The design of a lathe attachment for grinding non-circular cross- section shafts suitable for torque transmission

Abstract

The principle concern of this work is the design of a lathe attachment for grinding non-circular 'polygonal' shaped workpieces suitable for use as torque transmitting machine elements. In the course of the work substantial attention is also given to the general theory and development of computer aided error analysis procedures for planar linkage mechanisms. A further smaller part of the work investigates the torsion of polygonal shafts. The non-circular shapes considered here may be loosely defined as polygonal profiles. Their application is in torque transmitting couplings for which they represent an alternative to keyed and splined couplings, although, in comparison to keys and splines, their application has been limited, mainly due to the specialised nature of their manufacture. The main objective of this work is to investigate suitable profiles and the means for their production using an attachment which can be mounted on a conventional machine tool, such as a lathe or grinding machine. The work progresses from initial consideration of shapes produced by various geometric generating methods and conception of an 'ideal' profile generating linkage mechanism through to detailed design of a precision, polygonal profile grinding, lathe attachment, and final assessment of its feasibility based on a profile precision criterion. In order to assess the precision of the attachment, computer-aided procedures are developed, after consideration of existing error analysis methods and their limitations for use in this case. These consider the various effects of tolerances, clearances and deflections upon mechanism output. As a coincidental investigation, the mechanical behaviour and strength of polygonal shaft-hub connections is reported. In particular, the torsion of a polygonal bar is theoretically analysed, using a stress function method, to determine maximum shear stresses.