The FH hypoid gear of high performance drive axle is taken as the research object. The tooth surface modeling, tooth contact analysis, tooth surface error sensitivity analysis, ease off active design of paired tooth surface and reverse calculation of machining parameters are carried out, forming a complete set of meshing performance analysis and ease off active design method of FH hypoid gear.
First of all, through the cutter head used in hypoid gear machining, the imaginary profile wheel and the machining movement relationship between the workpiece and the large and small gear tooth surface model is established; then, the tooth contact analysis is carried out, and two kinds of tooth contact analysis methods are put forward here successively. First, the meshing equation is obtained according to the meshing relationship of the matched tooth surface. Given a certain variable, the two tooth surfaces can be obtained The first method can get the approximate boundary of ellipse without complicated curvature calculation, but it can’t get the real contact mark’s long axis, short axis and the whole tooth surface. In the second method, after calculating the instantaneous contact points, a series of axes passing through the instantaneous contact points and parallel to the normal of the contact points are used to obtain the major and minor axes and contact boundary of the instantaneous contact ellipse at corresponding positions. Finally, ABAQUS simulation is used to verify the correctness of the method.
Secondly, a non-linear sensitivity matrix of tooth surface error relative to machining parameters is proposed. The sensitivity of tooth surface error at different positions to each processing parameter is analyzed. The sensitivity function of each position of tooth surface relative to different machining parameters is calculated and fitted accurately. In this way, the sensitivity matrix established will be more accurate and the control of tooth surface performance will be more in place An accurate tooth surface error sensitivity function matrix is obtained to take into account the efficiency and accuracy of reverse machining parameter adjustment during tooth surface modification. Finally, a method for active design of hypoid gears with pair tooth surfaces ease off considering strength and dynamic performance is proposed.
1) The tooth contact analysis method based on numerical iteration avoids the derivation of complex curvature of two pairs of tooth surfaces. The real “major and minor axis” and contact boundary of each instantaneous “contact ellipse” can be obtained. It is found that the instantaneous “contact ellipse” is not a standard ellipse. The instantaneous contact line (i.e. the long axis of instantaneous contact ellipse) is not a straight line, which can reflect the actual contact situation of tooth surface.
2) The non-linear sensitivity matrix of tooth surface error relative to machining parameters is established, which takes into account the efficiency and accuracy of reverse processing parameters. The influence of tooth surface processing parameters on tooth surface is not all linear, so linear sensitivity matrix is not suitable for reverse calculation of machining parameter adjustment. At the same time, different processing parameters have different effects on the tooth surface, and the same processing parameter has different influence on different positions of the tooth surface. In actual production, the adjustment items should be reasonably selected according to the form of tooth surface error and equipment.
3) A case-off active design method for FH hypoid gears of drive axle is proposed, which takes into account the transmission strength and dynamic performance. The method is also suitable for the design and manufacture of other gears with complex tooth surfaces.