The figure shows the geometric relationship of the measuring ball in the alveolar. The N-N section is the normal section of thepassing through the center of the measuring ball with diameter DP. There are two tangent contact points between the measuring ball and the surface of the tooth groove. The projection points on the N-N section are B ‘and C’ respectively; The helix of the contact points between the excess ball and the surface of the tooth groove on the helical gear intersects the N-N section at points a ‘and d’ respectively. The points a ‘, B’, C ‘and d’ are simultaneously located on the circumference with diameter DZ, β Z is the helix angle of the helix on the diameter DZ circle. The circle of diameter DPT is tangent to the surface of the tooth groove, and is exactly the same as the center of the measuring ball DP. It is the imaginary circle of the measuring ball DP. On the M-M unfolding section, points E and F are the unfolded positions of the contact points between the measuring ball and the alveolar surface, and points a, B, C and D are the unfolded positions of points a ‘, B’, C ‘and d’, respectively.
In the N-N section, there are:
In the M-M development section, there are:
The relationship between sphere diameter DP and imaginary circle diameter DPT is as follows: