Research On Meshing Characteristics-Based Design & CNC Technology Of Point-Contact Spiral Bevel Gears Tooth Surface

Curved tooth bevel gears (spiral bevel gears and hypoid gears) are widely used in automobiles, tractors, construction machinery, machine tools and other mechanical products. The function requirement of the gears is to transmit expected motion and power smoothly, reliably and durably. To realize this requirement effectively, it is very important to obtain point-contact tooth surfaces with excellent gearing performance by proper design and manufacture. In current design and manufacture technique for the cured tooth bevel gears based on cradle machine tools, the gearing performance in whole tooth contact is not controlled directly in design, but in the situation of passive selection. The multi-axis simultaneous CNC bevel gear cutting machines provide an opportunity, but the design and manufacture technique for the cured tooth bevel gears based on cradle machine tools is still followed on the multi-axis simultaneous CNC bevel gear cutting machines absence of the design and manufacture technique for the cured tooth bevel gears fit with CNC technique. So the design and manufacture technique for the cured tooth bevel gears is not improved by the appliance of CNC technique. Therefore, this dissertation covers a research on the function-oriented tooth surface design and CNC manufacturing technology for the cured tooth surface, in which the capability of multi-axis simultaneous CNC bevel gear cutting machines is utilized to design function-oriented point-contact tooth surfaces and generate these tooth surfaces on multi-axis simultaneous CNC bevel gear cutting machines.A quantitative relation between the meshing characteristics and point-contact tooth surfaces geometry is established. The meshing characteristics constraint equations and in equations with respect to the tooth surface geometric parameter are deduced. These equations and in equations are fundamental of the meshing characteristics-based design of point-contact tooth surfaces. The linear relation between gear pair mounting errors and the position errors of the contact point is established by means of matrix equations and the sensitivity of gears mounting errors to contact point position errors is defined by means of the system matrix condition number of the linear equations. It is for the first time that the sensitivity of gears mounting errors to contact point position errors is studied quantitatively.The tooth surface design model is achieved by combining the restriction conditions of predesigned meshing characteristics:(â…°) path of contact, (â…±) motion graph, (â…²) sensitivity of the displacement of contact pattern position responding to mounting errors and (â…³) contact stress intensity etc. In this tooth surface design model, the geometry of the points on the path of contact is determined from the predesigned meshing characteristics and the geometry of the tooth surface's other area is achieved according to Load Tooth Contact Analysis (LTCA) yielded from Finite Element Analysis (FEA). The designed tooth surface is represented by geometric parameter instead of the specific machine tool adjustment parameter. The predesigned meshing characteristics is represented by the meshing characteristics equations and inequations with respect to the tooth surface geometric parameter instead of the dimension, position and orientation of the contact ellipse. By this tooth surface design approach, the tooth surface meshing characteristics is optimized globally and controlled strictly.A new kinematics is proposed, in which the related motions and situations between two meshing tooth surfaces are studied referred to a trihedron with respect to intrinsic geometry of tooth surfaces. The merits of this method applying to control the related motions between the tool and workpiece are:(â…°) improvement on generation of the tooth surfaces with predesigned geometrical structure (meshing characteristics) by means of generation motion of the tool, being free from artificial fixed coordinate system. (â…±) simplification of the tool generation motion design based on the trihedron with respect to intrinsic geometry of generated tooth surfaces by which the motion equations of generation are achieved referred to geometrical structures of tool surface and generated tooth surface. The proposed method of controlling the tool generating motion is foundations of the theory generating complex point-contact tooth surface according to predesigned geometrical structure (meshing characteristics) by application of the five-axis simultaneous CNC cutting machine.The surface-envelopment-approach theory generating complex point-contact tooth surface according to predesigned geometrical structure (meshing characteristics) by application of the five-axis simultaneous CNC cutting machine is proposed. The generated tooth surface based on the surface-envelopment-approach theory has the contact of second order with the generated objective along the path of contact and approaches the generated objective in the other area by principle of least warping. The surface-envelopment-approach theory is improvement and development of Gleason spiral bevel and hypoid gears generation technology and is CNC technology oriented point-contact tooth surface generation method. Just as rational B-spline theory of Free-Form surface in CAD/CAM, it is actually a new surface approximation method. The proposed theory is very useful both in generating point-contact spiral bevel gears and hypoid gears tooth surfaces by application of the five-axis simultaneous CNC cutting machine and machining complex surface by means of more effective generated surface machining method based on CNC technology.The CAD/CAM software based on the theory and method of this dissertation is developed. The calculation results of the software are proved valid and reliable through practical design and manufacture.