooth tip of the generating rack removes material from the root of the tooth, creating an undercut. - Improper Pressure Angle:
Smaller pressure angles increase the possibility of undercutting. This happens because the cutter must remove more material to generate the desired tooth shape. - Excessive Addendum:
A large addendum increases the contact depth of the cutting tool, which may lead to material removal from the base of the tooth. - Incorrect Cutter Design or Adjustment:
If the cutting tool is not correctly designed or positioned, it can remove unnecessary material near the base of the gear tooth. - Interference During Generation:
Sometimes, while cutting a gear with few teeth, the path of the cutter crosses the base circle, causing the lower part of the tooth to be chipped away.
Effect of Undercutting
Undercutting negatively affects the performance and durability of gears in several ways:
- Weakens the Tooth Strength:
The removal of material from the tooth base reduces the thickness and strength of the gear tooth, making it more likely to fail under load. - Reduces Load-Carrying Capacity:
Since the effective contact area between mating teeth decreases, the gear can carry less torque and power. - Distortion of Tooth Shape:
The involute portion of the gear tooth gets distorted, which affects the smoothness of engagement between gears. - Increases Wear and Noise:
The irregular shape of undercut teeth causes vibration and noise during operation, leading to faster wear. - Reduced Efficiency:
Due to poor contact and increased friction, the transmission efficiency decreases.
Mathematical Condition for Undercutting
For a spur gear to avoid undercutting, there is a minimum number of teeth that must be maintained. The minimum number of teeth on a standard 20° pressure angle gear to avoid undercutting is 17 teeth, while for a 14.5° pressure angle gear, it is 32 teeth.
The relationship between pressure angle (φ) and minimum number of teeth (Zₘᵢₙ) can be given by:
where,
- = minimum number of teeth required to avoid undercutting
- = pressure angle
- = constant related to addendum coefficient
This formula helps gear designers ensure that the number of teeth is sufficient to avoid undercutting during the cutting process.
Methods to Avoid Undercutting
There are several effective methods to prevent undercutting in gears:
- Increase the Number of Teeth:
By increasing the number of teeth, the curvature of the gear tooth decreases, and the cutter does not reach the base circle during manufacturing. - Use of Profile Shifting (Addendum Modification):
Profile shifting means slightly moving the cutter outward or inward from the standard position. A positive profile shift increases the tooth thickness near the root and prevents undercutting. - Increase the Pressure Angle:
A higher pressure angle shortens the contact path and reduces the risk of undercutting. Common pressure angles like 20° or 25° are preferred. - Reduce Addendum:
Decreasing the height of the tooth above the pitch circle limits how deep the cutter goes, helping to avoid excess material removal at the root. - Use Stub Teeth Gears:
Stub teeth have a smaller addendum and a larger dedendum, which reduces the risk of undercutting.
Example
For a spur gear with 20° pressure angle and 15 teeth:
Since the minimum number of teeth required to avoid undercutting is 17, the gear will experience undercutting during manufacturing. To eliminate this issue, the designer can increase the number of teeth to 17 or apply a positive profile shift to preserve the proper involute form.
Importance of Avoiding Undercutting
Avoiding undercutting ensures that the gear maintains its designed strength, contact ratio, and smooth motion. Gears without undercutting have better load distribution, less vibration, and longer life. Thus, in mechanical design, preventing undercutting is a crucial part of ensuring gear reliability and performance.
Conclusion
Undercutting is the removal of material from the base of gear teeth during manufacturing, leading to a weaker and distorted tooth profile. It mainly occurs in gears with a small number of teeth or incorrect pressure angles. The problem can be prevented by increasing the number of teeth, using profile shifting, or increasing the pressure angle. Avoiding undercutting is essential for maintaining gear strength, efficiency, and smooth operation. A properly designed gear without undercutting ensures durability and reliable power transmission.