Calculation principle of chord tooth thickness and chord tooth height measurement of double circular arc gear

The normal chord tooth thickness is the shortest distance between the two theoretical contact traces (spatial helix) on the left and right tooth surfaces. See the calculation diagram of chord tooth thickness.

According to the contact trace equation of tooth surface:

The distance between the two helices is:

Substituting the formula, let:

Differential post solution θ The formula is as follows

In the above formula β0 is the helix angle of the measuring point.

Then, the iterative calculation is repeated according to the following formula until θ I + 1 and θ I is basically equal (the error is less than or equal to 1 ″).

According to the θ The formula of chord tooth thickness s is as follows:

The chord tooth height h is the radius of the tooth top circle minus the X coordinate of the measuring point

The following parameters are substituted into the formula to calculate the chord tooth thickness and the measured chord tooth height

The calculation method of chord tooth thickness and chord tooth height of circular arc gear based on Newton iteration method, with the help of computer, greatly reduces the workload than manual calculation, and the accuracy is also well guaranteed, which provides convenience for production.