Complex surfaces such as helical ones are commonly used in machinery. Such surfaces can be obtained by various machining processes, one of these processes being thread whirling. The influence of machining conditions needs to be better understood to develop a more precise prediction of the specific resulting errors involved in thread whirling. This paper firstly presents the theoretical conditions which generate micro-deviations on whirled surfaces. A theoretical model which considers the geometrical parameters describing the whirling head and cutters and the process's whole kinematics was developed. The threaded surface was described as a complex compound surface resulting from intersecting successive ruled helical surfaces corresponding to the cutting edges of the set of cutters from the whirling head. Numerical simulation results were exemplified and validation experiments were both designed and performed. Empirical mathematical models were established to highlight the influence of the input factors such as thread pitch and external diameter, the ratio between the diameter of cutters' top edge disposal and the thread's external diameter, the rotary speed of the whirling head, and the rotary speed of the workpiece on some accuracy elements and roughness parameters of the threaded surface.
Keywords: empirical mathematical models; experimental research; helical surfaces; influence factors; numerical modeling and simulation; thread accuracy; thread whirling.