Method and apparatus for the free-form optimization of bevel and hypoid gears

A method for the optimization of the surface geometry, or of a variable or variables dependent on the surface geometry, of a bevel or hypoid gear for production on a free-form machine, the method comprising:

• selecting target values corresponding to said variable or variables to be optimized, said variable or variables to be optimized being dependent on the surface geometry of the gear;
• modeling the free-form basic machine to identify one or more control parameters, which has or have influence on the surface geometry;
• generating an initial setting for each control parameter based on the basic geometry of pinion and wheel or based on a random initial selection;
• simulating the gearwheel production process on the free-form basic machine to obtain a simulated gearwheel geometry, said variable or variables to be optimized, and deviations of said variable or variables to be optimized from the target value or target values;
• determining a new setting for each control parameter based on the deviations of said variable or variables to be optimized or based on a probabilistic process of genetic reproduction and genetic crossover;
• and
• repeating said steps of simulating and determining until the simulated value for each dependent variable thereby corresponds at least approximately to the corresponding target value,
• wherein said free-form machine can be mapped to a free-form basic machine with at most six axes uniquely in a reversible way, even to symmetries, said free-form basic machine having a gearwheel to be machined and a tool, each of which is rotatable about its own axis, and the tool and the gearwheel to be machined are displaceable or rotatable, with respect to one another along or about a plurality of axes.