When grinding the worm wheel, the key principle of selecting the worm wheel is that the number of worm wheel heads Z1 and the number of teeth of the workpiece Z2 are prime numbers (i.e., no common factors), which is the core reason to avoid periodic engagement error and ensure grinding uniformity.

If the number of worm wheel heads (Z1) and the number of workpiece teeth (Z2) share a common factor

(for example, Z1=2 and Z2=40, with a common factor of 2), the specific thread of the grinding wheel will consistently engage with the fixed tooth slots of the workpiece.

For example, when a double-head grinding wheel (Z1=2) is used to grind a 40-tooth gear (Z2=40): Head A of the grinding wheel only engages with the odd-numbered teeth (1, 3, 5,..., 39) of the gear; Head B only engages with the even-numbered teeth (2, 4, 6,..., 40) of the gear. As a result, the grinding wheel's trimming error (such as thread pitch deviation) will periodically affect the same set of tooth slots on the gear, causing the thread pitch error to change in a regular pattern.

This can lead to periodic grinding patterns or defects on the gear's tooth surface, reducing the precision and lifespan of the gear transmission, and also produce a fixed-frequency engagement noise.

To address this issue, use Z1 and Z2 as coprime numbers (for example, Z1=3 and Z2=40). This ensures that each head of the grinding wheel engages with all the teeth of the gear in sequence, distributing the error across the entire tooth surface and reducing periodic fluctuations.