# Time varying contact line algorithm for helical gears

The contact line of helical gear is the intersection of the meshing tooth surface and the meshing plane of the driving wheel and the driven wheel involved in meshing. The meshing contact line starts at the point of the tooth top of the driven wheel on the front end face, then the contact line changes from short to long, then from long to short, and finally separates at a point at the root of the driven tooth on the rear end face. Schematic diagram of contact line change of helical gear, as shown in the figure. Due to the variation of tooth width, helix angle or other helical gear parameters, btan β B is greater than or less than the width of the meshing plane, so that the maximum value of the helical gear contact line can be expressed in two different ways. The width LCD of the meshing plane is formed by the joint action of the meshing line EF and the tooth top circle of the driving wheel and the driven wheel, and the expression is as follows:

Where: rap is the radius of top circle of driving gear teeth; RBP is the pitch circle radius of driving wheel; Rag is the radius of the top circle of the driven gear; RBG is the pitch circle radius of the driven wheel.

For a single tooth, the length of the contact line when the helical gear enters meshing will remain constant for a period of time as the helical gear rotation time increases from zero to the maximum contact line length; When the helical gear pair starts to withdraw from meshing, the length of the contact line gradually decreases, and when it withdraws from meshing, the length of the contact line is zero. In figure (a), the maximum contact line length is LCD / sin β b. In figure (b), the maximum contact line length is B / sin β b 。

from εα And εβ There are two different expressions for the maximum value of helical gear contact line:

Comprehensive coincidence degree ε R the contact line of helical gear between 2 and 3 changes, as shown in the figure. A single pair of teeth enters the meshing from point D and passes through node P until it exits the meshing. The calculation expression of the contact length of a single pair of teeth in an meshing cycle is as follows:

Where: RP is the radius of driving wheel base circle; ω P is the angular speed of driving wheel;

Where, REM function is the function defined by the rounding down function fix:

Then the contact line length of a single pair of helical gears at any t time is expressed as:

The calculation expression of the contact length of a single pair of teeth in the meshing cycle of helical gear can be written as:

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