Determining the characteristic straight line generating the tooth surface point According to the tool parameter, the tooth height of the face gear tooth surface is determined, and the tooth length is arbitrarily selected first, so the tooth surface mesh can be pre-divided in the surface gear coordinate system S2. According to the tooth length and the tooth height parameter at the grid point, a set of straight lines parallel to the x2 axis is made in the surface gear coordinate system S2, and the tooth surface points are determined by the intersection of the tool plane and the straight lines of these characteristic lines, such as teeth. The relationship between the surface and the characteristic line. The equation of the characteristic straight line in the coordinate system S2 is r(l)2(t)=[t, y2, z2]T(4) where y2, z2 are values ​​determined by the tooth length and the tooth height.
Φs is the step angle, which is given during the search process, φ2=i2sφs, so M2s is determined. The intersection of the blade surface and the characteristic line can be obtained by the equation r(l)2(t)=r(s)2(θs,us)(6), and the intersection of the blade surface and the characteristic line can be obtained after the solution is solved. The following formal equation a[sin(θ0s θs)-θscos(θ0s θs)] b[cos(θ0s θs) θssin(θ0s θs)] c=0(7) can be obtained, where a, b, c, θ0s are constants, and The range of θs has been determined. Using the dichotomy, θs can be solved, and then the intersection of the flank and the characteristic line is obtained. The point generated by the different positions of the blade surface is obtained by the change of the step angle φs, and then the x2 coordinate of the intersection point can be used to determine whether the point is the new cutting point of the blade face.
The initial value of the step angle change amount is given a larger amount. If a tool position produces a new cut point, and the intersection of the next tool position is a cut point of the tool, the previous tool position is returned and the step angle is changed. After the amount is reduced by half, the cutting is continued, and the search is performed. The step value is changed by the step angle to change the limit value. The limit value controls the accuracy of the search.
The determination of the transition curve shows through simulation that when the tool cuts the transition curve to the root portion, the tool will always cut the tooth surface, that is, the blade surface has a point of intersection with the straight line here, then the intersection point is always a new generation point. From the transition curve to the top of the tooth, the tool will leave the tooth surface in advance, that is, after a certain point is formed on the straight line, that is, after the final tooth surface point, the intersection of the knife surface and the straight line here will be outside the tooth surface. There will be no new rollpoint generation. Based on this, the transition curve can be searched for, for example. The accuracy of the transition curve has a lot to do with the meshing of the tooth flanks and the amount of change in the step angle. Therefore, when determining the transition curve, the mesh should be as dense as possible and the step angle change should be as small as possible. Figure 3. Determination of the tooth length of the tooth surface transition curve. 6 Determine the tooth length, that is, determine the inner and outer diameters of the face gear.
A suitable tooth surface is the portion between the tip of the tooth tip and the root cut. The outer diameter is determined by the tip of the tooth tip. First, the points on the tooth surfaces on both sides of the tooth tip are obtained, and then the interference is determined according to the x2 coordinate. Here, the outer limit point of the appropriate tooth surface is taken. The inner diameter is determined by the root cut. For example, (a) according to the determination method of the tooth surface transition curve, the intersection point A of the transition curve and the crest top can be determined first, here the inner limit point of the tooth surface. But there are still some singularities on the transition curve, so remove the inappropriate parts. As shown in (b), the singular part of the transition curve from A to B, and the curve of the part A' to B' on the surface of the blade, the corresponding θs value range is [r2fs-r2bs/rbs, r2as-r2bs/rbs On the transition curve, B to C are formed by the cutter tip, which corresponds to θs value of r2as-r2bs/rbs.
Therefore, it is possible to search along the transition curve from point A and find the point B where the first θs value is r2as-r2bs/rbs, which is the inner limit point of the appropriate tooth surface. Figure 4 is based on the transition curve to find the tooth length. 7 This paper introduces a numerical simulation method of the face gear. The main idea of ​​this method is to simplify the complicated spatial entity Boolean operation in the gear machining simulation to a simple intersection of the space line and the surface. The accuracy of the method is related to the limit value of the step angle change. The smaller the limit value, the higher the accuracy.
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