Rounding and stability in centreless grinding

The paper presents a method for selecting grinding conditions and assists researchers to understand the complex dynamics of centreless grinding. It overcomes the problem of deriving dynamic stability charts for particular geometries and difficulty of interpreting such charts to adjust work speed to overcome lobing problems. Classic dynamic stability charts cannot assess stability levels in proximity to integer lobes, a particular problem for centreless grinding. The paper overcomes these problems employing a simply calculated new dynamic stability parameter A_dyn. The new parameter A_dyn simplifies the optimisation of grinding variables including set-up geometry and work speed in relation to resonant frequency. It is difficult to interpret relative dynamic stability of centreless grinding by classical methods for different set-ups, work speeds and numbers of lobes. A new method is employed in this paper based on the well-established Nyquist stability criterion. The dynamic stability parameter A_dyn is based on the real part of the characteristic equation. It is easily computed and presented on a single chart for particular work speed, resonant frequency and for a wide range of numbers of lobes. The method clearly shows the effect on rounding strength both for stable and unstable conditions. Most authors computing dynamic stability charts have ignored positive down boundaries and negative up boundaries showing a lack of a comprehensive treatment for a situation that conflicts with recommendations for conventional positive up boundaries. The new method simplifies this problem.Small differences in set-up geometry and work speed selection can be easily assessed. The new method can be used as a diagnostic tool for adjusting grinding conditions to overcome roundness problems. The user is not constrained by a historic set-up range since there are practical situations where other set-ups are preferred such as small tangent angles for large and heavy work-pieces, and even negative tangent angle for some types of centreless machine.Previous research is reviewed to provide an understanding of the need for a new approach to stability. Practical implications are explained for selection of grinding conditions. The method is supported by reference to experimental results.