Abstract: The guide wheel grinder described is a 4 axes simultaneous CNC grinder. It is based on a new ideas of kinematical axiom for grinding a thread with variable diameter, variable pitch and variable tooth angles. Convex cylindrical and conical rollers (with circular bus) can be obtained on center less grinding with the guide wheel processed by the previous grinder. Mother mathematical models on which programming for the guide which grinder are introduced.

Key words: CNC grinder, Convex roller, Guide wheel, Thread grinding, fatigue life, model for predicting material cyclic constitutive relationship, strain energy separation function, strain-fatigue test, transforming equations of strain amplitude and stress amplitude, millimeter-scaled slice specimen