AGMA 90FTM1-1990 pdf download.Contact Stresses in Gear Teeth.
The Need For a New Contact Stress Theory
A traditional line contact diagram for a worm and worm gear is shown in Figure 1. This is the contact diagram we obtain when there is no mismatch, so that the gear is exactly conjugate with the worm. The three lines shown in the diagram represent the contact lines on three adjacent tee th. To obtain the tooth forces and the corresponding contact stresses, we assume that the load intensity is constant along each contact line. From the specified torque, we calculate the total tooth force. We then divide the total tooth force by the total length of the contact lines, to obtain the load intensity, and to find the individual tooth forces we multiply the load intensity by the lengths of the individual contact lines. The contact stress at each point Is found by Hertz’s .line contact theory, using the relative curvature in the direction perpendicular to the contact line.
The assumption of constant load intensity is questionable, even when the worm and the gear are exactly conjugate, and the contact lines extend to the edges of the teeth. If the load intensity is constant along each contact line, it must be independent of the relative curvature, which does vary along the contact lines, and this independence seems unlikely. However, in the case where there is some mismatch the contact areas do not reach the edges of the teeth, and it Is quite certain that the load intensity is not uniform. Instead of line contact we have point contact, though the contact areas may be very elongated, and we therefore have to consider the use of Hertz’s point contact theory.
Figure 2 shows the contact diagram for the gear pair of Figure 1, when there is some mismatch between the worm and the gear. The worm is thread—milled with five threads, and has a lead angle of 21.31 degrees. The mismatch is obtained by modifying the profile of the bob that is used to cut the gear, by making its lead slightly shorter than that of the worm, and by swivelling the direction of its axis when the gear is cut. so that it is not exactly perpendicular to the gear axs. The contact diagram shows the contours of constant separation between the worm thread, and the envelope of the gear tooth positions relative to the worm. In other words, It shows how closely the gear teeth approach the worm thread during the entire meshing cycle, assuming that both are rigid and that the angular velocity ratio is exactly constant. The two curves in the diagram show the contours where the separation Is 0.0005 inches and 0.0010 inches. If we had included the curve where the separation Is 0.00025 inches, this would correspond approximately to the area that would be coloured by the marking compound In a bearing test.AGMA 90FTM1 pdf download.