The tooth surface error caused by gear heat treatment distortion is the main reason for the offset of gear contact area. Because the influence of tooth surface error on the contact area is vectorial, a more accurate first-order relative tooth surface error principle is used to explain the contact area offset principle after heat treatment. Among them, the first-order relative tooth surface error refers to the relative pressure angle error α And relative helix angle error β， It is defined as follows:
Where, Δα z、 Δα B pressure angle error of main and driven teeth respectively; Δβ z、 Δβ B helix angle error of main and driven teeth respectively.
Taking the offset analysis of the contact area generated by the meshing between the convex surface of the driving gear and the concave surface of the driven gear after heat treatment as an example, the error value of 45 points on the tooth surface of the driving and driven gear after heat treatment (composed of 5 points in the direction of tooth height I and 9 points in the direction of tooth length J) is shown in Fig.
Make the relative clearance between the big end tooth surface of the driving and driven teeth LH, the relative clearance between the small end tooth surface LT, the relative clearance between the top of the driving tooth and the tooth root of the driven tooth LF – t, and the relative clearance between the root of the driving tooth and the tooth surface of the top of the driven tooth LT – F, which is defined as follows:
Figure 2 (a) shows β The schematic diagram of the impact analysis on the contact area in the tooth length direction shows that the relative clearance of the large end of the driving and driven teeth increases from LH to L ′ h, and the relative clearance of the small end decreases from lt to L ′ t. Compared with the theoretical tooth profile, the decrease of the gap will lead to the first contact or non-contact to contact, the increase of the gap will lead to the later contact or contact to non-contact, and the contact area after heat treatment will shift to the small end relative to the theoretical contact area. Further, the helix angle error of the convex surface of the main gear Δβ The smaller the ZT, the smaller the helix angle error of the tooth concave surface Δβ When Ba is larger, l ′ H value will increase, l ′ t value will decrease, and the actual meshing contact area will deviate more towards the small end.
Figure 2 (b) shows α The schematic diagram of the impact analysis on the contact area in the tooth height direction shows that the relative clearance between the main tooth root and the top tooth surface of the driven tooth increases from LT – F to L ′ T – F, the relative clearance between the top tooth of the driven tooth and the root tooth decreases from LF – t to L ′ F – t, and the contact area after heat treatment will shift to the tooth root relative to the theoretical contact area. Similarly, the pressure angle error of the convex surface of the driving gear Δα The smaller ZT is, the pressure angle error of the concave surface of the tooth is Δα When Ba is larger, l ′ T – F value will increase, l ′ F – t value will decrease, and the actual meshing contact area will deviate more from the tooth root.