Calculation of Time varying Contact Line Length of Helical Gear Meshing Surface

(a) Left side of pitch line
(b) Right side of pitch line

As shown in Figure 1, the length of the contact lines on the left and right sides of the pitch line changes during the engagement of a single pair of helical gears from entry to exit. In Figure 1, εα Is the end face coincidence; εβ Is axial coincidence; εγ Is the total coincidence; β B is the helix angle of the base circle, (°); B is the tooth width, mm. According to the geometric relationship in Figure 2, it can be concluded that:

Where, zp is the number of teeth of helical driving gear.

As shown in Figure 1 (a) and Figure 1 (b), the length lL and lR of the helical gear engagement single pair of teeth contact line on the left and right sides of the pitch line are respectively:

The total length l of helical gear meshing single pair of teeth contact line is:

The total contact line length within one base circle pitch is:

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