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

A method for the production of a bevel or hypoid gear with optimized surface geometry comprising the steps of:

• modeling a basic design of a bevel or hypoid gear for a basic machine, in which each machine axis has a basic machine setting with a theoretical significance for the surface geometry of the gear,
• transforming the settings of the basic design for the basic machine to the settings of a free-form basic machine with at most six axes, having a first gearwheel to be machined and a first tool which are in each case rotatable about an associated axis, the first tool and the first gearwheel to be machined being displaceable or rotatable with respect to one another along or about a first plurality of axes,
• predetermining at least one target value for a variable or variables dependent on surface geometry of the bevel or hypoid gear,
• obtaining design values for the variable or variables dependent on surface geometry by at least one of a gearwheel production process simulation of the free-form basic machine, and a roll simulation of a design surface geometry produced by the simulated gearwheel production process;
• determining new free-form basic machine settings based on comparison of each design value to the target value for the corresponding variable;
• repeating the steps of obtaining design values and determining new settings until at least one of the variable or variables corresponds to the predetermined target value;
• mapping the new settings to control parameters for a free-form machine which can be mapped to the free-form basic machine with at most six axes, the former having a second gearwheel to be machined and a second tool which are in each case rotatable about an associated axis, and the second tool and the second gearwheel to be machined being displaceable or rotatable with respect to one another along or about a second plurality of axes;
• and
• controlling the free-form machine according to the control parameters in order, by means of the second tool, to remove material from the second gearwheel to be machined, so as to obtain the optimized bevel or hypoid surface geometry.