Design of circular gear hob blade shape by common rack method
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Manufacturing technology uses the common rack method to design the arc gear hob blade shape. Zhanjiang Ocean University Liu Jiehua provides a new method descriptive public rack arc gear hob as shown, when the hob worm 1 turns over the angle, the arc tooth shape The equation is: 1 刖 长期 For a long time, the design of the circular arc hob is the normal truncate of the basic tooth profile of the gear as the basic worm of the hob. Since the meshing of the hob and the gear is the meshing of the interlaced shaft gear, the hob The tooth shape of the basic worm must be calculated according to the principle of space meshing. Otherwise, the blade shape of the hob will cause a theoretical calculation error, resulting in the actual size of the gear not in conformity with the theoretical size. Moreover, according to the usual space meshing principle, it is also complicated to accurately design the hob blade shape according to the multi-degree of freedom method. To this end, this paper introduces the concept of a common rack, using plane meshing to accurately calculate the shape of the hob, so that the calculation of the shape of the hob is simple and easy to understand.
2 Arc gear hob blade shape calculation The common rack method is to imagine an intermediate medium common rack in the meshing of the gear and the basic worm of the hob, which meshes with the gear and meshes with the basic worm of the hob. According to the gear and the common tooth The meshing relationship of the strip is determined by the known tooth profile of the gear face, and the common rack tooth shape conjugated with the same is obtained, and then the common rack tooth shape which is conjugate with the basic worm of the hob is obtained, and the basic worm of the hob is obtained. Tooth shape, the calculation process is solved by simple plane meshing. 2.1 The mutual position of the hob worm and the arc gear is set. The arc position of the arc gear and the basic worm of the hob is rotated by the h-angle. In order to facilitate the analysis and calculation, the following two plane coordinate systems are selected: the moving coordinate system in which OXYi is fixed to the rack of the worm 1; the moving coordinate system in which the O1X171 and the hob worm 1 are fixed is n is the section of the hob worm The radius of the circle, p1 is the screw parameter of the hob worm (p1=nctgU), UU is the helix angle of the hob worm and the arc gear on the pitch circle (the hob is right-handed, the gear is left-handed), and the p point is the meshing node circle. The reference tooth profile of the arc gear is the normal tooth profile of the common rack. The Chinese standard specifies that the hob is approximated by the normal tooth profile of the arc gear hob.
2.2 The tooth profile equation of the common rack The reference tooth profile given in the standard is the normal tooth profile of the common rack. For the detailed parameters of the reference profile of the arc gear, see the rack normal tooth in the coordinate system OnXnYn. The mutual position of the worm and the arc gear is obviously the following relationship between the normal section of the common rack and the section along the end face of the hob: (2) 2.3. The worm tooth profile conjugated with the rack is found in the hob After the rack of the worm end face (common rack) is toothed, the tooth profile of the end face of the worm is solved by a flat toothed normal theorem. The enlarged section of the hob worm end is enlarged, and the normal equation of the overtone Mt(xt, yt) on the rack is in the OtXtYt system: it is known by the toothed normal theorem that when the Mt point enters the mesh, the Mt point is passed. The normal tooth profile should pass through the meshing node. In the Ot system, the coordinate of point P is (Vh,) substituted into the above formula: the meshing point is both the point on the rack and the upper part on the hob worm is the arc. The tooth profile equation of the basic worm of the gear hob makes it spiral around the axis of the hob worm, and the equation of the tooth surface of the worm can be obtained. The axial section of the worm can be obtained by axial sectioning to obtain the axial edge equation of the hob. . Take an auxiliary coordinate system O2X2Y2Z2 fixed to the worm. The original position 1 and 2 coincide at the initial position, and the X1Y1 axis coincides with the X2Y2 axis respectively, so that the worm does not move, and then the 1 series and the worm end face tooth shape fixed thereto are wound together. The Z2 axis is a spiral motion of P1, which forms the helical tooth surface of the worm. The transformation from 1 to O2 is: dispersion, 9 can be determined according to Table 1: Table 1 3 Calculation of known arc gear concave The parameters of the tooth are as follows: modulus mn=6, pressure angle 30, tooth profile arc radius 1.65m, tooth profile center offset 0.6289mn, X/= knife related parameters are as follows: pitch circle radius ri=51.02mm, spiral liter Angle 3°22', helix angle U= 18.8821434mm In order to facilitate the comparison of exact co糸 values ​​and approximations, here we give the approximate "normal rack method" axial edge calculation formula: in order to approximate the axial coordinates The value is consistent with the coordinate position calculated by equation (6), and the coordinates must be translated, that is, 3 axes = factory 1 - ynX axis = Xn. Here we only take the coordinate values ​​of the hob axial edge of the three points and the approximate design method. The axial edge coordinate values ​​are listed in Table 2. Table 2 Parameter T Tumbler Axial Edge Accurate Value Hob Axial Edge