Taking involute spur gear as an example, this paper explains the mapping, calculation and verification of involute spur gear. In the example, reverse engineering software is mainly used as a method of gear parameter verification.
Number of teeth z = 16, diameter of involute spur gear addendum circle Da = 93.98 mm, diameter of tooth root circle DF = 70.05 mm, length of common normal k = 3, wk = 39.36 mm; Wk － 1 = 24.84 mm, center distance a ‘= 165.12 mm.
Because the standard of involute spur gear generally adopts American Standard, that is, diameter control. There are four kinds of involute spur gears: 14.5 °, 20 °, 22.5 ° and 25 °. Calculate the module of the gear with the formula respectively, and the calculation results are shown in the table.
The value of M calculated by the formula is relatively close when the tooth shape angle is 20 ° and 25 °, h * a = 1, c * = 0.35, and the modulus is close to 5.08. At this time, it is determined that the gear diameter pitch is DP = 5. Calculate the displacement coefficient, tooth top circle diameter and tooth root circle diameter when the tooth shape angle is 20 ° and 25 ° respectively to determine the final tooth shape angle.
1) Check the diameter joint table. When the diameter joint DP = 5 and the pressure angle is 20 °, the common normal length w * 2 = 23.633 7 mm and w * 3 = 38.630 5 mm are calculated by formula. At this time, the displacement coefficients are x = 0.347 2 and x = 0.210 0 respectively, and take the average value x = 0.278 6; When x = 0.278 6, a = 20 °, h * a = 1, c * = 0.35, calculate the tooth top circle diameter Da = 94.270 6 mm and the tooth root circle diameter DF = 70.394 6 mm.
2) Check the diameter joint table. When the diameter joint DP = 5 and the pressure angle is 25 °, the common normal length w * 2 = 23.904 mm and w * 3 = 38.368 mm are calculated by formula. At this time, the displacement coefficients are x = 0.218 0 and x = 0.231 0 respectively, and take the average value x = 0.224 5; When x = 0.224 5, a = 25 °, h * a = 1, c * = 0.35, calculate the tooth top circle diameter Da = 93.720 9 mm and the tooth root circle diameter DF = 69.844 9 mm.
It can be seen from the two sets of data that when the tooth profile angle is a = 25 °, the tooth top circle diameter and tooth root circle diameter of involute spur cylindrical gear are close to the mapping value. Therefore, this set of data is taken as the basic parameters of tooth profile, that is, DP = 5, tooth profile angle is 25 °, h * a = 1, c * = 0.35, displacement coefficient is x = 0.224 5, tooth top circle diameter Da = 93.720 9 mm, tooth root circle diameter DF = 69.844 9 mm.