The establishment of hypoid gear tooth surface model mainly includes the following five parts:
- Tool equation. The research object is the hypoid gear processed by face milling method. Generally speaking, in the normal section of the cutting tool, it can be simplified into linear part and circular arc part. For other types of tools, you can modify them in the corresponding part of this part.
- Shaking table mechanism equation. In Gleason machine tool, there are several angle parameters in the table shaking mechanism: table shaking angle φ c. Eccentric angle φ e. Knife angle φ s. Knife inclination φ t 。 Through the shaking table mechanism, the hypothetical forming wheel in the workpiece processing process can be simulated. In this part, by establishing the geometric position relationship between the shaking table and the workpiece, the spatial position relationship equation between the shaking table and the gear blank is obtained.
- Establish and solve the coordinate equation of pinion tooth surface. What we study is HFT (hypoid gear form tilt) hypoid gear, that is, pinion generate and gear form machining. Based on the gear theory, the meshing equation of hypoid gears can be established when machining hypoid gears by generating method, which does not exist when machining hypoid gears by forming method. According to the geometric parameters of the tooth blank, the constraint equation of the tooth blank is established, and the coordinates of the midpoint of the tooth surface are solved. Taking this as the initial point, the coordinates of other points on the tooth surface are solved. Using the theoretical thickness of the top of the gear blank, the calculated coordinate of the tooth surface is rotated to obtain the theoretical relative position of the convex and concave tooth surface.
- Establish and solve the coordinate equation of gear tooth surface. Large gears are processed by forming method, and the solution of their corresponding tooth surface coordinates is similar to that of small gears.
- Example of hypoid gear modeling. Import the tooth surface coordinates obtained above into CATIA, establish a three-dimensional solid model of the gear, and compare it with the actual gear tooth surface coordinates.
In order to simplify the mathematical model, the following assumptions are made in the derivation process:
- All parts have no elastic deformation, and all parts move rigidly in the cutting process;
- The influence of dynamic force and temperature is not considered;
- All machine tool parameters and gear blank parameters are theoretical design values, and machining deviation and clearance are ignored in the machining process of hypoid gears.