# Finding the proper measuring ball diameter of helical gear

#### Diagramming the imaginary circle diameter DPT of helical gear measuring ball

The figure is a diagram of the imaginary circle diameter DPT of the measuring ball. Any tooth groove is selected for relevant drawing, so that the involutes of the tooth profile of the tooth groove are respectively J1 and J2, and the intersection points of the tooth top circle and the tooth top circle are respectively g, h, and the intersection points of J1 and the circle diameter DZ are a ‘.

Through the “straight line” command, draw the straight line GH, and make the straight line OK and OA ‘, so that K is the midpoint of GH; Through the “angle continuous” command in “dimension”, we can get ∠ a’ok = 5.195 °。 From the formula, we can get ∠ b’ok = 3. 688 °，β z= 32． 5889 °，β b= 28． 0243 °。 The line oo1 in the figure and the line OK in the figure 6 are the symmetrical center line of a tooth groove on the normal section of the helical gear.

Through the “straight line” command, through o point and with the line OK into 3. 688 ° If the straight line of the included angle intersects the circle with diameter DZ at point B ‘, then point B’ is the projection of the contact point between the measuring ball and the surface of the J1 tooth profile on the normal section of the helical gear with excess ball center. Then use the “straight line” command to make the tangent line of the base circle to the involute of the tooth profile in the direction of J1 through point B ‘, and intersect with J1 at point M; The straight line MB ‘is perpendicular to the involute of tooth profile J1. Extend the intersection of MB ‘and OK at O1 point through the “edge alignment” command, which is the center of the measuring ball.

Call the “circle” command to draw a circle with O1 point as the center and o1m as the radius, that is, the circle with diameter DPT in Figure 7, which is the imaginary circle of the measured ball. Dimension diameter DPT with dimension command= Φ 13.140。

#### Finding the proper measuring ball diameter DP of helical gear

The diameter of measuring ball DP can be obtained from the formula= Φ 11.599。 In order to select the standard steel ball conveniently, the diameter of the measuring ball obtained is rounded to the diameter of the standard steel ball close to 11.500mm, and then the measuring distance of the measuring ball can be obtained by graphic method.

For the internal helical gear, the proper measuring ball diameter can be obtained by imitating the graphic method of the external helical gear. Using the graphic method in this paper to calculate the proper measuring ball diameter of helical gear is suitable for both internal and external gears, as well as standard gears and modified gears. However, it should be pointed out that in caxa2009, the accuracy of drawing the tooth profile of internal helical gear end face is low, and it will be used after the accuracy of the version is improved. 