Gears are a common type of spare part used in various industries, including aviation, shipping, and automobiles.
When designing and producing gears, there is a requirement on the number of teeth.
Some people claim that gears with fewer than 17 teeth cannot rotate, while others argue that this is incorrect and that there are many gears with fewer than 17 teeth.
In reality, both statements are correct and the reason for this discrepancy is open to discussion. If you have any ideas, feel free to share them in the comments.
Why is the number of teeth 17?
Why is number 17 significant and not another number?
The meaning of 17 is related to arts processing methods, as illustrated in the illustration below. A common method is to use a cutting board.
This calculation is based on mathematical principles. This is not to say that gears with fewer than 17 teeth cannot rotate, but if there are fewer than 17 teeth, it is more likely that a portion of the gear root will be cut off during gear processing, known as undercutting. This can weaken the strength of the gear.
The pressure angle a=20 degrees and the minimum number of teeth without countersinking is 17, as determined by the formula mentioned above.
Some users have expressed the opinion that it is worth considering whether the number of teeth can be less than 17. However, for standard gears, the number of teeth cannot be less than 17. This is because when the number of teeth is less at 17, the gear is subject to undercutting.
Undercutting occurs when using the generation method to cut teeth and the tooth tip of the cutter cuts too deep into the root of the gear tooth, thereby cutting off a portion of the tooth's involute profile from the tooth root.
Generating Cut and Radical Cut
Generating cut
The generator cutting method is a process used in gear machining that follows the geometry principle known as envelope. This method involves the use of two gears with involute tooth profiles. The angular velocity of the driven gear can be determined by engaging the two tooth profiles and meshing them. The relationship between the angular velocity of the driving gear (w 1 ) and the driven gear (w 2 ) is fixed and is represented by i 12 = w 1 /c 2 .
During the engagement of the two tooth profiles, the gear pitch circles roll against each other in a pure rolling motion. As a result, the tooth profile of the drive gear will occupy a number of relative positions with respect to the driven gear. The envelope of these positions is the tooth profile of the driven gear. This means that when the two pitch circles are in pure rolling motion, the involute profiles of the gear teeth can be considered as involute lines that are mutual to each other.
Undercutting phenomenon
Reasons for reduction:
Undercutting occurs when the point of intersection of the upper tool tooth line and the mesh line passes the mesh limit point N1 and the tool continues to move from position II. This results in cutting out a portion of the tooth's involute profile that was previously cut at the root.
For non-standard gears, it is mentioned that the number of teeth is less than 17.
Consequences of the reduction:
Reduction can have significant consequences on the performance and strength of the gears. For one, it weakens the bending resistance of gear teeth, making them more susceptible to failure under load. On the other hand, it also reduces gear transmission engagement, which is unfavorable to transmission efficiency.
