Geometrical principles for analysing hypoidal gears in Coordinate Measuring Machines: Involutometry, protocols, data interpretation

The design of hypoidal gears has many degrees of freedom; some external such as eccentricity, diameters, surfaces of pitch; and others internal such as pressure angle, helix angle, or involute. All parameters are linked producing teeth which are continuously variable in their shape. Apart from indexing, Coordinate Measuring Machines are required for quality control, reverse engineering, analysis of faults, or for setting up manufacturing processes. To design measurement protocols with Coordinate Machines, it is necessary to define: involutometry, boundaries of teeth and paths for touching. To interpret the data from Coordinate Machines, mathematical tools are proposed as complementary to those proposed by previous authors in this field. Since couples of crown–pinion may differ from theoretical designs, it is necessary to define universal frames to aid the analysis of geometrical quality. Both mathematical tools and CAD tools are considered as part of the Coordinate Machines for these applications.

► A method for tracing profiles of hypoid gear’s teeth is proposed.
► The style of explanation for getting such profiles intends didactic purposes.
► Traces are modelled with B-splines meshes for analysing or for sending them to CAD.
► Slight differences: theoretical and real pieces may also be processed with B-splines.
► Measuring protocols in CMMs may be designed with B-splines and their derivatives.