Analysis of the Accuracy of the Tool Tip of Curved Gears
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When machining the small wheel, transfer Cp to the gear shaft section of the calculation point forming position, denoted as Cp, ie Cp=M(ih,)RCp(23) Let eph=Cp nhCp nh(24) make from th nh to The directional angle of eph is p1, and the direction and size of p1 can be obtained by sinp1=ephth(25).
Let the directional angle from ep to eph be p, then p=p1-2(26) from t(h)cn(h)c to the directional angle of eph p2= p1(27) small tooth tooth length The acute angle formed by the direction and the main direction of the small wheel non-busbar is p2=180-p2 (28) at the conjugate contact point of the tooth surface, the tooth length direction of the large and small wheels and the large and small wheel profile The main direction of the non-busbar is in the common plane of the contact point. But they have different directions.
Correction of tooth surface curvature and determination of tool nose radius The theoretical curvature and short-range torsion Kx1, G1 and Ky1 of the small-toothed tooth surface in the th nh and th directions have been obtained. From the generalized Euler's formula and the Bertrand formula, the normal curvature Ky2 of the small-toothed surface eh direction and the short-range torsion Kx2, G2 and eh nh directions can be obtained.
Since there is an angle between the longitudinal direction of the large and small tooth surface of the hypoid gear pair in the common cutting plane at the contact point, it is impossible to make the large and small tooth surfaces completely without diagonal contact. . In the curvature correction, in order to avoid diagonal contact, the short-range torsion in the tooth length direction is not corrected. According to different needs, the direction in which the short-range torsion is not corrected can be selected between eh and eph. In the following discussion, the eh direction is taken as the direction in which the short-range torsion is not corrected. The short-range torsion G2 of the corrected tooth length direction is G2=G2. The corrected curvatures in the eh direction and the nh eh direction are Kx2 and Ky2. Then Kx2=Kx2Kx(29)Ky2=Ky2KyG2=G2 In the above formula, the upper symbol (negative sign) is the outer knife (concave surface), and the upper (positive sign) is the inner knife (convex surface).
The directional angle from t(h)cn(h)x to eh is 3=2, the normal curvature of the small tooth surface t(h)cn(h)x direction, the normal curvature Kxc and Gc short-range torsion and t(h) The normal curvature Kyc in the c direction can be obtained separately. Let Kyd be the normal curvature of the busbar direction of the small wheel, and the normal curvature and short-range torsion of the main direction of the production plane are Kxd and Gd.
From the relationship between the curvature of the induced method and the Mounière's theorem, the desired tool nose radius r=coshpKxd-bpsinbp (30) is rounded and taken to the appropriate value rcp. The tooth cutting experiment is carried out by using the method of the present invention. When the calculation point is selected at any position of the tooth surface, the length, width and narrow size of the tooth surface contact area can be conveniently adjusted, and the adjustment does not affect other factors such as diagonal contact. The expected results were obtained.