Development and Analysis of a New Arc Gear
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Arc radius and center position For the above-mentioned tooth thickness calculation formula, it can be seen from the analysis that when the tooth height ha has been determined, if the pressure angle is increased, the radius a of the arc is increased so that the tooth top thickness Sa is constant. If the pressure angle is reduced, the arc radius a is decreased. When the tooth height ha is constant, if the pressure angle is increased, the tooth tip thickness is decreased so that the radius a of the arc does not change, and the tooth tip thickness is increased when the pressure angle is decreased. Therefore, when the tooth height is constant, the pressure angle, the radius of the arc, and the thickness of the crown are interdependent. The pressure angle is large, the tooth tip is narrow and the root is thick, and the bending strength is good. On the contrary, the pressure angle is small, and the flank has a relatively large radius of curvature, and the tooth surface contact strength is high. More importantly, the size of the pressure angle determines the shape of the gear. A reasonable tooth design should make the entire tooth profile close to the inline parabolic shape (equal strength beam profile).
The bending stress of the entire tooth surface along the tooth height tends to approach. The shape of the top of the tooth profile and the root tooth thickness should be avoided. It should also be noted that the magnitude of the pressure angle directly affects the force on the tooth surface. The pressure angle is increased, the circumferential force is reduced, the effective component force is reduced, and the efficiency is low. At the same time, the radial component of the tooth surface is large, which increases the load of the bearing and affects the service life of the bearing.
Tooth width Since the pure rolling gear is a point meshing gear, the end face coincidence of the gear is zero, and the continuous movement of the gear is ensured by the axial coincidence of the gear. The cylindrical surface of the pure rolling gear is unfolded. The spiral angle of the column is expanded for the cylindrical surface of the pitch rolling pure gear section. The thin oblique line part is the gear tooth, and the blank part is the tooth groove. At the point C of the front end face of the driven wheel tooth, the meshing is started, and when it is turned to the point D of the rear end face, the meshing process is completed, and the engagement process of the pair of teeth is completed.
The simulation of the meshing dynamic simulation of the meshing machine only needs to be carried out in the end face. This is because a pair of parallel-axis helical gears or curved gears with no relative sliding of the meshing tooth profiles in the end faces are a pair of pure rolling gears. The simulation conditions and parameters are: a pair of gears with end-face modulus m=3mm, the number of teeth is z1=23 and z2=56, the profile radius is 29m convex arc, the height of the tooth tip is 0.3m, the root height is 0.5m, pressure angle is 20.
In this paper, based on the principle of pure rolling engagement of gears, a new type of arc pure rolling meshing gear is constructed, that is, the gear teeth of the circular gear are narrower than the gear teeth of the involute helical gear with the same indexing scalar thickness. Both theoretical analysis and computer simulation prove the correctness of the new circular pure rolling gear meshing theory described in this paper. In addition, the method for determining the basic parameters of the gear and the relevant formula for estimating the parameters are also given. The data in this paper can be used as a reference for actual gear production design.