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Generation Line - Machining Method of Skew Bevel Gears

Modern preparing strategy of tooth surface with the era line as chord of confront circular cutters is put forward. Agreeing to creating rule of winding slope adapt and space coinciding hypothesis, arrangement hypothesis of era line of tooth surface almost skew incline gears is examined. Moving handle show of processing preparing with skew slope gears is built, and profile of the gears can be machined utilizing three tomahawks linkage strategy based on the demonstrate. Ma chining test of the gears is carried out on try stage outlined. Moreover, 3D focuses cloud demonstrate of tooth surface are calculated in light of scientific show of the tooth surface which has been built up, and datum of work hubs on genuine tooth surface are collected. At that point surface blunders is assessed by ordinary vector condition of the tooth surface which has been created. At last, this strategy is demonstrated to be compelling and feasible.

Mathematical Modeling and Generation Principle of Skew Bevel Gears

There is assumed a sphere which is setting radius dimension as R and a base cone which culmination and the sphere center coincide, as shown in figure1. The base cone and the great circle of a sphere-a plane Q are tangent to a line. When the base cone is fixed, the plane Q rotate around the base cone and they keep tangency all along. Under the condition of the above expression, the movement of the plane Q relative to the base cone is what is needed pure roll for generating spherical involute. If there is a straight line ML on the plane Q. In the expansion, the straight line ML can spread a curved surface, while the curved surface is then involute helicoids. As shown in figure. 2. Base cone angle δb generatrix of small end about base cone Rb base cone circle spreading angle φ plane Q spreading angle γ. Fixed coordinate systems S(o-x,y,z) are rigidly connected to the gear blanks. In this systems, origin o1 and x1-y1 plane coincide with center of cone and bottom of base cone respectively; At the same time, Matrix M1t provides the coordinate transformations from system S1 into the top coordinate system St(ot-xt,yt,zt) by offsetting A along the axis z1; And matrix Mts defines the relation between the stationary coordinate systems St and Ss(os-xs,ys,zs), in which coordinate systems Ss rotate φ on the axis zt ; Afterward Matrix Msb performs the coordinate transformations from system Ss into the top coordinate system Sb(ob-xb,yb,zb) by moving π/2-δb around the axis ys, at the same time axis xb and origin ob coincide with the line of base cone and the plane Q respectively Finally, Mbq denote the transformations from Sb into Sq(oq-xq,yq,zq) by revolving γ around zb connected to the plane Q.

Figure 1. Formation Principle Tooth Surface Figure 2. Coordinate Transform

In the spreading process, a cluster of tracing line that are formed by generation line ML make up involute helicoids. In the coordinate systems S, the value of the generation line ML can be acquired by Coordinate Transform from coordinate systems. When parameter φ continuous change, In the coordinates system S (o-x,y,z) the mathematical model of a point on the Tooth-surface can be performed by applying the following equation:

When big circle (plane Q) pure roll, the circular arc that base cone bottom circle is bypassed by big circle is same length. In the Cartesian coordinate system, the vector equation of tooth surface about circle spreading angle φ and polar Radius ρ is shown :

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